
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 16183
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000758000000005)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 33403
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000979999999998)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00122)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000407999999993)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.001414)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 27091
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000834000000012)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010887)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.014782)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000321)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.00052500000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00058700000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000464999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000524999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000539999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000534999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000598999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000546999999983)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000479999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000551000000002)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000468999999995)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 26591
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00103200000001)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 13789
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00173099999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00139200000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000402000000008)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000666999999993)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 41299
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000469999999993)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.009344)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011556)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000306999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000512999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000575000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000467)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000526999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000476000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000538000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000472000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000532000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000487000000021)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000880999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.00100299999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000794999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000884999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.00071299999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000793999999985)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000512999999998)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 25373
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000726999999998)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 12263
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000973000000002)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000952999999996)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000403999999989)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000675999999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 21319
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000500000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00922300000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011402)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000304999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000533000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000592999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000495000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000552000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000891999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.00101600000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000800000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000882000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.00072200000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000816)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000671000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000771000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000657000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000734000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000560000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000624000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000583000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000655000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.00055900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000625999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000526000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000589000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000554999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000547999999981)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000547999999981)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000546999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000629000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000509999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000586000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.00076399999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000855999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000636999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000723999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000478999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000558999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000467)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000537000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.00047099999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000469999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000555999999989)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000538000000006)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 39791
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000886999999992)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 39089
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000956999999985)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00110799999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000401999999994)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00067700000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 20773
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000489000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00995300000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.012225)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000382999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.00085399999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000953999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000662000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000782000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.00049700000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000557999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000679999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000784999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000609000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000703000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000538000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000608)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000493999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000546999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000608999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000556000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000639000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000815000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000927000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000565000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000643999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.00062299999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000709000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000552999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000637000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000546000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000627000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000561000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000642999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000541999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000616999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000535999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.00061199999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000546000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000628000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000584999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000664999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000596000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000550999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000627999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000921000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.001001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000501)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000569999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000705000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000785000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000496000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000568999999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000739999999993)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 18839
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000878999999998)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 44531
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001627)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001147)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000404000000003)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000746000000007)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 10589
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000798000000003)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011944)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.015887)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000400000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000716999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000779999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000656000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000789999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000502999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000589000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000479999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000555000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000559999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000523999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000594000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000919999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000996999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000598999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000501999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000568000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000506000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000576000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000504000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000576000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000506999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000576999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000506999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000581999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000515000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000584000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000557000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000495999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000556000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000517000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000578000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000501)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000575000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000617000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000720000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000669000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000759000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000571999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000655000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000553999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000625000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000545000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000610999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000894000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.001043)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000778999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000877999999986)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000644999999992)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 31469
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000856000000013)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 44351
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00137700000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001015)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000423000000012)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000760999999997)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 12347
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000797000000006)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.012327)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.01651)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000644000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000623000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00081999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000897000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.00100399999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000780000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000869000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000781000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000869000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000773000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000856000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000653000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000743)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000651999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000731000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000669999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000745999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000586999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000657000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000557000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000620999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000560999999976)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000627000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000548999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000610999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000486999999978)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000524999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000601000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000492000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000559999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000554000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000546999999983)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000540999999998)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 27017
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000764000000004)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 37217
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000966000000005)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000986000000012)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000400999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000664999999984)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 22751
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.00047099999999)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00958899999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011894)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.00045999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000692000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000780000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000678000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000797999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000495000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000554999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000688999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000752000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000507999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000569000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000533000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000610000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000498999999976)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000557000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000507000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000570999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000493999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000503000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000561000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000494999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000527000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000609000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000530999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000608999999983)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000803000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000899000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000795000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000889000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000794999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000883000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000788999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000885999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000772000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000861999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000776000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000868999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000765999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000861)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000780999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000867)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000574)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.00064900000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000502999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000579000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000503000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000564999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000509999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000574999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000496999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.00057000000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000536999999994)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 22567
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000942000000009)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 39419
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001075)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00101199999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000691000000003)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000901999999996)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 19441
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000838000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010992)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.014502)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000482000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000608999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000789999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000867999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000963999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000820999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000913999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000783999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000872000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000693999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000778000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000651999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000731999999985)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000686000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000771)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000657000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000731999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000554999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000619999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000554999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000620999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000558999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000624999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000509000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000569999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000546999999983)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000547999999981)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000548999999992)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000540000000001)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 14969
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000726)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 44789
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000968)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000993000000008)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000402000000008)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000671999999994)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 20521
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000486999999993)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00946999999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011702)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000347000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000608)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000671999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000891999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.00102800000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000570999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.00066600000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000892000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.00101500000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000799999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000910999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000778999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000874999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000509000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000585999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.00051400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000596000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000624000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000702000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000509000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000580999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.00051400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.00058700000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000579999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000652999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000502000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000561000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000510999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000589000000019)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000635000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000731000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.00074699999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000828000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000536999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000598999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000550999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000515000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000586999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000561999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000632999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000942999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.001079)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000813000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000910999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000783999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000882000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000773000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000866000000016)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000706000000008)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 36599
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000988000000007)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 32479
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001064)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00100999999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000690000000006)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.001232)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 14723
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000799000000015)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.012977)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.017625)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000513000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000873999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.001076)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000868000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000962000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000782000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000871000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000839999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000940999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000737999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000827999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000671000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000764000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000718999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000819000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000584000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000673000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000598000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000693999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000555999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000633000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000482000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000509999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000573000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000520999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000582999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000929999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.00102600000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000548000000009)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000521999999989)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 40693
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000715999999997)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 17881
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000953999999993)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000979999999998)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000418999999994)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000694999999993)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 38593
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000482000000005)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00961600000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.012179)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000382999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000687999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000762000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000927999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.00109400000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000764000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000847999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000647000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000720999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000647000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000723000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000648999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000724999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000653999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000722999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.00055900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000628999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000555000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000621999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000529)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000591)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000483000000017)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000482000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000541999999982)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000484000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000495000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000554999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000540999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000484000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000737000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000802000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000460999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000523000000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.001024)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 37607
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000784999999993)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 30763
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000964999999994)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000939000000002)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000419999999991)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000698999999997)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 26647
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000494000000003)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.009789)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.012262)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000522999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000610999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000676999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000675000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000788999999983)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000501999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000562000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000561999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.00053299999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000600999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000555000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000541999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.00062100000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000662999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000761999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000538000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000599000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000648999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000737000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000809000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000912)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000859000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000983000000019)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000646000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000734000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000577000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000655999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000509000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000586999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000596999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000528000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000605999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000738000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000848000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000578000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000666999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000480999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.00051599999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000589000000005)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000564999999995)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 31469
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000816999999998)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 27803
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001085)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00100300000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000779999999992)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00122499999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 28151
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000800999999981)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010838)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.01485)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000471999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000923)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00104899999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000795999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000889000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000782000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000873000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000717000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000799000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000649999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000722999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000854000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000945999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000649999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000724000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000555999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000624000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000555000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000620999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000587999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000657000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000555000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000556000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000543999999991)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000543999999991)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 35267
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000769999999989)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 16319
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000961000000004)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00101000000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000401000000011)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000674999999987)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 39043
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000500000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00975099999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.012331)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000356999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000614000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000692999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000799000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000930999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.00064900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000726)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000648999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000722999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000555999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.00062800000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000557000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000624000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000554000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000618999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000475999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000533000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000466999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000531000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000494000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000564999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000522000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000585000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000494000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000514999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000588000000022)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000554000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000504000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000563000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000551999999985)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000536999999994)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 23447
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000733000000011)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 33637
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001031)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000962000000015)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000419999999991)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000698999999997)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 17449
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000495999999998)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00942199999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011728)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000340000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000672000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000751000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000917000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.00106300000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.00075600000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000853000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000738999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000827999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000771)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000858000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000751999999977)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000840999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000781000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000872999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000781000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000878)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.00074699999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000838000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000692000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000779999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000528999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000613000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000523000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000599999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000596000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000670999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000764000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000800000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000895000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000805)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.00090999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000779999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000869999999978)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000741000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000827000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.00075099999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000838000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000585999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.00067)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000787000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000876000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000783999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000870000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000786000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000878999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000789000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000878)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000778999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000872999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000800000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000888999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000771999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000862999999995)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000554999999991)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 35671
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000802000000007)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 38569
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001048)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00113400000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.00074699999999)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00116899999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 27631
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000800999999996)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.013893)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.018286)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000668999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000545000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00061199999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000690000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000764999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000479999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000494000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000494000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000555000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000549000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000630999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000582000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000646000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000556999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000498000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000558000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000492999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000502999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000563)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000496999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000557000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000497999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000558999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000550000000004)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000519000000011)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 26003
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000762000000009)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 37337
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000954000000007)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001052)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000484)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000793000000002)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 23857
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000501999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011585)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.014265)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000558999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000534000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000598000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000482000000019)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000481999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000528999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000593999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000541000000013)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.00054999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000555000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000499000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.00056699999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000554999999991)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000540999999984)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 34297
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000790999999992)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 34123
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000973999999985)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00101100000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000510999999989)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000824000000009)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 25037
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000512999999984)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010508)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.013297)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000591999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000574)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000636999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000512999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.00058700000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000490999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000487000000021)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000515000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000585999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000550999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000471000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000532000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000548000000009)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.00051599999999)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 42787
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000765000000001)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 43597
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000962000000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00101000000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000490999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000805)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 28019
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000501999999983)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010862)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.013531)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000546)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000536999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000602000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000495000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000555999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000522999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000599000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000496000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000498000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000573999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000472000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000573000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000647999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000472999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000567999999987)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000557999999998)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 45553
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000722999999994)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 27299
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000939999999986)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000998999999993)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000520000000009)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000820000000004)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 28859
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000500000000017)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011917)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.014628)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000542999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000538000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000602999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000610999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000689000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000517999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000591000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000495000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000484000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000499000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000558999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000496999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000556000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.00046900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000530000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.00054999999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.00053299999999)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 42179
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000764999999987)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 40639
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000973999999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001604)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000562000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00080100000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 28573
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000500000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010449)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.013161)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000563999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000844000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000965999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.00075600000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000842999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000503999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000580999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000562000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000637999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000509000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000585999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000516000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000591999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000507000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000581999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000529)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000613999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000507999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000583999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000614999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000692999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000565999999978)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.00063200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000506000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000590000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000506999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000572999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000528000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000589000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000492000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000553000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000501000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000577000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000506999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000582000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.00050499999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000580999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000528999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000602000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000506000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000574999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000685999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000747999999987)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000920000000008)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 42071
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000846999999993)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 15373
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00171900000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00135299999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000411999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000728000000009)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 15091
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000493999999989)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.009118)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.01144)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000309999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000540999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000623000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000517000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000590000000017)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000535999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000613000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000498999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000571999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000531999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000603999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000557000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.00054999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000556000000017)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000495000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000556000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000518999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000596000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000498000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000692000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000744999999981)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.00082900000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000657000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000733999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000659999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000743)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000557999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000624999999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000536999999994)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 31957
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000769000000005)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 10247
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00098899999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000960000000006)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000491000000011)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000748000000002)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 17299
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000687999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00939699999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011944)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000311999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000833)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00092699999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000692000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000771)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000636000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.00070199999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000750000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000857999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000626000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000696000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000575000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000643999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000576999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000642999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.00055900000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000503999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000580000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000543999999977)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000492000000023)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000616000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.00071100000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000585999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.00065699999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000775999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000871000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000795999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000902000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000773999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000864000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000731000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000825000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000775000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000869000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000770999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000873999999996)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000516999999988)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 13367
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000740999999991)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 21011
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00107800000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000986000000012)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000482000000005)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000714000000002)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 34949
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000725999999986)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.012038)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.015086)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000382999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000911000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00103900000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000670999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000832000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000511000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000578999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000508999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000597999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000513999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000574)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000503999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000564000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.00049199999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000501000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000560000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000522999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.00059499999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000510000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000589000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000742000000017)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000825000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000794999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000886999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000806999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000899000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000787000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000887999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000788)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000878999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000741999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000844000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000791000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000880999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000509999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000585999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000539000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000616000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.00051599999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000592999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000510000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000585999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000799999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000897000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000810000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000906000000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000557000000001)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 24889
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000795999999994)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 24007
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00111299999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001636)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000453999999991)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000776000000002)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 34781
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.00081999999999)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.0133)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.016607)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000556000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000825000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00101600000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000876000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000973000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000788)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000874999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000746000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000826999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000653)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000726)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000654999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000731000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000652999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000727999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000559999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000625999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000562000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000630999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000572999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000638999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000534000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000612999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000494999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000558000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000523999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000603999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000496999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.00056099999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.00054999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000550999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000483000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000478000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000539999999987)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000544000000019)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 25793
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000766999999996)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 33911
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00100599999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00107199999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000418999999994)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000698)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 32261
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000492999999992)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.009325)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011597)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000338999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000562000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000624999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000927000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.00106599999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000778000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000868999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000786000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000876000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000761999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000844000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000648000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000732999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000648000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000727999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000646000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000722999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000582000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000655000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000552000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000619)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000551000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.00061700000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000549000000021)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000610999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000481999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000481999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000541999999982)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000481999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000539000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000483000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000483000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000482000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000540000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000541999999982)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000480999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000539999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000483000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000540999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000482999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000482000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000540000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000484000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000544000000005)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000533999999988)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 39079
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000726)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 45083
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000965000000008)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000995000000003)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000420000000005)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000698000000014)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 24923
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000489999999999)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010393)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.013837)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000521000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000848999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000945999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000884999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.00102800000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000652000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000727000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000657000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000733999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000647999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000722999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000641000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000709999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000554000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000625999999983)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000559999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000627000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000510000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000575000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000494999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000551000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000498000000022)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000557999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000540999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000550999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000500000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000559999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000553999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000496000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000555000000006)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000543999999991)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 30689
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000719000000018)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 14449
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000968)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00117800000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000413000000009)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000886999999992)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 26177
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000503999999992)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.010084)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.012547)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000343999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000553000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000612000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000674000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000800999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000513999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000593000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000502000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000578000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000514999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000592000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000538999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000618000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000765000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000855999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000776000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000867000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000743999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000840999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.00075600000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000852000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000788)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000885999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000564000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000643999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000527000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000599000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000521000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000586999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.00079199999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000872000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000612000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000694999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000496999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.00057799999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.00078400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000880000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000788999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000878999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000775000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000867000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000744000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000838999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000747000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000839999999982)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000791000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000879999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000787000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000880000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000788999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000880999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000585999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000495999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000557000000015)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000579999999999)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 37747
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000805999999997)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 23563
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00146100000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00160199999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000664)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00136799999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 32003
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000826000000004)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011736)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.016222)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000360000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000534000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000599999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000467999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000531000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000481999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000483000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000540000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000570999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000644000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000480999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000483000000017)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000617000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000692000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.00054999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000468000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000529999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000473999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000533000000004)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000540000000015)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 19801
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000724000000005)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 42307
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000966999999989)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00101799999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000664999999998)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00110900000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 16001
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000743000000014)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011664)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.01528)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000543000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000540999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000603999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000483000000017)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000539000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000483000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.00054200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000521000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000581000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000484999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.00054999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000509000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000573000000003)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000536000000011)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 38501
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000769999999989)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 45613
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001007)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00106399999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000723000000008)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00114099999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 39163
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000737000000015)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011066)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.014683)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000548999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000544000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000608999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000467)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000529)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.00049700000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000558999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000548999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000503000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000562000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000551999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000550999999987)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000490999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000491000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000534000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000591999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000492000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000554999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000490999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000500000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000558999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000520999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000584000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000553000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000498999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000569999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000490999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000477000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000572000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.00063200000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000537999999992)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 38567
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000718000000006)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 32203
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000996999999998)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001017)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000669000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000968)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 36061
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000523000000001)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00998200000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.013209)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000367000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000597999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000688999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000504000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000580999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000640999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000710999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000488000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000564999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000627000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000540999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000623000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000793000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000882000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000748999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000841000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000769999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000858999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.00078400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000872999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000788)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000876000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000781000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000872000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000517000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000602999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000516999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000595000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000505000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000585000000015)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000521000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000599000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000513999999981)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000591999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000512000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000613999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000790000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000889000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000513000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000578000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000501999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.00056099999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000499999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000558000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000587999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000650999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000510000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000585000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000522000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000603999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000533000000019)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000613000000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000867)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 27551
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001135)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 14447
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00107199999999)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00177099999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000484000000014)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000793000000002)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 39607
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.00051400000001)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00919)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.01167)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000312000000022)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000521999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000583999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000483000000017)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000540000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000484000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000540999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000496000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000571000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000541999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000484)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000490000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000564000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000627999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000701000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000468999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000529000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000463000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000523000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000483999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000544999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000567000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000626999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.00050499999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000563999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000542999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000887999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.00101200000002)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000538999999989)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 32401
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000731999999999)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 15749
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.001008)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000985999999997)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.00041800000001)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000700999999992)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 32719
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000501999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00943999999998)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011882)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000315999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000531000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000595000000018)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000523999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000599000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000496999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000563)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000736999999987)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.00081200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.00102899999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.001171)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000787000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000878)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000717999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000817999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000703999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000788)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000652000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000729000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000648999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000724000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000659000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000733000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000558999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000625000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000568000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000634000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.00056099999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000629000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000549000000021)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000550000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000488999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000486999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000489999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000707999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000780999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000515000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000587999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000467999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000540999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000517000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000602999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000471000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000543000000008)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000543000000008)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 18701
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000763000000006)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 42979
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000998999999993)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000966999999989)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000420000000005)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000682000000012)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 13763
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000497999999993)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00940399999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011769)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000327999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000602000000015)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000675999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000832000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000970999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000784999999979)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000870000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.00079199999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000880999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000787999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000878999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000787000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000878000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000778999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000869000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000777999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000872000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000758999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000850999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000670999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000748999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000513999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000585000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000528000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000618000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000510000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000588000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000509999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000592999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000517999999985)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000596999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000590000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000681)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000518000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000593000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000584000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000662000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000603999999981)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000684000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000505000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000586999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000535999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000619999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000512999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000595000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000503000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000568000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000554000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000493000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000579999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000671000000011)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000893000000019)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 27179
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00113)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 25693
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00106600000001)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00107300000001)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000501)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.001228)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 37379
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000765999999999)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.013216)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.016863)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.00051400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000962999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.001091)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000781000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000892999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000695999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000782000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000647999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000724000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000647999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000725000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000651000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000727999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000603999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000673000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000553999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000621999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000555000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000624000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.00046900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000534000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000480999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000540000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000539000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.00061199999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000467999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000529000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.00054999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000502000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000561000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000546000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000495000000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000557000000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000544000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000543000000008)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000485999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000545999999986)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000486000000009)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000545000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000485000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000543999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.00048799999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000549000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000484999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000544000000005)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000518999999997)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 17657
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000731000000002)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 27367
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000958999999995)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.001147)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000402999999991)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.000675999999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 27763
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000493999999989)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.009477)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011701)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000349)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000641999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000719000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000721999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000916000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.00104900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.001183)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000801999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000911000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000787000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000878999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000861999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000947000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000667000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000765999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000664)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000743)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000651000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000731000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000585999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.00065699999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000554000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000619999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000560000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000627999999992)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000546999999997)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000608000000014)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000507000000013)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000576000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000481000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000471000000005)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000533999999988)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000465999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000526999999991)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.00051400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.00057799999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000488000000018)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000546999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000548000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000489999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000551000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000547000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000489000000016)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000547999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000491999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000553000000011)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000490999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000552999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000548000000009)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000537000000008)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 11549
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000730000000004)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 16301
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000978999999987)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.000949000000006)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000399000000002)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.00066799999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 21031
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000473999999997)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.00969499999999)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.011924)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000349)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000602999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.000667000000007)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000834999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000968)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000622000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000718999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000895000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.001018)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000836000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000934999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.00078400000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000879999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.00077499999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000867999999983)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000765999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000859999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000740000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000831000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000524999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.00060400000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000528000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000610000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000498000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000558999999996)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.000507999999982)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.000579000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000487000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000546)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.00051599999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000590000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.001081)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.001244)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000602999999998)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000681999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.000501999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.000566000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.000595000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000665000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000822999999983)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000924999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000781000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000878)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000734999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000826000000004)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000641000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000727999999995)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000536999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000618000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000581000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000652000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000496999999996)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000574999999998)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000489000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.000567000000004)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) submatrix det: g=1235467825728256852623360
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) Falling back to PARI HNF since input matrix is ill conditioned for p-adic hnf algorithm.
verbose 1 (790: matrix_integer_dense_hnf.py, probable_hnf) generic random modular HNF algorithm failed -- we fall back to PARI
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) testing if matrix is in HNF
verbose 1 (747: matrix_integer_dense_hnf.py, is_in_hnf_form) not HNF because negative or too big above pivot position (time = 0.000906999999998)
verbose 1 (947: matrix_integer_dense_hnf.py, hnf) After attempt the return matrix is not in HNF form since pivots must have been wrong.  We try again.
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 32707
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.00079199999999)
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 30869
verbose 1 (634: matrix_integer_dense_hnf.py, probable_pivot_columns) done with linbox echelonize (time = 0.000975000000011)
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) starting slicings
verbose 1 (493: matrix_integer_dense_hnf.py, hnf_square) done slicing (time = 0.00102)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) starting double det
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Computing echelon form of 49 x 50 matrix over QQ using p-adic nullspace algorithm.
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Got integral matrix (time = 0.000828999999996)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) computing rank
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) done computing rank (time = 0.001277)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) calling linbox echelonize mod 31183
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) done with linbox echelonize (time = 0.000859999999989)
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) calling IML solver
verbose 2 (206: matrix_integer_dense_hnf.py, p-adic echelon) finished IML solver (time = 0.011435)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det)   Computed ZZ-echelon using p-adic algorithm. (time = 0.015777)
verbose 1 (206: matrix_integer_dense_hnf.py, double_det) Reconstructed solution over QQ, thus completing the echelonize (time = 0.000360999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) Multimodular det -- need to use about 27 primes.
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388617
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388617 (time = 0.000900999999999)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388617 which is 1 (of about 27) (time = 0.00102200000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388593
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388593 (time = 0.000854000000004)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388593 which is 2 (of about 27) (time = 0.000949000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388587
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388587 (time = 0.000770000000003)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388587 which is 3 (of about 27) (time = 0.000860000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388581
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388581 (time = 0.000787999999986)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388581 which is 4 (of about 27) (time = 0.000883000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388571
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388571 (time = 0.000778999999994)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388571 which is 5 (of about 27) (time = 0.000878)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388547
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388547 (time = 0.000756999999993)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388547 which is 6 (of about 27) (time = 0.000859000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388539
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388539 (time = 0.000527999999989)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388539 which is 7 (of about 27) (time = 0.000607000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388473
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388473 (time = 0.000538000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388473 which is 8 (of about 27) (time = 0.000617999999989)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388461
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388461 (time = 0.000520999999992)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388461 which is 9 (of about 27) (time = 0.000596000000016)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388451
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388451 (time = 0.000515000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388451 which is 10 (of about 27) (time = 0.000576000000009)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388449
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388449 (time = 0.000501)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388449 which is 11 (of about 27) (time = 0.000570999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388439
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388439 (time = 0.000518)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388439 which is 12 (of about 27) (time = 0.000596999999999)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388427
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388427 (time = 0.001017)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388427 which is 13 (of about 27) (time = 0.00117400000001)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388421
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388421 (time = 0.000750000000011)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388421 which is 14 (of about 27) (time = 0.000838000000002)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388409
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388409 (time = 0.000699999999995)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388409 which is 15 (of about 27) (time = 0.000797000000006)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388377
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388377 (time = 0.000796000000008)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388377 which is 16 (of about 27) (time = 0.000905000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388371
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388371 (time = 0.000820999999988)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388371 which is 17 (of about 27) (time = 0.000922000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388319
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388319 (time = 0.001082)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388319 which is 18 (of about 27) (time = 0.001255)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388301
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388301 (time = 0.00082900000001)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388301 which is 19 (of about 27) (time = 0.000934999999984)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388287
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388287 (time = 0.000512999999984)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388287 which is 20 (of about 27) (time = 0.000591)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388283
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388283 (time = 0.000793000000002)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388283 which is 21 (of about 27) (time = 0.000877000000003)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388277
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388277 (time = 0.000509999999991)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388277 which is 22 (of about 27) (time = 0.000589000000005)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388239
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388239 (time = 0.000712000000007)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388239 which is 23 (of about 27) (time = 0.000801999999993)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388209
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388209 (time = 0.000521000000006)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388209 which is 24 (of about 27) (time = 0.000598999999994)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388187
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388187 (time = 0.000580000000014)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388187 which is 25 (of about 27) (time = 0.000665000000012)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388113
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388113 (time = 0.000513000000012)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388113 which is 26 (of about 27) (time = 0.000591999999997)
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Multimodular stage of det calculation -- using p = 8388109
verbose 2 (39: matrix_integer_dense_hnf.py, det_from_modp_and_divisor) Finished multimodular det for p = 8388109 (time = 0.000957)
verbose 1 (81: matrix_integer_dense_hnf.py, det_given_divisor) computed det mod p=8388109 which is 27 (of about 27) (time = 0.00110500000001)
^Cr_dense_hnf.py, probable_pivot_columns) calling linbox echelonize mod 18523
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_296.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("UTdwbHVzLmdlbnMoKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/private/var/folders/7y/7y-O1iZOGTmMUMnLq7otq++++TI/-Tmp-/tmpl6v1qh/___code___.py", line 2, in <module>
    exec compile(u'Q7plus.gens()' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/misc/displayhook.py", line 174, in displayhook
    print_obj(sys.stdout, obj)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/misc/displayhook.py", line 142, in print_obj
    print >>out_stream, `obj`
  File "sage_object.pyx", line 154, in sage.structure.sage_object.SageObject.__repr__ (sage/structure/sage_object.c:1401)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/modules/fg_pid/fgp_element.py", line 300, in _repr_
    return self.vector().__repr__()
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/modules/fg_pid/fgp_element.py", line 341, in vector
    self.__vector = self.parent().coordinate_vector(self, reduce=True)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/modules/fg_pid/fgp_module.py", line 1086, in coordinate_vector
    self.optimized() # computes T as side effect -- see the "optimized" method.
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/modules/fg_pid/fgp_module.py", line 1217, in optimized
    H, U = B.hermite_form(transformation=True)
  File "matrix_integer_dense.pyx", line 1464, in sage.matrix.matrix_integer_dense.Matrix_integer_dense.hermite_form (sage/matrix/matrix_integer_dense.c:14124)
  File "matrix_integer_dense.pyx", line 1666, in sage.matrix.matrix_integer_dense.Matrix_integer_dense.echelon_form (sage/matrix/matrix_integer_dense.c:14725)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/matrix/matrix_integer_dense_hnf.py", line 1050, in hnf_with_transformation
    H, pivots = hnf(C, include_zero_rows=True, proof=proof)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/matrix/matrix_integer_dense_hnf.py", line 1006, in hnf
    H, pivots = probable_hnf(A, include_zero_rows = include_zero_rows, proof=True)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/matrix/matrix_integer_dense_hnf.py", line 832, in probable_hnf
    cols = probable_pivot_columns(B)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/matrix/matrix_integer_dense_hnf.py", line 652, in probable_pivot_columns
    pivots = A._reduce(p).pivots()
  File "matrix0.pyx", line 3108, in sage.matrix.matrix0.Matrix.pivots (sage/matrix/matrix0.c:17124)
  File "matrix2.pyx", line 4607, in sage.matrix.matrix2.Matrix.echelon_form (sage/matrix/matrix2.c:25573)
  File "matrix_modn_dense.pyx", line 1081, in sage.matrix.matrix_modn_dense.Matrix_modn_dense.echelonize (sage/matrix/matrix_modn_dense.c:8916)
  File "matrix_modn_dense.pyx", line 1105, in sage.matrix.matrix_modn_dense.Matrix_modn_dense._echelonize_linbox (sage/matrix/matrix_modn_dense.c:9184)
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/misc/misc.py", line 451, in verbose
    print s
  File "/Users/wstein/sage/install/current/local/lib/python2.6/site-packages/sage/interfaces/get_sigs.py", line 9, in my_sigint
    raise KeyboardInterrupt
KeyboardInterrupt
__SAGE__
