Hi Clement,
Any chance you could look into this. It's an 8x8 full matrix where
linbox (via SAGE)
computes the wrong determinant?
Here's the SAGE session that gives the bad result:
sage: M = matrix(
[
[-3821257660, -3821257669, -1736935303, -2779096486, -1736935306,
-2779096486, -2779096489, -2779096483],
[-3821257669, -3821257660, -1736935303, -2779096486, -1736935303,
-2779096489, -2779096486, -2779096489],
[-1736935303, -1736935303, -789516040, -1263225676, -789516049,
-1263225676, -1263225679, -1263225676],
[-2779096486, -2779096486, -1263225676, -2021161072, -1263225676,
-2021161081, -2021161081, -2021161084],
[-1736935306, -1736935303, -789516049, -1263225676, -789516040,
-1263225676, -1263225676, -1263225676],
[-2779096486, -2779096489, -1263225676, -2021161081, -1263225676,
-2021161072, -2021161081, -2021161081],
[-2779096489, -2779096486, -1263225679, -2021161081, -1263225676,
-2021161081, -2021161072, -2021161081],
[-2779096483, -2779096489, -1263225676, -2021161084, -1263225676,
-2021161081, -2021161081,-2021161072] ])
sage: M._det_linbox()
ERROR in reconstruction ?
0
The C++ code against linbox that's used for _det_linbox is:
void linbox_integer_dense_det(mpz_t ans, mpz_t** matrix, size_t nrows,
size_t ncols) {
commentator.setMaxDetailLevel(0);
commentator.setMaxDepth (0);
DenseMatrix<Integers> A(new_matrix_integers(matrix, nrows, ncols));
GMP_Integers::Element d;
det(d, A);
mpz_set(ans, spy.get_mpz(d));
}
Thoughts?
--
William Stein
Associate Professor of Mathematics
University of Washington
http://www.williamstein.org
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