void fmpq_mat_mul_fmpz_mat(fmpq_mat_t C, const fmpq_mat_t A, const fmpz_mat_t B) { slong i, j; fmpz_mat_t Aclear; fmpz_mat_t Cclear; fmpz * Aden; fmpz_mat_init(Aclear, A->r, A->c); fmpz_mat_init(Cclear, A->r, B->c); Aden = _fmpz_vec_init(A->r); fmpq_mat_get_fmpz_mat_rowwise(Aclear, Aden, A); fmpz_mat_mul(Cclear, Aclear, B); for (i = 0; i < C->r; i++) { for (j = 0; j < C->c; j++) { fmpz_set(fmpq_mat_entry_num(C, i, j), fmpz_mat_entry(Cclear, i, j)); fmpz_set(fmpq_mat_entry_den(C, i, j), Aden + i); fmpq_canonicalise(fmpq_mat_entry(C, i, j)); } } fmpz_mat_clear(Aclear); fmpz_mat_clear(Cclear); _fmpz_vec_clear(Aden, A->r); }
inline size_t rank(const DMatQQFlint& A) { // fmpq_mat has no rank function. // So we clear denominators row-wise (or column-wise), and compute the rank of that matrix. fmpz_mat_t m1; fmpz_mat_init(m1, A.numRows(), A.numColumns()); fmpq_mat_get_fmpz_mat_rowwise(m1, NULL, A.fmpq_mat()); //fmpz_mat_print_pretty(m1); size_t rk = fmpz_mat_rank(m1); fmpz_mat_clear(m1); return rk; }
inline size_t nullSpace(const DMatQQFlint& A, DMatQQFlint& result_nullspace) { fmpz_mat_t m1; fmpz_mat_t m2; fmpz_mat_init(m1, A.numRows(), A.numColumns()); fmpz_mat_init(m2, A.numColumns(), A.numColumns()); fmpq_mat_get_fmpz_mat_rowwise(m1, NULL, A.fmpq_mat()); //fmpz_mat_print_pretty(m1); size_t nullity = fmpz_mat_nullspace(m2,m1); // now copy the first 'nullity' columns into result_nullspace result_nullspace.resize(A.numColumns(), nullity); for (size_t c = 0; c < nullity; c++) for (size_t r = 0; r < A.numColumns(); r++) fmpz_set(fmpq_numref(& result_nullspace.entry(r,c)), fmpz_mat_entry(m2,r,c)); fmpz_mat_clear(m1); fmpz_mat_clear(m2); return nullity; }
int fmpq_mat_inv(fmpq_mat_t B, const fmpq_mat_t A) { long n = A->r; if (n == 0) { return 1; } else if (n == 1) { if (fmpq_is_zero(fmpq_mat_entry(A, 0, 0))) return 0; fmpq_inv(fmpq_mat_entry(B, 0, 0), fmpq_mat_entry(A, 0, 0)); return 1; } else if (n == 2) { fmpq_t d; int success; fmpq_init(d); fmpq_mul(d, fmpq_mat_entry(A, 0, 0), fmpq_mat_entry(A, 1, 1)); fmpq_submul(d, fmpq_mat_entry(A, 0, 1), fmpq_mat_entry(A, 1, 0)); success = !fmpq_is_zero(d); if (success) { fmpq_t t00, t01, t10, t11; fmpq_inv(d, d); fmpq_init(t00); fmpq_init(t01); fmpq_init(t10); fmpq_init(t11); fmpq_mul(t00, fmpq_mat_entry(A, 1, 1), d); fmpq_mul(t01, fmpq_mat_entry(A, 0, 1), d); fmpq_mul(t10, fmpq_mat_entry(A, 1, 0), d); fmpq_mul(t11, fmpq_mat_entry(A, 0, 0), d); fmpq_set(fmpq_mat_entry(B, 0, 0), t00); fmpq_neg(fmpq_mat_entry(B, 0, 1), t01); fmpq_neg(fmpq_mat_entry(B, 1, 0), t10); fmpq_set(fmpq_mat_entry(B, 1, 1), t11); fmpq_clear(t00); fmpq_clear(t01); fmpq_clear(t10); fmpq_clear(t11); } fmpq_clear(d); return success; } else { fmpz_mat_t Aclear, Bclear, I; fmpz * den; long i; int success; fmpz_mat_init(Aclear, n, n); fmpz_mat_init(Bclear, n, n); fmpz_mat_init(I, n, n); den = _fmpz_vec_init(n); fmpq_mat_get_fmpz_mat_rowwise(Aclear, den, A); for (i = 0; i < n; i++) fmpz_set(fmpz_mat_entry(I, i, i), den + i); success = fmpz_mat_solve(Bclear, den, Aclear, I); if (success) fmpq_mat_set_fmpz_mat_div_fmpz(B, Bclear, den); fmpz_mat_clear(Aclear); fmpz_mat_clear(Bclear); fmpz_mat_clear(I); _fmpz_vec_clear(den, A->r); return success; } }