void fmpz_mat_mul_classical(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B) { long ar, bc, br; long i, j, k; ar = A->r; br = B->r; bc = B->c; if (br == 0) { fmpz_mat_zero(C); return; } for (i = 0; i < ar; i++) { for (j = 0; j < bc; j++) { fmpz_mul(fmpz_mat_entry(C, i, j), fmpz_mat_entry(A, i, 0), fmpz_mat_entry(B, 0, j)); for (k = 1; k < br; k++) { fmpz_addmul(fmpz_mat_entry(C, i, j), fmpz_mat_entry(A, i, k), fmpz_mat_entry(B, k, j)); } } } }
int fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state, const fmpz * diag, long n) { int parity; long i; long * rows; long * cols; rows = malloc(sizeof(long) * mat->r); cols = malloc(sizeof(long) * mat->c); for (i = 0; i < mat->r; i++) rows[i] = i; for (i = 0; i < mat->c; i++) cols[i] = i; parity = shuffle(rows, state, mat->r); parity ^= shuffle(cols, state, mat->c); fmpz_mat_zero(mat); for (i = 0; i < n; i++) fmpz_set(&mat->rows[rows[i]][cols[i]], &diag[i]); free(rows); free(cols); return parity; }
void fmpz_mat_unit(fmpz_mat_t mat) { long i; fmpz_mat_zero(mat); for (i = 0; i < FLINT_MIN(mat->r, mat->c); i++) fmpz_set_ui(mat->rows[i] + i, 1UL); }
void _brute_force_all_pairs_longest_walk(fmpz_mat_t B, const bool_mat_t A) { slong i, j, n; n = bool_mat_nrows(A); /* set entries of B according to the longest observed walk */ { slong k; bool_mat_t T; bool_mat_init(T, n, n); bool_mat_one(T); fmpz_mat_zero(B); for (k = 0; k < 2*n+1; k++) { for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { if (bool_mat_get_entry(T, i, j)) { fmpz_set_si(fmpz_mat_entry(B, i, j), k); } } } bool_mat_mul(T, T, A); } bool_mat_clear(T); } /* set special values 0, -1, -2 */ { for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { slong x; fmpz *p; p = fmpz_mat_entry(B, i, j); x = fmpz_get_si(p); if (x < 1) { x = (i == j) ? 0 : -1; } else if (x > n-1) { x = -2; } fmpz_set_si(p, x); } } } }
int main(void) { long m, n, i, j, rep; flint_rand_t state; printf("zero...."); fflush(stdout); flint_randinit(state); for (rep = 0; rep < 1000; rep++) { fmpz_mat_t A; m = n_randint(state, 20); n = n_randint(state, 20); fmpz_mat_init(A, m, n); fmpz_mat_randtest(A, state, 100); fmpz_mat_zero(A); for (i = 0; i < m; i++) { for (j = 0; j < n; j++) { if (!fmpz_is_zero(fmpz_mat_entry(A,i,j))) { printf("FAIL: nonzero entry\n"); abort(); } } } fmpz_mat_clear(A); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }
slong bool_mat_nilpotency_degree(const bool_mat_t A) { slong n; if (!bool_mat_is_square(A)) { flint_printf("bool_mat_nilpotency_degree: a square matrix is required!\n"); abort(); } if (bool_mat_is_empty(A)) return 0; n = bool_mat_nrows(A); if (n == 1) { return bool_mat_get_entry(A, 0, 0) ? -1 : 1; } else { _toposort_s s; slong i; int has_cycle; int result; _toposort_init(&s, n); for (has_cycle = 0, i = 0; !has_cycle && i < n; i++) if (!s.v[i]) has_cycle = _toposort_visit(&s, A, i); if (has_cycle) { result = -1; } else { /* Find the length of the longest path within the DAG */ /* http://stackoverflow.com/a/10737524/4072759 */ slong x, y, z; slong max_overall; fmpz_mat_t E; fmpz_mat_init(E, n, n); fmpz_mat_zero(E); max_overall = 0; for (i = n - 1; i >= 0; i--) { slong max_in = 0; y = s.post[i]; for (x = 0; x < n; x++) { max_in = FLINT_MAX(max_in, fmpz_get_si(fmpz_mat_entry(E, x, y))); } for (z = 0; z < n; z++) { if (bool_mat_get_entry(A, y, z)) { fmpz_set_si(fmpz_mat_entry(E, y, z), max_in + 1); max_overall = FLINT_MAX(max_overall, max_in + 1); } } } fmpz_mat_clear(E); result = max_overall + 1; } _toposort_clear(&s); return result; } }
long fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat) { long i, j, k, m, n, rank, nullity; long * pivots; long * nonpivots; fmpz_mat_t tmp; fmpz_t den; m = mat->r; n = mat->c; fmpz_mat_init_set(tmp, mat); fmpz_init(den); rank = fmpz_mat_rref(tmp, den, NULL, mat); nullity = n - rank; fmpz_mat_zero(res); if (rank == 0) { for (i = 0; i < nullity; i++) fmpz_one(res->rows[i] + i); } else if (nullity) { pivots = flint_malloc(rank * sizeof(long)); nonpivots = flint_malloc(nullity * sizeof(long)); for (i = j = k = 0; i < rank; i++) { while (fmpz_is_zero(tmp->rows[i] + j)) { nonpivots[k] = j; k++; j++; } pivots[i] = j; j++; } while (k < nullity) { nonpivots[k] = j; k++; j++; } fmpz_set(den, tmp->rows[0] + pivots[0]); for (i = 0; i < nullity; i++) { for (j = 0; j < rank; j++) fmpz_set(res->rows[pivots[j]] + i, tmp->rows[j] + nonpivots[i]); fmpz_neg(res->rows[nonpivots[i]] + i, den); } flint_free(pivots); flint_free(nonpivots); } fmpz_clear(den); fmpz_mat_clear(tmp); return nullity; }
void nf_elem_rep_mat_fmpz_mat_den(fmpz_mat_t res, fmpz_t den, const nf_elem_t a, const nf_t nf) { if (nf->flag & NF_LINEAR) { fmpz_set(fmpz_mat_entry(res, 0, 0), LNF_ELEM_NUMREF(a)); fmpz_set(den, LNF_ELEM_DENREF(a)); } else if (nf->flag & NF_QUADRATIC) { nf_elem_t t; const fmpz * const anum = QNF_ELEM_NUMREF(a); const fmpz * const aden = QNF_ELEM_DENREF(a); fmpz * const tnum = QNF_ELEM_NUMREF(t); fmpz * const tden = QNF_ELEM_DENREF(t); nf_elem_init(t, nf); nf_elem_mul_gen(t, a, nf); if (fmpz_equal(tden, aden)) { fmpz_set(fmpz_mat_entry(res, 0, 0), anum); fmpz_set(fmpz_mat_entry(res, 0, 1), anum + 1); fmpz_set(fmpz_mat_entry(res, 1, 0), tnum); fmpz_set(fmpz_mat_entry(res, 1, 1), tnum + 1); fmpz_set(den, tden); } else { fmpz_lcm(den, tden, aden); fmpz_divexact(fmpz_mat_entry(res, 0, 0), den, aden); fmpz_mul(fmpz_mat_entry(res, 0, 1), anum + 1, fmpz_mat_entry(res, 0, 0)); fmpz_mul(fmpz_mat_entry(res, 0, 0), anum, fmpz_mat_entry(res, 0, 0)); fmpz_divexact(fmpz_mat_entry(res, 1, 0), den, tden); fmpz_mul(fmpz_mat_entry(res, 1, 1), tnum + 1, fmpz_mat_entry(res, 1, 0)); fmpz_mul(fmpz_mat_entry(res, 1, 0), tnum, fmpz_mat_entry(res, 1, 0)); } nf_elem_clear(t, nf); } else { slong i, j; nf_elem_t t; slong d = fmpq_poly_degree(nf->pol); nf_elem_init(t, nf); nf_elem_set(t, a, nf); if (NF_ELEM(a)->length == 0) { fmpz_mat_zero(res); fmpz_one(den); } else if (NF_ELEM(a)->length == 1) { fmpz_mat_zero(res); for (i = 0; i <= d - 1; i++) { fmpz_set(fmpz_mat_entry(res, i, i), fmpq_poly_numref(NF_ELEM(a))); } fmpz_set(den, fmpq_poly_denref(NF_ELEM(a))); } else { /* Special case if defining polynomial is monic and integral and the element also has trivial denominator */ if (nf->flag & NF_MONIC && fmpz_is_one(fmpq_poly_denref(nf->pol)) && fmpz_is_one(fmpq_poly_denref(NF_ELEM(a)))) { fmpz_one(den); for (i = 0; i <= NF_ELEM(a)->length - 1; i++) fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i); for (i = NF_ELEM(a)->length; i <= d - 1; i++) fmpz_zero(fmpz_mat_entry(res, 0, i)); for (j = 1; j <= d - NF_ELEM(a)->length; j++) { nf_elem_mul_gen(t, t, nf); for (i = 0; i < j; i++) fmpz_zero(fmpz_mat_entry(res, j, i)); for (i = 0; i <= NF_ELEM(a)->length - 1; i++) fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i); for (i = j + NF_ELEM(a)->length; i <= d - 1; i++) fmpz_zero(fmpz_mat_entry(res, j, i)); } for (j = d - NF_ELEM(a)->length + 1; j <= d - 1; j++) { nf_elem_mul_gen(t, t, nf); for (i = 0; i <= d - 1; i++) fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i); } } else { /* Now the general case. For 0 <= j < d - 2 we store the * denominator for row j at res[d - 1, j]. At the end we * divide the lcm of all of them by the corresponding * denominator of the row to get the correct multiplier for * row. */ for (i = 0; i <= NF_ELEM(a)->length - 1; i++) fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i); for (i = NF_ELEM(a)->length; i <= d - 1; i++) fmpz_zero(fmpz_mat_entry(res, 0, i)); fmpz_set(fmpz_mat_entry(res, d - 1, 0), fmpq_poly_denref(NF_ELEM(a))); for (j = 1; j <= d - NF_ELEM(a)->length; j++) { nf_elem_mul_gen(t, t, nf); for (i = 0; i < j; i++) fmpz_zero(fmpz_mat_entry(res, j, i)); for (i = 0; i <= NF_ELEM(a)->length - 1; i++) fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i); for (i = j + NF_ELEM(a)->length; i <= d - 1; i++) fmpz_zero(fmpz_mat_entry(res, j, i)); fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(a))); } for (j = d - NF_ELEM(a)->length + 1; j <= d - 2; j++) { nf_elem_mul_gen(t, t, nf); for (i = 0; i <= d - 1; i++) fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i); fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(t))); } nf_elem_mul_gen(t, t, nf); /* Now compute the correct denominator */ fmpz_set(fmpz_mat_entry(res, d - 1, d - 1), fmpq_poly_denref(NF_ELEM(t))); fmpz_set(den, fmpq_poly_denref(NF_ELEM(t))); for (j = 0; j <= d - 2; j++) fmpz_lcm(den, den, fmpz_mat_entry(res, d - 1, j)); for (j = 0; j <= d - 2; j++) { if (!fmpz_equal(den, fmpz_mat_entry(res, d - 1, j))) { fmpz_divexact(fmpz_mat_entry(res, d - 1, j), den, fmpz_mat_entry(res, d - 1, j)); for (i = 0; i <= d - 1; i++) fmpz_mul(fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, d - 1, j)); } } if (fmpz_equal(den, fmpz_mat_entry(res, d - 1, d - 1))) { for (i = 0; i < d; i++) fmpz_set(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i); } else { fmpz_divexact(fmpz_mat_entry(res, d - 1, d - 1), den, fmpq_poly_denref(NF_ELEM(t))); for (i = 0; i < d; i++) fmpz_mul(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i, fmpz_mat_entry(res, d - 1, d - 1)); } } } nf_elem_clear(t, nf); } }