void nmod_poly_xgcd_hgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T, const nmod_poly_t A, const nmod_poly_t B) { if (A->length < B->length) { nmod_poly_xgcd_hgcd(G, T, S, B, A); } else /* lenA >= lenB >= 0 */ { const slong lenA = A->length, lenB = B->length; mp_limb_t inv; if (lenA == 0) /* lenA = lenB = 0 */ { nmod_poly_zero(G); nmod_poly_zero(S); nmod_poly_zero(T); } else if (lenB == 0) /* lenA > lenB = 0 */ { inv = n_invmod(A->coeffs[lenA - 1], A->mod.n); nmod_poly_scalar_mul_nmod(G, A, inv); nmod_poly_zero(T); nmod_poly_set_coeff_ui(S, 0, inv); S->length = 1; } else if (lenB == 1) /* lenA >= lenB = 1 */ { nmod_poly_fit_length(T, 1); T->length = 1; T->coeffs[0] = n_invmod(B->coeffs[0], A->mod.n); nmod_poly_one(G); nmod_poly_zero(S); } else /* lenA >= lenB >= 2 */ { mp_ptr g, s, t; slong lenG; if (G == A || G == B) { g = _nmod_vec_init(FLINT_MIN(lenA, lenB)); } else { nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB)); g = G->coeffs; } if (S == A || S == B) { s = _nmod_vec_init(FLINT_MAX(lenB - 1, 2)); } else { nmod_poly_fit_length(S, FLINT_MAX(lenB - 1, 2)); s = S->coeffs; } if (T == A || T == B) { t = _nmod_vec_init(FLINT_MAX(lenA - 1, 2)); } else { nmod_poly_fit_length(T, FLINT_MAX(lenA - 1, 2)); t = T->coeffs; } if (lenA >= lenB) lenG = _nmod_poly_xgcd_hgcd(g, s, t, A->coeffs, lenA, B->coeffs, lenB, A->mod); else lenG = _nmod_poly_xgcd_hgcd(g, t, s, B->coeffs, lenB, A->coeffs, lenA, A->mod); if (G == A || G == B) { flint_free(G->coeffs); G->coeffs = g; G->alloc = FLINT_MIN(lenA, lenB); } if (S == A || S == B) { flint_free(S->coeffs); S->coeffs = s; S->alloc = FLINT_MAX(lenB - 1, 2); } if (T == A || T == B) { flint_free(T->coeffs); T->coeffs = t; T->alloc = FLINT_MAX(lenA - 1, 2); } G->length = lenG; S->length = FLINT_MAX(lenB - lenG, 1); T->length = FLINT_MAX(lenA - lenG, 1); MPN_NORM(S->coeffs, S->length); MPN_NORM(T->coeffs, T->length); if (G->coeffs[lenG - 1] != 1) { inv = n_invmod(G->coeffs[lenG - 1], A->mod.n); nmod_poly_scalar_mul_nmod(G, G, inv); nmod_poly_scalar_mul_nmod(S, S, inv); nmod_poly_scalar_mul_nmod(T, T, inv); } } } }
void nmod_poly_xgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T, const nmod_poly_t A, const nmod_poly_t B) { const long lenA = A->length, lenB = B->length; mp_limb_t inv; if (lenA == 0) { if (lenB == 0) { nmod_poly_zero(G); nmod_poly_zero(S); nmod_poly_zero(T); } else { inv = n_invmod(B->coeffs[lenB - 1], B->mod.n); nmod_poly_scalar_mul_nmod(G, B, inv); nmod_poly_zero(S); nmod_poly_set_coeff_ui(T, 0, inv); T->length = 1; } } else if (lenB == 0) { inv = n_invmod(A->coeffs[lenA - 1], A->mod.n); nmod_poly_scalar_mul_nmod(G, A, inv); nmod_poly_zero(T); nmod_poly_set_coeff_ui(S, 0, inv); S->length = 1; } else { nmod_poly_t tG, tS, tT; mp_ptr g, s, t; long lenG; if (G == A || G == B) { nmod_poly_init2(tG, A->mod.n, FLINT_MIN(lenA, lenB)); g = tG->coeffs; } else { nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB)); g = G->coeffs; } if (S == A || S == B) { nmod_poly_init2(tS, A->mod.n, lenB - 1); s = tS->coeffs; } else { nmod_poly_fit_length(S, lenB - 1); s = S->coeffs; } if (T == A || T == B) { nmod_poly_init2(tT, A->mod.n, lenA - 1); t = tT->coeffs; } else { nmod_poly_fit_length(T, lenA - 1); t = T->coeffs; } if (lenA >= lenB) lenG = _nmod_poly_xgcd(g, s, t, A->coeffs, lenA, B->coeffs, lenB, A->mod); else lenG = _nmod_poly_xgcd(g, t, s, B->coeffs, lenB, A->coeffs, lenA, A->mod); if (G == A || G == B) { nmod_poly_swap(tG, G); nmod_poly_clear(tG); } if (S == A || S == B) { nmod_poly_swap(tS, S); nmod_poly_clear(tS); } if (T == A || T == B) { nmod_poly_swap(tT, T); nmod_poly_clear(tT); } G->length = lenG; S->length = lenB - lenG; T->length = lenA - lenG; MPN_NORM(S->coeffs, S->length); MPN_NORM(T->coeffs, T->length); if (G->coeffs[lenG - 1] != 1) { inv = n_invmod(G->coeffs[lenG - 1], A->mod.n); nmod_poly_scalar_mul_nmod(G, G, inv); nmod_poly_scalar_mul_nmod(S, S, inv); nmod_poly_scalar_mul_nmod(T, T, inv); } } }
int main(void) { int iter; flint_rand_t state; flint_randinit(state); printf("factor...."); fflush(stdout); /* Default algorithm */ for (iter = 0; iter < 100; iter++) { int result = 1; nmod_poly_t pol1, poly, quot, rem, product; nmod_poly_factor_t res; mp_limb_t modulus, lead = 1; long length, num, i, j; ulong exp[5], prod1; modulus = n_randtest_prime(state, 0); nmod_poly_init(pol1, modulus); nmod_poly_init(poly, modulus); nmod_poly_init(quot, modulus); nmod_poly_init(rem, modulus); nmod_poly_zero(pol1); nmod_poly_set_coeff_ui(pol1, 0, 1); length = n_randint(state, 7) + 2; do { nmod_poly_randtest(poly, state, length); if (poly->length) nmod_poly_make_monic(poly, poly); } while ((!nmod_poly_is_irreducible(poly)) || (poly->length < 2)); exp[0] = n_randint(state, 30) + 1; prod1 = exp[0]; for (i = 0; i < exp[0]; i++) nmod_poly_mul(pol1, pol1, poly); num = n_randint(state, 5) + 1; for (i = 1; i < num; i++) { do { length = n_randint(state, 7) + 2; nmod_poly_randtest(poly, state, length); if (poly->length) { nmod_poly_make_monic(poly, poly); nmod_poly_divrem(quot, rem, pol1, poly); } } while ((!nmod_poly_is_irreducible(poly)) || (poly->length < 2) || (rem->length == 0)); exp[i] = n_randint(state, 30) + 1; prod1 *= exp[i]; for (j = 0; j < exp[i]; j++) nmod_poly_mul(pol1, pol1, poly); } nmod_poly_factor_init(res); switch (n_randint(state, 3)) { case 0: lead = nmod_poly_factor(res, pol1); break; case 1: lead = nmod_poly_factor_with_berlekamp(res, pol1); break; case 2: if (modulus == 2) lead = nmod_poly_factor(res, pol1); else lead = nmod_poly_factor_with_cantor_zassenhaus(res, pol1); break; } result &= (res->num == num); if (!result) { printf("Error: number of factors incorrect, %ld, %ld\n", res->num, num); abort(); } nmod_poly_init(product, pol1->mod.n); nmod_poly_set_coeff_ui(product, 0, 1); for (i = 0; i < res->num; i++) for (j = 0; j < res->exp[i]; j++) nmod_poly_mul(product, product, res->p + i); nmod_poly_scalar_mul_nmod(product, product, lead); result &= nmod_poly_equal(pol1, product); if (!result) { printf("Error: product of factors does not equal original polynomial\n"); nmod_poly_print(pol1); printf("\n"); nmod_poly_print(product); printf("\n"); abort(); } nmod_poly_clear(product); nmod_poly_clear(quot); nmod_poly_clear(rem); nmod_poly_clear(pol1); nmod_poly_clear(poly); nmod_poly_factor_clear(res); } /* Test deflation trick */ for (iter = 0; iter < 100; iter++) { nmod_poly_t pol1, poly, quot, rem; nmod_poly_factor_t res, res2; mp_limb_t modulus; long length, num, i, j; long exp[5], prod1; ulong inflation; int found; do { modulus = n_randtest_prime(state, 0); } while (modulus == 2); /* To compare with CZ */ nmod_poly_init(pol1, modulus); nmod_poly_init(poly, modulus); nmod_poly_init(quot, modulus); nmod_poly_init(rem, modulus); nmod_poly_zero(pol1); nmod_poly_set_coeff_ui(pol1, 0, 1); inflation = n_randint(state, 7) + 1; length = n_randint(state, 7) + 2; do { nmod_poly_randtest(poly, state, length); if (poly->length) nmod_poly_make_monic(poly, poly); } while ((!nmod_poly_is_irreducible(poly)) || (poly->length < 2)); nmod_poly_inflate(poly, poly, inflation); exp[0] = n_randint(state, 6) + 1; prod1 = exp[0]; for (i = 0; i < exp[0]; i++) nmod_poly_mul(pol1, pol1, poly); num = n_randint(state, 5) + 1; for (i = 1; i < num; i++) { do { length = n_randint(state, 6) + 2; nmod_poly_randtest(poly, state, length); if (poly->length) { nmod_poly_make_monic(poly, poly); nmod_poly_divrem(quot, rem, pol1, poly); } } while ((!nmod_poly_is_irreducible(poly)) || (poly->length < 2) || (rem->length == 0)); exp[i] = n_randint(state, 6) + 1; prod1 *= exp[i]; nmod_poly_inflate(poly, poly, inflation); for (j = 0; j < exp[i]; j++) nmod_poly_mul(pol1, pol1, poly); } nmod_poly_factor_init(res); nmod_poly_factor_init(res2); switch (n_randint(state, 3)) { case 0: nmod_poly_factor(res, pol1); break; case 1: nmod_poly_factor_with_berlekamp(res, pol1); break; case 2: nmod_poly_factor_with_cantor_zassenhaus(res, pol1); break; } nmod_poly_factor_cantor_zassenhaus(res2, pol1); if (res->num != res2->num) { printf("FAIL: different number of factors found\n"); abort(); } for (i = 0; i < res->num; i++) { found = 0; for (j = 0; j < res2->num; j++) { if (nmod_poly_equal(res->p + i, res2->p + j) && res->exp[i] == res2->exp[j]) { found = 1; break; } } if (!found) { printf("FAIL: factor not found\n"); abort(); } } nmod_poly_clear(quot); nmod_poly_clear(rem); nmod_poly_clear(pol1); nmod_poly_clear(poly); nmod_poly_factor_clear(res); nmod_poly_factor_clear(res2); } flint_randclear(state); printf("PASS\n"); return 0; }
int main(void) { int i, result; FLINT_TEST_INIT(state); flint_printf("scalar_mul_nmod...."); fflush(stdout); /* Check aliasing of a and b */ for (i = 0; i < 1000 * flint_test_multiplier(); i++) { nmod_poly_t a, b; mp_limb_t n = n_randtest_not_zero(state); mp_limb_t c = n_randint(state, n); nmod_poly_init(a, n); nmod_poly_init(b, n); nmod_poly_randtest(a, state, n_randint(state, 100)); nmod_poly_scalar_mul_nmod(b, a, c); nmod_poly_scalar_mul_nmod(a, a, c); result = (nmod_poly_equal(a, b)); if (!result) { flint_printf("FAIL:\n"); nmod_poly_print(a), flint_printf("\n\n"); nmod_poly_print(b), flint_printf("\n\n"); abort(); } nmod_poly_clear(a); nmod_poly_clear(b); } /* Check (a + b)*c = a*c + b*c */ for (i = 0; i < 1000 * flint_test_multiplier(); i++) { nmod_poly_t a, b, d1, d2; mp_limb_t n = n_randtest_not_zero(state); mp_limb_t c = n_randint(state, n); nmod_poly_init(a, n); nmod_poly_init(b, n); nmod_poly_init(d1, n); nmod_poly_init(d2, n); nmod_poly_randtest(a, state, n_randint(state, 100)); nmod_poly_randtest(b, state, n_randint(state, 100)); nmod_poly_add(d1, a, b); nmod_poly_scalar_mul_nmod(d1, d1, c); nmod_poly_scalar_mul_nmod(d2, a, c); nmod_poly_scalar_mul_nmod(b, b, c); nmod_poly_add(d2, d2, b); result = (nmod_poly_equal(d1, d2)); if (!result) { flint_printf("FAIL:\n"); nmod_poly_print(d1), flint_printf("\n\n"); nmod_poly_print(d2), flint_printf("\n\n"); abort(); } nmod_poly_clear(a); nmod_poly_clear(b); nmod_poly_clear(d1); nmod_poly_clear(d2); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }