void fmpz_poly_q_canonicalise(fmpz_poly_q_t rop) { fmpz_poly_t gcd; if (fmpz_poly_is_zero(rop->den)) { flint_printf("Exception (fmpz_poly_q_canonicalise). Denominator is zero.\n"); abort(); } if (fmpz_poly_is_one(rop->den)) return; fmpz_poly_init(gcd); fmpz_poly_gcd(gcd, rop->num, rop->den); if (!fmpz_poly_is_unit(gcd)) { fmpz_poly_div(rop->num, rop->num, gcd); fmpz_poly_div(rop->den, rop->den, gcd); } fmpz_poly_clear(gcd); if (fmpz_sgn(fmpz_poly_lead(rop->den)) < 0) { fmpz_poly_neg(rop->num, rop->num); fmpz_poly_neg(rop->den, rop->den); } }
void fmpz_poly_bit_pack(fmpz_t f, const fmpz_poly_t poly, mp_bitcnt_t bit_size) { long len; __mpz_struct * mpz; long i, d; int negate; len = fmpz_poly_length(poly); if (len == 0 || bit_size == 0) { fmpz_zero(f); return; } mpz = _fmpz_promote(f); mpz_realloc2(mpz, len * bit_size); d = mpz->_mp_alloc; mpn_zero(mpz->_mp_d, d); if (fmpz_sgn(fmpz_poly_lead(poly)) < 0) negate = -1; else negate = 0; _fmpz_poly_bit_pack(mpz->_mp_d, poly->coeffs, len, bit_size, negate); for (i = d - 1; i >= 0; i--) { if (mpz->_mp_d[i] != 0) break; } d = i + 1; mpz->_mp_size = d; _fmpz_demote_val(f); if (negate) fmpz_neg(f, f); }
void fmpz_mod_poly_divrem_f(fmpz_t f, fmpz_mod_poly_t Q, fmpz_mod_poly_t R, const fmpz_mod_poly_t A, const fmpz_mod_poly_t B) { const slong lenA = A->length; const slong lenB = B->length; const slong lenQ = lenA - lenB + 1; fmpz *q, *r; fmpz_t invB; fmpz_init(invB); fmpz_gcdinv(f, invB, fmpz_poly_lead(B), &(B->p)); if (!fmpz_is_one(f)) { fmpz_clear(invB); return; } if (lenA < lenB) { fmpz_mod_poly_set(R, A); fmpz_mod_poly_zero(Q); fmpz_clear(invB); return; } if (Q == A || Q == B) { q = _fmpz_vec_init(lenQ); } else { fmpz_mod_poly_fit_length(Q, lenQ); q = Q->coeffs; } if (R == A || R == B) { r = _fmpz_vec_init(lenA); } else { fmpz_mod_poly_fit_length(R, lenA); r = R->coeffs; } _fmpz_mod_poly_divrem_divconquer(q, r, A->coeffs, lenA, B->coeffs, lenB, invB, &(B->p)); if (Q == A || Q == B) { _fmpz_vec_clear(Q->coeffs, Q->alloc); Q->coeffs = q; Q->alloc = lenQ; Q->length = lenQ; } else { _fmpz_mod_poly_set_length(Q, lenQ); } if (R == A || R == B) { _fmpz_vec_clear(R->coeffs, R->alloc); R->coeffs = r; R->alloc = lenA; R->length = lenA; } _fmpz_mod_poly_set_length(R, lenB - 1); _fmpz_mod_poly_normalise(R); fmpz_clear(invB); }
long _fmpz_poly_hensel_start_lift(fmpz_poly_factor_t lifted_fac, long *link, fmpz_poly_t *v, fmpz_poly_t *w, const fmpz_poly_t f, const nmod_poly_factor_t local_fac, long N) { const long r = local_fac->num; long i, preve; fmpz_t p, P; fmpz_poly_t monic_f; fmpz_init(p); fmpz_init(P); fmpz_poly_init(monic_f); fmpz_set_ui(p, (local_fac->p + 0)->mod.n); fmpz_pow_ui(P, p, N); if (fmpz_is_one(fmpz_poly_lead(f))) { fmpz_poly_set(monic_f, f); } else if (fmpz_cmp_si(fmpz_poly_lead(f), -1) == 0) { fmpz_poly_neg(monic_f, f); } else { fmpz_t t; fmpz_init(t); fmpz_mod(t, fmpz_poly_lead(f), P); if (fmpz_invmod(t, t, P) == 0) { printf("Exception in fmpz_poly_start_hensel_lift.\n"); abort(); } fmpz_poly_scalar_mul_fmpz(monic_f, f, t); fmpz_poly_scalar_mod_fmpz(monic_f, monic_f, P); fmpz_clear(t); } fmpz_poly_hensel_build_tree(link, v, w, local_fac); { long *e, n = FLINT_CLOG2(N) + 1; e = flint_malloc(n * sizeof(long)); for (e[i = 0] = N; e[i] > 1; i++) e[i + 1] = (e[i] + 1) / 2; for (i--; i > 0; i--) { fmpz_poly_hensel_lift_tree(link, v, w, monic_f, r, p, e[i+1], e[i], 1); } if (N > 1) { fmpz_poly_hensel_lift_tree(link, v, w, monic_f, r, p, e[i+1], e[i], 0); } preve = e[i+1]; flint_free(e); } /* Now everything is lifted to p^N, we just need to insert the factors into their correct places in lifted_fac. */ fmpz_poly_factor_fit_length(lifted_fac, r); for (i = 0; i < 2*r - 2; i++) { if (link[i] < 0) { fmpz_poly_scalar_smod_fmpz(lifted_fac->p + (- link[i] - 1), v[i], P); lifted_fac->exp[- link[i] - 1] = 1L; } } lifted_fac->num = r; fmpz_clear(p); fmpz_clear(P); fmpz_poly_clear(monic_f); return preve; }
int main(void) { int i, result; flint_rand_t state; printf("hensel_start_continue_lift...."); fflush(stdout); flint_randinit(state); /* We check that lifting local factors of F yields factors */ for (i = 0; i < 1000; i++) { fmpz_poly_t F, G, H, R; nmod_poly_factor_t f_fac; fmpz_poly_factor_t F_fac; long bits, nbits, n, exp, j, part_exp; long r; fmpz_poly_t *v, *w; long *link; long prev_exp; bits = n_randint(state, 200) + 1; nbits = n_randint(state, FLINT_BITS - 6) + 6; fmpz_poly_init(F); fmpz_poly_init(G); fmpz_poly_init(H); fmpz_poly_init(R); nmod_poly_factor_init(f_fac); fmpz_poly_factor_init(F_fac); n = n_randprime(state, nbits, 0); exp = bits / (FLINT_BIT_COUNT(n) - 1) + 1; part_exp = n_randint(state, exp); /* Produce F as the product of random G and H */ { nmod_poly_t f; nmod_poly_init(f, n); do { do { fmpz_poly_randtest(G, state, n_randint(state, 200) + 2, bits); } while (G->length < 2); fmpz_randtest_not_zero(G->coeffs, state, bits); fmpz_one(fmpz_poly_lead(G)); do { fmpz_poly_randtest(H, state, n_randint(state, 200) + 2, bits); } while (H->length < 2); fmpz_randtest_not_zero(H->coeffs, state, bits); fmpz_one(fmpz_poly_lead(H)); fmpz_poly_mul(F, G, H); fmpz_poly_get_nmod_poly(f, F); } while (!nmod_poly_is_squarefree(f)); fmpz_poly_get_nmod_poly(f, G); nmod_poly_factor_insert(f_fac, f, 1); fmpz_poly_get_nmod_poly(f, H); nmod_poly_factor_insert(f_fac, f, 1); nmod_poly_clear(f); } r = f_fac->num; v = flint_malloc((2*r - 2)*sizeof(fmpz_poly_t)); w = flint_malloc((2*r - 2)*sizeof(fmpz_poly_t)); link = flint_malloc((2*r - 2)*sizeof(long)); for (j = 0; j < 2*r - 2; j++) { fmpz_poly_init(v[j]); fmpz_poly_init(w[j]); } if (part_exp < 1) { _fmpz_poly_hensel_start_lift(F_fac, link, v, w, F, f_fac, exp); } else { fmpz_t nn; fmpz_init_set_ui(nn, n); prev_exp = _fmpz_poly_hensel_start_lift(F_fac, link, v, w, F, f_fac, part_exp); _fmpz_poly_hensel_continue_lift(F_fac, link, v, w, F, prev_exp, part_exp, exp, nn); fmpz_clear(nn); } result = 1; for (j = 0; j < F_fac->num; j++) { fmpz_poly_rem(R, F, F_fac->p + j); result &= (R->length == 0); } for (j = 0; j < 2*r - 2; j++) { fmpz_poly_clear(v[j]); fmpz_poly_clear(w[j]); } flint_free(link); flint_free(v); flint_free(w); if (!result) { printf("FAIL:\n"); printf("bits = %ld, n = %ld, exp = %ld\n", bits, n, exp); fmpz_poly_print(F); printf("\n\n"); fmpz_poly_print(G); printf("\n\n"); fmpz_poly_print(H); printf("\n\n"); fmpz_poly_factor_print(F_fac); printf("\n\n"); abort(); } nmod_poly_factor_clear(f_fac); fmpz_poly_factor_clear(F_fac); fmpz_poly_clear(F); fmpz_poly_clear(H); fmpz_poly_clear(G); fmpz_poly_clear(R); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }