void fmpq_poly_resultant(fmpq_t r, const fmpq_poly_t f, const fmpq_poly_t g) { const long len1 = f->length; const long len2 = g->length; if (len1 == 0 || len2 == 0) { fmpq_zero(r); } else { if (len1 >= len2) { _fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r), f->coeffs, f->den, len1, g->coeffs, g->den, len2); } else { _fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r), g->coeffs, g->den, len2, f->coeffs, f->den, len1); if (((len1 | len2) & 1L) == 0L) fmpq_neg(r, r); } } }
renf_elem_class renf_elem_class::operator-() const noexcept { renf_elem_class ans(*this); if (nf == nullptr) fmpq_neg(ans.b, ans.b); else renf_elem_neg(ans.a, ans.a, ans.nf->renf_t()); return ans; }
void _dgsl_rot_mp_sqrt_sigma_2(fmpq_poly_t rop, const fmpz_poly_t g, const mpfr_t sigma, const int r, const long n, const mpfr_prec_t prec, const oz_flag_t flags) { fmpq_poly_zero(rop); fmpq_t r_q2; fmpq_init(r_q2); fmpq_set_si(r_q2, r, 1); fmpq_mul(r_q2, r_q2, r_q2); fmpq_neg(r_q2, r_q2); fmpq_poly_set_coeff_fmpq(rop, 0, r_q2); fmpq_clear(r_q2); fmpq_poly_t g_q; fmpq_poly_init(g_q); fmpq_poly_set_fmpz_poly(g_q, g); fmpq_poly_t ng; fmpq_poly_init(ng); fmpq_poly_oz_invert_approx(ng, g_q, n, prec, flags); fmpq_poly_t ngt; fmpq_poly_init(ngt); fmpq_poly_oz_conjugate(ngt, ng, n); fmpq_poly_t nggt; fmpq_poly_init(nggt); fmpq_poly_oz_mul(nggt, ng, ngt, n); /** We compute sqrt(g^-T · g^-1) to use it as the starting point for convergence on sqrt(σ^2 · g^-T · g^-1 - r^2) below. We can compute the former with less precision than the latter */ mpfr_t norm; mpfr_init2(norm, prec); fmpz_poly_eucl_norm_mpfr(norm, g, MPFR_RNDN); double p = mpfr_get_d(norm, MPFR_RNDN); /** |g^-1| ~= 1/|g| |g^-T| ~= |g^-1| |g^-1·g^-T| ~= sqrt(n)·|g^-T|·|g^-1| */ fmpq_poly_t sqrt_start; fmpq_poly_init(sqrt_start); p = log2(n) + 4*log2(p); int fail = -1; while (fail) { p = 2*p; if (fail<0) fail = fmpq_poly_oz_sqrt_approx_db(sqrt_start, nggt, n, p, prec/2, flags, NULL); else fail = fmpq_poly_oz_sqrt_approx_db(sqrt_start, nggt, n, p, prec/2, flags, sqrt_start); if(fail) fprintf(stderr, "FAILED for precision %7.1f with code (%d), doubling precision.\n", p, fail); } fmpq_t sigma2; fmpq_init(sigma2); fmpq_set_mpfr(sigma2, sigma, MPFR_RNDN); fmpq_poly_scalar_mul_fmpq(sqrt_start, sqrt_start, sigma2); fmpq_mul(sigma2, sigma2, sigma2); fmpq_poly_scalar_mul_fmpq(nggt, nggt, sigma2); fmpq_clear(sigma2); fmpq_poly_add(rop, rop, nggt); p = p + 2*log2(mpfr_get_d(sigma, MPFR_RNDN)); fmpq_poly_oz_sqrt_approx_babylonian(rop, rop, n, p, prec, flags, sqrt_start); mpfr_clear(norm); fmpq_poly_clear(g_q); fmpq_poly_clear(ng); fmpq_poly_clear(ngt); fmpq_poly_clear(nggt); fmpq_poly_clear(sqrt_start); }
void test_field2(flint_rand_t state) { /* test in QQ[3^(1/4)] */ renf_t nf; renf_elem_t a; fmpq_t d, k; fmpq_poly_t p; fmpq_init(d); fmpq_poly_init(p); fmpq_set_si(d, 3, 1); renf_init_nth_root_fmpq(nf, d, 4, 10 + n_randint(state, 10)); fmpq_clear(d); fmpq_init(k); renf_elem_init(a, nf); /* test rationals */ /* --> 3^(1/4) */ fmpq_poly_set_coeff_si(p, 1, 1); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 2, "3^(1/4)"); /* --> 3^(1/4) - p_34 / q_34 */ /* ceil = 1 */ fmpz_set_str(fmpq_numref(k), "3871793620206447926", 10); fmpz_set_str(fmpq_denref(k), "2941926960111028069", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 1, "3^(1/4)"); /* --> 3^(1/4) - p_35 / q_35 */ /* ceil = 0 */ fmpz_set_str(fmpq_numref(k), "4393442218385055959", 10); fmpz_set_str(fmpq_denref(k), "3338294180377262795", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 0, "3^(1/4)"); /* --> 3^(1/4) - p_200 / q_200 */ fmpz_set_str(fmpq_numref(k), "51566086581654990699052199424489069476470199719930170996263916596162993841059250500042162091", 10); fmpz_set_str(fmpq_denref(k), "39181752754141206003124111890355840072199542360218864430892618765033598468868752146602163065", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 1, "3^(1/4)"); /* --> 3^(1/4) - p_201 / q_201 */ fmpz_set_str(fmpq_numref(k), "80796322887694335717970676356641716096406222234122724217891106756946083353628876437327250032", 10); fmpz_set_str(fmpq_denref(k), "61391929399498685496270115285641595325756438975454257165479021482386018841773493669624721869", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 0, "3^(1/4)"); /* */ fmpz_set_str(fmpq_numref(k), "13231942875843754343234", 10); fmpz_set_str(fmpq_denref(k), "14321431341231112121", 10); fmpq_poly_set_coeff_fmpq(p, 3, k); fmpz_set_str(fmpq_numref(k), "148589873455543948591", 10); fmpz_set_str(fmpq_denref(k), "12332111221111", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 2, k); fmpz_set_str(fmpq_numref(k), "1233321469998711012392391", 10); fmpz_set_str(fmpq_denref(k), "11814121556810191", 10); fmpq_poly_set_coeff_fmpq(p, 1, k); fmpz_set_str(fmpq_numref(k), "1249152314425433983202991363672458443993964487436329478959287771807457205881969983777233465754608376177969464841", 10); fmpz_set_str(fmpq_denref(k), "10720278662399817731713810382544982753044312944075797382817281426908463944866446042500978893159281330135", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 231, "3^(1/4)"); renf_elem_clear(a, nf); renf_clear(nf); fmpq_clear(k); fmpq_poly_clear(p); }
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; } }
/** @name arithmetic @{ */ void negate(ElementType& result,const ElementType& a) const {fmpq_neg(&result,&a);}
int fmpq_poly_check_unique_real_root(const fmpq_poly_t pol, const arb_t a, slong prec) { if (pol->length < 2) return 0; else if (pol->length == 2) { /* linear polynomial */ fmpq_t root; int ans; fmpq_init(root); fmpq_set_fmpz_frac(root, fmpq_poly_numref(pol), fmpq_poly_numref(pol) + 1); fmpq_neg(root, root); ans = arb_contains_fmpq(a, root); fmpq_clear(root); return ans; } else { arb_t b, c; arf_t l, r; fmpz * der; int lsign, rsign; fmpz_poly_t pol2; slong n; /* 1 - cheap test: */ /* - sign(left) * sign(right) = -1 */ /* - no zero of the derivative */ arb_init(b); arb_init(c); arf_init(l); arf_init(r); arb_get_interval_arf(l, r, a, prec); arb_set_arf(b, l); _fmpz_poly_evaluate_arb(c, pol->coeffs, pol->length, b, 2*prec); lsign = arb_sgn2(c); arb_set_arf(b, r); _fmpz_poly_evaluate_arb(c, pol->coeffs, pol->length, b, 2*prec); rsign = arb_sgn2(c); arb_clear(c); if (lsign * rsign == -1) { der = _fmpz_vec_init(pol->length - 1); _fmpz_poly_derivative(der, pol->coeffs, pol->length); _fmpz_poly_evaluate_arb(b, der, pol->length - 1, a, prec); _fmpz_vec_clear(der, pol->length - 1); if (!arb_contains_zero(b)) { arf_clear(l); arf_clear(r); arb_clear(b); return 1; } } else return 0; arb_clear(b); /* 2 - expensive testing */ fmpq_t ql, qr; fmpq_init(ql); fmpq_init(qr); arf_get_fmpq(ql, l); arf_get_fmpq(qr, r); fmpz_poly_init(pol2); fmpz_poly_fit_length(pol2, pol->length); _fmpz_vec_set(pol2->coeffs, pol->coeffs, pol->length); pol2->length = pol->length; _fmpz_poly_scale_0_1_fmpq(pol2->coeffs, pol2->length, ql, qr); n = fmpz_poly_num_real_roots_0_1(pol2); fmpz_poly_clear(pol2); fmpq_clear(ql); fmpq_clear(qr); return (n == 1); } }