static void poly_mod2_to_modq(fmpz_poly_t Fq, const fmpz_poly_t a, const ntru_params *params) { int v = 2; fmpz_poly_t poly_tmp, two; fmpz_poly_init(poly_tmp); fmpz_poly_zero(poly_tmp); fmpz_poly_init(two); fmpz_poly_set_coeff_ui(two, 0, 2); while (v < (int)(params->q)) { v = v * 2; poly_starmultiply(poly_tmp, a, Fq, params, v); fmpz_poly_sub(poly_tmp, two, poly_tmp); fmpz_poly_mod_unsigned(poly_tmp, v); poly_starmultiply(Fq, Fq, poly_tmp, params, v); } fmpz_poly_clear(poly_tmp); fmpz_poly_clear(two); }
int main(void) { int i, result; flint_rand_t state; printf("revert_series...."); fflush(stdout); flint_randinit(state); /* Check aliasing */ for (i = 0; i < 50; i++) { fmpz_poly_t f, g; long n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_randtest(g, state, n_randint(state, 50), 1+n_randint(state,100)); fmpz_poly_set_coeff_ui(g, 0, 0); fmpz_poly_set_coeff_ui(g, 1, 1); if (n_randlimb(state) % 2) fmpz_poly_neg(g, g); /* get -x term */ n = n_randint(state, 50); fmpz_poly_revert_series(f, g, n); fmpz_poly_revert_series(g, g, n); result = (fmpz_poly_equal(f, g)); if (!result) { printf("FAIL (aliasing):\n"); fmpz_poly_print(f), printf("\n\n"); fmpz_poly_print(g), printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); } /* Check f(f^(-1)) = id */ for (i = 0; i < 50; i++) { fmpz_poly_t f, g, h; long n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_init(h); fmpz_poly_randtest(g, state, n_randint(state, 50), 10); fmpz_poly_set_coeff_ui(g, 0, 0); fmpz_poly_set_coeff_ui(g, 1, 1); if (n_randlimb(state) % 2) fmpz_poly_neg(g, g); /* get -x term */ n = n_randint(state, 50); fmpz_poly_revert_series(f, g, n); fmpz_poly_compose_series(h, g, f, n); result = ((n <= 1 && fmpz_poly_is_zero(h)) || (h->length == 2 && fmpz_is_zero(h->coeffs + 0) && fmpz_is_one(h->coeffs + 1))); if (!result) { printf("FAIL (comparison):\n"); fmpz_poly_print(f), printf("\n\n"); fmpz_poly_print(g), printf("\n\n"); fmpz_poly_print(h), printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_poly_clear(h); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }
int main(void) { int i, result; FLINT_TEST_INIT(state); flint_printf("revert_series_lagrange_fast...."); fflush(stdout); /* Check aliasing */ for (i = 0; i < 10 * flint_test_multiplier(); i++) { fmpz_poly_t f, g; slong n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_randtest(g, state, n_randint(state, 50), 1+n_randint(state,100)); fmpz_poly_set_coeff_ui(g, 0, 0); fmpz_poly_set_coeff_ui(g, 1, 1); if (n_randlimb(state) % 2) fmpz_poly_neg(g, g); /* get -x term */ n = n_randint(state, 50); fmpz_poly_revert_series_lagrange_fast(f, g, n); fmpz_poly_revert_series_lagrange_fast(g, g, n); result = (fmpz_poly_equal(f, g)); if (!result) { flint_printf("FAIL (aliasing):\n"); fmpz_poly_print(f), flint_printf("\n\n"); fmpz_poly_print(g), flint_printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); } /* Check f(f^(-1)) = id */ for (i = 0; i < 10 * flint_test_multiplier(); i++) { fmpz_poly_t f, g, h; slong n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_init(h); fmpz_poly_randtest(g, state, n_randint(state, 50), 1+n_randint(state,100)); fmpz_poly_set_coeff_ui(g, 0, 0); fmpz_poly_set_coeff_ui(g, 1, 1); if (n_randlimb(state) % 2) fmpz_poly_neg(g, g); /* get -x term */ n = n_randint(state, 50); fmpz_poly_revert_series_lagrange_fast(f, g, n); fmpz_poly_compose_series(h, g, f, n); result = ((n <= 1 && fmpz_poly_is_zero(h)) || (h->length == 2 && fmpz_is_zero(h->coeffs + 0) && fmpz_is_one(h->coeffs + 1))); if (!result) { flint_printf("FAIL (comparison):\n"); fmpz_poly_print(f), flint_printf("\n\n"); fmpz_poly_print(g), flint_printf("\n\n"); fmpz_poly_print(h), flint_printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_poly_clear(h); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
int main(void) { int i; FLINT_TEST_INIT(state); flint_printf("taylor_shift_divconquer...."); fflush(stdout); /* Check aliasing */ for (i = 0; i < 100 * flint_test_multiplier(); i++) { fmpz_poly_t f, g; fmpz_t c; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_init(c); fmpz_poly_randtest(f, state, 1 + n_randint(state, 20), 1 + n_randint(state, 200)); fmpz_randtest(c, state, n_randint(state, 200)); fmpz_poly_taylor_shift_divconquer(g, f, c); fmpz_poly_taylor_shift_divconquer(f, f, c); if (!fmpz_poly_equal(g, f)) { flint_printf("FAIL\n"); fmpz_poly_print(f); flint_printf("\n"); fmpz_poly_print(g); flint_printf("\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_clear(c); } /* Compare with composition */ for (i = 0; i < 100 * flint_test_multiplier(); i++) { fmpz_poly_t f, g, h1, h2; fmpz_t c; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_init(h1); fmpz_poly_init(h2); fmpz_init(c); fmpz_poly_randtest(f, state, 1 + n_randint(state, 20), 1 + n_randint(state, 200)); fmpz_randtest(c, state, n_randint(state, 200)); fmpz_poly_set_coeff_ui(g, 1, 1); fmpz_poly_set_coeff_fmpz(g, 0, c); fmpz_poly_taylor_shift_divconquer(h1, f, c); fmpz_poly_compose(h2, f, g); if (!fmpz_poly_equal(h1, h2)) { flint_printf("FAIL\n"); fmpz_poly_print(f); flint_printf("\n"); fmpz_poly_print(g); flint_printf("\n"); fmpz_poly_print(h1); flint_printf("\n"); fmpz_poly_print(h2); flint_printf("\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_poly_clear(h1); fmpz_poly_clear(h2); fmpz_clear(c); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
int main(int argc, char *argv[]) { fmpz_poly_t f, g; fmpz_poly_factor_t fac; fmpz_t t; slong compd, printd, i, j; if (argc < 2) { flint_printf("poly_roots [-refine d] [-print d] <poly>\n\n"); flint_printf("Isolates all the complex roots of a polynomial with integer coefficients.\n\n"); flint_printf("If -refine d is passed, the roots are refined to an absolute tolerance\n"); flint_printf("better than 10^(-d). By default, the roots are only computed to sufficient\n"); flint_printf("accuracy to isolate them. The refinement is not currently done efficiently.\n\n"); flint_printf("If -print d is passed, the computed roots are printed to d decimals.\n"); flint_printf("By default, the roots are not printed.\n\n"); flint_printf("The polynomial can be specified by passing the following as <poly>:\n\n"); flint_printf("a <n> Easy polynomial 1 + 2x + ... + (n+1)x^n\n"); flint_printf("t <n> Chebyshev polynomial T_n\n"); flint_printf("u <n> Chebyshev polynomial U_n\n"); flint_printf("p <n> Legendre polynomial P_n\n"); flint_printf("c <n> Cyclotomic polynomial Phi_n\n"); flint_printf("s <n> Swinnerton-Dyer polynomial S_n\n"); flint_printf("b <n> Bernoulli polynomial B_n\n"); flint_printf("w <n> Wilkinson polynomial W_n\n"); flint_printf("e <n> Taylor series of exp(x) truncated to degree n\n"); flint_printf("m <n> <m> The Mignotte-like polynomial x^n + (100x+1)^m, n > m\n"); flint_printf("coeffs <c0 c1 ... cn> c0 + c1 x + ... + cn x^n\n\n"); flint_printf("Concatenate to multiply polynomials, e.g.: p 5 t 6 coeffs 1 2 3\n"); flint_printf("for P_5(x)*T_6(x)*(1+2x+3x^2)\n\n"); return 1; } compd = 0; printd = 0; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_init(t); fmpz_poly_one(f); for (i = 1; i < argc; i++) { if (!strcmp(argv[i], "-refine")) { compd = atol(argv[i+1]); i++; } else if (!strcmp(argv[i], "-print")) { printd = atol(argv[i+1]); i++; } else if (!strcmp(argv[i], "a")) { slong n = atol(argv[i+1]); fmpz_poly_zero(g); for (j = 0; j <= n; j++) fmpz_poly_set_coeff_ui(g, j, j+1); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "t")) { arith_chebyshev_t_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "u")) { arith_chebyshev_u_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "p")) { fmpq_poly_t h; fmpq_poly_init(h); arith_legendre_polynomial(h, atol(argv[i+1])); fmpq_poly_get_numerator(g, h); fmpz_poly_mul(f, f, g); fmpq_poly_clear(h); i++; } else if (!strcmp(argv[i], "c")) { arith_cyclotomic_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "s")) { arith_swinnerton_dyer_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "b")) { fmpq_poly_t h; fmpq_poly_init(h); arith_bernoulli_polynomial(h, atol(argv[i+1])); fmpq_poly_get_numerator(g, h); fmpz_poly_mul(f, f, g); fmpq_poly_clear(h); i++; } else if (!strcmp(argv[i], "w")) { slong n = atol(argv[i+1]); fmpz_poly_zero(g); fmpz_poly_fit_length(g, n+2); arith_stirling_number_1_vec(g->coeffs, n+1, n+2); _fmpz_poly_set_length(g, n+2); fmpz_poly_shift_right(g, g, 1); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "e")) { fmpq_poly_t h; fmpq_poly_init(h); fmpq_poly_set_coeff_si(h, 0, 0); fmpq_poly_set_coeff_si(h, 1, 1); fmpq_poly_exp_series(h, h, atol(argv[i+1]) + 1); fmpq_poly_get_numerator(g, h); fmpz_poly_mul(f, f, g); fmpq_poly_clear(h); i++; } else if (!strcmp(argv[i], "m")) { fmpz_poly_zero(g); fmpz_poly_set_coeff_ui(g, 0, 1); fmpz_poly_set_coeff_ui(g, 1, 100); fmpz_poly_pow(g, g, atol(argv[i+2])); fmpz_poly_set_coeff_ui(g, atol(argv[i+1]), 1); fmpz_poly_mul(f, f, g); i += 2; } else if (!strcmp(argv[i], "coeffs")) { fmpz_poly_zero(g); i++; j = 0; while (i < argc) { if (fmpz_set_str(t, argv[i], 10) != 0) { i--; break; } fmpz_poly_set_coeff_fmpz(g, j, t); i++; j++; } fmpz_poly_mul(f, f, g); } } fmpz_poly_factor_init(fac); flint_printf("computing squarefree factorization...\n"); TIMEIT_ONCE_START fmpz_poly_factor_squarefree(fac, f); TIMEIT_ONCE_STOP TIMEIT_ONCE_START for (i = 0; i < fac->num; i++) { flint_printf("roots with multiplicity %wd\n", fac->exp[i]); fmpz_poly_complex_roots_squarefree(fac->p + i, 32, compd * 3.32193 + 2, printd); } TIMEIT_ONCE_STOP fmpz_poly_factor_clear(fac); fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_clear(t); flint_cleanup(); return EXIT_SUCCESS; }
bool poly_inverse_poly_p(fmpz_poly_t Fp, const fmpz_poly_t a, const ntru_params *params) { bool retval = false; int k = 0, j = 0; fmpz *b_last; fmpz_poly_t a_tmp, b, c, f, g; /* general initialization of temp variables */ fmpz_poly_init(b); fmpz_poly_set_coeff_ui(b, 0, 1); fmpz_poly_init(c); fmpz_poly_init(f); fmpz_poly_set(f, a); /* set g(x) = x^N − 1 */ fmpz_poly_init(g); fmpz_poly_set_coeff_si(g, 0, -1); fmpz_poly_set_coeff_si(g, params->N, 1); /* avoid side effects */ fmpz_poly_init(a_tmp); fmpz_poly_set(a_tmp, a); fmpz_poly_zero(Fp); while (1) { while (fmpz_poly_get_coeff_ptr(f, 0) && fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) { for (uint32_t i = 1; i <= params->N; i++) { fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i); fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i); /* f(x) = f(x) / x */ fmpz_poly_set_coeff_fmpz_n(f, i - 1, f_coeff); /* c(x) = c(x) * x */ fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i, c_coeff); } fmpz_poly_set_coeff_si(f, params->N, 0); fmpz_poly_set_coeff_si(c, 0, 0); k++; if (fmpz_poly_degree(f) == -1) goto cleanup; } if (fmpz_poly_is_zero(g) == 1) goto cleanup; if (fmpz_poly_degree(f) == 0) break; if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) { /* exchange f and g and exchange b and c */ fmpz_poly_swap(f, g); fmpz_poly_swap(b, c); } { fmpz_poly_t c_tmp, g_tmp; fmpz_t u, mp_tmp; fmpz_init(u); fmpz_zero(u); fmpz_init_set(mp_tmp, fmpz_poly_get_coeff_ptr(f, 0)); fmpz_poly_init(g_tmp); fmpz_poly_set(g_tmp, g); fmpz_poly_init(c_tmp); fmpz_poly_set(c_tmp, c); /* u = f[0] * g[0]^(-1) mod p */ /* = (f[0] mod p) * (g[0] inverse mod p) mod p */ fmpz_invmod_ui(u, fmpz_poly_get_coeff_ptr(g, 0), params->p); fmpz_mod_ui(mp_tmp, mp_tmp, params->p); fmpz_mul(u, mp_tmp, u); fmpz_mod_ui(u, u, params->p); /* f = f - u * g mod p */ fmpz_poly_scalar_mul_fmpz(g_tmp, g_tmp, u); fmpz_poly_sub(f, f, g_tmp); fmpz_poly_mod_unsigned(f, params->p); /* b = b - u * c mod p */ fmpz_poly_scalar_mul_fmpz(c_tmp, c_tmp, u); fmpz_poly_sub(b, b, c_tmp); fmpz_poly_mod_unsigned(b, params->p); fmpz_clear(u); fmpz_poly_clear(g_tmp); fmpz_poly_clear(c_tmp); } } k = k % params->N; b_last = fmpz_poly_get_coeff_ptr(b, params->N); if (fmpz_cmp_si_n(b_last, 0)) goto cleanup; /* Fp(x) = x^(N-k) * b(x) */ for (int i = params->N - 1; i >= 0; i--) { fmpz *b_i; /* b(X) = f[0]^(-1) * b(X) (mod p) */ { fmpz_t mp_tmp; fmpz_init(mp_tmp); fmpz_invmod_ui(mp_tmp, fmpz_poly_get_coeff_ptr(f, 0), params->p); if (fmpz_poly_get_coeff_ptr(b, i)) { fmpz_mul(fmpz_poly_get_coeff_ptr(b, i), fmpz_poly_get_coeff_ptr(b, i), mp_tmp); fmpz_mod_ui(fmpz_poly_get_coeff_ptr(b, i), fmpz_poly_get_coeff_ptr(b, i), params->p); } } j = i - k; if (j < 0) j = j + params->N; b_i = fmpz_poly_get_coeff_ptr(b, i); fmpz_poly_set_coeff_fmpz_n(Fp, j, b_i); } /* check if the f * Fp = 1 (mod p) condition holds true */ fmpz_poly_set(a_tmp, a); poly_starmultiply(a_tmp, a_tmp, Fp, params, params->p); if (fmpz_poly_is_one(a_tmp)) retval = true; else fmpz_poly_zero(Fp); cleanup: fmpz_poly_clear(a_tmp); fmpz_poly_clear(b); fmpz_poly_clear(c); fmpz_poly_clear(f); fmpz_poly_clear(g); return retval; }
bool poly_inverse_poly_q(fmpz_poly_t Fq, const fmpz_poly_t a, const ntru_params *params) { bool retval = false; int k = 0, j = 0; fmpz *b_last; fmpz_poly_t a_tmp, b, c, f, g; /* general initialization of temp variables */ fmpz_poly_init(b); fmpz_poly_set_coeff_ui(b, 0, 1); fmpz_poly_init(c); fmpz_poly_init(f); fmpz_poly_set(f, a); /* set g(x) = x^N − 1 */ fmpz_poly_init(g); fmpz_poly_set_coeff_si(g, 0, -1); fmpz_poly_set_coeff_si(g, params->N, 1); /* avoid side effects */ fmpz_poly_init(a_tmp); fmpz_poly_set(a_tmp, a); fmpz_poly_zero(Fq); while (1) { while (fmpz_poly_get_coeff_ptr(f, 0) && fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) { for (uint32_t i = 1; i <= params->N; i++) { fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i); fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i); /* f(x) = f(x) / x */ fmpz_poly_set_coeff_fmpz_n(f, i - 1, f_coeff); /* c(x) = c(x) * x */ fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i, c_coeff); } fmpz_poly_set_coeff_si(f, params->N, 0); fmpz_poly_set_coeff_si(c, 0, 0); k++; if (fmpz_poly_degree(f) == -1) goto cleanup; } if (fmpz_poly_is_zero(g) == 1) goto cleanup; if (fmpz_poly_degree(f) == 0) break; if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) { fmpz_poly_swap(f, g); fmpz_poly_swap(b, c); } fmpz_poly_add(f, g, f); fmpz_poly_mod_unsigned(f, 2); fmpz_poly_add(b, c, b); fmpz_poly_mod_unsigned(b, 2); } k = k % params->N; b_last = fmpz_poly_get_coeff_ptr(b, params->N); if (fmpz_cmp_si_n(b_last, 0)) goto cleanup; /* Fq(x) = x^(N-k) * b(x) */ for (int i = params->N - 1; i >= 0; i--) { fmpz *b_i; j = i - k; if (j < 0) j = j + params->N; b_i = fmpz_poly_get_coeff_ptr(b, i); fmpz_poly_set_coeff_fmpz_n(Fq, j, b_i); } poly_mod2_to_modq(Fq, a_tmp, params); /* check if the f * Fq = 1 (mod p) condition holds true */ fmpz_poly_set(a_tmp, a); poly_starmultiply(a_tmp, a_tmp, Fq, params, params->q); if (fmpz_poly_is_one(a_tmp)) retval = true; else fmpz_poly_zero(Fq); cleanup: fmpz_poly_clear(a_tmp); fmpz_poly_clear(b); fmpz_poly_clear(c); fmpz_poly_clear(f); fmpz_poly_clear(g); return retval; }
int main(void) { int i, result; FLINT_TEST_INIT(state); flint_printf("compose_series...."); fflush(stdout); /* Check aliasing of the first argument */ for (i = 0; i < 10 * flint_test_multiplier(); i++) { fmpz_poly_t f, g, h; slong n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_init(h); fmpz_poly_randtest(g, state, n_randint(state, 40), 80); fmpz_poly_randtest(h, state, n_randint(state, 20), 50); fmpz_poly_set_coeff_ui(h, 0, 0); n = n_randint(state, 20); fmpz_poly_compose_series(f, g, h, n); fmpz_poly_compose_series(g, g, h, n); result = (fmpz_poly_equal(f, g)); if (!result) { flint_printf("FAIL (aliasing 1):\n"); fmpz_poly_print(f), flint_printf("\n\n"); fmpz_poly_print(g), flint_printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_poly_clear(h); } /* Check aliasing of the second argument */ for (i = 0; i < 10 * flint_test_multiplier(); i++) { fmpz_poly_t f, g, h; slong n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_init(h); fmpz_poly_randtest(g, state, n_randint(state, 40), 80); fmpz_poly_randtest(h, state, n_randint(state, 20), 50); fmpz_poly_set_coeff_ui(h, 0, 0); n = n_randint(state, 20); fmpz_poly_compose_series(f, g, h, n); fmpz_poly_compose_series(h, g, h, n); result = (fmpz_poly_equal(f, h)); if (!result) { flint_printf("FAIL (aliasing 2):\n"); fmpz_poly_print(f), flint_printf("\n\n"); fmpz_poly_print(h), flint_printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_poly_clear(h); } /* Compare with compose */ for (i = 0; i < 10 * flint_test_multiplier(); i++) { fmpz_poly_t f, g, h, s, t; slong n; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_poly_init(h); fmpz_poly_init(s); fmpz_poly_init(t); fmpz_poly_randtest(g, state, n_randint(state, 40), 80); fmpz_poly_randtest(h, state, n_randint(state, 20), 50); fmpz_poly_set_coeff_ui(h, 0, 0); n = n_randint(state, 10); fmpz_poly_compose(s, g, h); fmpz_poly_truncate(s, n); fmpz_poly_compose_series(f, g, h, n); result = (fmpz_poly_equal(f, s)); if (!result) { flint_printf("FAIL (comparison):\n"); flint_printf("n = %wd\n", n); flint_printf("g = "), fmpz_poly_print(g), flint_printf("\n\n"); flint_printf("h = "), fmpz_poly_print(h), flint_printf("\n\n"); flint_printf("f = "), fmpz_poly_print(f), flint_printf("\n\n"); flint_printf("s = "), fmpz_poly_print(s), flint_printf("\n\n"); abort(); } fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_poly_clear(h); fmpz_poly_clear(s); fmpz_poly_clear(t); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
// Version Fq void fq_poly_compose_mod_kedlaya_umans(fq_poly_t fg, const fq_poly_t f, const fq_poly_t g, const fq_poly_t h, slong d, fq_ctx_t ctx) { slong n, i, j, m, dm, N, Nm, degree; fmpz* p; fmpz_t q; fq_multi_poly_t f_prime; fq_struct *vect_beta, *vect_alpha, *vect_alpha2, *vect_eval; fq_poly_t gi; // Vérification des paramètres n = FLINT_MAX(fq_poly_length(f,ctx),fq_poly_length(g,ctx)); i = fq_poly_length(h,ctx); if(n >= i) { printf("Erreur, f ou g n'a pas été modulé par h.\n"); exit(1); } // Les polynômes f et g étant réduits modulo h, n vaut le nombre de coefficients de h n = i; if(d < 2) { printf("d < 2\n"); exit(1); } if(d >= n) { printf("d >= n\n"); exit(1); } p = fq_ctx_prime(ctx); degree = fq_ctx_degree(ctx); m = n_clog(n,d); dm = n_pow(d,m); N = n_pow(d,m)*m*d; Nm = N*m; if(fmpz_cmp_ui(p,N) < 0) { flint_printf("\nErreur, pas assez de points d'interpolation !\n"); flint_printf("\np tient sur un mot machine, utilisez donc la version fq_nmod !\n"); exit(1); } // Étape 1 ////////////////////////////// fq_multi_poly_init(f_prime, dm, d, m, ctx); _fq_vec_zero(f_prime->poly, dm, ctx); for(i = 0 ; i < n ; i++) { fq_poly_get_coeff(&(f_prime->poly[i]),f,i,ctx); } // Étape 3 ////////////////////////////// vect_beta = _fq_vec_init(N,ctx); for(i = 0 ; i < N ; i++) { fmpz_poly_set_coeff_ui(vect_beta + i, 0, i); } vect_alpha = _fq_vec_init(N*m, ctx); fq_poly_init(gi,ctx); fq_poly_set(gi,g,ctx); fq_poly_evaluate_fq_vec(vect_alpha, gi, vect_beta, N, ctx); for(i = 1 ; i < m ; i++) { // Étape 2 ////////////////////////////// // Calcul du g^(d^i) avec g^(d^i) = [ (g^(d^(i-1))) ^ d ] mod h fq_poly_powmod_ui_binexp(gi,gi,d,h,ctx); fq_poly_evaluate_fq_vec(vect_alpha+i*N, gi, vect_beta, N, ctx); } fq_poly_clear(gi, ctx); // Transposition // Passe de m lignes N colonnes // à N lignes m colonnes ==> nécessaire pour EMM dans Fp vect_alpha2 = _fq_vec_init(Nm,ctx); for(i = 0 ; i < m ; i++) { for(j = 0 ; j < N ; j++) { fq_set(vect_alpha2 + j*m + i,vect_alpha + i*N + j,ctx); } } vect_alpha = vect_alpha2; // Étape 4 ////////////////////////////// // EMM vect_eval = _fq_vec_init(N,ctx); fq_multi_poly_multimodular(vect_eval, N, f_prime, vect_alpha, ctx); _fq_vec_clear(vect_alpha,Nm,ctx); fq_multi_poly_clear(f_prime,ctx); // Étape 5 ////////////////////////////// fq_poly_interpolate_fq_vec_fast(fg, vect_beta, vect_eval, N, ctx); _fq_vec_clear(vect_beta,N,ctx); _fq_vec_clear(vect_eval,N,ctx); // Étape 6 ////////////////////////////// fq_poly_rem(fg,fg,h,ctx); }