void fmpz_poly_factor_realloc(fmpz_poly_factor_t fac, long alloc) { if (alloc == 0) /* Clear up, reinitialise */ { fmpz_poly_factor_clear(fac); fmpz_poly_factor_init(fac); } else if (fac->alloc) /* Realloc */ { if (fac->alloc > alloc) { long i; for (i = alloc; i < fac->num; i++) fmpz_poly_clear(fac->p + i); fac->p = flint_realloc(fac->p, alloc * sizeof(fmpz_poly_struct)); fac->exp = flint_realloc(fac->exp, alloc * sizeof(long)); fac->alloc = alloc; } else if (fac->alloc < alloc) { long i; fac->p = flint_realloc(fac->p, alloc * sizeof(fmpz_poly_struct)); fac->exp = flint_realloc(fac->exp, alloc * sizeof(long)); for (i = fac->alloc; i < alloc; i++) { fmpz_poly_init(fac->p + i); fac->exp[i] = 0L; } fac->alloc = alloc; } } else /* Nothing allocated already so do it now */ { long i; fac->p = flint_malloc(alloc * sizeof(fmpz_poly_struct)); fac->exp = flint_calloc(alloc, sizeof(long)); for (i = 0; i < alloc; i++) fmpz_poly_init(fac->p + i); fac->num = 0; fac->alloc = alloc; } }
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; }
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; }