void nmod_poly_factor_cantor_zassenhaus(nmod_poly_factor_t res, const nmod_poly_t f) { nmod_poly_t h, v, g, x; slong i, j, num; nmod_poly_init_preinv(h, f->mod.n, f->mod.ninv); nmod_poly_init_preinv(g, f->mod.n, f->mod.ninv); nmod_poly_init_preinv(v, f->mod.n, f->mod.ninv); nmod_poly_init_preinv(x, f->mod.n, f->mod.ninv); nmod_poly_set_coeff_ui(h, 1, 1); nmod_poly_set_coeff_ui(x, 1, 1); nmod_poly_make_monic(v, f); i = 0; do { i++; nmod_poly_powmod_ui_binexp(h, h, f->mod.n, v); nmod_poly_sub(h, h, x); nmod_poly_gcd(g, h, v); nmod_poly_add(h, h, x); if (g->length != 1) { nmod_poly_make_monic(g, g); num = res->num; nmod_poly_factor_equal_deg(res, g, i); for (j = num; j < res->num; j++) res->exp[j] = nmod_poly_remove(v, res->p + j); } } while (v->length >= 2*i + 3); if (v->length > 1) nmod_poly_factor_insert(res, v, 1); nmod_poly_clear(g); nmod_poly_clear(h); nmod_poly_clear(v); nmod_poly_clear(x); }
void nmod_poly_compose_mod_horner(nmod_poly_t res, const nmod_poly_t poly1, const nmod_poly_t poly2, const nmod_poly_t poly3) { long len1 = poly1->length; long len2 = poly2->length; long len3 = poly3->length; long len = len3 - 1; mp_ptr ptr2; if (len3 == 0) { printf("exception: division by zero in nmod_poly_compose_mod_horner\n"); abort(); } if (len1 == 0 || len3 == 1) { nmod_poly_zero(res); return; } if (len1 == 1) { nmod_poly_set(res, poly1); return; } if (res == poly3 || res == poly1) { nmod_poly_t tmp; nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv); nmod_poly_compose_mod_horner(tmp, poly1, poly2, poly3); nmod_poly_swap(tmp, res); nmod_poly_clear(tmp); return; } ptr2 = _nmod_vec_init(len); if (len2 <= len) { mpn_copyi(ptr2, poly2->coeffs, len2); mpn_zero(ptr2 + len2, len - len2); } else { _nmod_poly_rem(ptr2, poly2->coeffs, len2, poly3->coeffs, len3, res->mod); } nmod_poly_fit_length(res, len); _nmod_poly_compose_mod_horner(res->coeffs, poly1->coeffs, len1, ptr2, poly3->coeffs, len3, res->mod); res->length = len; _nmod_poly_normalise(res); _nmod_vec_clear(ptr2); }
void nmod_poly_compose_mod_brent_kung(nmod_poly_t res, const nmod_poly_t poly1, const nmod_poly_t poly2, const nmod_poly_t poly3) { long len1 = poly1->length; long len2 = poly2->length; long len3 = poly3->length; long len = len3 - 1; mp_ptr ptr2; if (len3 == 0) { printf("exception: division by zero in " "nmod_poly_compose_mod_brent_kung\n"); abort(); } if (len1 >= len3) { printf("exception: nmod_poly_compose_brent_kung: the degree of the" " first polynomial must be smaller than that of the modulus\n"); abort(); } if (len1 == 0 || len3 == 1) { nmod_poly_zero(res); return; } if (len1 == 1) { nmod_poly_set(res, poly1); return; } if (res == poly3 || res == poly1) { nmod_poly_t tmp; nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv); nmod_poly_compose_mod_brent_kung(tmp, poly1, poly2, poly3); nmod_poly_swap(tmp, res); nmod_poly_clear(tmp); return; } ptr2 = _nmod_vec_init(len); if (len2 <= len) { mpn_copyi(ptr2, poly2->coeffs, len2); mpn_zero(ptr2 + len2, len - len2); } else { _nmod_poly_rem(ptr2, poly2->coeffs, len2, poly3->coeffs, len3, res->mod); } nmod_poly_fit_length(res, len); _nmod_poly_compose_mod_brent_kung(res->coeffs, poly1->coeffs, len1, ptr2, poly3->coeffs, len3, res->mod); res->length = len; _nmod_poly_normalise(res); _nmod_vec_clear(ptr2); }