/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Lina Kulakova Copyright (C) 2013 Martin Lee Copyright (C) 2013 Mike Hansen ******************************************************************************/ #ifdef T #include "templates.h" #include void TEMPLATE(T, poly_factor_distinct_deg) (TEMPLATE(T, poly_factor_t) res, const TEMPLATE(T, poly_t) poly, slong * const *degs, const TEMPLATE(T, ctx_t) ctx) { TEMPLATE(T, poly_t) f, g, s, reducedH0, v, vinv, tmp; TEMPLATE(T, poly_t) * h, *H, *I; fmpz_t q; slong i, j, l, m, n, index, d; double beta; TEMPLATE(T, mat_t) HH, HHH; TEMPLATE(T, poly_init) (v, ctx); TEMPLATE(T, poly_make_monic) (v, poly, ctx); n = TEMPLATE(T, poly_degree) (poly, ctx); if (n == 1) { TEMPLATE(T, poly_factor_insert) (res, poly, 1, ctx); (*degs)[0] = 1; TEMPLATE(T, poly_clear) (v, ctx); return; } beta = 0.5 * (1. - (log(2) / log(n))); l = ceil(pow(n, beta)); m = ceil(0.5 * n / l); fmpz_init(q); TEMPLATE(T, ctx_order) (q, ctx); TEMPLATE(T, poly_init) (f, ctx); TEMPLATE(T, poly_init) (g, ctx); TEMPLATE(T, poly_init) (s, ctx); TEMPLATE(T, poly_init) (reducedH0, ctx); TEMPLATE(T, poly_init) (vinv, ctx); TEMPLATE(T, poly_init) (tmp, ctx); if (! (h = flint_malloc((2 * m + l + 1) * sizeof(TEMPLATE(T, poly_struct))))) { TEMPLATE_PRINTF("Exception (%s_poly_factor_distinct_deg):\n", T); flint_printf("Not enough memory.\n"); abort(); } H = h + (l + 1); I = H + m; for (i = 0; i < l + 1; i++) TEMPLATE(T, poly_init) (h[i], ctx); for (i = 0; i < m; i++) { TEMPLATE(T, poly_init) (H[i], ctx); TEMPLATE(T, poly_init) (I[i], ctx); } TEMPLATE(T, poly_make_monic) (v, poly, ctx); TEMPLATE(T, poly_reverse) (vinv, v, v->length, ctx); TEMPLATE(T, poly_inv_series_newton) (vinv, vinv, v->length, ctx); /* compute baby steps: h[i]=x^{q^i}mod v */ /* h[0] = x */ TEMPLATE(T, poly_iterated_frobenius_preinv) (h, l + 1, v, vinv, ctx); /* compute coarse distinct-degree factorisation */ index = 0; TEMPLATE(T, poly_set) (s, v, ctx); TEMPLATE(T, poly_set) (H[0], h[l], ctx); TEMPLATE(T, poly_set) (reducedH0, H[0], ctx); TEMPLATE(T, mat_init) (HH, n_sqrt(v->length - 1) + 1, v->length - 1, ctx); TEMPLATE(T, poly_precompute_matrix) (HH, reducedH0, s, vinv, ctx); d = 1; for (j = 0; j < m; j++) { /* compute giant steps: H[j]=x^{q^(lj)}mod s */ if (j > 0) { if (I[j - 1]->length > 1) { _TEMPLATE(T, poly_reduce_matrix_mod_poly) (HHH, HH, s, ctx); TEMPLATE(T, mat_clear) (HH, ctx); TEMPLATE(T, mat_init_set) (HH, HHH, ctx); TEMPLATE(T, mat_clear) (HHH, ctx); TEMPLATE(T, poly_rem) (reducedH0, reducedH0, s, ctx); TEMPLATE(T, poly_rem) (tmp, H[j - 1], s, ctx); TEMPLATE(T, poly_compose_mod_brent_kung_precomp_preinv) (H[j], tmp, HH, s, vinv, ctx); } else { TEMPLATE(T, poly_compose_mod_brent_kung_precomp_preinv) (H[j], H[j - 1], HH, s, vinv, ctx); } } /* compute interval polynomials */ TEMPLATE(T, poly_one) (I[j], ctx); for (i = l - 1; (i >= 0) && (2 * d <= s->length - 1); i--, d++) { TEMPLATE(T, poly_rem) (tmp, h[i], s, ctx); TEMPLATE(T, poly_sub) (tmp, H[j], tmp, ctx); TEMPLATE(T, poly_mulmod_preinv) (I[j], tmp, I[j], s, vinv, ctx); } /* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */ /* F_j is stored on the place of I_j */ TEMPLATE(T, poly_gcd) (I[j], s, I[j], ctx); if (I[j]->length > 1) { TEMPLATE(T, poly_remove) (s, I[j], ctx); TEMPLATE(T, poly_reverse) (vinv, s, s->length, ctx); TEMPLATE(T, poly_inv_series_newton) (vinv, vinv, s->length, ctx); } if (s->length - 1 < 2 * d) { break; } } if (s->length > 1) { TEMPLATE(T, poly_factor_insert) (res, s, 1, ctx); (*degs)[index++] = s->length - 1; } /* compute fine distinct-degree factorisation */ for (j = 0; j < m; j++) { if (I[j]->length - 1 > (j + 1) * l || j == 0) { TEMPLATE(T, poly_set) (g, I[j], ctx); for (i = l - 1; i >= 0 && (g->length > 1); i--) { /* compute f^{[l*(j+1)-i]} */ TEMPLATE(T, poly_sub) (tmp, H[j], h[i], ctx); TEMPLATE(T, poly_gcd) (f, g, tmp, ctx); if (f->length > 1) { /* insert f^{[l*(j+1)-i]} into res */ TEMPLATE(T, poly_make_monic) (f, f, ctx); TEMPLATE(T, poly_factor_insert) (res, f, 1, ctx); (*degs)[index++] = l * (j + 1) - i; TEMPLATE(T, poly_remove) (g, f, ctx); } } } else if (I[j]->length > 1) { TEMPLATE(T, poly_make_monic) (I[j], I[j], ctx); TEMPLATE(T, poly_factor_insert) (res, I[j], 1, ctx); (*degs)[index++] = I[j]->length - 1; } } /* cleanup */ fmpz_clear(q); TEMPLATE(T, poly_clear) (f, ctx); TEMPLATE(T, poly_clear) (g, ctx); TEMPLATE(T, poly_clear) (s, ctx); TEMPLATE(T, poly_clear) (reducedH0, ctx); TEMPLATE(T, poly_clear) (v, ctx); TEMPLATE(T, poly_clear) (vinv, ctx); TEMPLATE(T, poly_clear) (tmp, ctx); TEMPLATE(T, mat_clear) (HH, ctx); for (i = 0; i < l + 1; i++) TEMPLATE(T, poly_clear) (h[i], ctx); for (i = 0; i < m; i++) { TEMPLATE(T, poly_clear) (H[i], ctx); TEMPLATE(T, poly_clear) (I[i], ctx); } flint_free(h); } #endif