241 lines
7.2 KiB
C
241 lines
7.2 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 William Hart
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Copyright (C) 2011 Sebastian Pancratz
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "fmpz_poly.h"
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#include "mpn_extras.h"
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void _fmpz_poly_xgcd_modular(fmpz_t r, fmpz * s, fmpz * t,
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const fmpz * poly1, slong len1,
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const fmpz * poly2, slong len2)
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{
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mp_ptr G, S, T, A, B, T1, T2;
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fmpz_t prod;
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int stabilised = 0, first;
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mp_limb_t p;
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mp_bitcnt_t s_bits = 0, t_bits = 0;
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/* Compute resultant of input polys */
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_fmpz_poly_resultant(r, poly1, len1, poly2, len2);
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if (fmpz_is_zero(r))
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return;
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fmpz_init(prod);
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fmpz_one(prod);
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_fmpz_vec_zero(s, len2);
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_fmpz_vec_zero(t, len1);
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p = (UWORD(1) << (FLINT_BITS - 1));
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G = _nmod_vec_init(4 * len1 + 5 * len2 - 2);
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S = G + len2;
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T = S + len2;
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A = T + len1;
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B = A + len1;
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T1 = B + len2;
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T2 = T1 + (len1 + len2 - 1);
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_nmod_vec_zero(S, len2 + len1); /* S = T = 0 */
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first = 1;
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for (;;)
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{
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mp_limb_t R;
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nmod_t mod;
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/* Get next prime */
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p = n_nextprime(p, 0);
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/* Resultant mod p */
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R = fmpz_fdiv_ui(r, p);
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/* If p divides resultant or either leading coeff, discard p */
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if ((fmpz_fdiv_ui(poly1 + len1 - 1, p) == WORD(0)) ||
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(fmpz_fdiv_ui(poly2 + len2 - 1, p) == WORD(0)) || (R == 0))
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continue;
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nmod_init(&mod, p);
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/* Reduce polynomials modulo p */
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_fmpz_vec_get_nmod_vec(A, poly1, len1, mod);
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_fmpz_vec_get_nmod_vec(B, poly2, len2, mod);
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if (stabilised) /* CRT has stabilised, probably don't need more xgcds */
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{
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slong tlen;
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/* Multiply out A*S + B*T to see if it is R mod p */
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_fmpz_vec_get_nmod_vec(S, s, len2, mod);
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_fmpz_vec_get_nmod_vec(T, t, len1, mod);
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_nmod_poly_mul(T1, A, len1, S, len2, mod);
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_nmod_poly_mul(T2, T, len1, B, len2, mod);
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_nmod_vec_add(T1, T1, T2, len1 + len2 - 1, mod);
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tlen = len1 + len2 - 1;
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FMPZ_VEC_NORM(T1, tlen);
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if (tlen == 1 && T1[0] == R) /* It is, so this prime is good */
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fmpz_mul_ui(prod, prod, p);
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else
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stabilised = 0; /* It's not, keep going with xgcds */
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}
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if (!stabilised) /* Need to keep computing xgcds mod p */
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{
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mp_limb_t RGinv;
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/* Compute xgcd mod p */
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_nmod_poly_xgcd(G, S, T, A, len1, B, len2, mod);
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RGinv = n_invmod(G[0], mod.n);
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RGinv = n_mulmod2_preinv(RGinv, R, mod.n, mod.ninv);
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/* Scale appropriately */
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_nmod_vec_scalar_mul_nmod(S, S, len2, RGinv, mod);
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_nmod_vec_scalar_mul_nmod(T, T, len1, RGinv, mod);
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if (first) /* First time around set s and t to S and T */
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{
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_fmpz_vec_set_nmod_vec(s, S, len2, mod);
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_fmpz_vec_set_nmod_vec(t, T, len1, mod);
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fmpz_set_ui(prod, p);
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stabilised = 1; /* Optimise the case where one prime is enough */
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first = 0;
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}
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else /* Otherwise do CRT */
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{
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mp_bitcnt_t new_s_bits, new_t_bits;
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_fmpz_poly_CRT_ui(s, s, len2, prod, S, len2, mod.n, mod.ninv, 1);
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_fmpz_poly_CRT_ui(t, t, len1, prod, T, len1, mod.n, mod.ninv, 1);
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fmpz_mul_ui(prod, prod, p);
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/* Check to see if CRT has stabilised */
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new_s_bits = FLINT_ABS(_fmpz_vec_max_bits(s, len2));
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new_t_bits = FLINT_ABS(_fmpz_vec_max_bits(t, len1));
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stabilised = (s_bits == new_s_bits && t_bits == new_t_bits);
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s_bits = new_s_bits;
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t_bits = new_t_bits;
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}
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}
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if (stabilised)
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{
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slong bound1, bound2, bound;
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bound1 = FLINT_BIT_COUNT(len2)
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+ FLINT_ABS(_fmpz_vec_max_bits(poly1, len1))
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+ FLINT_ABS(_fmpz_vec_max_bits(s, len2));
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bound2 = FLINT_BIT_COUNT(len2)
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+ FLINT_ABS(_fmpz_vec_max_bits(poly2, len2))
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+ FLINT_ABS(_fmpz_vec_max_bits(t, len1));
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bound = 4 + FLINT_MAX(fmpz_bits(r), FLINT_MAX(bound1, bound2));
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if (fmpz_bits(prod) > bound)
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break;
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}
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}
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_nmod_vec_clear(G);
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fmpz_clear(prod);
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}
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void
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fmpz_poly_xgcd_modular(fmpz_t r, fmpz_poly_t s, fmpz_poly_t t,
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const fmpz_poly_t poly1, const fmpz_poly_t poly2)
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{
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if (poly1->length < poly2->length)
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{
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fmpz_poly_xgcd_modular(r, t, s, poly2, poly1);
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} else /* len1 >= len2 >= 0 */
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{
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const slong len1 = poly1->length;
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const slong len2 = poly2->length;
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fmpz *S, *T;
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fmpz_poly_t temp1, temp2;
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if (len1 == 0 || len2 == 0)
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{
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fmpz_zero(r);
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}
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else /* len1 >= len2 >= 1 */
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{
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if (s == poly1 || s == poly2)
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{
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fmpz_poly_init2(temp1, len2);
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S = temp1->coeffs;
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}
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else
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{
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fmpz_poly_fit_length(s, len2);
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S = s->coeffs;
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}
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if (t == poly1 || t == poly2)
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{
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fmpz_poly_init2(temp2, len1);
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T = temp2->coeffs;
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}
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else
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{
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fmpz_poly_fit_length(t, len1);
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T = t->coeffs;
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}
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_fmpz_poly_xgcd_modular(r, S, T, poly1->coeffs, len1,
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poly2->coeffs, len2);
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if (s == poly1 || s == poly2)
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{
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fmpz_poly_swap(s, temp1);
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fmpz_poly_clear(temp1);
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}
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if (t == poly1 || t == poly2)
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{
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fmpz_poly_swap(t, temp2);
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fmpz_poly_clear(temp2);
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}
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_fmpz_poly_set_length(s, len2);
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_fmpz_poly_normalise(s);
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_fmpz_poly_set_length(t, len1);
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_fmpz_poly_normalise(t);
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}
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}
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}
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