244 lines
7.2 KiB
C
244 lines
7.2 KiB
C
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/*=============================================================================
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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) 2012 Sebastian Pancratz
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******************************************************************************/
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#include <stdlib.h>
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#include "fmpz_vec.h"
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#include "fmpz_mod_poly.h"
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slong _fmpz_mod_poly_xgcd_euclidean(fmpz *G, fmpz *S, fmpz *T,
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const fmpz *A, slong lenA,
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const fmpz *B, slong lenB,
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const fmpz_t invB, const fmpz_t p)
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{
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_fmpz_vec_zero(G, lenB);
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_fmpz_vec_zero(S, lenB - 1);
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_fmpz_vec_zero(T, lenA - 1);
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if (lenB == 1)
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{
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fmpz_set(G + 0, B + 0);
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fmpz_one(T + 0);
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return 1;
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}
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else
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{
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fmpz *Q, *R;
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slong lenQ, lenR;
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Q = _fmpz_vec_init(2 * lenA);
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R = Q + lenA;
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_fmpz_mod_poly_divrem(Q, R, A, lenA, B, lenB, invB, p);
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lenR = lenB - 1;
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FMPZ_VEC_NORM(R, lenR);
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if (lenR == 0)
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{
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_fmpz_vec_set(G, B, lenB);
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fmpz_one(T + 0);
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_fmpz_vec_clear(Q, 2 * lenA);
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return lenB;
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}
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else
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{
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fmpz_t inv;
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fmpz *D, *U, *V1, *V3, *W;
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slong lenD, lenU, lenV1, lenV3, lenW;
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fmpz_init(inv);
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W = _fmpz_vec_init(FLINT_MAX(5 * lenB, lenA + lenB));
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D = W + lenB;
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U = D + lenB;
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V1 = U + lenB;
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V3 = V1 + lenB;
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lenU = 0;
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_fmpz_vec_set(D, B, lenB);
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lenD = lenB;
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fmpz_one(V1 + 0);
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lenV1 = 1;
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lenV3 = 0;
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FMPZ_VEC_SWAP(V3, lenV3, R, lenR);
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do {
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fmpz_invmod(inv, V3 + (lenV3 - 1), p);
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_fmpz_mod_poly_divrem(Q, R, D, lenD, V3, lenV3, inv, p);
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lenQ = lenD - lenV3 + 1;
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lenR = lenV3 - 1;
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FMPZ_VEC_NORM(R, lenR);
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if (lenV1 >= lenQ)
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_fmpz_mod_poly_mul(W, V1, lenV1, Q, lenQ, p);
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else
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_fmpz_mod_poly_mul(W, Q, lenQ, V1, lenV1, p);
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lenW = lenQ + lenV1 - 1;
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_fmpz_mod_poly_sub(U, U, lenU, W, lenW, p);
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lenU = FLINT_MAX(lenU, lenW);
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FMPZ_VEC_NORM(U, lenU);
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FMPZ_VEC_SWAP(U, lenU, V1, lenV1);
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{
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fmpz *__t;
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slong __tn;
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__t = D;
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D = V3;
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V3 = R;
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R = __t;
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__tn = lenD;
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lenD = lenV3;
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lenV3 = lenR;
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lenR = __tn;
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}
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} while (lenV3 != 0);
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_fmpz_vec_set(G, D, lenD);
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_fmpz_vec_set(S, U, lenU);
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{
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lenQ = lenA + lenU - 1;
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_fmpz_mod_poly_mul(Q, A, lenA, S, lenU, p);
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_fmpz_mod_poly_neg(Q, Q, lenQ, p);
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_fmpz_mod_poly_add(Q, G, lenD, Q, lenQ, p);
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_fmpz_mod_poly_divrem(T, W, Q, lenQ, B, lenB, invB, p);
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}
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_fmpz_vec_clear(W, FLINT_MAX(5 * lenB, lenA + lenB));
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_fmpz_vec_clear(Q, 2 * lenA);
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fmpz_clear(inv);
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return lenD;
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}
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}
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}
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void
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fmpz_mod_poly_xgcd_euclidean(fmpz_mod_poly_t G,
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fmpz_mod_poly_t S, fmpz_mod_poly_t T,
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const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
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{
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if (A->length < B->length)
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{
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fmpz_mod_poly_xgcd_euclidean(G, T, S, B, A);
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}
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else /* lenA >= lenB >= 0 */
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{
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const slong lenA = A->length, lenB = B->length;
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fmpz_t inv;
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fmpz_init(inv);
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if (lenA == 0) /* lenA = lenB = 0 */
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{
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fmpz_mod_poly_zero(G);
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fmpz_mod_poly_zero(S);
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fmpz_mod_poly_zero(T);
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}
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else if (lenB == 0) /* lenA > lenB = 0 */
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{
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fmpz_invmod(inv, fmpz_mod_poly_lead(A), &A->p);
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fmpz_mod_poly_scalar_mul_fmpz(G, A, inv);
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fmpz_mod_poly_zero(T);
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fmpz_mod_poly_set_fmpz(S, inv);
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}
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else /* lenA >= lenB >= 2 */
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{
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fmpz *g, *s, *t;
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slong lenG;
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if (G == A || G == B)
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{
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g = _fmpz_vec_init(FLINT_MIN(lenA, lenB));
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}
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else
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{
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fmpz_mod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
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g = G->coeffs;
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}
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if (S == A || S == B)
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{
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s = _fmpz_vec_init(lenB);
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}
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else
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{
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fmpz_mod_poly_fit_length(S, lenB);
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s = S->coeffs;
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}
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if (T == A || T == B)
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{
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t = _fmpz_vec_init(lenA);
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}
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else
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{
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fmpz_mod_poly_fit_length(T, lenA);
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t = T->coeffs;
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}
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fmpz_invmod(inv, fmpz_mod_poly_lead(B), &B->p);
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lenG = _fmpz_mod_poly_xgcd_euclidean(g, s, t,
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A->coeffs, lenA, B->coeffs, lenB, inv, &B->p);
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if (G == A || G == B)
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{
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_fmpz_vec_clear(G->coeffs, G->alloc);
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G->coeffs = g;
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G->alloc = FLINT_MIN(lenA, lenB);
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}
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if (S == A || S == B)
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{
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_fmpz_vec_clear(S->coeffs, S->alloc);
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S->coeffs = s;
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S->alloc = lenB;
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}
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if (T == A || T == B)
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{
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_fmpz_vec_clear(T->coeffs, T->alloc);
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T->coeffs = t;
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T->alloc = lenA;
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}
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_fmpz_mod_poly_set_length(G, lenG);
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_fmpz_mod_poly_set_length(S, FLINT_MAX(lenB - lenG, 1));
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_fmpz_mod_poly_set_length(T, FLINT_MAX(lenA - lenG, 1));
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_fmpz_mod_poly_normalise(S);
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_fmpz_mod_poly_normalise(T);
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if (!fmpz_is_one(fmpz_mod_poly_lead(G)))
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{
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fmpz_invmod(inv, fmpz_mod_poly_lead(G), &A->p);
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fmpz_mod_poly_scalar_mul_fmpz(G, G, inv);
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fmpz_mod_poly_scalar_mul_fmpz(S, S, inv);
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fmpz_mod_poly_scalar_mul_fmpz(T, T, inv);
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}
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}
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fmpz_clear(inv);
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}
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}
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