static void fmpz_poly_mat_scalar_divexact_fmpz(fmpz_poly_mat_t B, const fmpz_poly_mat_t A, const fmpz_t f) { long i, j; for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) fmpz_poly_scalar_divexact_fmpz(fmpz_poly_mat_entry(B, i, j), fmpz_poly_mat_entry(A, i, j), f); }
void fmpz_poly_mat_add(fmpz_poly_mat_t C, const fmpz_poly_mat_t A, const fmpz_poly_mat_t B) { long i, j; for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) fmpz_poly_add(fmpz_poly_mat_entry(C, i, j), fmpz_poly_mat_entry(A, i, j), fmpz_poly_mat_entry(B, i, j)); }
/* Applies the operator $\sigma^e$ to all elements in the matrix \code{op}, setting the corresponding elements in \code{rop} to the results. */ static void fmpz_poly_mat_frobenius(fmpz_poly_mat_t B, const fmpz_poly_mat_t A, long e, const fmpz_t p, long N, const qadic_ctx_t ctx) { const long d = qadic_ctx_degree(ctx); e = e % d; if (e < 0) e += d; if (e == 0) { fmpz_t pN; fmpz_init(pN); fmpz_pow_ui(pN, p, N); fmpz_poly_mat_scalar_mod_fmpz(B, A, pN); fmpz_clear(pN); } else { long i, j; fmpz *t = _fmpz_vec_init(2 * d - 1); for (i = 0; i < B->r; i++) for (j = 0; j < B->c; j++) { const fmpz_poly_struct *a = fmpz_poly_mat_entry(A, i, j); fmpz_poly_struct *b = fmpz_poly_mat_entry(B, i, j); if (a->length == 0) { fmpz_poly_zero(b); } else { _qadic_frobenius(t, a->coeffs, a->length, e, ctx->a, ctx->j, ctx->len, p, N); fmpz_poly_fit_length(b, d); _fmpz_vec_set(b->coeffs, t, d); _fmpz_poly_set_length(b, d); _fmpz_poly_normalise(b); } } _fmpz_vec_clear(t, 2 * d - 1); } }
void fmpz_poly_mat_trace(fmpz_poly_t trace, const fmpz_poly_mat_t mat) { long i, n = fmpz_poly_mat_nrows(mat); if (n == 0) fmpz_poly_zero(trace); else { fmpz_poly_set(trace, fmpz_poly_mat_entry(mat, 0, 0)); for (i = 1; i < n; i++) fmpz_poly_add(trace, trace, fmpz_poly_mat_entry(mat, i, i)); } }
static void fmpz_poly_mat_compose_pow(fmpz_poly_mat_t B, const fmpz_poly_mat_t A, long k) { long i, j; if (!(A->r == B->r && A->c == B->c)) { printf("Exception (fmpz_poly_mat_compose_pow). Incompatible dimensions.\n"); abort(); } for (i = 0; i < B->r; i++) for (j = 0; j < B->c; j++) fmpz_poly_compose_pow(fmpz_poly_mat_entry(B, i, j), fmpz_poly_mat_entry(A, i, j), k); }
static void fmpz_poly_mat_get_fmpz_mat(fmpz_mat_t B, const fmpz_poly_mat_t A) { long i, j; if (!(A->r == B->r && A->c == B->c)) { printf("ERROR (fmpz_poly_mat_get_fmpz_mat). Incompatible dimensions.\n"); abort(); } for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) { const fmpz_poly_struct *poly = fmpz_poly_mat_entry(A, i, j); const long len = poly->length; if (len == 0) { fmpz_zero(fmpz_mat_entry(B, i, j)); } else if (len == 1) { fmpz_set(fmpz_mat_entry(B, i, j), poly->coeffs + 0); } else { printf("ERROR (fmpz_poly_mat_get_fmpz_mat).\n"); printf("A contains a polynomial of length greater than 1.\n"); abort(); } } }
void gmde_convert_soln(fmpz_poly_mat_t A, long *vA, const padic_mat_struct *C, long N, const fmpz_t p) { long i, j, k; fmpz_t s, t; assert(N > 0); assert(A->r == padic_mat(C)->r && A->c == padic_mat(C)->c); fmpz_init(s); fmpz_init(t); /* Find valuation */ *vA = LONG_MAX; for (k = 0; k < N; k++) *vA = FLINT_MIN(*vA, padic_mat_val(C + k)); fmpz_poly_mat_zero(A); for (k = N - 1; k >= 0; k--) { if (padic_mat_val(C + k) == *vA) { for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) if (!fmpz_is_zero(padic_mat_entry(C + k, i, j))) fmpz_poly_set_coeff_fmpz(fmpz_poly_mat_entry(A, i, j), k, padic_mat_entry(C + k, i, j)); } else { fmpz_pow_ui(s, p, padic_mat_val(C + k) - *vA); for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) if (!fmpz_is_zero(padic_mat_entry(C + k, i, j))) { fmpz_mul(t, s, padic_mat_entry(C + k, i, j)); fmpz_poly_set_coeff_fmpz(fmpz_poly_mat_entry(A, i, j), k, t); } } } fmpz_clear(s); fmpz_clear(t); }
void fmpz_poly_mat_pow(fmpz_poly_mat_t B, const fmpz_poly_mat_t A, ulong exp) { long d = fmpz_poly_mat_nrows(A); if (exp == 0 || d == 0) { fmpz_poly_mat_one(B); } else if (exp == 1) { fmpz_poly_mat_set(B, A); } else if (exp == 2) { fmpz_poly_mat_sqr(B, A); } else if (d == 1) { fmpz_poly_pow(fmpz_poly_mat_entry(B, 0, 0), fmpz_poly_mat_entry(A, 0, 0), exp); } else { fmpz_poly_mat_t T, U; long i; fmpz_poly_mat_init_set(T, A); fmpz_poly_mat_init(U, d, d); for (i = ((long) FLINT_BIT_COUNT(exp)) - 2; i >= 0; i--) { fmpz_poly_mat_sqr(U, T); if (exp & (1L << i)) fmpz_poly_mat_mul(T, U, A); else fmpz_poly_mat_swap(T, U); } fmpz_poly_mat_swap(B, T); fmpz_poly_mat_clear(T); fmpz_poly_mat_clear(U); } }
void fmpz_poly_mat_randtest(fmpz_poly_mat_t A, flint_rand_t state, slong len, mp_bitcnt_t bits) { slong i, j; for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) fmpz_poly_randtest(fmpz_poly_mat_entry(A, i, j), state, len, bits); }
void fmpz_poly_mat_truncate(fmpz_poly_mat_t A, long len) { long i, j; for (i = 0; i < fmpz_poly_mat_nrows(A); i++) for (j = 0; j < fmpz_poly_mat_ncols(A); j++) fmpz_poly_truncate(fmpz_poly_mat_entry(A, i, j), len); }
void fmpz_poly_mat_evaluate_fmpz(fmpz_mat_t B, const fmpz_poly_mat_t A, const fmpz_t x) { long i, j; for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) fmpz_poly_evaluate_fmpz(fmpz_mat_entry(B, i, j), fmpz_poly_mat_entry(A, i, j), x); }
long fmpz_poly_mat_find_pivot_any(const fmpz_poly_mat_t mat, long start_row, long end_row, long c) { long r; for (r = start_row; r < end_row; r++) { if (!fmpz_poly_is_zero(fmpz_poly_mat_entry(mat, r, c))) return r; } return -1; }
void fmpz_poly_mat_mullow(fmpz_poly_mat_t C, const fmpz_poly_mat_t A, const fmpz_poly_mat_t B, long len) { long ar, bc, br; long i, j, k; fmpz_poly_t t; ar = A->r; br = B->r; bc = B->c; if (br == 0 || len < 1) { fmpz_poly_mat_zero(C); return; } if (C == A || C == B) { fmpz_poly_mat_t T; fmpz_poly_mat_init(T, ar, bc); fmpz_poly_mat_mullow(T, A, B, len); fmpz_poly_mat_swap(C, T); fmpz_poly_mat_clear(T); return; } fmpz_poly_init(t); for (i = 0; i < ar; i++) { for (j = 0; j < bc; j++) { fmpz_poly_mullow(fmpz_poly_mat_entry(C, i, j), fmpz_poly_mat_entry(A, i, 0), fmpz_poly_mat_entry(B, 0, j), len); for (k = 1; k < br; k++) { fmpz_poly_mullow(t, fmpz_poly_mat_entry(A, i, k), fmpz_poly_mat_entry(B, k, j), len); fmpz_poly_add(fmpz_poly_mat_entry(C, i, j), fmpz_poly_mat_entry(C, i, j), t); } } } fmpz_poly_clear(t); }
void fmpz_poly_mat_randtest_sparse(fmpz_poly_mat_t A, flint_rand_t state, long len, mp_bitcnt_t bits, float density) { long i, j; for (i = 0; i < A->r; i++) { for (j = 0; j < A->c; j++) { if (n_randint(state, 1000) < density * 1000) { long l = n_randint(state, len + 1); l = FLINT_MAX(l, 1); fmpz_poly_randtest_not_zero(fmpz_poly_mat_entry(A, i, j), state, l, bits); } else { fmpz_poly_zero(fmpz_poly_mat_entry(A, i, j)); } } } }
static void _qadic_mat_mul(fmpz_poly_mat_t C, const fmpz_poly_mat_t A, const fmpz_poly_mat_t B, const fmpz_t pN, const qadic_ctx_t ctx) { long i, j; fmpz_poly_mat_mul(C, A, B); for (i = 0; i < C->r; i++) for (j = 0; j < C->c; j++) { fmpz_poly_struct *poly = fmpz_poly_mat_entry(C, i, j); _fmpz_mod_poly_reduce(poly->coeffs, poly->length, ctx->a, ctx->j, ctx->len, pN); } }
void fmpz_poly_mat_print(const fmpz_poly_mat_t A, const char * x) { slong i, j; flint_printf("<%wd x %wd matrix over Z[%s]>\n", A->r, A->c, x); for (i = 0; i < A->r; i++) { flint_printf("["); for (j = 0; j < A->c; j++) { fmpz_poly_print_pretty(fmpz_poly_mat_entry(A, i, j), x); if (j + 1 < A->c) flint_printf(", "); } flint_printf("]\n"); } flint_printf("\n"); }
static long fmpz_poly_mat_ord_p(const fmpz_poly_mat_t A, const fmpz_t p) { long i, j, v, w = LONG_MAX; for (i = 0; i < A->r; i++) for (j = 0; j < A->c; j++) { const fmpz_poly_struct *poly = fmpz_poly_mat_entry(A, i, j); if (!fmpz_poly_is_zero(poly)) { v = _fmpz_vec_ord_p(poly->coeffs, poly->length, p); w = FLINT_MIN(v, w); if (w == 0) return 0; } } return w; }
int main(int argc, char *args[])/* setup.txt, ct.txt{ct->lev, ct->row, ct->col, ct}, sk.txt{row, col, poly}*/ { FILE *fp; if((fp = fopen(args[1], "r")) == NULL) { printf("file read error\n"); exit(0); } fmpz_t tmp; fmpz_init(tmp); fgets(str, 100, fp); fmpz_set_str(tmp, str, 10); long lev, d, i, j; lev = fmpz_get_si(tmp); fgets(str, 100, fp); fmpz_set_str(tmp, str, 10); d = fmpz_get_si(tmp); fmpz_poly_t fx; fmpz_poly_init(fx); fmpz_poly_set_coeff_si(fx, 0, 1); fmpz_poly_set_coeff_si(fx, d, 1); param_node_t *ph, *pr, *ps, *param; ph = param_node_init(ph); ps = ph; for( i = 0 ; i <= lev; i++ ) { pr = param_node_init(pr); fgets(str, 100, fp); fmpz_set_str(pr->q, str, 10); fgets(str, 100, fp); fmpz_set_str(tmp, str, 10); pr->n = fmpz_get_si(tmp); fgets(str, 100, fp); fmpz_set_str(tmp, str, 10); pr->bign = fmpz_get_si(tmp); ps->next = pr; ps = pr; } ps->next = NULL; fclose(fp); param = ph->next; long row, col, ctlev; if((fp = fopen(args[2], "r")) == NULL) { printf("file read error\n"); exit(0); } fgets(str, 30, fp); fmpz_set_str(tmp, str,10); ctlev = fmpz_get_si(tmp); fgets(str, 30, fp); fmpz_set_str(tmp, str,10); row = fmpz_get_si(tmp); fgets(str, 30, fp); fmpz_set_str(tmp, str,10); col = fmpz_get_si(tmp); fmpz_poly_mat_t ct; fmpz_poly_mat_init(ct, row, col); for( i = 0 ; i < row ; i++) { for(j = 0; j < col ; j++) { fgets(str, 100000, fp); fmpz_poly_set_str(fmpz_poly_mat_entry(ct, i, j), str); } } fclose(fp); if((fp = fopen(args[3], "r")) == NULL) { printf("file read error\n"); exit(0); } long l; sk_node_t *sh, *ss, *sr; sh = (sk_node_t *)malloc(sizeof(sk_node_t)); ss = sh; for(l = 0; l <= lev ; l++){ sr = (sk_node_t *)malloc(sizeof(sk_node_t)); fgets(str, 30, fp); fmpz_set_str(tmp, str,10); row = fmpz_get_si(tmp); fgets(str, 30, fp); fmpz_set_str(tmp, str,10); col = fmpz_get_si(tmp); fmpz_poly_mat_init(sr->sk, row, col); for( i = 0 ; i < row ; i++) { for(j = 0; j < col ; j++) { fgets(str, 100000, fp); fmpz_poly_set_str(fmpz_poly_mat_entry(sr->sk, i, j), str); } } ss->next = sr; ss = sr; } ss->next = NULL; fclose(fp); sh = sh->next; while(lev > ctlev){ sh = sh->next; param = param->next; lev--; } fmpz_poly_t ms; fmpz_poly_init(ms); e_decrypt(ms, param, sh->sk, ct, fx); fmpz_poly_print(ms); printf("\n"); return 0; }
void frob(const mpoly_t P, const ctx_t ctxFracQt, const qadic_t t1, const qadic_ctx_t Qq, prec_t *prec, const prec_t *prec_in, int verbose) { const padic_ctx_struct *Qp = &Qq->pctx; const fmpz *p = Qp->p; const long a = qadic_ctx_degree(Qq); const long n = P->n - 1; const long d = mpoly_degree(P, -1, ctxFracQt); const long b = gmc_basis_size(n, d); long i, j, k; /* Diagonal fibre */ padic_mat_t F0; /* Gauss--Manin Connection */ mat_t M; mon_t *bR, *bC; fmpz_poly_t r; /* Local solution */ fmpz_poly_mat_t C, Cinv; long vC, vCinv; /* Frobenius */ fmpz_poly_mat_t F; long vF; fmpz_poly_mat_t F1; long vF1; fmpz_poly_t cp; clock_t c0, c1; double c; if (verbose) { printf("Input:\n"); printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n"); printf(" p = "), fmpz_print(p), printf("\n"); printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n"); printf("\n"); fflush(stdout); } /* Step 1 {M, r} *********************************************************/ c0 = clock(); mat_init(M, b, b, ctxFracQt); fmpz_poly_init(r); gmc_compute(M, &bR, &bC, P, ctxFracQt); { fmpz_poly_t t; fmpz_poly_init(t); fmpz_poly_set_ui(r, 1); for (i = 0; i < M->m; i++) for (j = 0; j < M->n; j++) { fmpz_poly_lcm(t, r, fmpz_poly_q_denref( (fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt))); fmpz_poly_swap(r, t); } fmpz_poly_clear(t); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Gauss-Manin connection:\n"); printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } { qadic_t t; qadic_init2(t, 1); fmpz_poly_evaluate_qadic(t, r, t1, Qq); if (qadic_is_zero(t)) { printf("Exception (deformation_frob).\n"); printf("The resultant r evaluates to zero (mod p) at t1.\n"); abort(); } qadic_clear(t); } /* Precisions ************************************************************/ if (prec_in != NULL) { *prec = *prec_in; } else { deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r)); } if (verbose) { printf("Precisions:\n"); printf(" N0 = %ld\n", prec->N0); printf(" N1 = %ld\n", prec->N1); printf(" N2 = %ld\n", prec->N2); printf(" N3 = %ld\n", prec->N3); printf(" N3i = %ld\n", prec->N3i); printf(" N3w = %ld\n", prec->N3w); printf(" N3iw = %ld\n", prec->N3iw); printf(" N4 = %ld\n", prec->N4); printf(" m = %ld\n", prec->m); printf(" K = %ld\n", prec->K); printf(" r = %ld\n", prec->r); printf(" s = %ld\n", prec->s); printf("\n"); fflush(stdout); } /* Initialisation ********************************************************/ padic_mat_init2(F0, b, b, prec->N4); fmpz_poly_mat_init(C, b, b); fmpz_poly_mat_init(Cinv, b, b); fmpz_poly_mat_init(F, b, b); vF = 0; fmpz_poly_mat_init(F1, b, b); vF1 = 0; fmpz_poly_init(cp); /* Step 2 {F0} ***********************************************************/ { padic_ctx_t pctx_F0; fmpz *t; padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT); t = _fmpz_vec_init(n + 1); c0 = clock(); mpoly_diagonal_fibre(t, P, ctxFracQt); diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0); padic_mat_transpose(F0, F0); c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Diagonal fibre:\n"); printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } _fmpz_vec_clear(t, n + 1); padic_ctx_clear(pctx_F0); } /* Step 3 {C, Cinv} ******************************************************/ /* Compute C as a matrix over Z_p[[t]]. A is the same but as a series of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t, the local solution of the differential equation replacing M by Mt. */ c0 = clock(); { const long K = prec->K; padic_mat_struct *A; gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt); gmde_convert_soln(C, &vC, A, K, p); for(i = 0; i < K; i++) padic_mat_clear(A + i); free(A); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Local solution:\n"); printf(" Time for C = %f\n", c); fflush(stdout); } c0 = clock(); { const long K = (prec->K + (*p) - 1) / (*p); mat_t Mt; padic_mat_struct *Ainv; mat_init(Mt, b, b, ctxFracQt); mat_transpose(Mt, M, ctxFracQt); mat_neg(Mt, Mt, ctxFracQt); gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt); gmde_convert_soln(Cinv, &vCinv, Ainv, K, p); fmpz_poly_mat_transpose(Cinv, Cinv); fmpz_poly_mat_compose_pow(Cinv, Cinv, *p); for(i = 0; i < K; i++) padic_mat_clear(Ainv + i); free(Ainv); mat_clear(Mt, ctxFracQt); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf(" Time for C^{-1} = %f\n", c); printf("\n"); fflush(stdout); } /* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/ /* Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K). This is done by first computing the unit part of the product exactly over the integers modulo t^K. */ c0 = clock(); { fmpz_t pN; fmpz_poly_mat_t T; fmpz_init(pN); fmpz_poly_mat_init(T, b, b); for (i = 0; i < b; i++) { /* Find the unique k s.t. F0(i,k) is non-zero */ for (k = 0; k < b; k++) if (!fmpz_is_zero(padic_mat_entry(F0, i, k))) break; if (k == b) { printf("Exception (frob). F0 is singular.\n\n"); abort(); } for (j = 0; j < b; j++) { fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j), fmpz_poly_mat_entry(Cinv, k, j), padic_mat_entry(F0, i, k)); } } fmpz_poly_mat_mul(F, C, T); fmpz_poly_mat_truncate(F, prec->K); vF = vC + padic_mat_val(F0) + vCinv; /* Canonicalise (F, vF) */ { long v = fmpz_poly_mat_ord_p(F, p); if (v == LONG_MAX) { printf("ERROR (deformation_frob). F(t) == 0.\n"); abort(); } else if (v > 0) { fmpz_pow_ui(pN, p, v); fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN); vF = vF + v; } } /* Reduce (F, vF) modulo p^{N2} */ fmpz_pow_ui(pN, p, prec->N2 - vF); fmpz_poly_mat_scalar_mod_fmpz(F, F, pN); fmpz_clear(pN); fmpz_poly_mat_clear(T); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Matrix for F(t):\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } /* Step 5 {G = r(t)^m F(t)} **********************************************/ c0 = clock(); { fmpz_t pN; fmpz_poly_t t; fmpz_init(pN); fmpz_poly_init(t); fmpz_pow_ui(pN, p, prec->N2 - vF); /* Compute r(t)^m mod p^{N2-vF} */ if (prec->denR == NULL) { fmpz_mod_poly_t _t; fmpz_mod_poly_init(_t, pN); fmpz_mod_poly_set_fmpz_poly(_t, r); fmpz_mod_poly_pow(_t, _t, prec->m); fmpz_mod_poly_get_fmpz_poly(t, _t); fmpz_mod_poly_clear(_t); } else { /* TODO: We don't really need a copy */ fmpz_poly_set(t, prec->denR); } fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t); fmpz_poly_mat_scalar_mod_fmpz(F, F, pN); /* TODO: This should not be necessary? */ fmpz_poly_mat_truncate(F, prec->K); fmpz_clear(pN); fmpz_poly_clear(t); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Analytic continuation:\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } /* Steps 6 and 7 *********************************************************/ if (a == 1) { /* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/ c0 = clock(); { const long N = prec->N2 - vF; fmpz_t f, g, t, pN; fmpz_init(f); fmpz_init(g); fmpz_init(t); fmpz_init(pN); fmpz_pow_ui(pN, p, N); /* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */ _padic_teichmuller(f, t1->coeffs + 0, p, N); if (prec->denR == NULL) { _fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN); fmpz_powm_ui(t, g, prec->m, pN); } else { _fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN); } _padic_inv(g, t, p, N); /* F1 := g G(\hat{t_1}) */ for (i = 0; i < b; i++) for (j = 0; j < b; j++) { const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j); const long len = poly->length; if (len == 0) { fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j)); } else { fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1); _fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN); fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t); fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN); _fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1); _fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j)); } } vF1 = vF; fmpz_poly_mat_canonicalise(F1, &vF1, p); fmpz_clear(f); fmpz_clear(g); fmpz_clear(t); fmpz_clear(pN); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Evaluation:\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } } else { /* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/ c0 = clock(); { const long N = prec->N2 - vF; fmpz_t pN; fmpz *f, *g, *t; fmpz_init(pN); f = _fmpz_vec_init(a); g = _fmpz_vec_init(2 * a - 1); t = _fmpz_vec_init(2 * a - 1); fmpz_pow_ui(pN, p, N); /* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */ _qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N); if (prec->denR == NULL) { fmpz_t e; fmpz_init_set_ui(e, prec->m); _fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a, Qq->a, Qq->j, Qq->len, pN); _qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN); fmpz_clear(e); } else { _fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN); _fmpz_poly_normalise(prec->denR); _fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a, Qq->a, Qq->j, Qq->len, pN); } _qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N); /* F1 := g G(\hat{t_1}) */ for (i = 0; i < b; i++) for (j = 0; j < b; j++) { const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j); const long len = poly->length; fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j); if (len == 0) { fmpz_poly_zero(poly2); } else { _fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a, Qq->a, Qq->j, Qq->len, pN); fmpz_poly_fit_length(poly2, 2 * a - 1); _fmpz_poly_mul(poly2->coeffs, g, a, t, a); _fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN); _fmpz_poly_set_length(poly2, a); _fmpz_poly_normalise(poly2); } } /* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */ vF1 = vF; fmpz_poly_mat_canonicalise(F1, &vF1, p); fmpz_clear(pN); _fmpz_vec_clear(f, a); _fmpz_vec_clear(g, 2 * a - 1); _fmpz_vec_clear(t, 2 * a - 1); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Evaluation:\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } /* Step 7 {Norm} *****************************************************/ /* Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate transpositions because our convention of columns vs rows is the opposite of that used by Gerkmann. Note that, in any case, transpositions do not affect the characteristic polynomial. */ c0 = clock(); { const long N = prec->N1 - a * vF1; fmpz_t pN; fmpz_poly_mat_t T; fmpz_init(pN); fmpz_poly_mat_init(T, b, b); fmpz_pow_ui(pN, p, N); fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq); _qadic_mat_mul(F1, F1, T, pN, Qq); for (i = 2; i < a; i++) { fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq); _qadic_mat_mul(F1, F1, T, pN, Qq); } vF1 = a * vF1; fmpz_poly_mat_canonicalise(F1, &vF1, p); fmpz_clear(pN); fmpz_poly_mat_clear(T); } c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Norm:\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } } /* Step 8 {Reverse characteristic polynomial} ****************************/ c0 = clock(); deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq); c1 = clock(); c = (double) (c1 - c0) / CLOCKS_PER_SEC; if (verbose) { printf("Reverse characteristic polynomial:\n"); printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n"); printf(" Time = %f\n", c); printf("\n"); fflush(stdout); } /* Clean up **************************************************************/ padic_mat_clear(F0); mat_clear(M, ctxFracQt); free(bR); free(bC); fmpz_poly_clear(r); fmpz_poly_mat_clear(C); fmpz_poly_mat_clear(Cinv); fmpz_poly_mat_clear(F); fmpz_poly_mat_clear(F1); fmpz_poly_clear(cp); }