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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ca.h"
#include "ca/impl.h"
#include "ca_ext.h"
#include "ca_field.h"
#include "ca_field/impl.h"
#include "fmpz_mpoly.h"
void
ca_field_build_ideal_gamma(ca_field_t K, ca_ctx_t ctx)
{
calcium_func_code Fi, Fj;
slong i, j, len, num_gamma;
len = CA_FIELD_LENGTH(K);
if (len < 2)
return;
num_gamma = 0;
for (i = 0; i < len; i++)
{
Fi = CA_EXT_HEAD(CA_FIELD_EXT_ELEM(K, i));
if (Fi == CA_Gamma)
{
num_gamma++;
}
}
if (num_gamma < 2)
return;
for (i = 0; i < len; i++)
{
Fi = CA_EXT_HEAD(CA_FIELD_EXT_ELEM(K, i));
if (Fi == CA_Gamma)
{
for (j = i + 1; j < len; j++)
{
Fj = CA_EXT_HEAD(CA_FIELD_EXT_ELEM(K, j));
if (Fj == CA_Gamma)
{
ca_ptr xi, xj;
ca_t t, u;
fmpz_t N;
slong n;
xi = CA_EXT_FUNC_ARGS(CA_FIELD_EXT_ELEM(K, i));
xj = CA_EXT_FUNC_ARGS(CA_FIELD_EXT_ELEM(K, j));
ca_init(t, ctx);
ca_init(u, ctx);
fmpz_init(N);
ca_sub(t, xi, xj, ctx);
if (ca_get_fmpz(N, t, ctx) && fmpz_cmp_si(N, -10) >= 0 && fmpz_cmp_si(N, 10) <= 0)
{
n = fmpz_get_si(N);
if (n == 0)
{
fmpz_mpoly_t poly;
fmpz_mpoly_init(poly, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_set_coeff_si_x(poly, 1, i, 1, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_set_coeff_si_x(poly, -1, j, 1, CA_FIELD_MCTX(K, ctx));
_ca_field_ideal_insert_clear_mpoly(K, poly, CA_FIELD_MCTX(K, ctx), ctx);
}
else
{
ca_field_struct * L; /* Field of t */
slong L_len;
slong * tgen_map;
slong k, m;
int success;
/* gamma(x+3) = (x+2)*(x+1)*x * gamma(x) */
/* (x-1)*(x-2)*(x-3) * gamma(x-3) = gamma(x) */
if (n > 0)
{
ca_set(t, xj, ctx);
for (k = 1; k < n; k++)
{
ca_add_ui(u, xj, k, ctx);
ca_mul(t, t, u, ctx);
}
}
else
{
ca_sub_ui(t, xj, 1, ctx);
for (k = 1; k < (-n); k++)
{
ca_sub_ui(u, xj, k + 1, ctx);
ca_mul(t, t, u, ctx);
}
}
L = CA_FIELD(t, ctx);
L_len = CA_FIELD_LENGTH(L);
success = 1;
tgen_map = flint_malloc(L_len * sizeof(slong));
for (m = 0; m < L_len; m++)
{
for (k = 0; k < len; k++)
{
if (CA_FIELD_EXT_ELEM(L, m) == CA_FIELD_EXT_ELEM(K, k))
{
tgen_map[m] = k;
break;
}
if (k == len - 1)
success = 0;
}
}
if (success)
{
fmpz_mpoly_t p, q, pxi, pxj;
fmpz_mpoly_init(p, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_init(q, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_init(pxi, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_init(pxj, CA_FIELD_MCTX(K, ctx));
/* todo: factor out */
if (L_len == 0)
{
fmpz_mpoly_set_fmpz(p, CA_FMPQ_NUMREF(t), CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_set_fmpz(q, CA_FMPQ_DENREF(t), CA_FIELD_MCTX(K, ctx));
}
else if (CA_FIELD_IS_NF(L))
{
fmpz_poly_t pol;
fmpz_t den;
_nf_elem_get_fmpz_poly_den_shallow(pol, den, CA_NF_ELEM(t), CA_FIELD_NF(L));
fmpz_mpoly_set_gen_fmpz_poly(p, tgen_map[0], pol, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_set_fmpz(q, den, CA_FIELD_MCTX(K, ctx));
}
else
{
fmpz_mpoly_compose_fmpz_mpoly_gen(p,
fmpz_mpoly_q_numref(CA_MPOLY_Q(t)),
tgen_map,
CA_FIELD_MCTX(L, ctx),
CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_compose_fmpz_mpoly_gen(q,
fmpz_mpoly_q_denref(CA_MPOLY_Q(t)),
tgen_map,
CA_FIELD_MCTX(L, ctx),
CA_FIELD_MCTX(K, ctx));
}
fmpz_mpoly_gen(pxi, i, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_gen(pxj, j, CA_FIELD_MCTX(K, ctx));
if (n < 0)
fmpz_mpoly_swap(p, q, CA_FIELD_MCTX(K, ctx));
/* pxi = (p/q) * pxj */
/* q * pxi - p * pxj = 0*/
fmpz_mpoly_mul(q, q, pxi, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_mul(p, p, pxj, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_sub(q, q, p, CA_FIELD_MCTX(K, ctx));
_ca_field_ideal_insert_clear_mpoly(K, q, CA_FIELD_MCTX(K, ctx), ctx);
fmpz_mpoly_clear(p, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_clear(pxi, CA_FIELD_MCTX(K, ctx));
fmpz_mpoly_clear(pxj, CA_FIELD_MCTX(K, ctx));
}
flint_free(tgen_map);
}
}
ca_clear(t, ctx);
ca_clear(u, ctx);
fmpz_clear(N);
}
}
}
}
}