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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"
ca_ext_ptr
ca_is_gen_as_ext(const ca_t x, ca_ctx_t ctx)
{
ca_field_ptr K;
if (CA_IS_SPECIAL(x))
return NULL;
K = CA_FIELD(x, ctx);
if (CA_FIELD_IS_QQ(K))
return NULL;
if (CA_FIELD_IS_NF(K))
{
if (!nf_elem_is_gen(CA_NF_ELEM(x), CA_FIELD_NF(K)))
return NULL;
return CA_FIELD_EXT_ELEM(K, 0);
}
if (fmpz_mpoly_is_one(fmpz_mpoly_q_denref(CA_MPOLY_Q(x)), CA_FIELD_MCTX(K, ctx)))
{
if (fmpz_mpoly_is_gen(fmpz_mpoly_q_numref(CA_MPOLY_Q(x)), -1, CA_FIELD_MCTX(K, ctx)))
{
slong i;
for (i = 0; ; i++)
if (fmpz_mpoly_is_gen(fmpz_mpoly_q_numref(CA_MPOLY_Q(x)), i, CA_FIELD_MCTX(K, ctx)))
return CA_FIELD_EXT_ELEM(K, i);
}
}
return NULL;
}