void
_fmpz_vec_lcm(fmpz_t res, const fmpz * vec, long len)
{
long i;
fmpz_one(res);
for (i = 0; i < len && !fmpz_is_zero(res); i++)
fmpz_lcm(res, res, vec + i);
fmpz_abs(res, res);
}
void
_fmpq_mat_get_fmpz_mat_rowwise(fmpz_mat_struct ** num, fmpz * den,
const fmpq_mat_struct ** mat, slong n)
{
fmpz_t t, lcm;
slong i, j, k;
if (fmpq_mat_is_empty(mat[0]))
return;
fmpz_init(t);
fmpz_init(lcm);
for (i = 0; i < mat[0]->r; i++)
{
/* Compute common denominator of row */
fmpz_set(lcm, fmpq_mat_entry_den(mat[0], i, 0));
for (k = 0; k < n; k++)
for (j = (k == 0); j < mat[k]->c; j++)
fmpz_lcm(lcm, lcm, fmpq_mat_entry_den(mat[k], i, j));
if (den != NULL)
fmpz_set(den + i, lcm);
for (k = 0; k < n; k++)
{
/* Rescale numerators in row */
if (fmpz_is_one(lcm))
{
for (j = 0; j < mat[k]->c; j++)
fmpz_set(fmpz_mat_entry(num[k], i, j),
fmpq_mat_entry_num(mat[k], i, j));
}
else
{
for (j = 0; j < mat[k]->c; j++)
{
fmpz_divexact(t, lcm, fmpq_mat_entry_den(mat[k], i, j));
fmpz_mul(fmpz_mat_entry(num[k], i, j),
fmpq_mat_entry_num(mat[k], i, j), t);
}
}
}
}
fmpz_clear(t);
fmpz_clear(lcm);
}
static void
_set_vec(fmpz * rnum, fmpz_t den,
const fmpz * xnum, const fmpz * xden, slong len)
{
slong j;
fmpz_t t;
fmpz_init(t);
fmpz_one(den);
for (j = 0; j < len; j++)
fmpz_lcm(den, den, xden + j);
for (j = 0; j < len; j++)
{
fmpz_divexact(t, den, xden + j);
fmpz_mul(rnum + j, xnum + j, t);
}
fmpz_clear(t);
}
void
fmpz_holonomic_get_nth_fmpq(fmpq_t res, const fmpz_holonomic_t op, const fmpq * initial, long n0, long n)
{
long r = fmpz_holonomic_order(op);
if (r == 0)
{
fmpq_zero(res);
return;
}
else if (n < n0)
{
printf("not implemented\n");
abort();
}
else if (n - n0 < r)
{
fmpq_set(res, initial + n - n0);
return;
}
else
{
fmpz_mat_t M;
long i;
fmpz_t Q;
fmpz_mat_init(M, r, r);
fmpz_init(Q);
fmpz_holonomic_forward_fmpz_mat(M, Q, op, n0, n - n0 - r + 1);
{
fmpz_t g, t;
fmpz_init(g);
fmpz_init(t);
fmpz_one(g);
for (i = 0; i < r; i++)
fmpz_lcm(g, g, fmpq_denref(initial + i));
fmpz_divexact(t, g, fmpq_denref(initial + 0));
fmpz_mul(t, t, fmpq_numref(initial + 0));
fmpz_mul(fmpz_mat_entry(M, r - 1, 0), fmpz_mat_entry(M, r - 1, 0), t);
for (i = 1; i < r; i++)
{
fmpz_divexact(t, g, fmpq_denref(initial + i));
fmpz_mul(t, t, fmpq_numref(initial + i));
fmpz_addmul(fmpz_mat_entry(M, r - 1, 0), fmpz_mat_entry(M, r - 1, i), t);
}
fmpz_set(fmpq_numref(res), fmpz_mat_entry(M, r - 1, 0));
fmpz_mul(fmpq_denref(res), Q, g);
fmpq_canonicalise(res);
fmpz_clear(g);
fmpz_clear(t);
}
fmpz_mat_clear(M);
fmpz_clear(Q);
}
}
void nf_elem_rep_mat_fmpz_mat_den(fmpz_mat_t res, fmpz_t den, const nf_elem_t a, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
fmpz_set(fmpz_mat_entry(res, 0, 0), LNF_ELEM_NUMREF(a));
fmpz_set(den, LNF_ELEM_DENREF(a));
}
else if (nf->flag & NF_QUADRATIC)
{
nf_elem_t t;
const fmpz * const anum = QNF_ELEM_NUMREF(a);
const fmpz * const aden = QNF_ELEM_DENREF(a);
fmpz * const tnum = QNF_ELEM_NUMREF(t);
fmpz * const tden = QNF_ELEM_DENREF(t);
nf_elem_init(t, nf);
nf_elem_mul_gen(t, a, nf);
if (fmpz_equal(tden, aden))
{
fmpz_set(fmpz_mat_entry(res, 0, 0), anum);
fmpz_set(fmpz_mat_entry(res, 0, 1), anum + 1);
fmpz_set(fmpz_mat_entry(res, 1, 0), tnum);
fmpz_set(fmpz_mat_entry(res, 1, 1), tnum + 1);
fmpz_set(den, tden);
}
else
{
fmpz_lcm(den, tden, aden);
fmpz_divexact(fmpz_mat_entry(res, 0, 0), den, aden);
fmpz_mul(fmpz_mat_entry(res, 0, 1), anum + 1, fmpz_mat_entry(res, 0, 0));
fmpz_mul(fmpz_mat_entry(res, 0, 0), anum, fmpz_mat_entry(res, 0, 0));
fmpz_divexact(fmpz_mat_entry(res, 1, 0), den, tden);
fmpz_mul(fmpz_mat_entry(res, 1, 1), tnum + 1, fmpz_mat_entry(res, 1, 0));
fmpz_mul(fmpz_mat_entry(res, 1, 0), tnum, fmpz_mat_entry(res, 1, 0));
}
nf_elem_clear(t, nf);
}
else
{
slong i, j;
nf_elem_t t;
slong d = fmpq_poly_degree(nf->pol);
nf_elem_init(t, nf);
nf_elem_set(t, a, nf);
if (NF_ELEM(a)->length == 0)
{
fmpz_mat_zero(res);
fmpz_one(den);
}
else if (NF_ELEM(a)->length == 1)
{
fmpz_mat_zero(res);
for (i = 0; i <= d - 1; i++)
{
fmpz_set(fmpz_mat_entry(res, i, i), fmpq_poly_numref(NF_ELEM(a)));
}
fmpz_set(den, fmpq_poly_denref(NF_ELEM(a)));
}
else
{
/* Special case if defining polynomial is monic and integral and the element also has trivial denominator */
if (nf->flag & NF_MONIC && fmpz_is_one(fmpq_poly_denref(nf->pol)) && fmpz_is_one(fmpq_poly_denref(NF_ELEM(a))))
{
fmpz_one(den);
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 1; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
}
else
{
/* Now the general case. For 0 <= j < d - 2 we store the
* denominator for row j at res[d - 1, j]. At the end we
* divide the lcm of all of them by the corresponding
* denominator of the row to get the correct multiplier for
* row.
*/
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
fmpz_set(fmpz_mat_entry(res, d - 1, 0), fmpq_poly_denref(NF_ELEM(a)));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(a)));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 2; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(t)));
}
nf_elem_mul_gen(t, t, nf);
/* Now compute the correct denominator */
fmpz_set(fmpz_mat_entry(res, d - 1, d - 1), fmpq_poly_denref(NF_ELEM(t)));
fmpz_set(den, fmpq_poly_denref(NF_ELEM(t)));
for (j = 0; j <= d - 2; j++)
fmpz_lcm(den, den, fmpz_mat_entry(res, d - 1, j));
for (j = 0; j <= d - 2; j++)
{
if (!fmpz_equal(den, fmpz_mat_entry(res, d - 1, j)))
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, j), den, fmpz_mat_entry(res, d - 1, j));
for (i = 0; i <= d - 1; i++)
fmpz_mul(fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, d - 1, j));
}
}
if (fmpz_equal(den, fmpz_mat_entry(res, d - 1, d - 1)))
{
for (i = 0; i < d; i++)
fmpz_set(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
else
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, d - 1), den, fmpq_poly_denref(NF_ELEM(t)));
for (i = 0; i < d; i++)
fmpz_mul(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i, fmpz_mat_entry(res, d - 1, d - 1));
}
}
}
nf_elem_clear(t, nf);
}
}
