void
fmpq_mat_mul_fmpz_mat(fmpq_mat_t C, const fmpq_mat_t A, const fmpz_mat_t B)
{
slong i, j;
fmpz_mat_t Aclear;
fmpz_mat_t Cclear;
fmpz * Aden;
fmpz_mat_init(Aclear, A->r, A->c);
fmpz_mat_init(Cclear, A->r, B->c);
Aden = _fmpz_vec_init(A->r);
fmpq_mat_get_fmpz_mat_rowwise(Aclear, Aden, A);
fmpz_mat_mul(Cclear, Aclear, B);
for (i = 0; i < C->r; i++)
{
for (j = 0; j < C->c; j++)
{
fmpz_set(fmpq_mat_entry_num(C, i, j), fmpz_mat_entry(Cclear, i, j));
fmpz_set(fmpq_mat_entry_den(C, i, j), Aden + i);
fmpq_canonicalise(fmpq_mat_entry(C, i, j));
}
}
fmpz_mat_clear(Aclear);
fmpz_mat_clear(Cclear);
_fmpz_vec_clear(Aden, A->r);
}
inline size_t rank(const DMatQQFlint& A) {
// fmpq_mat has no rank function.
// So we clear denominators row-wise (or column-wise), and compute the rank of that matrix.
fmpz_mat_t m1;
fmpz_mat_init(m1, A.numRows(), A.numColumns());
fmpq_mat_get_fmpz_mat_rowwise(m1, NULL, A.fmpq_mat());
//fmpz_mat_print_pretty(m1);
size_t rk = fmpz_mat_rank(m1);
fmpz_mat_clear(m1);
return rk;
}
inline size_t nullSpace(const DMatQQFlint& A,
DMatQQFlint& result_nullspace)
{
fmpz_mat_t m1;
fmpz_mat_t m2;
fmpz_mat_init(m1, A.numRows(), A.numColumns());
fmpz_mat_init(m2, A.numColumns(), A.numColumns());
fmpq_mat_get_fmpz_mat_rowwise(m1, NULL, A.fmpq_mat());
//fmpz_mat_print_pretty(m1);
size_t nullity = fmpz_mat_nullspace(m2,m1);
// now copy the first 'nullity' columns into result_nullspace
result_nullspace.resize(A.numColumns(), nullity);
for (size_t c = 0; c < nullity; c++)
for (size_t r = 0; r < A.numColumns(); r++)
fmpz_set(fmpq_numref(& result_nullspace.entry(r,c)), fmpz_mat_entry(m2,r,c));
fmpz_mat_clear(m1);
fmpz_mat_clear(m2);
return nullity;
}
int fmpq_mat_inv(fmpq_mat_t B, const fmpq_mat_t A)
{
long n = A->r;
if (n == 0)
{
return 1;
}
else if (n == 1)
{
if (fmpq_is_zero(fmpq_mat_entry(A, 0, 0)))
return 0;
fmpq_inv(fmpq_mat_entry(B, 0, 0), fmpq_mat_entry(A, 0, 0));
return 1;
}
else if (n == 2)
{
fmpq_t d;
int success;
fmpq_init(d);
fmpq_mul(d, fmpq_mat_entry(A, 0, 0), fmpq_mat_entry(A, 1, 1));
fmpq_submul(d, fmpq_mat_entry(A, 0, 1), fmpq_mat_entry(A, 1, 0));
success = !fmpq_is_zero(d);
if (success)
{
fmpq_t t00, t01, t10, t11;
fmpq_inv(d, d);
fmpq_init(t00);
fmpq_init(t01);
fmpq_init(t10);
fmpq_init(t11);
fmpq_mul(t00, fmpq_mat_entry(A, 1, 1), d);
fmpq_mul(t01, fmpq_mat_entry(A, 0, 1), d);
fmpq_mul(t10, fmpq_mat_entry(A, 1, 0), d);
fmpq_mul(t11, fmpq_mat_entry(A, 0, 0), d);
fmpq_set(fmpq_mat_entry(B, 0, 0), t00);
fmpq_neg(fmpq_mat_entry(B, 0, 1), t01);
fmpq_neg(fmpq_mat_entry(B, 1, 0), t10);
fmpq_set(fmpq_mat_entry(B, 1, 1), t11);
fmpq_clear(t00);
fmpq_clear(t01);
fmpq_clear(t10);
fmpq_clear(t11);
}
fmpq_clear(d);
return success;
}
else
{
fmpz_mat_t Aclear, Bclear, I;
fmpz * den;
long i;
int success;
fmpz_mat_init(Aclear, n, n);
fmpz_mat_init(Bclear, n, n);
fmpz_mat_init(I, n, n);
den = _fmpz_vec_init(n);
fmpq_mat_get_fmpz_mat_rowwise(Aclear, den, A);
for (i = 0; i < n; i++)
fmpz_set(fmpz_mat_entry(I, i, i), den + i);
success = fmpz_mat_solve(Bclear, den, Aclear, I);
if (success)
fmpq_mat_set_fmpz_mat_div_fmpz(B, Bclear, den);
fmpz_mat_clear(Aclear);
fmpz_mat_clear(Bclear);
fmpz_mat_clear(I);
_fmpz_vec_clear(den, A->r);
return success;
}
}
