// Solve the diophantine system Ax = 0 and return a basis set for solutions
// Reference:
// Evelyne Contejean, Herve Devie. An Efficient Incremental Algorithm for
// Solving
// Systems of Linear Diophantine Equations. Information and computation,
// 113(1):143-172,
// August 1994.
void homogeneous_lde(std::vector<DenseMatrix> &basis, const DenseMatrix &A)
{
unsigned p = A.nrows();
unsigned q = A.ncols();
unsigned n;
SYMENGINE_ASSERT(p > 0 and q > 1);
DenseMatrix row_zero(1, q);
zeros(row_zero);
DenseMatrix col_zero(p, 1);
zeros(col_zero);
std::vector<DenseMatrix> P;
P.push_back(row_zero);
std::vector<std::vector<bool>> Frozen(q, std::vector<bool>(q, true));
for (unsigned j = 0; j < q; j++) {
Frozen[0][j] = false;
}
std::vector<bool> F(q, false);
DenseMatrix t, transpose, product, T;
RCP<const Integer> dot;
product = DenseMatrix(p, 1);
transpose = DenseMatrix(q, 1);
while (P.size() > 0) {
n = P.size() - 1;
t = P[n];
P.pop_back();
t.transpose(transpose);
A.mul_matrix(transpose, product);
if (product.eq(col_zero) and not t.eq(row_zero)) {
basis.push_back(t);
} else {
for (unsigned i = 0; i < q; i++) {
F[i] = Frozen[n][i];
}
T = t;
for (unsigned i = 0; i < q; i++) {
SYMENGINE_ASSERT(is_a<Integer>(*T.get(0, i)));
T.set(0, i, rcp_static_cast<const Integer>(T.get(0, i))
->addint(*one));
if (i > 0) {
SYMENGINE_ASSERT(is_a<Integer>(*T.get(0, i - 1)));
T.set(0, i - 1,
rcp_static_cast<const Integer>(T.get(0, i - 1))
->subint(*one));
}
dot = zero;
for (unsigned j = 0; j < p; j++) {
SYMENGINE_ASSERT(is_a<Integer>(*product.get(j, 0)));
RCP<const Integer> p_j0
= rcp_static_cast<const Integer>(product.get(j, 0));
SYMENGINE_ASSERT(is_a<Integer>(*A.get(j, i)));
RCP<const Integer> A_ji
= rcp_static_cast<const Integer>(A.get(j, i));
dot = dot->addint(*p_j0->mulint(*A_ji));
}
if (F[i] == false and ((dot->is_negative()
and is_minimum(T, basis, basis.size()))
or t.eq(row_zero))) {
P.push_back(T);
n = n + 1;
for (unsigned j = 0; j < q; j++) {
Frozen[n - 1][j] = F[j];
}
F[i] = true;
}
}
}
}
}
