BitMatrix<dim> subquotientMap
(const Subquotient<dim>& source,
const Subquotient<dim>& dest,
const BitMatrix<dim>& m)
{
assert(m.numColumns()==source.rank());
assert(m.numRows()==dest.rank());
BitMatrix<dim> result(dest.dimension(),0);
// restrict m to source.space()
for (RankFlags::iterator it=source.support().begin(); it(); ++it)
{
SmallBitVector v = m*source.space().basis(*it);
assert(v.size()==dest.rank());
/*
// go to canonical representative modulo destination subspace
dest.denominator().mod_reduce(v);
assert(v.size()==dest.rank());
// get coordinates in canonical basis
v.slice(dest.space().support()); // express |v| in basis of |d_space|
assert(v.size()==dest.space().dimension());
v.slice(dest.support());
*/
v=dest.toBasis(v);
assert(v.size()==dest.dimension()); // dimension of the subquotient
result.addColumn(v);
}
return result;
}
void Subspace<dim>::apply(const BitMatrix<dim>& r)
{
assert(r.numColumns()==d_rank);
BitVectorList<dim> b;
b.reserve(dimension());
for (size_t j = 0; j<dimension(); ++j)
{
b.push_back(r*d_basis[j]);
assert(b.back().size()==r.numRows());
}
Subspace<dim> ns(b,r.numRows()); // construct (and normalize) new subspace
swap(ns); // and install it in our place
}
/*!
\brief Constructs the normalised subspace generated by the columns of
a |BitMatrix|, i.e., the image of that matrix
*/
template<size_t dim> Subspace<dim>::
Subspace(const BitMatrix<dim>& M)
: d_basis(M.image())
, d_support()
, d_rank(M.numRows())
{
// change |d_basis| to a normalised form, and set |d_support|:
bitvector::Gauss_Jordan(d_support,d_basis);
}