FreeModule *FreeModule::make_schreyer(const GBMatrix *m)
{
const FreeModule *F = m->get_free_module();
const PolynomialRing *R = F->get_ring()->cast_to_PolynomialRing();
if (R == 0)
{
ERROR("expected a polynomial ring");
return nullptr;
}
FreeModule *G = R->make_FreeModule();
int rk = INTSIZE(m->elems);
if (rk == 0) return G;
for (int i=0; i<rk; i++)
{
int *deg = R->degree_monoid()->make_one();
gbvector * v = m->elems[i];
if (v != 0)
R->get_gb_ring()->gbvector_multidegree(F, v, deg);
G->append(deg);
}
G->schreyer = SchreyerOrder::create(m);
return G;
}
FreeModule *FreeModule::exterior(int pp) const
// p th exterior power
{
FreeModule *result;
if (pp == 0)
return get_ring()->make_FreeModule(1);
else
result = new_free();
int rk = rank();
if (pp > rk || pp < 0) return result;
size_t p = static_cast<size_t>(pp);
Subset a(p, 0);
for (size_t i=0; i<p; i++) a[i] = i;
int *deg = degree_monoid()->make_one();
do
{
degree_monoid()->one(deg);
for (size_t r=0; r<p; r++)
degree_monoid()->mult(deg, degree(static_cast<int>(a[r])), deg);
result->append(deg);
}
while (Subsets::increment(rk, a));
degree_monoid()->remove(deg);
if (schreyer != NULL)
result->schreyer = schreyer->exterior(pp);
return result;
}
FreeModule *FreeModule::direct_sum(const FreeModule *G) const
// direct sum
{
int i;
if (get_ring() != G->get_ring())
{
ERROR("expected free modules over the same ring");
return 0;
}
FreeModule *result = new_free();
for (i=0; i<rank(); i++)
result->append(degree(i));
for (i=0; i<G->rank(); i++)
result->append(G->degree(i));
// if (schreyer != NULL && G->schreyer != NULL)
// result->schreyer = schreyer->direct_sum(G->schreyer);
return result;
}
FreeModule *FreeModule::transpose() const
{
FreeModule *result = new_free();
int *deg = degree_monoid()->make_one();
for (int i=0; i<rank(); i++)
{
degree_monoid()->power(degree(i), -1, deg);
result->append(deg);
}
// result has no schreyer order
degree_monoid()->remove(deg);
return result;
}
FreeModule *FreeModule::sub_space(int n) const
{
if (n < 0 || n > rank())
{
ERROR("subfreemodule: index out of bounds");
return NULL;
}
FreeModule *result = new_free();
for (int i=0; i<n; i++)
result->append(degree(i));
if (schreyer != NULL)
result->schreyer = schreyer->sub_space(n);
return result;
}
FreeModule *FreeModule::make_schreyer(const Matrix *m)
{
int i;
const Ring *R = m->get_ring();
FreeModule *F = R->make_FreeModule();
int rk = m->n_cols();
if (rk == 0) return F;
for (i=0; i<rk; i++)
F->append(m->cols()->degree(i));
F->schreyer = SchreyerOrder::create(m);
return F;
}
FreeModule *FreeModule::sub_space(M2_arrayint a) const
{
FreeModule *result = new_free();
for (unsigned int i=0; i<a->len; i++)
if (a->array[i] >= 0 && a->array[i] < rank())
result->append(degree(a->array[i]));
else
{
ERROR("subfreemodule: index out of bounds");
deleteitem(result);
return NULL;
}
if (schreyer != NULL)
result->schreyer = schreyer->sub_space(a);
return result;
}
FreeModule *FreeModule::shift(const int *d) const
// Shift degree by d.
{
FreeModule *result = new_free();
int *deg = degree_monoid()->make_one();
for (int i=0; i<rank(); i++)
{
degree_monoid()->mult(degree(i), d, deg);
result->append(deg);
}
if (schreyer != NULL)
result->schreyer = schreyer->copy();
degree_monoid()->remove(deg);
return result;
}
void symm1(int lastn, // can use lastn..rank()-1 in product
int pow) const // remaining power to take
{
if (pow == 0)
symm1_result->append(symm1_deg);
else
{
for (int i=lastn; i<F->rank(); i++)
{
// increase symm1_deg, with e_i
D->mult(symm1_deg, F->degree(i), symm1_deg);
symm1(i, pow-1);
// decrease symm1_deg back
D->divide(symm1_deg, F->degree(i), symm1_deg);
}
}
}
FreeModule *FreeModule::make_schreyer(const Matrix *m)
{
int i;
const PolynomialRing *R = m->get_ring()->cast_to_PolynomialRing();
if (R == 0)
{
ERROR("expected a polynomial ring");
return nullptr;
}
FreeModule *F = R->make_FreeModule();
int rk = m->n_cols();
if (rk == 0) return F;
for (i=0; i<rk; i++)
F->append(m->cols()->degree(i));
F->schreyer = SchreyerOrder::create(m);
return F;
}
FreeModule *FreeModule::tensor(const FreeModule *G) const
// tensor product
{
if (get_ring() != G->get_ring())
{
ERROR("expected free modules over the same ring");
return 0;
}
FreeModule *result = new_free();
int *deg = degree_monoid()->make_one();
for (int i=0; i<rank(); i++)
for (int j=0; j<G->rank(); j++)
{
degree_monoid()->mult(degree(i), G->degree(j), deg);
result->append(deg);
}
degree_monoid()->remove(deg);
if (schreyer != NULL && G->schreyer != NULL)
result->schreyer = schreyer->tensor(G->schreyer);
return result;
}
FreeModule *FreeModule::exterior(int p) const
// p th exterior power
{
FreeModule *result;
int rk = rank();
if (p == 0)
return get_ring()->make_FreeModule(1);
else
result = new_free();
if (p > rk || p < 0) return result;
int *a = newarray_atomic(int,p);
for (int i=0; i<p; i++)
a[i] = i;
int *deg = degree_monoid()->make_one();
do
{
degree_monoid()->one(deg);
for (int r=0; r<p; r++)
degree_monoid()->mult(deg, degree(a[r]), deg);
result->append(deg);
}
while (comb::increment(p, rk, a));
degree_monoid()->remove(deg);
deletearray(a);
if (schreyer != NULL)
result->schreyer = schreyer->exterior(p);
return result;
}
