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;
}
void FractionField::degree(const ring_elem a, int *d) const
{
const frac_elem *f = FRAC_VAL(a);
R_->degree(f->numer, d);
int *e = degree_monoid()->make_one();
R_->degree(f->denom, e);
degree_monoid()->divide(d, e, d);
degree_monoid()->remove(e);
}
bool FractionField::multi_degree(const ring_elem a, int *d) const
{
const frac_elem *f = FRAC_VAL(a);
bool tophom = R_->multi_degree(f->numer, d);
int *e = degree_monoid()->make_one();
bool bottomhom = R_->multi_degree(f->denom, e);
degree_monoid()->divide(d, e, d);
degree_monoid()->remove(e);
return tophom && bottomhom;
}
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;
}
void FreeModule::append_schreyer(const int *d, const int *base, int compare_num)
{
assert(schreyer != 0);
int *p = degree_monoid()->make_new(d);
components.append(p);
schreyer->append(compare_num,base);
}
void FreeModule::change_degree(int i, const int *deg)
{
// WARNING: this modifies the degree, and should only be used during
// the construction of a free module (or matrix).
assert(i >= 0);
assert(i < rank());
degree_monoid()->copy(deg, components[i]);
}
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;
}
unsigned int FreeModule::computeHashValue() const
{
unsigned int hashval = 13;
if (degree_monoid()->n_vars() == 0)
hashval += rank();
else
for (int i=0; i<rank(); i++)
hashval = 14535*hashval + degree(i)[0];
return hashval;
}
FreeModule::FreeModule(const Ring *RR, int n, bool has_schreyer_order)
// Create R^n, with all gradings zero.
{
initialize(RR);
int *deg = degree_monoid()->make_one();
for (int i=0; i<n; i++)
append(deg);
degree_monoid()->remove(deg);
if (has_schreyer_order)
{
const PolynomialRing *P = RR->cast_to_PolynomialRing();
assert(P != 0);
assert(n == 0);
schreyer = SchreyerOrder::create(P->getMonoid());
}
else
schreyer = 0;
}
void FreeModule::text_out(buffer &o) const
{
int i;
int rk = rank();
o << "free(rank " << rk << " degrees = {";
for (i=0; i<rk; i++)
{
if (i != 0) o << ", ";
degree_monoid()->elem_text_out(o, degree(i));
}
o << "}";
if (schreyer != NULL) schreyer->text_out(o);
o << ')';
}
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;
}
bool FreeModule::is_equal(const FreeModule *F) const
{
int i;
if (this == F) return true;
if (this->get_ring() != F->get_ring()) return false;
if (rank() != F->rank()) return false;
const Monoid *D = degree_monoid();
if (D->n_vars() > 0)
for (i=0; i<rank(); i++)
if (0 != D->compare(degree(i), F->degree(i)))
return false;
if (schreyer != NULL)
return schreyer->is_equal(F->schreyer);
if (F->schreyer != NULL) return false;
return true;
}
int FreeModule::primary_degree(int i) const
{
int result = degree_monoid()->degree_weights(degree(i),get_ring()->get_heft_vector());
return result;
}
void FreeModule::append(const int *d)
{
assert(schreyer == 0);
int *p = degree_monoid()->make_new(d);
components.append(p);
}