FreeModule* ResF4toM2Interface::to_M2_freemodule(const PolynomialRing* R,
SchreyerFrame& C,
int lev)
{
FreeModule* result = new FreeModule(R, 0, true);
if (lev < 0 or lev > C.maxLevel())
{
return result;
}
const Monoid* M = R->getMonoid();
auto& thislevel = C.level(lev);
const ResSchreyerOrder& S = C.schreyerOrder(lev);
res_ntuple_word* longexp = new res_ntuple_word[M->n_vars()];
int* exp = new int[M->n_vars()];
for (auto i = 0; i < thislevel.size(); ++i)
{
int d[1];
d[0] = thislevel[i].mDegree;
monomial deg = M->degree_monoid()->make_one();
M->degree_monoid()->from_expvector(d, deg);
// Now grab the Schreyer info
// unpack to exponent vector, then repack into monoid element
monomial totalmonom = M->make_one();
long comp;
C.monoid().to_exponent_vector(S.mTotalMonom[i], longexp, comp);
for (int j=0; j<M->n_vars(); ++j)
exp[j] = static_cast<int>(longexp[j]);
M->from_expvector(exp, totalmonom);
result->append_schreyer(deg, totalmonom, static_cast<int>(S.mTieBreaker[i]));
}
delete [] longexp;
delete [] exp;
return result;
}
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::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::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 *value() {
if (symm1_result == 0)
{
symm1_result = F->get_ring()->make_FreeModule();
if (n >= 0)
{
symm1_deg = D->make_one();
symm1(0, n);
D->remove(symm1_deg);
}
}
return symm1_result;
}
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;
}
void gbres_comp::setup(const Matrix *m,
int length,
int origsyz,
int strategy)
{
int i;
originalR = m->get_ring()->cast_to_PolynomialRing();
if (originalR == NULL) assert(0);
GR = originalR->get_gb_ring();
mi_stash = new stash("res mi nodes", sizeof(Nmi_node));
FreeModule *Fsyz = originalR->make_Schreyer_FreeModule();
if (length <= 0)
{
ERROR("resolution length must be at least 1");
length = 1;
}
// If origsyz, and length>1, create Fsyz as a Schreyer free
// if origsyz is smaller, truncate this module...
if (length > 1 && origsyz > 0)
{
if (origsyz > m->n_cols())
origsyz = m->n_cols();
int *one = originalR->getMonoid()->make_one();
const int *mon;
for (i=0; i<origsyz; i++)
{
if ((*m)[i] == NULL)
mon = one;
else
{
Nterm *t = (*m)[i]->coeff;
mon = t->monom;
}
Fsyz->append_schreyer(m->cols()->degree(i), mon, i);
}
originalR->getMonoid()->remove(one);
}
lo_degree = m->cols()->lowest_primary_degree();
last_completed_degree = lo_degree-1;
n_nodes = length + 1;
nodes = newarray(gb_node_ptr,n_nodes);
nodes[0] = new gb_emitter(m);
nodes[1] = new gb2_comp(Fsyz,mi_stash,nodes[0],lo_degree,origsyz,1,strategy);
nodes[0]->set_output(nodes[1]);
if (n_nodes == 2)
{
// Don't compute syzygies at all.
nodes[1]->set_output(NULL);
}
else if (n_nodes >= 3)
{
// Compute a resolution to length 'length', with last being
// a gb node.
int deg = lo_degree+1;
if (origsyz > 0) deg--;
for (i=2; i<n_nodes-1; i++)
{
FreeModule *F = originalR->make_Schreyer_FreeModule();
nodes[i] = new gb2_comp(F,mi_stash,nodes[i-1],deg++,-1,i,strategy);
nodes[i-1]->set_output(nodes[i]);
}
FreeModule *F = originalR->make_Schreyer_FreeModule();
nodes[n_nodes-1] = new gb2_comp(F,mi_stash,nodes[n_nodes-2],deg++,0,n_nodes-1,strategy);
nodes[n_nodes-1]->set_output(NULL);
}
strategy_flags = strategy;
}