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Added direct_sum module and some simple tests to main.

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This commit is contained in:
Cotton Seed 2012-02-29 22:21:45 -05:00
parent 9bed7282ac
commit 7d80c871ff
2 changed files with 168 additions and 15 deletions
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179
algebra/module.h
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@ -5,6 +5,7 @@ template<class R> class mod_span;
template<class R> class free_submodule;
template<class R> class quotient_module;
template<class R> class direct_sum;
template<class R> class tensor_product;
template<class R> class hom_module;
@ -17,11 +18,8 @@ class module : public refcounted
static unsigned id_counter;
#if 0
static map<basedvector<unsigned, 1>,
ptr<const direct_sum<R> > direct_sum_idx;
#endif
ptr<const direct_sum<R> > > direct_sum_idx;
static map<basedvector<unsigned, 1>,
ptr<const tensor_product<R> > > tensor_product_idx;
static map<pair<unsigned, unsigned>,
@ -78,6 +76,37 @@ class module : public refcounted
multivariate_laurentpoly<Z> free_poincare_polynomial () const;
multivariate_laurentpoly<Z> free_delta_poincare_polynomial () const;
ptr<const direct_sum<R> >
add (basedvector<ptr<const module<R> >, 1> compound_summands) const;
ptr<const direct_sum<R> > add (ptr<const module<R> > m) const
{
basedvector<ptr<const module<R> >, 1> summands (2);
summands[1] = this;
summands[2] = m;
return add (summands);
}
// g -> (g, 0)
unsigned inject_1 (unsigned g, ptr<const module<R> > m) const
{
return g;
}
// g -> (0, g)
unsigned inject_2 (ptr<const module<R> > m, unsigned g) const
{
return dim () + g;
}
pair<unsigned, unsigned> project (ptr<const module<R> > m, unsigned g) const
{
if (g <= dim ())
return pair<unsigned, unsigned> (1, g);
else
return pair<unsigned, unsigned> (2, g - dim ());
}
ptr<const tensor_product<R> > tensor (ptr<const module<R> > m) const
{
basedvector<ptr<const module<R> >, 1> factors (2);
@ -104,6 +133,11 @@ class module : public refcounted
return (i - 1) + (j - 1) * dim () + 1;
}
virtual void append_direct_summands (basedvector<ptr<const module<R> >, 1> &summands) const
{
summands.append (this);
}
virtual void append_tensor_factors (basedvector<ptr<const module<R> >, 1> &factors) const
{
factors.append (this);
@ -114,13 +148,16 @@ class module : public refcounted
};
template<class R> unsigned module<R>::id_counter = 1;
template<class R> map<basedvector<unsigned, 1>,
ptr<const direct_sum<R> > > module<R>::direct_sum_idx;
template<class R> map<basedvector<unsigned, 1>,
ptr<const tensor_product<R> > > module<R>::tensor_product_idx;
template<class R> map<pair<unsigned, unsigned>,
ptr<const hom_module<R> > > module<R>::hom_module_idx;
#if 0
template<class R>
class direct_sum : public module<R>
{
@ -130,25 +167,97 @@ class direct_sum : public module<R>
public:
direct_sum (basedvector<ptr<const module<R> >, 1> summands_)
: n(0),
summands(summands_)
summands(summands_)
{
#ifndef NDEBUG
for (unsigned i = 1; i <= terms.size (); i ++)
assert (terms[i]->is_free ());
for (unsigned i = 1; i <= summands.size (); i ++)
assert (summands[i]->is_free ());
#endif
for (unsigned i = 1; i <= terms.size (); i ++)
n += terms[i]->dim ();
for (unsigned i = 1; i <= summands.size (); i ++)
n += summands[i]->dim ();
}
~direct_sum () { }
unsigned dim () const { return n; }
unsigned free_rank () const { return n; }
// ???
grading generator_grading (unsigned i) const { abort (); }
void show_generator (unsigned i) const { abort (); }
grading generator_grading (unsigned i) const;
void show_generator (unsigned i) const;
R generator_ann (unsigned i) const { return R (0); }
void append_direct_summands (basedvector<ptr<const module<R> >, 1> &psummands) const
{
for (unsigned i = 1; i <= summands.size (); i ++)
psummands.append (summands[i]);
}
unsigned inject (unsigned i, unsigned g) const;
pair<unsigned, unsigned> project (unsigned g) const;
};
#endif
template<class R> grading
direct_sum<R>::generator_grading (unsigned i) const
{
pair<unsigned, unsigned> p = project (i);
return summands[p.first]->generator_grading (p.second);
}
template<class R> void
direct_sum<R>::show_generator (unsigned i) const
{
pair<unsigned, unsigned> p = project (i);
printf ("%d:", p.first);
return summands[p.first]->show_generator (p.second);
}
template<class R> unsigned
direct_sum<R>::inject (unsigned i, unsigned g) const
{
assert (i >= 1 && i <= summands.size ());
for (unsigned j = 1; j < i; j ++)
g += summands[j]->dim ();
return g;
}
template<class R> pair<unsigned, unsigned>
direct_sum<R>::project (unsigned g) const
{
assert (g <= n);
unsigned g0 = g;
for (unsigned j = 1; j <= summands.size (); j ++)
{
if (g <= summands[j]->dim ())
{
assert (inject (j, g) == g0);
return pair<unsigned, unsigned> (j, g);
}
else
g -= summands[j]->dim ();
}
abort (); // shouldn't get here
}
template<class R> ptr<const direct_sum<R> >
module<R>::add (basedvector<ptr<const module<R> >, 1> compound_summands) const
{
basedvector<ptr<const module<R> >, 1> summands;
for (unsigned i = 1; i <= compound_summands.size (); i ++)
compound_summands[i]->append_direct_summands (summands);
basedvector<unsigned, 1> summand_ids (summands.size ());
for (unsigned i = 1; i <= summands.size (); i ++)
summand_ids[i] = summands[i]->id;
pair<ptr<const direct_sum<R> > &, bool> p = direct_sum_idx.find (summand_ids);
if (!p.second)
p.first = new direct_sum<R> (summands);
return p.first;
}
template<class R>
class tensor_product : public module<R>
@ -597,6 +706,41 @@ class composition_impl : public map_impl<R>
}
};
template<class R>
class direct_sum_impl : public map_impl<R>
{
// f\oplus g
ptr<const map_impl<R> > f, g;
public:
direct_sum_impl (ptr<const map_impl<R> > f_, ptr<const map_impl<R> > g_)
: map_impl<R>(f_->from->add (g_->from),
f_->to->add (g_->to)),
f(f_),
g(g_)
{
}
linear_combination<R> column (unsigned i) const
{
pair<unsigned, unsigned> p = f->from->project (g->from, i);
linear_combination<R> r (this->to);
if (p.first == 1)
{
for (linear_combination_const_iter<R> j = f->column (p.second); j; j ++)
r.muladd (j.val (), f->to->inject_1 (j.key (), g->to));
}
else
{
assert (p.first == 2);
for (linear_combination_const_iter<R> j = g->column (p.second); j; j ++)
r.muladd (j.val (), f->to->inject_2 (g->to, j.key ()));
}
return r;
}
};
template<class R>
class tensor_impl : public map_impl<R>
{
@ -749,6 +893,13 @@ class mod_map
new composition_impl<R> (impl, m.impl));
}
// ??? in the sense of direct sum
mod_map add (const mod_map &m) const
{
return mod_map (IMPL,
new direct_sum_impl<R> (impl, m.impl));
}
mod_map tensor (const mod_map &m) const
{
return mod_map (IMPL,

4
main.cpp
View File

@ -193,7 +193,9 @@ main ()
gb[3].muladd (-6, 2);
mod_map<Q> g (gb);
display ("g:\n", g);
display ("f oplus g:\n", f.add (g));
map_builder<Q> hb (E, F);
hb[1].muladd (3, 2);
hb[2].muladd (-3, 1);