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mod_map is now just a wrapper for a map implementation. mod_map is

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now functional.  Added map_builder classes for imperatively
construction maps.  Initial collection of map implementations
(explicit, zero, 1, and composition.)
This commit is contained in:
Cotton Seed 2012-02-28 14:26:38 -05:00
parent 0ed96458e1
commit b337bd36ac
2 changed files with 340 additions and 266 deletions
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568
algebra/module.h
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@ -8,12 +8,6 @@ template<class R> class quotient_module;
template<class R> template<class R>
class module : public refcounted class module : public refcounted
{ {
typedef typename R::linear_combination linear_combination;
typedef typename R::linear_combination_const_iter linear_combination_const_iter;
typedef mod_map<R> Rmod_map;
typedef mod_span<R> Rmod_span;
public: public:
module () { } module () { }
module (const module &); // doesn't exist module (const module &); // doesn't exist
@ -51,10 +45,10 @@ class module : public refcounted
bool isomorphic (ptr<const module<R> > m) const; bool isomorphic (ptr<const module<R> > m) const;
ptr<const quotient_module<R> > quotient (const Rmod_span &span) const; ptr<const quotient_module<R> > quotient (const mod_span<R> &span) const;
ptr<const quotient_module<R> > quotient (ptr<const free_submodule<R> > m) const; ptr<const quotient_module<R> > quotient (ptr<const free_submodule<R> > m) const;
ptr<const free_submodule<R> > submodule (const Rmod_span &span) const; ptr<const free_submodule<R> > submodule (const mod_span<R> &span) const;
multivariate_laurentpoly<Z> free_poincare_polynomial () const; multivariate_laurentpoly<Z> free_poincare_polynomial () const;
multivariate_laurentpoly<Z> free_delta_poincare_polynomial () const; multivariate_laurentpoly<Z> free_delta_poincare_polynomial () const;
@ -115,16 +109,13 @@ class free_submodule : public module<R>
{ {
friend class module<R>; friend class module<R>;
typedef typename R::linear_combination linear_combination;
typedef typename R::linear_combination_const_iter linear_combination_const_iter;
ptr<const module<R> > parent; ptr<const module<R> > parent;
basedvector<linear_combination, 1> gens; basedvector<linear_combination<R>, 1> gens;
basedvector<unsigned, 1> pivots; basedvector<unsigned, 1> pivots;
public: public:
free_submodule (ptr<const module<R> > parent_, free_submodule (ptr<const module<R> > parent_,
basedvector<linear_combination, 1> gens_, basedvector<linear_combination<R>, 1> gens_,
basedvector<unsigned, 1> pivots_) basedvector<unsigned, 1> pivots_)
: parent(parent_), : parent(parent_),
gens(gens_), gens(gens_),
@ -142,12 +133,12 @@ class free_submodule : public module<R>
void show_generator (unsigned i) const { show (gens[i]); } void show_generator (unsigned i) const { show (gens[i]); }
R generator_ann (unsigned i) const { abort (); } R generator_ann (unsigned i) const { abort (); }
linear_combination inject_generator (unsigned i) const { return gens[i]; } linear_combination<R> inject_generator (unsigned i) const { return gens[i]; }
linear_combination inject (linear_combination v) const; linear_combination<R> inject (linear_combination<R> v) const;
mod_map<R> injection_map () const; mod_map<R> injection_map () const;
linear_combination restrict (linear_combination v0) const; linear_combination<R> restrict (linear_combination<R> v0) const;
ptr<const free_submodule<R> > restrict_submodule (ptr<const free_submodule<R> > m) const; ptr<const free_submodule<R> > restrict_submodule (ptr<const free_submodule<R> > m) const;
}; };
@ -156,9 +147,6 @@ class quotient_module : public module<R>
{ {
friend class module<R>; friend class module<R>;
typedef typename R::linear_combination linear_combination;
typedef typename R::linear_combination_const_iter linear_combination_const_iter;
ptr<const module<R> > parent; ptr<const module<R> > parent;
// note: these get filled in by module::quotient // note: these get filled in by module::quotient
@ -166,7 +154,7 @@ class quotient_module : public module<R>
basedvector<R, 1> ann; basedvector<R, 1> ann;
// parent lc representing i // parent lc representing i
basedvector<linear_combination, 1> rep; basedvector<linear_combination<R>, 1> rep;
// map from parent generator to lc in quotient // map from parent generator to lc in quotient
basedvector<map<unsigned, R>, 1> pi; basedvector<map<unsigned, R>, 1> pi;
@ -198,63 +186,219 @@ class quotient_module : public module<R>
return ann[i - r]; return ann[i - r];
} }
linear_combination project_generator (unsigned i) const linear_combination<R> project_generator (unsigned i) const
{ {
assert (i >= 1 && i <= parent->dim ()); assert (i >= 1 && i <= parent->dim ());
linear_combination r (this); linear_combination<R> r (this);
for (typename map<unsigned, R>::const_iter j = pi[i]; j; j ++) for (typename map<unsigned, R>::const_iter j = pi[i]; j; j ++)
r.muladd (j.val (), j.key ()); r.muladd (j.val (), j.key ());
return r; return r;
} }
linear_combination project (linear_combination v) const linear_combination<R> project (linear_combination<R> v) const
{ {
assert (v.m == parent); assert (v.m == parent);
linear_combination r (this); linear_combination<R> r (this);
for (linear_combination_const_iter i = v; i; i ++) for (linear_combination_const_iter<R> i = v; i; i ++)
r.muladd (i.val (), project_generator (i.key ())); r.muladd (i.val (), project_generator (i.key ()));
return r; return r;
} }
linear_combination generator_rep (unsigned i) const { return rep[i]; } linear_combination<R> generator_rep (unsigned i) const { return rep[i]; }
}; };
template<class R>
class map_impl : public refcounted
{
public:
ptr<const module<R> > from;
ptr<const module<R> > to;
public:
map_impl (const map_impl &); // doesn't exist
map_impl (ptr<const module<R> > fromto)
: from(fromto), to(fromto)
{ }
map_impl (ptr<const module<R> > from_, ptr<const module<R> > to_)
: from(from_), to(to_)
{ }
virtual ~map_impl () { }
map_impl &operator = (const map_impl &); // doesn't exist
virtual linear_combination<R> column (unsigned i) const = 0;
linear_combination<R> map (linear_combination<R> &lc) const
{
linear_combination<R> r;
for (linear_combination_const_iter<R> i = lc; i; i ++)
r.muladd (i.val (), column (i.key ()));
return r;
};
};
template<class R>
class explicit_map_impl : public map_impl<R>
{
basedvector<linear_combination<R>, 1> columns;
public:
explicit_map_impl (ptr<const module<R> > fromto,
basedvector<linear_combination<R>, 1> columns_)
: map_impl<R>(fromto),
columns(columns_)
{ }
explicit_map_impl (ptr<const module<R> > from, ptr<const module<R> > to,
basedvector<linear_combination<R>, 1> columns_)
: map_impl<R>(from, to),
columns(columns_)
{ }
~explicit_map_impl () { }
linear_combination<R> column (unsigned i) const { return columns[i]; }
};
template<class R>
class zero_map_impl : public map_impl<R>
{
public:
zero_map_impl (ptr<const module<R> > fromto) : map_impl<R>(fromto) { }
zero_map_impl (ptr<const module<R> > from, ptr<const module<R> > to) : map_impl<R>(from, to) { }
linear_combination<R> column (unsigned i) const { return linear_combination<R> (this->to); }
};
template<class R>
class id_map_impl : public map_impl<R>
{
public:
id_map_impl (ptr<const module<R> > fromto) : map_impl<R>(fromto) { }
id_map_impl (ptr<const module<R> > from, ptr<const module<R> > to) : map_impl<R>(from, to) { }
linear_combination<R> column (unsigned i) const
{
linear_combination<R> r (this->to);
r.muladd (1, i);
return r;
}
};
template<class R>
class composition_impl : public map_impl<R>
{
// f(g(x))
ptr<map_impl<R> > f, g;
public:
composition_impl (ptr<map_impl<R> > f_, ptr<map_impl<R> > g_)
: map_impl<R>(g_->from, f_->to),
f(f_),
g(g_)
{
assert (g->to == f->from);
}
linear_combination<R> column (unsigned i) const
{
return f->map (g->column (i));
}
};
template<class R>
class map_builder
{
public:
ptr<const module<R> > from, to;
basedvector<linear_combination<R>, 1> columns;
void init ();
public:
map_builder (ptr<const module<R> > fromto) : from(fromto), to(fromto) { init (); }
map_builder (ptr<const module<R> > fromto, int i) : from(fromto), to(fromto)
{
init ();
if (i == 1)
{
for (unsigned i = 1; i <= from->dim (); i ++)
columns[i].muladd (1, i);
}
else
assert (i == 0);
}
map_builder (ptr<const module<R> > from_, ptr<const module<R> > to_)
: from(from_), to(to_)
{
init ();
}
linear_combination<R> &operator [] (unsigned i) { return columns[i]; }
const linear_combination<R> &operator [] (unsigned i) const { return columns[i]; }
};
template<class R> void
map_builder<R>::init ()
{
columns.resize (from->dim ());
for (unsigned i = 1; i <= from->dim (); i ++)
columns[i] = linear_combination<R> (to);
}
template<class R> template<class R>
class mod_map class mod_map
{ {
typedef const module<R> Rmod; ptr<map_impl<R> > impl;
typedef typename R::linear_combination linear_combination;
// typedef typename R::linear_combination_iter linear_combination_iter;
typedef typename R::linear_combination_const_iter linear_combination_const_iter;
ptr<const Rmod> from, mod_map (ptr<map_impl<R> > impl_) : impl(impl_) { }
to;
basedvector<linear_combination, 1> columns;
public: public:
mod_map () { } mod_map () { }
mod_map (ptr<const Rmod> fromto); mod_map (const mod_map &m) : impl(m.impl) { }
mod_map (ptr<const Rmod> fromto, int i);
mod_map (ptr<const Rmod> from_, ptr<const Rmod> to_);
mod_map (ptr<const Rmod> from_,
ptr<const Rmod> to_,
basedvector<linear_combination, 1> columns_)
: from(from_), to(to_), columns(columns_)
{ }
mod_map (copy, const mod_map &m) mod_map (ptr<const module<R> > fromto) : impl(new zero_map_impl<R>(fromto)) { }
: from(m.from), to(m.to), columns(COPY, m.columns) mod_map (ptr<const module<R> > fromto, int i)
{ }
mod_map (copy2, const mod_map &m)
: from(m.from), to(m.to), columns(COPY2, m.columns)
{ }
bool operator == (const mod_map &m2) const
{ {
assert (from == m2.from); if (i == 1)
assert (to == m2.to); impl = new id_map_impl<R> (fromto);
return columns == m2.columns; else
{
assert (i == 0);
impl = new zero_map_impl<R> (fromto);
}
}
mod_map (ptr<const module<R> > from, ptr<const module<R> > to)
: impl(new zero_map_impl<R> (from, to))
{ }
mod_map (ptr<const module<R> > fromto,
basedvector<linear_combination<R>, 1> columns)
: impl(new explicit_map_impl<R> (fromto, columns))
{ }
mod_map (ptr<const module<R> > from,
ptr<const module<R> > to,
basedvector<linear_combination<R>, 1> columns)
: impl(new explicit_map_impl<R> (from, to, columns))
{ }
mod_map (const map_builder<R> &b)
: impl(new explicit_map_impl<R> (b.from, b.to, b.columns))
{ }
~mod_map () { }
mod_map &operator = (const mod_map &m) { impl = m.impl; return *this; }
bool operator == (const mod_map &m) const
{
assert (impl->from == m.impl->from);
assert (impl->to == m.impl->to);
for (unsigned i = 1; i <= impl->from->dim (); i ++)
{
if (impl->columns (i) != m.impl->columns (i))
return 0;
}
return 1;
} }
bool operator == (int x) const bool operator == (int x) const
@ -262,9 +406,9 @@ class mod_map
R c (x); R c (x);
assert (c == 0); assert (c == 0);
for (unsigned i = 1; i <= from->dim (); i ++) for (unsigned i = 1; i <= impl->from->dim (); i ++)
{ {
if (columns[i] != 0) if (impl->column (i) != 0)
return 0; return 0;
} }
return 1; return 1;
@ -272,24 +416,14 @@ class mod_map
bool operator != (int x) const { return !operator == (x); } bool operator != (int x) const { return !operator == (x); }
mod_map &operator = (const mod_map &m) linear_combination<R> column (unsigned i) const { return impl->column (i); }
{ linear_combination<R> operator [] (unsigned i) const { return impl->column (i); }
from = m.from;
to = m.to;
columns = m.columns;
return *this;
}
linear_combination &operator [] (unsigned i) { return columns[i]; } linear_combination<R> map (const linear_combination<R> &lc) const { return impl->map (lc); }
const linear_combination &operator [] (unsigned i) const { return columns[i]; } mod_map compose (const mod_map &m) const { return new composition_impl<R> (impl, m.impl); }
linear_combination map (const linear_combination &lc) const; // ?? add and other map operations should not be explicit
mod_map compose (const mod_map &m2) const; mod_map operator + (const mod_map &m) const;
mod_map &operator *= (R c);
mod_map &operator += (const mod_map &m2);
mod_map operator + (const mod_map &m2) const;
bool homogeneous () const; bool homogeneous () const;
void check_grading (grading delta) const; void check_grading (grading delta) const;
@ -316,6 +450,9 @@ class mod_map
mod_map induced_map_to (ptr<const quotient_module<R> > new_to); mod_map induced_map_to (ptr<const quotient_module<R> > new_to);
mod_map induced_map (ptr<const quotient_module<R> > new_fromto); mod_map induced_map (ptr<const quotient_module<R> > new_fromto);
// ???
basedvector<linear_combination<R>, 1> explicit_columns () const;
void show_self () const; void show_self () const;
void display_self () const; void display_self () const;
}; };
@ -323,40 +460,33 @@ class mod_map
template<class R> template<class R>
class mod_span class mod_span
{ {
typedef typename R::linear_combination linear_combination;
typedef typename R::linear_combination_const_iter linear_combination_const_iter;
public: public:
basedvector<linear_combination, 1> gens; basedvector<linear_combination<R>, 1> gens;
basedvector<unsigned, 1> pivots; basedvector<unsigned, 1> pivots;
public: public:
mod_span (ptr<const module<R> > mod, basedvector<linear_combination, 1> xs); mod_span (ptr<const module<R> > mod, basedvector<linear_combination<R>, 1> xs);
~mod_span () { } ~mod_span () { }
}; };
template<class R> template<class R>
class quotient_helper class quotient_helper
{ {
public:
typedef typename R::linear_combination linear_combination;
typedef typename R::linear_combination_const_iter linear_combination_const_iter;
public: public:
ptr<const module<R> > mod; ptr<const module<R> > mod;
// rows of the presentation matrix // rows of the presentation matrix
basedvector<linear_combination, 1> rows; basedvector<linear_combination<R>, 1> rows;
basedvector<linear_combination, 1> generators; basedvector<linear_combination<R>, 1> generators;
basedvector<linear_combination, 1> generators_inv; basedvector<linear_combination<R>, 1> generators_inv;
bool improve_pivot_row (unsigned i, unsigned j, unsigned i2); bool improve_pivot_row (unsigned i, unsigned j, unsigned i2);
bool improve_pivot_column (unsigned i, unsigned j, unsigned j2); bool improve_pivot_column (unsigned i, unsigned j, unsigned j2);
void improve_pivot (unsigned i, unsigned j); void improve_pivot (unsigned i, unsigned j);
public: public:
quotient_helper (ptr<const module<R> > mod_, basedvector<linear_combination, 1> rows); quotient_helper (ptr<const module<R> > mod_, basedvector<linear_combination<R>, 1> rows);
void normalize (); void normalize ();
}; };
@ -421,7 +551,7 @@ module<R>::isomorphic (ptr<const module<R> > m) const
template<class R> template<class R>
quotient_helper<R>::quotient_helper (ptr<const module<R> > mod_, quotient_helper<R>::quotient_helper (ptr<const module<R> > mod_,
basedvector<linear_combination, 1> rows_) basedvector<linear_combination<R>, 1> rows_)
: mod(mod_), : mod(mod_),
rows(rows_), rows(rows_),
generators(mod->dim ()), generators(mod->dim ()),
@ -431,11 +561,11 @@ quotient_helper<R>::quotient_helper (ptr<const module<R> > mod_,
for (unsigned i = 1; i <= mod->dim (); i ++) for (unsigned i = 1; i <= mod->dim (); i ++)
{ {
linear_combination v (mod); linear_combination<R> v (mod);
v.muladd (1, i); v.muladd (1, i);
generators[i] = v; generators[i] = v;
linear_combination vinv (mod); linear_combination<R> vinv (mod);
vinv.muladd (1, i); vinv.muladd (1, i);
generators_inv[i] = vinv; generators_inv[i] = vinv;
} }
@ -446,7 +576,7 @@ quotient_helper<R>::improve_pivot_row (unsigned i, unsigned j, unsigned i2)
{ {
assert (i != i2); assert (i != i2);
const linear_combination &r = rows[i], const linear_combination<R> &r = rows[i],
&r2 = rows[i2]; &r2 = rows[i2];
R rc = r(j), R rc = r(j),
r2c = r2(j); r2c = r2(j);
@ -484,17 +614,17 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
assert (j != j2); assert (j != j2);
#if 0 #if 0
basedvector<linear_combination, 1> orig_row_image (rows.size ()); basedvector<linear_combination<R>, 1> orig_row_image (rows.size ());
for (unsigned k = 1; k <= rows.size (); k ++) for (unsigned k = 1; k <= rows.size (); k ++)
{ {
linear_combination r (mod); linear_combination<R> r (mod);
for (linear_combination_const_iter l = rows[k]; l; l ++) for (linear_combination_const_iter<R> l = rows[k]; l; l ++)
r.muladd (l.val (), generators[l.key ()]); r.muladd (l.val (), generators[l.key ()]);
orig_row_image[k] = r; orig_row_image[k] = r;
} }
#endif #endif
const linear_combination &r = rows[i]; const linear_combination<R> &r = rows[i];
R rc = r(j), R rc = r(j),
rc2 = r(j2); rc2 = r(j2);
@ -510,7 +640,7 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
R q = rc2.div (rc); R q = rc2.div (rc);
for (unsigned k = 1; k <= rows.size (); k ++) for (unsigned k = 1; k <= rows.size (); k ++)
{ {
linear_combination &rk = rows[k]; linear_combination<R> &rk = rows[k];
rk.mulsub (rk(j) * q, j2); rk.mulsub (rk(j) * q, j2);
} }
@ -525,7 +655,7 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
for (unsigned k = 1; k <= rows.size (); k ++) for (unsigned k = 1; k <= rows.size (); k ++)
{ {
linear_combination &rk = rows[k]; linear_combination<R> &rk = rows[k];
R rkc = rk(j), R rkc = rk(j),
rkc2 = rk(j2); rkc2 = rk(j2);
@ -535,7 +665,7 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
j2); j2);
} }
linear_combination g = generators[j], linear_combination<R> g = generators[j],
g2 = generators[j2]; g2 = generators[j2];
assert (g.hq () == g2.hq ()); assert (g.hq () == g2.hq ());
@ -546,8 +676,8 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
#if 0 #if 0
for (unsigned k = 1; k <= rows.size (); k ++) for (unsigned k = 1; k <= rows.size (); k ++)
{ {
linear_combination r2 (mod); linear_combination<R> r2 (mod);
for (linear_combination_const_iter l = rows[k]; l; l ++) for (linear_combination_const_iter<R> l = rows[k]; l; l ++)
r2.muladd (l.val (), generators[l.key ()]); r2.muladd (l.val (), generators[l.key ()]);
assert (r2 == orig_row_image[k]); assert (r2 == orig_row_image[k]);
} }
@ -555,7 +685,7 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
for (unsigned k = 1; k <= mod->dim (); k ++) for (unsigned k = 1; k <= mod->dim (); k ++)
{ {
linear_combination &ginv = generators_inv[k]; linear_combination<R> &ginv = generators_inv[k];
R d = ginv(j), R d = ginv(j),
d2 = ginv(j2); d2 = ginv(j2);
@ -567,11 +697,11 @@ quotient_helper<R>::improve_pivot_column (unsigned i, unsigned j, unsigned j2)
#if 0 #if 0
for (unsigned k = 1; k <= mod->dim (); k ++) for (unsigned k = 1; k <= mod->dim (); k ++)
{ {
linear_combination r (mod); linear_combination<R> r (mod);
r.muladd (1, k); r.muladd (1, k);
linear_combination r2 (mod); linear_combination<R> r2 (mod);
for (linear_combination_const_iter l = generators_inv[k]; l; l ++) for (linear_combination_const_iter<R> l = generators_inv[k]; l; l ++)
r2.muladd (l.val (), generators[l.key ()]); r2.muladd (l.val (), generators[l.key ()]);
assert (r == r2); assert (r == r2);
@ -608,7 +738,7 @@ quotient_helper<R>::improve_pivot (unsigned i, unsigned j)
#if 0 #if 0
L: L:
for (linear_combination_const_iter k = rows[i]; k; k ++) for (linear_combination_const_iter<R> k = rows[i]; k; k ++)
{ {
if (k.key () != j) if (k.key () != j)
{ {
@ -679,7 +809,7 @@ quotient_helper<R>::normalize ()
} }
template<class R> ptr<const quotient_module<R> > template<class R> ptr<const quotient_module<R> >
module<R>::quotient (const Rmod_span &span) const module<R>::quotient (const mod_span<R> &span) const
{ {
unsigned n = dim (); unsigned n = dim ();
@ -701,7 +831,7 @@ module<R>::quotient (const Rmod_span &span) const
ptr<quotient_module<R> > Q = new quotient_module<R> (this); ptr<quotient_module<R> > Q = new quotient_module<R> (this);
unsigned quot_r = 0; unsigned quot_r = 0;
basedvector<linear_combination, 1> quot_rep; basedvector<linear_combination<R>, 1> quot_rep;
basedvector<unsigned, 1> generator_quot_gen (n); basedvector<unsigned, 1> generator_quot_gen (n);
for (unsigned i = 1; i <= n; i ++) for (unsigned i = 1; i <= n; i ++)
@ -737,7 +867,7 @@ module<R>::quotient (const Rmod_span &span) const
for (unsigned i = 1; i <= n; i ++) for (unsigned i = 1; i <= n; i ++)
{ {
map<unsigned, R> v; map<unsigned, R> v;
for (linear_combination_const_iter j = h.generators_inv[i]; j; j ++) for (linear_combination_const_iter<R> j = h.generators_inv[i]; j; j ++)
{ {
unsigned qg = generator_quot_gen[j.key ()]; unsigned qg = generator_quot_gen[j.key ()];
if (qg) if (qg)
@ -771,7 +901,7 @@ module<R>::quotient (ptr<const free_submodule<R> > m) const
} }
template<class R> ptr<const free_submodule<R> > template<class R> ptr<const free_submodule<R> >
module<R>::submodule (const Rmod_span &span) const module<R>::submodule (const mod_span<R> &span) const
{ {
assert (free_rank () == dim ()); assert (free_rank () == dim ());
return new free_submodule<R> (this, return new free_submodule<R> (this,
@ -851,11 +981,11 @@ module<R>::display_self () const
} }
} }
template<class R> typename R::linear_combination template<class R> linear_combination<R>
free_submodule<R>::inject (linear_combination v) const free_submodule<R>::inject (linear_combination<R> v) const
{ {
linear_combination r (parent); linear_combination<R> r (parent);
for (linear_combination_const_iter i = v; i; i ++) for (linear_combination_const_iter<R> i = v; i; i ++)
r.muladd (i.val (), gens[i.key ()]); r.muladd (i.val (), gens[i.key ()]);
return r; return r;
} }
@ -869,78 +999,78 @@ free_submodule<R>::injection_map () const
template<class R> mod_map<R> template<class R> mod_map<R>
mod_map<R>::induced_map_to (ptr<const quotient_module<R> > new_to) mod_map<R>::induced_map_to (ptr<const quotient_module<R> > new_to)
{ {
assert (new_to->parent_module () == to); assert (new_to->parent_module () == impl->to);
mod_map r (from, new_to); basedvector<linear_combination<R>, 1> v (impl->from->dim ());
for (unsigned i = 1; i <= from->dim (); i ++) for (unsigned i = 1; i <= impl->from->dim (); i ++)
r[i] = new_to->project (columns[i]); v[i] = new_to->project (column (i));
return r; return new explicit_map_impl<R> (impl->from, new_to, v);
} }
template<class R> mod_map<R> template<class R> mod_map<R>
mod_map<R>::induced_map (ptr<const quotient_module<R> > new_fromto) mod_map<R>::induced_map (ptr<const quotient_module<R> > new_fromto)
{ {
assert (from == new_fromto->parent_module ()); assert (impl->from == new_fromto->parent_module ());
assert (to == new_fromto->parent_module ()); assert (impl->to == new_fromto->parent_module ());
// ??? doesn't check induced map is well-defined // ??? doesn't check induced map is well-defined
mod_map r (new_fromto, new_fromto); basedvector<linear_combination<R>, 1> v (new_fromto->dim ());
for (unsigned i = 1; i <= new_fromto->dim (); i ++) for (unsigned i = 1; i <= new_fromto->dim (); i ++)
r[i] = new_fromto->project (map (new_fromto->generator_rep (i))); v[i] = new_fromto->project (map (new_fromto->generator_rep (i)));
return r; return new explicit_map_impl<R> (new_fromto, v);
} }
template<class R> mod_map<R> template<class R> mod_map<R>
mod_map<R>::restrict_from (ptr<const free_submodule<R> > new_from) const mod_map<R>::restrict_from (ptr<const free_submodule<R> > new_from) const
{ {
assert (new_from->parent_module () == from); assert (new_from->parent_module () == impl->from);
mod_map<R> r (new_from, to); basedvector<linear_combination<R>, 1> v (new_from->dim ());
for (unsigned i = 1; i <= new_from->dim (); i ++) for (unsigned i = 1; i <= new_from->dim (); i ++)
r[i] = map (new_from->inject_generator (i)); v[i] = map (new_from->inject_generator (i));
return r; return new explicit_map_impl<R> (new_from, impl->to, v);
} }
template<class R> mod_map<R> template<class R> mod_map<R>
mod_map<R>::restrict_to (ptr<const free_submodule<R> > new_to) const mod_map<R>::restrict_to (ptr<const free_submodule<R> > new_to) const
{ {
assert (new_to->parent_module () == to); assert (new_to->parent_module () == impl->to);
mod_map<R> r (from, new_to); basedvector<linear_combination<R>, 1> v (impl->from->dim ());
for (unsigned i = 1; i <= from->dim (); i ++) for (unsigned i = 1; i <= impl->from->dim (); i ++)
r[i] = new_to->restrict (columns[i]); v[i] = new_to->restrict (column (i));
return r; return new explicit_map_impl<R> (impl->from, new_to, v);
} }
template<class R> mod_map<R> template<class R> mod_map<R>
mod_map<R>::restrict (ptr<const free_submodule<R> > new_from, mod_map<R>::restrict (ptr<const free_submodule<R> > new_from,
ptr<const free_submodule<R> > new_to) const ptr<const free_submodule<R> > new_to) const
{ {
assert (new_from->parent_module () == from); assert (new_from->parent_module () == impl->from);
assert (new_to->parent_module () == to); assert (new_to->parent_module () == impl->to);
mod_map<R> r (new_from, new_to); basedvector<linear_combination<R>, 1> v (new_from->dim ());
for (unsigned i = 1; i <= new_from->dim (); i ++) for (unsigned i = 1; i <= new_from->dim (); i ++)
r[i] = new_to->restrict (map (new_from->inject_generator (i))); v[i] = new_to->restrict (map (new_from->inject_generator (i)));
return r; return new explicit_map_impl<R> (new_from, new_to, v);
} }
template<class R> typename R::linear_combination template<class R> linear_combination<R>
free_submodule<R>::restrict (linear_combination v0) const free_submodule<R>::restrict (linear_combination<R> v0) const
{ {
assert (v0.m == parent); assert (v0.m == parent);
linear_combination v (COPY, v0); linear_combination<R> v (COPY, v0);
linear_combination r (this); linear_combination<R> r (this);
for (unsigned i = 1; i <= gens.size (); i ++) for (unsigned i = 1; i <= gens.size (); i ++)
{ {
unsigned j = pivots[i]; unsigned j = pivots[i];
R vc = v(j); R vc = v(j);
if (vc != 0) if (vc != 0)
{ {
const linear_combination &g = gens[i]; const linear_combination<R> &g = gens[i];
R gc = g(j); R gc = g(j);
assert (gc | vc); assert (gc | vc);
@ -961,7 +1091,7 @@ free_submodule<R>::restrict_submodule (ptr<const free_submodule<R> > m) const
{ {
assert (m->parent == parent); assert (m->parent == parent);
basedvector<linear_combination, 1> span (m->dim ()); basedvector<linear_combination<R>, 1> span (m->dim ());
for (unsigned i = 1; i <= m->dim (); i ++) for (unsigned i = 1; i <= m->dim (); i ++)
span[i] = restrict (m->inject_generator (i)); span[i] = restrict (m->inject_generator (i));
@ -969,66 +1099,18 @@ free_submodule<R>::restrict_submodule (ptr<const free_submodule<R> > m) const
return submodule (span2); return submodule (span2);
} }
template<class R>
mod_map<R>::mod_map (ptr<const Rmod> fromto)
: from(fromto),
to(fromto),
columns(fromto->dim ())
{
for (unsigned i = 1; i <= from->dim (); i ++)
columns[i] = linear_combination (to);
}
template<class R>
mod_map<R>::mod_map (ptr<const Rmod> fromto, int i)
: from(fromto),
to(fromto),
columns(fromto->dim ())
{
assert (i == 0 || i == 1);
for (unsigned j = 1; j <= from->dim (); j ++)
columns[j] = linear_combination (to);
if (i == 1)
{
for (unsigned i = 1; i <= fromto->dim (); i ++)
columns[i] += i;
}
}
template<class R>
mod_map<R>::mod_map (ptr<const Rmod> from_, ptr<const Rmod> to_)
: from(from_),
to(to_),
columns(from_->dim ())
{
for (unsigned i = 1; i <= from->dim (); i ++)
columns[i] = linear_combination (to);
}
template<class R> typename R::linear_combination
mod_map<R>::map (const linear_combination &lc) const
{
assert (lc.m == from);
linear_combination r (to);
for (linear_combination_const_iter i = lc; i; i ++)
r.muladd (i.val (), columns[i.key ()]);
return r;
}
template<class R> bool template<class R> bool
mod_map<R>::homogeneous () const mod_map<R>::homogeneous () const
{ {
for (unsigned i = 1; i <= from->dim (); i ++) for (unsigned i = 1; i <= impl->from->dim (); i ++)
{ {
if (columns[i] != 0) if (column (i) != 0)
{ {
grading dhq = columns[i].hq () - from->generator_grading (i); grading dhq = column (i).hq () - impl->from->generator_grading (i);
for (unsigned j = i + 1; j <= from->dim (); j ++) for (unsigned j = i + 1; j <= impl->from->dim (); j ++)
{ {
if (columns[j] != 0 if (column (j) != 0
&& dhq != columns[j].hq () - from->generator_grading (j)) && dhq != column (j).hq () - impl->from->generator_grading (j))
return 0; return 0;
} }
return 1; return 1;
@ -1040,69 +1122,44 @@ mod_map<R>::homogeneous () const
template<class R> void template<class R> void
mod_map<R>::check_grading (grading delta) const mod_map<R>::check_grading (grading delta) const
{ {
for (unsigned i = 1; i <= from->dim (); i ++) for (unsigned i = 1; i <= impl->from->dim (); i ++)
{ {
if (columns[i] != 0) if (column (i) != 0)
assert (columns[i].hq () - from->generator_grading (i) == delta); assert (column (i).hq () - impl->from->generator_grading (i) == delta);
} }
} }
template<class R> mod_map<R> template<class R> mod_map<R>
mod_map<R>::compose (const mod_map<R> &m2) const mod_map<R>::operator + (const mod_map &m) const
{ {
assert (m2.to == from); assert (impl->from == m.impl->from && impl->to == m.impl->to);
basedvector<linear_combination, 1> r (m2.from->dim ()); basedvector<linear_combination<R>, 1> v (impl->from->dim ());
for (unsigned i = 1; i <= m2.from->dim (); i ++) for (unsigned i = 1; i <= m.impl->from->dim (); i ++)
r[i] = map (m2[i]); v[i] = column (i) + m.columns (i);
return mod_map (m2.from, to, r); return explicit_map_impl<R> (impl->from, impl->to, v);
}
template<class R> mod_map<R> &
mod_map<R>::operator += (const mod_map &m2)
{
assert (from == m2.from && to == m2.to);
for (unsigned i = 1; i <= from->dim (); i ++)
columns[i] += m2.columns[i];
return *this;
}
template<class R> mod_map<R>
mod_map<R>::operator + (const mod_map &m2) const
{
assert (from == m2.from && to == m2.to);
basedvector<linear_combination, 1> r (from->dim ());
for (unsigned i = 1; i <= m2.from->dim (); i ++)
r[i] = columns[i] + m2.columns[i];
return mod_map (from, to, r);
}
template<class R> mod_map<R> &
mod_map<R>::operator *= (R c)
{
for (unsigned i = 1; i <= from->dim (); i ++)
columns[i] *= c;
return *this;
} }
template<class R> ptr<const free_submodule<R> > template<class R> ptr<const free_submodule<R> >
mod_map<R>::kernel () const mod_map<R>::kernel () const
{ {
basedvector<linear_combination, 1> from_xs (from->dim ()); ptr<const module<R> > from = impl->from,
to = impl->to;
basedvector<linear_combination<R>, 1> from_xs (from->dim ());
for (unsigned i = 1; i <= to->dim (); i ++) for (unsigned i = 1; i <= to->dim (); i ++)
{ {
linear_combination x (from); linear_combination<R> x (from);
x.muladd (1, i); x.muladd (1, i);
from_xs[i] = x; from_xs[i] = x;
} }
basedvector<linear_combination, 1> to_xs (COPY2, columns); basedvector<linear_combination<R>, 1> to_xs (COPY2, explicit_columns ());
for (unsigned i = 1; i <= to->dim (); i ++) for (unsigned i = 1; i <= to->dim (); i ++)
{ {
linear_combination from_v (from), linear_combination<R> from_v (from),
to_v (to); to_v (to);
for (unsigned j = 1; j <= to_xs.size (); j ++) for (unsigned j = 1; j <= to_xs.size (); j ++)
@ -1111,7 +1168,7 @@ mod_map<R>::kernel () const
if (to_vc.is_unit ()) if (to_vc.is_unit ())
break; break;
linear_combination &to_x = to_xs[j], linear_combination<R> &to_x = to_xs[j],
&from_x = from_xs[j]; &from_x = from_xs[j];
R to_xc = to_x(i); R to_xc = to_x(i);
if (! (to_vc | to_xc)) if (! (to_vc | to_xc))
@ -1131,7 +1188,7 @@ mod_map<R>::kernel () const
{ {
for (unsigned j = 1; j <= to_xs.size (); j ++) for (unsigned j = 1; j <= to_xs.size (); j ++)
{ {
linear_combination &to_x = to_xs[j], linear_combination<R> &to_x = to_xs[j],
&from_x = from_xs[j]; &from_x = from_xs[j];
R to_xc = to_x(i); R to_xc = to_x(i);
if (to_xc != 0) if (to_xc != 0)
@ -1155,15 +1212,15 @@ mod_map<R>::kernel () const
template<class R> ptr<const free_submodule<R> > template<class R> ptr<const free_submodule<R> >
mod_map<R>::image () const mod_map<R>::image () const
{ {
mod_span<R> span (to, columns); mod_span<R> span (impl->to, explicit_columns ());
return to->submodule (span); return impl->to->submodule (span);
} }
template<class R> ptr<const quotient_module<R> > template<class R> ptr<const quotient_module<R> >
mod_map<R>::cokernel () const mod_map<R>::cokernel () const
{ {
mod_span<R> span (to, columns); mod_span<R> span (impl->to, explicit_columns ());
return to->quotient (span); return impl->to->quotient (span);
} }
template<class R> ptr<const quotient_module<R> > template<class R> ptr<const quotient_module<R> >
@ -1182,17 +1239,26 @@ mod_map<R>::homology () const
return ker->quotient (im2); return ker->quotient (im2);
} }
template<class R> basedvector<linear_combination<R>, 1>
mod_map<R>::explicit_columns () const
{
basedvector<linear_combination<R>, 1> v;
for (unsigned i = 1; i <= impl->from->dim (); i ++)
v[i] = column (i);
return v;
}
template<class R> template<class R>
mod_span<R>::mod_span (ptr<const module<R> > mod, mod_span<R>::mod_span (ptr<const module<R> > mod,
basedvector<linear_combination, 1> xs0) basedvector<linear_combination<R>, 1> xs0)
{ {
assert (mod->free_rank () == mod->dim ()); assert (mod->free_rank () == mod->dim ());
basedvector<linear_combination, 1> xs (COPY2, xs0); basedvector<linear_combination<R>, 1> xs (COPY2, xs0);
for (unsigned i = 1; i <= mod->dim (); i ++) for (unsigned i = 1; i <= mod->dim (); i ++)
{ {
linear_combination v (mod); linear_combination<R> v (mod);
for (unsigned j = 1; j <= xs.size (); j ++) for (unsigned j = 1; j <= xs.size (); j ++)
{ {
@ -1200,7 +1266,7 @@ mod_span<R>::mod_span (ptr<const module<R> > mod,
if (vc.is_unit ()) if (vc.is_unit ())
break; break;
linear_combination &x = xs[j]; linear_combination<R> &x = xs[j];
R xc = x(i); R xc = x(i);
if (! (vc | xc)) if (! (vc | xc))
@ -1219,7 +1285,7 @@ mod_span<R>::mod_span (ptr<const module<R> > mod,
{ {
for (unsigned j = 1; j <= xs.size (); j ++) for (unsigned j = 1; j <= xs.size (); j ++)
{ {
linear_combination &x = xs[j]; linear_combination<R> &x = xs[j];
R xc = x(i); R xc = x(i);
if (xc != 0) if (xc != 0)
{ {
@ -1242,19 +1308,19 @@ template<class R> void
mod_map<R>::show_self () const mod_map<R>::show_self () const
{ {
printf ("mod_map "); printf ("mod_map ");
show (*from); show (*impl->from);
printf (" -> "); printf (" -> ");
show (*to); show (*impl->to);
} }
template<class R> void template<class R> void
mod_map<R>::display_self () const mod_map<R>::display_self () const
{ {
show_self (); newline (); show_self (); newline ();
for (unsigned i = 1; i <= from->dim (); i ++) for (unsigned i = 1; i <= impl->from->dim (); i ++)
{ {
printf (" %d: ", i); printf (" %d: ", i);
show (columns[i]); show (column (i));
newline (); newline ();
} }
} }

38
cube_impl.h
View File

@ -30,7 +30,7 @@ cube<R>::compute_map (unsigned dh, unsigned max_n,
unsigned to_reverse, unsigned to_reverse,
const map_rules &rules) const const map_rules &rules) const
{ {
mod_map<R> r (khC); map_builder<R> b (khC);
smoothing from_s (kd); smoothing from_s (kd);
smoothing to_s (kd); smoothing to_s (kd);
@ -167,7 +167,7 @@ cube<R>::compute_map (unsigned dh, unsigned max_n,
assert (!unsigned_bittest (v_to, p)); assert (!unsigned_bittest (v_to, p));
} }
r[generator (fromstate, v_from)].muladd b[generator (fromstate, v_from)].muladd
(sign, generator (tostate, v_to)); (sign, generator (tostate, v_to));
} }
} }
@ -180,7 +180,7 @@ cube<R>::compute_map (unsigned dh, unsigned max_n,
fprintf (stderr, "computing differential done.\n"); fprintf (stderr, "computing differential done.\n");
} }
return r; return mod_map<R> (b);
} }
class d_rules : public map_rules class d_rules : public map_rules
@ -247,7 +247,7 @@ cube<R>::compute_nu () const
{ {
assert (!markedp_only); assert (!markedp_only);
mod_map<R> nu (khC); map_builder<R> b (khC);
for (unsigned i = 0, j = 1; i < n_resolutions; i ++) for (unsigned i = 0, j = 1; i < n_resolutions; i ++)
{ {
smoothing s (kd, smallbitset (n_crossings, i)); smoothing s (kd, smallbitset (n_crossings, i));
@ -258,11 +258,14 @@ cube<R>::compute_nu () const
if (!unsigned_bittest (j, k)) if (!unsigned_bittest (j, k))
{ {
unsigned j2 = unsigned_bitset (j, k); unsigned j2 = unsigned_bitset (j, k);
nu[generator (i, j)].muladd (1, generator (i, j2)); b[generator (i, j)].muladd (1, generator (i, j2));
} }
} }
} }
} }
mod_map<R> nu (b);
nu.check_grading (0, 2); nu.check_grading (0, 2);
assert (nu.compose (nu) == 0); assert (nu.compose (nu) == 0);
@ -275,7 +278,7 @@ cube<R>::compute_X (unsigned p) const
assert (!markedp_only); assert (!markedp_only);
/* define Khovanov's map X */ /* define Khovanov's map X */
mod_map<R> X (khC); map_builder<R> b (khC);
for (unsigned i = 0, j = 1; i < n_resolutions; i ++) for (unsigned i = 0, j = 1; i < n_resolutions; i ++)
{ {
smoothing r (kd, smallbitset (n_crossings, i)); smoothing r (kd, smallbitset (n_crossings, i));
@ -285,10 +288,12 @@ cube<R>::compute_X (unsigned p) const
if (unsigned_bittest (j, s)) if (unsigned_bittest (j, s))
{ {
unsigned j2 = unsigned_bitclear (j, s); unsigned j2 = unsigned_bitclear (j, s);
X[generator (i, j)].muladd (1, generator (i, j2)); b[generator (i, j)].muladd (1, generator (i, j2));
} }
} }
} }
mod_map<R> X (b);
assert (X.compose (X) == 0); assert (X.compose (X) == 0);
return X; return X;
@ -297,7 +302,7 @@ cube<R>::compute_X (unsigned p) const
template<class R> mod_map<R> template<class R> mod_map<R>
cube<R>::H_i (unsigned c) cube<R>::H_i (unsigned c)
{ {
mod_map<R> H_c (khC, 0); mod_map<R> b (khC, 0);
for (unsigned i = 0; i < n_resolutions; i ++) for (unsigned i = 0; i < n_resolutions; i ++)
{ {
if (unsigned_bittest (i, c)) if (unsigned_bittest (i, c))
@ -323,7 +328,7 @@ cube<R>::H_i (unsigned c)
j2 = unsigned_bitset (j2, to_s.edge_circle[from_circle_edge_rep[s]]); j2 = unsigned_bitset (j2, to_s.edge_circle[from_circle_edge_rep[s]]);
} }
linear_combination &v = H_c[generator (i, j)]; linear_combination &v = b[generator (i, j)];
if (from == to if (from == to
&& unsigned_bittest (j, from)) && unsigned_bittest (j, from))
{ {
@ -343,6 +348,9 @@ cube<R>::H_i (unsigned c)
} }
} }
} }
mod_map<R> H_c (b);
H_c.check_grading (grading (1, 2)); H_c.check_grading (grading (1, 2));
return H_c; return H_c;
@ -522,7 +530,7 @@ twisted_cube<F>::compute_twisted_map (basedvector<int, 1> edge_weight,
unsigned dh, unsigned to_reverse, unsigned dh, unsigned to_reverse,
const twisted_map_rules &rules) const const twisted_map_rules &rules) const
{ {
mod_map<R> r (c.khC); map_builder<R> b (c.khC);
knot_diagram &kd = c.kd; knot_diagram &kd = c.kd;
unsigned n_crossings = c.n_crossings; unsigned n_crossings = c.n_crossings;
@ -653,7 +661,7 @@ twisted_cube<F>::compute_twisted_map (basedvector<int, 1> edge_weight,
} }
// ??? sign // ??? sign
r[c.generator (fromstate, v_from)].muladd b[c.generator (fromstate, v_from)].muladd
(polynomial<F> (1) + polynomial<F> (1, w), (polynomial<F> (1) + polynomial<F> (1, w),
c.generator (tostate, v_to)); c.generator (tostate, v_to));
} }
@ -661,7 +669,7 @@ twisted_cube<F>::compute_twisted_map (basedvector<int, 1> edge_weight,
} }
} }
return r; return mod_map<R> (b);
} }
class twisted_barE_rules : public twisted_map_rules class twisted_barE_rules : public twisted_map_rules
@ -692,7 +700,7 @@ twisted_cube<F>::compute_twisted_barE (basedvector<int, 1> edge_weight,
template<class F> mod_map<typename twisted_cube<F>::R> template<class F> mod_map<typename twisted_cube<F>::R>
twisted_cube<F>::twisted_d0 (basedvector<int, 1> edge_weight) const twisted_cube<F>::twisted_d0 (basedvector<int, 1> edge_weight) const
{ {
mod_map<R> d0 (c.khC); map_builder<R> b (c.khC);
for (unsigned i = 0, j = 1; i < c.n_resolutions; i ++) for (unsigned i = 0, j = 1; i < c.n_resolutions; i ++)
{ {
smoothing r (c.kd, smallbitset (c.n_crossings, i)); smoothing r (c.kd, smallbitset (c.n_crossings, i));
@ -718,11 +726,11 @@ twisted_cube<F>::twisted_d0 (basedvector<int, 1> edge_weight) const
w += edge_weight[k]; w += edge_weight[k];
unsigned j2 = unsigned_bitclear (j, s); unsigned j2 = unsigned_bitclear (j, s);
d0[c.generator (i, j)].muladd (polynomial<F> (1) + polynomial<F> (1, w), b[c.generator (i, j)].muladd (polynomial<F> (1) + polynomial<F> (1, w),
c.generator (i, j2)); c.generator (i, j2));
} }
} }
} }
} }
return d0; return mod_map<R> (b);
} }