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Fixeds to module reader (not carry unnecessary refcounts?). main

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checks for homotopy type differences.  Added planar_diagram::{show,
display}_knottheory.
This commit is contained in:
Cotton Seed 2012-05-21 10:09:17 -04:00
parent a0f94aad47
commit 3797868325
6 changed files with 565 additions and 107 deletions
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25
algebra/module.h
View File

@ -21,7 +21,7 @@ class module : public refcounted
static unsigned id_counter; static unsigned id_counter;
static basedvector<ptr<const module<R> >, 1> id_module; static map<unsigned, ptr<const module<R> > > reader_id_module;
static map<basedvector<unsigned, 1>, static map<basedvector<unsigned, 1>,
ptr<const direct_sum<R> > > direct_sum_idx; ptr<const direct_sum<R> > > direct_sum_idx;
@ -35,9 +35,6 @@ class module : public refcounted
{ {
id_counter ++; id_counter ++;
id = id_counter; id = id_counter;
id_module.append (this);
assert (id_module.size () == id_counter);
} }
module (const module &) = delete; module (const module &) = delete;
virtual ~module () { } virtual ~module () { }
@ -162,7 +159,7 @@ class module : public refcounted
template<class R> unsigned module<R>::id_counter = 0; template<class R> unsigned module<R>::id_counter = 0;
template<class R> basedvector<ptr<const module<R> >, 1> module<R>::id_module; template<class R> map<unsigned, ptr<const module<R> > > module<R>::reader_id_module;
template<class R> map<basedvector<unsigned, 1>, template<class R> map<basedvector<unsigned, 1>,
ptr<const direct_sum<R> > > module<R>::direct_sum_idx; ptr<const direct_sum<R> > > module<R>::direct_sum_idx;
@ -507,7 +504,9 @@ class explicit_module : public module<R>
basedvector<R, 1> ann_, basedvector<R, 1> ann_,
basedvector<grading, 1> hq_) basedvector<grading, 1> hq_)
: r(r_), ann(ann_), hq(hq_) : r(r_), ann(ann_), hq(hq_)
{ } {
assert (hq.size () == r + ann.size ());
}
explicit explicit_module (unsigned r_, basedvector<grading, 1> hq_) : r(r_), hq(hq_) { } explicit explicit_module (unsigned r_, basedvector<grading, 1> hq_) : r(r_), hq(hq_) { }
~explicit_module () { } ~explicit_module () { }
@ -952,6 +951,7 @@ class mod_map
// inj : im -> to // inj : im -> to
ptr<const free_submodule<R> > image () const; ptr<const free_submodule<R> > image () const;
ptr<const free_submodule<R> > image (basedvector<linear_combination<R>, 1> vs) const;
ptr<const quotient_module<R> > cokernel () const; ptr<const quotient_module<R> > cokernel () const;
@ -1874,6 +1874,15 @@ mod_map<R>::image () const
return impl->to->submodule (span); return impl->to->submodule (span);
} }
template<class R> ptr<const free_submodule<R> >
mod_map<R>::image (basedvector<linear_combination<R>, 1> vs) const
{
mod_span<R> span (impl->from, vs);
ptr<const free_submodule<R> > s = impl->from->submodule (span);
mod_map<R> r = restrict_from (s);
return r.image ();
}
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
{ {
@ -2034,11 +2043,13 @@ reader::read_mod ()
ptr<const module<R> > m = new explicit_module<R> (r, ann, gr); ptr<const module<R> > m = new explicit_module<R> (r, ann, gr);
ar->io_id_id.push ((unsigned)(-io_id), m->id); ar->io_id_id.push ((unsigned)(-io_id), m->id);
module<R>::reader_id_module.push (m->id, m);
return m; return m;
} }
else else
{ {
unsigned id = ar->io_id_id(io_id); unsigned id = ar->io_id_id(io_id);
return module<R>::id_module[id]; return module<R>::reader_id_module(id);
} }
} }

50
cube_impl.h
View File

@ -410,11 +410,59 @@ cube<R>::cube (knot_diagram &kd_, bool markedp_only_)
// printf ("smoothings:\n"); // printf ("smoothings:\n");
unsigned max = 0;
smoothing s (kd); smoothing s (kd);
for (unsigned i = 0; i < n_resolutions; i ++) for (unsigned i = 0; i < n_resolutions; i ++)
{ {
smallbitset state (n_crossings, i); smallbitset state (n_crossings, i);
s.init (kd, state); s.init (kd, state);
#if 1
unsigned fromstate = i;
smoothing &from_s = s;
unsigned n_zerocrossings = n_crossings - unsigned_bitcount (fromstate);
unsigned n_cobordisms = ((unsigned)1) << n_zerocrossings;
for (unsigned j = 0; j < n_cobordisms; j ++)
{
unsigned tostate = unsigned_pack (n_crossings, fromstate, j);
unsigned crossings = tostate & ~fromstate;
smoothing to_s (kd, smallbitset (n_crossings, tostate));
set<unsigned> starting_circles,
ending_circles;
for (unsigned_const_iter k = crossings; k; k ++)
{
unsigned c = k.val ();
unsigned starting_from = s.ept_circle (kd, kd.crossings[c][2]),
starting_to = s.ept_circle (kd, kd.crossings[c][4]);
starting_circles += starting_from;
starting_circles += starting_to;
unsigned ending_from = to_s.ept_circle (kd, kd.crossings[c][2]),
ending_to = to_s.ept_circle (kd, kd.crossings[c][4]);
ending_circles += ending_from;
ending_circles += ending_to;
}
if (starting_circles.card () == 1
&& ending_circles.card () == 1)
{
unsigned k = unsigned_bitcount (crossings);
if (k > max)
max = k;
#if 0
s.show_self (kd, state);
printf (" crossings "); show (smallbitset (n_crossings, crossings));
newline ();
#endif
}
}
#endif
resolution_circles[i] = s.n_circles; resolution_circles[i] = s.n_circles;
resolution_generator1[i] = n_generators + 1; resolution_generator1[i] = n_generators + 1;
n_generators += s.num_generators (markedp_only); n_generators += s.num_generators (markedp_only);
@ -425,6 +473,8 @@ cube<R>::cube (knot_diagram &kd_, bool markedp_only_)
#endif #endif
} }
printf ("max = %d\n", max);
// printf ("(cube) n_generators = %d\n", n_generators); // printf ("(cube) n_generators = %d\n", n_generators);
khC = new base_module<R, khC_generators<R> > (khC_generators<R> (*this)); khC = new base_module<R, khC_generators<R> > (khC_generators<R> (*this));
} }

6
knot_tables.cpp
View File

@ -782,6 +782,12 @@ std::string
knot_desc::name () const knot_desc::name () const
{ {
char buf[1000]; char buf[1000];
#if 0
sprintf (buf, "knot_desc(%d, %d, %d)", (int)t, i, j);
return buf;
#endif
switch (t) switch (t)
{ {
case ROLFSEN: case ROLFSEN:

475
main.cpp
View File

@ -202,6 +202,29 @@ compute_show_kh_sq (knot_desc desc
#endif #endif
} }
unsigned
homological_width (ptr<const module<Z2> > H)
{
int maxd = -1000,
mind = 1000;
set<grading> gs = H->gradings ();
for (set_const_iter<grading> gg = gs; gg; gg ++)
{
grading hq = gg.val ();
int d = 2 * hq.h - hq.q;
if (d < mind)
mind = d;
if (d > maxd)
maxd = d;
}
int dwidth = maxd - mind;
unsigned hwidth = (dwidth / 2) + 1;
return hwidth;
}
basedvector<unsigned, 1> hwidth_knots;
void void
load (map<knot_desc, load (map<knot_desc,
pair<mod_map<Z2>, mod_map<Z2> > > &knot_kh_sq, pair<mod_map<Z2>, mod_map<Z2> > > &knot_kh_sq,
@ -252,6 +275,17 @@ load (map<knot_desc,
for (map<knot_desc, for (map<knot_desc,
pair<mod_map<Z2>, mod_map<Z2> > >::const_iter i = m; i; i ++) pair<mod_map<Z2>, mod_map<Z2> > >::const_iter i = m; i; i ++)
{ {
mod_map<Z2> sq1 = i.val ().first;
ptr<const module<Z2> > H = sq1.domain ();
unsigned hwidth = homological_width (H);
hwidth_knots[hwidth] ++;
if (hwidth == 2)
continue;
if (i.key ().t == knot_desc::MT
&& i.key ().diagram ().num_components () == 1)
continue;
knot_kh_sq.push (i.key (), i.val ()); knot_kh_sq.push (i.key (), i.val ());
} }
@ -260,15 +294,182 @@ load (map<knot_desc,
static const int block_size = 100; static const int block_size = 100;
void
show_st (map<knot_desc,
pair<mod_map<Z2>, mod_map<Z2> > > knot_kh_sq,
knot_desc desc)
{
pair<mod_map<Z2>, mod_map<Z2> > p = knot_kh_sq(desc);
mod_map<Z2> sq1 = p.first;
mod_map<Z2> sq2 = p.second;
printf ("%s ", desc.name ().c_str ());
assert (sq1.compose (sq1) == 0);
assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
ptr<const module<Z2> > H = sq1.domain ();
map<grading, basedvector<int, 1> > st;
bool first = 1;
set<grading> gs = H->gradings ();
for (set_const_iter<grading> gg = gs; gg; gg ++)
{
grading hq = gg.val (),
h1q (hq.h + 1, hq.q),
h2q (hq.h + 2, hq.q);
ptr<const free_submodule<Z2> > H_hq = H->graded_piece (hq),
H_h1q = H->graded_piece (h1q),
H_h2q = H->graded_piece (h2q);
mod_map<Z2> S = sq2.restrict (H_hq, H_h2q),
A = sq1.restrict (H_hq, H_h1q),
B = sq1.restrict (H_h1q, H_h2q);
ptr<const free_submodule<Z2> > S_im = S.image (),
A_ker = A.kernel (),
B_im = B.image ();
ptr<const free_submodule<Z2> > inter = S_im->intersection (B_im);
mod_map<Z2> S_res = S.restrict_from (A_ker);
ptr<const free_submodule<Z2> > S_res_im = S_res.image ();
ptr<const free_submodule<Z2> > res_inter = S_res_im->intersection (B_im);
int r1 = S_im->dim ();
int r2 = S_res_im->dim ();
int r3 = inter->dim ();
int r4 = res_inter->dim ();
if (r1 == 0
&& r2 == 0
&& r3 == 0
&& r4 == 0)
continue;
// printf (" r = (%d, %d, %d, %d)\n", r1, r2, r3, r4);
int s1 = r2 - r4,
s2 = r1 - r2 - r3 + r4,
s3 = r4,
s4 = r3 - r4;
if (s1 != 0)
{
if (first)
first = 0;
else
printf (", ");
printf ("(%d, %d) -> (%d, %d, %d, %d)",
hq.h, hq.q,
s1, s2, s3, s4);
}
}
newline ();
}
int int
main () main ()
{ {
#if 0 #if 0
knot_diagram kd (mt_link (10, 0, 9));
cube<Z2> c (kd);
#endif
#if 0
for (unsigned i = 1; i <= 10; i ++)
for (unsigned j = 1; j <= mt_links (i, 0); j ++)
{
knot_diagram kd (mt_link (i, 0, j));
kd.marked_edge = 1;
cube<Z2> c (kd, 1);
sseq ss = compute_szabo_sseq (c);
ss.texshow (stdout, kd.name);
}
#endif
#if 0
#if 1
for (unsigned i = 10; i <= 10; i ++)
for (unsigned j = 124; j <= rolfsen_crossing_knots (i); j ++)
{
knot_diagram kd (rolfsen_knot (i, j));
#endif
#if 0
for (unsigned i = 1; i <= 10; i ++)
for (unsigned j = 1; j <= mt_links (i, 0); j ++)
{
#endif
#if 0
for (unsigned i = 11; i <= 11; i ++)
for (unsigned j = 1; j <= htw_knots (i, 0); j ++)
{
#endif
// knot_diagram kd (htw_knot (i, 0, j));
// knot_diagram kd (mt_link (i, 0, j));
kd.marked_edge = 1;
show (kd); newline ();
cube<Z2> c (kd, 1);
#if 0
mod_map<Z2> d1 = c.compute_d (1, 0, 0, 0, 0);
chain_complex_simplifier<Z2> s (c.khC, d1, 1);
assert (s.new_d == 0);
#endif
sseq ss = compute_szabo_sseq (c);
multivariate_laurentpoly<Z> Phat =
ss.pages[ss.pages.size ()].delta_poincare_polynomial (ss.bounds);
typedef spanning_tree_complex<Z2>::R R;
spanning_tree_complex<Z2> spanc (kd);
mod_map<R> d2 = spanc.twisted_d2 ();
mod_map<R> d2U = spanc.twisted_d2Un (1);
chain_complex_simplifier<R> s2 (spanc.C, d2, 2);
assert (s2.new_d == 0);
mod_map<R> H_d2U = s2.pi.compose (d2U).compose (s2.iota);
assert (H_d2U.compose (H_d2U) == 0);
ptr<const module<R> > ker = H_d2U.kernel ();
ptr<const module<R> > quot = s2.new_C->quotient (H_d2U.image ());
multivariate_laurentpoly<Z> Pminus1
= ker->free_delta_poincare_polynomial (),
PminusU = quot->free_delta_poincare_polynomial ();
if (PminusU != Pminus1)
{
display (" HFhat: ", Phat);
// display (" HF-: ", Pminus);
display (" HF- (1): ", Pminus1);
display (" HF- (U): ", PminusU);
}
}
#endif
#if 1
hwidth_knots = basedvector<unsigned, 1> (10);
for (unsigned i = 1; i <= hwidth_knots.size (); i ++)
hwidth_knots[i] = 0;
map<knot_desc, map<knot_desc,
pair<mod_map<Z2>, mod_map<Z2> > > knot_kh_sq; pair<mod_map<Z2>, mod_map<Z2> > > knot_kh_sq;
for (unsigned i = 12; i >= 1; i --) for (unsigned i = 14; i >= 1; i --)
{ {
#if 0
if (i <= 10) if (i <= 10)
{ {
for (unsigned j = 1; j <= rolfsen_crossing_knots (i); j += block_size) for (unsigned j = 1; j <= rolfsen_crossing_knots (i); j += block_size)
@ -276,6 +477,7 @@ main ()
load (knot_kh_sq, knot_desc (knot_desc::ROLFSEN, i, j)); load (knot_kh_sq, knot_desc (knot_desc::ROLFSEN, i, j));
} }
} }
#endif
for (unsigned j = 1; j <= htw_knots (i); j += block_size) for (unsigned j = 1; j <= htw_knots (i); j += block_size)
{ {
@ -289,21 +491,50 @@ main ()
load (knot_kh_sq, knot_desc (knot_desc::MT, i, j)); load (knot_kh_sq, knot_desc (knot_desc::MT, i, j));
} }
} }
if (i == 14)
{
for (unsigned j = 1; j <= mt_links (14, 0); j += block_size)
{
load (knot_kh_sq, knot_desc (knot_desc::MT, 14, mt_links (14, 1) + j));
}
}
} }
unsigned total_knots = 0;
printf ("hwidth_knots:\n");
for (unsigned i = 1; i <= hwidth_knots.size (); i ++)
{
printf (" % 2d: %d\n", i, hwidth_knots[i]);
total_knots += hwidth_knots[i];
}
printf ("total_knots = %d\n", total_knots);
printf ("|knot_kh_sq| = %d\n", knot_kh_sq.card ()); printf ("|knot_kh_sq| = %d\n", knot_kh_sq.card ());
#if 1
map<pair<multivariate_laurentpoly<Z>,
map<grading, unsigned> >,
pair<knot_desc,
map<grading, basedvector<int, 1> > > > P_sq1_knot_st;
set<multivariate_laurentpoly<Z> > Ps;
basedvector<unsigned, 1> collisons (10);
for (unsigned i = 1; i <= 10; i ++)
collisons[i] = 0;
for (map<knot_desc, for (map<knot_desc,
pair<mod_map<Z2>, mod_map<Z2> > >::const_iter i = knot_kh_sq; i; i ++) pair<mod_map<Z2>, mod_map<Z2> > >::const_iter i = knot_kh_sq; i; i ++)
{ {
if (i.key ().t != knot_desc::ROLFSEN) show_st (knot_kh_sq, i.key ());
continue;
mod_map<Z2> sq1 = i.val ().first; mod_map<Z2> sq1 = i.val ().first;
mod_map<Z2> sq2 = i.val ().second; mod_map<Z2> sq2 = i.val ().second;
#if 0
display ("sq1:\n", sq1); display ("sq1:\n", sq1);
display ("sq2:\n", sq2); display ("sq2:\n", sq2);
#endif
printf ("%s ", i.key ().name ().c_str ()); printf ("%s ", i.key ().name ().c_str ());
@ -311,70 +542,230 @@ main ()
assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0); assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
ptr<const module<Z2> > H = sq1.domain (); ptr<const module<Z2> > H = sq1.domain ();
unsigned hwidth = homological_width (H);
map<grading, basedvector<unsigned, 1> > st; map<grading, basedvector<int, 1> > st;
map<grading, unsigned> sq1_ranks;
bool first = 1; bool first = 1;
set<grading> gs = H->gradings (); set<grading> gs = H->gradings ();
for (set_const_iter<grading> i = gs; i; i ++)
for (set_const_iter<grading> gg = gs; gg; gg ++)
{ {
grading hq = i.val (), grading hq = gg.val (),
h1q (hq.h + 1, hq.q), h1q (hq.h + 1, hq.q),
h2q (hq.h + 2, hq.q); h2q (hq.h + 2, hq.q),
h3q (hq.h + 3, hq.q);
// printf ("(%d, %d):\n", hq.h, hq.q); // printf ("(%d, %d):\n", hq.h, hq.q);
ptr<const free_submodule<Z2> > H_hq = H->graded_piece (hq), ptr<const free_submodule<Z2> > H_hq = H->graded_piece (hq),
H_h1q = H->graded_piece (h1q), H_h1q = H->graded_piece (h1q),
H_h2q = H->graded_piece (h2q); H_h2q = H->graded_piece (h2q),
H_h3q = H->graded_piece (h3q);
mod_map<Z2> whole = sq2.restrict (H_hq, H_h2q), mod_map<Z2> S = sq2.restrict (H_hq, H_h2q),
tail = sq1.restrict (H_hq, H_h1q), T = sq2.restrict (H_h1q, H_h3q),
head = sq1.restrict (H_h1q, H_h2q); A = sq1.restrict (H_hq, H_h1q),
B = sq1.restrict (H_h1q, H_h2q),
C = sq1.restrict (H_h2q, H_h3q);
ptr<const free_submodule<Z2> > whole_im = whole.image (), ptr<const free_submodule<Z2> > Sker = S.kernel (),
tail_ker = tail.kernel (), Sim = S.image (),
head_im = head.image (); Tker = T.kernel (),
ptr<const free_submodule<Z2> > inter = whole_im->intersection (head_im); Tim = T.image (),
Aker = A.kernel (),
Aim = A.image (),
Bker = B.kernel (),
Bim = B.image (),
Cker = C.kernel (),
Cim = C.image ();
mod_map<Z2> whole_res = whole.restrict_from (tail_ker); sq1_ranks.push (hq, Aim->dim ());
ptr<const free_submodule<Z2> > whole_res_im = whole_res.image ();
ptr<const free_submodule<Z2> > res_inter = whole_res_im->intersection (head_im); mod_map<Z2> ArSker = A.restrict_from (Sker);
mod_map<Z2> SrAker = S.restrict_from (Aker);
int r1 = whole_im->dim (); mod_map<Z2> TrAim = T.restrict_from (Aim);
int r2 = whole_res_im->dim (); mod_map<Z2> TrBker = T.restrict_from (Bker);
int r3 = inter->dim (); mod_map<Z2> BrTker = B.restrict_from (Tker);
int r4 = res_inter->dim ();
if (r1 == 0 mod_map<Z2> CrSim = C.restrict_from (Sim);
&& r2 == 0
&& r3 == 0
&& r4 == 0)
continue;
// printf (" r = (%d, %d, %d, %d)\n", r1, r2, r3, r4); ptr<const free_submodule<Z2> > ArSker_im = ArSker.image ();
ptr<const free_submodule<Z2> > SrAker_im = SrAker.image ();
#if 1 ptr<const free_submodule<Z2> > TrAim_im = TrAim.image ();
int s1 = r2 - r4, ptr<const free_submodule<Z2> > TrBker_im = TrBker.image ();
s2 = r1 - r2 - r3 + r4, ptr<const free_submodule<Z2> > BrTker_im = BrTker.image ();
s3 = r4,
s4 = r3 - r4;
if (first) ptr<const free_submodule<Z2> > CrSim_im = CrSim.image ();
first = 0;
else mod_map<Z2> CrSrAker_im = C.restrict_from (SrAker_im);
printf (", "); mod_map<Z2> TrArSker_im = T.restrict_from (ArSker_im);
printf ("(%d, %d) -> (%d, %d, %d, %d)",
hq.h, hq.q, ptr<const free_submodule<Z2> > CrSrAker_im_im = CrSrAker_im.image ();
s1, s2, s3, s4); ptr<const free_submodule<Z2> > TrArSker_im_im = TrArSker_im.image ();
#endif
ptr<const free_submodule<Z2> > Aker_cap_Sker = Aker->intersection (Sker);
ptr<const free_submodule<Z2> > Aim_cap_Tker = Aim->intersection (Tker);
ptr<const free_submodule<Z2> > Bker_cap_Tker = Bker->intersection (Tker);
ptr<const free_submodule<Z2> > ArSker_im_cap_Tker = ArSker_im->intersection (Tker);
ptr<const free_submodule<Z2> > Sim_cap_Bim = Sim->intersection (Bim);
ptr<const free_submodule<Z2> > Sim_cap_BrTker_im = Sim->intersection (BrTker_im);
ptr<const free_submodule<Z2> > Sim_cap_Cker = Sim->intersection (Cker);
ptr<const free_submodule<Z2> > SrAker_im_cap_Bim = SrAker_im->intersection (Bim);
ptr<const free_submodule<Z2> > SrAker_im_cap_BrTker_im = SrAker_im->intersection (BrTker_im);
ptr<const free_submodule<Z2> > SrAker_im_cap_Cker = SrAker_im->intersection (Cker);
ptr<const free_submodule<Z2> > Tim_cap_Cim = Tim->intersection (Cim);
ptr<const free_submodule<Z2> > TrAim_im_cap_Cim = TrAim_im->intersection (Cim);
ptr<const free_submodule<Z2> > TrBker_im_cap_Cim = TrBker_im->intersection (Cim);
ptr<const free_submodule<Z2> > TrArSker_im_im_cap_Cim = TrBker_im->intersection (Cim);
ptr<const free_submodule<Z2> > Tim_cap_CrSim_im = Tim->intersection (CrSim_im);
ptr<const free_submodule<Z2> > TrAim_im_cap_CrSim_im = TrAim_im->intersection (CrSim_im);
ptr<const free_submodule<Z2> > TrBker_im_cap_CrSim_im = TrBker_im->intersection (CrSim_im);
ptr<const free_submodule<Z2> > TrArSker_im_im_cap_CrSim_im = TrBker_im->intersection (CrSim_im);
ptr<const free_submodule<Z2> > Tim_cap_CrSrAker_im_im = Tim->intersection (CrSrAker_im_im);
ptr<const free_submodule<Z2> > TrAim_im_cap_CrSrAker_im_im = TrAim_im->intersection (CrSrAker_im_im);
ptr<const free_submodule<Z2> > TrBker_im_cap_CrSrAker_im_im = TrBker_im->intersection (CrSrAker_im_im);
ptr<const free_submodule<Z2> > TrArSker_im_im_cap_CrSrAker_im_im = TrBker_im->intersection (CrSrAker_im_im);
basedvector<int, 1> v;
v.append (Sker->dim ());
v.append (Sim->dim ());
v.append (Tker->dim ());
v.append (Tim->dim ());
v.append (Aker->dim ());
v.append (Aim->dim ());
v.append (Bker->dim ());
v.append (Bim->dim ());
v.append (Cker->dim ());
v.append (Cim->dim ());
v.append (ArSker_im->dim ());
v.append (SrAker_im->dim ());
v.append (TrAim_im->dim ());
v.append (TrBker_im->dim ());
v.append (BrTker_im->dim ());
v.append (CrSim_im->dim ());
v.append (CrSrAker_im_im->dim ());
v.append (TrArSker_im_im->dim ());
v.append (Aker_cap_Sker->dim ());
v.append (Aim_cap_Tker->dim ());
v.append (Bker_cap_Tker->dim ());
v.append (ArSker_im_cap_Tker->dim ());
v.append (Sim_cap_Bim->dim ());
v.append (Sim_cap_BrTker_im->dim ());
v.append (Sim_cap_Cker->dim ());
v.append (SrAker_im_cap_Bim->dim ());
v.append (SrAker_im_cap_BrTker_im->dim ());
v.append (SrAker_im_cap_Cker->dim ());
v.append (Tim_cap_Cim->dim ());
v.append (TrAim_im_cap_Cim->dim ());
v.append (TrBker_im_cap_Cim->dim ());
v.append (TrArSker_im_im_cap_Cim->dim ());
v.append (Tim_cap_CrSim_im->dim ());
v.append (TrAim_im_cap_CrSim_im->dim ());
v.append (TrBker_im_cap_CrSim_im->dim ());
v.append (TrArSker_im_im_cap_CrSim_im->dim ());
v.append (Tim_cap_CrSim_im->dim ());
v.append (TrAim_im_cap_CrSim_im->dim ());
v.append (TrBker_im_cap_CrSim_im->dim ());
v.append (TrArSker_im_im_cap_CrSim_im->dim ());
st.push (hq, v);
} }
newline ();
multivariate_laurentpoly<Z> P = H->free_poincare_polynomial ();
pair<pair<knot_desc,
map<grading, basedvector<int, 1> > > &,
bool> p = P_sq1_knot_st.find (pair<multivariate_laurentpoly<Z>,
map<grading, unsigned> > (P, sq1_ranks));
if (p.second)
{
collisons[hwidth] ++;
Ps += P;
if (p.first.second != st)
{
printf ("DIFFER:\n");
printf ("hwidth = %d\n", hwidth);
show_st (knot_kh_sq, p.first.first);
show_st (knot_kh_sq, i.key ());
printf ("Kh[");
planar_diagram (p.first.first.diagram ()).show_knottheory ();
printf (", Modulus -> Null][q,t] === Kh[");
planar_diagram (i.key ().diagram ()).show_knottheory ();
printf (", Modulus -> Null][q,t]\n");
#if 0
printf ("%s:\n",
p.first.first.name ().c_str ());
for (map<grading, basedvector<int, 1> >::const_iter j = p.first.second; j; j ++)
{
printf (" (%d, %d) -> [",
j.key ().h, j.key ().q);
for (unsigned k = 1; k <= j.val ().size (); k ++)
{
if (k > 1)
printf (",");
printf ("%d", j.val ()[k]);
}
newline ();
}
printf ("%s:\n",
i.key ().name ().c_str ());
for (map<grading, basedvector<int, 1> >::const_iter j = st; j; j ++)
{
printf (" (%d, %d) -> [",
j.key ().h, j.key ().q);
for (unsigned k = 1; k <= j.val ().size (); k ++)
{
if (k > 1)
printf (",");
printf ("%d", j.val ()[k]);
}
newline ();
}
#endif
}
}
else
{
p.first.first = i.key ();
p.first.second = st;
}
} }
printf ("groups = %d\n", Ps.card ());
printf ("collisons:\n");
for (unsigned i = 1; i <= 10; i ++)
printf (" % 2d: %d\n", i, collisons[i]);
#endif
#endif #endif
#if 1 #if 0
knot_diagram kd (rolfsen_knot (5, 2)); knot_diagram kd (rolfsen_knot (5, 2));
show (kd); newline (); show (kd); newline ();

9
planar_diagram.cpp
View File

@ -19,21 +19,20 @@ planar_diagram::planar_diagram (const knot_diagram &kd)
} }
void void
planar_diagram::display_bohua () const planar_diagram::show_knottheory () const
{ {
printf ("%s\t[", name.c_str ()); printf ("PD[");
for (unsigned i = 1; i <= crossings.size (); i ++) for (unsigned i = 1; i <= crossings.size (); i ++)
{ {
if (i > 1) if (i > 1)
printf (","); printf (",");
printf ("[%d,%d,%d,%d]", printf ("X[%d,%d,%d,%d]",
crossings[i][1], crossings[i][1],
crossings[i][2], crossings[i][2],
crossings[i][3], crossings[i][3],
crossings[i][4]); crossings[i][4]);
} }
printf ("]\n"); printf ("]");
} }
void void

3
planar_diagram.h
View File

@ -21,7 +21,8 @@ public:
{ } { }
~planar_diagram () { } ~planar_diagram () { }
void display_bohua () const; void show_knottheory () const;
void display_knottheory () const { show_knottheory (); newline (); }
void show_self () const { printf ("planar_diagram %s", name.c_str ()); } void show_self () const { printf ("planar_diagram %s", name.c_str ()); }
void display_self () const; void display_self () const;