Added code in main to to compare sq1/2 in knot computation output.

This commit is contained in:
Cotton Seed 2012-04-14 12:36:25 -04:00
parent 56e3070bc4
commit b44d6f3699

195
main.cpp
View File

@ -157,6 +157,123 @@ square (knot_diagram &kd)
multivariate_laurentpoly<Z> > (P, sq1_P, sq2_P);
}
void
compute_show_kh_sq (knot_desc desc
#if 0
,
multivariate_laurentpoly<Z> orig_P,
multivariate_laurentpoly<Z> orig_sq1_P,
multivariate_laurentpoly<Z> orig_sq2_P
#endif
)
{
knot_diagram kd = desc.diagram ();
printf ("computing %s...\n", kd.name.c_str ());
cube<Z2> c (kd);
mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
chain_complex_simplifier<Z2> s (c.khC, d, 1);
steenrod_square sq (c, d, s);
mod_map<Z2> sq1 = sq.sq1 ();
mod_map<Z2> sq2 = sq.sq2 ();
assert (sq1.compose (sq1) == 0);
assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
multivariate_laurentpoly<Z> P = s.new_C->free_poincare_polynomial ();
ptr<const free_submodule<Z2> > sq1_im = sq1.image ();
multivariate_laurentpoly<Z> sq1_P = sq1_im->free_poincare_polynomial ();
ptr<const free_submodule<Z2> > sq2_im = sq2.image ();
multivariate_laurentpoly<Z> sq2_P = sq2_im->free_poincare_polynomial ();
printf (" P "); display (P);
printf (" sq1_P "); display (sq1_P);
printf (" sq2_P "); display (sq2_P);
#if 0
assert (P == orig_P);
assert (sq1_P == orig_sq1_P);
assert (sq2_P == orig_sq2_P);
#endif
}
void
load (map<knot_desc,
triple<multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > > &knot_kh_sq,
knot_desc desc)
{
char buf[1000];
if (desc.t == knot_desc::TORUS)
{
sprintf (buf, "kh_sq/T.dat");
}
else
{
unsigned j0 = desc.j;
switch (desc.t)
{
case knot_desc::ROLFSEN:
sprintf (buf, "kh_sq/%d_%d.dat", desc.i, j0);
break;
case knot_desc::HTW:
sprintf (buf, "kh_sq/K%d_%d.dat", desc.i, j0);
break;
case knot_desc::MT:
sprintf (buf, "kh_sq/L%d_%d.dat", desc.i, j0);
break;
default: abort ();
}
}
printf ("loading %s...\n", buf);
reader r (buf);
map<knot_desc,
triple<multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > > m (r);
for (map<knot_desc,
triple<multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > >::const_iter i = m; i; i ++)
{
// ??? check computations agree!!
if (! (knot_kh_sq % i.key ()))
{
#if 0
assert (i.key ().t == desc.t);
assert (i.key ().i == desc.i);
assert (desc.j <= i.key ().j);
assert (i.key ().j <= desc.j + 4000);
if (i.key ().t == knot_desc::MT
&& i.key ().i == 11
&& (i.key ().j == 862
|| i.key ().j == 865))
compute_show_kh_sq (i.key (),
i.val ().first,
i.val ().second,
i.val ().third);
#endif
knot_kh_sq.push (i.key (), i.val ());
}
}
printf ("done.\n");
}
int
main ()
{
@ -234,6 +351,84 @@ main ()
#endif
#if 1
compute_show_kh_sq (knot_desc (knot_desc::ROLFSEN, 8, 19));
map<knot_desc,
triple<multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > > knot_kh_sq;
for (unsigned i = 1; i <= 10; i ++)
for (unsigned j = 1; j <= rolfsen_crossing_knots (i); j += 4000)
{
load (knot_kh_sq, knot_desc (knot_desc::ROLFSEN, i, j));
}
for (unsigned i = 1; i <= 12; i ++)
for (unsigned j = 1; j <= htw_knots (i); j += 4000)
{
load (knot_kh_sq, knot_desc (knot_desc::HTW, i, j));
}
for (unsigned i = 1; i <= 13; i ++)
for (unsigned j = 1; j <= mt_links (i); j += 4000)
{
load (knot_kh_sq, knot_desc (knot_desc::MT, i, j));
}
map<multivariate_laurentpoly<Z>,
triple<knot_desc,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > > m;
multivariate_laurentpoly<Z> groups;
for (map<knot_desc,
triple<multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > >::const_iter i = knot_kh_sq; i; i ++)
{
multivariate_laurentpoly<Z> P = i.val ().first,
P_sq1 = i.val ().second,
P_sq2 = i.val ().third;
pair<triple<knot_desc,
multivariate_laurentpoly<Z>,
multivariate_laurentpoly<Z> > &,
bool> p = m.find (P);
if (p.second)
{
groups += P;
if (p.first.second != P_sq1
|| p.first.third != P_sq2)
{
printf ("DIFFER ");
display (P);
printf (" %s\n", p.first.first.name ().c_str ());
printf (" sq1 "); display (p.first.second);
printf (" sq2 "); display (p.first.third);
printf (" %s\n", i.key ().name ().c_str ());
printf (" sq1 "); display (P_sq1);
printf (" sq2 "); display (P_sq2);
}
}
else
{
p.first.first = i.key ();
p.first.second = P_sq1;
p.first.third = P_sq2;
}
}
printf ("|groups| = %d\n", groups.card ());
printf ("done.\n");
#endif
#if 0
reader r ("kh_knot_map.dat");
map<multivariate_laurentpoly<Z>,
set<triple<unsigned, int, unsigned> > > kh_knot_map (r);