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Updated link forgetful spectral sequence verification to include

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ell-grading.
This commit is contained in:
Cotton Seed 2012-08-31 13:44:18 -04:00
parent 6e46c5a8ce
commit 307719de67
3 changed files with 58 additions and 22 deletions
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15
algebra/module.h
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@ -82,6 +82,7 @@ class module : public refcounted
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;
multivariate_laurentpoly<Z> free_ell_poincare_polynomial () const;
ptr<const direct_sum<R> > ptr<const direct_sum<R> >
add (basedvector<ptr<const module<R> >, 1> compound_summands) const; add (basedvector<ptr<const module<R> >, 1> compound_summands) const;
@ -1481,6 +1482,20 @@ module<R>::free_delta_poincare_polynomial () const
return r; return r;
} }
template<class R> multivariate_laurentpoly<Z>
module<R>::free_ell_poincare_polynomial () const
{
multivariate_laurentpoly<Z> r;
for (unsigned i = 1; i <= free_rank (); i ++)
{
grading hq = generator_grading (i);
multivariate_laurent_monomial m;
m.push_exponent (1, hq.h - hq.q);
r.muladdeq (1, m);
}
return r;
}
template<class R> set<grading> template<class R> set<grading>
module<R>::gradings () const module<R>::gradings () const
{ {

6
algebra/multivariate_laurentpoly.h
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@ -205,6 +205,12 @@ class multivariate_laurentpoly
coeffs.push (monomial (VARIABLE, i), c); coeffs.push (monomial (VARIABLE, i), c);
} }
multivariate_laurentpoly (T c, variable, unsigned i, int e)
{
if (c != 0)
coeffs.push (monomial (VARIABLE, i, e), c);
}
multivariate_laurentpoly (T c, const monomial &m) multivariate_laurentpoly (T c, const monomial &m)
{ {
if (c != 0) if (c != 0)

59
main.cpp
View File

@ -816,34 +816,43 @@ test_forgetful_ss ()
} }
assert (t == n); assert (t == n);
unsigned disj_rank = 1; printf (" kd w: %d\n", kd.writhe ());
multivariate_laurentpoly<Z> disj_P = 1;
for (unsigned k = 1; k <= n; k ++) for (unsigned k = 1; k <= n; k ++)
{ {
knot_diagram comp (SUBLINK, smallbitset (n, unsigned_2pow (k - 1)), kd); knot_diagram comp (SUBLINK, smallbitset (n, unsigned_2pow (k - 1)), kd);
unsigned w = 0;
for (unsigned i = 1; i <= kd.n_crossings; i ++)
{
if (root_comp(u.find (kd.ept_edge (kd.crossings[i][1]))) == k
&& root_comp(u.find (kd.ept_edge (kd.crossings[i][2]))) == k)
{
if (kd.is_to_ept (kd.crossings[i][1]) == kd.is_to_ept (kd.crossings[i][4]))
w ++;
else
w --;
}
}
printf (" % 2d w: %d\n", k, w);
cube<R> c (comp); cube<R> c (comp);
mod_map<R> d = c.compute_d (1, 0, 0, 0, 0); mod_map<R> d = c.compute_d (1, 0, 0, 0, 0);
chain_complex_simplifier<R> s (c.khC, d, 1); chain_complex_simplifier<R> s (c.khC, d, 1);
assert (s.new_d == 0); assert (s.new_d == 0);
printf (" % 2d: rank %d\n", k, s.new_C->dim ()); multivariate_laurentpoly<Z> P = s.new_C->free_ell_poincare_polynomial ();
printf (" % 2d P: ", k);
display (P);
disj_rank *= s.new_C->dim (); disj_P *= (P
* multivariate_laurentpoly<Z> (1, VARIABLE, 1, w)
);
} }
{
knot_diagram comp (SUBLINK, smallbitset (n, unsigned_bitclear (unsigned_fill (n), 1)), kd);
cube<R> c (comp);
mod_map<R> d = c.compute_d (1, 0, 0, 0, 0);
chain_complex_simplifier<R> s (c.khC, d, 1);
assert (s.new_d == 0);
printf (" 11...10: rank %d\n", s.new_C->dim ());
}
cube<R> c (kd); cube<R> c (kd);
#if 0 #if 0
@ -862,7 +871,10 @@ test_forgetful_ss ()
chain_complex_simplifier<R> s1 (c.khC, untwisted_d, 1); chain_complex_simplifier<R> s1 (c.khC, untwisted_d, 1);
assert (s1.new_d == 0); assert (s1.new_d == 0);
printf ("untwisted rank = %d\n", s1.new_C->dim ()); multivariate_laurentpoly<Z> P1 = s1.new_C->free_ell_poincare_polynomial ();
display (" link P : ", P1);
display (" disj_P (adj): ", disj_P);
mod_map<R> d = untwisted_d; mod_map<R> d = untwisted_d;
for (unsigned x = 1; x <= kd.n_crossings; x ++) for (unsigned x = 1; x <= kd.n_crossings; x ++)
@ -898,13 +910,16 @@ test_forgetful_ss ()
chain_complex_simplifier<R> s2 (c.khC, d, -1); chain_complex_simplifier<R> s2 (c.khC, d, -1);
assert (s2.new_d == 0); assert (s2.new_d == 0);
multivariate_laurentpoly<Z> P2 = (s2.new_C->free_ell_poincare_polynomial ()
* multivariate_laurentpoly<Z> (1, VARIABLE, 1, kd.writhe ())
);
display (" Einf P (adj): ", P2);
printf ("twisted rank = %d\n", s2.new_C->dim ()); if (disj_P == P2)
printf (" disj_P == Einf P (adj): YES!\n");
if (disj_rank == s2.new_C->dim ())
printf (" %d == %d: YES!\n", disj_rank, s2.new_C->dim ());
else else
printf (" %d == %d: NO :-(\n", disj_rank, s2.new_C->dim ()); printf (" disj_P != Einf P (adj): NO :-(!\n");
} }
} }