Added convert_mut15 to consolidate /u/cseed/mut15.bak into
knot_sq/K15_sq_part.dat.gz. (For newcomp.) Added test_kh_htt_stronger to find examples where the homotopy type distinguishes knots with identical Khovanov homology.
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Cotton Seed
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169
main.cpp
169
main.cpp
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@ -912,6 +912,118 @@ compute_st (mod_map<Z2> sq1,
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return st;
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}
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void
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display_st (map<grading, basedvector<int, 1> > st)
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{
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bool first = 1;
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for (map_const_iter<grading, basedvector<int, 1> > i = st; i; i ++)
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{
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grading hq = i.key ();
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int s1 = i.val ()[1],
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s2 = i.val ()[2],
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s3 = i.val ()[3],
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s4 = i.val ()[4];
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if (s1 == 0 && s2 == 0 && s3 == 0 && s4 == 0)
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continue;
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if (first)
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first = 0;
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else
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printf (",");
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printf ("$(%d, %d) \\mapsto (%d, %d, %d, %d)$", hq.h, hq.q, s1, s2, s3, s4);
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}
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newline ();
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}
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void
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test_kh_htt_stronger ()
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{
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map<pair<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> >,
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pair<knot_desc,
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map<grading, basedvector<int, 1> > > > P_sq1_knot_st;
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const char *knot_sq_files[] = {
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"knot_sq/rolfsen_sq.dat.gz",
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"knot_sq/Ksmall_sq.dat.gz",
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"knot_sq/K11_sq.dat.gz",
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"knot_sq/K12_sq.dat.gz",
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"knot_sq/K13_sq.dat.gz",
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"knot_sq/K14_sq.dat.gz",
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"knot_sq/Lsmall_sq.dat.gz",
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"knot_sq/L11_sq.dat.gz",
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"knot_sq/L12_sq.dat.gz",
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"knot_sq/L13_sq.dat.gz",
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"knot_sq/L14_sq.dat.gz",
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0,
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};
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for (unsigned i = 0; knot_sq_files[i]; i ++)
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{
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gzfile_reader r (knot_sq_files[i]);
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printf ("loading %s...\n", knot_sq_files[i]);
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unsigned n = r.read_unsigned ();
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for (unsigned i = 1; i <= n; i ++)
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{
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knot_desc desc (r);
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pair<mod_map<Z2>, mod_map<Z2> > p1 (r);
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if (desc.t == knot_desc::MT
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|| desc.t == knot_desc::MT_ALT
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|| desc.t == knot_desc::MT_NONALT)
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{
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knot_diagram kd = desc.diagram ();
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if (kd.num_components () == 1)
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continue;
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}
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mod_map<Z2> sq1 = p1.first,
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sq2 = p1.second;
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ptr<const module<Z2> > H = sq1.domain ();
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multivariate_laurentpoly<Z> P = H->free_poincare_polynomial ();
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unsigned hwidth = homological_width (H);
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map<grading, basedvector<int, 1> > st
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= compute_st (sq1, sq2);
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ptr<const free_submodule<Z2> > sq1_im = sq1.image ();
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multivariate_laurentpoly<Z> sq1_im_P = sq1_im->free_poincare_polynomial ();
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pair<pair<knot_desc,
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map<grading, basedvector<int, 1> > > &,
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bool> p2 = P_sq1_knot_st.find (pair<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > (P, sq1_im_P));
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if (p2.second)
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{
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if (p2.first.second != st)
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{
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printf ("DIFFER:\n");
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printf ("hwidth = %d\n", hwidth);
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show (p2.first.first);
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display_st (p2.first.second);
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show (desc);
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display_st (st);
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printf ("Kh[");
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planar_diagram (p2.first.first.diagram ()).show_knottheory ();
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printf (", Modulus -> Null][q,t] === Kh[");
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planar_diagram (desc.diagram ()).show_knottheory ();
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printf (", Modulus -> Null][q,t]\n");
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}
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}
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else
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{
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p2.first.first = desc;
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p2.first.second = st;
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}
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}
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}
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}
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void
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test_knot_sq ()
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{
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@ -923,6 +1035,7 @@ test_knot_sq ()
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"knot_sq/K13_sq.dat.gz",
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#if 0
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"knot_sq/K14_sq.dat.gz",
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"knot_sq/K15_sq_part.dat.gz",
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"knot_sq/Lsmall_sq.dat.gz",
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"knot_sq/L11_sq.dat.gz",
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"knot_sq/L12_sq.dat.gz",
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@ -1120,6 +1233,56 @@ test_knot_sq ()
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printf ("compared = %d\n", compared);
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}
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bool
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file_exists (const char *buf)
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{
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struct stat stat_buf;
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if (stat (buf, &stat_buf) != 0)
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{
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if (errno == ENOENT)
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return 0;
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stderror ("stat: %s", buf);
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exit (EXIT_FAILURE);
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}
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return 1;
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}
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void
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convert_mut15 ()
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{
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hashmap<knot_desc,
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pair<mod_map<Z2>, mod_map<Z2> > > knot15_sq_part;
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basedvector<basedvector<unsigned, 1>, 1> groups = mutant_knot_groups (15);
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for (unsigned i = 1; i <= groups.size (); i ++)
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{
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for (unsigned j = 1; j <= groups[i].size (); j ++)
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{
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knot_desc desc (knot_desc::HTW, i, groups[i][j]);
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char buf[1000];
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sprintf (buf, "/u/cseed/mut15.bak/K15_%d.dat.gz", groups[i][j]);
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if (file_exists (buf))
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{
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gzfile_reader r (buf);
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mod_map<Z2> sq1 (r);
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mod_map<Z2> sq2 (r);
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knot15_sq_part.push (desc,
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pair<mod_map<Z2>, mod_map<Z2> > (sq1, sq2));
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}
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}
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}
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printf ("|knot15_sq_part| = %d\n", knot15_sq_part.card ());
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gzfile_writer w ("/u/cseed/src/knotkit/knot_sq/K15_sq_part.dat.gz");
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write (w, knot15_sq_part);
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}
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void
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compute_mutant_mirrors ()
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{
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@ -1280,9 +1443,13 @@ convert_mknots ()
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int
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main ()
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{
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compute_mutant_mirrors ();
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convert_mut15 ();
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return 0;
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test_kh_htt_stronger ();
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compute_mutant_mirrors ();
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test_knot_sq ();
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convert_mknots ();
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