Added code in main to to compare sq1/2 in knot computation output.
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Cotton Seed
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56e3070bc4
commit
b44d6f3699
195
main.cpp
195
main.cpp
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@ -157,6 +157,123 @@ square (knot_diagram &kd)
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multivariate_laurentpoly<Z> > (P, sq1_P, sq2_P);
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}
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void
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compute_show_kh_sq (knot_desc desc
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#if 0
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,
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multivariate_laurentpoly<Z> orig_P,
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multivariate_laurentpoly<Z> orig_sq1_P,
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multivariate_laurentpoly<Z> orig_sq2_P
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#endif
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)
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{
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knot_diagram kd = desc.diagram ();
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printf ("computing %s...\n", kd.name.c_str ());
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cube<Z2> c (kd);
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mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
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chain_complex_simplifier<Z2> s (c.khC, d, 1);
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steenrod_square sq (c, d, s);
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mod_map<Z2> sq1 = sq.sq1 ();
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mod_map<Z2> sq2 = sq.sq2 ();
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assert (sq1.compose (sq1) == 0);
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assert (sq2.compose (sq2) + sq1.compose (sq2).compose (sq1) == 0);
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multivariate_laurentpoly<Z> P = s.new_C->free_poincare_polynomial ();
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ptr<const free_submodule<Z2> > sq1_im = sq1.image ();
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multivariate_laurentpoly<Z> sq1_P = sq1_im->free_poincare_polynomial ();
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ptr<const free_submodule<Z2> > sq2_im = sq2.image ();
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multivariate_laurentpoly<Z> sq2_P = sq2_im->free_poincare_polynomial ();
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printf (" P "); display (P);
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printf (" sq1_P "); display (sq1_P);
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printf (" sq2_P "); display (sq2_P);
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#if 0
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assert (P == orig_P);
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assert (sq1_P == orig_sq1_P);
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assert (sq2_P == orig_sq2_P);
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#endif
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}
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void
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load (map<knot_desc,
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triple<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > > &knot_kh_sq,
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knot_desc desc)
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{
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char buf[1000];
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if (desc.t == knot_desc::TORUS)
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{
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sprintf (buf, "kh_sq/T.dat");
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}
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else
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{
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unsigned j0 = desc.j;
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switch (desc.t)
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{
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case knot_desc::ROLFSEN:
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sprintf (buf, "kh_sq/%d_%d.dat", desc.i, j0);
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break;
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case knot_desc::HTW:
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sprintf (buf, "kh_sq/K%d_%d.dat", desc.i, j0);
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break;
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case knot_desc::MT:
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sprintf (buf, "kh_sq/L%d_%d.dat", desc.i, j0);
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break;
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default: abort ();
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}
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}
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printf ("loading %s...\n", buf);
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reader r (buf);
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map<knot_desc,
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triple<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > > m (r);
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for (map<knot_desc,
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triple<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > >::const_iter i = m; i; i ++)
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{
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// ??? check computations agree!!
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if (! (knot_kh_sq % i.key ()))
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{
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#if 0
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assert (i.key ().t == desc.t);
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assert (i.key ().i == desc.i);
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assert (desc.j <= i.key ().j);
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assert (i.key ().j <= desc.j + 4000);
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if (i.key ().t == knot_desc::MT
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&& i.key ().i == 11
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&& (i.key ().j == 862
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|| i.key ().j == 865))
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compute_show_kh_sq (i.key (),
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i.val ().first,
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i.val ().second,
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i.val ().third);
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#endif
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knot_kh_sq.push (i.key (), i.val ());
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}
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}
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printf ("done.\n");
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}
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int
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main ()
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{
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@ -234,6 +351,84 @@ main ()
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#endif
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#if 1
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compute_show_kh_sq (knot_desc (knot_desc::ROLFSEN, 8, 19));
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map<knot_desc,
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triple<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > > knot_kh_sq;
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for (unsigned i = 1; i <= 10; i ++)
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for (unsigned j = 1; j <= rolfsen_crossing_knots (i); j += 4000)
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{
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load (knot_kh_sq, knot_desc (knot_desc::ROLFSEN, i, j));
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}
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for (unsigned i = 1; i <= 12; i ++)
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for (unsigned j = 1; j <= htw_knots (i); j += 4000)
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{
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load (knot_kh_sq, knot_desc (knot_desc::HTW, i, j));
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}
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for (unsigned i = 1; i <= 13; i ++)
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for (unsigned j = 1; j <= mt_links (i); j += 4000)
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{
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load (knot_kh_sq, knot_desc (knot_desc::MT, i, j));
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}
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map<multivariate_laurentpoly<Z>,
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triple<knot_desc,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > > m;
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multivariate_laurentpoly<Z> groups;
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for (map<knot_desc,
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triple<multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > >::const_iter i = knot_kh_sq; i; i ++)
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{
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multivariate_laurentpoly<Z> P = i.val ().first,
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P_sq1 = i.val ().second,
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P_sq2 = i.val ().third;
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pair<triple<knot_desc,
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multivariate_laurentpoly<Z>,
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multivariate_laurentpoly<Z> > &,
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bool> p = m.find (P);
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if (p.second)
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{
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groups += P;
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if (p.first.second != P_sq1
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|| p.first.third != P_sq2)
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{
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printf ("DIFFER ");
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display (P);
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printf (" %s\n", p.first.first.name ().c_str ());
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printf (" sq1 "); display (p.first.second);
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printf (" sq2 "); display (p.first.third);
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printf (" %s\n", i.key ().name ().c_str ());
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printf (" sq1 "); display (P_sq1);
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printf (" sq2 "); display (P_sq2);
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}
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}
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else
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{
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p.first.first = i.key ();
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p.first.second = P_sq1;
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p.first.third = P_sq2;
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}
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}
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printf ("|groups| = %d\n", groups.card ());
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printf ("done.\n");
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#endif
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#if 0
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reader r ("kh_knot_map.dat");
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map<multivariate_laurentpoly<Z>,
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set<triple<unsigned, int, unsigned> > > kh_knot_map (r);
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