Code to extract component(s) of links in knot_diagram. main.cpp set
to test inequality conjecture implied by forgetful spectral sequence for Kh.
This commit is contained in:
Cotton Seed
parent
1ea96353a7
commit
0ed96458e1
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@ -4,3 +4,5 @@
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/main
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/testsurfaces
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/serial.cmd*
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/save
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*/save
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180
knot_diagram.cpp
180
knot_diagram.cpp
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@ -295,6 +295,165 @@ knot_diagram::knot_diagram (const dt_code &dt)
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calculate_smoothing_orientation ();
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}
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knot_diagram::knot_diagram (sublink,
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smallbitset c,
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const knot_diagram &kd)
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: name(kd.name),
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n_crossings(0),
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marked_edge(0),
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nminus(0),
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nplus(0)
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{
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// ??? assert (!kd.marked_edge);
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assert (c.card () > 0); // no empty diagrams
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// edge x component
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unionfind<1> u (kd.num_edges ());
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for (unsigned i = 1; i <= kd.n_crossings; i ++)
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{
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u.join (kd.ept_edge (kd.crossings[i][1]),
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kd.ept_edge (kd.crossings[i][3]));
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u.join (kd.ept_edge (kd.crossings[i][2]),
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kd.ept_edge (kd.crossings[i][4]));
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}
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assert (u.num_sets () == c.size ());
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ullmanset<1> u_sets (kd.num_edges ());
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for (unsigned i = 1; i <= kd.num_edges (); i ++)
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u_sets += u.find (i);
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ullmanset<1> sub_crossings (kd.n_crossings),
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sub_edges (kd.num_edges ());
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for (unsigned i = 1; i <= kd.num_edges (); i ++)
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{
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if (c % (u_sets.position (u.find (i)) + 1))
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sub_edges.push (i);
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}
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// sub edge x sublink edge
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unionfind<1> subu (sub_edges.card ());
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set<unsigned> active_comps;
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for (unsigned i = 1; i <= kd.n_crossings; i ++)
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{
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unsigned c1 = u_sets.position (u.find (kd.ept_edge (kd.crossings[i][1]))) + 1,
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c2 = u_sets.position (u.find (kd.ept_edge (kd.crossings[i][2]))) + 1;
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if (c % c1
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&& c % c2)
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{
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sub_crossings.push (i);
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active_comps += c1;
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active_comps += c2;
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}
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else
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{
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if (c % (u_sets.position (u.find (kd.ept_edge (kd.crossings[i][1]))) + 1))
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{
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subu.join (sub_edges.position (kd.ept_edge (kd.crossings[i][1])) + 1,
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sub_edges.position (kd.ept_edge (kd.crossings[i][3])) + 1);
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}
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if (c % (u_sets.position (u.find (kd.ept_edge (kd.crossings[i][2]))) + 1))
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{
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subu.join (sub_edges.position (kd.ept_edge (kd.crossings[i][2])) + 1,
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sub_edges.position (kd.ept_edge (kd.crossings[i][4])) + 1);
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}
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}
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}
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n_crossings = (sub_crossings.card ()
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+ (c.card () - active_comps.card ()));
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assert (n_crossings > 0);
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ullmanset<1> subu_sets (sub_edges.card ());
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for (unsigned i = 1; i <= sub_edges.card (); i ++)
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subu_sets += subu.find (i);
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crossings = basedvector<basedvector<unsigned, 1>, 1> (n_crossings);
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for (unsigned i = 1; i <= n_crossings; i ++)
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crossings[i] = basedvector<unsigned, 1> (4);
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for (ullmanset_const_iter<1> i = sub_crossings; i; i ++)
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{
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unsigned c = i.val (),
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new_c = i.pos () + 1;
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unsigned e1 = (subu_sets.position
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(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][1])) + 1)) + 1),
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e2 = (subu_sets.position
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(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][2])) + 1)) + 1),
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e3 = (subu_sets.position
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(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][3])) + 1)) + 1),
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e4 = (subu_sets.position
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(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][4])) + 1)) + 1);
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if (kd.is_from_ept (kd.crossings[c][1]))
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crossings[new_c][1] = edge_from_ept (e1);
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else
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crossings[new_c][1] = edge_to_ept (e1);
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if (kd.is_from_ept (kd.crossings[c][2]))
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crossings[new_c][2] = edge_from_ept (e2);
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else
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crossings[new_c][2] = edge_to_ept (e2);
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if (kd.is_from_ept (kd.crossings[c][3]))
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crossings[new_c][3] = edge_from_ept (e3);
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else
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crossings[new_c][3] = edge_to_ept (e3);
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if (kd.is_from_ept (kd.crossings[c][4]))
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crossings[new_c][4] = edge_from_ept (e4);
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else
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crossings[new_c][4] = edge_to_ept (e4);
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}
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unsigned e = subu.num_sets ();
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unsigned new_c = sub_crossings.card ();
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for (smallbitset_const_iter i = c; i; i ++)
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{
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if (active_comps % i.val ())
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continue;
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unsigned e1 = (subu_sets.position
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(subu.find (sub_edges.position (u_sets.nth (i.val () - 1)) + 1)) + 1);
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unsigned e2 = ++ e;
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unsigned c = ++ new_c;
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crossings[c][1] = edge_from_ept (e1);
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crossings[c][2] = edge_to_ept (e1);
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crossings[c][3] = edge_to_ept (e2);
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crossings[c][4] = edge_from_ept (e2);
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}
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assert (e == num_edges ());
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assert (new_c == n_crossings);
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// ?? break this out into aux function
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ept_crossing = basedvector<unsigned, 1> (num_epts ());
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ept_index = basedvector<unsigned, 1> (num_epts ());
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for (unsigned i = 1; i <= n_crossings; i ++)
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{
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for (unsigned j = 1; j <= 4; j ++)
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{
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unsigned p = crossings[i][j];
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ept_crossing[p] = i;
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ept_index[p] = j;
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}
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}
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#ifndef NDEBUG
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check_crossings ();
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#endif
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calculate_smoothing_orientation ();
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calculate_nminus_nplus ();
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}
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knot_diagram::knot_diagram (mirror, const knot_diagram &kd)
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: name("mirror(" + kd.name + ")"),
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n_crossings(kd.n_crossings),
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@ -342,6 +501,12 @@ knot_diagram::check_crossings ()
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assert (ept_index[p] == j);
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}
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}
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for (unsigned i = 1; i <= num_edges (); i ++)
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{
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unsigned to = edge_to_ept (i);
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assert (is_from_ept (crossings[ept_crossing[to]][add_base1_mod4 (ept_index[to], 2)]));
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}
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}
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void
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@ -596,6 +761,21 @@ static unsigned corner_index (unsigned x)
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return ((x - 1) % 4) + 1;
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}
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unsigned
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knot_diagram::num_components () const
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{
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unionfind<1> u (num_edges ());
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for (unsigned i = 1; i <= n_crossings; i ++)
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{
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u.join (ept_edge (crossings[i][1]),
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ept_edge (crossings[i][3]));
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u.join (ept_edge (crossings[i][2]),
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ept_edge (crossings[i][4]));
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}
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return u.num_sets ();
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}
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directed_multigraph
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knot_diagram::black_graph (basedvector<unsigned, 1> &bg_edge_height) const
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{
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@ -10,6 +10,7 @@ add_base1_mod4 (unsigned x, unsigned y)
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enum mirror { MIRROR };
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enum connect_sum { CONNECT_SUM };
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enum sublink { SUBLINK };
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class knot_diagram
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{
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@ -96,6 +97,8 @@ class knot_diagram
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}
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bool is_smoothing_to_ept (unsigned p) const { return !is_smoothing_from_ept (p); }
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unsigned num_components () const;
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void orient ();
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void calculate_nminus_nplus ();
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void calculate_smoothing_orientation ();
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@ -106,9 +109,9 @@ class knot_diagram
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public:
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knot_diagram ()
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: n_crossings(0),
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marked_edge(0),
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nminus(0),
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nplus(0)
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marked_edge(0),
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nminus(0),
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nplus(0)
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{ }
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explicit knot_diagram (const planar_diagram &pd);
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explicit knot_diagram (const dt_code &dt);
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@ -116,6 +119,9 @@ class knot_diagram
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knot_diagram (connect_sum,
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const knot_diagram &d1,
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const knot_diagram &d2);
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knot_diagram (sublink,
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smallbitset c,
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const knot_diagram &kd);
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knot_diagram (const std::string &name_, unsigned n_crossings_, unsigned crossings_ar[][4]);
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knot_diagram (const std::string &name_, const basedvector<basedvector<unsigned, 1>, 1> &crossings_);
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65
main.cpp
65
main.cpp
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@ -108,9 +108,72 @@ test_field ()
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}
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}
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void
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check (const dt_code &dt)
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{
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if (dt.num_components () > 1)
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{
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knot_diagram kd (dt);
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kd.marked_edge = 1;
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show (kd); newline ();
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cube<Z2> c (kd, 1);
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mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
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sseq_builder b (c.khC, d);
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sseq ss = b.build_sseq ();
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unsigned n_comps = kd.num_components ();
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assert (n_comps == dt.num_components ());
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unsigned split = 1;
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for (unsigned k = 1; k < unsigned_2pow (n_comps) - 1; k ++)
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{
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knot_diagram kd2 (SUBLINK,
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smallbitset (n_comps, k),
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kd);
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kd2.marked_edge = 1;
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unsigned n_comps2 = kd2.num_components ();
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assert (n_comps2 == unsigned_bitcount (k));
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assert (n_comps2 > 0);
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assert (n_comps2 < n_comps);
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cube<Z2> c2 (kd2, 1);
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mod_map<Z2> d2 = c2.compute_d (1, 0, 0, 0, 0);
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sseq_builder b2 (c2.khC, d2);
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sseq ss2 = b2.build_sseq ();
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printf (" k = %d, %d <=? %d\n",
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k,
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ss2.pages[1].total_rank (),
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ss.pages[1].total_rank ());
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if (ss2.pages[1].total_rank () > ss.pages[1].total_rank ())
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printf (" !! COUNTEREXAMPLE\n");
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if (unsigned_bitcount (k) == 1)
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split *= ss2.pages[1].total_rank ();
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}
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printf (" split %d <=? %d\n",
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split,
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ss.pages[1].total_rank ());
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if (split > ss.pages[1].total_rank ())
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printf (" !! COUNTEREXAMPLE\n");
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}
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}
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int
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main ()
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{
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for (unsigned i = 1; i <= 14; i ++)
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{
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for (unsigned j = 1; j <= mt_links (i, 0); j ++)
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check (mt_link (i, 0, j));
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for (unsigned j = 1; j <= mt_links (i, 1); j ++)
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check (mt_link (i, 1, j));
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}
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#if 0
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knot_diagram kd (rolfsen_knot (8, 19));
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cube<Z2> c (kd);
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@ -143,6 +206,7 @@ main ()
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}
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#endif
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#if 0
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multivariate_laurentpoly<Z> p = -11;
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p.muladdeq (5, VARIABLE, 1);
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p.muladdeq (7, VARIABLE, 2);
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@ -187,6 +251,7 @@ main ()
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assert (m2(p) == "p");
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assert (m2(q) == "q");
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assert (m2(r) == "thisisr");
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#endif
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#if 0
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test_ring<Z2> (2);
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