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Code to extract component(s) of links in knot_diagram. main.cpp set

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to test inequality conjecture implied by forgetful spectral sequence
for Kh.
This commit is contained in:
Cotton Seed 2012-02-23 19:04:13 -05:00
parent 1ea96353a7
commit 0ed96458e1
4 changed files with 256 additions and 3 deletions
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2
.gitignore vendored
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@ -4,3 +4,5 @@
/main
/testsurfaces
/serial.cmd*
/save
*/save

180
knot_diagram.cpp
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@ -295,6 +295,165 @@ knot_diagram::knot_diagram (const dt_code &dt)
calculate_smoothing_orientation ();
}
knot_diagram::knot_diagram (sublink,
smallbitset c,
const knot_diagram &kd)
: name(kd.name),
n_crossings(0),
marked_edge(0),
nminus(0),
nplus(0)
{
// ??? assert (!kd.marked_edge);
assert (c.card () > 0); // no empty diagrams
// edge x component
unionfind<1> u (kd.num_edges ());
for (unsigned i = 1; i <= kd.n_crossings; i ++)
{
u.join (kd.ept_edge (kd.crossings[i][1]),
kd.ept_edge (kd.crossings[i][3]));
u.join (kd.ept_edge (kd.crossings[i][2]),
kd.ept_edge (kd.crossings[i][4]));
}
assert (u.num_sets () == c.size ());
ullmanset<1> u_sets (kd.num_edges ());
for (unsigned i = 1; i <= kd.num_edges (); i ++)
u_sets += u.find (i);
ullmanset<1> sub_crossings (kd.n_crossings),
sub_edges (kd.num_edges ());
for (unsigned i = 1; i <= kd.num_edges (); i ++)
{
if (c % (u_sets.position (u.find (i)) + 1))
sub_edges.push (i);
}
// sub edge x sublink edge
unionfind<1> subu (sub_edges.card ());
set<unsigned> active_comps;
for (unsigned i = 1; i <= kd.n_crossings; i ++)
{
unsigned c1 = u_sets.position (u.find (kd.ept_edge (kd.crossings[i][1]))) + 1,
c2 = u_sets.position (u.find (kd.ept_edge (kd.crossings[i][2]))) + 1;
if (c % c1
&& c % c2)
{
sub_crossings.push (i);
active_comps += c1;
active_comps += c2;
}
else
{
if (c % (u_sets.position (u.find (kd.ept_edge (kd.crossings[i][1]))) + 1))
{
subu.join (sub_edges.position (kd.ept_edge (kd.crossings[i][1])) + 1,
sub_edges.position (kd.ept_edge (kd.crossings[i][3])) + 1);
}
if (c % (u_sets.position (u.find (kd.ept_edge (kd.crossings[i][2]))) + 1))
{
subu.join (sub_edges.position (kd.ept_edge (kd.crossings[i][2])) + 1,
sub_edges.position (kd.ept_edge (kd.crossings[i][4])) + 1);
}
}
}
n_crossings = (sub_crossings.card ()
+ (c.card () - active_comps.card ()));
assert (n_crossings > 0);
ullmanset<1> subu_sets (sub_edges.card ());
for (unsigned i = 1; i <= sub_edges.card (); i ++)
subu_sets += subu.find (i);
crossings = basedvector<basedvector<unsigned, 1>, 1> (n_crossings);
for (unsigned i = 1; i <= n_crossings; i ++)
crossings[i] = basedvector<unsigned, 1> (4);
for (ullmanset_const_iter<1> i = sub_crossings; i; i ++)
{
unsigned c = i.val (),
new_c = i.pos () + 1;
unsigned e1 = (subu_sets.position
(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][1])) + 1)) + 1),
e2 = (subu_sets.position
(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][2])) + 1)) + 1),
e3 = (subu_sets.position
(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][3])) + 1)) + 1),
e4 = (subu_sets.position
(subu.find (sub_edges.position (kd.ept_edge (kd.crossings[c][4])) + 1)) + 1);
if (kd.is_from_ept (kd.crossings[c][1]))
crossings[new_c][1] = edge_from_ept (e1);
else
crossings[new_c][1] = edge_to_ept (e1);
if (kd.is_from_ept (kd.crossings[c][2]))
crossings[new_c][2] = edge_from_ept (e2);
else
crossings[new_c][2] = edge_to_ept (e2);
if (kd.is_from_ept (kd.crossings[c][3]))
crossings[new_c][3] = edge_from_ept (e3);
else
crossings[new_c][3] = edge_to_ept (e3);
if (kd.is_from_ept (kd.crossings[c][4]))
crossings[new_c][4] = edge_from_ept (e4);
else
crossings[new_c][4] = edge_to_ept (e4);
}
unsigned e = subu.num_sets ();
unsigned new_c = sub_crossings.card ();
for (smallbitset_const_iter i = c; i; i ++)
{
if (active_comps % i.val ())
continue;
unsigned e1 = (subu_sets.position
(subu.find (sub_edges.position (u_sets.nth (i.val () - 1)) + 1)) + 1);
unsigned e2 = ++ e;
unsigned c = ++ new_c;
crossings[c][1] = edge_from_ept (e1);
crossings[c][2] = edge_to_ept (e1);
crossings[c][3] = edge_to_ept (e2);
crossings[c][4] = edge_from_ept (e2);
}
assert (e == num_edges ());
assert (new_c == n_crossings);
// ?? break this out into aux function
ept_crossing = basedvector<unsigned, 1> (num_epts ());
ept_index = basedvector<unsigned, 1> (num_epts ());
for (unsigned i = 1; i <= n_crossings; i ++)
{
for (unsigned j = 1; j <= 4; j ++)
{
unsigned p = crossings[i][j];
ept_crossing[p] = i;
ept_index[p] = j;
}
}
#ifndef NDEBUG
check_crossings ();
#endif
calculate_smoothing_orientation ();
calculate_nminus_nplus ();
}
knot_diagram::knot_diagram (mirror, const knot_diagram &kd)
: name("mirror(" + kd.name + ")"),
n_crossings(kd.n_crossings),
@ -342,6 +501,12 @@ knot_diagram::check_crossings ()
assert (ept_index[p] == j);
}
}
for (unsigned i = 1; i <= num_edges (); i ++)
{
unsigned to = edge_to_ept (i);
assert (is_from_ept (crossings[ept_crossing[to]][add_base1_mod4 (ept_index[to], 2)]));
}
}
void
@ -596,6 +761,21 @@ static unsigned corner_index (unsigned x)
return ((x - 1) % 4) + 1;
}
unsigned
knot_diagram::num_components () const
{
unionfind<1> u (num_edges ());
for (unsigned i = 1; i <= n_crossings; i ++)
{
u.join (ept_edge (crossings[i][1]),
ept_edge (crossings[i][3]));
u.join (ept_edge (crossings[i][2]),
ept_edge (crossings[i][4]));
}
return u.num_sets ();
}
directed_multigraph
knot_diagram::black_graph (basedvector<unsigned, 1> &bg_edge_height) const
{

6
knot_diagram.h
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@ -10,6 +10,7 @@ add_base1_mod4 (unsigned x, unsigned y)
enum mirror { MIRROR };
enum connect_sum { CONNECT_SUM };
enum sublink { SUBLINK };
class knot_diagram
{
@ -96,6 +97,8 @@ class knot_diagram
}
bool is_smoothing_to_ept (unsigned p) const { return !is_smoothing_from_ept (p); }
unsigned num_components () const;
void orient ();
void calculate_nminus_nplus ();
void calculate_smoothing_orientation ();
@ -116,6 +119,9 @@ class knot_diagram
knot_diagram (connect_sum,
const knot_diagram &d1,
const knot_diagram &d2);
knot_diagram (sublink,
smallbitset c,
const knot_diagram &kd);
knot_diagram (const std::string &name_, unsigned n_crossings_, unsigned crossings_ar[][4]);
knot_diagram (const std::string &name_, const basedvector<basedvector<unsigned, 1>, 1> &crossings_);

65
main.cpp
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@ -108,9 +108,72 @@ test_field ()
}
}
void
check (const dt_code &dt)
{
if (dt.num_components () > 1)
{
knot_diagram kd (dt);
kd.marked_edge = 1;
show (kd); newline ();
cube<Z2> c (kd, 1);
mod_map<Z2> d = c.compute_d (1, 0, 0, 0, 0);
sseq_builder b (c.khC, d);
sseq ss = b.build_sseq ();
unsigned n_comps = kd.num_components ();
assert (n_comps == dt.num_components ());
unsigned split = 1;
for (unsigned k = 1; k < unsigned_2pow (n_comps) - 1; k ++)
{
knot_diagram kd2 (SUBLINK,
smallbitset (n_comps, k),
kd);
kd2.marked_edge = 1;
unsigned n_comps2 = kd2.num_components ();
assert (n_comps2 == unsigned_bitcount (k));
assert (n_comps2 > 0);
assert (n_comps2 < n_comps);
cube<Z2> c2 (kd2, 1);
mod_map<Z2> d2 = c2.compute_d (1, 0, 0, 0, 0);
sseq_builder b2 (c2.khC, d2);
sseq ss2 = b2.build_sseq ();
printf (" k = %d, %d <=? %d\n",
k,
ss2.pages[1].total_rank (),
ss.pages[1].total_rank ());
if (ss2.pages[1].total_rank () > ss.pages[1].total_rank ())
printf (" !! COUNTEREXAMPLE\n");
if (unsigned_bitcount (k) == 1)
split *= ss2.pages[1].total_rank ();
}
printf (" split %d <=? %d\n",
split,
ss.pages[1].total_rank ());
if (split > ss.pages[1].total_rank ())
printf (" !! COUNTEREXAMPLE\n");
}
}
int
main ()
{
for (unsigned i = 1; i <= 14; i ++)
{
for (unsigned j = 1; j <= mt_links (i, 0); j ++)
check (mt_link (i, 0, j));
for (unsigned j = 1; j <= mt_links (i, 1); j ++)
check (mt_link (i, 1, j));
}
#if 0
knot_diagram kd (rolfsen_knot (8, 19));
cube<Z2> c (kd);
@ -143,6 +206,7 @@ main ()
}
#endif
#if 0
multivariate_laurentpoly<Z> p = -11;
p.muladdeq (5, VARIABLE, 1);
p.muladdeq (7, VARIABLE, 2);
@ -187,6 +251,7 @@ main ()
assert (m2(p) == "p");
assert (m2(q) == "q");
assert (m2(r) == "thisisr");
#endif
#if 0
test_ring<Z2> (2);