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cobordism.cpp
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cobordism.cpp
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#include <knotkit.h>
class rd_unify
{
public:
ullmanmap<unsigned, 1> cpt_map,
starting_circle_map,
ending_circle_map;
bool unify_starting_circle (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned x1, unsigned x2);
bool unify_ending_circle (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned y1, unsigned y2);
bool unify_crossing (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned c1, unsigned c2);
bool unify_cpt (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned c1, unsigned c2);
public:
rd_unify ();
rd_unify (const rd_unify &) = delete;
~rd_unify () { }
rd_unify &operator = (const rd_unify &) = delete;
bool unify (const resolution_diagram &rd1, const resolution_diagram &rd2);
unsigned map_starting_monomial (unsigned m);
unsigned map_ending_monomial (unsigned m);
};
bool
rd_unify::unify_starting_circle (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned x1, unsigned x2)
{
pair<unsigned &, bool> p = starting_circle_map.find (x1);
if (p.second)
return p.first == x2;
p.first = x2;
return 1;
}
bool
rd_unify::unify_ending_circle (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned y1, unsigned y2)
{
pair<unsigned &, bool> p = ending_circle_map.find (y1);
if (p.second)
return p.first == y2;
p.first = y2;
return 1;
}
bool
rd_unify::unify_crossing (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned c1, unsigned c2)
{
return (rd1.resolved(c1) == rd2.resolved(c2)
&& rd1.to_resolve(c1) == rd2.to_resolve(c2)
&& unify_cpt (rd1, rd2,
rd1.crossing_from_cpt (c1), rd2.crossing_from_cpt (c2))
&& unify_cpt (rd1, rd2,
rd1.crossing_to_cpt (c1), rd2.crossing_to_cpt (c2)));
}
bool
rd_unify::unify_cpt (const resolution_diagram &rd1, const resolution_diagram &rd2,
unsigned c1, unsigned c2)
{
pair<unsigned &, bool> p = cpt_map.find (c1);
if (p.second)
return p.first == c2;
p.first = c2;
return (rd1.is_from_cpt (c1) == rd2.is_from_cpt (c2)
&& rd1.cpt_inside(c1) == rd2.cpt_inside(c2)
&& (rd1.marked_edge == c1) == (rd2.marked_edge == c2)
&& (rd1.marked_edge2 == c1) == (rd2.marked_edge2 == c2)
&& unify_crossing (rd1, rd2,
rd1.cpt_crossing (c1), rd2.cpt_crossing (c2))
&& unify_starting_circle (rd1, rd2,
rd1.cpt_starting_circle[c1], rd2.cpt_starting_circle[c2])
&& unify_ending_circle (rd1, rd2,
rd1.cpt_ending_circle[c1], rd2.cpt_ending_circle[c2])
&& unify_cpt (rd1, rd2,
rd1.next[c1], rd2.next[c2])
&& unify_cpt (rd1, rd2,
rd1.prev[c1], rd2.prev[c2]));
}
rd_unify::rd_unify ()
: cpt_map(max_cpts),
starting_circle_map(max_circles),
ending_circle_map(max_circles)
{
}
bool
rd_unify::unify (const resolution_diagram &rd1,
const resolution_diagram &rd2)
{
if (rd1.n_crossings != rd2.n_crossings
|| rd1.n_starting_circles != rd2.n_starting_circles
|| rd1.n_ending_circles != rd2.n_ending_circles
|| (rd1.marked_edge == 0) != (rd2.marked_edge == 0)
|| (rd1.marked_edge2 == 0) != (rd2.marked_edge2 == 0))
return 0;
#if 0
cpt_map.clear ();
starting_circle_map.clear ();
ending_circle_map.clear ();
for (unsigned i = 1; i <= rd1.n_crossings; i ++)
{
if (!unify_crossing (rd1, rd2, i, i))
return 0;
}
assert (cpt_map.card () == rd1.num_cpts ());
assert (starting_circle_map.card () == rd1.n_starting_circles);
assert (ending_circle_map.card () == rd1.n_ending_circles);
#endif
for (unsigned i = 1; i <= rd1.n_crossings; i ++)
{
cpt_map.clear ();
starting_circle_map.clear ();
ending_circle_map.clear ();
if (unify_crossing (rd1, rd2, i, 1))
{
assert (cpt_map.card () == rd1.num_cpts ());
assert (starting_circle_map.card () == rd1.n_starting_circles);
assert (ending_circle_map.card () == rd1.n_ending_circles);
return 1;
}
}
return 0;
}
unsigned
rd_unify::map_starting_monomial (unsigned m1)
{
unsigned m2 = 0;
for (unsigned_const_iter i = m1; i; i ++)
{
m2 = unsigned_bitset (m2,
starting_circle_map(i.val ()));
}
return m2;
}
unsigned
rd_unify::map_ending_monomial (unsigned m1)
{
unsigned m2 = 0;
for (unsigned_const_iter i = m1; i; i ++)
{
m2 = unsigned_bitset (m2,
ending_circle_map(i.val ()));
}
return m2;
}
rd_unify the_rd_unifier;
bool
resolution_diagram::crossing_orientation (unsigned common, unsigned i) const
{
if (crossing_is_split (i))
{
if (crossing_from_outside (i))
return next[crossing_from_cpt (i)] == crossing_to_cpt (i);
else
return next[crossing_to_cpt (i)] == crossing_from_cpt (i);
}
else
return crossing_to (i) == common;
}
bool
resolution_diagram::marked_edge_left (unsigned pt) const
{
assert (marked_edge);
if (cpt_inside % pt)
return marked_edge == pt;
else
return marked_edge == prev[pt];
}
resolution_diagram::resolution_diagram ()
: n_crossings(0),
n_starting_circles(0),
n_ending_circles(0),
marked_edge(0),
marked_edge2(0)
{
}
void
resolution_diagram::compute_prev ()
{
for (unsigned i = 1; i <= num_cpts (); i ++)
prev[next[i]] = i;
}
void
resolution_diagram::check ()
{
for (unsigned i = 1; i <= num_cpts (); i ++)
{
assert (prev[next[i]] == i);
assert (next[prev[i]] == i);
assert (cpt_starting_circle[i] == cpt_starting_circle[next[i]]);
assert (1 <= cpt_starting_circle[i]
&& cpt_starting_circle[i] <= n_starting_circles);
assert (1 <= cpt_ending_circle[i]
&& cpt_ending_circle[i] <= n_ending_circles);
}
}
resolution_diagram::resolution_diagram (unsigned n_crossings_,
unsigned n_starting_circles_,
unsigned n_ending_circles_)
: n_crossings(n_crossings_),
resolved(n_crossings_),
to_resolve(n_crossings_, ~0),
n_starting_circles(n_starting_circles_),
n_ending_circles(n_ending_circles_),
marked_edge(0),
marked_edge2(0),
cpt_inside(num_cpts ()),
prev(num_cpts ()),
next(num_cpts ()),
cpt_starting_circle(num_cpts ()),
cpt_ending_circle(num_cpts ())
{
}
resolution_diagram::resolution_diagram (reverse_crossing_t,
const resolution_diagram &rd,
smallbitset to_reverse)
: n_crossings(rd.n_crossings),
resolved(rd.resolved),
to_resolve(rd.to_resolve),
n_starting_circles(rd.n_starting_circles),
n_ending_circles(rd.n_ending_circles),
marked_edge(rd.marked_edge),
marked_edge2(rd.marked_edge2),
cpt_inside(rd.cpt_inside),
prev(num_cpts ()),
next(num_cpts ()),
cpt_starting_circle(num_cpts ()),
cpt_ending_circle(num_cpts ())
{
map<unsigned, unsigned> m;
for (unsigned i = 1; i <= n_crossings; i ++)
{
if (to_reverse % i)
{
m.push (crossing_from_cpt (i),
crossing_to_cpt (i));
m.push (crossing_to_cpt (i),
crossing_from_cpt (i));
}
else
{
m.push (crossing_from_cpt (i),
crossing_from_cpt (i));
m.push (crossing_to_cpt (i),
crossing_to_cpt (i));
}
}
for (unsigned i = 1; i <= num_cpts (); i ++)
{
next[i] = m(rd.next[m(i)]);
prev[i] = m(rd.prev[m(i)]);
cpt_starting_circle[i] = rd.cpt_starting_circle[m(i)];
cpt_ending_circle[i] = rd.cpt_ending_circle[m(i)];
}
#ifndef NDEBUG
check ();
#endif
}
resolution_diagram::resolution_diagram (reverse_orientation_t,
const resolution_diagram &rd)
: n_crossings(rd.n_crossings),
resolved(rd.resolved),
to_resolve(rd.to_resolve),
n_starting_circles(rd.n_starting_circles),
n_ending_circles(rd.n_ending_circles),
marked_edge(rd.marked_edge),
marked_edge2(rd.marked_edge2),
cpt_inside(rd.cpt_inside),
prev(num_cpts (), rd.next),
next(num_cpts (), rd.prev),
cpt_starting_circle(num_cpts (), rd.cpt_starting_circle),
cpt_ending_circle(num_cpts (), rd.cpt_ending_circle)
{
cpt_inside.toggle ();
#ifndef NDEBUG
check ();
#endif
}
resolution_diagram::resolution_diagram (const resolution_diagram &rd)
: n_crossings(rd.n_crossings),
resolved(rd.resolved),
to_resolve(rd.to_resolve),
n_starting_circles(rd.n_starting_circles),
n_ending_circles(rd.n_ending_circles),
marked_edge(rd.marked_edge),
marked_edge2(rd.marked_edge2),
cpt_inside(rd.cpt_inside),
prev(num_cpts (), rd.prev),
next(num_cpts (), rd.next),
cpt_starting_circle(num_cpts (), rd.cpt_starting_circle),
cpt_ending_circle(num_cpts (), rd.cpt_ending_circle)
{
}
resolution_diagram::resolution_diagram (copy, const resolution_diagram &rd)
: n_crossings(rd.n_crossings),
resolved(rd.resolved),
to_resolve(rd.to_resolve),
n_starting_circles(rd.n_starting_circles),
n_ending_circles(rd.n_ending_circles),
marked_edge(rd.marked_edge),
marked_edge2(rd.marked_edge2),
cpt_inside(rd.cpt_inside),
prev(num_cpts (), rd.prev),
next(num_cpts (), rd.next),
cpt_starting_circle(num_cpts (), rd.cpt_starting_circle),
cpt_ending_circle(num_cpts (), rd.cpt_ending_circle)
{
}
resolution_diagram::resolution_diagram (reader &r)
{
read (r, n_crossings);
read (r, resolved);
read (r, to_resolve);
read (r, n_starting_circles);
read (r, n_ending_circles);
read (r, marked_edge);
read (r, marked_edge2);
read (r, cpt_inside);
read (r, next);
read (r, cpt_starting_circle);
read (r, cpt_ending_circle);
prev = basedvector<unsigned, 1> (num_cpts ());
for (unsigned i = 1; i <= num_cpts (); i ++)
prev[next[i]] = i;
}
resolution_diagram &
resolution_diagram::operator = (const resolution_diagram &rd)
{
n_crossings = rd.n_crossings;
resolved = rd.resolved;
to_resolve = rd.to_resolve;
n_starting_circles = rd.n_starting_circles;
n_ending_circles = rd.n_ending_circles;
marked_edge = rd.marked_edge;
marked_edge2 = rd.marked_edge2;
cpt_inside = rd.cpt_inside;
prev = rd.prev;
next = rd.next;
cpt_starting_circle = rd.cpt_starting_circle;
cpt_ending_circle = rd.cpt_ending_circle;
return *this;
}
bool
resolution_diagram::operator == (const resolution_diagram &rd) const
{
return the_rd_unifier.unify (*this, rd);
}
void
resolution_diagram::write_self (writer &w) const
{
write (w, n_crossings);
write (w, resolved);
write (w, to_resolve);
write (w, n_starting_circles);
write (w, n_ending_circles);
write (w, marked_edge);
write (w, marked_edge2);
write (w, cpt_inside);
write (w, next);
write (w, cpt_starting_circle);
write (w, cpt_ending_circle);
}
hash_t
resolution_diagram::hash_self () const
{
assert (cpt_inside.size () == num_cpts ());
hash_t h = hash (n_crossings);
h = hash_combine (h, hash (n_starting_circles));
h = hash_combine (h, hash (n_ending_circles));
h = hash_combine (h, hash (marked_edge == 0));
h = hash_combine (h, hash (marked_edge2 == 0));
return h;
}
resolution_diagram_builder::resolution_diagram_builder ()
: gl_crossings(max_crossings),
gl_starting_circles(max_circles),
gl_ending_circles(max_circles)
{
rd.prev = basedvector<unsigned, 1> (max_cpts);
rd.next = basedvector<unsigned, 1> (max_cpts);
rd.cpt_starting_circle = basedvector<unsigned, 1> (max_cpts);
rd.cpt_ending_circle = basedvector<unsigned, 1> (max_cpts);
}
void
resolution_diagram_builder::init (const knot_diagram &d,
smallbitset from_state, const smoothing &from_s,
smallbitset to_state, const smoothing &to_s,
smallbitset crossings)
{
gl_crossings.clear ();
gl_starting_circles.clear ();
gl_ending_circles.clear ();
for (smallbitset_const_iter i = crossings; i; i ++)
{
unsigned c = i.val ();
gl_crossings += c;
unsigned starting_from = from_s.ept_circle (d, d.crossings[c][2]),
starting_to = from_s.ept_circle (d, d.crossings[c][4]);
gl_starting_circles += starting_from;
gl_starting_circles += starting_to;
unsigned ending_from = to_s.ept_circle (d, d.crossings[c][2]),
ending_to = to_s.ept_circle (d, d.crossings[c][4]);
gl_ending_circles += ending_from;
gl_ending_circles += ending_to;
}
#ifndef NDEBUG
for (ullmanset_const_iter<1> i = gl_crossings; i; i ++)
{
unsigned c1 = i.val ();
unsigned lc1 = i.pos () + 1;
for (ullmanset_const_iter<1> j = gl_crossings; j; j ++)
{
unsigned c2 = j.val ();
unsigned lc2 = j.pos () + 1;
assert ((c1 < c2) == (lc1 < lc2));
}
}
#endif
rd.n_crossings = gl_crossings.card ();
rd.resolved = smallbitset (rd.n_crossings);
rd.to_resolve = smallbitset (rd.n_crossings);
rd.n_starting_circles = gl_starting_circles.card ();
rd.n_ending_circles = gl_ending_circles.card ();
rd.marked_edge = 0;
rd.marked_edge2 = 0;
rd.cpt_inside = smallbitset (rd.num_cpts ());
for (smallbitset_const_iter i = crossings; i; i ++)
{
unsigned c = i.val ();
unsigned lc = gl_crossings.position (c) + 1;
if (from_state(c))
rd.resolved.push (lc);
else if (to_state(c))
rd.to_resolve.push (lc);
if (from_s.crossing_from_inside (d, from_state, c))
rd.cpt_inside.push (rd.crossing_from_cpt (lc));
if (from_s.crossing_to_inside (d, from_state, c))
rd.cpt_inside.push (rd.crossing_to_cpt (lc));
unsigned from = from_s.ept_circle (d, d.crossings[c][2]),
to = from_s.ept_circle (d, d.crossings[c][4]);
unsigned lfrom = gl_starting_circles.position (from) + 1,
lto = gl_starting_circles.position (to) + 1;
rd.cpt_starting_circle[rd.crossing_from_cpt (lc)] = lfrom;
rd.cpt_starting_circle[rd.crossing_to_cpt (lc)] = lto;
unsigned ending_from = to_s.ept_circle (d, d.crossings[c][2]),
ending_to = to_s.ept_circle (d, d.crossings[c][4]);
unsigned lending_from = gl_ending_circles.position (ending_from) + 1,
lending_to = gl_ending_circles.position (ending_to) + 1;
rd.cpt_ending_circle[rd.crossing_from_cpt (lc)] = lending_from;
rd.cpt_ending_circle[rd.crossing_to_cpt (lc)] = lending_to;
}
lg_edges = basedvector<set<unsigned>, 1> (rd.num_cpts ());
smallbitset done (d.num_edges ());
for (unsigned i = 1; i <= d.num_edges (); i ++)
{
if (done % i)
continue;
bool saw_marked_edge = 0,
first_saw_marked_edge = 0;
unsigned first_lcpt = 0,
prev_lcpt = 0;
set<unsigned> first_saw_gedges;
for (unsigned e = i;;)
{
done.push (e);
if (e == d.marked_edge)
saw_marked_edge = 1;
if (prev_lcpt)
lg_edges[prev_lcpt].push (e);
else
first_saw_gedges.push (e);
unsigned p = from_s.edge_to (d, e);
unsigned c = d.ept_crossing (p);
if (crossings % c)
{
unsigned lc = gl_crossings.position (c) + 1;
unsigned next_lcpt = from_s.is_crossing_from_ept (d, from_state, p)
? rd.crossing_from_cpt (lc)
: rd.crossing_to_cpt (lc);
if (!first_lcpt)
{
assert (prev_lcpt == 0);
first_lcpt = next_lcpt;
assert (first_saw_marked_edge == 0);
first_saw_marked_edge = saw_marked_edge;
saw_marked_edge = 0;
}
if (prev_lcpt)
{
rd.next[prev_lcpt] = next_lcpt;
rd.prev[next_lcpt] = prev_lcpt;
if (saw_marked_edge)
{
assert (rd.marked_edge == 0);
rd.marked_edge = prev_lcpt;
}
saw_marked_edge = 0;
}
prev_lcpt = next_lcpt;
}
e = from_s.next_edge (d, from_state, e);
if (e == i)
break;
}
if (first_lcpt)
{
assert (prev_lcpt);
rd.next[prev_lcpt] = first_lcpt;
rd.prev[first_lcpt] = prev_lcpt;
if (saw_marked_edge || first_saw_marked_edge)
{
assert (rd.marked_edge == 0);
rd.marked_edge = prev_lcpt;
first_saw_marked_edge = saw_marked_edge = 0;
}
lg_edges[prev_lcpt] |= first_saw_gedges;
}
else
assert (!prev_lcpt);
assert (!first_saw_marked_edge);
}
#ifndef NDEBUG
if (rd.marked_edge)
{
assert (d.marked_edge);
assert (rd.marked_starting_circle ()
== gl_starting_circles.position (from_s.edge_circle[d.marked_edge]) + 1);
#if 0
assert (rd.marked_ending_circle ()
== gl_ending_circles.position (to_s.edge_circle[d.marked_edge]) + 1);
#endif
}
else if (d.marked_edge)
{
assert (!gl_starting_circles(from_s.edge_circle[d.marked_edge]));
assert (!gl_ending_circles(to_s.edge_circle[d.marked_edge]));
}
#endif
assert (done.card () == d.num_edges ());
}
void
resolution_diagram_builder::mirror ()
{
abort (); // ???
}
void
resolution_diagram_builder::reverse_orientation ()
{
abort (); // ???
}
void
resolution_diagram_builder::reverse_crossing (const knot_diagram &d,
const smoothing &from_s, const smoothing &to_s,
unsigned c)
{
#ifndef NDEBUG
for (unsigned i = 1; i <= rd.num_cpts (); i ++)
{
assert (rd.prev[rd.next[i]] == i);
assert (rd.next[rd.prev[i]] == i);
}
#endif
if (! (gl_crossings % c))
return;
unsigned lc = gl_crossings.position (c) + 1;
unsigned from = rd.crossing_from_cpt (lc),
to = rd.crossing_to_cpt (lc);
unsigned from_prev = rd.prev[from],
from_next = rd.next[from],
to_prev = rd.prev[to],
to_next = rd.next[to];
if ((from_next == to
&& to_next == from)
|| (from_next == from
&& to_next == to))
;
else if (from_next == to)
{
rd.next[from_prev] = to;
rd.prev[to] = from_prev;
rd.next[to] = from;
rd.prev[from] = to;
rd.next[from] = to_next;
rd.prev[to_next] = from;
}
else if (to_next == from)
{
rd.next[to_prev] = from;
rd.prev[from] = to_prev;
rd.next[from] = to;
rd.prev[to] = from;
rd.next[to] = from_next;
rd.prev[from_next] = to;
}
else if (from_next == from)
{
rd.next[from] = to_next;
rd.prev[from] = to_prev;
rd.next[to_prev] = from;
rd.prev[to_next] = from;
rd.prev[to] = rd.next[to] = to;
}
else if (to_next == to)
{
rd.next[to] = from_next;
rd.prev[to] = from_prev;
rd.next[from_prev] = to;
rd.prev[from_next] = to;
rd.prev[from] = rd.next[from] = from;
}
else
{
rd.prev[from] = to_prev;
rd.next[from] = to_next;
rd.prev[to] = from_prev;
rd.next[to] = from_next;
rd.next[from_prev] = to;
rd.prev[from_next] = to;
rd.next[to_prev] = from;
rd.prev[to_next] = from;
}
#ifndef NDEBUG
for (unsigned i = 1; i <= rd.num_cpts (); i ++)
{
assert (rd.prev[rd.next[i]] == i);
assert (rd.next[rd.prev[i]] == i);
}
#endif
bool from_inside = rd.cpt_inside % from,
to_inside = rd.cpt_inside % to;
rd.cpt_inside -= from;
rd.cpt_inside -= to;
if (from_inside)
rd.cpt_inside.push (to);
if (to_inside)
rd.cpt_inside.push (from);
unsigned cfrom = rd.cpt_starting_circle[from],
cto = rd.cpt_starting_circle[to],
c_ending_from = rd.cpt_ending_circle[from],
c_ending_to = rd.cpt_ending_circle[to];
rd.cpt_starting_circle[from] = cto;
rd.cpt_starting_circle[to] = cfrom;
rd.cpt_ending_circle[from] = c_ending_to;
rd.cpt_ending_circle[to] = c_ending_from;
if (rd.marked_edge == from)
rd.marked_edge = to;
else if (rd.marked_edge == to)
rd.marked_edge = from;
set<unsigned> t = lg_edges[from];
lg_edges[from] = lg_edges[to];
lg_edges[to] = t;
#if 0
gl_starting_circles.clear ();
gl_ending_circles.clear ();
for (ullmanset<1>::const_iter i = gl_crossings; i; i ++)
{
unsigned c2 = i.val (),
lc2 = i.pos () + 1;
unsigned from, to, left, right;
if (c2 == c)
{
from = from_s.ept_circle (d, d.crossings[c2][3]);
to = from_s.ept_circle (d, d.crossings[c2][1]);
left = to_s.ept_circle (d, d.crossings[c2][3]);
right = to_s.ept_circle (d, d.crossings[c2][1]);
}
else
{
from = from_s.ept_circle (d, d.crossings[c2][1]);
to = from_s.ept_circle (d, d.crossings[c2][3]);
left = to_s.ept_circle (d, d.crossings[c2][1]);
right = to_s.ept_circle (d, d.crossings[c2][3]);
}
gl_starting_circles += from;
gl_starting_circles += to;
gl_ending_circles += left;
gl_ending_circles += right;
unsigned lfrom = gl_starting_circles.position (from) + 1,
lto = gl_starting_circles.position (to) + 1;
unsigned lleft = gl_ending_circles.position (left) + 1,
lright = gl_ending_circles.position (right) + 1;
rd.cpt_starting_circle[rd.crossing_to_cpt (lc2)] = lto;
rd.cpt_starting_circle[rd.crossing_from_cpt (lc2)] = lfrom;
rd.cpt_ending_circle[rd.crossing_to_cpt (lc2)] = lleft;
rd.cpt_ending_circle[rd.crossing_from_cpt (lc2)] = lright;
}
#endif
}
void
resolution_diagram::reverse ()
{
basedvector<unsigned, 1> new_prev (num_cpts ()),
new_next (num_cpts ()),
new_cpt_starting_circle (num_cpts ()),
new_cpt_ending_circle (num_cpts ());
for (unsigned i = 1; i <= num_cpts (); i ++)
{
unsigned j = other_cpt (i);
new_prev[i] = other_cpt (prev[j]);
new_next[i] = other_cpt (next[j]);
new_cpt_starting_circle[i] = cpt_starting_circle[j];
new_cpt_ending_circle[i] = cpt_ending_circle[j];
}
unsigned new_marked_edge = marked_edge ? other_cpt (marked_edge) : 0;
prev = new_prev;
next = new_next;
cpt_starting_circle = new_cpt_starting_circle;
cpt_ending_circle = new_cpt_ending_circle;
marked_edge = new_marked_edge;
}
void
resolution_diagram::reverse_orientation ()
{
if (marked_edge)
marked_edge = next[marked_edge];
for (unsigned i = 1; i <= num_cpts (); i ++)
std::swap (prev[i], next[i]);
cpt_inside.toggle ();
}
knot_diagram
resolution_diagram::as_knot_diagram () const
{
unsigned n_edges = num_cpts ();
unsigned n_epts = n_edges * 2;
basedvector<basedvector<unsigned, 1>, 1> crossings (n_crossings);
for (unsigned i = 1; i <= n_crossings; i ++)
{
basedvector<unsigned, 1> v (4);
v[1] = v[2] = v[3] = v[4] = 0;
crossings[i] = v;
}
for (unsigned pt = 1; pt <= num_cpts (); pt ++)
{
unsigned c = cpt_crossing (pt);
unsigned prev_pt = prev[pt];
unsigned prev_c = cpt_crossing (prev_pt);
if (is_to_cpt (pt))
{
assert (crossings[c][3] == 0
&& crossings[c][4] == 0);
if (cpt_inside % pt)
{
crossings[c][4] = 2 * pt - 1;
crossings[c][3] = 2 * prev_pt;
}
else
{
crossings[c][3] = 2 * pt - 1;
crossings[c][4] = 2 * prev_pt;
}
}
else
{
assert (crossings[c][1] == 0
&& crossings[c][2] == 0);
if (cpt_inside % pt)
{
crossings[c][2] = 2 * pt - 1;
crossings[c][1] = 2 * prev_pt;
}
else
{
crossings[c][1] = 2 * pt - 1;
crossings[c][2] = 2 * prev_pt;
}
}
}
knot_diagram kd ("<from rd>", crossings);
if (marked_edge)
kd.marked_edge = marked_edge;
return kd;
}
void
resolution_diagram::d (basedvector<pair<unsigned, unsigned>, 1> &out) const
{
if (n_crossings == 1)
{
if (n_starting_circles == 1)
{
assert (n_ending_circles == 2);
/* 1 -> x + y */
out.append (pair<unsigned, unsigned> (unsigned_fill (n_starting_circles),
unsigned_bitmask (1)));
out.append (pair<unsigned, unsigned> (unsigned_fill (n_starting_circles),
unsigned_bitmask (2)));
/* a -> xy */
out.append (pair<unsigned, unsigned> (0, 0));
}
else
{
assert (n_starting_circles == 2);
/* 1 -> 1 */
out.append (pair<unsigned, unsigned> (unsigned_fill (n_starting_circles),
unsigned_fill (n_ending_circles)));
/* a -> x, b -> x */
out.append (pair<unsigned, unsigned> (unsigned_bitmask (1), 0));
out.append (pair<unsigned, unsigned> (unsigned_bitmask (2), 0));
}
return;
}
unsigned self_crossed = 0;
bool self_inside = 0,
self_outside = 0;
for (unsigned i = 1; i <= n_crossings; i ++)
{
unsigned from = crossing_from (i),
to = crossing_to (i);
if (from == to)
{
if (self_crossed)
{
if (self_crossed != from)
{
assert (out.size () == 0);
return;
}
}
else
self_crossed = from;
if (crossing_from_inside (i))
self_inside = 1;
else
self_outside = 1;
}
}
unsigned common_from = crossing_from (1);
for (unsigned i = 2; i <= n_crossings; i ++)
{
if (common_from != crossing_from (i))
{
common_from = 0;
break;
}
}
unsigned common_to = crossing_to (1);
for (unsigned i = 2; i <= n_crossings; i ++)
{
if (common_to != crossing_to (i))
{
common_to = 0;
break;
}
}
basedvector<unsigned, 1> incoming (n_starting_circles),
outgoing (n_starting_circles);
for (unsigned i = 1; i <= n_starting_circles; i ++)
incoming[i] = outgoing[i] = 0;
for (unsigned i = 1; i <= n_crossings; i ++)
{
incoming[crossing_to (i)] ++;
outgoing[crossing_from (i)] ++;
}
bool single_entry_single_exit = 1;
unsigned double_entry_double_exit = 0;
for (unsigned i = 1; i <= n_starting_circles; i ++)
{
if (incoming[i] != 1
|| outgoing[i] != 1)
single_entry_single_exit = 0;
if (incoming[i] == 2
&& outgoing[i] == 2)
{
if (double_entry_double_exit)
{
double_entry_double_exit = 0;
break;
}
else
double_entry_double_exit = i;
}
}
/* type A_k */
if (common_from && common_to && n_starting_circles == 2)
{
/* 1 -> 1 */
out.append (pair<unsigned, unsigned> (unsigned_fill (n_starting_circles),
unsigned_fill (n_ending_circles)));
}
/* type B_k */
if (single_entry_single_exit)
{
/* prod a_i -> xy */
out.append (pair<unsigned, unsigned> (0, 0));
}