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Ready to compute splitting bound data for paper.

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This commit is contained in:
Cotton Seed 2013-01-17 11:05:44 -05:00
parent a09ca308d9
commit e19a274c8e
5 changed files with 296 additions and 18 deletions
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4
Makefile
View File

@ -8,8 +8,8 @@ CXX = clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -I/u/cseed/llvm
INCLUDES = -I/opt/local/include -I.
OPTFLAGS = -g
# OPTFLAGS = -O2 -g
# OPTFLAGS = -g
OPTFLAGS = -O2 -g
# OPTFLAGS = -O2 -DNDEBUG
LDFLAGS = -L/opt/local/lib -L/u/cseed/llvm-3.1/lib

1
algebra/Z2.h
View File

@ -22,6 +22,7 @@ class Z2
Z2 &operator = (int x) { v = (bool)(x & 1); return *this; }
bool operator == (const Z2 &x) const { return v == x.v; }
bool operator != (const Z2 &x) const { return v != x.v; }
bool operator == (int x) const { return v == (bool)(x & 1); }
bool operator != (int x) const { return !operator == (x); }

7
algebra/fraction_field.h
View File

@ -67,6 +67,11 @@ template<class T> class fraction_field
return fraction_field (new_num, denom*xe);
}
fraction_field operator - () const
{
return fraction_field (-num, denom);
}
fraction_field operator * (const fraction_field &x) const
{
T d1 = num.gcd (x.denom);
@ -211,7 +216,6 @@ fraction_field<T>::reduce ()
}
T d = num.gcd (denom);
num = num.divide_exact (d);
denom = denom.divide_exact (d);
}
@ -221,7 +225,6 @@ fraction_field<T>::check ()
{
if (num == 0)
return;
// check denom == 1
// assert (num.gcd (denom) == 1);
}

8
algebra/multivariate_polynomial.h
View File

@ -5,7 +5,7 @@
template<unsigned n>
class multivariate_monomial
{
private:
public:
unsigned v[n];
public:
@ -265,6 +265,12 @@ public:
monomial common_monomial () const;
multivariate_polynomial gcd (const multivariate_polynomial &b) const
{
// ???
return multivariate_polynomial (1);
}
pair<multivariate_polynomial, multivariate_polynomial>
uncommon_factors (multivariate_polynomial b, basedvector<multivariate_polynomial, 1> ds);
maybe<multivariate_polynomial>

294
main.cpp
View File

@ -1114,11 +1114,11 @@ test_forgetful_signs ()
}
template<class R> sseq
compute_forgetfulss (knot_diagram &kd)
compute_forgetfulss (knot_diagram &kd,
basedvector<R, 1> comp_weight)
{
unsigned n = kd.num_components ();
unionfind<1> u (kd.num_edges ());
for (unsigned i = 1; i <= kd.n_crossings; i ++)
{
@ -1139,11 +1139,9 @@ compute_forgetfulss (knot_diagram &kd)
}
}
assert (t == n);
basedvector<R, 1> comp_weight (n);
for (unsigned i = 1; i <= n; i ++)
comp_weight[i] = R ((int)i);
assert (comp_weight.size () == n);
map<unsigned, R> crossing_over_sign;
// crossings
@ -1275,18 +1273,15 @@ compute_forgetfulss (knot_diagram &kd)
}
#endif
#if 0
printf ("E_%d: ", (-dq) / 2);
display (C->free_poincare_polynomial ());
#endif
if (d == 0)
break;
}
#if 0
sseq_builder b (c.khC, d);
return b.build_sseq ();
#endif
return sseq (bounds, pages);
}
@ -2209,9 +2204,281 @@ compare_gss_splitting ()
}
}
template<class R> unsigned
splitting_bound (knot_diagram &kd,
basedvector<R, 1> comp_weight)
{
sseq ss = compute_forgetfulss<R> (kd, comp_weight);
assert (ss.pages.size () >= 1);
return ss.pages.size () - 1;
}
basedvector<basedvector<unsigned, 1>, 1>
permutations (basedvector<unsigned, 1> v)
{
unsigned n = v.size ();
basedvector<basedvector<unsigned, 1>, 1> ps;
if (n == 1)
{
ps.append (v);
return ps;
}
for (unsigned i = 1; i <= n; i ++)
{
unsigned x = v[i];
basedvector<unsigned, 1> v2 (n - 1);
for (unsigned j = 1; j < i; j ++)
v2[j] = v[j];
for (unsigned j = i + 1; j <= n; j ++)
v2[j - 1] = v[j];
basedvector<basedvector<unsigned, 1>, 1> ps2 = permutations (v2);
for (unsigned j = 1; j <= ps2.size (); j ++)
{
basedvector<unsigned, 1> p2 = ps2[j];
assert (p2.size () == n - 1);
basedvector<unsigned, 1> v3 (n);
v3[1] = x;
for (unsigned k = 1; k <= n - 1; k ++)
v3[k + 1] = p2[k];
ps.append (v3);
}
}
return ps;
}
basedvector<basedvector<unsigned, 1>, 1>
permutations (unsigned n)
{
basedvector<unsigned, 1> v (n);
for (unsigned i = 1; i <= n; i ++)
v[i] = i;
return permutations (v);
}
void
compute_splitting_bounds ()
{
typedef fraction_field<polynomial<Z2> > Z2x;
for (unsigned i = 1; i <= 12; i ++)
for (unsigned j = 1; j <= mt_links (i); j ++)
{
knot_diagram kd (mt_link (i, j));
unsigned m = kd.num_components ();
if (m == 1)
continue;
show (kd); newline ();
printf (" m = %d\n", m);
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 () == m);
map<unsigned, unsigned> root_comp;
unsigned t = 0;
for (unsigned i = 1; i <= kd.num_edges (); i ++)
{
if (u.find (i) == i)
{
++ t;
root_comp.push (i, t);
}
}
assert (t == m);
basedvector<Q, 1> comp_weightQ (m);
for (unsigned i = 1; i <= m; i ++)
comp_weightQ[i] = Q (i);
unsigned bQ = splitting_bound<Q> (kd, comp_weightQ);
basedvector<Z2x, 1> comp_weightZ2x (m);
for (unsigned i = 1; i <= m; i ++)
comp_weightZ2x[i] = Z2x (polynomial<Z2> (Z2 (1), i));
unsigned bZ2x = splitting_bound<Z2x> (kd, comp_weightZ2x);
// lower bound
unsigned b = std::max (bQ, bZ2x);
printf (" bQ = %d\n", bQ);
printf (" bZ2x = %d\n", bZ2x);
printf (" b = %d\n", b);
unsigned total_lk = kd.total_linking_number ();
unsigned b_lk_weak = total_lk == 0 ? 2 : total_lk;
printf (" b_lk_weak = %d\n", b_lk_weak);
basedvector<basedvector<unsigned, 1>, 1> ps = permutations (m);
#if 0
printf ("ps, |ps| = %d, m = %d:\n", ps.size (), m);
for (unsigned i = 1; i <= ps.size (); i ++)
{
basedvector<unsigned, 1> p = ps[i];
assert (p.size () == m);
printf (" % 3d: ", i);
for (unsigned j = 1; j <= m; j ++)
printf (" %d", p[j]);
newline ();
}
#endif
unsigned r = kd.n_crossings;
for (unsigned i = 1; i <= ps.size (); i ++)
{
basedvector<unsigned, 1> p = ps[i];
unsigned ri = 0;
for (unsigned j = 1; j <= kd.n_crossings; j ++)
{
unsigned upper_e = kd.ept_edge (kd.crossings[j][2]),
lower_e = kd.ept_edge (kd.crossings[j][1]);
unsigned upper_c = root_comp(u.find (upper_e)),
lower_c = root_comp(u.find (lower_e));
if (upper_c != lower_c
&& p[upper_c] < p[lower_c])
ri ++;
}
if (ri < r)
r = ri;
}
printf (" r = %d\n", r);
assert (b <= r);
// non-trivial link, sp at least 1.
assert (b_lk_weak >= 1);
if (b <= 1
&& b_lk_weak == 1)
continue;
if (b > b_lk_weak)
{
if (b == r)
printf (" > sp = %d (b)\n", b);
else
printf (" > %d <= sp <= %d (b)\n", b, r);
}
else if (b == b_lk_weak)
{
if (b == r)
printf (" > sp = %d (b + b_lk_weak)\n", b);
else
printf (" > %d <= sp <= %d (b + b_lk_weak)\n", b, r);
}
else if (b_lk_weak == r)
{
assert (b < b_lk_weak);
printf (" > sp = %d (b_lk_weak)\n", b_lk_weak);
}
}
}
void
compute_forgetful_tables ()
{
// typedef fraction_field<multivariate_polynomial<Z2, 10> > R;
typedef Z2 R;
#if 0
for (unsigned i = 1; i <= 10; i ++)
for (unsigned j = 1; j <= mt_links (i); j ++)
{
knot_diagram kd (mt_link (i, j));
#endif
{
// knot_diagram kd (mt_link (12, 0, 2087));
// knot_diagram kd (mt_link (12, 0, 1705));
// knot_diagram kd (mt_link (14, 0, 66759));
// knot_diagram kd (mt_link (14, 0, 65798));
knot_diagram kd (mt_link (13, 0, 8862));
abort ();
// sseq ss = compute_forgetfulss<R> (kd);
sseq ss;
#if 0
if (ss.pages.size () < 2)
continue;
#endif
for (unsigned k = 1; k <= ss.pages.size (); k ++)
{
if (k == 1)
printf ("%s &", kd.name.c_str ());
else
printf (" &");
printf (" $E_%d$ & %d & $", k, ss.pages[k].total_rank ());
bool first = 1;
const sseq_bounds &b = ss.bounds;
for (int i = b.minh; i <= b.maxh; i ++)
for (int j = b.minq; j <= b.maxq; j ++)
{
unsigned r = ss.pages[k].rank[i - b.minh][j - b.minq];
if (r > 0)
{
if (first)
first = 0;
else
printf (" + ");
if (i == 0
&& j == 0)
printf ("%d", r);
else
{
if (r != 1)
printf ("%d", r);
if (i != 0)
printf ("t^{%d}", i);
if (j != 0)
printf ("q^{%d}", j);
}
}
}
printf ("$ \\\\\n");
}
}
}
int
main ()
{
compute_splitting_bounds ();
return 0;
compute_forgetful_tables ();
return 0;
#if 0
{
knot_diagram kd (mt_link (5, 1, 3));
show (kd); newline ();
@ -2220,6 +2487,7 @@ main ()
ss.texshow (stdout, "L5a3");
}
return 0;
#endif
compute_lee_bound ();
return 0;