Ready to compute splitting bound data for paper.
This commit is contained in:
Cotton Seed
parent
a09ca308d9
commit
e19a274c8e
4
Makefile
4
Makefile
@ -8,8 +8,8 @@ CXX = clang++ -fno-color-diagnostics --stdlib=libc++ --std=c++11 -I/u/cseed/llvm
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INCLUDES = -I/opt/local/include -I.
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OPTFLAGS = -g
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# OPTFLAGS = -O2 -g
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# OPTFLAGS = -g
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OPTFLAGS = -O2 -g
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# OPTFLAGS = -O2 -DNDEBUG
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LDFLAGS = -L/opt/local/lib -L/u/cseed/llvm-3.1/lib
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@ -22,6 +22,7 @@ class Z2
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Z2 &operator = (int x) { v = (bool)(x & 1); return *this; }
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bool operator == (const Z2 &x) const { return v == x.v; }
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bool operator != (const Z2 &x) const { return v != x.v; }
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bool operator == (int x) const { return v == (bool)(x & 1); }
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bool operator != (int x) const { return !operator == (x); }
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@ -67,6 +67,11 @@ template<class T> class fraction_field
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return fraction_field (new_num, denom*xe);
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}
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fraction_field operator - () const
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{
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return fraction_field (-num, denom);
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}
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fraction_field operator * (const fraction_field &x) const
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{
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T d1 = num.gcd (x.denom);
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@ -211,7 +216,6 @@ fraction_field<T>::reduce ()
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}
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T d = num.gcd (denom);
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num = num.divide_exact (d);
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denom = denom.divide_exact (d);
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}
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@ -221,7 +225,6 @@ fraction_field<T>::check ()
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{
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if (num == 0)
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return;
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// check denom == 1
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// assert (num.gcd (denom) == 1);
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}
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@ -5,7 +5,7 @@
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template<unsigned n>
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class multivariate_monomial
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{
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private:
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public:
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unsigned v[n];
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public:
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@ -265,6 +265,12 @@ public:
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monomial common_monomial () const;
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multivariate_polynomial gcd (const multivariate_polynomial &b) const
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{
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// ???
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return multivariate_polynomial (1);
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}
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pair<multivariate_polynomial, multivariate_polynomial>
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uncommon_factors (multivariate_polynomial b, basedvector<multivariate_polynomial, 1> ds);
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maybe<multivariate_polynomial>
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288
main.cpp
288
main.cpp
@ -1114,11 +1114,11 @@ test_forgetful_signs ()
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}
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template<class R> sseq
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compute_forgetfulss (knot_diagram &kd)
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compute_forgetfulss (knot_diagram &kd,
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basedvector<R, 1> comp_weight)
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{
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unsigned n = kd.num_components ();
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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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@ -1140,9 +1140,7 @@ compute_forgetfulss (knot_diagram &kd)
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}
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assert (t == n);
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basedvector<R, 1> comp_weight (n);
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for (unsigned i = 1; i <= n; i ++)
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comp_weight[i] = R ((int)i);
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assert (comp_weight.size () == n);
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map<unsigned, R> crossing_over_sign;
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@ -1275,18 +1273,15 @@ compute_forgetfulss (knot_diagram &kd)
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}
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#endif
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#if 0
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printf ("E_%d: ", (-dq) / 2);
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display (C->free_poincare_polynomial ());
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#endif
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if (d == 0)
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break;
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}
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#if 0
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sseq_builder b (c.khC, d);
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return b.build_sseq ();
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#endif
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return sseq (bounds, pages);
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}
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@ -2209,9 +2204,281 @@ compare_gss_splitting ()
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}
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}
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template<class R> unsigned
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splitting_bound (knot_diagram &kd,
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basedvector<R, 1> comp_weight)
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{
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sseq ss = compute_forgetfulss<R> (kd, comp_weight);
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assert (ss.pages.size () >= 1);
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return ss.pages.size () - 1;
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}
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basedvector<basedvector<unsigned, 1>, 1>
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permutations (basedvector<unsigned, 1> v)
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{
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unsigned n = v.size ();
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basedvector<basedvector<unsigned, 1>, 1> ps;
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if (n == 1)
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{
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ps.append (v);
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return ps;
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}
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for (unsigned i = 1; i <= n; i ++)
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{
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unsigned x = v[i];
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basedvector<unsigned, 1> v2 (n - 1);
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for (unsigned j = 1; j < i; j ++)
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v2[j] = v[j];
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for (unsigned j = i + 1; j <= n; j ++)
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v2[j - 1] = v[j];
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basedvector<basedvector<unsigned, 1>, 1> ps2 = permutations (v2);
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for (unsigned j = 1; j <= ps2.size (); j ++)
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{
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basedvector<unsigned, 1> p2 = ps2[j];
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assert (p2.size () == n - 1);
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basedvector<unsigned, 1> v3 (n);
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v3[1] = x;
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for (unsigned k = 1; k <= n - 1; k ++)
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v3[k + 1] = p2[k];
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ps.append (v3);
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}
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}
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return ps;
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}
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basedvector<basedvector<unsigned, 1>, 1>
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permutations (unsigned n)
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{
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basedvector<unsigned, 1> v (n);
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for (unsigned i = 1; i <= n; i ++)
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v[i] = i;
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return permutations (v);
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}
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void
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compute_splitting_bounds ()
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{
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typedef fraction_field<polynomial<Z2> > Z2x;
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for (unsigned i = 1; i <= 12; i ++)
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for (unsigned j = 1; j <= mt_links (i); j ++)
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{
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knot_diagram kd (mt_link (i, j));
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unsigned m = kd.num_components ();
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if (m == 1)
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continue;
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show (kd); newline ();
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printf (" m = %d\n", m);
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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 () == m);
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map<unsigned, unsigned> root_comp;
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unsigned t = 0;
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for (unsigned i = 1; i <= kd.num_edges (); i ++)
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{
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if (u.find (i) == i)
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{
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++ t;
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root_comp.push (i, t);
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}
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}
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assert (t == m);
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basedvector<Q, 1> comp_weightQ (m);
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for (unsigned i = 1; i <= m; i ++)
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comp_weightQ[i] = Q (i);
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unsigned bQ = splitting_bound<Q> (kd, comp_weightQ);
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basedvector<Z2x, 1> comp_weightZ2x (m);
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for (unsigned i = 1; i <= m; i ++)
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comp_weightZ2x[i] = Z2x (polynomial<Z2> (Z2 (1), i));
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unsigned bZ2x = splitting_bound<Z2x> (kd, comp_weightZ2x);
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// lower bound
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unsigned b = std::max (bQ, bZ2x);
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printf (" bQ = %d\n", bQ);
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printf (" bZ2x = %d\n", bZ2x);
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printf (" b = %d\n", b);
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unsigned total_lk = kd.total_linking_number ();
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unsigned b_lk_weak = total_lk == 0 ? 2 : total_lk;
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printf (" b_lk_weak = %d\n", b_lk_weak);
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basedvector<basedvector<unsigned, 1>, 1> ps = permutations (m);
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#if 0
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printf ("ps, |ps| = %d, m = %d:\n", ps.size (), m);
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for (unsigned i = 1; i <= ps.size (); i ++)
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{
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basedvector<unsigned, 1> p = ps[i];
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assert (p.size () == m);
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printf (" % 3d: ", i);
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for (unsigned j = 1; j <= m; j ++)
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printf (" %d", p[j]);
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newline ();
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}
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#endif
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unsigned r = kd.n_crossings;
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for (unsigned i = 1; i <= ps.size (); i ++)
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{
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basedvector<unsigned, 1> p = ps[i];
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unsigned ri = 0;
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for (unsigned j = 1; j <= kd.n_crossings; j ++)
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{
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unsigned upper_e = kd.ept_edge (kd.crossings[j][2]),
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lower_e = kd.ept_edge (kd.crossings[j][1]);
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unsigned upper_c = root_comp(u.find (upper_e)),
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lower_c = root_comp(u.find (lower_e));
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if (upper_c != lower_c
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&& p[upper_c] < p[lower_c])
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ri ++;
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}
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if (ri < r)
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r = ri;
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}
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printf (" r = %d\n", r);
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assert (b <= r);
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// non-trivial link, sp at least 1.
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assert (b_lk_weak >= 1);
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if (b <= 1
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&& b_lk_weak == 1)
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continue;
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if (b > b_lk_weak)
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{
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if (b == r)
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printf (" > sp = %d (b)\n", b);
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else
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printf (" > %d <= sp <= %d (b)\n", b, r);
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}
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else if (b == b_lk_weak)
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{
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if (b == r)
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printf (" > sp = %d (b + b_lk_weak)\n", b);
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else
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printf (" > %d <= sp <= %d (b + b_lk_weak)\n", b, r);
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}
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else if (b_lk_weak == r)
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{
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assert (b < b_lk_weak);
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printf (" > sp = %d (b_lk_weak)\n", b_lk_weak);
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}
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}
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}
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void
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compute_forgetful_tables ()
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{
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// typedef fraction_field<multivariate_polynomial<Z2, 10> > R;
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typedef Z2 R;
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#if 0
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for (unsigned i = 1; i <= 10; i ++)
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for (unsigned j = 1; j <= mt_links (i); j ++)
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{
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knot_diagram kd (mt_link (i, j));
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#endif
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{
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// knot_diagram kd (mt_link (12, 0, 2087));
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// knot_diagram kd (mt_link (12, 0, 1705));
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// knot_diagram kd (mt_link (14, 0, 66759));
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// knot_diagram kd (mt_link (14, 0, 65798));
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knot_diagram kd (mt_link (13, 0, 8862));
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abort ();
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// sseq ss = compute_forgetfulss<R> (kd);
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sseq ss;
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#if 0
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if (ss.pages.size () < 2)
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continue;
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#endif
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for (unsigned k = 1; k <= ss.pages.size (); k ++)
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{
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if (k == 1)
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printf ("%s &", kd.name.c_str ());
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else
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printf (" &");
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printf (" $E_%d$ & %d & $", k, ss.pages[k].total_rank ());
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bool first = 1;
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const sseq_bounds &b = ss.bounds;
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for (int i = b.minh; i <= b.maxh; i ++)
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for (int j = b.minq; j <= b.maxq; j ++)
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{
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unsigned r = ss.pages[k].rank[i - b.minh][j - b.minq];
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if (r > 0)
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{
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if (first)
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first = 0;
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else
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printf (" + ");
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if (i == 0
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&& j == 0)
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printf ("%d", r);
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else
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{
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if (r != 1)
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printf ("%d", r);
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if (i != 0)
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printf ("t^{%d}", i);
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if (j != 0)
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printf ("q^{%d}", j);
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}
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}
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}
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printf ("$ \\\\\n");
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}
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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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compute_splitting_bounds ();
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return 0;
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compute_forgetful_tables ();
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return 0;
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#if 0
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{
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knot_diagram kd (mt_link (5, 1, 3));
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show (kd); newline ();
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@ -2220,6 +2487,7 @@ main ()
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ss.texshow (stdout, "L5a3");
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}
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return 0;
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#endif
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compute_lee_bound ();
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return 0;
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