203477c3a8
Verification of Przytycki's congruence works fine, however there are some small modifications that could be made. The, naive, approach to the verification of periodicity congruence for the Khovanov polynomial didn't work. There are just too many cases to check. Generation of all of them can exhaust the memory.
130 lines
2.7 KiB
C++
130 lines
2.7 KiB
C++
#ifndef _KNOTKIT_KNOTKIT_H
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#define _KNOTKIT_KNOTKIT_H
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// includes lib.h
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#include <algebra/algebra.h>
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extern bool verbose;
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static const unsigned max_edges = 58;
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static const unsigned max_crossings = 29;
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static const unsigned max_circles = 58;
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class knot_diagram;
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#include <planar_diagram.h>
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#include <dt_code.h>
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#include <knot_diagram.h>
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#include <simplify_chain_complex.h>
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#include <sseq.h>
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#include <smoothing.h>
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#include <cobordism.h>
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#include <cube.h>
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#include <steenrod_square.h>
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#include <spanning_tree_complex.h>
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class knot_desc
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{
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public:
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enum table
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{
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NONE,
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ROLFSEN,
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HTW,
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HTW_ALT,
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HTW_NONALT,
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MT,
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MT_ALT,
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MT_NONALT,
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TORUS,
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};
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table t;
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unsigned i;
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unsigned j;
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public:
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knot_desc () : t(NONE) { }
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knot_desc (table t_, unsigned i_, unsigned j_)
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: t(t_), i(i_), j(j_)
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{ }
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knot_desc (const knot_desc &desc)
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: t(desc.t), i(desc.i), j(desc.j)
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{ }
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knot_desc (reader &r);
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~knot_desc () { }
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knot_desc &operator = (const knot_desc &desc)
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{
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t = desc.t;
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i = desc.i;
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j = desc.j;
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return *this;
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}
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bool operator == (const knot_desc &desc) const
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{
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return t == desc.t && i == desc.i && j == desc.j;
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}
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bool operator < (const knot_desc &desc) const
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{
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if ((int)t < (int)desc.t)
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return 1;
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else if ((int)t > (int)desc.t)
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return 0;
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if (i < desc.i)
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return 1;
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else if (i > desc.i)
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return 0;
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return j < desc.j;
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}
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knot_diagram diagram () const;
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std::string name () const;
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unsigned table_crossing_knots () const;
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hash_t hash_self () const
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{
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return hash_combine (hash ((int)t),
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hash_combine (hash (i),
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hash (j)));
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}
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void write_self (writer &w) const;
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void show_self () const { printf ("%s", name ().c_str ()); }
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void display_self () const { show_self (); newline (); }
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};
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unsigned rolfsen_crossing_knots (unsigned n);
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planar_diagram rolfsen_knot (unsigned n, unsigned k);
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unsigned htw_knots (unsigned n, bool alternating);
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unsigned htw_knots (unsigned n);
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dt_code htw_knot (unsigned n, bool alternating, unsigned k);
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dt_code htw_knot (unsigned n, unsigned k);
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unsigned mt_links (unsigned n, bool alternating);
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unsigned mt_links (unsigned n);
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dt_code mt_link (unsigned n, bool alternating, unsigned k);
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dt_code mt_link (unsigned n, unsigned k);
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planar_diagram torus_knot (unsigned n_strands, unsigned n_shifts);
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knot_diagram braid (unsigned n_strands, const basedvector<int, 1> &twists);
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knot_diagram braid (unsigned n_strands, unsigned n_twists, int twists_ar[]);
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knot_diagram parse_knot (const char *s);
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resolution_diagram parse_resolution_diagram (const char *s);
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// 11 <= n <= 15
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basedvector<basedvector<unsigned, 1>, 1> mutant_knot_groups (unsigned n);
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#endif // _KNOTKIT_KNOTKIT_H
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