Added descriptions of periodicity test to usage and README
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Wojciech Politarczyk
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README
21
README
@ -3,6 +3,11 @@ knotkit is a C++ software package written by Cotton Seed
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invariants appearing in low-dimensional topology. Other contributors
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include Josh Batson.
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This is a slightly modified version of knotkit. It includes a periodicity
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testing functionality based on the Przytycki's criterion in terms of
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Jones polynomial and a periodicity criterion from the upcoming paper by
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Maciej Borodzik, Anna Kosiorek and Wojciech Politarczyk.
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TABLE OF CONTENTS
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1. INTRO
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@ -101,7 +106,8 @@ sequence. The output for the command sq2 matches the output for the
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program written by Lipshitz-Sarkar and is suitable for loading into
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Sage. The command s outputs a single line of text.
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usage: kk <invariant> [options...] <link>
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usage: %s <invariant> [options...] <link>
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/home/wojtek/ownCloud/src/knotkit/kk
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compute <invariant> for knot or link <link>
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<invariant> can be one of:
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kh: Khovanov homology
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@ -113,10 +119,14 @@ usage: kk <invariant> [options...] <link>
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leess: spectral sequence coming from Bar-Natan analogue of Lee's
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deformation of Khovanov's complex (whew!)
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s: Rasmussen's s-invariant coming from lee
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khp: computes Khovanov polynomial of a link
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jones: computes Jones polynomial of a link
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periodicity: uses periodicity criterion of Przytycki and
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the criterion in terms of Khovanov polynomial
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output:
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kh, gss, lsss, leess: .tex file
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sq2: text in Sage format
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s: text
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s, khp, jones, periodicity: text
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options:
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-r : compute reduced theory
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-h : print this message
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@ -125,6 +135,13 @@ options:
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-f <field> : ground field (if applicable)
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(Z2 is the default)
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-v : verbose: report progress as the computation proceeds
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-p : period when verifying periodicity, can be equal to
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5,7,11,13,17 or 19
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-t : type of periodicity test:
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- Przytycki - Przytycki's periodicity test
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- Kh - periodicity criterion in terms of Khovanov homology
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- all - uses both criteria and tests for all prime
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periods between 5 and 19
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<field> can be one of:
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Z2, Z3, Q
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<link> can be one of:
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95
kk.cpp
95
kk.cpp
@ -9,47 +9,58 @@ const char *program_name;
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void
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usage ()
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{
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printf ("usage: %s <invariant> [options...] <link>\n", program_name);
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printf (" compute <invariant> for knot or link <link>\n");
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printf ("<invariant> can be one of:\n");
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printf (" kh: Khovanov homology\n");
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printf (" gss: Szabo's geometric spectral sequence\n");
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printf (" lsss: Batson-Seed link splitting spectral sequence\n");
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printf (" component weights are 0, 1, ..., m\n");
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printf (" sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh\n");
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printf (" output suitable for Sage\n");
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printf (" leess: spectral sequence coming from Bar-Natan analogue of Lee's\n");
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printf (" deformation of Khovanov's complex (whew!)\n");
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printf (" s: Rasmussen's s-invariant coming from lee\n");
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printf ("output:\n");
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printf (" kh, gss, lsss, leess: .tex file\n");
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printf (" sq2: text in Sage format\n");
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printf (" s: text\n");
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printf ("options:\n");
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printf (" -r : compute reduced theory\n");
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printf (" -h : print this message\n");
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printf (" -o <file> : write output to <file>\n");
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printf (" (stdout is the default)\n");
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printf (" -f <field> : ground field (if applicable)\n");
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printf (" (Z2 is the default)\n");
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printf (" -v : verbose: report progress as the computation proceeds\n");
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printf ("<field> can be one of:\n");
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printf (" Z2, Z3, Q\n");
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printf ("<link> can be one of:\n");
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printf (" - the unknot, e.g. U or unknot\n");
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printf (" - a torus knot, e.g. T(2,3)\n");
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printf (" - a Rolfsen table knot, e.g. 10_124\n");
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printf (" - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214\n");
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printf (" - a Morwen Thistlethwaite link, e.g. L8n9 or L13n8862\n");
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printf (" - a planar diagram, e.g.\n");
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printf (" PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or\n");
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printf (" PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]\n");
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printf (" - a Dowker-Thistlethwaite code, e.g.\n");
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printf (" DTCode[6,8,2,4],\n");
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printf (" DT[dadbcda] or\n");
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printf (" DT[{6, -8}, {-10, 12, -14, 2, -4}]\n");
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printf (" - a braid, e.g. BR[2, {-1, -1, -1}]\n");
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printf (" - disjoint union (juxtaposition), e.g. T(2,3) U\n");
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std::cout << "usage: %s <invariant> [options...] <link>\n" << program_name << "\n"
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<< " compute <invariant> for knot or link <link>\n"
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<< "<invariant> can be one of:\n"
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<< " kh: Khovanov homology\n"
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<< " gss: Szabo's geometric spectral sequence\n"
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<< " lsss: Batson-Seed link splitting spectral sequence\n"
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<< " component weights are 0, 1, ..., m\n"
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<< " sq2: Lipshitz-Sarkar Steenrod square on Z/2 Kh\n"
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<< " output suitable for Sage\n"
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<< " leess: spectral sequence coming from Bar-Natan analogue of Lee's\n"
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<< " deformation of Khovanov's complex (whew!)\n"
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<< " s: Rasmussen's s-invariant coming from lee\n"
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<< " khp: computes Khovanov polynomial of a link\n"
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<< " jones: computes Jones polynomial of a link\n"
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<< " periodicity: uses periodicity criterion of Przytycki and\n"
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<< " the criterion in terms of Khovanov polynomial\n"
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<< "output:\n"
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<< " kh, gss, lsss, leess: .tex file\n"
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<< " sq2: text in Sage format\n"
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<< " s, khp, jones, periodicity: text\n"
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<< "options:\n"
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<< " -r : compute reduced theory\n"
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<< " -h : print this message\n"
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<< " -o <file> : write output to <file>\n"
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<< " (stdout is the default)\n"
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<< " -f <field> : ground field (if applicable)\n"
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<< " (Z2 is the default)\n"
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<< " -v : verbose: report progress as the computation proceeds\n"
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<< " -p : period when verifying periodicity, can be equal to\n"
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<< " 5,7,11,13,17 or 19\n"
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<< " -t : type of periodicity test:\n"
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<< " - Przytycki - Przytycki's periodicity test\n"
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<< " - Kh - periodicity criterion in terms of Khovanov homology\n"
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<< " - all - uses both criteria and tests for all prime\n"
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<< " periods between 5 and 19\n"
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<< "<field> can be one of:\n"
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<< " Z2, Z3, Q\n"
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<< "<link> can be one of:\n"
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<< " - the unknot, e.g. U or unknot\n"
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<< " - a torus knot, e.g. T(2,3)\n"
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<< " - a Rolfsen table knot, e.g. 10_124\n"
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<< " - a Hoste-Thistlethwaite-Weeks knot, e.g. 11a12 or 12n214\n"
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<< " - a Morwen Thistlethwaite link, e.g. L8n9 or L13n8862\n"
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<< " - a planar diagram, e.g.\n"
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<< " PD[X[1, 4, 2, 5], X[3, 6, 4, 1], X[5, 2, 6, 3]] or\n"
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<< " PD[[1, 4, 2, 5], [3, 6, 4, 1], [5, 2, 6, 3]]\n"
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<< " - a Dowker-Thistlethwaite code, e.g.\n"
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<< " DTCode[6,8,2,4],\n"
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<< " DT[dadbcda] or\n"
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<< " DT[{6, -8}, {-10, 12, -14, 2, -4}]\n"
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<< " - a braid, e.g. BR[2, {-1, -1, -1}]\n"
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<< " - disjoint union (juxtaposition), e.g. T(2,3) U\n";
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}
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FILE *outfp = stdout;
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@ -336,7 +347,7 @@ void check_periodicity(std::string out_file) {
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}
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auto result = std::find(primes_list.begin(), primes_list.end(), period);
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if(result == primes_list.end()) {
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std::cout << "For now you can only check periodicity for primes up to 31..." << "\n";
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std::cout << "For now you can only check periodicity for primes up to 19..." << "\n";
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exit(EXIT_FAILURE);
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}
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std::ofstream out(out_file, std::ios_base::app);
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