source: git/dyn_modules/callpolymake/polymake_documentation.cc @ 69b2c1

#include <polymake_conversion.h>

#include <dyn_modules/callgfanlib/bbcone.h>
#include <dyn_modules/callgfanlib/bbfan.h>
#include <dyn_modules/callgfanlib/bbpolytope.h>

#include <Singular/blackbox.h>
#include <Singular/ipshell.h>
#include <Singular/subexpr.h>
#include <Singular/ipid.h>

void init_polymake_help()
{

  const char *polymake_banner =
    "Welcome to polymake\nCopyright (c) 1997-2012\nEwgenij Gawrilow, Michael Joswig (TU Darmstadt)\nhttp://www.polymake.org\n";

  PrintS(polymake_banner);

  const char* polymake_help =
    "SHARED LIBRARY: polymake.so  Interface to polymake (http://www.polymake.org)\nAUTHORS: Janko Boehm, boehm@mathematik.uni-kl.de\n         Yue Ren,     ren@mathematik.uni-kl.de\n\nOVERVIEW:\nPolymake is a tool to study the combinatorics \nand the geometry of convex polytopes and polyhedra. \nIt is also capable of dealing with simplicial complexes, \nmatroids, polyhedral fans, graphs, tropical objects.\nThe interface relies on the callable library functionality,\nby Ewgenij Gawrilow.\n\nREFERENCES:\nEwgenij Gawrilow and Michael Joswig. polymake: a framework for analyzing convex polytopes. \nPolytopes—combinatorics and computation (Oberwolfach, 1997), 43–73, DMV Sem., 29, BirkhÀuser, Basel, 2000. MR1785292 (2001f:52033)\n\nPROCEDURES:\n  boundaryLatticePoints(polytope p);\n  ehrhartPolynomialCoeff(polytope p);\n  facetVertexLatticeDistances(polytope p);\n  facetWidth(polytope p);\n  facetWidths(polytope p);\n  fVector(polytope p);\n  gorensteinIndex(polytope p);\n  gorensteinVector(polytope p);\n  hilbertBasis(cone c);\n  hStarVector(polytope p);\n  hVector(polytope p);\n  interiorLatticePoints(polytope p);\n  isBounded(polytope p);\n  isCanonical(polytope p);\n  isCompressed(polytope p);\n  isGorenstein(polytope p);\n  isLatticeEmpty(polytope p);\n  isNormal(polytope p);\n  isReflexive(polytope p);\n  isSmooth(polytope p);\n  isVeryAmple(polytope p);\n  latticeCodegree(polytope p);\n  latticeDegree(polytope p);\n  latticePoints(polytope p);\n  latticeVolume(polytope p);\n  maximalFace(polytope p, intvec v);\n  maximalValue(polytope p, intvec v);\n  minimalFace(polytope p, intvec v);\n  minimalValue(polytope p, intvec v);\n  minkowskiSum(polytope p, polytope q);\n  nBoundaryLatticePoints(polytope p);\n  nHilbertBasis(cone c);\n";

  module_help_main("polymake.so",polymake_help);


  const char*isReflexive_help =
    "USAGE:    isReflexive(polytope p)\nRETURN:   int, 1 if p is reflexive and 0 otherwise\nKEYWORDS: polytopes; polymake; reflexive\nEXAMPLE:  example isReflexive shows an example\nexample\n{ \"EXAMPLE: \";\nintmat M[4][4]=1,1,0,0, 1,0,1,0, 1,0,0,1, 1,-1,-1,-1;\npolytope p = polytopeViaVertices(M);\nPolymake::isReflexive(p);\nintmat N[4][4]=1,2,0,0, 1,0,2,0, 1,0,0,2, 1,-2,-2,-2;\nq = polytopeViaVertices(N);\nPolymake::isReflexive(q);\n}\n";

 module_help_proc("polymake.so","isReflexive", isReflexive_help);

  const char* isBounded_help =
    "USAGE:    isBounded(polytope p)\nRETURN:   int, 1 if p is bounded, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isBounded shows an example\n";

 module_help_proc("polymake.so","isBounded", isBounded_help);

  const char* isGorenstein_help =
    "USAGE:    isGorenstein(polytope p)\nRETURN:   int, 1 if p is gorenstein (i.e. reflexive after dilatation and translation), 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isGorenstein shows an example\n";

 module_help_proc("polymake.so","isGorenstein", isGorenstein_help);

  const char* gorensteinIndex_help =
    "USAGE:    gorensteinIndex(polytope p)\nRETURN:   int, n if p is reflexive after dilatation by n and translation, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example gorensteinIndex shows an example\n";

 module_help_proc("polymake.so","gorensteinIndex", gorensteinIndex_help);

  const char* gorensteinVector_help =
    "USAGE:    gorensteinVector(polytope p)\nRETURN:   intvec, v if p is reflexive after dilatation and translation by v, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example gorensteinVector shows an example\n";

 module_help_proc("polymake.so","gorensteinVector", gorensteinVector_help);

  const char* isCanonical_help =
    "USAGE:    isCanonical(polytope p)\nRETURN:   intvec, 1 if p has exactly one interior lattice point, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isCanonical shows an example\n";

 module_help_proc("polymake.so","isCanonical", isCanonical_help);

  const char* isTerminal_help =
    "USAGE:    isLatticeEmpty(polytope p)\nRETURN:   int, 1 if p contains no lattice points other than the vertices, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isLatticeEmpty shows an example\n";

 module_help_proc("polymake.so","isTerminal", isTerminal_help);

  const char* latticeVolume_help =
    "USAGE:    latticeVolume(polytope p)\nRETURN:   int, the normalized lattice volume of p, that is, (dim(P))! times the volume of P.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example latticeVolume shows an example\n";

 module_help_proc("polymake.so","latticeVolume", latticeVolume_help);

  const char* latticeDegree_help =
    "USAGE:    latticeDegree(polytope p)\nRETURN:   int, the lattice degree of p, i.e. degree of the Ehrhart polynomial of P.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example latticeDegree shows an example\n";

 module_help_proc("polymake.so","latticeDegree", latticeDegree_help);

  const char* latticeCodegree_help =
    "USAGE:    latticeCodegree(polytope p)\nRETURN:   int, getDimension(p)+1-latticeDegree(p), which is the smallest number k such that k*p has an interior latt\\nice point.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example latticeCodegree shows an example\n";

 module_help_proc("polymake.so","latticeCodegree", latticeCodegree_help);

  const char* ehrhartPolynomialCoeff_help =
    "USAGE:    ehrhartPolynomialCoeff(polytope p)\nRETURN:   intvec, coefficients of the Ehrhart polynomial of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example ehrhartPolynomialCoeff shows an example\n";

 module_help_proc("polymake.so","ehrhartPolynomialCoeff", ehrhartPolynomialCoeff_help);

  const char* hStarVector_help =
    "USAGE:    hStarVector(polytope p)\nRETURN:   intvec, h*-vector of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example hStarVector shows an example\n";

 module_help_proc("polymake.so","hStarVector", hStarVector_help);

  const char* hVector_help =
    "USAGE:    hVector(polytope p)\nRETURN:   intvec, h-vector of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example hVector shows an example\n";

 module_help_proc("polymake.so","hVector", hVector_help);

  const char* fVector_help =
    "USAGE:    fVector(polytope p)\nRETURN:   intvec, the f-vector of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example fVector shows an example\n";

 module_help_proc("polymake.so","fVector", fVector_help);

  const char* isNormal_help =
    "USAGE:    isNormal(polytope p)\nRETURN:   int, 1 if p is normal, i.e. the projective toric variety defined by p is projectively normal, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isNormal shows an example\n";

 module_help_proc("polymake.so","isNormal", isNormal_help);

  const char* facetWidths_help =
    "USAGE:    facetWidths(polytope p)\nRETURN:   intvec, vector with the integral widths of p with respect to all facet normals.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example facetWidths shows an example\n";

 module_help_proc("polymake.so","facetWidths", facetWidths_help);

  const char* facetWidth_help =
    "USAGE:    facetWidth(polytope p)\nRETURN:   int, maximum of the integral widths of p over all facet normals.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example facetWidth shows an example\n";

 module_help_proc("polymake.so","facetWidth", facetWidth_help);

  const char* facetVertexLatticeDistances_help =
    "USAGE:    facetVertexLatticeDistances(polytope p)\nRETURN:   intmat, matrix of lattice distances between vertices (columns) and facets (rows).\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example facetVertexLatticeDistances shows an example\n";

 module_help_proc("polymake.so","facetVertexLatticeDistances", facetVertexLatticeDistances_help);

  const char* isCompressed_help =
    "USAGE:    isCompressed(polytope p)\nRETURN:   int, 1 if facetWidth(p)=1, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isCompressed shows an example\n";

 module_help_proc("polymake.so","isCompressed", isCompressed_help);

  const char* isSmooth_help =
    "USAGE:    isSmooth(polytope p)\n          isSmooth(cone c)\n          isSmooth(fan F)\nRETURN:   int, 1 if p, c, or F is smooth, 0 otherwise.\nKEYWORDS: polytopes; cones; fans; polymake;\nEXAMPLE:  example isSmooth shows an example\n";

 module_help_proc("polymake.so","isSmooth", isSmooth_help);

  const char* isVeryAmple_help =
    "USAGE:    isVeryAmple(polytope p)\nRETURN:   int, 1 if p is very ample, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isVeryAmple shows an example\n";

 module_help_proc("polymake.so","isVeryAmple", isVeryAmple_help);

  const char* latticePoints_help =
    "USAGE:    latticePoints(polytope p)\nRETURN:   intmat, matrix whose rows are the lattice points of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example latticePoints shows an example\n";

 module_help_proc("polymake.so","latticePoints", latticePoints_help);

  const char* nLatticePoints_help =
    "USAGE:    nLatticePoints(polytope p)\nRETURN:   int, number of lattice points of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example nLatticePoints shows an example\n";

 module_help_proc("polymake.so","nLatticePoints", nLatticePoints_help);

  const char* interiorLatticePoints_help =
    "USAGE:    interiorLatticePoints(polytope p)\nRETURN:   intmat, an matrix whose rows are the lattice points in the relative interior of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example interiorLatticePoints shows an example\n";

 module_help_proc("polymake.so","interiorLatticePoints", interiorLatticePoints_help);

  const char* nInteriorLatticePoints_help =
    "USAGE:    nInteriorLatticePoints(polytope p)\nRETURN:   int, number of lattice points in the relative interior of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example nInteriorLatticePoints shows an example\n";

 module_help_proc("polymake.so","nInteriorLatticePoints", nInteriorLatticePoints_help);

  const char* boundaryLatticePoints_help =
    "USAGE:    boundaryLatticePoints(polytope p)\nRETURN:   intmat, matrix whose rows are the lattice points in the relative boundary of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example boundaryLatticePoints shows an example\n";

 module_help_proc("polymake.so","boundaryLatticePoints", boundaryLatticePoints_help);

  const char* nBoundaryLatticePoints_help =
    "USAGE:    nBoundaryLatticePoints(polytope p)\nRETURN:   int, number of lattice points in the relative boundary of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example nBoundaryLatticePoints shows an example\n";

 module_help_proc("polymake.so","nBoundaryLatticePoints", nBoundaryLatticePoints_help);

  const char* hilbertBasis_help =
    "USAGE:    hilbertBasis(cone c)\nRETURN:   intmat, Hilbert basis of the semigroup of c.\nKEYWORDS: cones; polymake;\nEXAMPLE:  example hilbertBasis shows an example\n";

 module_help_proc("polymake.so","hilbertBasis", hilbertBasis_help);

  const char* nHilbertBasis_help =
    "USAGE:    nHilbertBasis(cone c)\nRETURN:   int, size of the Hilbert basis of the semigroup of c.\nKEYWORDS: cones; polymake;\nEXAMPLE:  example nHilbertBasis shows an example\n";

 module_help_proc("polymake.so","nHilbertBasis", nHilbertBasis_help);

  const char* minkowskiSum_help =
    "USAGE:    minkowskiSum(polytope p, polytope q)\nRETURN:   polytope, Minkowski sum of p and q.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example minkowskiSum shows an example\n";

 module_help_proc("polymake.so","minkowskiSum", minkowskiSum_help);

  const char* minimalValue_help =
    "USAGE:    minimalValue(polytope p, intvec v)\nRETURN:   int, the minimal value of the linear form v on p.\n          The first coordinate of v corresponds to a shift of the\n          minimal value since p is considered as a polytope\n          in the plane (first coordinate) = 1.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example minimalValue shows an example\n";

 module_help_proc("polymake.so","minimalValue", minimalValue_help);

  const char* maximalValue_help =
    "USAGE:    maximalValue(polytope p, intvec v)\nRETURN:   int, maximal value of the linear form v on p.\n          The first coordinate of v corresponds to a shift of the\n          maximal value since p is considered as a polytope\n          in the plane (first coordinate) = 1.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example maximalValue shows an example\n";

 module_help_proc("polymake.so","maximalValue", maximalValue_help);

  const char* minimalFace_help =
    "USAGE:    minimalFace(polytope p, intvec v)\nRETURN:   intmat, vertices of the face of p on which the linear form v\n          is minimal.\n          The first coordinate of v corresponds to a shift of the\n          minimal value since p is considered as a polytope\n          in the plane (first coordinate) = 1. Hence\n          the minimal face is independent of the first coordinate of v.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example minimalFace shows an example\n";

 module_help_proc("polymake.so","minimalFace", minimalFace_help);

  const char* maximalFace_help =
    "USAGE:    maximalFace(polytope p, intvec v)\nRETURN:   intmat, vertices of the face of p on which the linear form v\n          is maximal.\n          The first coordinate of v corresponds to a shift of the\n          maximal value since p is considered as a polytope\n          in the plane (first coordinate) = 1. Hence\n          the maximal face is independent of the first coordinate of v.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example maximalFace shows an example\n";

 module_help_proc("polymake.so","maximalFace", maximalFace_help);

  const char* visual_help =
    "USAGE:    visual(polytope p)\n          visual(fan F)\nRETURN:   none, draws the polytope p or fan F using jreality.\nKEYWORDS: polytopes; polymake; visualization;\nEXAMPLE:  example visual shows an example\n";

 module_help_proc("polymake.so","visual", visual_help);

  const char* normalFan_help =
    "USAGE:    normalFan(polytope p)\nRETURN:   fan,\nKEYWORDS: polytopes; polymake; visualization;\nEXAMPLE:  example visual shows an example\n";

    module_help_proc("polymake.so","normalFan", normalFan_help);

}