# source:git/dyn_modules/callpolymake/polymake_documentation.cc@62de8de

jengelh-datetimespielwiese
Last change on this file since 62de8de was 62de8de, checked in by Yue Ren <ren@…>, 9 years ago
chg: updated callpolymake to newest version
• Property mode set to `100644`
File size: 14.6 KB
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1#include <Singular/ipid.h>
2
3void init_polymake_help()
4{
5
6  const char *polymake_banner =
8
9  PrintS(polymake_banner);
10
11  const char* polymake_help =
12    "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. \nPolytopesâcombinatorics and computation (Oberwolfach, 1997), 43â73, DMV Sem., 29, BirkhÃ€user, 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";
13
14  module_help_main("polymake.so",polymake_help);
15
16
17  const char*isReflexive_help =
18    "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";
19
20 module_help_proc("polymake.so","isReflexive", isReflexive_help);
21
22  const char* isBounded_help =
23    "USAGE:    isBounded(polytope p)\nRETURN:   int, 1 if p is bounded, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isBounded shows an example\n";
24
25 module_help_proc("polymake.so","isBounded", isBounded_help);
26
27  const char* isGorenstein_help =
28    "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";
29
30 module_help_proc("polymake.so","isGorenstein", isGorenstein_help);
31
32  const char* gorensteinIndex_help =
33    "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";
34
35 module_help_proc("polymake.so","gorensteinIndex", gorensteinIndex_help);
36
37  const char* gorensteinVector_help =
38    "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";
39
40 module_help_proc("polymake.so","gorensteinVector", gorensteinVector_help);
41
42  const char* isCanonical_help =
43    "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";
44
45 module_help_proc("polymake.so","isCanonical", isCanonical_help);
46
47  const char* isTerminal_help =
48    "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";
49
50 module_help_proc("polymake.so","isTerminal", isTerminal_help);
51
52  const char* latticeVolume_help =
53    "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";
54
55 module_help_proc("polymake.so","latticeVolume", latticeVolume_help);
56
57  const char* latticeDegree_help =
58    "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";
59
60 module_help_proc("polymake.so","latticeDegree", latticeDegree_help);
61
62  const char* latticeCodegree_help =
63    "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";
64
65 module_help_proc("polymake.so","latticeCodegree", latticeCodegree_help);
66
67  const char* ehrhartPolynomialCoeff_help =
68    "USAGE:    ehrhartPolynomialCoeff(polytope p)\nRETURN:   intvec, coefficients of the Ehrhart polynomial of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example ehrhartPolynomialCoeff shows an example\n";
69
70 module_help_proc("polymake.so","ehrhartPolynomialCoeff", ehrhartPolynomialCoeff_help);
71
72  const char* hStarVector_help =
73    "USAGE:    hStarVector(polytope p)\nRETURN:   intvec, h*-vector of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example hStarVector shows an example\n";
74
75 module_help_proc("polymake.so","hStarVector", hStarVector_help);
76
77  const char* hVector_help =
78    "USAGE:    hVector(polytope p)\nRETURN:   intvec, h-vector of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example hVector shows an example\n";
79
80 module_help_proc("polymake.so","hVector", hVector_help);
81
82  const char* fVector_help =
83    "USAGE:    fVector(polytope p)\nRETURN:   intvec, the f-vector of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example fVector shows an example\n";
84
85 module_help_proc("polymake.so","fVector", fVector_help);
86
87  const char* isNormal_help =
88    "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";
89
90 module_help_proc("polymake.so","isNormal", isNormal_help);
91
92  const char* facetWidths_help =
93    "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";
94
95 module_help_proc("polymake.so","facetWidths", facetWidths_help);
96
97  const char* facetWidth_help =
98    "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";
99
100 module_help_proc("polymake.so","facetWidth", facetWidth_help);
101
102  const char* facetVertexLatticeDistances_help =
103    "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";
104
105 module_help_proc("polymake.so","facetVertexLatticeDistances", facetVertexLatticeDistances_help);
106
107  const char* isCompressed_help =
108    "USAGE:    isCompressed(polytope p)\nRETURN:   int, 1 if facetWidth(p)=1, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isCompressed shows an example\n";
109
110 module_help_proc("polymake.so","isCompressed", isCompressed_help);
111
112  const char* isSmooth_help =
113    "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";
114
115 module_help_proc("polymake.so","isSmooth", isSmooth_help);
116
117  const char* isVeryAmple_help =
118    "USAGE:    isVeryAmple(polytope p)\nRETURN:   int, 1 if p is very ample, 0 otherwise.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example isVeryAmple shows an example\n";
119
120 module_help_proc("polymake.so","isVeryAmple", isVeryAmple_help);
121
122  const char* latticePoints_help =
123    "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";
124
125 module_help_proc("polymake.so","latticePoints", latticePoints_help);
126
127  const char* nLatticePoints_help =
128    "USAGE:    nLatticePoints(polytope p)\nRETURN:   int, number of lattice points of p.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example nLatticePoints shows an example\n";
129
130 module_help_proc("polymake.so","nLatticePoints", nLatticePoints_help);
131
132  const char* interiorLatticePoints_help =
133    "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";
134
135 module_help_proc("polymake.so","interiorLatticePoints", interiorLatticePoints_help);
136
137  const char* nInteriorLatticePoints_help =
138    "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";
139
140 module_help_proc("polymake.so","nInteriorLatticePoints", nInteriorLatticePoints_help);
141
142  const char* boundaryLatticePoints_help =
143    "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";
144
145 module_help_proc("polymake.so","boundaryLatticePoints", boundaryLatticePoints_help);
146
147  const char* nBoundaryLatticePoints_help =
148    "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";
149
150 module_help_proc("polymake.so","nBoundaryLatticePoints", nBoundaryLatticePoints_help);
151
152  const char* hilbertBasis_help =
153    "USAGE:    hilbertBasis(cone c)\nRETURN:   intmat, Hilbert basis of the semigroup of c.\nKEYWORDS: cones; polymake;\nEXAMPLE:  example hilbertBasis shows an example\n";
154
155 module_help_proc("polymake.so","hilbertBasis", hilbertBasis_help);
156
157  const char* nHilbertBasis_help =
158    "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";
159
160 module_help_proc("polymake.so","nHilbertBasis", nHilbertBasis_help);
161
162  const char* minkowskiSum_help =
163    "USAGE:    minkowskiSum(polytope p, polytope q)\nRETURN:   polytope, Minkowski sum of p and q.\nKEYWORDS: polytopes; polymake;\nEXAMPLE:  example minkowskiSum shows an example\n";
164
165 module_help_proc("polymake.so","minkowskiSum", minkowskiSum_help);
166
167  const char* minimalValue_help =
168    "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";
169
170 module_help_proc("polymake.so","minimalValue", minimalValue_help);
171
172  const char* maximalValue_help =
173    "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";
174
175 module_help_proc("polymake.so","maximalValue", maximalValue_help);
176
177  const char* minimalFace_help =
178    "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";
179
180 module_help_proc("polymake.so","minimalFace", minimalFace_help);
181
182  const char* maximalFace_help =
183    "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";
184
185 module_help_proc("polymake.so","maximalFace", maximalFace_help);
186
187  const char* visual_help =
188    "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";
189
190 module_help_proc("polymake.so","visual", visual_help);
191
192  const char* normalFan_help =
193    "USAGE:    normalFan(polytope p)\nRETURN:   fan,\nKEYWORDS: polytopes; polymake; visualization;\nEXAMPLE:  example visual shows an example\n";
194
195    module_help_proc("polymake.so","normalFan", normalFan_help);
196