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[Axiom-developer] [polymake]
From: |
Bill Page |
Subject: |
[Axiom-developer] [polymake] |
Date: |
Sat, 27 Aug 2005 23:30:33 -0500 |
Changes http://www.axiom-developer.org/zope/mathaction/Polymake/diff
--
??changed:
-\begin{axiom}
\begin{spad}
--removed:
-
- fVector: % -> Vector Integer
-
- f2Vector: % -> Matrix Integer
-
- hVector: % -> Vector Integer
-
- simple: % -> Boolean
++added:
nPoints: % -> Cardinal
++ Number of points.
nInequalities: % -> Cardinal
++ Number of inequalities.
vertexBarycenter: % -> Vector Scalar
++ The center of gravity of the vertices of a bounded polytope.
minimalVertexAngle: % -> Scalar
++ The minimum angle between any two vertices (seen from the
++ VERTEXBARYCENTER).
zonotopeInputVectors: % -> Matrix Scalar
++ Contains the vector configuration for which a zonotope can be built.
reverseTransformation: % -> Matrix Scalar
++ Some invertible linear transformation that can be used to get back a
++ previous coordinate repersentation of the polytope. It operates from
++ the right on point row vectors (e.g. in properties like POINTS,
++ VERTICES, REL_INT_POINT); its inverse operates from the left on
++ hyperplane column vectors.
-- vertexLabels: % -> array<label>
-- ++ Unique names assigned to the VERTICES. If specified, they are shown
by
-- ++ visualization tools instead of vertex indices. For a polytope build
-- ++ from scratch, you should create this property by yourself, either
-- ++ manually in a text editor, or with a client program. If you build a
-- ++ polytope with a construction client taking some other input
-- ++ polytope(s), you can create the labels automatically if you call the
-- ++ client with a -relabel option. The exact format of the labels is
-- ++ dependent on the construction, and is described by the corresponding
-- ++ client.
-- facetLabels: % -> array<label>
-- ++ Unique names assigned to the FACETS, analogous to VERTEX_LABELS.
galeTransform: % -> Matrix Scalar
++ Coordinates of the Gale transform.
steinerPoints: % -> Matrix Scalar
++ A weighted inner point depending on the outer angle called Steiner
++ point for all faces of dimensions 2 to d.
-- Combinatorics
nVertices: % -> Cardinal
++ Number of vertices.
nBoundedVertices: % -> Cardinal
++ Number of bounded vertices (non-rays).
nFacets: % -> Cardinal
++ Number of facets.
nVertexFacetInc: % -> Cardinal
++ Number of pairs of incident vertices and facets.
-- verticesInFacets: % -> incidence_matrix
-- ++ Vertex-facet incidence matrix, with rows corresponding to facets and
-- ++ columns to vertices. Vertices and facets are numbered from 0 to
-- ++ N_VERTICES-1 rsp. N_FACETS-1, according to their order in VERTICES
-- ++ rsp. FACETS.
-- facetsThruVertices: % -> incidence_matrix
-- ++ transposed VERTICES_IN_FACETS
-- hasseDiagram: % -> face_lattice
-- ++ The face lattice of the polytope organized as a directed graph. Each
-- ++ node corresponds to some proper face of the polytope. The nodes
-- ++ corresponding to the vertices and facets appear in the same order as
-- ++ the elements of VERTICES and FACETS properties. Two special nodes
-- ++ represent the whole polytope and the empty face.
-- vertexSizes: % -> array<Cardinal>
-- ++ Number of incident facets for each vertex.
-- facetSizes: % -> array<Cardinal>
-- ++ Number of incident vertices for each facet.
--
-- graph: % -> graph
-- ++ Vertex-edge graph.
--
-- dualGraph: % -> graph
-- ++ Facet-ridge graph. Dual to GRAPH.
nEdges: % -> Cardinal
++ Number of edges.
nRidges: % -> Cardinal
++ Number of ridges.
-- vertexDegrees: % -> array<Cardinal>
-- ++ Degrees of vertices in the GRAPH.
-- facetDegrees: % -> array<Cardinal>
-- ++ Degrees of facets in the DUAL_GRAPH.
diameter: % -> Cardinal
++ Graph theoretical diameter of GRAPH.
dualDiameter: % -> Cardinal
++ Graph theoretical diameter of DUAL_GRAPH.
triangleFree: % -> Boolean
++ True if GRAPH does not contain a triangle.
dualTriangleFree: % -> Boolean
++ True if DUAL_GRAPH does not contain a triangle.
altshulerDet: % -> Cardinal
++ Let M be the vertex-facet incidence matrix, then the Altshulter
++ determinant is defined as max{det(M?MT), det(MT?M)}.
fVector: % -> Vector Cardinal
++ fk is the number of k-faces.
f2Vector: % -> Matrix Cardinal
++ fik is the number of incident pairs of i-faces and k-faces; the main
++ diagonal contains the F_VECTOR.
flagVector: % -> Vector Cardinal
++ Condensed form of the flag vector. Use Dehn-Sommerville equations, via
++ user function N_FLAGS, to extend.
cdIndexCoefficients: % -> Vector Cardinal
++ Coefficients of the cd-index.
hVector: % -> Vector Cardinal
++ Simplicial h-vector. Defined for simplicial polytopes and also for
++ their duals.
cubicalHVector: % -> Vector Cardinal
++ undocumented
essentiallyGeneric: % -> Boolean
++ all intermediate polytopes (with respect to the given insertion order)
++ in the beneath-and-beyond algorithm are simplicial. We have the ++
++ implication : VERTICES in general position => ESSENTIALLY_GENERIC =>
++ SIMPLICIAL
simplicial: % -> Boolean
++ True if the polytope is simplicial.
simple: % -> Boolean
++ True if the polytope is simple. Dual to SIMPLICIAL.
even: % -> Boolean
++ True if the GRAPH of the polytope is bipartite.
dualEven: % -> Boolean
++ True if the DUAL_GRAPH of the polytope is bipartite. Dual to EVEN.
connectivity: % -> Cardinal
++ Node connectivity of the GRAPH of the polytope, that is, the minimal
++ number of nodes to be removed from the graph such that the result is
++ disconnected.
dualConnectivity: % -> Cardinal
++ Node connectivity of the DUAL_GRAPH of the polytope. Dual to
++ CONNECTIVITY.
simpliciality: % -> Cardinal
++ Maximal dimension in which all faces are simplices.
simplicity: % -> Cardinal
++ Maximal dimension in which all dual faces are simplices.
faceSimplicity: % -> Cardinal
++ Maximal dimension in which all faces are simple polytopes.
cubical: % -> Boolean
++ True if all facets are cubes.
cubicality: % -> Cardinal
++ Maximal dimension in which all facets are cubes.
cocubical: % -> Boolean
++ Dual to CUBICAL.
cocubicality: % -> Cardinal
++ Dual to CUBICALITY.
neighborly: % -> Boolean
++ True if the polytope is neighborly.
neighborliness: % -> Cardinal
++ Maximal dimension in which all facets are neighborly.
balanced: % -> Boolean
++ Dual to NEIGHBORLY.
balance: % -> Cardinal
++ Maximal dimension in which all facets are balanced.
fatness: % -> Scalar
++ Parameter describing the shape of the face-lattice of a 4-polytope.
complexity: % -> Scalar
??changed:
- polylib: String := "/usr/local/polymake/bin/"
polylib: String := "/usr/local/polymake/bin"
??changed:
- systemCommand("system " polylib cmd " " polydir rep ".poly " prm)_
systemCommand("system " cmd " " polydir rep ".poly " prm)_
??changed:
- systemCommand("system " polylib "polymake " polydir (rep::Rep) ".poly
"_
systemCommand("system polymake " polydir (rep::Rep) ".poly "_
--removed:
- fVector s ==
- polyprop(s, "F__VECTOR")
- getVectorInteger(polytmpfile)$ReadFile
-
- f2Vector s ==
- polyprop(s, "F2__VECTOR")
- getMatrixInteger(polytmpfile)$ReadFile
-
- hVector s ==
- polyprop(s, "H__VECTOR")
- getVectorInteger(polytmpfile)$ReadFile
-
- simple s ==
- polyprop(s, "SIMPLE")
- getBoolean(polytmpfile)$ReadFile
-
??changed:
- map(#1 pretend Cardinal, getSetInteger(polytmpfile)$ReadFile)_
- $FiniteSetAggregateFunctions2(Integer, Set Integer,
- Cardinal, Set Cardinal)
-
getSetInteger(polytmpfile)$ReadFile pretend Set Cardinal
??changed:
- polyprop(s, "UNBOUNDED__FACETS")
- map(#1 pretend Cardinal, getSetInteger(polytmpfile)$ReadFile)_
- $FiniteSetAggregateFunctions2(Integer, Set Integer,
- Cardinal, Set Cardinal)
polyprop(s, "UNBOUNDED__FACETS")
getSetInteger(polytmpfile)$ReadFile pretend Set Cardinal
??changed:
-\end{axiom}
nPoints s ==
polyprop(s, "N__POINTS")
getInteger(polytmpfile)$ReadFile :: Cardinal
nInequalities s ==
polyprop(s, "N__INEQUALITIES")
getInteger(polytmpfile)$ReadFile :: Cardinal
vertexBarycenter s ==
polyprop(s, "VERTEX__BARYCENTER")
getVectorFraction(polytmpfile)$ReadFile
minimalVertexAngle s ==
polyprop(s, "MINIMAL__VERTEX__ANGLE")
getFraction(polytmpfile)$ReadFile
zonotopeInputVectors s ==
polyprop(s, "ZONOTOPE__INPUT__VECTORS")
getMatrixFraction(polytmpfile)$ReadFile
reverseTransformation s ==
polyprop(s, "REVERSE__TRANSFORMATION")
getMatrixFraction(polytmpfile)$ReadFile
-- vertexLabels: % -> array<label>
-- facetLabels: % -> array<label>
galeTransform s ==
polyprop(s, "GALE__TRANSFORM")
getMatrixFraction(polytmpfile)$ReadFile
steinerPoints s ==
polyprop(s, "STEINER__POINTS")
getMatrixFraction(polytmpfile)$ReadFile
-- Combinatorics
nVertices s ==
polyprop(s, "N__VERTICES")
getInteger(polytmpfile)$ReadFile :: Cardinal
nBoundedVertices s ==
polyprop(s, "N__BOUNDED__VERTICES")
getInteger(polytmpfile)$ReadFile :: Cardinal
nFacets s ==
polyprop(s, "N__FACETS")
getInteger(polytmpfile)$ReadFile :: Cardinal
nVertexFacetInc s ==
polyprop(s, "N__VERTEX__FACET__INC")
getInteger(polytmpfile)$ReadFile :: Cardinal
-- verticesInFacets: % -> incidence_matrix
-- ++ Vertex-facet incidence matrix, with rows corresponding to facets and
-- ++ columns to vertices. Vertices and facets are numbered from 0 to
-- ++ N_VERTICES-1 rsp. N_FACETS-1, according to their order in VERTICES
-- ++ rsp. FACETS.
-- facetsThruVertices: % -> incidence_matrix
-- ++ transposed VERTICES_IN_FACETS
-- hasseDiagram: % -> face_lattice
-- ++ The face lattice of the polytope organized as a directed graph. Each
-- ++ node corresponds to some proper face of the polytope. The nodes
-- ++ corresponding to the vertices and facets appear in the same order as
-- ++ the elements of VERTICES and FACETS properties. Two special nodes
-- ++ represent the whole polytope and the empty face.
-- vertexSizes: % -> array<Cardinal>
-- ++ Number of incident facets for each vertex.
-- facetSizes: % -> array<Cardinal>
-- ++ Number of incident vertices for each facet.
--
-- graph: % -> graph
-- ++ Vertex-edge graph.
--
-- dualGraph: % -> graph
-- ++ Facet-ridge graph. Dual to GRAPH.
nEdges s ==
polyprop(s, "N__EDGES")
getInteger(polytmpfile)$ReadFile :: Cardinal
nRidges s ==
polyprop(s, "N__RIDGES")
getInteger(polytmpfile)$ReadFile :: Cardinal
-- vertexDegrees: % -> array<Cardinal>
-- ++ Degrees of vertices in the GRAPH.
-- facetDegrees: % -> array<Cardinal>
-- ++ Degrees of facets in the DUAL_GRAPH.
diameter s ==
polyprop(s, "DIAMETER")
getInteger(polytmpfile)$ReadFile :: Cardinal
dualDiameter s ==
polyprop(s, "DUAL__DIAMETER")
getInteger(polytmpfile)$ReadFile :: Cardinal
triangleFree s ==
polyprop(s, "TRIANGLE__FREE")
getBoolean(polytmpfile)$ReadFile
dualTriangleFree s ==
polyprop(s, "DUAL__TRIANGLE__FREE")
getBoolean(polytmpfile)$ReadFile
altshulerDet s ==
polyprop(s, "ALTSHULER__DET")
getInteger(polytmpfile)$ReadFile :: Cardinal
fVector s ==
polyprop(s, "F__VECTOR")
getVectorInteger(polytmpfile)$ReadFile pretend Vector Cardinal
f2Vector s ==
polyprop(s, "F2__VECTOR")
getMatrixInteger(polytmpfile)$ReadFile pretend Matrix Cardinal
flagVector s ==
polyprop(s, "FLAG__VECTOR")
getVectorInteger(polytmpfile)$ReadFile pretend Vector Cardinal
cdIndexCoefficients s ==
polyprop(s, "CD__INDEX__COEFFICIENTS")
getVectorInteger(polytmpfile)$ReadFile pretend Vector Cardinal
hVector s ==
polyprop(s, "H__VECTOR")
getVectorInteger(polytmpfile)$ReadFile pretend Vector Cardinal
cubicalHVector s ==
polyprop(s, "CUBICAL__H__VECTOR")
getVectorInteger(polytmpfile)$ReadFile pretend Vector Cardinal
essentiallyGeneric s ==
polyprop(s, "ESSENTIALLY__GENERIC")
getBoolean(polytmpfile)$ReadFile
simplicial s ==
polyprop(s, "SIMPLICIAL")
getBoolean(polytmpfile)$ReadFile
simple s ==
polyprop(s, "SIMPLE")
getBoolean(polytmpfile)$ReadFile
even s ==
polyprop(s, "EVEN")
getBoolean(polytmpfile)$ReadFile
dualEven s ==
polyprop(s, "DUAL__EVEN")
getBoolean(polytmpfile)$ReadFile
connectivity s ==
polyprop(s, "CONNECTIVITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
dualConnectivity s ==
polyprop(s, "DUAL__CONNECTIVITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
simpliciality s ==
polyprop(s, "SIMPLICIALITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
simplicity s ==
polyprop(s, "SIMPLICITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
faceSimplicity s ==
polyprop(s, "FACE__SIMPLICITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
cubical s ==
polyprop(s, "CUBICAL")
getBoolean(polytmpfile)$ReadFile
cubicality s ==
polyprop(s, "CUBICALITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
cocubical s ==
polyprop(s, "COCUBICAL")
getBoolean(polytmpfile)$ReadFile
cocubicality s ==
polyprop(s, "COCUBICALITY")
getInteger(polytmpfile)$ReadFile :: Cardinal
neighborly s ==
polyprop(s, "NEIGHBORLY")
[75 more lines...]
--
forwarded from http://www.axiom-developer.org/zope/mathaction/address@hidden