[Axiom-developer] [polymake]

[Bill Page]

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