[Axiom-developer] [polymake] (nouveau)

[kratt6]

Changes http://page.axiom-developer.org/zope/mathaction/Polymake/diff
--
This is a trivial wrapper for the wonderful polymake package from Berlin, 
http://www.math.tu-berlin.de/polymake/ .
Note that this is rather a proof of concept, so if you think you've got a 
better design idea, go ahead and comment below.
So far, only little of the polymake functionality is covered, but it's mostly 
very easy to extend.

Usage

  You can find some simple examples in [SandBox polymake]. There, you can also 
try it out online!

Design

  I've decided to communicate with polymake for a start via file I/O, but would 
be easy to change this if necessary. Every polymake object created is stored 
with a "canonical" name: For example, if you ask for a cube of dimension 4, 
axiom will issue the shell command 'cube cube4.poly 4'. Then, when you ask for 
a property of this cube, for example, the hvector, then the shell command 
'polymake cube4.poly H_VECTOR > tmp.poly' is issued. Finally axiom reads the 
contents of 'tmp.poly' and converts it to the appropriate type. Thus, the only 
thing that really has to be programmed is a conversion routine for every 
polymake type. Some of these are trivial, like the Boolean, vector or matrix 
types, some others need more thought.


  Currently there are only two domains: 'Polytope' and 'SimplicialComplex'. If 
you want a particular polymake property or construction supported, or want to 
have a new domain like 'Graph', go ahead and change the contents of this file. 
If you need help, you can always ask me.

\begin{axiom}
)abbrev domain POLYTOPE Polytope
Polytope(): Exports == Implementation where
    Exports == with

      coerce: % -> OutputForm

-------------------------------------------------------------------------------
--               polytope constructions                                      --
-------------------------------------------------------------------------------

      cube: Integer -> %

      cross: Integer -> %

      rand01: (Integer, Integer) -> %

      randSphere: (Integer, Integer) -> %

-------------------------------------------------------------------------------
--               polytope properties                                         --
-------------------------------------------------------------------------------

      fVector: % -> Vector Integer

      f2Vector: % -> Matrix Integer

      hVector: % -> Vector Integer

      facets: % -> Matrix Integer

      vertices: % -> Matrix Integer

      simple: % -> Boolean

    Implementation == add

      Rep := String

      coerce p == coerce(p)$Rep

      String2ListInteger: String -> List Integer
      
      String2ListInteger r ==
        map(PARSE_-INTEGER(#1)$Lisp, split(r, char(" "))$String)_
          $FiniteLinearAggregateFunctions2(String, List String, Integer, _
                                           List Integer)

      getBoolean: () -> Boolean

      getBoolean ==
        f := open(("tmp.poly")::FileName)$TextFile
        read!(f)$TextFile
        r:String := read!(f)$TextFile
        close!(f)$TextFile

        (r="1")

      getIntegerList: () -> List Integer

      getIntegerList ==
        f := open(("tmp.poly")::FileName)$TextFile
        read!(f)$TextFile
        r:String := read!(f)$TextFile
        close!(f)$TextFile

        String2ListInteger(r)

      getIntegerVector: () -> Vector Integer

      getIntegerVector == vector(getIntegerList())$Vector(Integer)

      getIntegerMatrix: () -> Matrix Integer

      getIntegerMatrix ==
        f := open(("tmp.poly")::FileName)$TextFile
        read!(f)$TextFile
        m: List List Integer := []
        r: String
        while not endOfFile?(f) repeat
          r := read!(f)$TextFile
          if not empty? r then 
            m := cons(String2ListInteger r, m)

        close!(f)$TextFile
        matrix(reverse m)$Matrix(Integer)

-------------------------------------------------------------------------------
--               polytope constructions                                      --
-------------------------------------------------------------------------------

      cube n == 
        s: String := "cube" string(n)
        systemCommand("system cube " s ".poly " string(n))$MoreSystemCommands
        s::Rep

      cross n == 
        s: String := "cross" string(n)
        systemCommand("system cross " s ".poly " string(n))$MoreSystemCommands
        s::Rep

      rand01(d, n)  == 
        s: String := "rand01" string(d) string(n) 
        systemCommand("system rand01 " s ".poly " string(d) " " 
string(n))$MoreSystemCommands
        s::Rep

      randSphere(d, n)  == 
        s: String := "randsphere" string(d) string(n)
        systemCommand("system rand__sphere " s ".poly " string(d) " " 
string(n))$MoreSystemCommands
        s::Rep

-------------------------------------------------------------------------------
--               polytope properties                                         --
-------------------------------------------------------------------------------

      fVector s ==
        systemCommand("system polymake " (s::Rep) ".poly F__VECTOR > tmp.poly")_
          $MoreSystemCommands
      
        getIntegerVector()

      f2Vector s ==
        systemCommand("system polymake " (s::Rep) ".poly F2__VECTOR > 
tmp.poly")_
          $MoreSystemCommands
      
        getIntegerMatrix()
        
      hVector s ==
        systemCommand("system polymake " (s::Rep) ".poly H__VECTOR > tmp.poly")_
          $MoreSystemCommands
        
        getIntegerVector()

      facets s ==
        systemCommand("system polymake " (s::Rep) ".poly FACETS > tmp.poly")_
          $MoreSystemCommands
        
        getIntegerMatrix()

      vertices s ==
        systemCommand("system polymake " (s::Rep) ".poly VERTICES > tmp.poly")_
          $MoreSystemCommands
        
        getIntegerMatrix()

      simple s == 
        systemCommand("system polymake " (s::Rep) ".poly SIMPLE > tmp.poly")_
          $MoreSystemCommands

        getBoolean()

)abbrev domain TOPAZ SimplicialComplex
SimplicialComplex(): Exports == Implementation where
    Exports == with

      coerce: % -> OutputForm

-------------------------------------------------------------------------------
--                  topaz constructions                                      --
-------------------------------------------------------------------------------

      boundaryComplex: Polytope -> %

-------------------------------------------------------------------------------
--                  topaz properties                                         --
-------------------------------------------------------------------------------

      facets: % -> List Set Integer

    Implementation == add

      Rep := String

      coerce p == coerce(p)$Rep


      String2SetInteger: String -> Set Integer
      
      String2SetInteger r ==
        s: String := delete(delete(r, #r), 1)
        brace(map(PARSE_-INTEGER(#1)$Lisp, split(s, char(" "))$String)_
          $FiniteLinearAggregateFunctions2(String, List String, Integer, _
                                           List Integer))$Set(Integer)


      getListSetInteger: () -> List Set Integer

      getListSetInteger ==
        f := open(("tmp.poly")::FileName)$TextFile
        read!(f)$TextFile
        m: List Set Integer := []
        r: String
        while not endOfFile?(f) repeat
          r := read!(f)$TextFile
          if not empty? r then 
            m := cons(String2SetInteger r, m)

        close!(f)$TextFile
        reverse m

-------------------------------------------------------------------------------
--                  topaz properties                                         --
-------------------------------------------------------------------------------

      facets s ==
        systemCommand("system polymake -A topaz " (s::Rep) ".top FACETS > 
tmp.poly")_
          $MoreSystemCommands
        
        getListSetInteger()

-------------------------------------------------------------------------------
--                  topaz constructions                                      --
-------------------------------------------------------------------------------

      boundaryComplex s ==
        systemCommand("system boundary__complex " (s pretend String) ".top " (s 
pretend String) ".poly")_
          $MoreSystemCommands

        s pretend String :: Rep
\end{axiom}
--
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden