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Polymake.m2
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Polymake.m2
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needsPackage "Polyhedra"
newPackage(
"Polymake",
Version => "0.2",
Date => "March 1, 2011",
Authors => {{Name => "Josephine Yu",
Email => "[email protected]",
HomePage => "http://people.math.gatech.edu/~jyu67"}},
Headline => "a package for interfacing with polymake",
DebuggingMode => true
)
export { --PolymakeObject,
polymakeObject, toPolymakeFormat, writePolymakeFile, runPolymake,getPropertyNames, getProperty, getMatrixProperty, getListProperty, getVectorProperty, makevec, makemat }
---------------------------------------------------------------------------
-- Code
---------------------------------------------------------------------------
needsPackage "gfanInterface2"
needsPackage "Polyhedra"
needsPackage "SimpleDoc"
--PolymakeObject = new Type of MutableHashTable
polymakeObject = method()
polymakeObject(String, List) := (filename, properties) -> (
-- F := removeComments lines get filename;
new PolymakeObject from apply(properties, p -> p => getMatrixProperty(filename,p))
)
polymakeObject(String) := (filename) -> (
-- F := removeComments lines get filename;
-- properties = getPropertyNames(F);
properties := getPropertyNames(filename);
new PolymakeObject from apply(properties, p -> p => getMatrixProperty(filename,p))
)
---------------------------------------------------------------------------
-- toPolymakeFormat
toPolymakeFormat = method(TypicalValue => String)
toPolymakeFormat(String, Matrix) := (propertyname, M) -> (
if M === null then ""
else(
S := propertyname|"\n";
if numRows M > 0 then
S = S|replace("\\|", "", toString net M);
S
)
)
toPolymakeFormat(String,Vector) := (propertyname,V) -> (
if V === null then ""
else(
S := propertyname|"\n";
if length V > 0 then
S = S|replace("\\|", "", toString net matrix{V});
S
)
)
toPolymakeFormat(String,ZZ) := (propertyname,x) -> (
if x === null then ""
else(
S := propertyname|"\n"|x|"\n";
S
)
)
toPolymakeFormat(PolymakeObject) := (P) -> (
concatenate apply(pairs P, a -> toPolymakeFormat(a)|"\n\n")
)
toPolymakeFormat(Polyhedron) := (P) -> (
if P === null then ""
else(
S := "";
S = S|toPolymakeFormat("DIM", P#"dimension of polyhedron")|"\n\n";
if(P#"dimension of lineality space" == 0) then (
S = S|toPolymakeFormat("VERTICES", transpose(P#"homogenizedVertices"#0))|"\n\n";
S = S|toPolymakeFormat("N_VERTICES", P#"number of rays" + P#"number of vertices")|"\n\n";
);
S = S|toPolymakeFormat("INEQUALITIES", transpose(P#"homogenizedHalfspaces"#0))|"\n\n";
S = S|toPolymakeFormat("EQUATIONS", transpose(P#"homogenizedHalfspaces"#1))|"\n\n";
S
)
)
---------------------------------------------------------------------------
-------- Create polymake input files from a Polyhedron
writePolymakeFile = method(TypicalValue => String)
writePolymakeFile(Polyhedron,String) := (P, filename) ->(
filename << toPolymakeFormat(P) << endl << close;
filename
)
writePolymakeFile(Polyhedron) := (P) ->(
filename := temporaryFileName()|currentTime()|".poly";
<< "using temporary file " << filename << endl;
filename << toPolymakeFormat(P) << endl << close;
filename
)
---------------------------------------------------------------------------
----- Run Polymake
runPolymake = method(TypicalValue => String)
runPolymake(String,String) := (filename, propertyname)->(
get("!"|"polymake "|filename|" "|propertyname)
)
runPolymake(PolymakeObject, String) := (P, propertyname) -> (
filename := temporaryFileName()|currentTime()|".poly";
<< "using temporary file " << filename << endl;
filename << toPolymakeFormat(P) << endl << close;
runPolymake(filename, propertyname)
)
runPolymake(Polyhedron, String) := (P, propertyname) -> (
filename := temporaryFileName()|currentTime()|".poly";
<< "using temporary file " << filename << endl;
filename << toPolymakeFormat(P) << endl << close;
runPolymake(filename, propertyname)
)
---------------------------------------------------------------------------
----- Utilities
isBlankLine = (s) -> (
#s == 0 or
match("^[[:space:]]*$",s) or
match("^[[:space:]]*#",s)
)
makevec = (str) -> (
t := separateRegexp(" +", removeComment str);
t = apply(t,value);
select(t, x-> x =!= null)
)
makemat = (L) -> (
if #L == 0 then map(QQ^0,QQ^0,0)
else matrix(L/makevec)
)
makelist = (L) -> (
if #L == 0 then {}
else apply(removeComments(L), t-> value replace(" ", ",", t))
)
removeComments = (F) -> (
-- F is a list of lines
-- removes comments beginning with #
-- also removes trailing blank spaces
if F === null then return null
else
apply(F, s-> replace("[[:space:]]*#.*|[[:space:]]+$","" ,s))
)
removeComment = (str) -> (
-- F is a list of lines
-- removes comments beginning with #
-- also removes trailing blank spaces
replace("[[:space:]]*#.*|[[:space:]]+$","" ,str)
)
------------------------------------------------------------------------------
------- Getting Properties of Polyhedra using Polymake
-- This is for Polymake version 2
-- returns a list of strings, names of known properties
getPropertyNames = method(TypicalValue => String)
getPropertyNames(List) := (F) -> (
-- F is a list of lines, as from a polymake file (old version)
nameLines := select(F, s-> match("property name", s) );
apply(nameLines, s->
replace( "\".*$" , "" ,replace("^.*property name=\"", "", s))
)
)
getPropertyNames(String) := (filename) -> (
-- filename is the name of a polymake file (may be in XML format)
F := lines get filename;
nameLines := select(F, s-> match("property name", s) );
apply(nameLines, s->
replace( "\".*$" , "" ,replace("^.*property name=\"", "", s))
)
)
----- Old Version -----
--getPropertyNames(List) := (F) -> (
-- F is a list of lines, as from a polymake file
-- returns a list of strings, names of known properties
-- FF = removeComments(F);
-- PP = select(FF, s-> match("^[[:space:]]*[[:alpha:]]", s));
-- apply(PP, s -> toString s)
-- )
------------------------------------------------------------------------------
getProperty = method(TypicalValue => List)
getProperty(List, String) := (F, section) -> (
-- F is a list of lines, as from a polymake file
n := position(F, s -> match("^"|section|///[:space:]*$///,s) or
match("^"|section|///[:space:]*#///,s));
if(n =!= null) then
(
p := n+1;
if isBlankLine F_p then {}
else
while p < #F and not isBlankLine F_p list (p=p+1; F_(p-1))
)
else null
)
getProperty(String,String) := (filename, propertyname) -> (
F := lines runPolymake(filename, propertyname);
getProperty(F, propertyname)
)
getProperty(Polyhedron,String) := (P, propertyname) -> (
F := lines runPolymake(P, propertyname);
getProperty(F, propertyname)
)
---------------------------------------------------------------------------
getMatrixProperty = method(TypicalValue => Matrix)
getMatrixProperty(List, String) := (F, section) -> (
L := getProperty(F,section);
if L === null then null
else makemat L
)
getMatrixProperty(String,String) := (filename, propertyname) -> (
F := lines runPolymake(filename, propertyname);
getMatrixProperty(F, propertyname)
)
getMatrixProperty(Polyhedron,String) := (P, propertyname) -> (
F := lines runPolymake(P, propertyname);
getMatrixProperty(F, propertyname)
)
---------------------------------------------------------------------------
getListProperty = method(TypicalValue => List)
getListProperty(List, String) := (F, section) -> (
L := getProperty(F,section);
if L === null then null
else makelist L
)
getListProperty(String,String) := (filename, propertyname) -> (
F := lines runPolymake(filename, propertyname);
getListProperty(F, propertyname)
)
getListProperty(Polyhedron,String) := (P, propertyname) -> (
F := lines runPolymake(P, propertyname);
getListProperty(F, propertyname)
)
---------------------------------------------------------------------------
getVectorProperty = method(TypicalValue => List)
getVectorProperty(List, String) := (F, section) -> (
L := getProperty(F,section);
if L === null then null
else if #L > 1 then error "property is not a vector"
else if #L == 0 then {}
else makevec L_0
)
getVectorProperty(String,String) := (filename, propertyname) -> (
F := lines runPolymake(filename, propertyname);
getVectorProperty(F, propertyname)
)
getVectorProperty(Polyhedron,String) := (P, propertyname) -> (
F := lines runPolymake(P, propertyname);
getVectorProperty(F, propertyname)
)
---------------------------------------------------------------------------
-----------------------DOCUMENTATION----------------------
---------------------------------------------------------------------------
beginDocumentation()
doc ///
Key
Polymake
Headline
Interface for Polymake
Description
Text
{\tt Polymake} is a software for convex polyhedra, simplicial complexes, and other discrete geometric objects, written by Ewgenij Gawrilow and Michael Joswig. It is available at @HREF "http://www.math.tu-berlin.de/polymake/"@. The user should have {\tt Polymake} installed on their machine.
Text
Warning: this package is not complete, and is mostly undocumented, but it is used in @TO "gfanInterface::gfanInterface"@.
Text
We can use the interface to get properties of @TO "Polyhedra::Polyhedron"@
Example
P = cyclicPolytope(3,5)
getVectorProperty(P, "F_VECTOR")
getMatrixProperty(P, "VERTEX_NORMALS")
Text
Instead of creating a new temporary file every time, we can reuse one and also save computation time.
Example
polyFile = writePolymakeFile(P)
runPolymake(polyFile, "F_VECTOR")
runPolymake(polyFile, "VERTEX_NORMALS")
Text
Look in the polymake file for the properties already computed.
Example
getPropertyNames(polyFile)
runPolymake(polyFile, "VERTICES_IN_FACETS")
Text
We can save the {\tt Polymake} output as a vector, a matrix or a list of things.
Example
getVectorProperty(polyFile, "VERTEX_DEGREES")
getMatrixProperty(polyFile, "VERTEX_NORMALS")
getListProperty(polyFile, "VERTICES_IN_FACETS")
getProperty(polyFile, "SIMPLICIAL")
removeFile(polyFile)
Caveat
You may need to manually remove the temporary files created in {\tt /tmp}.
SeeAlso
Polyhedra
///
{*
doc ///
Key
PolymakeObject
Headline
Polymake object
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
*}
{*
doc ///
Key
polymakeObject
(polymakeObject,String)
(polymakeObject,String,List)
Headline
Makes PolymakeObject either from the name of a polymake file, or the file name and a list of properties.
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
getPropertyNames
(getPropertyNames, String)
(getPropertyNames, List)
Headline
Get the list of known properties in a polymake file or a list containing lines of a polymake (xml) format file.
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
getListProperty
(getListProperty, List,String)
(getListProperty, Polyhedron,String)
(getListProperty, String,String)
Headline
get proprety of a polyhedron as a list
Usage
getListProperty(dataLines, property)
getListProperty(P, property)
getListProperty(polyFileName, property)
Inputs
dataLines: List
list of strings, typically output of polymake
property: String
name of polymake property
polyFileName: String
file name of {\tt Polymake} file
P: Polyhedron
Outputs
L:List
whose entries are values of the strings in dataLines or output of , with {\tt Polymake} comments removed.
Consequences
Description
Text
Text
Example
P = cyclicPolytope(3,5)
getListProperty(P, "VERTICES_IN_FACETS")
Text
Example
Caveat
A temporary file may get created.
SeeAlso
///
doc ///
Key
getMatrixProperty
(getMatrixProperty,String,String)
(getMatrixProperty,Polyhedron,String)
(getMatrixProperty,List,String)
Headline
Get a property as a matrix, given a @TO Polyhedra::Polyhedron@, a polymake file name, or a list of lines in a polymake output.
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
getProperty
(getProperty,List,String)
(getProperty,Polyhedron,String)
(getProperty,String,String)
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
getVectorProperty
(getVectorProperty,List,String)
(getVectorProperty,Polyhedron,String)
(getVectorProperty,String,String)
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
makemat
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
makevec
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
runPolymake
(runPolymake,Polyhedron,String)
(runPolymake,PolymakeObject,String)
(runPolymake,String,String)
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
toPolymakeFormat
(toPolymakeFormat,Polyhedron)
(toPolymakeFormat,PolymakeObject)
(toPolymakeFormat,String,Matrix)
(toPolymakeFormat,String,Vector)
(toPolymakeFormat,String,ZZ)
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
doc ///
Key
writePolymakeFile
(writePolymakeFile,Polyhedron)
(writePolymakeFile,Polyhedron,String)
Headline
Usage
Inputs
Outputs
Consequences
Description
Text
Text
Example
Text
Example
Caveat
SeeAlso
///
*}
---------------------------------------------------------------------------
------------------------- TEST ---------------------------
---------------------------------------------------------------------------
TEST ///
///
end
---------------------------------------------------------------------------
------------------------- END ---------------------------
---------------------------------------------------------------------------
restart
installPackage("Polymake")
installPackage("Polymake", FileName => "~/Documents/math/M2codes/packageRepository/development/aim2009/Polymake.m2", MakeDocumentation => true)
needsPackage("Polymake")
viewHelp(Polymake)
P = cyclicPolytope(3,5)
Vertices = transpose (matrix {{1, 0, 0, 0}, {1, 1, 1, 1}, {1, 2, 4, 8}, {1, 3, 9, 27}, {1, 4,16, 64}})
Rays = transpose(matrix{{1,2,3,4},{-1,-2,-3,-4}})
P2 = convexHull(Vertices,Rays)
Rays = transpose(matrix{{1,2,3,4},{1,-2,-3,-4}})
P3 = convexHull(Vertices,Rays)
P4 = convexHull(transpose (matrix {{1, 0, 0, -1}, {1, -1,-1,1}, {1, 2, 4, -7}, {1, -10, 9, 0}, {8, 4,-16, 4}}))
toPolymakeFormat(P)
toPolymakeFormat(P2)
toPolymakeFormat(P3)
toPolymakeFormat(P4)
runPolymake(P, "FACETS")
filename = writePolymakeFile(P)
runPolymake(filename, "PROPERTY_NAMES")
getProperty(filename, "AMBIENT_DIM")
getProperty(filename, "VERTICES")
getMatrixProperty(filename, "VERTICES")
getVectorProperty(filename, "F_VECTOR")
getProperty(filename, "F_VECTOR")
------------------ TO DO ---------------------
get other properties such as lists, graphs, simplicial complexes
if can't process, just read as list of strings