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<Section><Heading>Calling Polymake and converting its output</Heading>
<ManSection>
<Meth Name="Polymake" Arg="poly option : PolymakeNolookup"/>
<Description>
This method calls the polymake program (see <Ref
Var="POLYMAKE_COMMAND"/>) with the option
<A>option</A>. You may use several keywords such as
<C>"FACETS VERTICES"</C> as an option. The returned value is cut into blocks
starting with keywords (which are taken from output and not
looked up in <A>option</A>). Each block is then
interpreted and translated into &GAP; readable form. This
translation is done using the functions given in <Ref
Var="ObjectConverters"/>.
The first line of each block of polymake output is taken as a
keyword and the according entry in <Ref Var="ObjectConverters"/>
is called to convert the block into &GAP; readable form. If no
conversion function is known, an info string is printed and <K>fail</K> is
returned.
If only one keyword has been given as <A>option</A>,
<C>Polymake</C> returns the result of the conversion operation.
If more than one keyword has been given or the output consists of
more than one block, <C>Polymake</C> returns <K>fail</K>.
In any case, the calculated values for each block are stored as
known properties of the <K>PolymakeObject</K> <A>poly</A> as long
as they are not <K>fail</K>.
If <K>Polymake</K> is called with an option that corresponds to a
name of a known property of <A>poly</A>, the known property is
returned. In this case, there is no call of the external program.
(see below for suppression of this feature).<P/>
Note that the command <K>Polymake</K> returns <K>fail</K> if
nothing is returned by the program polymake or more than one
block of data is returned. For example, the returned value of
<C>Polymake(poly,"VISUAL")</C> is always
<K>fail</K>. Likewise, <C>Polymake(poly,"POINTS VERTICES")</C>
will return <K>fail</K> (but may add new known properties to
<A>poly</A>).
For a description of the conversion functions, see chapter <Ref
Chap="Converting"/>.<P/>
If the option <A>PolymakeNolookup</A> is set to anything else
than false, the polymake program is called even if <A>poly</A>
already has a known property with name <A>option</A>.
</Description>
</ManSection>
Note that whenever <Ref Meth="Polymake"/> returns <K>fail</K>, a description
of the problem is stored in <Ref Var="POLYMAKE_LAST_FAIL_REASON"/>.
If you call <Ref Meth="Polymake"/> with more than one keyword,
<Ref Var="POLYMAKE_LAST_FAIL_REASON"/> is changed before polymake is
called. So any further reason to return <K>fail</K> will overwrite it.
</Section>
<Section><Heading>An Example</Heading>
Let's generate a three dimensional permutahedron.
<Example>
<![CDATA[
gap> S:=SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> v:=[1,2,3];
[ 1, 2, 3 ]
gap> points3:=Orbit(S,v,Permuted);;
# project to reduce ambient dimension
gap> points:=points3{[1..6]}{[1,2]};;
gap> permutahedron:=CreatePolymakeObject();
<polymake object. No properties known>
gap> AppendPointlistToPolymakeObject(permutahedron,points);
gap> Polymake(permutahedron,"VOLUME");
3
gap> Polymake(permutahedron,"N_VERTICES");
6
#Now <permutahedron> knows its number of vertices, but not the vertices:
gap> PropertyOfPolymakeObject(permutahedron,"VERTICES");
fail
gap> NamesKnownPropertiesOfPolymakeObject(permutahedron);
[ "VOLUME", "N_VERTICES" ]
#Let's look at the object!
gap> Polymake(permutahedron,"VISUAL");
#I There was no or wrong polymake output
fail
gap> Polymake(permutahedron,"DIM");
2
]]>
</Example>
</Section>
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