see my comment on trac #9136 for a complete example.
On Nov 24, 11:17 pm, Dima Pasechnik <dimp...@gmail.com> wrote:
> Are you reinventing the wheel? :-)
>
> One should be able to import into Sage any graph that GAP can make
> using its package Grape. Grape is essentially doing what you seem to
> be doing: takes a permutation group and constructs a graph invariant
> under it.
> E.g.
> gap> LoadPackage("grape");
> gap> G:=NullGraph(DihedralGroup(IsPermGroup,20),10);
> rec( isGraph := true, order := 10,
> group := Group([ (1,2,3,4,5,6,7,8,9,10), (2,10)(3,9)(4,8)(5,7) ]),
> schreierVector := [ -1, 1, 1, 1, 1, 1, 2, 2, 2, 2 ], adjacencies :=
> [ [ ] ],
> representatives := [ 1 ], isSimple := true )
> gap> AddEdgeOrbit(G,[1,2]);
> gap> G;
> rec( isGraph := true, order := 10,
> group := Group([ (1,2,3,4,5,6,7,8,9,10), (2,10)(3,9)(4,8)(5,7) ]),
> schreierVector := [ -1, 1, 1, 1, 1, 1, 2, 2, 2, 2 ],
> adjacencies := [ [ 2, 10 ] ], representatives := [ 1 ], isSimple :=
> true )
> gap> AddEdgeOrbit(G,[1,3]);
> gap> G;
> rec( isGraph := true, order := 10,
> group := Group([ (1,2,3,4,5,6,7,8,9,10), (2,10)(3,9)(4,8)(5,7) ]),
> schreierVector := [ -1, 1, 1, 1, 1, 1, 2, 2, 2, 2 ],
> adjacencies := [ [ 2, 3, 9, 10 ] ], representatives := [ 1 ],
> isSimple := true )
>
> we thus constructed a vertex-transitive degree 4 graph on 10 vertices,
> with the dihedral group of order 20 as an automorphism group.
>
> Unfortunately Sage does not handle graphs that are specified by edge
> orbits, last time I checked.
>
> Dima
>
> On Nov 24, 6:28 pm, Nathann Cohen <nathann.co...@gmail.com> wrote:
>
>
>
> > Hello everybody !!!
>
> > Working on Minh's patches for new graph generators, I had to create
> > Dihedral groups, which took me more than.... half a second. Which mean
> > it can be improved :-D
>
> > More seriously, the way I found to create them was to use the
> > DihedralGroup() method, which one does not have to import first. It is
> > nice, but it also means that I still do not know how to list all the
> > group Sage knows how to build.. Well, for graphs and words we already
> > have something nice :
>
> > We create a graph/word with the Graph/Word constructor, which appears
> > in the namespace. If we omit the upper case, we have a graphs/words
> > object, whose methods are the different constructors of graphs/words.
> > So graphs.<tab>/words.<tab> gives you the list of all constructors,
> > which is the best way to find one quickly. What about doing the same
> > with groups, or finding a common way to organise this ? :-)
>
> > Nathann
>
> > P.S. (if anybody has any smart idea about how to deal with classes
> > having *far too many* different methods, I am also very interested.
> > Something will have to be decided soon for the Graph class anyway...
> > :-/ )
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