#19018: More SRGs using Regular Symmetric Hadamard matric with Constant Diagonal
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 1cae2dc761cd1e784f0a5a4239d90f1aa6ea48ce
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/19018 |
Dependencies: |
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Comment (by dimpase):
Replying to [comment:25 dimpase]:
> Here is a slight modification that is very fast:
>
> {{{
> def g1():
> from sage.groups.finitely_presented import FinitelyPresentedGroup
> G = FreeGroup('x,y,z')
> x,y,z = G.gens()
> rels =
(x**5,y**5,z**4,x*y*x**(-1)*y**(-1),z*x*z**(-1)*x**(-2),z*y*z**(-1)*y**(-2))
> G = FinitelyPresentedGroup(G,rels)
> x,y,z = G.gens()
> H = G.as_permutation_group()
>
L=["120","140","200","210","201","401","411","321","002","012","022","042","303","403","013","413","240","031","102","323","300","231","132","133","310","141","142","233","340","241","202","333","410","341","222","433","430","441","242","302","312","322","332","442","143"]
> L = map(lambda x:map(int,x),L)
> x,y,z=(H.0,H.1,H.2) # from now on we work in H
> L = [H(x**xx*y**yy*z**zz) for xx,yy,zz in L]
> GG = Graph()
> for v in H:
> GG.add_edges(map(lambda u: (v,u*v), L)) # and we add edges in
bunches
> return GG
> }}}
in fact the lines
{{{
GG = Graph()
for v in H:
GG.add_edges(map(lambda u: (v,u*v), L)) # and we add edges in
bunches
}}}
can be replaced by
{{{
GG = Graph(H.cayley_graph(generators=L, simple=True))
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/19018#comment:26>
Sage <http://www.sagemath.org>
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