#20445: Iteration through Coxeter groups
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Reporter: stumpc5 | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.2
Component: combinatorics | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The algorithm in chevie is very different from the algorithm we currently
have:
{{{
ForEachElement:=function(W,f)local l,g;
if not IsFinite(W) then Error("only for finite Coxeter groups");
elif W.nbGeneratingReflections=0 then f(W.identity);return;
fi;
l:=List([0..W.nbGeneratingReflections],i->
ReflectionSubgroup(W,W.reflectionsLabels{[1..i]}));
l:=List([1..Length(l)-1],i->ReducedRightCosetRepresentatives(l[i+1],l[i]));
g:=function(x,v)local y;
if Length(v)=0 then f(x);
else for y in v[1] do g(x*y,v{[2..Length(v)]});od;
fi;
end;
g(W.identity,l);
end;
}}}
We should also implement that algorithm (maybe even with hard-coded coset
representatives in the finite case) so that we can see if this is indeed
faster.
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Ticket URL: <http://trac.sagemath.org/ticket/20445>
Sage <http://www.sagemath.org>
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