#5877: [with patch; needs review] calling a group character is broken
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Reporter: saliola | Owner: saliola
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.2
Component: algebra | Keywords:
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Comment(by saliola):
Hello David, thanks for your comments.
Replying to [comment:3 dmharvey]:
> I know very little about GAP and the implementation of groups in Sage,
but is this really the most efficient way to do this? It looks like the
code has to enumerate the conjugacy classes of the group on every call, is
that for real?
I know very little about GAP as well. I just followed the method described
below, which I found at
[http://www.gap-
system.org/ForumArchive/Hulpke.1/Alexande.1/Re__Char.11/2.html GAP-Forum]:
{{{
You will (if you like it or not) have to identify the class of the element
g.
You can do this in general, by a specific test with \in (but see below):
gap> cl:=ConjugacyClasses(G);;
gap> First([1..Length(cl)],i->g in cl[i]);
4
So you know the class is class number 4, with the name:
gap> ClassNames(CharacterTable(G))[4];
"9a"
So the character value is:
gap> Irr(G)[3][4];
E(9)^2+E(9)^4+E(9)^5+E(9)^7
}}}
I did a bit more research, and I found a direct method to evaluate the
class function via GAP. Of course, the computation still needs to
determine the class to which the element belongs, but at least there won't
be the extra interface overhead of going back and forth between Sage and
GAP for each test. Moreover, GAP must have speedups for particular types
of groups (the above method is for the generic case).
I'll replace the patch right-away with the better version.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5877#comment:4>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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