#4487: [with patch; needs work] add method to evaluate characters of permutation
and matrix groups
--------------------------+-------------------------------------------------
Reporter: wdj | Owner: joyner
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: group_theory | Resolution:
Keywords: |
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Changes (by wdj):
* summary: [with patch; needs review] add method to evaluate characters
of permutation and matrix groups => [with
patch; needs work] add method to evaluate
characters of permutation and matrix groups
Comment:
First, I am running sage on ubuntu 8.10 where doctesting seems to be
broken, so I have not tested this.
I like this addition so much, I am going to give it a positive review once
one important change is made.
This output:
{{{
sage: G = GL(2,3)
sage: irrs = G.irreducible_characters()
sage: chi1 = irrs[3]; chi1
Character of General Linear Group of degree 2 over Finite Field of size 3
sage: g = G.conjugacy_class_representatives()[6]
sage: chi1(g)
E(8)+E(8)^3
}}}
is unacceptable, IMHO, because it is easy to fix and (as the author
himself noted) should be a Sage value.
In addition to the things I noted above which might be changed but don't
have to be (yet or ever), is the following somewhat odd behaviour:
{{{
sage: len(G.conjugacy_class_representatives())
8
sage: chi2 = GroupCharacter(G, [-1, -1, -1, -1, -1, 1, -1, -1])
sage: chi2.irreducible_constituents()
[]
sage: chi2 = GroupCharacter(G, [1, 1, 1, 1, 1,1, 1, 1])
sage: chi2.irreducible_constituents()
[Character of General Linear Group of degree 2 over Finite Field of size
3]
sage: chi2 = GroupCharacter(G, [2, 2, 2, 2, 2, 2, 2, 2])
sage: chi2.irreducible_constituents()
[Character of General Linear Group of degree 2 over Finite Field of size
3]
}}}
It seems to be a coefficient is missing somewhere here. (I agree that this
simply interfaces with GAP, but still!) Anyway, this can be fixed later
and I want to minimize the required work so this can be included in Sage
ASAP.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4487#comment:5>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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