Hey Amit,
I think I've found a (rather alarming) bug regarding Iwahori-Hecke algebras:
>
That is not true; you've found a very subtle behavior with matrices and
coercion. There's nothing wrong with the Iwahori-Hecke algebra.
>
> sage: L.<q>=LaurentPolynomialRing(ZZ)
> sage: H=IwahoriHeckeAlgebra('A1',q^2)
> sage: T=H.T(); Cp=H.Cp()
> sage: T(q*Cp[1])
> T[1] + 1
> sage: M=MatrixSpace(H,1,1)
> sage: M(q)*M(Cp[1])
> [q*T[1]]
> sage: q*T[1]==T[1]+1
> False
>
> Briefly, sage does not appear to multiply in the Iwahori-Hecke algebra
> correctly when doing matrix multiplication! This affects larger matrices
> too. The bug goes away if everything is in the T() basis or in the Cp()
> basis.
>
> This is likely a bug, but there's some subtleties going on. The first is
that H is not an actual parent:
sage: H(q).parent()
Iwahori-Hecke algebra of type A1 in q^2,-1 over Univariate Laurent
Polynomial Ring in q over Integer Ring in the T-basis
That is why I am hesitant to say that this is an honest bug.
There is also a cmp running around behind the scenes being called, which
(at least in 7.5.beta2) is being deprecated:
sage: M(Cp(q)) * M(Cp[1])
/home/travis/sage-build/local/lib/python2.7/site-packages/sage/categories/
modules_with_basis.py:1647: DeprecationWarning: the 'cmp' keyword is
deprecated, use 'key' instead
See http://trac.sagemath.org/21043 for details.
return min_cmp(self.support(), *args, **kwds)
[T[1] + 1]
There is also an issue with what basis the elements are considered in and
the coercions involved. The fact that the above output is being forced into
the T basis is indicative of this. The short version is the matrix code was
not designed to handle entries in a multiple realization parent like H. I'm
glad that it is now working for non-Ring subclass parents (I believe my
thank you goes to Jeroen for weakening type restrictions).
TL;DR Be explicit about what basis you want the entries of the matrix to be
in.
Best,
Travis
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at https://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
