Hi Simon,
One advantage of having a similar set up to AlgebrasWithBasis would be the
following
commands which are often quite useful:
sage: G = AlgebrasWithBasis(ZZ).example()
sage: G
An example of an algebra with basis: the free algebra on the generators
('a', 'b', 'c') over Integer Ring
sage: x = G.algebra_generators()
sage: p = x[1]*x[0]*x[2] + x[1]
sage: p.support()
[word: b, word: bac]
It currently does not seem so easy to get the support of an element in the free
algebra
sage: F = FreeAlgebra(QQ, 3, 'a', implementation='letterplace')
sage: a = F.gens()
sage: p = a[0]*a[1]*a[1]+a[0]*a[1]*a[2]
sage: p.support()
does not work.
The quotient seems to be working well! Great!
Cheers,
Anne
On 3/26/11 3:28 AM, Simon King wrote:
Hi Nicolas,
On 26 Mrz., 11:00, Simon King<simon.k...@uni-jena.de> wrote:
Sorry, I first saw your post on sage-algebra and answered there,
although it might have been better to do it on combinat-devel. Anyway,
I am very unhappy with the documentation of the "...WithBasis" stuff.
After several attempts, I still do not understand how to do even the
most basic operations with it.
Rather than trying to understand how
AlgebrasWithBasis(QQ).example().basis() is implemented, it might be
better to ask what purpose F.basis() (F a free algebra with generators
x,y,z) should have, in general?
I guess that F.basis() should have some index set. Here, it seems
natural to me to choose M=FreeMonoid(3,['x','y','z']): If m is in M
then F.basis()[m] returns the corresponding element of F.
Is that the only requirement to F.basis()?
Concerning compatibility: Rather than indexing the basis with the
elements of M, one could index it by the words in the alphabet
'x','y','z'. Is there a protocol for doing conversion by changing the
index set, yet? Such conversions could indeed facilitate consistency
between different implementations of "the same" algebra.
Cheers,
Simon
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