Dear Sage / Sage-combinat devs,
This is a short call for votes about leading terms and triangular
morphisms.
On Wed, Feb 10, 2010 at 11:06:50AM +0100, Nicolas M. Thiery wrote:
> I finally started to review #7914. One thing that did slip through
> my fingers. I just noticed that leading_term returns the term with
> smallest support. I instead assumed it would return that with
> largest support, as is the case for polynomials:
>
> sage: p = 3*x^2+2*x+1
> sage: p.leading_coefficient()
> 3
Florent is also +1 on this convention, and I just fixed the patch
accordingly. But it is still time to rollback. Please vote!
A related call for votes: what do we want to mean by upper/lower
triangular morphisms? Let X be a module with basis, and b its basis.
Then, a morphism f: X->X is upper triangular if, for all i,
- Option 1: f( b[i] ) = c * b[i] + smaller terms
- Option 2: f( b[i] ) = c * b[i] + larger terms
Intuitively, I vote for Option 1. An argument is that this matches
with upper triangularity of the matrix A of f when writing the images
f(b[i]) as column vectors, which is the usual convention when f(x) is
calculated by A * X.
Please vote!
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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