creating regular representation for the quotient ring over a 0-dimensional ideal

[Dima Pasechnik]

I need to do computations with matrices representing elements of the quotient ring A of a polynomial ring k[x1,...,xn] modulo a 0-dimensional ideal.

I don't seem to find such basic functionality as constructing these matrices implemented. 

It is of course easy, once you have a Groebner basis; from this you can find a basis of the regular representation of A as

"monomials under the staircase" (i.e. all the monomials occurring in the Groebner basis elements on the non-leading positions),

and compute matrices representing multiplication of variables x1,..., xn with these elements, my question is whether this is already

implemented in Sage.

 

[Simon King]

Hi Dima,

Not to my knowledge. I had to do similar things and was missing that
functionality, too. Actually not just for polynomial rings but for
non-commutative versions thereof.

Best regards,
Simon

[Dima Pasechnik]

Isn't all that functionality for "combinatorial algebras" (not clear what exactly they do) meant to do such things trivially?

True, it appears that for a basis of the quotient ring they create for you something called "Lazy family", elements of which you cannot even list(), even though you know that

there are just finitely many!

There is even a regular_representation() menthod, that is probably meant to do just what I need, but how?

Dima 

Best regards,
Simon