Singular

Thanks to some off-line help from Viktor, and a course in remedial reading :?, I have some success.

The problem I reported is due to the fact that I misread the example of an ncalgebra computation in the manual. Once I got that right, I was able to get sensible results.

For the record, the "nc" relation I was using is [b]xy + yx + x + 1[/b]. I filled in the two arrays with
[code]
C[2][2] = 1
D[2][2] = x + 1
[/code]
which, unfortunately, represents [b]yx - xy - x - 1[/b]. As usual, the computer did exactly what I told it to.

Using the latter relation, it was easy to see that the ideal generated by the algebraic relations for [b]x, y[/b] is in fact the unit ideal. This accounts for the fact that in the quotient ring, everything came up as [b]0[/b].

Justin

Hi Justin,

basically you're given say the generators x,y over some field K
and three relations, xy + yx + ... = 0, f(x)=0, g(y) = 0.
The classical way to input such an algebra is
1) define the algebra, say A, in x,y with the relation xy + yx + ... = 0 (with, say, [b]ncalg[/b] command)
2) compute a two-sided Groebner basis of the ideal in A,
generated by polynomials f(x), g(y):
[code]poly f = ...; poly g = ...;
ideal Q = f,g;
Q = twostd(Q);[/code]
Here it would be interesting to see what Q gives
3) pass to the factor algebra modulo Q
[code]qring q = Q;[/code]

If you have further problems, please send me some examples you're playing with to levandov at mathematik.uni-kl.de

Best regards.
Viktor

Hi,

I've tried out the examples in the Plural doc, and looked at
some postings in the Forum, but I am still unclear on how to
do the following.

I want an algebra, A, with generators 1,x,y,..., subject to relations
like this:
f(x)=0
g(y)=0
(so each generator generates a number field, assuming the base
field is Q).

Then there are relations like xy + yx + ... = 0.

The latter seems clear from the examples. I am having problems
with the former. I would think that creating a base qring using an
ideal generated by f,g,... would be the way to start, but the results
aren't what I expect (e.g., I always get a reduced value of 0 for x^2).

What am I missing?

Thanks!

Justin