Simplifying expressions in a quotient ring

Justin · Wed Jun 20, 2007 6:43 pm

Hi,

With my ncalgebra definition in good shape, I now want to verify some computations that I've made by hand.

For example, in addition to the "nc" relation xy + yx + x + 1=0, I have a relation x^2+2=0. Singular uses the former

Code:

> y*x;
-xy-x-1

whereas it seems to ignore the latter

Code:

> x^2;
x2

It seems that Singular(Plural) opts for an expression in terms of variables, rather than scalars.

Is there any way to pursuade Singular to take account of the fact (in this case) that x^2 is -2? The simplify() and reduce() calls don't do this.

Thanks!

Justin

Re: Simplifying expressions in a quotient ring

Guest · Sat Jun 23, 2007 6:19 am

Closing this, for the record:

Justin wrote:

Is there any way to pursuade Singular to take account of the fact (in this case) that x^2 is -2? The simplify() and reduce() calls don't do this.

'reduce()' is, in fact, the way to do it. I managed to gloss over this in my first readiing (the remedial reading course, mentioned earlier, obviously hasn't helped), but

Code:

> reduce(x^2, std(0));
-2

shows what I was after.

Thanks to Viktor, again, for his help.

Justin