Singular

[quote="greuel"]Hi,
I guess 'division' is what you want.[/quote]
Thanks. Unfortunately, B is not necessarily a standard basis, and division appears to compute a standard basis of B before doing the division. For example,[code]> ring R=0,(x,y),dp;
> ideal l = xy+1,y2+1;
> poly f = x-y;
> division(f,l);
[1]:
_[1,1]=-y
_[2,1]=x
[2]:
_[1]=0
[3]:
_[1,1]=1
[/code]The answer I [i]want[/i] is[code][1]:
_[1,1]=0
_[2,1]=0
[2]:
_[1]=x-y
[3]:
_[1,1]=1
[/code]If I read the documentation correctly, division computes a standard basis, then lifts to l; I want the result from the non-standard basis. Is there an option to turn that behavior off?

Hi,
I guess 'division' is what you want.

[quote="bricken"]Hi John!
Lift might do the job.
http://www.singular.uni-kl.de/Manual/3-0-4/sing_235.htm
Michael[/quote]Thanks, that helps a great deal. I don't know that it's as efficient as I'd like, maybe you can say. To use lift to "recover" the H's, I understand that I need to type[code]r = reduce(f,B);
lift(B,f-r);
[/code]When Singular performs the reduction, it computes H once.

Then, when Singular computes the lift, it computes H a second time.

I'd prefer to compute H only the first time, and recover it without having Singular go through it again.

Hi John!
Lift might do the job.
http://www.singular.uni-kl.de/Manual/3-0-4/sing_235.htm
Michael

Suppose that B is an ideal, f is a polynomial, and r is obtained via
r = reduce(f,B);
Then there exists a list H of polynomials such that
f == H1*B1 + ... + Hm*Bm + r

Does Singular have a function/option to determine H, after computing r?