ideal membership test

Hi,
Currently, I am running some experiments about ideal membership test using command "reduce".
For example:
ring r=(2,X),(a,b,c),dp;
minpoly=1+X^3+X^4;
ideal I=b,c;
slimgb(I);
_[1]=c
_[2]=b
reduce(a*b+a*c,I);
0

The problem now is that how to get the quotient of the ideal division.
For example, given ideal <b,c>, given polynomial "a*b+a*c", the ideal membership testing is actually polynomial division. Now I want to get the quotient, in this example, it is (a,a).

Is there a command to get the quotient which is similar to the Maple command "NormalForm" in link:
http://www.maplesoft.com/support/help/M ... NormalForm
The 4th parameter of "NormalForm" stores the quotients.

thanks.
Gepo

Probably "lift" is what you want

> lift(I,a*b+a*c);
_[1,1]=a
_[2,1]=a
>