Dear Vinay Wagh,
> In my last mail I forgot to mention this...
> I am also interested in finding the quotient of two ideals.
> R: ring, I,J subset R be the ideals in R. Then I want to
> find the ideal I:J.
In SINGULAR, you can find it with the help of command "quotient", seehttp://www.singular.uni-kl.de/Manual/2-0-5/sing_261.htm
> So I want to know the algorithm/theory used to find out the
> generators of I:J.
Theoretical issues could be found, for example, in the SINGULAR book, p.79-80, subsection 1.8.8.
Alternatively, there is a short description of the algorithm in the paper of Hans Schoenemann "Algorithms in SINGULAR".
The HTML version of the article is available athttp://www.mathematik.uni-kl.de/~zca/Re ... paper.html
With best regards,