degBound coupled with elim1 question

[e.allman@…]

I have been talking with some mathematicians about a problem/question/development I have found when using Singular's debBound option with elim1.

We have somewhat understood the problem, but I thought I should e-mail you all to 1) get a better understanding of how elim1 and degBound interact 2) suggest that you might want to update the (excellent) manual with such information.

I describe the issue below and attach a sample file that will illustrate the problem.

%%% The Problem: In essence I have a homogeneous ideal and I am trying to eliminate variables. This is computationally too difficult a problem so I have set the degBound option to just get elements in this elimination ideal up to various degrees. I am using the "dp" ordering and the command "elim1."

Rather oddly, it seems that when the degBound is set to 10, Singular finds ideal elements of degrees 1 and 2, but when the degBound is set to 4, the quadratic elements are not found.

I've read the Singular manual and see that degBound is interpreted differently depending on which command is used to compute a groebner basis; however, since I am using elim1 I am not sure how to interpret this.

What I would like is to know for sure that I have found all the elements of the elimination ideal up to a particular degree. These results of course have me quite skeptical about having found this.

Any ideas, suggestions, or comments?

Many thanks,

Elizabeth Allman

[e.allman@…]

sample Singular code to illustrate the problem