Singular

Dear Singular team,

I try to compute Gröbner bases for the Conti-Traverso procedure, and I need to use a weighted lexicographical ordering (Wp) (in order to obtain a feasible point with minimal costs). Usually, I would just use the cost vector c of my integer linear program. Unfortunately, it contains zero entries (due to the use of slack variables, so this might be a very common problem), and Singular's help says that only positive entries are allowed. However, as I learned from several papers about Conti-Traverso, there should be no problem with working with a weighted lexicographical ordering from arbitrary nonnegative integer vectors in this case. Do you have any suggestions how I could solve or circumvent this problem?
Thanks! Katrin

PS: By the way, Singular produces a seg fault when I use zeros for Wp, and it tells me to inform the authors...

> ring R = 0, (w1,w2,w3,t,x1,x2,x3,x4,x5), (lp(4),Wp(1,1,0,0,0));
> poly f1 = w1^2*w2;
Singular : signal 11 (v: 3130/ 14130 ):
current line:>>poly f1 = w1^2*w2;<<
Segment fault/Bus error occurred at 853b33f because of 4 (r:1323172969)
please inform the authors
trying to restart...
o*w2

I can't reproduce this crash with Singular 3-1-3-3

Download the recent version from

and try again.

If the problem still occurs, then indicate on which machine and with
which operationg system you are working.

Concerning your inqueries the zeroes in the weight vector:

Where did you find:

The manpage on Global orderings
http://www.singular.uni-kl.de/Manual/la ... htm#SEC795
only says:

As long as Singular does not complain with the definition you make,
it should work in (some sense). The question is whether it is a global ordering.

Thank you very much for the quick help. I downloaded the new version and now everything works fine! Thanks!