Another bug of std with additional generators

[Simon King]

Ticket #224 was about a bug in std with additional generators. I also found such bug, but I believe that it is a different problem, since my bug was already in Singular-3-1-0 (while the one from #224 was new in Singular-3-1-1).

Please download the attachment. Then do

                     SINGULAR                             /  Development
 A Computer Algebra System for Polynomial Computations   /   version 3-1-1
                                                       0<
     by: G.-M. Greuel, G. Pfister, H. Schoenemann        \   Feb 2010
FB Mathematik der Universitaet, D-67653 Kaiserslautern    \
> < "bugreport";
> i = groebner(i);
> dim(std(i+p));
0
> dim(std(i,p));
2
> ideal g = std(i,ideal(p[1..3]));
> dim(g);
1
> dim(std(g,p[4]));
0

In other words, dim(std(i,p)) is greater than dim(std(i,ideal(p[1..3]))).

The situation in Singular-3-0-0 was slightly different:

                     SINGULAR                             /  Development
 A Computer Algebra System for Polynomial Computations   /   version 3-1-0
                                                       0<
     by: G.-M. Greuel, G. Pfister, H. Schoenemann        \   Mar 2009
FB Mathematik der Universitaet, D-67653 Kaiserslautern    \
> < "bugreport";
> i = groebner(i);
> dim(std(i,p));
1
> dim(std(i+p));
0
> ideal g = std(i,ideal(p[1..3]));
> dim(g);
1
> dim(std(g,p[4]));
0

So, apparently dim(std(i,p)) was wrong in 3-1-0 and is worse in 3-1-1.

I think this is very severe and thus mark it as blocker.

[Simon King]

An example exhibiting the bug

[hannes]

does not occur with a current Singular version. (was solved with #224)