standard bases over integers yield redundant basis elements

[ren]

                     SINGULAR                                 /  Development
 A Computer Algebra System for Polynomial Computations       /   version 4.0.1
                                                           0<
 by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann     \   Sep 2014
FB Mathematik der Universitaet, D-67653 Kaiserslautern        \
// ** executing /home/ren/Sources/Singular/LIB/.singularrc
> ring r=integer,(t,x(1..3)),ws(1,-1,-1,-1);
> ideal I = x(1)^2+2*x(1)*x(2)+3*x(2)*x(3), 3*x(1)*x(2)+4*x(2)*x(3)+5*x(3)^2, 2-t;
> std(I);
_[1]=x(2)^2*x(3)-15*x(1)*x(3)^2-14*x(2)*x(3)^2+20*x(3)^3+t*x(2)^2*x(3)
_[2]=30*x(1)*x(3)^2+28*x(2)*x(3)^2-40*x(3)^3+t*x(1)^2*x(2)+2*t*x(1)*x(2)^2
_[3]=10*x(3)^3-t*x(1)*x(2)*x(3)+t*x(2)^2*x(3)-5*t*x(1)*x(3)^2-6*t*x(2)*x(3)^2
_[4]=x(1)^2+2*x(1)*x(2)+3*x(2)*x(3)
_[5]=x(1)*x(2)+4*x(2)*x(3)+5*x(3)^2+t*x(1)*x(2)
_[6]=2-t

The 2nd and 3rd standard basis elements are redundant, as their leading term is divisible by the leading term of the 6th basis element. This leads to problems parts of my code, as it assumes that standard basis is irredundant.

[hannes]

fixed in 4.0.3p5