Opened 8 years ago

Closed 6 years ago

# standard bases over integers yield redundant basis elements

Reported by: Owned by: ren popescu major 4-1-0 and higher dontKnow 4-0-1

### Description

```                     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.

### comment:1 Changed 8 years ago by Oleksandr

Owner: changed from somebody to popescu

### comment:2 Changed 6 years ago by hannes

Resolution: → fixed new → closed

fixed in 4.0.3p5

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