Opened 9 years ago

Closed 9 years ago

# Factoring over a finite field sometimes returns wrong result

Reported by: Owned by: jdemeyer@… somebody critical 3-1-5 and higher dontKnow 3-1-5

### Description

```                     SINGULAR                                 /  Development
A Computer Algebra System for Polynomial Computations       /   version 3-1-5
0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann     \   Jul 2012
FB Mathematik der Universitaet, D-67653 Kaiserslautern        \
> ring r = (2,a),(x,y),dp; minpoly = a^2+a+1;
> poly g = x7y11+xy17+(a)*x7y10+(a)*xy16+(a)*x8y8+(a+1)*x8y7+(a)*y12+(a+1)*x8y3+(a+1)*x2y9+(a+1)*y11+x9+xy4;
> factorize(g);
:
_=1
_=x7y3+xy9+(a)*x8+(a)*y4
_=y8+(a)*y7+(a+1)*x
:
1,1,1
> factorize(g);
:
_=1
_=x7y3+xy9+(a+1)*x8+(a+1)*y4
_=y8+(a)*y7+(a+1)*x
:
1,1,1
> factorize(g);
:
_=1
_=x7y3+xy9+x8+y4
_=y8+(a)*y7+(a+1)*x
:
1,1,1
```

Note the results vary if computed several times (these are the 3 possibilities), but only the first one is correct.

### comment:1 Changed 9 years ago by anonymous

FWIW, I also get a fourth result (same Singular version from Sage trac #13237):

```...
> factorize(g);
:
_=1
_=x7y3+xy9
_=y8+(a)*y7+(a+1)*x
:
1,1,1
```

-leif

### comment:2 Changed 9 years ago by mlee

Resolution: → fixed new → closed

fixed with 15123

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