Factoring over a finite field sometimes returns wrong result

[jdemeyer@…]

                     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]:
   _[1]=1
   _[2]=x7y3+xy9+(a)*x8+(a)*y4
   _[3]=y8+(a)*y7+(a+1)*x
[2]:
   1,1,1
> factorize(g);
[1]:
   _[1]=1
   _[2]=x7y3+xy9+(a+1)*x8+(a+1)*y4
   _[3]=y8+(a)*y7+(a+1)*x
[2]:
   1,1,1
> factorize(g);
[1]:
   _[1]=1
   _[2]=x7y3+xy9+x8+y4
   _[3]=y8+(a)*y7+(a+1)*x
[2]:
   1,1,1

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

[anonymous]

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

...
> factorize(g);
[1]:
   _[1]=1
   _[2]=x7y3+xy9
   _[3]=y8+(a)*y7+(a+1)*x
[2]:
   1,1,1

-leif

[mlee]

fixed with 15123