Opened 10 years ago

Closed 10 years ago

## #441 closed bug (fixed)

# Factoring over a finite field sometimes returns wrong result

Reported by: | Owned by: | somebody | |
---|---|---|---|

Priority: | critical | Milestone: | 3-1-5 and higher |

Component: | dontKnow | Version: | 3-1-5 |

Keywords: | Cc: |

### 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]: _[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.

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

-leif