critical bug in multivariate polynomial factorization over GF(2)

[zimmerma]

consider the following (both with Sage 4.8 and Sage 5.0.beta13 without proof=False):

sage: R.<x,y>=GF(2)[]
sage: factor(x^6 + y^6 + x^5 + x^3 + x + 1,proof=False)
x^6 + y^6 + x^5 + x^3 + x + 1
sage: (x^4+y^2*x^2+x^2+y^2*x+y^4+y^2+1)*(x^2+x+y^2+1)     
x^6 + y^6 + x^5 + x^3 + x + 1

This seems to be a bug in Singular factorization. I set the priority to "critical" since this is really a very basic routine.

Paul

[zimmerma]

here is another example:

sage: R.<x,t> = GF(2)[]
sage: f=x^6 + (t^5 + t^2)*x + t^5 + t^4 + t^3 + 1
sage: factor(f,proof=False)                      
x^6 + x*t^5 + t^5 + t^4 + x*t^2 + t^3 + 1
sage: f % (x+t+1)
0

Note that the factorization algorithm seems not to be deterministic, thus some times the factorization is correct.

Paul

[zimmerma]

Note that for the example given in the description, the "bug" seems to be deterministic.

Paul

[malb]

Hi, can you guys report this upstream? I am travelling this week.

[zimmerma]

reported upstream, see  http://www.singular.uni-kl.de:8002/trac/ticket/424

[zimmerma]

the bug is fixed upstream. I have asked in which release the patch will be.

Paul

[zimmerma]

upstream says it is fixed in 3-1-4-4.

Paul

[jdemeyer]

Fixed by #13237.