# Ticket #12928(closed defect: duplicate)

Opened 14 months ago

## critical bug in multivariate polynomial factorization over GF(2)

Reported by: Owned by: zimmerma tbd critical sage-duplicate/invalid/wontfix factorization malb Fixed upstream, in a later stable release. Jeroen Demeyer

### Description

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

## Change History

### comment:2 Changed 14 months ago by 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

### comment:3 Changed 13 months ago by zimmerma

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

Paul

### comment:4 Changed 13 months ago by malb

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

### comment:5 Changed 13 months ago by zimmerma

• Report Upstream changed from N/A to Reported upstream. Little or no feedback.

### comment:6 Changed 13 months ago by zimmerma

• Report Upstream changed from Reported upstream. Little or no feedback. to Fixed upstream, in a later stable release.

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

Paul

### comment:7 Changed 12 months ago by zimmerma

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

Paul

### comment:8 Changed 11 months ago by jdemeyer

• Status changed from new to needs_review
• Reviewers set to Jeroen Demeyer
• Milestone changed from sage-5.3 to sage-duplicate/invalid/wontfix

Fixed by #13237.

### comment:9 Changed 11 months ago by jdemeyer

• Status changed from needs_review to positive_review

### comment:10 Changed 10 months ago by jdemeyer

• Status changed from positive_review to closed
• Resolution set to duplicate
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