Might be fixed in Singular-3.1.6, changelog mentions "several bug fixes in 
factorization code". Haven't tried though. 
See http://trac.sagemath.org/14333



On Monday, April 8, 2013 10:18:32 AM UTC+1, Georgi Guninski wrote:
>
> Wrong factorization in QQ['x,y'] 
>
> 5.8 on ubuntu and on sagenb.org. 
>
> sage: Kxy.<x,y>=QQ[] 
> sage: P=-10*x^4*y + 40*x^3*y^2 - 80*x^2*y^3 + 80*x*y^4 - 30*y^5 + 20/9*y^3 
> + 10/81*y 
> sage: fa=factor(P);fa 
> (-10/81) * y * (-3*x + 3*y + 1) * (-27*x^3 + 81*x^2*y - 135*x*y^2 + 81*y^3 
> - 9*x^2 + 18*x*y - 27*y^2 - 3*x + 3*y - 1) 
> sage: factor(fa[-1][0]) 
> (-3*x + 3*y - 1) * (9*x^2 - 18*x*y + 27*y^2 + 1) 
> sage: fa[-1][0] 
> -27*x^3 + 81*x^2*y - 135*x*y^2 + 81*y^3 - 9*x^2 + 18*x*y - 27*y^2 - 3*x + 
> 3*y - 1 
>

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