On a related note, it is usually a bad idea to create polynomial rings over 
polynomial rings if you really want multivariate polynomials. If anything, 
the proper multivariate polynomials will be much faster:

sage: R.<x,t> = GF(5)[]      
sage: f = x^10+2*x^6+2*x^5+x+2-t
sage: f = x^10+2*x^6+2*x^5+x+2  
sage: R.<x,t> = GF(5)[]         
sage: f = x^10+2*x^6+2*x^5+x+2
sage: (f-t).discriminant(x)
-t^5
sage: (f-t).discriminant(t)
1


On Sunday, January 20, 2013 2:06:00 PM UTC, Peter Mueller wrote:
>
> I believe the following Sage code (version 4.5.1) exhibits a bug:
>
> sage: K.<t>=GF(5)[]
> sage: R.<x>=K[]
> sage: S.<y>=GF(5)[]
> sage: f=x^10+2*x^6+2*x^5+x+2
> sage: 
> sage: S(f).factor()
> (y + 3)^6 * (y^4 + 2*y^3 + 4*y^2 + 3*y + 3)
>
>

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