Hello,

sage: version()
'Sage Version 5.5, Release Date: 2012-12-22'

On Sun, Jan 20, 2013 at 7:36 PM, Peter Mueller <[email protected]>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)
>
> The code and its up to here correct results show that f is inseparable, so
> 0 should be a root of the discriminant of f-t. However, we get
>
> sage: (f-t).discriminant().factor()
> (3) * (t + 3)^5
>
>
In Sage 5.5 and the 5.6.5c1, I get 4 as the output. May be upgrade Sage? :)
But, it would still be interesting to find out, what fixed this bug.

HTH, KnS


> which is wrong. Even worse, -3 isn't a root of the discriminant of f-t, for
>
> sage: S(f+3).factor()
> y * (y + 1) * (y^2 + y + 1) * (y^3 + 2*y + 4) * (y^3 + 3*y^2 + 4)
>
> so f+3 is separable.
>
> Best wishes,
> Peter Mueller
>
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