Really?

sage: x^4
s^4 + 4294967296*h/(4294967296*l)*s^3 +
29710560942849126597578981376*h^2/(79228162514264337593543950336*l^2)*s^2
+ 17592186044416*h^3/(281474976710656*l^3)*s + h^4/(256*l^4)
sage: 79228162514264337593543950336.factor()
2^96


so I think you just have some large powers of 2 in there.

John Cremona

On 5 February 2013 16:04, Michael Beeson <[email protected]> wrote:
> K.<p,d,e,g,m,f,h,l,r,N> = FractionField(PolynomialRing(QQ,10,'pdegmfhlrN'))
> R.<s> = K[]
> x = s + h/(4*l)
> G = e*l*x^4 - e*h*x^3 + (-3*e*l-e*r+N)*x^2 + 2*e*h*s + 2*e*l + 2*e*r-N
> print G
>
> The response looks fishy:
>
> e*l*s^4 + ((-30423614405477505635920876929024*e*h^2 -
> 243388915243820045087367015432192*e*l^2 -
> 81129638414606681695789005144064*e*l*r +
> 81129638414606681695789005144064*l*N)/(81129638414606681695789005144064*l))*s^2
> + ((-2417851639229258349412352*e*h^3 + 9671406556917033397649408*e*h*l^2 -
> 9671406556917033397649408*e*h*l*r +
> 9671406556917033397649408*h*l*N)/(19342813113834066795298816*l^2))*s +
> (-3072*e*h^4 - 49152*e*h^2*l^2 + 524288*e*l^4 - 16384*e*h^2*l*r +
> 524288*e*l^3*r + 16384*h^2*l*N - 262144*l^3*N)/(262144*l^3)
>
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