On 16 June 2014 14:25, John Cremona <john.crem...@gmail.com> wrote:
> sage: K.<a> = QuadraticField(22)
> sage: D = -926246528884912528275985458927067632*a +
> 4344481316563541186659879867597013188
> sage: D.is_square()
> (boom)
> MemoryError: Unable to allocate 256000000000 bytes for the PARI stack
> (instead, allocated 204800000000 bytes)
>
> Sage Version 6.3.beta3
>
> Any ideas?  Other arithmetic with this works fine, and in fact:
>
> sage: eps = 197-42*a
> sage: rootD = eps^8 * (14+3*a)^2
> sage: rootD^2 == D
> True
>
> so the problem is in a call to Pari to factor the polynomial x^2-D.
>

Using the same pari/gp version (2.5.5) I have no problem doing the
same factorization diectly in gp:

? nf = bnfinit(t^2-22);
? a = Mod(t,t^2-22);
? D = -926246528884912528275985458927067632*a +
4344481316563541186659879867597013188;
? factor(x^2-D)
%4 =
[x + Mod(-314226370217524044*t + 1473852319020386314, t^2 - 22) 1]

[x + Mod(314226370217524044*t - 1473852319020386314, t^2 - 22) 1]



> John

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