On Mon, Apr 14, 2008 at 02:40:14PM +0100, John Cremona wrote:
> Does anyone know how Magma handles this?
>From what I can tell, magma seems to choose 'default' finite fields of a
given size at run-time, and presumably also injections between them.
Which fields become default can depend on the order in which they are
created. For example,
K := FiniteField(3^100);
L := FiniteField(3^500);
gives a different field ('measured' by MinimalPolynomial(K.1) ) than
L := FiniteField(3^500);
K := FiniteField(3^100);
while "IsDefault(K);" returns true in both cases.
In the first case, MinimalPolynomial(K.1) is a sparse polynomial, in the
second case we have L.1^( (3^500-1) div (3^100-1) ) eq L!K.1 .
In the first case, L!K.1 can change between two magma runs, so the
chosen injection appears to be chosen randomly at run-time.
Note that this behaviour may of course be different for smaller or
larger finite fields.
-Willem Jan
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