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Re: [Axiom-developer] Issue 351
From: |
Martin Rubey |
Subject: |
Re: [Axiom-developer] Issue 351 |
Date: |
12 May 2007 01:16:57 +0200 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |
Dear Waldek,
Waldek Hebisch <address@hidden> writes:
> I wonder what shall we do with issue 351.
[...]
> One possibility is to prevent creation of fake fields: when creating COMPLEX
> F we may try to check if x^2 - 1 is irreducible over F. In general this may
> be hard to check, but just looking at characteristic we can reject PF 5
> cheaply.
I just tried to find out when x^2+1 factors in a finite field, but it seems
that the characteristic is not enough to determine this.
It seems that
* For prime fields with characteristic p, x^2+1 factors if and only if
p mod 4 = 1
* More generally, for finite fields with p^m elements and m odd, x^2+1 factors
if p mod 4 = 1, if m is even, x^2+1 always factors.
Maybe for infinite fields we just try to factor(x^2+1) and check the number of
factors.
However, there is a problem: currently, SPAD does not allow conditional exports
being triggered by functions, but only by "has" and "is" statements, it seems.
At least, I couldn't find an example, nor could I make up one.
:-(
Martin