[Top][All Lists]

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

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

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.



reply via email to

[Prev in Thread] Current Thread [Next in Thread]