Bill Allombert on Fri, 21 May 2004 00:23:46 +0200

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Re: galoisinit() bug

On Tue, May 18, 2004 at 09:11:23PM -0400, Igor Schein wrote:
> Hi,
> ? galoisinit(x^4+272*x^3+40256*x^2+1740800*x+25397248);
>   ***   prime too small in fixedfield.
> It was already broken in 2.2.4.
... and even in 2.2.0.

The bug is in a function that include the following disclaimer:

/*We try hard to find a polynomial R squarefree mod p.
Unfortunately, it may be too much asked.
A less bugprone way would be to only ask it to be squarefree mod p^e
with e not too big. Most of the code is here, but I lack the theoretical
knowledge to make it to work smoothly.B.A.

and indeed, this is too much asked here. Now I have a better theoretical
knowledge, but this is not very encouraging: the theoretical 
upper bound on the exponent e is so large than this would make the 
excercise rather pointless.

So, barring rewriting the whole code to work at an higher level, I
see no 100% solution that does not need a ridiculous amount of code
to handle oddball case.

So until I decide to rewrite galoisinit, I will add an extra pass to 
catch this one (the one implemented in 2.1).