Igor Schein on Sun, 23 May 2004 03:39:26 +0200

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Re: peculiar galoisinit() behavior

On Sat, May 22, 2004 at 04:22:55PM +0200, Bill Allombert wrote:
> On Fri, May 21, 2004 at 08:07:08PM -0400, Igor Schein wrote:
> > So we have a contradiction - p64 is a subfield of p128, and p16 is a
> > subfield of p64, yet p16 is not a subfield of p128?  It can only mean
> > that p64 is in fact not a subfield of p128, and galoisinit() returned
> > a corrupted structure.  Now, I can make an obvious guess it has to do
> > with the partial result warnings.  However, *partial* doesn't usually
> > imply *wrong*, but it seems to be the case here.
> p64 is Galois, so it is a safe bet it _is_ a subfield of p128!
> What criterium do you use to assert that p16 is not a subfield of p128 ?
> For what I see, you just proved that r128 factor over r16 as a product
> of 16 polynomials of degree 8, which imply that r16 is a subfield of
> r128. 
> For what it worth,
> ? matsize(nffactor(bnf,r64))
> %43 = [16, 2]

Come to think of it, I wasn't even drinking when I posted this
garbage :-(.  I hallucinated twice, first when I thought I saw
something wrong, and again when I tried to support it with false
argument.  Sorry.