Re: record size computation

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Thu, Jun 26, 2003 at 01:33:15PM -0400, Igor Schein wrote:
> Hi,
> 
> I have computed galoisinit(P324), where P324 is a degree-324
> polynomial, using a 64bit gp binary on a 950MHz Solaris machine with
> 64GB of RAM.   The initial stack was 16GB.  The largest the process
> grew in the memory was 8GB.  The size of the output is 500MB.  The
> total runtime was 12hours.
> 
> All those are huge numbers.  Most people don't have 64GB RAM 64bit
> machines at their disposal.  For once, the bottleneck is not a
> runtime complexity of algorithm, but hardware limitations due to
> the implementation.  
> 
> Any comments, Bill? :)

That great, but you did not beat my record a sfar as degree is
considered!

My record was made with a 1Gb stack on 1GHz pentium III.
Here the entry: 
Degree:336
Time:13h 43mn
Size of result:2581 kb
Polynomial:polresultant(x^28-2,subst(polcyclo(28),x,(a-2*x)*x^27/2))*2^12

What is the galois group of your polynomial (use galoisexport and GAP,
galoisidentify does not handle degree 324) ? Did you used GMP ?

I was not able to find a larger centerless Galois group such that 
galoisinit would finish and that exist a very sparse polynomial
with this Galois group.

Cheers,
Bill.