Re: Magma Computation needed !

Roman Pearce wrote:
>
> Sure enough I ran out of memory (4GB). You may be able to do this with
> an 8GB machine. Does it have to be over the ring of integers, or did
> you want rational number coefficients ?

Let me first thank you for your fast answer and your generous offer
of so much computer time.

Regarding the question of coefficients: This is a good question, that
I could not fully answer to myself. The goal of the computation is to
prove the squarefreeness of the so called division-polynomial of an
elliptic curve y^2=x^3+A*x+B over a field K with char K != 2, 3

If char K = 0 it would be enough to compute over the rational numbers,
but with characteristic p it would be useful to know that the hoped-for
element n1*(4*A^3+27*B^2)^n2 has only 2 and 3 as prime factors in n1.

At first I was quite sure that this had to be true, so it would be
worthwhile to find a groebner base over Z, but now it came to my mind
that [p] :E->E (multiplication by p on an elliptic curve E) has not
kernel Z/pZ x Z/pZ for p=char K. So the reasons to assume squarefreeness
of the division-polynomial psi[p] seem to break down in this case.

What is the conclusion of all this ? I think it would be worthwhile to
do the calculation over Q if this is easier, and I will have to do some
experimental calculations to see, if my conjecture is actually true in
char K = p.

By the way: What machine did you use ? Was it an Apple with PPC or do
other workstations with PPC also exist ? (The magma online calculator
says to use a dual Opteron Sun-workstation - I would be very happy if I
could afford such a system and one of these expensive Magma licenses
too..)

Jürgen

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Dipl.-Math. Jürgen Böhm e-mail: reverse: net dot gmx at jboehm
"At a time when so many scholars in the world are calculating, is it not
desirable that some, who can, dream ?" R. Thom
.