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[Axiom-developer] Permission
From: |
daly |
Subject: |
[Axiom-developer] Permission |
Date: |
Wed, 15 Jun 2005 09:59:06 -0500 |
*
Michael Stoll has given us permission to use his CREAL lisp code in
Axiom. He has power series code which we can use if we want. Further,
he doing work in finding rational points on curves (a private
discussion elsewhere) so this is another area of potential
interest. He points out that the main inner loop is in assembler for
speed.
It turns out that my new job involves assembly code and machine
architecture and I had planned to practice on the gmp numeric
code so there is a bit of overlap.
Many thanks to Michael.
Tim
=====================================================================
Dear Tim,
please feel free to use whatever you like (giving appropriate credit, of
course). I wasn't even aware that the stuff is available somewhere - I'd be
hard put to find it myself by now!
BTW, I have also written code to deal with power series in a similar spirit
(including a macro that solves fairly complicated (fixed point) equations if
that is formally possible, i.e., the n-th coefficient of the right hand side
only involves earlier coefficients of the left hand side, as in
F(z) = 1 + zF(z)
where the multiplication by z is encoded by a shift), which might be
interesting for you. I'm not sure I can find it, but Bruno (who I would guess
is the "someone" pointing out my work to you) probably has that somewhere,
too.
Thanks for your interest,
Michael Stoll
On Monday 13 June 2005 17:53, you wrote:
> Michael,
>
> I'm Tim Daly, the lead developer on Axiom. Axiom was originally
> developed at IBM Research, was bought to NAG and was a commercial
> competitor to Mathematica and Maple. It was withdrawn from the
> market and is now free and open source software. (see
> http://savannah.nongnu.org/projects/axiom
> http://sourceforge.net/projects/axiom
> http://page.axiom-developer.org
>
> We've been discussing a new infinite-precision reals package and
> someone pointed me to your work. I'd like your permission to use
> and modify the common lisp code which is available at:
> http://www.haible.de/bruno/MichaelStoll/reals.html
>
> Axiom is released under the Modified BSD license. I don't see a
> license associated with your code so I'm not sure if I have your
> permission to use and modify it.
>
> Almost all of the code will end up being written in our algebra
> language which will simplify the whole type issue.
>
> Tim Daly
> address@hidden
--
Michael Stoll * Professor of Mathematics * International University Bremen
address@hidden * http://www.faculty.iu-bremen.de/stoll/
Dear Tim,
this is a very complex subject in general. What is certainly possible (and
maybe this is what you are referring to) is to use my "ratpoints" program to
search for rational points on curves of the form y^2 = f(x). However, it will
be quite hard to achieve the same speed by an implementation in Lisp - it
mostly depends on the efficiency of the innermost loop, which in the best
case consists only of a handful of assembler instructions without memory
references. It would be interesting to see, though, how fast you can get with
Common Lisp bit vectors. Maybe it's not so bad if they are efficiently
implemented...
Other than this, algorithms in this area tend to be rather complex and involve
lots of number theory, which is why I am implementing these things in Magma
(which might be interesting for you to check out if you don't know it yet; it
appears to have some similarities regarding the strong typing with algebraic
structures).
Best wishes,
Michael Stoll
On Monday 13 June 2005 18:51, you wrote:
> Michael,
>
> I also understand from your web page that you've done work in
> finding rational points on curves.
>
> Do you have explicit algorithms that you can point me to?
> I'd like to look at how these might be implemented in Axiom.
>
> Tim Daly
--
Michael Stoll * Professor of Mathematics * International University Bremen
address@hidden * http://www.faculty.iu-bremen.de/stoll/
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