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Re: [Axiom-developer] Axiom volunteer work ideas

From: Tim Daly
Subject: Re: [Axiom-developer] Axiom volunteer work ideas
Date: Sat, 27 Feb 2010 04:38:47 -0500
User-agent: Thunderbird (Windows/20090302)


These are just ideas (well, mostly) at this point.
I've done some simple experiments with some of them
but I'm too busy scraping the last of the Axiom source
code into literate form to attack them at the moment.

As to the Fortran vs C question... I'd be happy with either
but, truth be told, I'd really prefer a lisp implementation.
That said, I have seen a Fortran-to-C conversion program
somewhere although how well it would work on BLAS is unclear.
But it would be easy to embed a C version directly into GCL.

The choice of python was motivated by the fact that I am
using python for a task in work. A general framework that
handled a common subset of any language would be ideal. This
would allow us to generate ruby/python/haskell/fortress/go/etc

Axiom can handle several forms of output. Some bright spot
only needs to architect a generalization of the existing code,
make it more table-driven, and ... bob's your uncle, as the
Brits say.

I did an FFT many years ago in lisp but it was on a very
old, non-common-lisp. I think the sources are on paper tape.
I suppose I could parse out the 7-bit ascii but I'm lazy.

In any case, I'm just paging through my pile of notes to find
something that doesn't seem too tedious for volunteers. Nobody
wants to resurrect the Doyen work, pretty up the website (not
the content but the CSS), or struggle with a Mac port. Other
ideas like embedding ACL2 under Axiom for proof work are just
too invasive and way too steep a learning curve for volunteers.

I suppose I should journal more of these ideas to the mailing
list so others can think about them. I have partial implementations
of a lot of things, like a Cohen algebra domain that allows
explanations to be printed for each step in a solution. It is
based on Joel Cohen's Computer Algebra and Symbolic Computation books.
And I've done some more special function work but not had the
cycles to put it into the algebra yet.

Time, time, time.... sigh.


M. Edward (Ed) Borasky wrote:
Quoting Tim Daly <address@hidden>:

Interactive 3D Object in Axiom documentation

Axiom is being rewritten into a literate programming style.
That means that all of the source code will be in pdfs.
There is a site:
which allows someone to put a 3D object into a pdf yet keep
it interactive. Axiom can create 3D images. I'd like to be able
to put one of those images into the Axiom pdfs. If you look at
Volume 1, Chapter 10 it shows how to draw 3D objects.
Demonstrate an Axiom 3D graph being used interactively in a pdf.

PDFs with embedded 3D objects are extremely cool - there's a piece of magic called "U3D" involved. Adobe has proprietary tools that do this magic, but I'm not sure there's a fully open-source tool set with a reasonable work flow. I remember downloading some stuff a couple of years ago and giving up on it. A quad core and 8 GB of RAM might be a big help. ;-)

Fortran Library work

If you want something more mathematical there are a large number of
fortran library routines that were part of the commercial version of
Axiom but were not released to open source. See Volume 10.3 and look
for the ASP domains. These are Axiom "covers" for the NAG fortran
library. There are 2 possible paths to explore, either to find a
standard fortran library and rewrite the cover routines or find
algorithms (e.g. runga-kutta integration) and write lisp routines
to fit "under the covers" (Axiom is written in Lisp).
Demonstrate the lisp or fortran routine being used from Axiom.

How much of this number crunching is already in GSL? Does it *have* to be FORTRAN? Why not C? The C compilers may have sucked wet dog fur when NAG was selling FORTRAN libraries, but they're fine now. Now that I think about it, I'd love to be able to simply "shell out to R" from Axiom. The closest thing to that is to run R and use Ryacas to talk to a Yacas server for the symbolic stuff. I'd rather work in a symbolic language and use a *numerical* server.


Axiom generates Fortran output. I want to change this to also
generate Python output. See )set output fortran on
I want to be able to do )set output python on
Demonstrate automatically constructing a python program from Axiom

How about Ruby? Rationals and Matrices thereof are a "standard library" in Ruby. How about R or Octave code?

Fast Fourier Transform

I have a need for FFTs. Figure out how to implement this in Lisp:
Demonstrate an FFTW in Axiom called from the command line

I've seen FFTs in Lisp, although I can't remember where. There's probably a Scheme macro to do it, too. ;-)

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