Real Algebraic Closure

Renaud Rioboo has been working in the area of Real Algebraic Closures.
He maintains the RECLOS package under Axiom. I am working with him to
create a literate program version of this package.

Further details of this work are available on the Axiom website in the
file src/algebra/reclos.spad.pamphlet.
See the axiom-developer mailing list for detailed discussions.

Hopf Algebra

Bertfried Fauser has written two packages for Mathematica, one for
Clifford algebras and one for Hopf Algebras. Both packages are widely
used in Physics. Axiom has some facility with these but Dr. Fauser's
packages are more recent and more advanced. I am working with Dr. Fauser
to create Axiom packages and literate programs for these areas.

Further details of this work are not yet publicly available.
See the axiom-developer mailing list for detailed discussions.

Parametric Linear Algebra

William Sit created a package for Axiom which solves parametric linear
systems of equations. I am working with him to create a literate
program version of this package.

The code is on the Axiom website in src/algebra/pleqn.spad.pamphlet
Further details of this work are not yet publicly available.
See the axiom-developer mailing list for detailed discussions.

Infinite Group Theory

Gilbert Baumslag has created the Magnus system to do Infinite Group
Theory computation. I have created a series of Axiom domains that
are intended to be a base for similar functionality within Axiom.

Further details of this work are not yet publicly available.

Axiom Type Resolution

Nicolas has done a Phd Thesis on the subject of Axiom Type resolution.
I am working with him to try to bring this code into Axiom

Further details of this work are available in his PhD Thesis.

OpenMath

OpenMath is a standard for exchanging semantically correct mathematical
expressions between a variety of computational mathematics tools. Axiom
previously supported OpenMath when it was a commercial product. I am
working with a commercial firm and Camm Maquire (the Gnu Common Lisp
Lead Developer) to recover this functionality in the open source version
of Axiom.

The code is available on the Axiom website
Further details of this work are not yet publicly available.
See the axiom-developer mailing list for detailed discussions.

Symbolic Summation

Fabrizio Capara has implemented Symbolic Summation which is a way of
constructing closed form formulas for infinite summations, similar in
theory to closed form integration. I cam working with him to build a
package and a literate program to perform this computation in Axiom.

Further details of this work are not yet publicly available.
See the axiom-developer mailing list for detailed discussions.

Literate Journal

Carlo Traverso (Math Dept, Univ. Pisa) has a grant to create a Literate
Journal. This Journal will accept papers that include executable source
code. The goal is to combine Mathematics and Computer Science into
Computational Mathematics. I will be building the first version of the
Journal on CD.

Further details of this work are not yet publicly available.
See the axiom-developer mailing list for detailed discussions.

Symbolic Group Theory

CAISS is examining the idea of Symbolic Group Theory. That is, to provide
group theory computations that include the indefinite value as part of
the computation. This is a joint effort with Gilbert Baumslag,
Doug Troeger, and William Sit.

Further details of this work are not yet publicly available.

Fedora

Fedora is the free software release of the Linux Red Hat distribution.
Axiom depends on a worldwide community for its support. In order to
guarantee that the Linux community makes choices that benefit and
sustain Axiom I'm cooperating (as a developer) with Fedora.

Further details of this can be found in the Fedora mailing lists.

ACM ISSAC Proceedings

The Association for Computing Machinery sponsers a Journal, called
SIGSAM and a conference called ISSAC. I am working with Emil Volcheck
of ACM to create an electronic journal and an electronic proceedings
for ISSAC 2004.

Further details of this work will be available in June at ISSAC.