[Axiom-developer] Re: What is a CAS?

[TimDaly]

On Sep 1, 9:42 am, "David Park" <address@hidden> wrote:
> What is the purpose of a CAS?
> What kind of people use a CAS?
> How does a CAS fit into their activities?
> What is the output product of a CAS?
> What is the output product of a CAS used for?
>
> --
> David Park
> address@hidden://home.comcast.net/~djmpark/ 

As a CAS developer I have a different answer.

Computational mathematics is the intersection of
mathematics and computer science. This is a new
science in that we can create effective algorithms
and reduce them to measurable implementations. My
particular interest (Axiom) lies in the organization
of these algorithms against a categorically defined,
algebraic structure.

What is the purpose of a CAS?

The purpose of a CAS is to host research in
computational mathematics. The CAS serves the
purpose of collecting and communicating these
algorithms to other researchers. Algorithms can
be measured and compared, proven and improved.

What kind of people use a CAS?

I'm afraid I'm an amatuer academic since I don't
have a job that will pay me to develop Axiom. I
do it purely for the fun of advancing a new field
of science. The long term value (Axiom's theme is
"The 30 year horizon") is that the next generation
can build on the platform of the previous.

How does a CAS fit into their activities?

Other than consuming 100% of my free time? :-)

What is the output product of a CAS?

The output product is the CAS itself. To me
this is like asking, "What is the output
product of mathematics?"

What is the output product of a CAS used for?

I view the Axiom CAS system as a long term
repository of knowledge of computational
science. Most of the current Axiom effort is
directed toward deep documentation of the system
so that it can be used for teaching and research.

The collision of mathematics with computers has
created this new science. Unfortunately a lot of
this new science is commercially oriented. This
puts us all back into the early days of mathematics
where someone discovered a formula but would not
reveal it. They could prove it worked ("send me
a problem and I'll return the solution") but no
one else could study or improve it.

Beyond developing the algorithms, Axiom studies
the problem of how to organize the algorithms
into their most general setting.

Tim Daly
Axiom Lead Developer