[Axiom-mail] Abstract Vector Algebra

[Gabriel Dos Reis]

On Fri, Apr 5, 2013 at 11:44 PM, u1204 <address@hidden> wrote:
>>This is probably not very practical, but I was just trying to do a
>>thought experiment to investigate what would be required to have
>>variables that range over domains that are not numbers.
>
> Actually, I wrote an NSF proposal to introduce "indeterminate integers".

I did something like this in 2009 -- some of it made it to released OpenAxiom.

> This would be a first example of a special symbolic domain that would
> create "arbitrary integers" rather than actual integers.
>
> This is my approach to the Maple "assume" facility. I want to say that
> the uderlying domain is an "indeterminate integer" rather than
> "assume x is an integer". This idea seems more in-line with Axiom's
> approach to computational mathematics.

OpenAxiom's syntax is " assume x : T" where T can be any domain.


>
> I'm working on creating a sort-of "indeterminate matrix" domain based
> on a prior question on this list so you can perform operations like
>
>    (A B)^T => B^T A^T
>
> where A and B are "indeterminate matrices".
>
> I will note that the NSF will not fund open source projects.
> Science can only occur if you are at a University. Sigh.

I don't know why you are saying that, NSF certainly has been
funding many open source projects, as long as they enable or
they are part of fundamental research.  Check out the projects
that made it through this program:

   http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=504817

-- Gaby