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## [Axiom-developer] Re: [Axiom-math] musings on notation

 From: Martin Rubey Subject: [Axiom-developer] Re: [Axiom-math] musings on notation Date: Tue, 10 Aug 2004 21:42:11 +0000

```root writes:
...

> However, I've been scratching at a more general idea that could be
> explored in Axiom. Axiom adds some ideas new, novel, and unique in
> mathematics which we have not recognized notationally. For example,
> the idea of "process", the idea of "functors", or "provisos".
>
> We have been limiting the idea of "process" to represent traditional
> mathematical functions. We tend to adopt the notation f(x)=
>
> However, one of the ideas we're pondering (indefinites) seems to me
> to need a new notation. It is clear that one way to think about an
> indefinite integer, for example, is as a loop. So, as Fateman pointed
> out, we might want to raise a matrix M to an indefinite power N. This
> could be expressed as
>   (let (X=I) for i in 1..N do X=X*M)
>
> This is a procedural, semi-function, way of thinking about the solution.
> We do not yet have a decent notation for a process. Such a notation
> would be as valuable as the leap from summation to integration. It would
> allow the "30 year horizon computational mathematician" to write process
> objects, compute functions over processes as well as processes over
> functions (which we now do).
...

Hm, what's wrong with the current notation "f(x)=" ? Axiom does allow you to
define, for example

^(x, n)==reduce(*, [x for i in 1..n])

and use it as you would use any other function:

matrix([[0,1],[1,0]]) ^ 2.

What could be more decent?

Yes, "Indefinite Integers" are missing, but we do have good notation (and
representation for "procedural" functions)

Do I miss something?

Martin

```