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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