Re: A(n orthogonal) set of essential operations for CAS

Hatto von Aquitanien wrote:

> Mathematica has several "commands" which manipulate expressions in ways that
> most application development languages (C, C++, Java, etc.) do not directly
> support. For example, Apply[], Map[], Fold[], Position[], Through[],
> Inner[] (supported in C++), etc. It is probably fairly easy to implement
> these using the C++ Standard Library, but C++ is not an ideal language for
> doing the kinds of things Mathematica is used for.

Programming symbolic computation in C++ or Java
would likely result in reinventing some substantial part of Lisp.
I don't recommend it.

The useful features of Lisp, for symbolic computation, are
that code and data are indistinguishable, and symbols are
first-class objects. Another language which has those features
is probably also suitable to write an algebra system.

> I'm interested in finding out if similar operations are supported in other
> languages and CAS programs.

Maybe the Rosetta page is helpful to you:
http://www.univ-orleans.fr/EXT/ASTEX/astex/doc/en/rosetta/htmla/roseta.htm

> Roman Meader discusses a programming style
> distinct from procedural and functional programming which he
> calls /mathematical/ programming. I have not yet read the chapter in
> _Programming in Mathematica_ where he develops the ideas of mathematical
> programming. Glancing over the chapter, I have the impression that this is
> what others will call /rule-based/ programming.

Rule-based seems accurate. In other contexts I've seen similar
concepts called "declarative" or "intensional".

for what it's worth,
Robert Dodier

.

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