[Axiom-developer] Axiom mathematical algorithms... Notation matters

[daly]

I've been thinking about the best method of presenting mathematical
algorithms. There is a gap between equations that represent the
mathematics and the actual code that represents the algorithm.

The actual code has loops and does low-level data manipulation
that has been optimized away from the formula definition. This
is especially true of numerics, where I've been doing a lot of
recent work.

The form of presentation in this paper seems to be the perfect
combination of formula and algorithm. See, for example, p14:
http://slicot.org/objects/software/reports/SLWN2014_1.pdf

It would be ideal if this was the Axiom algebra language (Spad2?).
Constructing a parser/compiler for such input is easily a PhD thesis.
It would represent a major step forward in computational mathematics.

That said, I think we should adopt this style for documentation.

Tim