[Axiom-math] Re: [Axiom-developer] APL, J, and Axiom documentation

[root]

>> I have been looking at the question of documenting Axiom's algorithms.
>>
>> Beyond the english description I've been pondering the use of J (an
>> ascii version of APL).
>
>I have been studying Sun's Fortress mathematics-oriented programming
>language recently and it seems to be able to encode mathematics
>algorithm pseudocode that looks very close to the pseudocode.  Here is
>a .pdf file I put together that contains slides from a Fortress talk
>which shows this:
>
>http://sage.ssu.portsmouth.oh.us/tmp/fortress_compared_with_algorithm_pseudocode.pdf
>

Interesting. I particularly liked the unicode version. I'm puzzled by
the last slide though. It seems to show that Fortress will handle
2D equations, which would be a complete surprise. The ability to
directly write 2D equation input in a programming language would be
a huge leap forward. Its the late 90s and we should be able to handle
such things but I'm unaware of any language that can.

I had a 2D parser on my desk at IBM. Our Scratchpad group had an
effort to do handwritten input. Maple had one also but I don't know
what the outcome was. I gave a sample at ECCAD in Phila. If you ignore
the handwritten portion of the problem it seems you could create a
parser to handle 2D linear typewritten input. Thus a single program
assignment statement such as:

            b
     a  = ------
             t
            p q

Ideally it would be print/read equivalent to Axiom's Charybdis output.
Ron Avitzur had a really nice, but small, subset of this.
Sounds like a fantastic student project to me.

I've had a small amount of correspondence with Guy Steele about
whether Fortress can support Provisos natively but I've not actually
seen the language up until now.

I'm not sure what ability Fortress will have to handle Axiom-style
types. They aren't required for Fortran and Steele seems to have taken
Fortran as the target replacement language. I'm also not sure if it
can handle the category/domain questions.





>If Fortress was suitable for what you had in mind, my thought is that
>there is a chance that Sun would provide funding for encoding Axiom's
>algorithms in it.

As for funding Axiom from anywhere by anyone... sigh.  The only hope I
see for funding is if

  (a) Axiom is deeply documented,
  (b) Computational Mathematics becomes its own department in many schools,
  (c) Axiom gets picked up as the canonical teaching platform. 

A fully documented Axiom system would teach people how to read, write
and understand computational mathematics as opposed to the current
"trade-school" mentality which teaches how to use Mathematica, Matlab
and Maple. Of course, by the time these conditions occur a fair portion
of the documentation work will have already been done. I doubt that
the NSF or INRIA have any interest in allocating grants for teaching
computational mathematics as a separate discipline. Instead it seems to
be viewed as a stepchild of either the Math or Comp. Sci. departments. 
Curiously, this is exactly where Comp. Sci. was when I went to school. 
There were no Comp. Sci. departments or majors. You learned it from the 
Math (Fortran), Business (COBOL), or Engineering (Fortran) departments.

Maybe in 10 years....

Tim