It is possible to define a a program that will take a single language
and produce from it either TeX, Lisp, Sage, Mathematica, Maple,
Maxima, MathML, etc.
That does not solve the problem of taking some random TeX formula, not
using that language of macros etc, and converting it into a CAS
formula.
The newer version of Gradshteyn has, as its base, all of the formulas
in such a language, and there is a translator into some CAS. I think
the translator is written in TeX.
This was done by hand, and using it makes it rather simple to produce
(sort of) code in any CAS. See the paper for why I say "sort of".
I don't have the code for Caspi's project; I've asked him to post it
though.
As for whether more recent work has surpassed it... I think that a
program that works in 1997 might still work just fine. And the design
is probably OK too. Reminds me of the quip..
"Algol 60 was not only an improvement on its predecessors, but also
on nearly all its successors.
-- C. A. R. Hoare"
Now if you want to switch back and forth, starting with the CAS, then
it is quite easy. You embed the CAS code into the TeX so that
translating back is simply extracting a comment.
e.g.
\int_a^bf(x)dx % maxima% integrate(f(x),x,a,b)
RJF
On May 14, 9:23 am, daly <d...@axiom-developer.org> wrote:
> Since TeX is turing complete and allows macros,
> would it be possible to create a set of macros
> that are not ambiguous? For instance, an integral
> macro that specifies the limits and differential
> variable?
>
> \integrate{0}{\infty}{r}{sin(\theta)}
>
> In this case it seems to me that the latex macros
> would closely approximate the actual linear input
> to the CAS.
>
> Tim Daly
>
>
>
>
>
>
>
> On Sat, 2011-05-14 at 08:25 -0700, rjf wrote:
> > Look at
> >http://moralfiber.org/eylon/berkeley/cs282/
> > to see a paper,
> > Parsing Mathematics Typeset in TeX
> > that successfully parsed many many formulas
> > from Gradshteyn and Rhyzik, a table of integrals.
>
> > The result was Lisp, which presumably could be Maxima.
> > If you have a result in Maxima, presumably Sage can make sense of it.
>
> > Or the same design can directly produce whatever Sage-speak you had in
> > mind.
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