|Subject:||Re: [Axiom-developer] Design Thoughts on Semantic Latex (SELATEX)|
|Date:||Thu, 25 Aug 2016 21:59:10 +0000|
Thanks for taking the time to address my ignorant questions.
You wrote: "For instance, are your formulas given over the real or complex domain?"
This question is of course relevant in computation. Even in Axiom, which allows domains (belonging to a specific Axiom category) as parameters in function or package calls, the compiler needs to know the exact domain at compile time (and with some more effort,
delay this knowledge to run time). Your example with \AT for matrix multiplication MN illustrates that.
However, mathematics is different. We do NOT have to name any specific domain. We can say, the algorithm works for any field k. How do you turn that into computer code without making a choice for k? Or, we can say the algorithm works for any matrix in GL(n,
k), for any positive integer n over any field k.
Your answer to the question on overloading is of course the "middle way", but the problem above (unspecified domains in a category, or element in a domain) could cascade and so there has to be a non-specific translation (or way to mark-up), perhaps with
a "default" specification in case computation becomes necessary.
Somehow I got (perhaps incorrectly) the impression that your proposed target is weaver(latex paper, axiom paper)---of course, a paper is also a string.
For a limited application (formulas like integrals), such generality is perhaps not needed. For that purpose, I do not believe we need a new semantic mark-up layer---if I follow your progress correctly, you already have a direct [semi-automatic?] translation
program (or a bunch of macros) that inputs the latex source for a formula (or a scanned image with "mathematical OCR" software) and outputs the Axiom code (or better still, an Axiom package that allows [domain] parameters). As you acknowledged, the selatex
test file with weaver(latex string, axiom string) does not yet provide the semantic content (that's the semi-automatic part: choosing default domains). Why do we need to "unweave" an axiom string with semantic mark-up back to latex (with or without semantic)?
Is it to ensure that weave has an inverse? I don't see that to be the case, since we have to make choices for domains to give full computational semantics but don't for in the latex string, even including full mathematical semantics. I think weave is one to
many in general, but unweave can be one to one and thus possibly loses the generality of input latex string given to the weave routine.
Department of Mathematics
The City College of The City University of New York
New York, NY 10031
From: Tim Daly <address@hidden>
Sent: Thursday, August 25, 2016 2:50 PM
To: William Sit
Cc: Dan Zwillinger; Richard Fateman; James Davenport; address@hidden; Mike Dewar; axiom-dev; address@hidden
Subject: Re: [Axiom-developer] Design Thoughts on Semantic Latex (SELATEX)
William,It is unlikely that authors will provide a special chunk for Axiom in papers.
are quite interesting (see http://mathpix.com). Unfortunately, there isn't
enough information in the latex. For instance, are your formulas given
over the real or complex domain?
In the longer term I am campaigning to bend these tomes toward a
more computational mathematics basis. Instead of listing the names of
20 invariant graph algorithms we really need reference versions of the
algorithms. And we need them in machine-readable form. And we need
them now so a whole generation of computational mathematicians do
not write yet-another-CAS from scratch.
On Thu, Aug 25, 2016 at 9:13 AM, William Sit <address@hidden> wrote:
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