There has been an effort in the past to extract mathematics from latex. It seems that the usual latex markup does not carry enoughtries to guess and the compiler insists on type specifications. Axiom provides an abbreviation for each type, such as FRAC for Fraction and INT for Integer. Might it be possible to create latex macros that take advantage of this to provide unambiguous markup. For instance, instead of \frac{3x+b}{2x} we might have a latex markup of \FRAC[\INT]{3x+b}{2x} where there was a latex macro for each Axiom type. This would turn into an latex \usepackage{AxiomType} There would be a map from the \FRAC[\INT] form to the \frac form which seems reasonably easy to do in latex. There would be a parser that maps \FRAC[\INT] to the Axiom input syntax. The problem would be to take the NIST Math Handbook sources (is the latex available?) and decorate them with additional markup so they could parse to valid Axiom input and valid latex input (which they already are, but would validate the mapping back to latex). Comments? Tim _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
Indeed, the semantics of LaTeX is pretty weak. I REALLY wouldn't like to start from there - even (good) MathML-P, with ⁢ etc. is much better.
However, LaTeX is what we have, and what we are likely to have in the near future, so we must live with it, and yours seems like as good an accommodation as any. Another problem is that mathematicians do not mean what they write: $\frac{x+1}2$ is logically an element of Z(x), but the mathematician probably intended Q[x]. James Sent from my iPhone > On 10 Aug 2016, at 11:50, "Tim Daly" <[hidden email]> wrote: > > There has been an effort in the past to extract mathematics from > latex. It seems that the usual latex markup does not carry enough > semantic information to disambiguate expressions. > > Axiom has a similar problem occasionally where the interpreter > tries to guess and the compiler insists on type specifications. > > Axiom provides an abbreviation for each type, such as FRAC for > Fraction and INT for Integer. > > Might it be possible to create latex macros that take advantage > of this to provide unambiguous markup. For instance, instead of > > \frac{3x+b}{2x} > > we might have a latex markup of > > \FRAC[\INT]{3x+b}{2x} > > where there was a latex macro for each Axiom type. This would > turn into an latex \usepackage{AxiomType} > > There would be a map from the \FRAC[\INT] form to the \frac > form which seems reasonably easy to do in latex. There would > be a parser that maps \FRAC[\INT] to the Axiom input syntax. > > The problem would be to take the NIST Math Handbook sources > (is the latex available?) and decorate them with additional markup > so they could parse to valid Axiom input and valid latex input > (which they already are, but would validate the mapping back to > latex). > > Comments? > > Tim > _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
On 8/14/2016 11:05 AM, James Davenport wrote:
> Indeed, the semantics of LaTeX is pretty weak. I REALLY wouldn't like to start from there - even (good) MathML-P, with ⁢ etc. is much better. > However, LaTeX is what we have, and what we are likely to have in the near future, so we must live with it, and yours seems like as good an accommodation as any. Face it: Mathematicians do it all the time. They read journal articles with no more information than the position of glyphs on a piece of paper. There are poorly printed papers and reference books in which it is impossible to be sure what the glyphs are (esp. books printed on crude paper in Moscow...) And there are poorly written papers which cannot be read in isolation -- the authors (and reviewers, editors) have so much absorbed the context of their field that they neglect to define their peculiar notation. Nevertheless, that's what the literature looks like. when I was trying to scan Gradshteyn & Rhyzik or similar books, we stumbled over it page by page. I recall finding a place where we figured out what the typeset integration result was by trying out our various semantic opinions and differentiating. Talking with run-of-the-mill professional academic applied mathematicians is sometimes revealing. At one demonstration (in Essen, Germany, a conference on "Retrodigitalization" of mathematics -- {It may sound better in German}, A program of mine read in a page or two from Archiv der Mathematik, and spit it out -- but with a modern font, and in two-columns, other changes too. The mathematicians in the audience were thunderstruck, because they thought that the program must have understood the mathematics to make that kind of transformation. Of course all it did was guess at the appropriate TeX to produce the equivalent spacing, and "knew" nothing of the semantics. Actually, I was amazed by the result when I saw it, but for two reasons. (a) Someone else had actually used my program; (b) There were no errors. [The reason for (b) is that the recognition program had been trained on exactly -- maybe only -- that page -- it was trained so that defective/broken/linked characters were mapped to the right answers]. But the point remains that if we wrote a program that was as smart as (the collection of...) smartest human mathematicians, then TeX would be enough semantics. > > Another problem is that mathematicians do not mean what they write: $\frac{x+1}2$ is logically an element of Z(x), but the mathematician probably intended Q[x]. I think that most people using DLMF.nist.gov would not know or care. It's not their part of mathematics. It is probably unfortunate if Axiom (or Openmath or MathML) cares and consequently requires such users to know. RJF > James > > Sent from my iPhone > >> On 10 Aug 2016, at 11:50, "Tim Daly" <[hidden email]> wrote: >> >> There has been an effort in the past to extract mathematics from >> latex. It seems that the usual latex markup does not carry enough >> semantic information to disambiguate expressions. >> >> Axiom has a similar problem occasionally where the interpreter >> tries to guess and the compiler insists on type specifications. >> >> Axiom provides an abbreviation for each type, such as FRAC for >> Fraction and INT for Integer. >> >> Might it be possible to create latex macros that take advantage >> of this to provide unambiguous markup. For instance, instead of >> >> \frac{3x+b}{2x} >> >> we might have a latex markup of >> >> \FRAC[\INT]{3x+b}{2x} >> >> where there was a latex macro for each Axiom type. This would >> turn into an latex \usepackage{AxiomType} >> >> There would be a map from the \FRAC[\INT] form to the \frac >> form which seems reasonably easy to do in latex. There would >> be a parser that maps \FRAC[\INT] to the Axiom input syntax. >> >> The problem would be to take the NIST Math Handbook sources >> (is the latex available?) and decorate them with additional markup >> so they could parse to valid Axiom input and valid latex input >> (which they already are, but would validate the mapping back to >> latex). >> >> Comments? >> >> Tim >> _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
>>Another problem is that mathematicians do not mean what they write: >> $\frac{x+1}2$ is logically an element of Z(x), but the mathematician
probably intended Q[x].
>I think that most people using DLMF.nist.gov would not know or care. > It's not their part of mathematics formula valid over R and one valid over C (based on a simplification). On Sun, Aug 14, 2016 at 7:05 PM, Richard Fateman <[hidden email]> wrote: On 8/14/2016 11:05 AM, James Davenport wrote: _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer |
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