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The referenced paper only looked at the DLMF Airy functions. The results
are:
"Of the 17 sections in the DLMF sample chapter on Airy functions we can
handle the mathematical
formulas completely in 6, partially in 5 (without the transformation to
MathML), and 6 remain
incomplete.
The grammar currently contains approximately 1000 productions, of which ca.
350 are dictionaries.
There are about 550 rewrite rules. There are fewer rewrite rules than
grammar rules, partly because
dictionaries can be treated uniformly by manipulating literals, and partly
because it is still incomplete
with respect to the grammar.
Our project shows that parsing mathematics in the form of LATEX documents
written to project-specific
rules is feasible, but due to the variations in notation the grammar needs
to be engineered specifically
for the project, or even for different chapters written by different
mathematicians (e.g. the chapter on
elementary transcendental functions and on Airy functions)."
Many have tried to parse DLMF but there is not sufficient information in
the latex. This
effort used many rules to try to decide if w(x+y) is a multiplication or a
function application.
There are rules to decide if sin a/b means (sin a)/b or sin(a/b), either of
which is trivial to
distinguish if the latex read {sin a}/b or sin{a/b}
Trivial amounts of semantic markup in the DLMF would communicate semantics
without using
1000 productions which still get wrong answers.
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