These functions are represented as LaTeX, because that's the gold standard for rendering math. But, they also want them available as XML so they're in a more sensible format for archiving.
So, funnily, as part of this, NIST maintain a LaTeX to XML converter.[0] It's a pretty complete LaTeX runtime. (Yes, runtime -- TeX is a programming language, not a markup language!)
This is the thing that powers arXiv Vanity[1] and other academic publishing projects.
I just find it quite amusing that the US Government maintains a LaTeX runtime written in Perl.
Depends what the authors upload. You can just upload a PDF. But if arXiv detects that the PDF came out of pdflatex it will pretty instantly nag you to give it the TeX sources. It will then render the PDF itself and also offer the sources for download. That is also how astro-ph-leaks [1] works.
> The Mathematical Functions Grimoire (Fungrim) is an open source library of formulas and data for special functions. Fungrim currently consists of 456 symbols (named mathematical objects), 3130 entries (definitions, formulas, tables, plots), and 82 topics (listings of entries).
This is great, but I wish there were a broader library that went beyond special functions.
For example, last year I was doing some statistical modelling and ended up with a complicated integral that yielded to analysis much more easily than I expected. I wanted to see if the resulting formula had a name or had been studied by anyone, but it's really hard to search for something like that. Anyone who did that analysis previously might have used different variable names or different conventions to represent the same underlying idea, factored it differently, etc.
Will the intersection of deep learning and differential geometry obviate the need for Euclidean representations altogether? It would be amazing if these functions became almost like fossils. Historical curiosities of a bygone civilization ;)
Tensors. Triangle meshes in rendering. All the comfortable human abstractions we come to rely on. But which can be inefficient in high dimensional real world data
It reminds me of Rubi [0], a rule-based symbolic integration system. Unlike many CASs that use a variant of the Risch algorithm, Rubi simply solves the integrals by using a large number (6700+) of rules in its database. Benchmarks (72000+ test cases) show that it's able to get better and cleaner antiderivatives than Mathematica and Maple. All the rules [1] are both human and machine-readable.
The engine can be installed in Mathematica, SymPy and SymJa.
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[ 4.1 ms ] story [ 45.9 ms ] threadSo, funnily, as part of this, NIST maintain a LaTeX to XML converter.[0] It's a pretty complete LaTeX runtime. (Yes, runtime -- TeX is a programming language, not a markup language!)
This is the thing that powers arXiv Vanity[1] and other academic publishing projects.
I just find it quite amusing that the US Government maintains a LaTeX runtime written in Perl.
[0] https://dlmf.nist.gov/LaTeXML/
[1] https://www.arxiv-vanity.com/
There are ways of exporting MathML within that schema, I think.
Never heard of this. Does it have access to the LaTeX source of the arXiv paper? I didn't know arXiv hosted sources.
[1] https://twitter.com/LeaksPh
> The Mathematical Functions Grimoire (Fungrim) is an open source library of formulas and data for special functions. Fungrim currently consists of 456 symbols (named mathematical objects), 3130 entries (definitions, formulas, tables, plots), and 82 topics (listings of entries).
"FunGrim: a symbolic library for special functions" https://arxiv.org/abs/2003.06181
For example, last year I was doing some statistical modelling and ended up with a complicated integral that yielded to analysis much more easily than I expected. I wanted to see if the resulting formula had a name or had been studied by anyone, but it's really hard to search for something like that. Anyone who did that analysis previously might have used different variable names or different conventions to represent the same underlying idea, factored it differently, etc.
Differential geometry for deep learning
https://metacademy.org/roadmaps/rgrosse/dgml
https://dawn.cs.stanford.edu/2019/10/10/noneuclidean/
Or on Math Stackexchange: https://math.stackexchange.com/
The engine can be installed in Mathematica, SymPy and SymJa.
[0] https://rulebasedintegration.org/
[1] https://rulebasedintegration.org/integrationRules.html