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NIST Digital Library of Mathematical Functions

101 点作者 maxwelljoslyn超过 4 年前

4 条评论

bfirsh超过 4 年前
These functions are represented as LaTeX, because that&#x27;s the gold standard for rendering math. But, they also want them available as XML so they&#x27;re in a more sensible format for archiving.<p>So, funnily, as part of this, NIST maintain a LaTeX to XML converter.[0] It&#x27;s a pretty complete LaTeX runtime. (Yes, runtime -- TeX is a programming language, not a markup language!)<p>This is the thing that powers arXiv Vanity[1] and other academic publishing projects.<p>I just find it quite amusing that the US Government maintains a LaTeX runtime written in Perl.<p>[0] <a href="https:&#x2F;&#x2F;dlmf.nist.gov&#x2F;LaTeXML&#x2F;" rel="nofollow">https:&#x2F;&#x2F;dlmf.nist.gov&#x2F;LaTeXML&#x2F;</a><p>[1] <a href="https:&#x2F;&#x2F;www.arxiv-vanity.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.arxiv-vanity.com&#x2F;</a>
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segfaultbuserr超过 4 年前
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&#x27;s able to get better and cleaner antiderivatives than Mathematica and Maple. All the rules [1] are both human and machine-readable.<p>The engine can be installed in Mathematica, SymPy and SymJa.<p>[0] <a href="https:&#x2F;&#x2F;rulebasedintegration.org&#x2F;" rel="nofollow">https:&#x2F;&#x2F;rulebasedintegration.org&#x2F;</a><p>[1] <a href="https:&#x2F;&#x2F;rulebasedintegration.org&#x2F;integrationRules.html" rel="nofollow">https:&#x2F;&#x2F;rulebasedintegration.org&#x2F;integrationRules.html</a>
carapace超过 4 年前
See also FunGrim: <a href="https:&#x2F;&#x2F;fungrim.org&#x2F;" rel="nofollow">https:&#x2F;&#x2F;fungrim.org&#x2F;</a><p>&gt; 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).<p>&quot;FunGrim: a symbolic library for special functions&quot; <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;2003.06181" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;2003.06181</a>
jbay808超过 4 年前
This is great, but I wish there were a broader library that went beyond special functions.<p>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&#x27;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.
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