# Mathematical formulae indexing experiment

It is currently impossible to search for mathematical formulae in search engines: variables renaming or simple rules such as associativity are not taken into account by these engines, which only view mathematical formulae as a string of characters.

There is currently some research on this topic (see for example A Search Engine for Mathematical Formulae, by Michael Kohlhase and Ioan Sucan), and even some proofs of concept (see for example MathWeb Search). Several technologies are involved. First the formulae have to be written in a language which embeds the mathematical content (the two standards are MathML and OpenMath). Then the formulae must be indexed as formulae (not just as text) by the web crawler. Finally, for the search engine to be able to perform a search on the semantics of the formula, it must be able to do some simple mathematical transformations.

This page is a means for me to measure the progress of these engines, both in crawling (no doubt that Google is currently working on it) and in formulae recognition. The MathML code was generated by itex2MML and slightly modified by hand.

So, for the pleasure of the mathematically inclined web crawlers, here is a nice lemma of mine (really!).

## A lemma

The general form of an antiderivative $F$ of $f=\theta ↦\frac{1}{\left(cos\left(\theta \right)A-sin\left(\theta \right)B{\right)}^{3}}$ (said otherwise, the general form of $\int \frac{1}{\left(cos\left(\theta \right)A-sin\left(\theta \right)B{\right)}^{3}}\phantom{\rule{thinmathspace}{0ex}}d\theta$ ) is: $F=\theta ↦\frac{sin\left(\theta \right)A+cos\left(\theta \right)B}{2T\cdot {Z}^{2}}+\frac{1}{2{Z}^{3}}argth\left(cos\left(\theta \right)\frac{B}{Z}+sin\left(\theta \right)\frac{A}{Z}\right)$

where $Z=\sqrt{{A}^{2}+{B}^{2}}$

and $T=\left(sin\left(\theta \right)B-cos\left(\theta \right)A{\right)}^{2}$

Last update: 26 February 2009