TeX Math Parser

TeX Math Parser parses TeX math into a MathJS expression tree which can then be further manipulated and evaluated by MathJS. The library also provides convenience functions for directly evaluating TeX math with MathJS.

This library works well as a bridge between MathQuill and MathJS. Use this library to parse the TeX formatted output from MathQuill into a format that can be manipulated by MathJS.

TeX Features

• Common operators available in TeX math mode: +, -, *, ^, /, \cdot, || (absolute value), \times (cross product)
• Basic functions: \sqrt, \frac, \sin, \cos, \tan, \csc, \sec, \cot, \arcsin, \arccos, \arctan, \log, \ln, \det
• Custom functions implemented with MathJS: eigenvectors, eigenvalues, cross, proj, comp, norm, inv
  • Since these are custom functions, they should be formatted as \operatorname{function} in TeX.
• Constants: \pi, e
• Environments: matrix
• Variables
  • ^T is interpreted as the transpose operation

Browser Support

Any browser with ES6 support.

Installation

Install with NPM:

npm install tex-math-parser 

or link to it from a CDN:

<script src=https://cdn.jsdelivr.net/npm/tex-math-parser></script>

Usage

Given the following TeX source string:

\begin{bmatrix}1&3\\2&4\end{bmatrix}\begin{bmatrix}-5\\-6\end{bmatrix}+\left|\sqrt{7}-\sqrt{8}\right|^{\frac{9}{10}}\begin{bmatrix}\cos\left(\frac{\pi}{6}\right)\\\sin\left(\frac{\pi}{6}\right)\end{bmatrix}

Load the package and escape the string:

import { parseTex, evaluateTex } from 'tex-math-parser' // ES6 module

// Make sure to escape the string!
const escapedTex = String.raw`\begin{bmatrix}1&3\\2&4\end{bmatrix}\begin{bmatrix}-5\\-6\end{bmatrix}+\left|\sqrt{7}-\sqrt{8}\right|^{\frac{9}{10}}\begin{bmatrix}\cos\left(\frac{\pi}{6}\right)\\\sin\left(\frac{\pi}{6}\right)\end{bmatrix}`; // ES6 raw template string

Evaluate the string and get an answer in TeX:

const texAnswer = evaluateTex(escapedTex); 
console.log(texAnswer); 
// \begin{bmatrix}-22.812481734548864\\-33.89173627896382\\\end{bmatrix}

Parse the string and get a a MathJS expression tree:

const mathJSTree = parseTex(escapedTex);

Variables

If the TeX string contains variables, the value of the variables must be supplied when evaluating.

const texStr = String.raw`\frac{x}{4}+\frac{y}{2}`;
const answer = evaluateTex(texStr, {x: 2, y: 1});
console.log(answer); // 1

API

evaluateTex(texStr: string, scope?: Object)

Evaluate a TeX string, replacing any variable occurences with their values in scope. The answer is returned as a TeX string.

parseTex(texStr: string)

Convert a TeX string into a MathJS expression tree. The function returns the root node of the tree.

Contributing

Please feel free to make a PR and add any features, add unit tests, or refactor any of the code. Both tokenizeTex and the Parser are quite messy and could really use a clean-up (maybe someday I'll get around to it...).

Run npm test to run some unit tests and make sure they're passing!

Adding support for new TeX functions is relatively simple (see this commit for an example)

TODO: include better documentation on how to do this

Details

parseTex first lexes the TeX string into tokens, which are then passed to the parser to create the expression tree. A context-free grammar for the simplified version of TeX math used by the parser is as follows:

expr = term ((PLUS | MINUS) term)*

term = factor ((CDOT factor | primary )* // primary and factor must both not be NUMBERs

factor = MINUS? power

power = primary (CARET primary)*

primary = grouping
        | environnment
        | frac
        | function
        | NUMBER
        | VARIABLE

grouping = LEFT LPAREN expr RIGHT RPAREN
         | LPAREN expr RPAREN
         | LBRACE expr RBRACE
         | LEFT BAR expr RIGHT BAR
         | BAR expr BAR

environnment = matrix

frac = FRAC LBRACE expr RBRACE LBRACE expr RBRACE

function = (SQRT | SIN | COS | TAN ...) grouping

matrix = BEGIN LBRACE MATRIX RBRACE ((expr)(AMP | DBLBACKSLASH))* END LBRACE MATRIX RBRACE

As the grammar is not left-recursive, the parser was implemented as a recursive descent parser with each production being represented by a separate function. This keeps the parser easily extensible.