A TeX math parser that can evaluate TeX math and convert it into a MathJS expression tree.
npm install tex-math-parserTeX 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.
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
Any browser with ES6 support.
Install with NPM:
``
npm install tex-math-parser
or link to it from a CDN:
`html`
Given the following TeX source string:
!Example TeX
`latex`
\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:
`javascript
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:
`javascript`
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:
`javascript`
const mathJSTree = parseTex(escapedTex);
`javascript\frac{x}{4}+\frac{y}{2}
const texStr = String.raw;`
const answer = evaluateTex(texStr, {x: 2, y: 1});
console.log(answer); // 1
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.
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 pnpm 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
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.