380 lines
12 KiB
Markdown
380 lines
12 KiB
Markdown
# Customization
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Besides parsing and evaluating expressions, the expression parser supports
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a number of features to customize processing and evaluation of expressions
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and outputting expressions.
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On this page:
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- [Function transforms](#function-transforms)
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- [Custom argument parsing](#custom-argument-parsing)
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- [Custom LaTeX handlers](#custom-latex-handlers)
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- [Custom HTML, LaTeX and string output](#custom-html-latex-and-string-output)
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- [Customize supported characters](#customize-supported-characters)
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## Function transforms
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It is possible to preprocess function arguments and post process a functions
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return value by writing a *transform* for the function. A transform is a
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function wrapping around a function to be transformed or completely replaces
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a function.
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For example, the functions for math.js use zero-based matrix indices (as is
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common in programing languages), but the expression parser uses one-based
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indices. To enable this, all functions dealing with indices have a transform,
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which changes input from one-based to zero-based, and transforms output (and
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error message) from zero-based to one-based.
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```js
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// using plain JavaScript, indices are zero-based:
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const a = [[1, 2], [3, 4]] // a 2x2 matrix
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math.subset(a, math.index(0, 1)) // returns 2
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// using the expression parser, indices are transformed to one-based:
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const a = [[1, 2], [3, 4]] // a 2x2 matrix
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let scope = {
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a: a
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}
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math.evaluate('subset(a, index(1, 2))', scope) // returns 2
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```
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To create a transform for a function, the transform function must be attached
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to the function as property `transform`:
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```js
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import { create, all } from 'mathjs'
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const math = create(all)
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// create a function
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function addIt(a, b) {
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return a + b
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}
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// attach a transform function to the function addIt
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addIt.transform = function (a, b) {
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console.log('input: a=' + a + ', b=' + b)
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// we can manipulate input here before executing addIt
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const res = addIt(a, b)
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console.log('result: ' + res)
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// we can manipulate result here before returning
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return res
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}
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// import the function into math.js
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math.import({
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addIt: addIt
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})
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// use the function via the expression parser
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console.log('Using expression parser:')
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console.log('2+4=' + math.evaluate('addIt(2, 4)'))
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// This will output:
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//
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// input: a=2, b=4
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// result: 6
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// 2+4=6
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// when used via plain JavaScript, the transform is not invoked
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console.log('')
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console.log('Using plain JavaScript:')
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console.log('2+4=' + math.addIt(2, 4))
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// This will output:
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//
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// 6
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```
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Functions with a transform must be imported in the `math` namespace, as they
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need to be processed at compile time. They are not supported when passed via a
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scope at evaluation time.
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## Custom argument parsing
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The expression parser of math.js has support for letting functions
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parse and evaluate arguments themselves, instead of calling them with
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evaluated arguments. This is useful for example when creating a function
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like `plot(f(x), x)` or `integrate(f(x), x, start, end)`, where some of the
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arguments need to be processed in a special way. In these cases, the expression
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`f(x)` will be evaluated repeatedly by the function, and `x` is not evaluated
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but used to specify the variable looping over the function `f(x)`.
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Functions having a property `rawArgs` with value `true` are treated in a special
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way by the expression parser: they will be invoked with unevaluated arguments,
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allowing the function to process the arguments in a customized way. Raw
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functions are called as:
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```
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rawFunction(args: Node[], math: Object, scope: Object)
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```
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Where :
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- `args` is an Array with nodes of the parsed arguments.
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- `math` is the math namespace against which the expression was compiled.
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- `scope` is a shallow _copy_ of the `scope` object provided when evaluating
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the expression, optionally extended with nested variables like a function
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parameter `x` of in a custom defined function like `f(x) = x^2`.
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Raw functions must be imported in the `math` namespace, as they need to be
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processed at compile time. They are not supported when passed via a scope
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at evaluation time.
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A simple example:
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```js
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function myFunction(args, math, scope) {
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// get string representation of the arguments
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const str = args.map(function (arg) {
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return arg.toString()
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})
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// evaluate the arguments
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const res = args.map(function (arg) {
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return arg.compile().evaluate(scope)
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})
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return 'arguments: ' + str.join(',') + ', evaluated: ' + res.join(',')
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}
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// mark the function as "rawArgs", so it will be called with unevaluated arguments
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myFunction.rawArgs = true
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// import the new function in the math namespace
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math.import({
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myFunction: myFunction
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})
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// use the function
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math.evaluate('myFunction(2 + 3, sqrt(4))')
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// returns 'arguments: 2 + 3, sqrt(4), evaluated: 5, 2'
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```
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## Custom LaTeX handlers
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You can attach a `toTex` property to your custom functions before importing them to define their LaTeX output. This
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`toTex` property can be a handler in the format described in the next section 'Custom LaTeX and String conversion'
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or a template string similar to ES6 templates.
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### Template syntax
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- `${name}`: Gets replaced by the name of the function
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- `${args}`: Gets replaced by a comma separated list of the arguments of the function.
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- `${args[0]}`: Gets replaced by the first argument of a function
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- `$$`: Gets replaced by `$`
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#### Example
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```js
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const customFunctions = {
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plus: function (a, b) {
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return a + b
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},
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minus: function (a, b) {
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return a - b
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},
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binom: function (n, k) {
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return 1
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}
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}
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customFunctions.plus.toTex = '${args[0]}+${args[1]}' //template string
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customFunctions.binom.toTex = '\\mathrm{${name}}\\left(${args}\\right)' //template string
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customFunctions.minus.toTex = function (node, options) { //handler function
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return node.args[0].toTex(options) + node.name + node.args[1].toTex(options)
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}
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math.import(customFunctions)
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math.parse('plus(1,2)').toTex() // '1+2'
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math.parse('binom(1,2)').toTex() // '\\mathrm{binom}\\left(1,2\\right)'
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math.parse('minus(1,2)').toTex() // '1minus2'
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```
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## Custom HTML, LaTeX and string output
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All expression nodes have a method `toTex` and `toString` to output an expression respectively in HTML or LaTex format or as regular text .
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The functions `toHTML`, `toTex` and `toString` accept an `options` argument to customise output. This object is of the following form:
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```js
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{
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parenthesis: 'keep', // parenthesis option
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handler: someHandler, // handler to change the output
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implicit: 'hide' // how to treat implicit multiplication
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}
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```
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### Parenthesis
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The `parenthesis` option changes the way parentheses are used in the output. There are three options available:
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- `keep` Keep the parentheses from the input and display them as is. This is the default.
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- `auto` Only display parentheses that are necessary. Mathjs tries to get rid of as much parentheses as possible.
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- `all` Display all parentheses that are given by the structure of the node tree. This makes the output precedence unambiguous.
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There's two ways of passing callbacks:
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1. Pass an object that maps function names to callbacks. Those callbacks will be used for FunctionNodes with
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functions of that name.
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2. Pass a function to `toTex`. This function will then be used for every node.
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```js
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const expression = math.parse('(1+1+1)')
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expression.toString() // (1 + 1 + 1)
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expression.toString({parenthesis: 'keep'}) // (1 + 1 + 1)
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expression.toString({parenthesis: 'auto'}) // 1 + 1 + 1
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expression.toString({parenthesis: 'all'}) // (1 + 1) + 1
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```
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### Handler
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You can provide the `toTex` and `toString` functions of an expression with your own custom handlers that override the internal behaviour. This is especially useful to provide LaTeX/string output for your own custom functions. This can be done in two ways:
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1. Pass an object that maps function names to callbacks. Those callbacks will be used for FunctionNodes that contain functions with that name.
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2. Pass a callback directly. This callback will run for every node, so you can replace the output of anything you like.
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A callback function has the following form:
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```js
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function callback (node, options) {
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...
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}
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```
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Where `options` is the object passed to `toHTML`/`toTex`/`toString`. Don't forget to pass this on to the child nodes, and `node` is a reference to the current node.
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If a callback returns nothing, the standard output will be used. If your callback returns a string, this string will be used.
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**Although the following examples use `toTex`, it works for `toString` and `toHTML` in the same way**
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#### Examples for option 1
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```js
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const customFunctions = {
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binomial: function (n, k) {
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//calculate n choose k
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// (do some stuff)
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return result
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}
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}
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const customLaTeX = {
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'binomial': function (node, options) { //provide toTex for your own custom function
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return '\\binom{' + node.args[0].toTex(options) + '}{' + node.args[1].toTex(options) + '}'
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},
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'factorial': function (node, options) { //override toTex for builtin functions
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return 'factorial\\left(' + node.args[0] + '\\right)'
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}
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}
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```
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You can simply use your custom toTex functions by passing them to `toTex`:
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```js
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math.import(customFunctions)
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const expression = math.parse('binomial(factorial(2),1)')
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const latex = expression.toTex({handler: customLaTeX})
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// latex now contains "\binom{factorial\\left(2\\right)}{1}"
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```
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#### Examples for option 2:
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```js
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function customLaTeX(node, options) {
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if ((node.type === 'OperatorNode') && (node.fn === 'add')) {
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//don't forget to pass the options to the toTex functions
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return node.args[0].toTex(options) + ' plus ' + node.args[1].toTex(options)
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}
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else if (node.type === 'ConstantNode') {
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if (node.value === 0) {
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return '\\mbox{zero}'
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}
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else if (node.value === 1) {
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return '\\mbox{one}'
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}
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else if (node.value === 2) {
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return '\\mbox{two}'
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}
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else {
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return node.value
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}
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}
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}
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const expression = math.parse('1+2')
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const latex = expression.toTex({handler: customLaTeX})
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// latex now contains '\mbox{one} plus \mbox{two}'
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```
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Another example in conjunction with custom functions:
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```js
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const customFunctions = {
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binomial: function (n, k) {
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//calculate n choose k
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// (do some stuff)
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return result
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}
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}
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function customLaTeX(node, options) {
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if ((node.type === 'FunctionNode') && (node.name === 'binomial')) {
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return '\\binom{' + node.args[0].toTex(options) + '}{' + node.args[1].toTex(options) + '}'
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}
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}
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math.import(customFunctions)
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const expression = math.parse('binomial(2,1)')
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const latex = expression.toTex({handler: customLaTeX})
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// latex now contains "\binom{2}{1}"
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```
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### Implicit multiplication
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You can change the way that implicit multiplication is converted to a string or LaTeX. The two options are `hide`, to not show a multiplication operator for implicit multiplication and `show` to show it.
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Example:
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```js
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const node = math.parse('2a')
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node.toString() // '2 a'
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node.toString({implicit: 'hide'}) // '2 a'
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node.toString({implicit: 'show'}) // '2 * a'
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node.toTex() // '2~ a'
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node.toTex({implicit: 'hide'}) // '2~ a'
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node.toTex({implicit: 'show'}) // '2\\cdot a'
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```
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## Customize supported characters
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It is possible to customize the characters allowed in symbols and digits.
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The `parse` function exposes the following test functions:
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- `math.parse.isAlpha(c, cPrev, cNext)`
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- `math.parse.isWhitespace(c, nestingLevel)`
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- `math.parse.isDecimalMark(c, cNext)`
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- `math.parse.isDigitDot(c)`
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- `math.parse.isDigit(c)`
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The exact signature and implementation of these functions can be looked up in
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the [source code of the parser](https://github.com/josdejong/mathjs/blob/master/lib/expression/parse.js). The allowed alpha characters are described here: [Constants and variables](syntax.md#constants-and-variables).
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For example, the phone character <code>☎</code> is not supported by default. It can be enabled
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by replacing the `isAlpha` function:
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```js
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const isAlphaOriginal = math.parse.isAlpha
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math.parse.isAlpha = function (c, cPrev, cNext) {
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return isAlphaOriginal(c, cPrev, cNext) || (c === '\u260E')
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}
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// now we can use the \u260E (phone) character in expressions
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const result = math.evaluate('\u260Efoo', {'\u260Efoo': 42}) // returns 42
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console.log(result)
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```
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