Compute Engine

A JavaScript library for symbolic computing and numeric evaluation of mathematical expressions.

Note

To use Compute Engine, you must write JavaScript or TypeScript code. This guide assumes you’re familiar with these languages.

console.log("exp(i*pi) =", ce.parse("e^{i\\pi}").evaluate());

const expr = ce.parse("(a+b)^2"); ce.box(["Expand", expr]).evaluate().print();

const lhs = ce.parse("1 + x(1 + 2x) + 2x"); const rhs = ce.parse("2x^2 + 3x + 1"); console.log(lhs, lhs.isEqual(rhs) ? "=" : "≠", rhs);

The Compute Engine is for educators, students, scientists, and engineers who need to run technical computing apps in browsers or server-side JavaScript environments like Node.js.

The Compute Engine manipulates math expressions represented with the MathJSON format.

The expression \(x^2 + 2x + 1\) is represented in MathJSON as:

["Add", ["Power", "x", 2], ["Multiply", 2, "x"], 1]

The Compute Engine can:

• parse and serialize expressions from and to LaTeX.
• simplify symbolic expressions
• evaluate expression symbolically or numerically
• solve equations, calculate derivatives and integrals, and perform other calculus operations
• compile expressions to JavaScript

Try the interactive demo now

Getting Started

The easiest way to get started is to load the Compute Engine JavaScript module from a CDN, then create a ComputeEngine instance.

Using JavaScript Modules

To load the Compute Engine module from the jsdelivr CDN, use a <script> tag with the type="module" attribute and an import statement.

<script type="module">
  import { ComputeEngine } from "https://esm.run/@cortex-js/compute-engine";

  const ce = new ComputeEngine();
  ce.parse("e^{i\\pi}").evaluate().print();
  // ➔ "-1"
</script>

Alternatively, you can use the unpkg CDN to load the module:

import { ComputeEngine } from 
  "https://unpkg.com/@cortex-js/compute-engine?module";

The ESM (module) version is also available in the npm package as /compute-engine.min.esm.js

Using Vintage JavaScript

If you are using a vintage environment, or if your toolchain does not support modern JavaScript features, use the UMD version.

For example, WebPack 4 does not support the optional chaining operator, using the UMD version will make use of polyfills as necessary.

To load the UMD version, use a <script> tag with the src attribute.

<script 
  src="https://cdn.jsdelivr.net/npm/@cortex-js/compute-engine/compute-engine.min.js">
</script>
<script>
  window.onload = function() {
    const ce = new ComputeEngine.ComputeEngine();
    console.log(ce.parse("e^{i\\pi}").evaluate());
    // ➔ "-1"
  }
</script>

Alternatively, use the unpkg CDN to load the library:

<script src="//unpkg.com/@cortex-js/compute-engine"></script>

The UMD version is also available in the npm package in /compute-engine.min.js

Other Versions

A non-minified module which may be useful for debugging is available in the npm package as /compute-engine.esm.js.

MathJSON Standard Library

The operators in a MathJSON expression are defined in libraries. The MathJSON Standard Library is a collection of functions and symbols that are available by default to a ComputeEngine instance.

Topic
Arithmetic	Add Multiply Power Exp Log ExponentialE ImaginaryUnit...
Calculus	D Derivative Integrate...
Collections	List Reverse Filter...
Complex	Real Conjugate, ComplexRoots...
Control Structures	If Block Loop ...
Core	Declare Assign Error LatexString...
Functions	Function Apply Return ...
Logic	And Or Not True False ...
Sets	Union Intersection EmptySet RealNumbers Integers ...
Special Functions	Gamma Factorial...
Statistics	StandardDeviation Mean Erf...
Styling	Delimiter Style...
Trigonometry	Pi Cos Sin Tan...

Note

In this guide, the ce. prefix in ce.box() or ce.parse() indicates that the function is a method of the ComputeEngine class.

To create a new ComputeEngine instance use ce = new ComputeEngine()

The expr. prefix in expr.evaluate() or expr.simplify() indicates that the function is a method of the BoxedExpression class.

To create a new boxed expression use expr = ce.parse() or expr = ce.box()

Read more about the MathJSON Standard Library

You can add your own definitions to the built-in definitions from the MathJSON Standard Library.

Read more about Extending the MathJSON Standard Library

If you use a custom LaTeX syntax, such as macros, you can add your own definitions to the LaTeX dictionary, which defines how to parse and serialize LaTeX to MathJSON.

Read more about Parsing and Serializing LaTeX