# MathLive

> Scientific Web Computing. Documentation for MathLive (math input for the web) and the Compute Engine (symbolic computation in JavaScript). The Epsil language is documented at https://epsil.dev.

Every page below is also available as HTML at the same URL without the `.md` suffix.

## Mathfield

- [All Mathfield documentation, concatenated](https://mathlive.io/llms-mathfield.txt)
- [Introduction](https://mathlive.io/mathfield.md): MathLive is a web component for editing and displaying beautifully typeset math formulas, with LaTeX output and a virtual keyboard, in any web page.
- [Mathfield Demo](https://mathlive.io/mathfield/demo.md): An interactive mathfield playground: edit a formula and watch its LaTeX, along with the simplified, evaluated and numeric forms, update as you type.
- [Changelog - Mathfield](https://mathlive.io/mathfield/changelog.md): Release notes for MathLive: new features, behavior changes, deprecations and bug fixes, version by version.
- [Math Virtual Keyboard](https://mathlive.io/mathfield/virtual-keyboard.md): Typing math requires access to many special symbols. While
- [Matrix Editor](https://mathlive.io/mathfield/matrix.md): A matrix is a useful way to represent and manipulate linear transformations. They are also used to represent systems of linear equations and many
- [LaTeX Commands](https://mathlive.io/mathfield/reference/commands.md): Mathfields support over 800 LaTeX commands.
- [Keyboard Shortcuts](https://mathlive.io/mathfield/reference/keybindings.md): // Substitute a text label for the glyphs
- [Getting Started](https://mathlive.io/mathfield/guides/getting-started.md): Let's add an editable mathfield to a web page.
- [Add A Mathfield to Your Project](https://mathlive.io/mathfield/guides/integration.md): As discussed in Getting Started the
- [Using A Mathfield with React](https://mathlive.io/mathfield/guides/react.md): Add an editable mathfield to a React application: render the <math-field> tag in JSX, get a reference with useRef, and customize it on mount.
- [Using a Mathfield with Svelte](https://mathlive.io/mathfield/guides/svelte.md): Use a mathfield in a Svelte application with a wrapper component that forwards all attributes to the underlying <math-field> web component.
- [Interacting with a Mathfield](https://mathlive.io/mathfield/guides/interacting.md): Changing the Content of a Mathfield
- [Customizing a Mathfield](https://mathlive.io/mathfield/guides/customizing.md): The appearance and behavior of the mathfield is highly customizable.
- [Menu](https://mathlive.io/mathfield/guides/menu.md): The Mathfield Context Menu provides a set of commands to perform common
- [Virtual Keyboard](https://mathlive.io/mathfield/guides/virtual-keyboard.md): The Mathfield virtual keyboard is a keyboard displayed on screen that gives
- [Keybindings and Inline Shortcuts](https://mathlive.io/mathfield/guides/shortcuts.md): Customize mathfield input: override or extend the default keybindings, and define inline shortcuts that expand a typed sequence into a math expression.
- [Fill-in-the-Blank](https://mathlive.io/mathfield/guides/fill-in-the-blank.md): To have one or more portions of a mathfield editable, while the rest is
- [Commands](https://mathlive.io/mathfield/guides/commands.md): You can perform editing operations on the mathfield programmatically.
- [Macros](https://mathlive.io/mathfield/guides/macros.md): Define your own LaTeX macros in a mathfield, override or remove the predefined ones, and control which of the 800+ built-in commands stay available.
- [Speech](https://mathlive.io/mathfield/guides/speech.md): Speech output for mathfields: keyboard shortcuts to speak a formula or the selection, the speak command, and how to configure the speech engine.
- [Static Math Formulas](https://mathlive.io/mathfield/guides/static.md): Converting LaTeX to Various Formats
- [Web Component Lifecycle](https://mathlive.io/mathfield/lifecycle.md): A mathfield web component goes through various stages during its lifecycle.
- [Security](https://mathlive.io/compute-engine/guides/security.md): Deploy mathfields safely: the Content Security Policy directives MathLive needs, Trusted Types support, and disabling commands that can modify the DOM.
- [Mathfield API Reference](https://mathlive.io/mathfield/api.md): Complete API reference for MathLive: the MathfieldElement class, its properties, methods and events, and the options that configure a mathfield.

## Compute Engine

- [All Compute Engine documentation, concatenated](https://mathlive.io/llms-compute-engine.txt)
- [Introduction - Compute Engine](https://mathlive.io/compute-engine.md): The Compute Engine is a JavaScript/TypeScript library for symbolic computing and numeric evaluation of mathematical expressions.
- [Compute Engine Demo](https://mathlive.io/compute-engine/demo.md): By default expressions are put in canonical form.
- [Changelog - Compute Engine](https://mathlive.io/compute-engine/changelog.md): Release notes for the Compute Engine: new features, behavior changes, deprecations and bug fixes, version by version.
- [Expressions](https://mathlive.io/compute-engine/guides/expressions.md): The Compute Engine produces and manipulates
- [Evaluation of Expressions](https://mathlive.io/compute-engine/guides/evaluate.md): Evaluating an expression is the process of determining the value of the
- [Symbolic Computing](https://mathlive.io/compute-engine/guides/symbolic-computing.md): The Compute Engine essentially performs computation by applying
- [Numeric Evaluation](https://mathlive.io/compute-engine/guides/numeric-evaluation.md): To obtain an exact numeric evaluation of an expression use expr.evaluate().
- [Canonical Form](https://mathlive.io/compute-engine/guides/canonical-form.md): Many mathematical objects can be represented by several equivalent expressions.
- [Symbols](https://mathlive.io/compute-engine/guides/symbols.md): A symbol is a named object in the Compute Engine. It has a type and may
- [Custom Functions and Symbols](https://mathlive.io/compute-engine/guides/augmenting.md): The MathJSON Standard Library is a
- [Parsing and Serializing LaTeX](https://mathlive.io/compute-engine/guides/latex-syntax.md): The Compute Engine manipulates MathJSON expressions. It can also convert LaTeX strings to
- [Types](https://mathlive.io/compute-engine/guides/types.md): In the Compute Engine, the type of an expression is the set of the
- [Units and Quantities](https://mathlive.io/compute-engine/guides/units.md): The Compute Engine supports physical units and quantities. You can parse LaTeX
- [Simplify](https://mathlive.io/compute-engine/guides/simplify.md): A complicated mathematical expression can often be transformed into a form that
- [Compiling Expressions](https://mathlive.io/compute-engine/guides/compiling.md): The Compute Engine can compile LaTeX expressions to JavaScript functions!
- [Python/NumPy Compilation Target](https://mathlive.io/compute-engine/guides/python-target.md): The Python compilation target generates NumPy-compatible Python code from mathematical expressions, enabling seamless integration with scientific Python workflows.
- [Assumptions](https://mathlive.io/compute-engine/guides/assumptions.md): Assumptions are statements about symbols that are assumed to be true. For
- [Patterns and Rules](https://mathlive.io/compute-engine/guides/patterns-and-rules.md): Recognizing patterns and applying rules is a powerful symbolic computing tool to
- [Extended Rules — The Identities Library](https://mathlive.io/compute-engine/guides/identities.md): The Identities Library is an optional add-on that teaches the Compute
- [Logic and First-Order Logic](https://mathlive.io/compute-engine/guides/logic.md): This guide covers working with logical expressions and First-Order Logic (FOL)
- [Linear Algebra](https://mathlive.io/compute-engine/guides/linear-algebra.md): This guide covers working with vectors, matrices, and tensors in the Compute
- [MathJSON Format](https://mathlive.io/math-json.md): MathJSON is a lightweight data interchange format for mathematical notation
- [Compute Engine API Reference](https://mathlive.io/compute-engine/api.md): Complete API reference for the Compute Engine: the ComputeEngine and BoxedExpression classes, their properties and methods, and the supporting types.
- [MathJSON Standard Library](https://mathlive.io/compute-engine/standard-library.md): The MathJSON standard library defines the vocabulary used by a MathJSON
- [Arithmetic](https://mathlive.io/compute-engine/reference/arithmetic.md)
- [Calculus](https://mathlive.io/compute-engine/reference/calculus.md): Calculus is the mathematical study of continuous change.
- [Collections](https://mathlive.io/compute-engine/reference/collections.md): In the Compute Engine, collections group together multiple elements
- [Colors](https://mathlive.io/compute-engine/reference/colors.md): The colors library provides functions for color manipulation,
- [Complex](https://mathlive.io/compute-engine/reference/complex.md): Complex numbers in the Compute Engine: the ImaginaryUnit constant and the Real, Imaginary, Conjugate, Abs, Arg and ComplexRoots functions.
- [Control Structures](https://mathlive.io/compute-engine/reference/control-structures.md): Control Structures define how a sequence of expressions is evaluated.
- [Core](https://mathlive.io/compute-engine/reference/core.md): The functions described in this section are part of the core of the Compute
- [Functions](https://mathlive.io/compute-engine/reference/functions.md): Functions are first-class values in the Compute Engine. This means that
- [Linear Algebra](https://mathlive.io/compute-engine/reference/linear-algebra.md): Linear algebra is the branch of
- [Logic](https://mathlive.io/compute-engine/reference/logic.md): Boolean logic in the Compute Engine: the True and False constants and the And, Or, Not, implication and equivalence operators, with their LaTeX notation.
- [Sets](https://mathlive.io/compute-engine/reference/sets.md): A set is a collection of distinct elements.
- [Special Functions](https://mathlive.io/compute-engine/reference/special-functions.md): Special functions in the Compute Engine: error and Gamma functions, Zeta, Beta, Lambert W, Fresnel integrals, Bessel and Airy functions, and elliptic integrals.
- [Statistics](https://mathlive.io/compute-engine/reference/statistics.md): For the following functions, when the input is a collection, it can take the
- [Combinatorics](https://mathlive.io/compute-engine/reference/combinatorics.md): Combinatorics functions in the Compute Engine provide essential tools for counting and enumerating discrete structures. These functions enable computation of binomial and multinomial coefficients,…
- [Number Theory](https://mathlive.io/compute-engine/reference/number-theory.md): The functions in this section provide tools for number-theoretic computations:
- [Strings and Text](https://mathlive.io/compute-engine/reference/strings.md): Strings and text in the Compute Engine: Unicode-aware operations over grapheme clusters, scalars and code points, and why strings are not collections.
- [Trigonometry](https://mathlive.io/compute-engine/reference/trigonometry.md): Trigonometry in the Compute Engine: the Pi and Degrees constants, trigonometric and hyperbolic functions, and the principal values their inverses return.
- [Units and Quantities](https://mathlive.io/compute-engine/reference/units.md): The Compute Engine provides a unit system for representing and computing with
- [Extended Rules — Symbolic Integration](https://mathlive.io/compute-engine/guides/integration-rules.md): The Integration Rules library is an optional add-on that extends the
- [Sequences](https://mathlive.io/compute-engine/guides/sequences.md): Mathematical sequences like the Fibonacci numbers, arithmetic progressions, or
- [The Structural Tier](https://mathlive.io/compute-engine/guides/structural-tier.md): The structural tier is the middle ground between a raw parse and a
- [Fungrim Identities — Bessel and hypergeometric functions](https://mathlive.io/compute-engine/reference/fungrim-bessel-hypergeometric.md): Part of the Fungrim Identities reference — 115 identities for bessel and hypergeometric functions.
- [Fungrim Identities — Complex numbers](https://mathlive.io/compute-engine/reference/fungrim-complex.md): Part of the Fungrim Identities reference — 36 identities for complex numbers.
- [Fungrim Identities — Elementary functions](https://mathlive.io/compute-engine/reference/fungrim-elementary.md): Part of the Fungrim Identities reference — 211 identities for elementary functions.
- [Fungrim Identities — Elliptic integrals](https://mathlive.io/compute-engine/reference/fungrim-elliptic-integrals.md): Part of the Fungrim Identities reference — 304 identities for elliptic integrals.
- [Fungrim Identities — Gamma and related functions](https://mathlive.io/compute-engine/reference/fungrim-gamma.md): Part of the Fungrim Identities reference — 162 identities for gamma and related functions.
- [Fungrim Identities — Modular forms and theta functions](https://mathlive.io/compute-engine/reference/fungrim-modular-theta.md): Part of the Fungrim Identities reference — 318 identities for modular forms and theta functions.
- [Fungrim Identities — Number theory](https://mathlive.io/compute-engine/reference/fungrim-number-theory.md): Part of the Fungrim Identities reference — 70 identities for number theory.
- [Fungrim Identities — Orthogonal polynomials](https://mathlive.io/compute-engine/reference/fungrim-orthogonal-polynomials.md): Part of the Fungrim Identities reference — 74 identities for orthogonal polynomials.
- [Fungrim Identities — Combinatorial and integer sequences](https://mathlive.io/compute-engine/reference/fungrim-sequences.md): Part of the Fungrim Identities reference — 65 identities for combinatorial and integer sequences.
- [Fungrim Identities — Zeta and L-functions](https://mathlive.io/compute-engine/reference/fungrim-zeta.md): Part of the Fungrim Identities reference — 80 identities for zeta and l-functions.
- [Fungrim Identities](https://mathlive.io/compute-engine/reference/fungrim.md): The Compute Engine ships a library of special-function identities derived from the Fungrim "Mathematical Functions Grimoire". These identities drive symbolic simplification, expansion, and equation…

## Tutorials

- [All Tutorials documentation, concatenated](https://mathlive.io/llms-tutorials.txt)
- [Tutorial: Simple Quiz](https://mathlive.io/tutorials/simple-quiz.md): In this tutorial, we'll create a web-based quiz application that allows

## Additional Resources

- [All Additional Resources documentation, concatenated](https://mathlive.io/llms-additional-resources.txt)
- [About Us](https://mathlive.io/about.md): Arno Gourdol on the path from WinMath in 1984 to Apple and Adobe, and why Farfield Studio is building open source tools for scientific computing.
- [MathLive SDKs](https://mathlive.io/sdk.md): MathLive provides several SDKs to help you build scientific and technical applications.