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MathLive

website·Indexed 33 days ago

https://mathlive.io

A mathematical input and computation framework featuring Mathfield, an interactive web component for math input with LaTeX support and a virtual keyboard, and the Compute Engine for evaluating and managing symbolic expressions using the MathJSON standard library.

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What's inside MathLive

  1. Overview of the Python/NumPy Compilation Target

    The PythonTarget class compiles Compute Engine expressions into idiomatic Python code that leverages NumPy for numerical operations. The generated code is vectorized (working with both scalars and NumPy arrays), readable, and compatible with the scientific Python ecosystem, including SciPy and Pandas.

  2. Overview of the MathJSON Standard Library

    The MathJSON standard library defines the vocabulary and semantic meaning of symbols used in MathJSON expressions. It is independent of the syntax used for parsing or serialization (such as LaTeX). The library is organized into several functional topics including Arithmetic, Calculus, Collections, Colors, Complex numbers, Control Structures, Core, Functions, Logic, Sets, Special Functions, Statistics, Strings/Text, and Trigonometry.

  3. Overview of MathJSON Format

    MathJSON is a lightweight data interchange format built on JSON, designed to facilitate the exchange of mathematical data between software programs. It is human-readable and machine-parsable, serving as a bridge between different mathematical representations. It is not a visual representation format (like LaTeX or MathML) but rather a data structure for symbolic manipulation and numeric evaluation. The Compute Engine library provides JavaScript/TypeScript utilities to parse LaTeX to MathJSON and serialize MathJSON back to LaTeX.

  4. Overview of MathLive SDKs

    MathLive provides a suite of JavaScript/TypeScript SDKs for building scientific and technical applications. The ecosystem consists of three primary components: MathJSON for expression representation, Mathfield for user input, and Compute Engine for evaluation.

  5. Overview of Compute Engine

    Compute Engine is a JavaScript library designed for symbolic computing and numeric evaluation of mathematical expressions. It is suitable for browser-based or server-side (Node.js) technical computing applications. It represents mathematical expressions using the MathJSON format (e.g., x^2 + 2x + 1 is represented as ["Add", ["Power", "x", 2], ["Multiply", 2, "x"], 1]).

    Key capabilities include:

    • Parsing and serializing LaTeX expressions.
    • Symbolic simplification and evaluation.
    • Numeric evaluation.
    • Calculus operations (derivatives, integrals, solving equations).
    • Compiling expressions to JavaScript.

  6. Overview of MathJSON format

    MathJSON is a JSON-based data interchange format designed for mathematical notation. It allows software programs to exchange mathematical data in a human-readable and machine-parsable way. The MathLive Compute Engine provides JavaScript/TypeScript utilities to parse LaTeX to MathJSON, serialize MathJSON back to LaTeX, and perform symbolic manipulation or numeric evaluations on these expressions.

  7. Overview of Collections in MathLive Compute Engine

    Collections in the Compute Engine group multiple elements (each being an Expression) into a single unit. All collections are immutable; operations on them produce new collections rather than modifying the existing ones.

    Common collection types include:

    • list: Indexed elements, duplicates allowed.
    • set: Unique elements.
    • tuple: Fixed size, optional names.
    • range: A contiguous, ascending run of 1-based indexes.
    • string: An indexed collection of characters (grapheme clusters).
    • dictionary: Key-value pairs with string keys.
    • record: Structured data with a fixed set of known string keys.

    All collections support enumeration, counting, membership checks, and subset relationship checks.

  8. Overview of MathField capabilities

    MathField is an open-source web math editor with the following core capabilities:

    • LaTeX Support: Supports 800+ LaTeX commands for high-quality typesetting.
    • Virtual Keyboards: Includes fully customizable virtual keyboards optimized for both desktop and mobile input.
    • Integration: Can be used for interactive quizzes (fill-in-the-blank), symbolic manipulation, and numeric evaluation when paired with the Compute Engine.

  9. Overview of Compute Engine Collections

    Collections in the Compute Engine group multiple elements (each being an Expression) into a single unit. All collections are immutable; operations on them produce new collections rather than modifying the existing ones.

    Common collection types include:

    • list: Indexed elements, duplicates allowed.
    • set: Unique elements.
    • tuple: Fixed size, optional names.
    • range: A contiguous, ascending run of 1-based indexes.
    • string: An indexed collection of grapheme clusters (characters).
    • dictionary: Key-value pairs with string keys.
    • record: Structured data with a fixed set of known string keys.

    All collections support enumeration, counting, membership checks, and subset relationship checks. Indexed collections additionally support index-based access and finding elements via predicates.

  10. Overview of MathLive and Compute Engine

    MathLive provides two primary open-source tools for scientific computing:

    1. mathfield: A web component designed for editing beautifully typeset mathematical equations.
    2. Compute Engine: A JavaScript library used for symbolic computing and numeric evaluation.

  11. Measure distribution shape with Skewness and Kurtosis

    The Skewness function measures the asymmetry of the distribution of a real-valued random variable about its mean. The Kurtosis function measures the "tailedness" of the distribution.

  12. Inspect a symbol or constant using the About function

    The About function returns a dictionary containing metadata about a symbol or constant. Key properties include:

    • kind: The operand type (e.g., "symbol", "constant", "function", "number", "expression").
    • type: The static type of the expression (e.g., real for finite reals).
    • name: The symbol name.
    • value: The evaluation result if distinct from itself.
    • signature: The function signature.
    • clauses: Clause listing for multi-clause functions.
    • attributes: Algebraic attributes (e.g., "commutative associative").
    • description, wikidata, url: Documentation metadata.
    ["About", "Pi"]
// Result: {kind: "constant", name: "Pi", type: "real<3.141592653589793..3.141592653589794>", description: "The constant π ≈ 3.14159…", wikidata: "Q167"}