MathJSON.jl

A Julia package for parsing, manipulating, and generating mathematical expressions in the MathJSON format.

MathJSON is a JSON-based format for representing mathematical expressions, providing interoperability with web-based mathematical tools like MathLive and the Cortex Compute Engine.

Features

• Parse MathJSON: Convert MathJSON strings to Julia expression trees
• Generate MathJSON: Serialize Julia expressions to MathJSON format
• Validation: Verify expressions conform to the MathJSON specification
• Symbolics.jl Integration: Bidirectional conversion with Symbolics.jl expressions
• Cortex Compute Engine Compatible: Full support for all 382 operators from the official MathJSON standard library

Installation

using Pkg
Pkg.add("MathJSON")

Quick Start

using MathJSON

# Parse a MathJSON expression
expr = parse(MathJSONFormat, """["Add", 1, 2]""")

# Generate MathJSON from an expression
json = generate(MathJSONFormat, FunctionExpr(:Multiply, [NumberExpr(3), SymbolExpr("x")]))

# Validate an expression
result = validate(expr)

Symbolics.jl Integration

MathJSON.jl provides seamless integration with Symbolics.jl:

using MathJSON
using Symbolics

# Convert MathJSON to Symbolics
expr = parse(MathJSONFormat, """["Add", "x", 1]""")
symbolic = to_symbolics(expr)

# Convert Symbolics to MathJSON
@variables x
mathjson = to_mathjson(x + 1)

Operator Registry

MathJSON.jl includes an extensive operator registry based on the Cortex Compute Engine standard library:

• 382 operators across 15 categories
• Arithmetic: Add, Subtract, Multiply, Divide, Power, Sqrt, Abs, Exp, Log, ...
• Trigonometry: Sin, Cos, Tan, Arcsin, Arccos, Arctan, Sinh, Cosh, ...
• Calculus: D (derivative), Integrate, Limit, Sum, Product, ...
• Linear Algebra: Determinant, Transpose, Inverse, Eigenvalues, ...
• Logic: And, Or, Not, Xor, Implies, Equivalent, ...
• Statistics: Mean, Median, Variance, StandardDeviation, ...
• And more: Collections, Combinatorics, Number Theory, Polynomials, ...

See the Operator Registry page for complete documentation.

API

See the API Reference page for complete documentation of all exported functions and types.