Explore comprehensive mathematical documentation with interactive examples
113 topics available
6 topics
Comprehensive guide to using MathHook including expression creation with macros and constructors, simplification, pattern matching, symbol manipulatio...
Common patterns and best practices when using MathHook, including macro usage guidelines, polynomial construction, substitution patterns, function com...
Complete installation guide for MathHook across Rust, Python, and Node.js platforms, including platform-specific requirements, troubleshooting, and op...
MathHook is a high-performance educational computer algebra system (CAS) written in Rust, designed to combine mathematical correctness with exceptiona...
Choose your journey based on background and goals. Structured learning paths for Python data scientists, Node.js developers, Rust programmers, mathema...
Get up and running with MathHook in 5 minutes. Learn basic expression creation, parsing, differentiation, and common operations across Rust, Python, a...
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MathHook provides built-in mathematical constants with exact symbolic representation and high-precision numerical evaluation. Constants include π, e, ...
The Expression type is the foundation of MathHook. Expressions are represented as an enum with variants for different mathematical constructs includin...
MathHook provides a comprehensive mathematical function system with intelligent evaluation, symbolic manipulation, and educational explanations. Funct...
Pattern matching is a powerful technique in MathHook for identifying, transforming, and simplifying mathematical expressions. MathHook combines Rust's...
Symbols represent mathematical variables (x, y, θ, etc.) using efficient string interning. Numbers support integers, rationals, floats, and complex nu...
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Symbolic differentiation in MathHook uses automatic differentiation with the chain rule, product rule, quotient rule, and function-specific derivative...
MathHook provides two fundamental operations for working with expressions: 1. **Evaluation** - Compute numerical values with domain checking 2. **Sim...
Transform expressions between expanded and factored forms for easier manipulation and analysis.
MathHook's integration system provides symbolic integration capabilities with an 8-layer strategy architecture from fast heuristics to complete Risch ...
Compute limits of expressions as variables approach values, infinity, or points of discontinuity.
Expand functions as infinite series for numerical approximation and analysis.
MathHook provides comprehensive symbolic simplification for mathematical expressions, with full support for noncommutative algebra (matrices, operator...
Find solutions to equations symbolically and numerically.
Replace variables with values or expressions to evaluate, simplify, or transform expressions.
Symbolic summation and products in MathHook provide closed-form formulas for arithmetic series, geometric series, power sums, and convergence analysis...
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Polynomial division algorithms including long division, exact division, and factorization capabilities such as square-free factorization, resultant, a...
Multiple GCD (Greatest Common Divisor) algorithms for polynomials, optimized for different use cases including univariate, multivariate, and modular G...
Groebner bases are fundamental tools in computational algebraic geometry for working with polynomial ideals, enabling ideal membership testing, polyno...
Comprehensive symbolic polynomial manipulation capabilities in MathHook. Implements a trait-based architecture for automatic classification, property ...
Classical orthogonal polynomial families including Legendre, Chebyshev (1st and 2nd kind), Hermite, and Laguerre polynomials with both symbolic expans...
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Extend MathHook's parser for domain-specific mathematical notation. Add custom functions, operators, preprocessors, and grammar modifications.
Format mathematical expressions for display in multiple notations. Supports LaTeX, Unicode, Wolfram, and custom formatters for different output target...
Parse and generate beautiful LaTeX notation for mathematical expressions. MathHook provides full bidirectional support: Parse LaTeX → Expression, Expr...
Design documentation for MathHook's type-aware LaTeX parser that automatically infers symbol types. Enables seamless support for noncommutative algebr...
Parse and generate Mathematica/Wolfram Language syntax for compatibility with Wolfram products. Supports bidirectional conversion between MathHook exp...
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The Educational API provides programmatic access to MathHook's educational features for external applications. Integrate step-by-step explanations, as...
The message registry system provides organized, mappable, hashable educational content separated from code logic. Instead of hardcoding explanatory te...
Educational explanations transform mathematical operations from black boxes into transparent learning experiences. The step-by-step system generates d...
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Comprehensive symbolic simplification for mathematical expressions, with full support for noncommutative algebra (matrices, operators, quaternions). I...
Symbolic differentiation and integration using automatic differentiation rules, integration strategies, and the Risch algorithm. Supports chain rule, ...
The Expression type is the foundation of MathHook. Expressions are immutable, 32-byte cache-optimized structures representing mathematical constructs ...
Symbolic and numeric matrix operations with full support for noncommutative algebra. Matrix symbols preserve multiplication order (AB ≠ BA), enabling ...
Parse and generate LaTeX notation for mathematical expressions. Full bidirectional support: LaTeX → Expression and Expression → LaTeX. Automatic type ...
Find solutions to equations symbolically and numerically. Supports linear, quadratic, polynomial, and transcendental equations with automatic strategy...
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Complete guide to using MathHook from Node.js and TypeScript via NAPI bindings. Provides comprehensive documentation for the JavaScript/TypeScript API...
Complete guide to using MathHook from Python via PyO3 bindings. Provides comprehensive documentation for the Python API including installation, quick ...
WebAssembly (WASM) bindings for MathHook, enabling browser-based symbolic mathematics without requiring Node.js. Documentation is under development.
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MathHook workspace organization with specialized crates for different concerns. Covers the modular architecture from core mathematical engine to langu...
MathHook's function intelligence registry that enables automatic simplification, differentiation, and symbolic manipulation of mathematical functions....
32-byte expression constraint and cache-line optimization strategy for maximum performance. Covers memory layout details and performance implications....
Five core principles of MathHook in strict priority order: mathematical correctness, performance, ergonomic API, educational value, and multi-language...
Immutable expressions enable thread-safe sharing and parallel processing without locks. Covers concurrency patterns and safety guarantees in MathHook....
MathHook's type system design and constraints. Covers Expression, Number, and Symbol types with their memory layout and performance characteristics.
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This chapter is under development. Please check back soon for complete documentation on MathHook's performance architecture design.
This chapter is under development. Please check back soon for complete documentation on MathHook's caching and memoization strategies for performance ...
This chapter is under development. Please check back soon for complete documentation on MathHook's parallel processing and concurrency strategies.
This chapter is under development. Please check back soon for complete documentation on MathHook's SIMD (Single Instruction Multiple Data) vectorizati...
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Declare properties about symbols to enable better simplification, solving, and mathematical operations. Assumptions like positivity, reality, integer ...
Work with complex numbers in MathHook including imaginary unit i, complex arithmetic, polar form, Euler's formula, and operations like conjugate, magn...
Solve ordinary differential equations (ODEs) and partial differential equations (PDEs) symbolically in MathHook, with support for initial conditions, ...
Understand the key differences between evaluation (computing numerical results) and simplification (algebraic transformation) in MathHook's symbolic e...
Work with matrices symbolically and numerically in MathHook, with full support for noncommutative algebra where order matters. Create matrices, perfor...
Support for noncommutative algebra in MathHook with four symbol types: Scalar (commutative), Matrix, Operator, and Quaternion (all noncommutative). Es...
Complete API reference for MathHook's noncommutative algebra support, including symbol creation macros, type queries, and equation solving.
Comprehensive examples of noncommutative algebra in MathHook covering quantum mechanics, matrix algebra, and quaternion rotations.
Define functions with different formulas in different regions, essential for modeling discontinuous behavior, conditional logic, step functions, and t...
Find poles of rational and transcendental functions for applications in control theory, signal processing, and complex analysis. SymPy-validated pole ...
Comprehensive support for special mathematical functions including the Gamma function family (Gamma, Digamma, Polygamma), Beta function, and other adv...
Solve systems of equations (linear and nonlinear) with multiple unknowns using substitution, elimination, matrix methods, and Newton's method for nonl...
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Boundary conditions (BCs) specify constraints on the PDE solution at domain boundaries. They determine eigenvalues and influence solution behavior. Co...
Mathematical classification of partial differential equations into elliptic, parabolic, and hyperbolic types using the discriminant formula. Different...
Three complete, real-world examples demonstrating MathHook's PDE solving capabilities across heat, wave, and Laplace equations. Each example includes ...
Explanation of why Fourier coefficients in PDE solutions are returned as symbolic expressions rather than numerical values. Covers the orthogonality p...
The heat equation (also called diffusion equation) governs how temperature distributes through materials over time. Solves parabolic PDEs with boundar...
Laplace's equation describes steady-state (equilibrium) distributions in physics. Solves elliptic PDEs with boundary conditions for harmonic functions...
The Method of Characteristics is the primary technique for solving first-order partial differential equations (PDEs). It transforms the PDE into a sys...
Comprehensive overview of partial differential equations in MathHook CAS. Covers mathematical foundations, classification, solution methods, and curre...
Comprehensive performance benchmarks for the MathHook PDE module, establishing baseline metrics for regression detection and optimization efforts. Inc...
One-page cheat sheet for Method of Characteristics covering standard forms, solution templates, common patterns, shock formation, and troubleshooting ...
Quick-start tutorial for solving partial differential equations with MathHook. Covers transport equation solving in 30 seconds, common PDE patterns, a...
MathHook uses a registry-based dispatch system for PDE solvers, eliminating hardcoded match statements and enabling O(1) solver lookup. This architect...
Separation of Variables is the fundamental technique for solving linear second-order partial differential equations (PDEs) with boundary conditions. I...
SymPy serves as the authoritative reference for validating MathHook PDE solvers. With 15+ years of development, extensive test coverage, and academic ...
Rigorous mathematical treatment of partial differential equations with proofs and references. Covers formal definitions, method of characteristics wit...
Comprehensive user guide for solving partial differential equations with MathHook. Covers fundamental PDE concepts, classification systems, the method...
The wave equation governs oscillatory phenomena and wave propagation in physical systems. Solves hyperbolic PDEs with boundary conditions and two init...
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Module structure patterns, implementation checklists, and templates for implementing math functions in MathHook. Covers elementary functions, special ...
Mathematical correctness is Priority Level 1. Nothing else matters if the math is wrong. Covers validation, edge cases, symbol assumptions, numerical ...
Setup and workflow for MathHook development.
Documentation must be accurate, complete, and match the actual code. Covers API documentation, doctests, mdbook, and keeping docs updated.
Code style ensures maintainability and consistency across MathHook. Covers macros, file organization, naming conventions, and comments policy.
Testing ensures mathematical correctness—the highest priority in MathHook. Covers unit tests, integration tests, doctests, and mathematical validation...
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Analysis of actual code complexity in MathHook repository to verify educational integration effort estimates. Identifies complexity hotspots and adjus...
Comprehensive review verifying effort estimates for 12% → 95% educational coverage transformation. Analyzes actual code complexity to validate 100-120...
Actionable implementation plan to transform MathHook from computation tool to educational CAS, achieving 12% → 95% educational coverage in 100-120 hou...
Analysis of MathHook's error type hierarchy, fallback strategies, and critical gaps in domain error handling. Overall score: 6/10 with MEDIUM-HIGH ris...
Archive of test cases documenting features not yet implemented in MathHook. Tests were removed from test suite - copy back when implementing features....
Master consolidated document covering type dispatch architecture, educational integration audit, documentation accuracy, and educational traits mappin...
Single entry point for all investigation findings on MathHook architecture, module status, educational coverage, and priority actions.
Comprehensive performance analysis of ALL derivative and integral operations in MathHook, including derivative rules, integration methods, parsing ove...
Deep architectural analysis comparing MathHook's polynomial operations (GCD, factorization, expansion) against Symbolica, identifying performance gaps...
Comprehensive performance analysis of MathHook's simplification and expansion operations, revealing catastrophic expansion performance (52-257x slower...
Comprehensive performance analysis of MathHook's equation solving operations including linear equations, quadratic equations, systems of equations, an...
Comprehensive 3-phase roadmap to achieve 2.5-3.8x overall performance improvement through hybrid architecture approach, combining Expression tree stre...
Comprehensive analysis of 15+ high-priority opportunities for IntPoly and NumericMatrix fast-paths across MathHook's algebra, calculus, and matrix ope...
Connect existing matrix decompositions (LU, QR, Cholesky) with solver infrastructure. Eliminates code duplication where SystemSolver.solve_nxn_system(...
Summary of Phase 3 (Educational Layer verification) and Phase 5 (Eliminate Internal Bridging) implementation status. Phase 3 confirmed educational mod...
Module-by-module review examining type inference/dispatch, performance, abstraction quality, and educational stepping coverage across all MathHook mod...
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Complete changelog of MathHook releases following Keep a Changelog format and Semantic Versioning. Tracks all notable changes, features, and known iss...
Common error messages in MathHook and their solutions, including parse errors, domain errors, and solver errors with actionable guidance for users.
Frequently asked questions about MathHook covering general information, usage patterns, performance characteristics, development guidelines, and troub...
Comprehensive glossary of technical terms used throughout MathHook documentation, covering computer algebra, mathematical concepts, and performance op...
Documentation of mathematical notation used throughout MathHook, including LaTeX support, standard notation, Wolfram Language syntax, and operator pre...
Complete guide to MathHook's Risch algorithm implementation for symbolic integration. Covers algorithm phases, implementation details, examples, non-e...