mathr — Pure-Rust Math Library & CLI

A pure-Rust mathematics library and command-line tool for symbolic and numerical computation — built from scratch with zero external math dependencies.

Features

• Symbolic differentiation — product, quotient, and chain rules with automatic simplification
• Numerical integration — trapezoidal, Simpson's, and adaptive quadrature
• FFT (Fast Fourier Transform) — Cooley–Tukey radix-2 from scratch: forward, inverse, 2D, real-input, magnitude/power spectra, convolution, cross-correlation, window functions
• Equation solving — bisection, Newton–Raphson, secant method, Durand–Kerner polynomial root finding
• Matrix operations — arithmetic, determinant, inverse, linear system solver, trace, transpose
• Statistics — mean, median, variance, standard deviation, quartiles, IQR, correlation, linear regression
• Number theory — GCD, LCM, primality (trial + Miller–Rabin), factorization, sieve of Eratosthenes, binomial coefficients, factorial, Fibonacci, Euler's totient, Chinese Remainder Theorem, modular exponentiation
• ODE solvers — Euler, RK4, RK4 systems, adaptive RKF45
• Taylor series — symbolic expansion around any point
• Interpolation — Lagrange, Newton divided-difference, linear
• Special functions — Gamma, log-Gamma, Beta, erf, erfc, sinc, incomplete gamma P
• Complex numbers — generic Complex<T> with arithmetic, polar conversion, powers
• Plotting — PNG output via plotters (line, multi-series, scatter)
• LaTeX/TeX input — parse \frac, \sqrt, \sin, \pi, \left(\right), ^{...}, \Gamma, \log_2, and more; supports $...$, $$...$$, \[...\], \(...\) delimiters
• Interactive REPL — rustyline-powered with history, bracket matching, variable/function bindings
• Expression parser — recursive-descent, implicit multiplication, scientific notation, 27+ built-in functions

Quick Start

cargo install mathr

Or build from source:

git clone https://github.com/yingkitw/mathr.git
cd mathr
cargo build --release

CLI Usage

Just pass a string — mathr figures out what to do:

mathr "sin(pi/4) + 2^3"          # evaluate an expression
mathr "gamma(0.5)"               # special functions
mathr "diff x^3 + 2*x^2"         # symbolic derivative
mathr "simplify 2*x + 3*x + 0"   # algebraic simplification
mathr "solve x^2 - 4"            # find roots (Newton–Raphson)
mathr "int sin(x) 0 pi"          # numerical integral over [0, π]
mathr "taylor exp(x) 0 5"        # Taylor series (5 terms around 0)
mathr "poly-roots 1 -5 6"        # polynomial roots (Durand–Kerner)
mathr "fft 1 0 -1 0 1 0 -1 0"    # FFT magnitude spectrum
mathr "conv 1 2 3 x 1 1"         # convolution (x separates signals)
mathr "stats 1 2 3 4 5 6 7 8"    # descriptive statistics
mathr "gcd 48 36"                # number theory
mathr "is-prime 97"              # primality test
mathr "factor 360"               # prime factorization
mathr "fib 50"                   # Fibonacci number
mathr "mr-prime 2305843009213693951"  # Miller–Rabin primality
mathr "plot sin(x) -6.28 6.28 wave.png"  # plot to PNG
echo "sin(pi/2)" | mathr         # read from stdin
mathr                            # interactive REPL

LaTeX / TeX Input

mathr accepts LaTeX math formulas — with or without Markdown delimiters:

mathr "\frac{1}{2} + \frac{3}{4}"           # → 1.25
mathr "$\sin(\pi / 4)$"                     # → 0.7071...  (inline $...$)
mathr "$$\sqrt{16} + \cos(\pi)$$"           # → 3          (display $$...$$)
mathr "\[\frac{x^2 - 4}{1}\]"               # → evaluate with \[...\]
mathr "\(\log_2{8}\)"                       # → 3          (\(...\) inline)
mathr "2 \cdot 3 + 4"                       # → 10
mathr "\left( 1 + 2 \right) \cdot 3"        # → 9
mathr "\Gamma{0.5}"                         # → 1.7724...  (√π)
mathr "diff \sin(x^2)"                      # → cos(x^2)*2*x
mathr "solve $\frac{x^2 - 4}{1}$"           # → root ≈ 2

Supported delimiters: $...$, $$...$$, \[...\], \(...\), or raw TeX with no delimiters.

Supported TeX commands: \frac, \sqrt, \pi, \tau, \infty, \cdot, \times, \left(, \right), ^{...}, \sin, \cos, \tan, \arcsin, \arccos, \arctan, \sinh, \cosh, \tanh, \exp, \ln, \log, \log_2, \log_{10}, \Gamma, \operatorname{...}, \text{...}.

REPL

mathr> sin(pi/4)
0.7071067812
mathr> let x = 3
mathr> x^2 + 1
10
mathr> fn f(x) = x^2 + 2*x + 1
mathr> f(5)
36
mathr> diff sin(x^2)
2*x*cos(x^2)
mathr> taylor exp(x) 0 5
1 + x + 0.5*x^2 + 0.1666666667*x^3 + 0.0416666667*x^4
mathr> quit

Crate API

use mathr::prelude::*;

// Evaluate an expression
let val = eval_str("sin(pi/4) + 2^3", &[])?;

// Symbolic differentiation
let expr = Parser::parse("x^3 + 2*x")?;
let deriv = differentiate(&expr, "x")?;

// FFT magnitude spectrum
let samples = vec![1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -1.0, 0.0];
let mags = mathr::fft::magnitude_spectrum(&samples)?;

// Matrix determinant and inverse
let m = Matrix::from_rows(&[vec![1.0, 2.0], vec![3.0, 4.0]])?;
let det = m.determinant()?;
let inv = m.inverse()?;

// Descriptive statistics
let data = vec![1.0, 2.0, 3.0, 4.0, 5.0];
let s = mathr::stats::summary(&data)?;

// Number theory: sieve, Fibonacci, Miller–Rabin
let primes = mathr::numtheory::sieve_primes(100);
let fib50 = mathr::numtheory::fibonacci(50);
let is_prime = mathr::numtheory::is_prime_miller_rabin(2305843009213693951, 20);

// ODE: solve y' = y, y(0) = 1, on [0, 1]
let y = mathr::ode::rk4(|_t, y| y, 0.0, 1.0, 1.0, 100)?;

// Taylor series expansion
let series = mathr::taylor::taylor_series_str("exp(x)", "x", 0.0, 5)?;

// Lagrange interpolation
let pts = vec![(0.0, 1.0), (1.0, 2.0), (2.0, 5.0)];
let y = lagrange_interp(&pts, 0.5)?;

// Special functions
let g = mathr::special::gamma(0.5); // √π
let e = mathr::special::erf(1.0);

Modules

Dependencies

License

Apache-2.0