Crate mathr 

mathr

A pure-Rust mathematics library and CLI that bundles symbolic and numerical computation:

• Expression AST, parser and evaluator (expr, parser, eval) with a standard library of elementary functions (sin, cos, exp, log, …) and constants (pi, e, …).
• FFT from scratch (fft): Cooley–Tukey radix-2 (forward, inverse, 2D, real-input) plus magnitude / power spectra, convolution, cross-correlation, and window functions (Hann, Hamming, Blackman).
• Numerical calculus (calculus): high-order finite-difference derivatives, trapezoidal and Simpson’s integrators, adaptive quadrature, partial derivatives and gradients.
• Symbolic algebra (symbolic, simplify): differentiation by the usual calculus rules, plus a simplifier that flattens identities and folds constants. Expression equality via canonical form (expr).
• Equation solving (solver): bisection, Newton–Raphson (with numeric-derivative fallback), secant, and Durand–Kerner for polynomial roots.
• Plotting (plot): PNG output via plotters, with single-, multi- and scatter-plot variants.
• Matrix operations (matrix): arithmetic, determinant, inverse, linear system solving, trace, LU decomposition with partial pivoting, and rank estimation.
• Statistics (stats): mean, median, variance, stddev, quartiles, correlation, linear regression.
• Number theory (numtheory): GCD, LCM, primality, factorization, binomial coefficients, Fibonacci, sieve, Euler’s totient, Miller–Rabin, Chinese Remainder Theorem, modular exponentiation, Jacobi symbol, continued fractions, linear Diophantine solver.
• ODE solvers (ode): Euler, RK4, RK4 systems, adaptive RKF45.
• Taylor series (taylor): symbolic Taylor expansion around a point.
• Interpolation (interpolate): Lagrange, Newton divided-difference, linear interpolation, and natural / clamped cubic splines.
• Special functions (special): Gamma, log-Gamma, Beta, erf, erfc, sinc, incomplete gamma P, Bessel functions J_0, J_1, J_n.

The CLI (mathr "<expr or command>") is a thin wrapper around the same library functions. It accepts plain math expressions, LaTeX/TeX input, and command keywords like diff, solve, int, gcd, etc.

Re-exports

pub use error::MathError;

pub use error::Result;

Modules

calculus

Numerical calculus: differentiation, integration, vector calculus helpers.

complex

error

eval

expr

fft

FFT implementation from scratch.

interpolate

Polynomial interpolation from scratch.

matrix

Matrix operations from scratch.

numtheory

Number theory from scratch.

ode

Ordinary differential equation (ODE) solvers from scratch.

parser

plot

Plotting via the plotters crate. Output is rendered to PNG files.

prelude

Re-exports of the most common types for downstream use mathr::*;.

repl

An interactive REPL that ties together the parser, evaluator, symbolic differentiation, numeric integration, root-finders and plotter.

simplify

Algebraic simplification of Expr values.

solver

Equation solvers: Newton–Raphson, bisection, secant, and polynomial root finding via the Durand–Kerner method.

special

Special functions from scratch.

stats

Descriptive statistics from scratch.

symbolic

Symbolic differentiation.

taylor

Symbolic Taylor series expansion from scratch.