API#
The full API reference for every subpackage: every public class and function.
Foundations
Cyclic/permutation groups, subgroups and cosets, finite fields, and polynomial ring arithmetic.
Counting and generation, Pascal’s triangle, integer partitions, inclusion-exclusion, and Stirling/Catalan/Bell numbers.
Modular arithmetic, primality testing, the Chinese Remainder Theorem, continued fractions, and Diophantine equations.
Analysis
Numerical differentiation/integration, forward- and reverse-mode automatic differentiation, and Taylor series.
Contour integrals, Cauchy’s theorem and formula, residues and the argument principle, conformal maps, and domain coloring.
Root finding with convergence-order verification, polynomial interpolation, and least-squares regression.
Heat, wave, advection and Poisson/Laplace problems: the method of lines, Crank-Nicolson, CFL stability, and spectral methods.
Gamma/beta functions, Bessel functions, orthogonal polynomials, the FFT, and signal transforms: convolution, filters, Z/Laplace transforms, and wavelets.
Linear Algebra & Optimization
LU/QR/Cholesky decompositions, eigenvalue algorithms, SVD, iterative Krylov solvers, and least-squares stability.
Gradient descent, nonlinear conjugate gradient, Newton/BFGS, constrained optimization, and linear programming.
Geometry & Graphs
Convex hull, Delaunay triangulation/Voronoi diagrams, segment intersection/point-in-polygon, and the Frenet-Serret frame.
Shortest paths, minimum spanning trees, maximum flow/minimum cut, graph coloring, and spectral graph theory.
Simplicial homology and torsion, the fundamental group, classification of surfaces, fixed-point theorems, and persistent homology.
Dynamics & Chaos
Lyapunov exponents, fractal dimension, Mandelbrot/Julia sets, iterated function systems, and cellular automata.
Fixed-point stability, phase portraits, bifurcation normal forms, limit cycles, and Poincare sections.
Probability & Statistics
Entropy and mutual information, Huffman and arithmetic coding, channel capacity, and Hamming, convolutional and LDPC codes.
Discrete/continuous distributions, Monte Carlo integration, limit theorems, and Markov chains.
Descriptive statistics, hypothesis tests, confidence intervals, OLS regression, and bootstrap resampling.
The ODE integrators shared by every subpackage, including stiff solvers and boundary-value problems, are documented in mathematicskit.integrators.