Examples#
Runnable examples for every subpackage: an auto-generated gallery built
directly from the scripts under examples/<name>/. Where a narrative,
worked-through tutorial also exists, the gallery links out to it.
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.