> For the complete documentation index, see [llms.txt](https://docs.algenta.ai/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.algenta.ai/numerical-and-mathematical-computing.md).

# Numerical & mathematical computing

- [Core linear algebra](https://docs.algenta.ai/numerical-and-mathematical-computing/core-linear-algebra-kernels.md): Dense matrix arithmetic, LU/QR/Cholesky decompositions, 2×2 eigenvalues and power iteration, and elementwise matrix operations, split across two independent in-tree matrix representations.
- [Exact numerics and graph kernels](https://docs.algenta.ai/numerical-and-mathematical-computing/exact-numerics-and-graph-kernels.md): Double-double error-free-transform arithmetic and compensated Householder least squares, plus explicit-graph traversal, shortest paths, MST, and union-find.
- [Sparse structures & tensor primitives](https://docs.algenta.ai/numerical-and-mathematical-computing/sparse-and-tensor-kernels.md): Coordinate-format sparse matrices and paired-array sparse vectors, a dense 1D tensor type, and the standalone scalar index/accumulation formulas an N-D tensor implementation composes.
- [Probability distributions & dependence](https://docs.algenta.ai/numerical-and-mathematical-computing/probability-distributions-and-dependence-kernels.md): Sampling and MLE/method-of-moments fitting for twenty-six probability distributions, core probability theory (Bayes, combinatorics, entropy), a Gaussian copula with rank-correlation measures, and Chol
- [Statistical computing](https://docs.algenta.ai/numerical-and-mathematical-computing/statistical-computing-kernels.md): Descriptive statistics with a bundled introsort, bootstrap and jackknife resampling for confidence intervals and bias, and Monte Carlo simulation of random walks, diffusions, and point processes.
- [Calculus & differential equations](https://docs.algenta.ai/numerical-and-mathematical-computing/calculus-and-differential-equation-kernels.md): Interpolation between data points, quadrature over sampled data, initial-value ODE solvers (Euler, RK4), and explicit/Jacobi finite-difference PDE solvers with their CFL stability limits.
- [Polynomial, root-finding & number theory](https://docs.algenta.ai/numerical-and-mathematical-computing/polynomial-root-finding-and-number-theory-kernels.md): Dense-coefficient polynomial arithmetic and calculus, five classical root-finding algorithms run against a fixed menu of test functions, and integer number theory -- primality, GCD, modular exponentia
- [Combinatorics, convex optimization & scipy-compat](https://docs.algenta.ai/numerical-and-mathematical-computing/combinatorics-convex-optimization-and-scipy-compat-kernels.md): Combinatorial search heuristics, an unconstrained convex-optimization sandbox, a frozen two-variable LP solver, quasi-random sampling, and the scalar formulas behind scipy.optimize and scipy.stats.
- [Signal transforms & processing](https://docs.algenta.ai/numerical-and-mathematical-computing/signal-transforms-and-processing-kernels.md): Radix-2 FFT and Haar wavelet transforms, two independently-implemented frequency-domain feature modules, window/peak/zero-crossing signal utilities, whole-column statistical data transforms, and the f
- [Dimensionality, information theory & complex systems](https://docs.algenta.ai/numerical-and-mathematical-computing/dimensionality-information-theory-and-complex-systems-kernels.md): Six unrelated math primitives grouped by name-similarity rather than shared subject -- business unit-consistency checking, PCA, Shannon information theory, special functions, chaotic dynamical systems
- [Quantum computing & formal logic](https://docs.algenta.ai/numerical-and-mathematical-computing/quantum-computing-and-formal-logic-kernels.md): Single-qubit state-vector simulation plus closed-form quantum-computing estimators, propositional/boolean logic and truth tables, fuzzy-set membership and defuzzification, gate-level digital circuit s
- [Geometry and simulation-physics kernels](https://docs.algenta.ai/numerical-and-mathematical-computing/geometry-and-simulation-physics-kernels.md): 2D Euclidean geometry, rigid-body game-engine kinematics, chemical reaction-rate kinetics, and point-cloud topological data analysis -- four self-contained modules that share no code with each other o


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