Mathematics Foundations

Overview

Reusable mathematics across quantsmind.math, algebra, calculus, numerical, statistics, optimization, and ml_math: vectors and matrices, polynomials, differentiation, root finding, distributions, gradient optimizers, and loss functions. Pure Python, no dependencies.

Purpose

Give science and domain layers one tested numerical vocabulary instead of scattered reimplementations.

Concept

Value objects (CoordinateVector, DenseMatrix, Polynomial, distributions) plus stateless functions (distances, losses) and stateful solvers/optimizers with histories.

API

See each package: math.linear_algebra, math.numerical, algebra.Polynomial, calculus.Differentiator, statistics.NormalDistribution/PoissonDistribution, optimization.AdamOptimizer, ml_math.MSELoss.

Input / Processing / Output

Input: vectors, matrices, coefficients, callables. Processing: exact or finite-difference numerics. Output: floats, vectors, histories.

Examples

examples/math/linear_algebra.py, examples/calculus/differentiation.py, examples/statistics/distributions.py, examples/optimization/adam_descent.py.

Limitations

No batched/accelerated kernels (see the pairwise batch helper in the quantum data layer for the pattern); single-threaded iterative methods; math/* vs top-level mirrors are historical — both work, consolidation is a future decision, not this page.