Crate sim_lib_discrete_algebra 

Discrete algebra spine.

This crate hosts the Semiring trait, the standard semiring instances, and a generic dense / coordinate-list sparse matrix with power and Kleene-closure engines. Graph reachability and all-pairs shortest paths are derived from these (boolean closure, min-plus closure, counting powers) rather than re-implemented per algorithm.

Boundary: depends only on thiserror (and later num-bigint). It must never depend on sim-lib-rank or any music crate.

Re-exports

pub use boolean::BoolRing;

pub use cookbook::SemiringMatrixDemo;

pub use cookbook::semiring_matrix_demo;

pub use counting::Counting;

pub use error::AlgebraError;

pub use gf2::Gf2;

pub use matrix::AlgebraLimits;

pub use matrix::Matrix;

pub use real::RealF64;

pub use semiring::Semiring;

pub use sparse::SparseEntry;

pub use sparse::SparseMatrix;

pub use tropical_max::MaxPlus;

pub use tropical_min::MinPlus;

pub use views::DiagonalView;

pub use views::IdentityView;

pub use views::PermutationView;

Modules

boolean

The boolean semiring (OR, AND). Closure gives transitive reachability.

closure

Kleene closure A* = I + A + A^2 + ... over a closed semiring.

cookbook

Deterministic cookbook builders for discrete algebra recipes.

counting

The counting semiring over BigUint. Powers count walks; closure counts paths in a nilpotent (acyclic) setting.

error

Error type for the discrete algebra spine.

gf2

The two-element field GF(2): add is XOR, mul is AND. Used for linear algebra over Z/2 (rank, coding theory).

matrix

Generic dense matrix over a Semiring, with semiring matrix multiply.

power

Matrix power by square-and-multiply. A^k[i][j] over the counting semiring counts walks of length k; over min-plus it bounds k-edge shortest paths.

real

The real semiring over f64 with ordinary + and *, plus a total order for algorithms that need to compare entries. No star (left as default).

semiring

The Semiring trait: the algebraic core of the discrete-math family.

sparse

Coordinate-list sparse matrix over a Semiring.

tropical_max

The bounded max-plus (tropical) semiring.

tropical_min

The bounded min-plus (tropical) semiring.

views

Implicit matrix views that act without materializing dense storage.

Statics

RECIPES

Cookbook recipes for this lib, embedded at build time.