modular_linalg.H File Reference

Linear algebra operations over finite fields (modulo a prime). More...

#include <cstdint>
#include <algorithm>
#include <optional>
#include <type_traits>
#include <ah-errors.H>
#include <tpl_array.H>
#include <tpl_dynMat.H>
#include <modular_arithmetic.H>
#include <primality.H>
#include <concepts>
#include <utility>

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Classes
class	Aleph::Modular_Matrix< MatrixT >
	Matrix operations modulo a prime. More...
struct	Aleph::Modular_Matrix< MatrixT >::skip_validation_t

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.

Concepts
concept	Aleph::SparseMatrix
	Expresses requirements for sparse matrix backends like DynMatrix.
concept	Aleph::DenseMatrix
	Expresses requirements for dense matrix backends like Array<Array<uint64_t>>.
concept	Aleph::ModularMatrixBackend
	Union of supported matrix backends for modular operations.

Typedefs
using	Aleph::ModularMatrix = Modular_Matrix< Array< Array< uint64_t > > >
	Alias for common Array-based modular matrix.
using	Aleph::ModularSparseMatrix = Modular_Matrix< DynMatrix< uint64_t > >
	Alias for sparse DynMatrix-based modular matrix.

Functions
template<DenseMatrix MatrixT>
constexpr std::pair< size_t, size_t >	Aleph::matrix_dims (const MatrixT &m) noexcept
	Get dimensions of a matrix (dense or sparse).

Detailed Description

Linear algebra operations over finite fields (modulo a prime).

Provides Gaussian elimination, determinant computation, and matrix inversion modulo a prime number. Supports both dense (Array of Array) and sparse (DynMatrix) backends.

Definition in file modular_linalg.H.