LinBox — FFLAS-FFPACK — Givaro
LinBox is a C++ template library for exact, high-performance linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields.
It can solve linear systems, and compute matrix invariants such as minimal and characteristic polynomials, rank, determinant, Frobenius normal form, Smith normal form. Dense and sparse LU type factorizations are available.
Miscellaneous features include least-norm, least-squares solutions to singular and inconsistent linear systems and capability for positive definiteness determination and signature (inertia) of symmetric integer matrices.
FFLAS-FFPACK is a C++ library for fast dense linear algebra on word size prime fields
FFLAS contains BLAS-like routines for dense matrix and vector arithmetic over Z/pZ fields, while FFPACK, LAPACK-like, implements higher level algorithms for dense matricesover Z/pZ.
Givaro is a C++ library for exact arithmetic on integer, rationals, finite fields and polynomials.