- Class BlockCoppersmithDomain< _Domain, _Sequence >
- Yuhasz thesis ...
- Class BlockLanczosSolver< Field, Matrix >
- [Montgomery '95]
- Class BlockMasseyDomain< _Field, _Sequence >
- Giorgi, Jeannerod, Villard algorithm from ISSAC'03
- Class CRABuilderFullMultip< Domain_Type >
- Jean-Guillaume Dumas, Thierry Gautier et Jean-Louis Roch. Generic design of Chinese remaindering schemes PASCO 2010, pp 26-34, 21-23 juillet, Grenoble, France.
- Global GaussDomain< _Field >::QLUPin (size_t &rank, Element &determinant, Perm &Q, _Matrix &L, _Matrix &U, Perm &P, size_t Ni, size_t Nj) const
- Jean-Guillaume Dumas and Gilles Villard, Computing the rank of sparse matrices over finite fields. In Ganzha et~al. CASC'2002, pages 47–62.
- Class GivaroRnsFixedCRA< Domain_Type >
- Global LinBox::cia (Polynomial &P, const Blackbox &A, const Method::DenseElimination &M)
- [Dumas-Pernet-Wan ISSAC05]
- Global LinBox::FastCharPolyDumasPernetWanBound (const IMatrix &A, const Integer &infnorm)
"Efficient Computation of the Characteristic Polynomial".
"Efficient Computation of the Characteristic Polynomial".
"Efficient Computation of the Characteristic Polynomial".
"Efficient Computation of the Characteristic Polynomial".
- Module padic
- Robert T. Moenck and John H. Carter Approximate algorithms to derive exact solutions to system of linear equations. In Proc. EUROSAM'79, volume 72 of Lectures Note in Computer Science, pages 65-72, Berlin-Heidelberger-New York, 1979. Springer-Verlag.
- John D. Dixon Exact Solution of linear equations using p-adic expansions. Numerische Mathematik, volume 40, pages 137-141, 1982.
File rational-solver2.h Implementation of the algorithm in manuscript, available at http://www.cis.udel.edu/~wan/jsc_wan.ps
LinBox::RationalSolver< Ring, Field, RandomPrime, Method::BlockWiedemann > Class RationalSolver< Ring, Field, RandomPrime, Method::BlockWiedemann >
- Douglas H. Wiedemann Solving sparse linear equations over finite fields. IEEE Transaction on Information Theory, 32(1), pages 54-62, 1986.
- Don Coppersmith Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm. Mathematic of computation, 62(205), pages 335-350, 1994.
LinBox::RationalSolver< Ring, Field, RandomPrime, Method::Dixon > Class RationalSolver< Ring, Field, RandomPrime, Method::Dixon >
- John D. Dixon Exact Solution of linear equations using p-adic expansions. Numerische Mathematik, volume 40, pages 137-141, 1982.
LinBox::RationalSolver< Ring, Field, RandomPrime, Method::SymbolicNumericNorm > Class RationalSolver< Ring, Field, RandomPrime, Method::SymbolicNumericNorm >
- Zhendong Wan Exactly solve integer linear systems using numerical methods. Submitted to Journal of Symbolic Computation, 2004. .
LinBox::RationalSolver< Ring, Field, RandomPrime, Method::Wiedemann > Class RationalSolver< Ring, Field, RandomPrime, Method::Wiedemann >
- Douglas H. Wiedemann Solving sparse linear equations over finite fields. IEEE Transaction on Information Theory, 32(1), pages 54-62, 1986.
- Erich Kaltofen and B. David Saunders On Wiedemann's method of solving sparse linear systems. In Applied Algebra, Algebraic Algorithms and Error Correcting Codes - AAECC'91, volume 539 of Lecture Notes in Computer Sciences, pages 29-38, 1991.
LinBox::SigmaBasis Class SigmaBasis< _Field >
- P. Giorgi, C.P. Jeannerod and G. Villard. On the complexity of polynomial matrix computations. ISSAC'03 doi.
LinBox::SmithFormIliopoulos Class SmithFormIliopoulos Worst Case Complexity Bounds on Algorithms for computing the Canonical Structure of Finite Abelian Groups and the Hermite and Smith Normal Forms of an Integer Matrix, by Costas Iliopoulos.
