linbox
Bibliography
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 >

LinBox::RationalSolver< Ring, Field, RandomPrime, Method::Dixon > Class RationalSolver< Ring, Field, RandomPrime, Method::Dixon >

LinBox::RationalSolver< Ring, Field, RandomPrime, Method::SymbolicNumericNorm > Class RationalSolver< Ring, Field, RandomPrime, Method::SymbolicNumericNorm >

LinBox::RationalSolver< Ring, Field, RandomPrime, Method::Wiedemann > Class RationalSolver< Ring, Field, RandomPrime, Method::Wiedemann >

LinBox::SigmaBasis Class SigmaBasis< _Field >

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.