Class BlockCoppersmithDomain< _Domain, _Sequence >
Yuhasz thesis ...
Class BlockLanczosSolver< Field, Matrix >
[Montgomery '95]
Class BlockMasseyDomain< _Field, _Sequence >
Giorgi, Jeannerod, Villard algorithm from ISSAC'03
Class FullMultipCRA< 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 (unsigned long &rank, Element &determinant, Perm &Q, Matrix &L, Matrix &U, Perm &P, unsigned long Ni, unsigned long 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::BlasElimination &M)
[Dumas-Pernet-Wan ISSAC05]
Group 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

Class RationalSolver< Ring, Field, RandomPrime, BlockWiedemannTraits >

Class RationalSolver< Ring, Field, RandomPrime, DixonTraits >

Class RationalSolver< Ring, Field, RandomPrime, NumSymNormTraits >

Class RationalSolver< Ring, Field, RandomPrime, WiedemannTraits >

Class SigmaBasis< _Field >

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.