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IliopoulosElimination Class Reference

#include <iliopoulos-elimination.h>

List of all members.

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Detailed Description

This is Iliopoulos' algorithm do diagonalize. @doc Compute Smith Form by elimination modulo m, for some modulus m such as S(n), the last invariant factor. The elimination method is originally described in "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.

Static Public Methods
template<class Matrix> Matrix &	smithIn (Matrix &A)
Static Protected Methods
template<class Matrix, class Ring> Matrix &	eliminationRow (Matrix &A, const Ring &r)
	eliminationRow will make the first row (*, 0, ..., 0) by col operations. It is the implementation of Iliopoulos algorithm
template<class Matrix, class Ring> Matrix &	eliminationCol (Matrix &A, const Ring &r)
	eliminationCol will make the first col (*, 0, ..., 0) by elementary row operation. It is the implementation of Iliopoulos algorithm
template<class Matrix, class Ring> bool	check (const Matrix &A, const Ring &r)
template<class Matrix, class Ring> Matrix &	diagonalizationIn (Matrix &A, const Ring &r)
	Diagonalize the matrix A.

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Member Function Documentation

bool check (  const Matrix &    A, const Ring &    r )  [inline, static, protected]

Matrix& diagonalizationIn (  Matrix &    A, const Ring &    r )  [inline, static, protected]

Diagonalize the matrix A.

Matrix& eliminationCol (  Matrix &    A, const Ring &    r )  [inline, static, protected]

eliminationCol will make the first col (*, 0, ..., 0) by elementary row operation. It is the implementation of Iliopoulos algorithm

Matrix& eliminationRow (  Matrix &    A, const Ring &    r )  [inline, static, protected]

eliminationRow will make the first row (*, 0, ..., 0) by col operations. It is the implementation of Iliopoulos algorithm

Matrix& smithIn (  Matrix &    A )  [inline, static]

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