Provides various complex matrix calculations. More...

#include "regina-core.h"
#include "maths/matrix.h"
#include <vector>

Namespaces
namespace	regina
	Contains the entire Regina calculation engine.

Functions
void	regina::smithNormalForm (MatrixInt &matrix)
	Transforms the given integer matrix into Smith normal form.

void	regina::smithNormalForm (MatrixInt &matrix, MatrixInt &rowSpaceBasis, MatrixInt &rowSpaceBasisInv, MatrixInt &colSpaceBasis, MatrixInt &colSpaceBasisInv)
	A Smith normal form algorithm that also returns change of basis matrices.

void	regina::metricalSmithNormalForm (MatrixInt &matrix, MatrixInt &rowSpaceBasis, MatrixInt &rowSpaceBasisInv, MatrixInt &colSpaceBasis, MatrixInt &colSpaceBasisInv)
	An alternative Smith normal form algorithm that also returns change of basis matrices.

size_t	regina::rowBasis (MatrixInt &matrix)
	Find a basis for the row space of the given matrix.

size_t	regina::rowBasisAndOrthComp (MatrixInt &input, MatrixInt &complement)
	Finds a basis for the row space of the given matrix, as well as an "incremental" basis for its orthogonal complement.

void	regina::columnEchelonForm (MatrixInt &M, MatrixInt &R, MatrixInt &Ri, const std::vector< size_t > &rowList)
	Transforms a given matrix into column echelon form with respect to a collection of rows.

MatrixInt	regina::preImageOfLattice (const MatrixInt &hom, const std::vector< Integer > &sublattice)
	Given a homomorphism from Z^n to Z^k and a sublattice of Z^k, compute the preimage of this sublattice under this homomorphism.

MatrixInt	regina::torsionAutInverse (const MatrixInt &input, const std::vector< Integer > &invF)
	Given an automorphism of an abelian group, this procedure computes the inverse automorphism.

Detailed Description

Provides various complex matrix calculations.

Todo: Feature (long-term): Add a routine to find the rank of an integer matrix; use this to show the rank of the matching equations.

Namespaces