#ifndef LINEARALGEBRA_H
#define LINEARALGEBRA_H
#include "Singular/lists.h"
#include "kernel/linear_algebra/linearAlgebra.h"
/**
* Computes all eigenvalues of a given real quadratic matrix with
* multiplicities.
*
* The method assumes that the current ground field is the complex numbers.
* Computations are based on the QR double shift algorithm involving
* Hessenberg form and householder transformations.
* If the algorithm works, then it returns a list with two entries which
* are again lists of the same size:
* _[1][i] is the i-th mutually distinct eigenvalue that was found,
* _[2][i] is the (int) multiplicity of _[1][i].
* If the algorithm does not work (due to an ill-posed matrix), a list with
* the single entry (int)0 is returned.
* 'tol1' is used for detection of deflation in the actual qr double shift
* algorithm.
* 'tol2' is used for ending Heron's iteration whenever square roots
* are being computed.
* 'tol3' is used to distinguish between distinct eigenvalues: When
* the Euclidean distance between two computed eigenvalues is less then
* tol3, then they will be regarded equal, resulting in a higher
* multiplicity of the corresponding eigenvalue.
*
* @return a list with one entry (int)0, or two entries which are again lists
**/
lists qrDoubleShift(
const matrix A, /**< [in] the quadratic matrix */
const number tol1, /**< [in] tolerance for deflation */
const number tol2, /**< [in] tolerance for square roots */
const number tol3, /**< [in] tolerance for distinguishing
eigenvalues */
const ring r= currRing
);
#endif