polyMatrix-package: Implementation of matrices of polynomials

In polyMatrix: Infrastructure for Manipulation Polynomial Matrices

Description

Implementation of class "polyMatrix" for storing a matrix of polynomials and implements basic matrix operations; including a determinant and characteristic polynomial. It is based on the package 'polynom' and uses a lot of its methods to implement matrix operations. This package includes 3 methods of triangularization of polynomial matrices: Extended Euclidean algorithm which is most classical but numerically unstable; Sylvester algorithm based on LQ decomposition; Interpolation algorithm is based on LQ decomposition and Newton interpolation. Both methods are described in D. Henrion & M. Sebek, Reliable numerical methods for polynomial matrix triangularization, IEEE Transactions on Automatic Control (Volume 44, Issue 3, Mar 1999, Pages 497-508) <doi:10.1109/9.751344> and in Salah Labhalla, Henri Lombardi & Roger Marlin, Algorithmes de calcule de la reduction de Hermite d'une matrice a coefficients polynomeaux, Theoretical Computer Science (Volume 161, Issue 1-2, July 1996, Pages 69-92) <doi:10.1016/0304-3975(95)00090-9>.

Details

This package add transperent support of matrices of polynomials to R language.

Input

• low level input of matrix: polyMatrix()

• string ibpuy of polynomial: parse.polynomial()

• string input of matrix: parse.polyMatrix()

Output

Matrices of polynomials uses same format as numerical matrices

Operators

Basic arithmetic operations were implemented.

Functions

The most important matrix functions are implemented:

• the determinant det()

Author(s)

Maintainer: Nikolai Ryzhkov [e-mail] (ORCID)

Authors:

• Tamas Prohle [e-mail]

• Peter Prohle [e-mail]

• Ildiko Laszlo (ORCID)

Other contributors:

• Ulas Onat Alakent [contributor]

See Also

Useful links:

• https://github.com/namezys/polymatrix

• Report bugs at https://github.com/namezys/polymatrix/issues

polyMatrix documentation built on July 18, 2021, 5:06 p.m.