polyMatrix0.9.16 package

Infrastructure for Manipulation Polynomial Matrices

adjoint

Adjungate or classical adjoint of a square matrix

cbind

Combine polynomial matrices by rows or columns

charpolynom

Characteristic polynomial of a matrix

cofactor

Cofactor of a matrix

degree

Gets the maximum degree of polynomial objects

diag

Polynomial matrix Diagonals Extract or construct a diagonal polynomial...

GCD

GCD for polynomial matrices

inv

Inverse polynomial matrix

is.polyMatrix

Check if object is polyMatrix

is.proper

Proper polynomial matrices

is.zero

Tests if something is zero or not

LCM

LCM for polynomial matrices

matrix.degree

Degree of each item of the matrix

minor

Minor of matrix item

newton

Build matrix of polynimal decomposition using Newton interpolation in ...

parse.polyMatrix

Parse polynomial matrix from strings

parse.polynomial

Parse polynomial from string

polyMatrix-Arith

Arithmetic Operators

polyMatrix-class

A class to represent a matrix of polynomials

polyMatrix-mmult

Matrix multiplication

polyMatrix-package

Implementation of matrices of polynomials

polyMatrix-subscript

Extract or Replace Parts of a polynomial matrix

polyMatrix.apply

Apply for polynomial matrix

polyMatrix

Create polyMatrix object

polyMatrixCharPolynomial-class

A class to repesent characteristic polynomial of a polynomial matrix

t-polyMatrix-method

Polynomial matrix transpose

tr

Trace of a 'matrix' or 'polyMatrix' class matrix

triang_Interpolation

Triangularization of a polynomial matrix by interpolation method

triang_Sylvester

Triangularization of a polynomial matrix by Sylvester method

zero.round

Rounds objects to zero if there is too small

zero_lead_hyp_rows

Get zero lead hyper rows of size sub_nrow of matrix M

zero_lead_rows

Get zero lead rows of matrix M

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>.

  • Maintainer: Nikolai Ryzhkov
  • License: MIT + file LICENSE
  • Last published: 2021-07-18