# polyMatrix-class: A class to represent a matrix of polynomials In polyMatrix: Infrastructure for Manipulation Polynomial Matrices

## Description

A class to represent a matrix of polynomials

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50``` ```## S4 method for signature 'polyMatrix,numeric' x[[i]] ## S4 method for signature 'polyMatrix' det(x) ## S4 method for signature 'polyMatrix' nrow(x) ## S4 method for signature 'polynomial' nrow(x) ## S4 method for signature 'polyMatrix' ncol(x) ## S4 method for signature 'polynomial' ncol(x) ## S4 method for signature 'polyMatrix' dim(x) ## S4 method for signature 'polyMatrix' predict(object, newdata) ## S4 method for signature 'polyMatrix' round(x, digits = 0) ## S4 method for signature 'polyMatrix' show(object) ## S4 method for signature 'polyMatrix,polyMatrix' e1 == e2 ## S4 method for signature 'polyMatrix,polynomial' e1 == e2 ## S4 method for signature 'polyMatrix,matrix' e1 == e2 ## S4 method for signature 'polyMatrix,numeric' e1 == e2 ## S4 method for signature 'ANY,polyMatrix' e1 == e2 ## S4 method for signature 'polyMatrix,ANY' e1 != e2 ## S4 method for signature 'ANY,polyMatrix' e1 != e2 ```

## Arguments

 `x` a matrix object `i` the degree of the matrix of coefficient to be extracted `object` an R object `newdata` the value to be evaluated `digits` an integer indicating the number of decimal places (round) or significant digits (signif) to be used `e1` an left operand `e2` an right operand

## Methods (by generic)

• `[[`: get coefficient matrix by degree

• `det`: determinant of a polynomial matrix

• `nrow`: the number of rows of a polynomial matrix

• `nrow`: a polynomial has only one row

• `ncol`: the number of columns of a polynomial matrix

• `ncol`: a polynomial has only one column

• `dim`: the dimension of a polynomial matrix

• `predict`: the value of a polynomial matrix in a point

• `round`: rounding of a polynomial matrix is rounding of polynomial coefficients

• `show`: prints out a text representation of a polynomial matrix

• `==`: equal operator for two polinomial matrices, result is a boolean matrix

• `==`: equal operator for polinomail matrix and polinomail, result is a matrix

• `==`: equal operator for polinomial and numerical matrices

• `==`: equal operator for polinomial matrix and number, result is a matrix

• `==`: equal operator for aby object and polinomial matrix

• `!=`: not equal operator

• `!=`: not equal operator

## Slots

`coef`

A matrix of coefficients which are joined into one matrix from lower degree to higher

`ncol`

The actual number of columns in the polynomial matrix

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```# create a new polynomial matrix by parsing strings pm <- parse.polyMatrix( "x; 1 + x^2; 3 x - x^2", "1; 1 + x^3; - x + x^3" ) # get coefficient matrix for degree 0 pm[] ## [,1] [,2] [,3] ## [1,] 0 1 0 ## [2 ] 1 1 0 # get coefficient matrix for degree 1 pm[] ## [,1] [,2] [,3] ## [1,] 1 0 3 ## [2 ] 0 0 -1 # dimensions nrow(pm) ## 2 ncol(pm) ## 3 dim(pm) ##  2 3 # round round(parse.polyMatrix( " 1.0001 - x, 1 - x^2, 1 + 2.0003*x + x^2", "0.0001 + x - x^2, 1 + x + 0.0001 x^2, 1 - 2*x + x^2" )) ## [,1] [,2] [,3] ## [1,] 1 - x 1 - x^2 1 + 2x + x^2 ## [2,] x - x^2 1 + x 1 - 2x + x^2 # print out a polynomial matrix show(parse.polyMatrix( " 1.0001 - x, 1 - x^2, 1 + 2.0003*x + x^2", "0.0001 + x - x^2, 1 + x, 1 - 2*x + x^2", " 12.3 x^3, 2 + 3.5 x + x^4, -0.7 + 1.6e-3 x^3" )) ## [,1] [,2] [,3] ## [1,] 1.0001 - x 1 - x^2 1 + 2.0003x + x^2 ## [2,] 1e-04 + x - x^2 1 + x 1 - 2x + x^2 ## [3,] 12.3x^3 2 + 3.5x + x^4 -0.7 + 0.0016x^3 ```

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