Polynomial Degree — degree • rationalmatrices

Compute the polynomial degrees (of the elements) of a polynomial matrix. Note that for a (scalar) polynomial with zero coefficients the degree is set to \(-1\).

Usage

degree(x, which = c("elements", "rows", "columns", "matrix"))

Arguments

x: A polynomial matrix, i.e. an object of class polm.
which: (character string) decides whether a matrix with the respectives degrees of the entries of the matrix, or a vector with the respective maximal degrees in each row or column, or simply the maximum degree of all elements of the polynomial matrix is computed.

Value

The outcome depends on the parameter which:

elements: A matrix with the degrees of the respective elements of the polynomial matrix.
rows: A vector with the maximum degrees within each row.
columns: A vector with the maximum degrees within each column.
matrix: maximum of the degrees of the elements of the matrix.

Details

The main advantage of setting the degree of a zero polynomial to \(-1\) rather than -Inf is that indexing and assigning is programmatically easier: E.g., p[,,(deg+2):(max_deg+1)] = 0 (in obvious notation) also works when deg = -1. When multiplying with zero polynomials, it does not make a difference whether one needs to check for deg = -Inf or deg = -1.

Examples

x = polm(array(c(0,1,1,0,
                 0,0,1,0,
                 0,0,0,1,
                 0,0,0,0), dim = c(2,2,4)))
x
#> ( 2 x 2 ) matrix polynomial with degree <= 3 
#>      z^0 [,1]  [,2] z^1 [,1]  [,2] z^2 [,1]  [,2] z^3 [,1]  [,2]
#> [1,]        0     1        0     1        0     0        0     0
#> [2,]        1     0        0     0        0     1        0     0
degree(x)
#>      [,1] [,2]
#> [1,]   -1    1
#> [2,]    0    2
degree(x, 'rows')
#> [1] 1 2
degree(x, 'columns')
#> [1] 0 2
degree(x, 'matrix')
#> [1] 2