components: Polynomial components

In dkahle/mpoly: Symbolic Computation and More with Multivariate Polynomials

Polynomial components

Description

Compute quantities/expressions related to a multivariate polynomial.

Usage

## S3 method for class 'mpoly'
x[ndx]

LT(x, varorder = vars(x), order = "lex")

LC(x, varorder = vars(x), order = "lex")

LM(x, varorder = vars(x), order = "lex")

multideg(x, varorder = vars(x), order = "lex")

totaldeg(x)

monomials(x, unit = FALSE)

exponents(x, reduced = FALSE)

## S3 method for class 'mpoly'
coef(object, ...)

normalize_coefficients(p, norm = function(x) sqrt(sum(x^2)))

Arguments

x	an object of class mpoly
ndx	a subsetting index
varorder	the order of the variables
order	a total order used to order the terms
unit	for monomials(), should the monomials have coefficient 1?
reduced	if TRUE, don't include zero degrees
object	mpoly object to pass to coef()
...	In coef(), additional arguments passed to print.mpoly() for the names of the resulting vector
p	an object of class mpoly or mpolyList
norm	a norm (function) to normalize the coefficients of a polynomial, defaults to the Euclidean norm

Value

An object of class mpoly or mpolyList, depending on the context

Examples

(p <- mp("x y^2 + x (x+1) (x+2) x z + 3 x^10"))
p[2]
p[-2]
p[2:3]

LT(p)
LC(p)
LM(p)

multideg(p)
totaldeg(p)
monomials(p)
monomials(p, unit = TRUE)
coef(p)

exponents(p)
exponents(p, reduce = TRUE)
lapply(exponents(p), is.integer)

homogeneous_components(p)

(p <- mp("(x + y)^2"))
normalize_coefficients(p)
norm <- function(v) sqrt(sum(v^2))
norm(coef( normalize_coefficients(p) ))

abs_norm <- function(x) sum(abs(x))
normalize_coefficients(p, norm = abs_norm)

p <- mp(c("x", "2 y"))
normalize_coefficients(p)

# normalize_coefficients on the zero polynomial returns the zero polynomial
normalize_coefficients(mp("0"))

dkahle/mpoly documentation built on July 27, 2023, 11:44 p.m.