homogenize {mpoly}

Homogenize a polynomial

Description

Homogenize a polynomial.

Usage

homogenize(x, indeterminate = "t")

dehomogenize(x, indeterminate = "t")

is.homogeneous(x)

homogeneous_components(x)

Arguments

x

an mpoly object, see mpoly()

indeterminate

name of homogenization

Value

a (de/homogenized) mpoly or an mpolyList

Examples

x <- mp("x^4 + y + 2 x y^2 - 3 z")
is.homogeneous(x)
(xh <- homogenize(x))
is.homogeneous(xh)

homogeneous_components(x)

homogenize(x, "o")

xh <- homogenize(x)
dehomogenize(xh) # assumes indeterminate = "t"
plug(xh, "t", 1) # same effect, but dehomogenize is faster



# the functions are vectorized
(ps <- mp(c("x + y^2", "x + y^3")))
(psh <- homogenize(ps))
dehomogenize(psh)


# demonstrating a leading property of homogeneous polynomials
library(magrittr)
p  <- mp("x^2 + 2 x + 3")
(ph <- homogenize(p, "y"))
lambda <- 3
(d <- totaldeg(p))
ph %>%
  plug("x", lambda*mp("x")) %>%
  plug("y", lambda*mp("y"))
lambda^d * ph