Function Repository Resource:

# PolynomialHomogenize

Homogenize a polynomial with respect to a given set of variables

Contributed by: Daniel Lichtblau
 ResourceFunction["PolynomialHomogenize"][poly,vars,t] homogenizes the expanded polynomial poly in total degree of vars using the new variable t. ResourceFunction["PolynomialHomogenize"][{poly1,poly2,…},vars,t] homogenizes each of polyi.

## Details

Each term in ResourceFunction["PolynomialHomogenize"][poly,vars,t] will have the same total degree. Terms in poly of lower degree are augmented by an appropriate power of t.

## Examples

### Basic Examples (2)

Homogenize the equation for a hyperbola:

 In:= Out= Create a homogenized polynomial of total degree 4:

 In:= Out= ### Scope (1)

Any variables appearing in a polynomial that are not specified in vars are treated as parameters (that is, part of the coefficients):

 In:= Out= ### Properties and Relations (1)

A polynomial can be de-homogenized by setting the homogenizing variable to unity:

 In:= Out= In:= Out= ### Possible Issues (1)

PolynomialHomogenize requires the input polynomial to be fully expanded:

 In:= Out= ## Requirements

Wolfram Language 11.3 (March 2018) or above

## Version History

• 1.0.1 – 03 January 2022
• 1.0.0 – 13 February 2019