Concepts

Homogeneity

Algebratic Homogeneity

A function is homogeneous of degree if . For example,

is homogeneous of degree 0 because:

Homogeneous polynomials

Loosely speaking, polynomials of are homogeneous if powers of add up to the same total degree. For example,

is homogeneous because . Homogeneous polynomials are always homogeneous in degree which is equal to the polynomial’s degree (its largest power). For example,

is homogeneous of degree :

Rational functions

Rational functions are functions that are quotients of two polynomials. For example, the function

where are polynomials, is a rational function.