# Homogeneous function

$LaTeX: f(ax) = (a^p)f(x)$ for all $LaTeX: a$.
It is positively homogeneous if we restrict $LaTeX: a > 0$. When the degree is not specified (even by context), it is generally assumed to be 1. For example, $LaTeX: x$ is homogeneous, $LaTeX: xy + x^2$ is homogeneous of degree 2, $LaTeX: x + x^2$ is not homogeneous, and $LaTeX: xy/(x+y)$ is positively homogeneous on the positive elements of $LaTeX: {\mathbb R}^2$.