Definition:Homogeneous Polynomial

This page is about Homogeneous Polynomial. For other uses, see Homogeneous.

Definition

A homogeneous polynomial is a polynomial whose monomials with nonzero coefficients all have the same total degree.

Examples

Arbitrary Example $1$

The polynomial:

$\map P {x, y} = x^2 + 3 x y + y^2$

is a homogeneous polynomial in which the degree of each term is $2$.

Also see

• Results about homogeneous polynomials can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): homogeneous: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): homogeneous
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): homogeneous
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): homogeneous polynomial