Definition:Homogeneous Polynomial
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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