# homogeneous polynomial

A polynomial $P(x_{1},\cdots,x_{n})$ of degree $k$ is called homogeneous if $P(cx_{1},\cdots,cx_{n})=c^{k}P(x_{1},\cdots,x_{n})$ for all constants $c$.

An equivalent definition is that all terms of the polynomial have the same degree (i.e. $k$).

Observe that a polynomial $P$ is homogeneous iff $\deg P=\operatorname{ord}P$.

As an important example of homogeneous polynomials one can mention the symmetric polynomials.

Title homogeneous polynomial HomogeneousPolynomial 2013-03-22 13:21:11 2013-03-22 13:21:11 jgade (861) jgade (861) 11 jgade (861) Definition msc 12-00