HomogenousPolynomial 2003-01-04 17:15:55 2005-02-26 10:41:31 Definition \usepackage{amsmath,amssymb,amsthm} \DeclareMathOperator{\ord}{ord} 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 $\deg P = \ord P$. As an important example of homogeneous polynomials one can mention the symmetric polynomials.