In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.[1]
For example, P^5 + 2P^3Q^2 + 9PQ^4 is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5.
A polynomial is homogeneous if and only if it defines a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial.[2]
A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called a constant or a scalar.
Wikipedia
|