In
mathematics, a
homogeneous polynomial is a
polynomial whose nonzero terms all have the same
degree. For example,
is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial
is not homogeneous, because the sum of exponents does not match from term to term. 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. A
binary form is a form in two variables. A
form is also a function defined on a
vector space, which may be expressed as a homogeneous function of the coordinates over any
basis.