Homogeneous polynomial

In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree. For example, $x^5 + 2 x^3 y^2 + 9 x y^4$ is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial $x^3 + 3 x^2 y + z^7$ 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.

单词	Homogeneous polynomials
释义	Homogeneous polynomials 英语百科 Homogeneous polynomial In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree. For example, $x^5 + 2 x^3 y^2 + 9 x y^4$ is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial $x^3 + 3 x^2 y + z^7$ 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.
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Homogeneous polynomials

Homogeneous polynomial