In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example...

quadratic form; and more generally, the discriminant of a form, of a homogeneous polynomial, or of a projective hypersurface (these three concepts are essentially...

s ≠ 0. {\displaystyle s\neq 0.} For example, a homogeneous polynomial of degree k defines a homogeneous function of degree k. The above definition extends...

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

\lambda z)=\lambda ^{k}f(x,y,z)=0.} A polynomial g(x, y) of degree k can be turned into a homogeneous polynomial by replacing x with x/z, y with y/z and...

the polynomial that follows it. The dimension of the vector space K [ x 1 , … , x n ] d {\displaystyle K[x_{1},\ldots ,x_{n}]_{d}} of homogeneous polynomial...

The zero polynomial is homogeneous, and, as a homogeneous polynomial, its degree is undefined. For example, x3y2 + 7x2y3 − 3x5 is homogeneous of degree...

and drawing of curves defined by a bivariate polynomial equation. The resultant of n homogeneous polynomials in n variables (also called multivariate resultant...

quotient by a homogeneous ideal of a multivariate polynomial ring, graded by the total degree. The quotient by an ideal of a multivariate polynomial ring, filtered...

weight or the degree of the polynomial. The term quasi-homogeneous comes from the fact that a polynomial f is quasi-homogeneous if and only if f ( λ w 1...