Thus, it generalizes those algebraic curves ( dimension one ), and those algebraic surfaces ( dimension two ), when they are defined by homogeneous polynomials.
22.
They play a fundamental role in algebraic geometry, as a projective algebraic variety is defined as the set of the common zeros of a set of homogeneous polynomials.
23.
A very nice class of cones are given by the zero sets of non-degenerate homogeneous polynomials ( of any degree, and in any number of variables ).
24.
The total degree defines also a graduation, but it depends on the choice of coordinates, as a change of affine coordinates may map indeterminates on non-homogeneous polynomials.
25.
But in 1966 Guy Terjanian constructed a homogeneous polynomial of degree 4 over "'Q "'2 in 18 variables that has no non-trivial zero.
26.
By Chow's theorem, a projective complex manifold is also a smooth projective algebraic variety, that is, it is the zero set of a collection of homogeneous polynomials.
27.
In mathematics, specifically in number theory, a "'binomial number "'is an integer which can be obtained by evaluating a homogeneous polynomial containing two terms.
28.
A "'projective surface "'in a projective space of dimension three is the set of points whose homogeneous coordinates are zeros of a single homogeneous polynomial in three variables.
29.
Given a homogeneous polynomial of degree " k ", it is possible to get a homogeneous function of degree 1 by raising to the power 1 / " k ".
30.
Multiplying this by the generating function for the complete homogeneous symmetric polynomials, one obtains the constant series 1, and the relation between the elementary and complete homogeneous polynomials follows from comparing coefficients of.
