homogeneous polynomial in a sentence

Examples

1. Similarly, a projective variety is the projectivization of the zero set of a collection of homogeneous polynomials.
2. Let I ( Y ) be the homogeneous ideal, generated by the homogeneous polynomials vanishing on Y.
3. One can show that f is a homogeneous polynomial of degree n, therefore it can be written as
4. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor.
5. One example is the close relationship between homogeneous polynomials and projective varieties . ( cf . homogeneous coordinate ring .)
6. In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables.
7. A variety is projective if it is defined in some projective space by homogeneous polynomials ( with coefficients in ).
8. When all nonzero coefficients ( including the leading one ) appear as variables, these are homogeneous polynomials of respective degrees 2, 4 and 6.
9. A "'Binomial number "'is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial.
10. One might ask, since the homogeneous polynomials are not really functions on P ( " V " ), what are they, geometrically speaking?