| 11. | Similarly, a projective variety is the projectivization of the zero set of a collection of homogeneous polynomials.
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| 12. | Let I ( Y ) be the homogeneous ideal, generated by the homogeneous polynomials vanishing on Y.
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| 13. | One can show that f is a homogeneous polynomial of degree n, therefore it can be written as
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| 14. | Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor.
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| 15. | One example is the close relationship between homogeneous polynomials and projective varieties . ( cf . homogeneous coordinate ring .)
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| 16. | In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables.
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| 17. | A variety is projective if it is defined in some projective space by homogeneous polynomials ( with coefficients in ).
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| 18. | When all nonzero coefficients ( including the leading one ) appear as variables, these are homogeneous polynomials of respective degrees 2, 4 and 6.
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| 19. | A "'Binomial number "'is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial.
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| 20. | One might ask, since the homogeneous polynomials are not really functions on P ( " V " ), what are they, geometrically speaking?
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