homogeneous polynomial वाक्य
उदाहरण वाक्य
मोबाइल
- Let in be a homogeneous polynomial of degree " d ".
- Homogeneous polynomials are ubiquitous in mathematics and physics.
- For more details, see homogeneous polynomial.
- The zero polynomial is homogeneous, and, as homogeneous polynomial, its degree is undefined.
- This corresponds to a symmetric homogeneous polynomial
- It is then defined by a single equation, a homogeneous polynomial in the homogeneous coordinates.
- Additionally, one can look at curves in the projective plane, given by homogeneous polynomials.
- Note that quadratic forms and cubic forms are precisely homogeneous polynomials of degrees 2 and 3.
- For her thesis, Noether extended Gordan's computational proof to homogeneous polynomials in three variables.
- Therefore if " S " is any set of homogeneous polynomials we may reasonably speak of
- Similarly, a projective variety is the projectivization of the zero set of a collection of homogeneous polynomials.
- Let I ( Y ) be the homogeneous ideal, generated by the homogeneous polynomials vanishing on Y.
- One can show that f is a homogeneous polynomial of degree n, therefore it can be written as
- Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor.
- One example is the close relationship between homogeneous polynomials and projective varieties . ( cf . homogeneous coordinate ring .)
- In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables.
- A variety is projective if it is defined in some projective space by homogeneous polynomials ( with coefficients in ).
- When all nonzero coefficients ( including the leading one ) appear as variables, these are homogeneous polynomials of respective degrees 2, 4 and 6.
- A "'Binomial number "'is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial.
- One might ask, since the homogeneous polynomials are not really functions on P ( " V " ), what are they, geometrically speaking?
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