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homogeneous polynomial sentence in Hindi

"homogeneous polynomial" meaning in Hindihomogeneous polynomial in a sentence
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  • Thus, it generalizes those algebraic curves ( dimension one ), and those algebraic surfaces ( dimension two ), when they are defined by homogeneous polynomials.
  • 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.
  • 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 ).
  • 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.
  • But in 1966 Guy Terjanian constructed a homogeneous polynomial of degree 4 over "'Q "'2 in 18 variables that has no non-trivial zero.
  • 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.
  • In mathematics, specifically in number theory, a "'binomial number "'is an integer which can be obtained by evaluating a homogeneous polynomial containing two terms.
  • 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.
  • 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 ".
  • 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.
  • Explicitly, it is used to define the degree of a polynomial and the notion of homogeneous polynomial, as well as for graded monomial orderings used in formulating and computing Taylor series in several variables.
  • The flag variety may be identified with the complex projective line with homogeneous coordinates and the space of the global sections of the line bundle is identified with the space of homogeneous polynomials of degree on.
  • Let P, Q be two homogeneous polynomials respectively of degree d ^ \ circ ( P ) and d ^ \ circ ( Q ) with N variables, then, the following inequality holds:
  • Let P, Q be two homogeneous polynomials respectively of degree d ^ \ circ ( P ) and d ^ \ circ ( Q ) with N variables, then, the following inequality holds:
  • Any nonzero polynomial may be decomposed, in a unique way, as a sum of homogeneous polynomials of different degrees, which are called the "'homogeneous components "'of the polynomial.
  • Ellipsoids are examples of algebraic varieties; and so, for general rank, symmetric tensors, in the guise of homogeneous polynomials, are used to define projective varieties, and are often studied as such.
  • :If no seven points out of are co-conic, then the vector space of cubic homogeneous polynomials that vanish on ( the affine cones of ) ( with multiplicity for double points ) has dimension two.
  • Despite their name, spherical harmonics take their simplest form in Cartesian coordinates, where they can be defined as homogeneous polynomials of degree \ ell in ( x, y, z ) that obey Laplace's equation.
  • A useful property of the degree reverse lexicographical order is that a homogeneous polynomial is a multiple of the least indeterminate if and only if its leading monomial ( its greater monomial ) is a multiple of this least indeterminate.
  • For each set " S " of homogeneous polynomials, define the zero-locus of " S " to be the set of points in on which the functions in " S " vanish:
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