In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example...
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Discriminant (redirect from Discriminant of a polynomial)
quadratic form; and more generally, the discriminant of a form, of a homogeneous polynomial, or of a projective hypersurface (these three concepts are essentially...
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s ≠ 0. {\displaystyle s\neq 0.} For example, a homogeneous polynomial of degree k defines a homogeneous function of degree k. The above definition extends...
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elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...
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\lambda z)=\lambda ^{k}f(x,y,z)=0.} A polynomial g(x, y) of degree k can be turned into a homogeneous polynomial by replacing x with x/z, y with y/z and...
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the polynomial that follows it. The dimension of the vector space K [ x 1 , … , x n ] d {\displaystyle K[x_{1},\ldots ,x_{n}]_{d}} of homogeneous polynomial...
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The zero polynomial is homogeneous, and, as a homogeneous polynomial, its degree is undefined. For example, x3y2 + 7x2y3 − 3x5 is homogeneous of degree...
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Resultant (redirect from Polynomial resultant)
and drawing of curves defined by a bivariate polynomial equation. The resultant of n homogeneous polynomials in n variables (also called multivariate resultant...
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quotient by a homogeneous ideal of a multivariate polynomial ring, graded by the total degree. The quotient by an ideal of a multivariate polynomial ring, filtered...
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weight or the degree of the polynomial. The term quasi-homogeneous comes from the fact that a polynomial f is quasi-homogeneous if and only if f ( λ w 1...
4 KB (845 words) - 15:44, 29 October 2021