Multivariate discriminant and iterated resultant
نویسندگان
چکیده
منابع مشابه
Resultant and Discriminant of Polynomials
This is a collection of classical results about resultants and discriminants for polynomials, compiled mainly for my own use. All results are well-known 19th century mathematics, but I have not investigated the history, and no references are given. 1. Resultant Definition 1.1. Let f(x) = anx n + · · ·+ a0 and g(x) = bmx + · · ·+ b0 be two polynomials of degrees (at most) n and m, respectively, ...
متن کاملThe Univariate Discriminant via the Sylvester Resultant
Remark 1.2 The Fundamental Theorem of Algebra enters in the very last inequality: the fact that having d distinct roots implies that Res(d,d−1)(f, f ) 6= 0. Later we will see a refinement of the above theorem giving a positive lower bound even when Res(d,d−1)(f, f )=0. ⋄ A key result we’ll need is the following algebraic identity. Lemma 1.3 Following the notation of Theorem 1.1, we have Res(d,d...
متن کاملMultivariate subresultants using Jouanolou’s resultant matrices
Earlier results expressing multivariate subresultants as ratios of two subdeterminants of the Macaulay matrix are extended to Jouanolou’s resultant matrices. These matrix constructions are generalizations of the classical Macaulay matrices and involve matrices of significantly smaller size. Equivalence of the various subresultant constructions is proved. The resulting subresultant method improv...
متن کامل0 Explicit Formulas for the Multivariate Resultant
We present formulas for the multivariate resultant as a quotient of two determinants. They extend the classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the given polynomials and coefficients of their Bezoutian. These formulas can also be viewed as an explicit computation of the morphisms and the determinant of a result...
متن کاملOn the Complexity of the Multivariate Resultant
The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the system’s coefficients which vanishes if and only if the system is satisfiable). In this paper, we investigate the complexity of computing the multivariate resul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2016
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-016-5586-0