Multivariate subresultants in roots
نویسندگان
چکیده
منابع مشابه
Multivariate 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 کاملResultants and Subresultants: Univariate vs. Multivariate Case
It is very well-known that this system has a non-trivial solution if and only if AD −BC equals to zero. One can generalize the previous situation in two different directions. The most classical one is the notion of determinant, which is the condition under which a system of n homogeneous equations in n unknowns A11x1 + A12x2 + . . . + A1nxn = 0 A21x1 + A22x2 + . . . + A2nxn = 0 .. .. ...
متن کاملOre Subresultants in Solutions
The subresultants play a fundamental role in elimination theory and computer algebra. Recently they have been extended to Ore polynomials. They are de ̄ned by an expression in the coe±cients of Ore polynomials. In this paper, we provide another expression for them. This expression is written in terms of the \solutions" of Ore polynomials (in \generic" case). It is a generalization of our previou...
متن کاملar X iv : m at h / 05 01 28 1 v 1 [ m at h . A G ] 1 9 Ja n 20 05 Multivariate Subresultants in Roots
We give a rational expression for the subresultants of n+ 1 generic polynomials f1, . . . , fn+1 in n variables as a function of the coordinates of the common roots of f1, . . . , fn and their evaluation in fn+1. We present a simple technique to prove our results, giving new proofs and generalizing the classical Poisson product formula for the projective resultant, as well as the expressions of...
متن کاملOn the irreducibility of multivariate subresultants Sur l’irréductibilité des sous-résultants multivariés
Let P1, . . . , Pn be generic homogeneous polynomials in n variables of degrees d1, . . . , dn respectively. We prove that if ν is an integer satisfying Pn i=1 di − n + 1−min{di} < ν, then all multivariate subresultants associated to the family P1, . . . , Pn in degree ν are irreducible. We show that the lower bound is sharp. As a byproduct, we get a formula for computing the residual resultant...
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: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.08.016