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 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 کاملDifferential Resultants and Subresultants
Consider two differential operators L1 = ∑ aid i and L2 = ∑ bjd j with coefficients in a differential field, say C(t) with d = ∂ ∂t for example. If the ai and bj are constants, the condition for the existence of a solution y of L1(y) = L2(y) = 0 is that the resultant in X of the polynomials (in C[X]) ∑ aiX i and ∑ bjX j is zero. A natural question is: how one could extend this for the case of n...
متن کاملSymmetric Subresultants and Applications
Schur’s transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we show that they satisfy a structure theorem which allows us to compute them with a type of Euclidean division. As a consequence, a fast algorithm based on a dich...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1995
ISSN: 0022-4049
DOI: 10.1016/0022-4049(95)90926-c