منابع مشابه
Ore 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...
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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...
متن کاملSubresultants Under Composition
It is a well known fact that the resultants are invariant under translation. We extend this fact to arbitrary composition (where a translation is a particular composition with a linear monic polynomial), and to arbitrary subresultants (where the resultant is the 0-th subresultant).
متن کاملNew Structure Theorem for Subresultants
We give a new structure theorem for subresultants precising their gap structure and derive from it a new algorithm for computing them. If d is a bound on the degrees and τ a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d2) arithmetic operations and size of intermediate computations 2τ . The key idea is to precise the relations between the successive Sy...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.11.004