Constructing Sylvester-type resultant matrices using the Dixon formulation
نویسندگان
چکیده
منابع مشابه
Constructing Sylvester-type resultant matrices using the Dixon formulation
A new method for constructing Sylvester-type resultant matrices for multivariate elimination is proposed. Unlike sparse resultant constructions discussed recently in the literature or the Macaulay resultant construction, the proposed method does not explicitly use the support of a polynomial system in the construction. Instead, a multiplier set for each polynomial is obtained from the Dixon for...
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Efficient algorithms are derived for computing the entries of the Bezout resultant matrix for two univariate polynomials of degree n and for calculating the entries of the Dixon–Cayley resultant matrix for three bivariate polynomials of bidegree (m, n). Standard methods based on explicit formulas require O(n3) additions and multiplications to compute all the entries of the Bezout resultant matr...
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The behavior of the Cayley-Dixon resultant construction and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substituted by a univariate polynomial in a distinct variable. It is shown that a Dixon projection operator (a multiple of the resultant) of the composed system can be expressed as a power of the...
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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...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2004
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2003.11.003