Sparse Resultant of Composed Polynomials I Mixed–Unmixed Case
نویسندگان
چکیده
منابع مشابه
Sparse Resultant of Composed Polynomials IMixed-. Unmixed Case
The main question of this paper is: What happens to sparse resultants under composition? More precisely, let f1, . . . , fn be homogeneous sparse polynomials in the variables y1, . . . , yn and g1, . . . , gn be homogeneous sparse polynomials in the variables x1, . . . , xn. Let fi ◦ (g1, . . . , gn) be the sparse homogeneous polynomial obtained from fi by replacing yj by gj . Naturally a quest...
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The main question of this paper is: What is the dense (Macaulay) resultant of composed polynomials? By a composed polynomial f ◦ (g1, . . . , gn), we mean the polynomial obtained from a polynomial f in the variables y1, . . . , yn by replacing yj by by some polynomial gj . Cheng, McKay and Wang and Jouanolou have provided answers for two particular subcases. The main contribution of this paper ...
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We study systems of three bivariate polynomials whose Newton polygons are scaled copies of a single polygon. Our main contribution is to construct square resultant matrices, which are submatrices of those introduced by Cattani et al. (1998), and whose determinants are nontrivial multiples of the sparse (or toric) resultant. The matrix is hybrid in that it contains a submatrix of Sylvester type ...
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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, ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2002
ISSN: 0747-7171
DOI: 10.1006/jsco.2001.0516