Explicit formulas for the multivariate resultant
نویسندگان
چکیده
منابع مشابه
0 Explicit Formulas for the Multivariate Resultant
We present formulas for the multivariate resultant as a quotient of two determinants. They extend the classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the given polynomials and coefficients of their Bezoutian. These formulas can also be viewed as an explicit computation of the morphisms and the determinant of a result...
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Let P be a system of n linear nonhomogeneous generic sparse ordinary differential polynomials in n − 1 differential indeterminates. In this paper, differential resultant formulas are presented to compute, whenever it exists, the sparse differential resultant ∂Res(P) introduced by Li, Gao and Yuan in [12], as the determinant of the coefficient matrix of an appropriate set of derivatives of diffe...
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In 1979, building on S. Lie’s theory of symmetries of (partial) differential equations, P.J. Olver formulated inductive formulas which are appropriate for the computation of the prolongations of an infinitesimal Lie symmetry to jet spaces, for an arbitrary number n ≥ 1 of independent variables (x, . . . , x) and for an arbitrary number m ≥ 1 of dependent variables (y, . . . , y). This paper is ...
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The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the system’s coefficients which vanishes if and only if the system is satisfiable). In this paper, we investigate the complexity of computing the multivariate resul...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2001
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00145-6