MultiPolynomial Resultant Algorithms

Eecient Algorithms for Multipolynomial Resultant

The multipolynomial resultant of a set of equations is fundamental in quantiier elimination over the elementary theory of real and algebraically closed elds. Earlier algorithms for resultant computation and symbolic elimination are considered slow in practice. In this paper we present eecient algorithms to compute multi-polynomial resultants and demonstrates their use for polynomial manipulatio...

Approximate Polynomial Common Divisor Problem Relates to Noisy Multipolynomial Reconstruction

In this paper, we investigate the hardness of the approximate polynomial common divisor problem, which is regarded as a polynomial analogy of the approximate integer common divisor problem. In order to solve this problem, we present a simple method by using the polynomial lattice reduction algorithm and contain complete theoretical analyses. Further, we propose an improved lattice attack to red...

Laughlin the Probability - Resultant

D-resultant for Rational Functions

In this paper we introduce the D-resultant of two rational functions f(t), g(t) ∈ K(t) and show how it can be used to decide if K(f(t), g(t)) = K(t) or if K[t] ⊂ K[f(t), g(t)] and to find the singularities of the parametric algebraic curve define by X = f(t), Y = g(t). In the course of our work we extend a result about implicitization of polynomial parametric curves to the rational case, which ...

Linear sparse differential resultant formulas

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...