Simultaneous elimination by using several tools from real algebraic geometry
There are several methods in computer algebra to eliminate variables: Gröbner bases, resultants, Ritt-characteristic sets, etc. This paper presents two new elimination procedures for two particular problems: The simultaneous elimination of one variable from several polynomial that is based in a linear-algebra method to compute the degree of the gcd of several univariate polynomials over an integral domain, called \textit{S. Barnett}'s method [Proc. Camb. Philos. Soc. 70, 263-268 (1971; Zbl 0224.15018)], and the simultaneous elimination of several variables in several equations containing a Pham system (a zero-dimensional polynomial system with very good parameter specialization properties) that is based on Hermite's method. The extension of the technique above to more general systems is difficult because it depends on the existence of the universal base for a quotient ring.
scientific article; zbMATH DE number 1369540
scientific article