Details:
Title  Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases  Author(s)  Patrizia M. Gianni, Ferdinando Mora  Type  Article in Conference Proceedings  Abstract  This paper, together with the application to the present problem of an algorithm by Gianni that computes the radical of a Odimensional ideal after a "generic" change of coordinates, a different approach, based on her "splitting algorithm", to compute solutions of systems of polynomial equations without the need of polynomial factorisations has been proposed by D,Duval ([DUV]); also her algorithm should be simplified by a "generic" change of coordinates.
The algorithms discussed in this paper are implemented in SCRATCHPAD TT.
In the first section we recall some wellknown properties of Gröbner bases and properties on the structure of Gröbner bases of zerodimensional ideals from [GTZ]; in the second section we recall the Gröbner basis algorithm for solving systems of algebraic equations.
The original results are contained in Sections 3 to 5; in Section 3 we take advantage of the obvious fact that density can be controlled performing "small" changes of coordinates: we show that such approach is possible during a Gröbner basis computation, in such a way that computations done before a change of coordinates are valid also after it; in Section 4 we propose a "linear algebra" approach to obtain the Gröbner basis w.r.t. the lexicographical ordering from the one w.r.t. the totaldegree ordering; in Section 5, we present a zerodimensional radical algorithm and show how to apply it to the present problem. 
Language  English  Pages  247257  Year  1987  Edition  0  Translation 
No  Refereed 
No 
