Solving zero-dimensional algebraic systems

Authors:
D. Lazard
Affiliations:
LITP, Institut Blaise Pascal, Boite 168, 4, place Jussieu, F-75252 Paris Cedex 05, France
Venue:
Journal of Symbolic Computation
Year:
1992

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Abstract

It is shown that a good output for a solver of algebraic systems of dimension zero consists of a family of ''triangular sets of polynomials''. Such an output is simple, readable and contains all information which may be wanted. Different algorithms are described for handling triangular systems and obtaining them from Grobner bases. These algorithms are practicable, and most of them are polynomial in the number of solutions.