×

Counting solutions of polynomial systems via iterated fibrations. (English) Zbl 1180.14053

The counting polynomial for a system of polynomial equations and inequalities in affine or projective space is defined via a decomposition of the solution set into subsets that can be defined by triangular-like systems, in the sense of J. M. Thomas [Differential systems. AMS Coll. Publ. 21 (1937; JFM 63.0438.03)]. Its properties are similar to those of the Hilbert polynomial: its degree is the dimension of the solution set, and if the number of solution is finite, then the polynomial is the number of solutions.

MSC:

14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14D06 Fibrations, degenerations in algebraic geometry
12Y05 Computational aspects of field theory and polynomials (MSC2010)
13P99 Computational aspects and applications of commutative rings
14Q99 Computational aspects in algebraic geometry

Citations:

JFM 63.0438.03
PDFBibTeX XMLCite
Full Text: DOI