Algebraic decomposition of regular curves

Authors:
Stefan Arnborg;Huichun Feng
Affiliations:
Department of Numerical Analysis and Computing Science The Royal Institute of Technology S-100 44 Stockholm, Sweden;Department of Numerical Analysis and Computing Science The Royal Institute of Technology S-100 44 Stockholm, Sweden
Venue:
Journal of Symbolic Computation
Year:
1988

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Abstract

The cylindrical algebraic decomposition method decomposes E^r into regions over which a given polynomial has constant sign by extension of one complicated decomposition of E^r^-^1. We investigate a method which decomposes E^r into sign-invariant region by combining several but simpler decompositions of E^r^-^1. We can obtain a sign-invariaat decomposition of E^2 defined by a bivariate polynomial of total degree n and coefficient size d in time O(n^1^2 (d + log n)^2 log n). Preliminary experiments suggest that the method is useful in practice.