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 12 (d + log n) 2 log n) . Preliminary experiments suggest that the method is useful in practice.

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