0. Introduction. The cylindrical algebraic decomposition method of Collins [Arnon et al.] decomposes E’ into regions over which a given polynomial has constant sign by extension of one complicated decomposition of E’-I. We investigate a method which decomposes E’ into sign-invariant regions by combining several but simpler decompositions of E’-‘. As a first. result in thii work we can obtain a decomposition of E*, sign-invariant over a bi-variate polynomial of total degree n, coefficient size d… CONTINUE READING