On propagation of equational constraints in CAD-based quantifier elimination

Collins [4] observed that quantifier elimination problems often have equational constraints, and he asserted that such constraints can be used to reduce the projection sets required for cylindrical algebraic decomposition (cad) based quantifier elimination. This paper follows on from [11], and validates the use of a semi-restricted equational projection scheme throughout the projection phase of cad. The fully restricted projection scheme as originally proposed in [4] is proved valid for four variable problems under certain conditions.

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