Guaranteed solution formula construction

Quantifier elimination transfornls i1 description of it semialgebraic set as a formula with quantified variables into a dcscrilAion of t,llc set as a qant,ificr-free forniula. Quant,ifier clirnination by cylindrical algebraic di:c.omI)ositioIl (C-AD) does this via an intermediate representation of the seniialgebraic set as a CAD. A quantifier-free formula representation of t.lic set is then construct,4 frown t.liis CAD. One dcsirablc property of the CAD-l-xwtl quant,ificr clirnination algorithm is its abilit,y to prodwr .simplc solution fornnll;Ls via methods such >Ls that. of [7]. These nlet.hods require that the CAD produced as an int,ernlediate representation bc yi,ojcction-flefinclble, which is not. the cast for all cluant,ificr-elimina.t,i~n problems. This paper presents an efficient method for transforrning an xrbitrar? C!-%D int.o a l)rojection-defirlable CAD: thereb?; rendering smple solution fornlula construction nwthods applicable lo all quantifier cliniination prol)lcIns.