Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
An improved projection operation for cylindrical algebraic decomposition of three-dimensional space
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An improved projection operation for cylindrical algebraic decomposition (computer algebra, geometry, algorithms)
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
On delineability of varieties in CAD-based quantifier elimination with two equational constraints
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Efficient preprocessing methods for quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Solving polynomial systems over semialgebraic sets represented by cylindrical algebraic formulas
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Theoretical Computer Science
Cylindrical algebraic decompositions for boolean combinations
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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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.