Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Mechanical geometry theorem proving
Mechanical geometry theorem proving
The complexity of linear problems in fields
Journal of Symbolic Computation
Quantifier elimination: Optimal solution for two classical examples
Journal of Symbolic Computation
An improvement of the projection operator in cylindrical algebraic decomposition
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Simplification of quantifier-free formulae over ordered fields
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Guaranteed solution formula construction
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Efficient projection orders for CAD
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The complexity of quantifier elimination and cylindrical algebraic decomposition
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Automatic discovery of geometry theorems using minimal canonical comprehensive Gröbner systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
A package for solving parametric polynomial systems
ACM Communications in Computer Algebra
Dominance in the family of Sugeno--Weber t-norms
Fuzzy Sets and Systems
New domains for applied quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Robust stability for parametric linear ODEs
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
A local Fourier convergence analysis of a multigrid method using symbolic computation
Journal of Symbolic Computation
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This paper provides a starting point for generic quantifier elimination by partial cylindrical algebraic decomposition pcad. On input of a first-order formula over the reals generic pcad outputs a theory and a quantifier-free formula. The theory is a set of negated equations in the free variables of the input formula. The quantifier-free formula is equivalent to the input for all parameter values satisfying the theory. For obtaining this generic elimination procedure, we derive a generic projection operator from the standard Collins--Hong projection operator. Our operator particularly addresses formulas with many parameters thus filling a gap in the applicability of pcad. It restricts decomposition to a reasonable subset of the entire space. The above-mentioned theory describes this subset. The approach is compatible with other improvements in the framework of pcad. It turns out that the theory contains assumptions that are easily interpretable and that are most often non-degeneracy conditions. The applicability of our generic elimination procedure significantly extends that of the corresponding regular procedure. Our procedure is implemented in the computer logic system redlog.