Nonlinear control system design by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Computing in the field of complex algebraic numbers
Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
On propagation of equational constraints in CAD-based quantifier elimination
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Solution formula construction for truth invariant cad's
Solution formula construction for truth invariant cad's
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computation with semialgebraic sets represented by cylindrical algebraic formulas
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Variant quantifier elimination
Journal of Symbolic Computation
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Cylindrical algebraic formulas are an explicit representation of semialgebraic sets as finite unions of cylindrically arranged disjoint cells bounded by graphs of algebraic functions. We present a version of the Cylindrical Algebraic Decomposition (CAD) algorithm customized for solving systems of polynomial equations and inequalities over semialgebraic sets given in this representation. The algorithm can also be used to solve conjunctions of polynomial conditions in an incremental manner. We show application examples and give an empirical comparison of incremental and direct CAD computation.