Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
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This paper looks at the feasibility of applying the quantifier elimination program QEPCAD-B to obtain quantifier-free conditions for the approximate factorization of a simple hyperbolic linear partial differential operator (LPDO) of order 2 over some given bounded rectangular domain in the plane. A condition for approximate factorization of such an operator to within some given tolerance over some given bounded rectangular domain is first stated as a quantified formula of elementary real algebra. Then QEPCAD-B is applied to try to eliminate the quantifiers from the formula. While QEPCAD-B required too much space and time to finish its task, it was able to find a partial solution to the problem. That is, it was able to find a nontrivial quantifier-free sufficient condition for the original quantified formula.