Abstract
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.
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Kartashova, E., McCallum, S. (2007). Quantifier Elimination for Approximate Factorization of Linear Partial Differential Operators. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds) Towards Mechanized Mathematical Assistants. MKM Calculemus 2007 2007. Lecture Notes in Computer Science(), vol 4573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73086-6_9
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DOI: https://doi.org/10.1007/978-3-540-73086-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73083-5
Online ISBN: 978-3-540-73086-6
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