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The Computer Journal 1993 36(5):432-438; doi:10.1093/comjnl/36.5.432
© 1993 by British Computer Society
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Solving Polynomial Strict Inequalities Using Cylindrical Algebraic Decomposition

S. McCallum *

Department of Computing, School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, Australia 2109

We consider the problem of determining the consistency over the real number of a system of integral polynomial strict inequalities. This problem has applications in geometric modelling. The cylindrical algebraic decomposition (cad) algorithm [2] can be used to solve this problem, though not very efficiently. In this paper we present a less powerful version of the cad algorithm which can be used to solve the consistency problem for conjunctions of strict inequalities, and which runs considerably faster than the original method applied to this problem. In the case that a given conjunction of strict inequalities is consistent, the modified cad algorithm constructs solution points with rational coordinates.

Received October 1992. revised April 1993.

* Department of Computing, School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, Australia 2109


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