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Cylindrical Algebraic Decomposition With Frontier Condition

Hollie Baker
Dec 2022
摘要
We propose a novel algorithm for computing Cylindrical AlgebraicDecomposition satisfying the frontier condition without preliminary change ofcoordinates, i.e., in the potential presence of blow-ups. Frontier conditionmeans that the frontier of each cell is made up of a union of some other cellsin the decoposition. This construction can be useful for computing topologicalproperties of semialgebraic sets defined by first-order formulas withquantifiers. The algorithm uses a recursion on lexicographic order of cells inthe initial decomposition.
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