Bibliographic Details
| Title: |
A geometric approach to cylindrical algebraic decomposition. |
| Authors: |
Chen, Rizeng1 (AUTHOR) |
| Source: |
Mathematics of Computation. Jul2026, Vol. 95 Issue 360, p2025-2059. 35p. |
| Subjects: |
Geometric approach, Mathematic morphism, Algorithms, Semialgebraic sets, Algebraic geometry, Semianalytic sets |
| Abstract: |
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this paper, we revisit this problem from a more geometric perspective, where the construction of cylindrical algebraic decomposition is related to the study of morphisms between real varieties. It is showed that the geometric fiber cardinality (geometric property) decides the existence of semi-algebraic continuous sections (semi-algebraic property). As a result, all equations can be systematically exploited in the projection phase, leading to a new simple algorithm whose efficiency is demonstrated by experimental results. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
