Results 11 to 20 of about 40,102 (181)
Regular cylindrical algebraic decomposition [PDF]
Journal of the London Mathematical Society, 2018 We show that a strong well‐based cylindrical algebraic decomposition P of a bounded semi‐algebraic set S is a regular cell decomposition, in any dimension and independently of the method by which P is constructed.
J. Davenport +2 more
semanticscholar +7 more sources
Clustering in the Lazard method for Cylindrical Algebraic Decomposition [PDF]
ACM Communications in Computer Algebra, 2023 Cylindrical Algebraic Decomposition (CAD) is an algorithm originally proposed by Collins in [4]. Given a set of multivariate polynomials, CAD decomposes the multidimensional real space into connected subsets called cells, within which those polynomials ...
Tereso del Río +2 more
semanticscholar +4 more sources
Cylindrical Algebraic Decomposition with Equational Constraints [PDF]
Journal of Symbolic Computation, 2019 Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals.
M. England, R. Bradford, J. Davenport
semanticscholar +7 more sources
Cylindrical algebraic decomposition for nonlinear arithmetic problems
, 2020 Satisfiability modulo theories solving is a technology to solve logically encoded problems for many applications like verification, testing, or planning. Among the many theories that are considered within this logical framework, nonlinear real arithmetic
Gereon Kremer
semanticscholar +4 more sources
Improving the Use of Equational Constraints in Cylindrical Algebraic Decomposition [PDF]
Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, 2015 When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula.
M. England, R. Bradford, J. Davenport
semanticscholar +6 more sources
Computing cylindrical algebraic decomposition via triangular decomposition [PDF]
Proceedings of the 2009 international symposium on Symbolic and algebraic computation, 2009 Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets.
Yang, Lu +7 more
core +3 more sources
Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition [PDF]
Journal of symbolic computation, 2023 In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms.
Lynn Pickering +3 more
semanticscholar +3 more sources
A geometric approach to cylindrical algebraic decomposition
Mathematics of Computation, 2023 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.
Rizeng Chen
semanticscholar +3 more sources
Cylindrical Algebraic Decomposition in Macaulay2
CoRRCylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant.
Corinne Lee +2 more
semanticscholar +3 more sources
Improved Projection for Cylindrical Algebraic Decomposition
Journal of Symbolic Computation, 2001 McCallum’s projection operator for cylindrical algebraic decomposition (CAD) represented a huge step forward for the practical utility of the CAD algorithm.
Brown, Christopher W.
core +3 more sources