Results 21 to 30 of about 40,102 (181)

New heuristic to choose a cylindrical algebraic decomposition variable ordering motivated by complexity analysis [PDF]

Computer Algebra in Scientific Computing, 2022
. It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm.
Tereso del R'io, M. England
semanticscholar   +2 more sources

Optimising Problem Formulation for Cylindrical Algebraic Decomposition [PDF]

, 2013
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere.
Matthew England, Bradford, Russell, David Wilson, Russell Bradford, James H. Davenport, Wilson, David, England, Matthew, Davenport, James H   +7 more
core   +5 more sources

Cylindrical Algebraic Decomposition With Frontier Condition

, 2023
A Cylindrical Algebraic Decomposition (CAD) is a decomposition of R^n into a finite collection of semialgebraic cells. A CAD satisfies the "frontier condition" if, for every cell C, there is a collection of cells of the decomposition whose union is the ...
Baker, Hollie
core   +2 more sources

Cylindrical Algebraic Decomposition in Coq/Rocq

Proceedings of the 15th ACM SIGPLAN International Conference on Certified Programs and Proofs
The Cylindrical Algebraic Decomposition (CAD in short) is a fundamental tool of semi-algebraic geometry. It is a doubly-exponential time algorithm that enables most famously to eliminate quantifiers from a formula in the theory of real closed fields.
Quentin Vermande
semanticscholar   +3 more sources

Truth table invariant cylindrical algebraic decomposition [PDF]

Journal of Symbolic Computation, 2016
When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae
Bradford, Russell, Bradford, R., McCallum, Scott, Wilson, D., Davenport, J. H., England, Matthew; id_orcid, McCallum, S., Davenport, James H., Wilson, David, England, Matthew   +9 more
core   +4 more sources

Towards Incremental Cylindrical Algebraic Decomposition in Maple [PDF]

CoRR, 2018
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals.
England, Matthew; id_orcid, Cowen-Rivers, Alexander   +1 more
core   +5 more sources

Using Machine Learning to Improve Cylindrical Algebraic Decomposition [PDF]

Mathematics and Computer Science, 2018
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in the size of the
Zongyan Huang, M. England, D. Wilson, J. Davenport, Lawrence Charles Paulson   +4 more
semanticscholar   +3 more sources

Speeding up cylindrical algebraic decomposition by Gröbner bases [PDF]

, 2012
Gröebner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities.
D. J. Wilson, David J. Wilson, Russell J. Bradford, R. J. Bradford, Bradford, Russell J, Wilson, David J, J. H. Davenport, James H. Davenport, Davenport, James H   +8 more
core   +4 more sources

A cluster-based cylindrical algebraic decomposition algorithm

Journal of Symbolic Computation, 1988
Let A ⊂ Z [x1,000, xr be a finite set. An A-invariant cylindrical algebraic decomposition (cad) is a certain partitlon of r-dlmensional euclidean space Er into semi-algebralc cells such that the value of each Ai ∈ A has constant sign (positive, negative,
Arnon, Dennis S.
core   +3 more sources

Cylindrical Algebraic Decomposition - an Introduction

, 1995
In this report we give an introduction to a constructive way of treating systems of polynomial equations and inequalities. We present a method called cylindrical algebraic decomposition (CAD) discovered 1973 by Collins.
Jirstrand, Mats
core   +2 more sources