61 citations · 265 across the 12 of their papers we have counts for
12 papers
Using Machine Learning to Improve Cylindrical Algebraic Decomposition
Zongyan Huang, Matthew England, David Wilson +2
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. How…
An implementation of Sub-CAD in Maple
Matthew England, David Wilson
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously…
Using the distribution of cells by dimension in a cylindrical algebraic decomposition
David Wilson, Matthew England, Russell Bradford +1
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independe…
Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting
Matthew England, David Wilson, Russell Bradford +1
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built thro…
A comparison of three heuristics to choose the variable ordering for CAD
Zongyan Huang, Matthew England, David Wilson +2
Cylindrical algebraic decomposition (CAD) is a key tool for problems in real algebraic geometry and beyond. When using CAD there is often a choice over the variable ordering to use…
Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
Zongyan Huang, Matthew England, David Wilson +3
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there i…
Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
R. Bradford, C. Chen, J. H. Davenport +3
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meanin…
Cylindrical Algebraic Sub-Decompositions
D. J. Wilson, R. J. Bradford, J. H. Davenport +1
Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. I…
Truth Table Invariant Cylindrical Algebraic Decomposition
Russell Bradford, James H. Davenport, Matthew England +2
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…
Branch Cuts in Maple 17
M. England, E. Cheb-Terrab, R. Bradford +2
Accurate and comprehensible knowledge about the position of branch cuts is essential for correctly working with multi-valued functions, such as the square root and logarithm. We di…
Cylindrical Algebraic Decompositions for Boolean Combinations
Russell Bradford, James H. Davenport, Matthew England +2
This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs…
Speeding up Cylindrical Algebraic Decomposition by Gröbner Bases
David J. Wilson, Russell J. Bradford, James H. Davenport
Gröbner 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…