61 citations · 109 across the 8 of their papers we have counts for
8 papers
Enhanced CAD-Based Quantifier Elimination With Multiple Equational Constraints
James H. Davenport, Matthew England, Scott McCallum
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present i…
Linear Regression in p-adic metric spaces
Gregory D. Baker, Scott McCallum, Dirk Pattinson
Many real-world machine learning problems involve inherently hierarchical data, yet traditional approaches rely on Euclidean metrics that fail to capture the discrete, branching na…
Iterated Resultants and Rational Functions in Real Quantifier Elimination
James H. Davenport, Matthew England, Scott McCallum +1
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quant…
Validity proof of Lazard's method for CAD construction
Scott McCallum, Adam Parusinski, Laurentiu Paunescu
In 1994 Lazard proposed an improved method for cylindrical algebraic decomposition (CAD). The method comprised a simplified projection operation together with a generalized cell li…
On Lazard's Valuation and CAD Construction
Scott McCallum, Hoon Hong
In 1990 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate…
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…
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…
Quantifier elimination for approximate Beals-Kartashova factorization
Elena Kartashova, Scott McCallum
The only known constructive factorization algorithm for linear partial differential operators (LPDOs) is Beals-Kartashova (BK) factorization \cite{bk2005}. One of the most interest…