37 citations · 96 across the 5 of their papers we have counts for
5 papers
Recent Advances in Real Geometric Reasoning
James H. Davenport, Matthew England
In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which w…
Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
Matthew England, Russell Bradford, James H. Davenport +1
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular…
Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
Matthew England, Russell Bradford, Changbo Chen +3
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advan…
Understanding Branch Cuts of Expressions
Matthew England, Russell Bradford, James H. Davenport +1
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. T…
Program Verification in the presence of complex numbers, functions with branch cuts etc
James H. Davenport, Russell Bradford, Matthew England +1
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there i…