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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 of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This motivates our definition of a Truth… (More)

- James H. Davenport, Russell J. Bradford, Matthew England, David J. Wilson
- 2012 14th International Symposium on Symbolic and…
- 2012

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 is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between… (More)

- Russell J. Bradford, James H. Davenport, Matthew England, David J. Wilson
- MKM/Calculemus/DML
- 2013

This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract. Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential… (More)

A new algorithm to compute cylindrical algebraic decompo-sitions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of… (More)

- David J. Wilson, Russell J. Bradford, James H. Davenport, Matthew England
- Mathematics in Computer Science
- 2014

Cylindrical Algebraic Decompositions (CADs) have been studied since their creation as a tool for working with semi-algebraic sets and eliminating quantifiers of the reals. In this paper we are concerned with Cylindrical Algebraic Sub-Decompositions (sub-CADs), defined as subsets of CADs sufficient to describe the solutions for given formulae. We discuss… (More)

- Matthew England
- ArXiv
- 2013

Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications within algebraic geometry and beyond. We recently reported on a new implementation of CAD in Maple which implemented the original algorithm of Collins and the subsequent improvement to projection by McCallum. Our implementation was… (More)

- Matthew England
- ArXiv
- 2013

This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found… (More)

(2014) Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract. Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in… (More)

- Matthew England, Russell J. Bradford, James H. Davenport, David J. Wilson
- MKM/Calculemus/DML
- 2013

This version is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract. 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. Typical examples include the… (More)