Matthew England

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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)
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)
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)
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)
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)
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)
Ruminally undegraded protein (RUP) values of blood meal (n = 2), hydrolyzed feather meal (n = 2), fish meal (n = 2), meat and bone meal, and soybean meal were estimated using an in situ method, an inhibitor in vitro method, and an inhibitor in vitro technique applying Michaelis-Menten saturation kinetics. Degradation rates for in situ and inhibitor in vitro(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)