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  1. Chapter and Conference Paper

    Certifying Irreducibility in \({\mathbb Z}[x]\)

    We consider the question of certifying that a polynomial in \({\mathbb Z}[x]\) or \({\mathbb Q}[x]\) is irreducible. Knowing that a polynomial is irreducible lets us recognise that a quotient ring is actuall...

    John Abbott in Mathematical Software – ICMS 2020 (2020)

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    Chapter and Conference Paper

    \(\mathsf {SC}^\mathsf{2} \) : Satisfiability Checking Meets Symbolic Computation

    Symbolic Computation and Satisfiability Checking are two research areas, both having their individual scientific focus but sharing also common interests in the development, implementation and application...

    Erika Ábrahám, John Abbott, Bernd Becker in Intelligent Computer Mathematics (2016)

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    Chapter and Conference Paper

    What Is New in CoCoA?

    CoCoA is a well-established Computer Algebra System for Computations in Commutative Algebra, and specifically for Gröbner bases.

    John Abbott, Anna Maria Bigatti in Mathematical Software – ICMS 2014 (2014)

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    Chapter and Conference Paper

    Application of Data Assimilation to the UK Air Quality Forecast

    An operational air quality forecasting model based on the Weather Research and Forecasting (WRF) model and the Community Multiscalar Air Quality (CMAQ) model is used to produce a three day forecast for O3, NO2, S...

    Andrea Fraser, John Abbott in Air Pollution Modeling and its Application XXIII (2014)

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    Chapter and Conference Paper

    Integration of Libnormaliz in CoCoALib and CoCoA 5

    libnormaliz is a C++ library for computations with rational cones and affine monoids and CoCoALib/CoCoA-5 offers a general environment for computations in Commutative Algebra. For mutual benefit ...

    John Abbott, Anna Maria Bigatti, Christof Söger in Mathematical Software – ICMS 2014 (2014)

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    Chapter and Conference Paper

    CoCoALib: A C++ Library for Computations in Commutative Algebra... and Beyond

    First released in 1988,CoCoAis a special-purpose system for doing Computations in Commutative Algebra: i.e. it is a system specialized in the algorithmic treatment of polynomials. It is freely available and offer...

    John Abbott, Anna M. Bigatti in Mathematical Software – ICMS 2010 (2010)

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    Chapter and Conference Paper

    Some ideas about fault-tolerant Chinese Remaindering

    We present some algorithms for performing Chinese Remaindering allowing for the fact that one or more residues may be erroneous — we suppose also that an a priori upper bound on the number of erroneous residues i...

    John Abbott in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (1991)

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    Chapter and Conference Paper

    Integration: Solving the Risch differential equation

    We describe the first complete implementation of Davenport's algorithm [Davenport86] for the solution of the Risch differential equation. Our code forms part of a new integration package written in REDUCE which o...

    John Abbott in Eurocal '87 (1989)