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Methodologies of Symbolic Computation

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Artificial Intelligence and Symbolic Computation (AISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11110))

Abstract

The methodologies of computer algebra are about making algebra (in the broad sense) algorithmic, and efficient as well. There are ingenious algorithms, even in the obvious settings, and also mechanisms where problems are translated into other (generally smaller) settings, solved there, and translated back. Much of the efficiency of modern systems comes from these translations. One of the major challenges is sparsity, and the complexity of algorithms in the sparse setting is often unknown, as many problems are NP-hard, or much worse.

In view of this, it is argued that the traditional complexity-theoretic method of measuring progress has its limits, and computer algebra should look to the work of the SAT community, with its large families of benchmarks and serious contests, for lessons.

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Notes

  1. 1.

    This analysis is mostly taken from [9, 10], but with one change (originally an error, but it makes the point better): \(-21\) instead of \(+21\) for the trailing coefficient of B.

  2. 2.

    The probability of a “random” irreducible polynomial f remaining irreducible modulo p is \(1/\deg (f)\).

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Acknowledgements

I am grateful to Russell Bradford, Akshar Nair, Zak Tonks and the AISC 2018 organisers for useful comments and corrections. As always, I am grateful to David Carlisle for advice.

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Authors and Affiliations

  1. University of Bath, Bath, UK

    James Davenport

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  1. James Davenport
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Correspondence to James Davenport .

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Editors and Affiliations

  1. University of Edinburgh, Edinburgh, United Kingdom

    Jacques Fleuriot

  2. Beihang University, Beijing, China

    Dongming Wang

  3. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Jacques Calmet

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Davenport, J. (2018). Methodologies of Symbolic Computation. In: Fleuriot, J., Wang, D., Calmet, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2018. Lecture Notes in Computer Science(), vol 11110. Springer, Cham. https://doi.org/10.1007/978-3-319-99957-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-99957-9_2

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