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Symbolic Collection using Deep Thought

Published online by Cambridge University Press:  01 February 2010

C. R. Leedham-Green  and
Leonard H. Soicher
C. R. Leedham-Green
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, U.K., C.R.Leedham-Green@qmw.ac.uk
Leonard H. Soicher
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, U.K., L.H.Soicher@qmw.ac.uk

Abstract

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We describe the “Deep Thought” algorithm, which can, among other things, take a commutator presentation for a finitely generated torsion-free nilpotent group G, and produce explicit polynomials for the multiplication of elements of G. These polynomials were first shown to exist by Philip Hall, and allow for “symbolic collection” in finitely generated nilpotent groups. We discuss various practicalissues in calculations in such groups, including the construction of a hybrid collector, making use of both the polynomials and ordinary collection from the left.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 1 , 1998 , pp. 9 - 24
Copyright
Copyright © London Mathematical Society 1998

References

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