The Product Replacement Prospector

Authors:
Henrik Bäärnhielm;C. R. Leedham-Green
Affiliations:
Department of Mathematics, University of Auckland, Auckland, New Zealand;School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom
Venue:
Journal of Symbolic Computation
Year:
2012

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Abstract

We present a heuristic extension to the product replacement algorithm, called the Prospector. The aim is to find hopefully good quality 'random' elements with short straight line programs in the given generators. This is achieved by saving the random state at certain points and later restoring it. Statistical tests are employed in order to determine when to save the state. We also give evidence for the surprisingly good effect of using an accelerator. The Prospector has been implemented in Magma, and experimental evidence is provided which indicates that it is a very practical method.