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Concept
Computational group theory
Summary
In mathematics, computational group theory is the study of
groups by means of computers. It is concerned
with designing and analysing algorithms and
data structures to compute information about groups. The subject
has attracted interest because for many interesting groups
(including most of the sporadic groups) it is impractical
to perform calculations by hand.
Important algorithms in computational group theory include:
the Schreier–Sims algorithm for finding the order of a permutation group
the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration
the product-replacement algorithm for finding random elements of a group
Two important computer algebra systems (CAS) used for group theory are
GAP and Magma. Historically, other systems such as CAS (for character theory) and Cayley (a predecessor of Magma) were important.
Official source
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