Closures.hpp File Reference

Plans on computing hulls for groupoids. More...

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Detailed Description

Plans on computing hulls for groupoids.

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Closures extended
  • A fundamental operation is the closure of a subset under the operations.
  • This is realised by closure_bydef_grd.
  • An extension is that we obtain the closure *plus* shortest terms in the generators representing the elements of the closure, plus all relations found such that the generated structure is determined by these relations.
  • Easiest for semigroups, where the terms are just words over the generators (for which it should be possible to specify names).
  • Here, starting with a set of elements, which yields the set of words of length 1, we form all words of length 2, determine equalities to the already existing elements and to the new elements, which yield new relations, given that all existing relations have been taken into account; iterating this process expands only the words of full length.
  • For groups we have to take inversion into account; and relations, which for semigroups are equations, that is, 2-element sets of words, can now be simplified to just single words (equal to the neutral element).

Definition in file Closures.hpp.