Fix iterators for free inverse semigroups (issue #536) and some new methods for free inverse semigroups #545
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added 2 commits
September 28, 2018 18:03
This commit removes the previous iterator code for free inverse semigroups. The code did not function as it was intended. If I understand it correctly it was attempting to enumerate canonical forms for elements of the free inverse semigroup, which are words of the form: w_1 w_1 ^ -1 w_2 w_2 ^ -1 ... w_k w_k ^ -1 u where w_1, w_2, ..., w_k, u are words in the free group with the same number of generators as the free inverse semigroup. The previous approach (when fixed) essentially iterated through all such expressions. Unfortunately, distinct expressions of the above form do not yield distinct elements of the free inverse semigroup. In fact, of the first 10,000 values iterated through, there were only 119 distinct elements. In this commit, I have: 1. Fixed (I think) the iterator code, then realised it doesn't work. 2. Commented the iterator code out, in case it can be fixed later. 3. Added methods for Random, \<, and, ChooseHashFunction for free inverse semigroups and their elements. 4. Tweaked the doc and comments slightly. 5. Add some missing HasIsFinite and not IsFinite to Green's classes. 6. FreeInverseSemigroups know they are infinite now.
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@wilfwilson please review when you have a moment |
wilfwilson
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I think that this resolves Issue #536.
This PR removes the previous iterator code for free inverse semigroups. The code did not function as it was intended. If I understand it correctly it was attempting to enumerate canonical forms for elements of the free inverse semigroup, which are words of the form:
where w_1, w_2, ..., w_k, u are words in the free group with the same number of generators as the free inverse semigroup. The previous approach (when fixed) essentially iterated through all such expressions. Unfortunately, distinct expressions of the above form do not yield distinct elements of the free inverse semigroup. In fact, of the first 10,000 values iterated through, there were only 119 distinct elements.
In this PR, I have:
inverse semigroups and their elements.
FreeInverseSemigroups belong toIsEnumerableSemigroupRep