#18758: Allow actions of a parent on itself
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Reporter: SimonKing | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: coercion | Resolution:
Keywords: actions on itself | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #18756 | Stopgaps:
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Comment (by SimonKing):
I had a look at sage.combinat, and it turns out that the situation is not
sooooo bad as I thought.
1. `Permutation` needs to be sanitised. It inherits from `Element`. Since
here I plan to introduce a default `Element.__mul__` using coercion model,
`Permutation.__mul__` needs to be removed, and instead we need an action.
It would be easy to implement, and I bet it is faster.
2. `Word` does not even inherit from `Element`, but it mimics the element-
parent scheme (by providing a cdef `_parent` attribute and a `parent()`
method). It should be possible to determine the result of multiplication
by looking at the involved parents. Hence:
- It would be a good idea to implement something like pushouts for
families of words. Thus:
- It would make sense to have a `WordFunctor` construction functor from
`Sets()` to an appropriate category. The appropriate category could be
`Monoids()` in the case of finite or infinite words, but could be `Sets()`
in the case of "words avoiding 12" and those things (i.e., the product of
two pattern avoiding words is not necessarily pattern avoiding).
Then, one could finally take advantage of Sage's coercion framework for
words.
I suggest to sanitise Permutation here, but keep Word for a later ticket.
--
Ticket URL: <http://trac.sagemath.org/ticket/18758#comment:9>
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