#8920: Factor code between words's alphabets and sets/enumerated sets/ordered
sets
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Reporter: hivert | Owner:
sage-combinat
Type: defect | Status:
needs_review
Priority: major | Milestone:
sage-5.7
Component: combinatorics | Resolution:
Keywords: Words, Sets, Cernay2012 | Work issues:
Report Upstream: N/A | Reviewers: Travis
Scrimshaw
Authors: Vincent Delecroix, Stepan Starosta | Merged in:
Dependencies: #13801 | Stopgaps:
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Comment (by tscrim):
Hey Stepan and Vincent,
Replying to [comment:13 tscrim]:
> - I'm still uncomfortable with the change to `is_endomorphism()` since I
would (naively) expect the map `a->a, b->aa, c->aaa` be an endomorphism.
The problem is word morphism automatically sets the codomain based on the
image. As for the mathematics, yes, if it is a proper subset, it is not an
endomorphism, but it naturally extends to one. I believe that having
anything that is naturally extendable to an endomorphism should be
considered an endomorphism by sage via the coercion model. Also in case
you're worried, the above morphism worked with composition.
>
> If a third party agrees with the changes in the patch, then I would
add a warning to `is_endomorphism()` and/or to `WordMorphism` about
defining endomorphisms and add the tests
> {{{
> sage: w = WordMorphism('a->a,b->aa,c->aaa', codomain=Words('abc'))
> sage: w.is_endomorphism()
> True
> sage: w2 = WordMorphism('a->a,b->aa,c->aaa')
> sage: w == w2
> False
> }}}
> However there is one problem with this, and that is `w == w2` returns
`True`. Thus the equality operator will need to be changed to reflect the
dependency on the codomain.
I talked with Nicolas about this, and he agreed with the changes in your
patch, but also said we needed to change the `==` operator to check the
codomain (in particular, we don't want a map `f` to be surjective and `g`
to not be and compare equal because `g` has a larger codomain). This might
be a more general problem, and I'll take a look at it today and let you
know what I find.
Best,[[BR]]
Travis
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8920#comment:14>
Sage <http://www.sagemath.org>
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