#14249: There should be no need to have _an_element_ implement to multiply
elements
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Reporter: SimonKing | Owner: robertwb
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: coercion | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Simon King | Merged in:
Dependencies: #14264 | Stopgaps:
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Comment (by nbruin):
Isn't it a logical flaw that there should even be elements for an action
to exist? I think it's entirely possible to have a group acting on an
empty set. In fact, in number theory these things often arise. If C is a
smooth projective genus 1 curve then it is a torsor under its jacobian E.
This gives a functorial way for E(k) to act on C(k), for any extension k
of the field of definition. In the interesting cases, C(k) is empty, so
you have a finitely generated group E(k) acting on the empty set C(k).
This particular scenario isn't particularly relevant for the coercion
framework, but it does show that actions on empty sets are natural to
consider, so if we're not supporting that, there may be something wrong
with our model.
Can't we just ditch the sanity check (or skip it if an element isn't
easily obtained)?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14249#comment:2>
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