#9819: Add a default gcd and lcm methods for fields
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Reporter: lftabera | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.6.2
Component: algebra | Keywords: lcm, gcd, fields
Author: Luis Felipe Taberea | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
Replying to [comment:3 mstreng]:
> related ticket with different proposal: #10771
I wouldn't say that it is a different proposal. #10771 treats the case of
fields that happen to be the fraction field of a unique factorization
domain. In this case, one can do better than to return either 0 or 1.
However, #10771 does not consider the case of fields that are no fraction
fields, or are fraction fields of rings that do not provide lcm and gcd. I
suggest that for that purpose, one should implement gcd and lcd as element
methods of the category of `Fields()`. That would also solve the problem
that `IntegerMod_int` does not derive from `FieldElement`.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9819#comment:4>
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