#14401: Arithmetic functions should be methods of Sage integers
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Reporter: kedlaya | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.4
Component: number theory | Resolution:
Keywords: arithmetic functions | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by kedlaya):
I agree that the notion is too broad, but not in the way you have in mind:
in Python, one generally tries to avoid clogging up the global namespace
with things that really should be member functions of a particular class.
So if I were starting from scratch, I would strongly consider implementing
these functions exclusively as member functions of Sage integers; but I
don't think it's appropriate to move in that direction now.
In any case, this case is much more special than the general discussion,
because arithmetic functions are distinguished by the property of
multiplicativity: if {{{gcd(m,n) == 1}}} then {{{f(m*n) = f(m)*f(n)}}}. So
in a sense, they are more deeply linked to the class of integers than,
say, the binomial or factorial functions.
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Ticket URL: <http://trac.sagemath.org/ticket/14401#comment:7>
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