#16477: implement Dirichlet series
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-wishlist
Component: number theory | Resolution:
Keywords: moebius, zeta, | Merged in:
sigma, euler_phi, euler | Reviewers:
Authors: Jonathan Hanke, | Work issues: use pari, g.f. input
Ralf Stephan | Commit:
Report Upstream: N/A | 949082ca407de7df7ae2ce31ecfad4f5d21f3ffa
Branch: public/dirichlet- | Stopgaps:
series |
Dependencies: #18038, #18041 |
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Comment (by jj):
Just for your information:
I started some preliminary (poc) test implementation of arithmetic
functions (no tests/documentation etc). The first idea was to use symbolic
expressions but they don't work well together with sums which are
absolutely crucial for operations on arithmetic functions...
The test implementation is available on u/jj/arith_functions:
http://git.sagemath.org/sage.git/commit/?id=526e1ae40f94cff95e5dc6926208b831643edfb4
Here is a simple example:
{{{
sigma3 = ArithmeticFunction(lambda n: sigma(n,3), lambda n,_:
"sigma({},3)".format(n), lambda n,_:
"\\sigma_{{3}}\\left({}\\right)".format(n))
sigma3^2
show(sigma3^2)
(sigma3^2)(5)
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16477#comment:33>
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