#16477: implement Dirichlet series
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
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 | 5698ef17c2be57ebe3826737cdba43f12c6bb8d6
Branch: u/rws/16477-1 | Stopgaps:
Dependencies: |
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Comment (by rws):
Replying to [comment:38 vdelecroix]:
Thanks, I accept points 1 and 6 but:
> 2. Why is this new module in `sage.modular`? It makes no sense.
The Dirichlet characters are there too. I don't see why not.
> 3. You should try harder to use `pari` and not `gp`. Since #17631, most
functions are available directly in `pari`.
But not those needing closures, see comment:16 and #18038
> 4. `DirichletSeries` would better inherit from `RingElement`. In that
case, you must not define `__add__`, `__mul__`, `__div__` etc but `_add_`,
`_mul_`, `_div_`. That way you will get benefits from coercion (e.g.
multiplication by scalars). You might have a look to polynomials (in
`sage.rings.polynomials.*` or power series (in
`sage.rings.power_series_*`).
This is clearly a separate ticket.
> 5. What is the purpose of the commented code?
I didn't want to erase useful ideas of the original author.
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Ticket URL: <http://trac.sagemath.org/ticket/16477#comment:39>
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