#16477: implement Dirichlet series
-------------------------------------+-------------------------------------
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: documentation,
Ralf Stephan | elementary operations
Report Upstream: N/A | Commit:
Branch: u/rws/16477-1 | 7f254972105d6555d1a1d209fe17e65beec557db
Dependencies: | Stopgaps:
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Comment (by rws):
Replying to [comment:52 vdelecroix]:
> 8. How do I get the coefficients of the Dirichlet L functions obtained
with the command `dirichlet_L(3,2,s)`?
Analogous to polynomial coefficients, now added as example:
{{{
sage: D=dirichlet_series(dirichlet_L(3,2,s))
sage: D.list()
[1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1]
sage: D.list(5)
[1, -1, 0, 1, -1]
}}}
> 10. In `__mul__` I do not understand
> {{{
> R = self.base_ring()
> try:
> _ = RR(other)
> }}}
> Did you want to write `R(other)`?
I haven't looked extensively at Jon's code as long as it worked.
> You should really use coercion here (i.e. the item 4 in [comment:38
comment:38]) or do stronger type check such as {{{parent(other) is
self.base_ring()}}}.
> 11. This should work
> {{{
> sage: D1 = dirichlet_series([1,1,1])
> sage: D1 + 1
> Traceback (most recent call last):
> ...
> }}}
No, this is a feature request. With this ticket you can do as well:
{{{
sage: D1 = dirichlet_series([1,1,1])
sage: one = dirichlet_series(1)
sage: D1 + one
2 + 1/(2^s) + 1/(3^s) + O(4^(-s))
}}}
> 12. What is the purpose of this nested `MaskFunction` class?
As this is only of developer interest I added at l.156:
{{{
# the specific form of the factors returned by Maxima
# (see ticket #18081) makes masking necessary
arg = dirichlet_series._mask_exp_factors(arg)
}}}
The rest should be addressed with the latest commit.
--
Ticket URL: <http://trac.sagemath.org/ticket/16477#comment:54>
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