#13200: Add a function for computing Dedekind sums
-------------------------------------+--------------------------------------
Reporter: fredrik.johansson | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: number theory | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Frédéric Chapoton,
Travis Scrimshaw
Authors: Fredrik Johansson | Merged in:
Dependencies: #13199 | Stopgaps:
-------------------------------------+--------------------------------------
Changes (by tscrim):
* status: needs_info => needs_review
Old description:
> The patch adds dedekind_sum() to arith.py, wrapping the FLINT
> implementation.
>
> Pari is also exposed (inefficiently, using the gp interface) for
> reference purposes. Note that FLINT and Pari return different results
> when gcd(p,q) != 1. The Dedekind is usually simply not defined in this
> case. If anyone knows a use for Dedekind sums with gcd(p,q) != 1, and a
> reason to prefer one definition over the other, I would be interested in
> hearing about it.
>
> We could, alternatively, check that gcd(p,q) = 1 and otherwise return 0
> or raise an exception (this would add a bit of overhead).
>
> The patch depends on #13199 for a library file added there.
New description:
The patch adds dedekind_sum() to arith.py, wrapping the FLINT
implementation.
Pari is also exposed (inefficiently, using the gp interface) for reference
purposes. Note that FLINT and Pari return different results when gcd(p,q)
!= 1. The Dedekind is usually simply not defined in this case. If anyone
knows a use for Dedekind sums with gcd(p,q) != 1, and a reason to prefer
one definition over the other, I would be interested in hearing about it.
We could, alternatively, check that gcd(p,q) = 1 and otherwise return 0 or
raise an exception (this would add a bit of overhead).
The patch depends on #13199 for a library file added there.
----
Apply:
* [attachment:trac_13200_dedekind_sum_v2.patch]
* [attachment:trac_13200-dedekind_sum-review-ts.patch]
--
Comment:
Sorry about that. Here they are.
Apply: trac_13200_dedekind_sum_v2.patch, trac_13200-dedekind_sum-review-
ts.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13200#comment:8>
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