#17586: Inconsistency in DirichletGroup(1)[0].bernoulli(1)
-------------------------------------+-------------------------------------
Reporter: pbruin | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.5
Component: modular forms | Resolution:
Keywords: Dirichlet | Merged in:
character Bernoulli number | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | ada9c0109f1eefff8164278fbc15440724cbf31b
u/pbruin/17586-bernoulli_1 | Stopgaps:
Dependencies: |
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Changes (by {'newvalue': u'Peter Bruin', 'oldvalue': ''}):
* status: new => needs_review
* commit: => ada9c0109f1eefff8164278fbc15440724cbf31b
* branch: => u/pbruin/17586-bernoulli_1
* author: => Peter Bruin
Old description:
> If `chi` is the trivial Dirichlet character, then `chi.bernoulli(1)`
> returns different results depending on the algorithm:
> {{{
> sage: chi = DirichletGroup(1)[0]
> sage: chi.bernoulli(1) # algorithm='recurrence'
> -1/2
> sage: chi.bernoulli(1, algorithm='definition', cache=False)
> 1/2
> }}}
> The documentation is consistent with the answer `1/2`. The answer `-1/2`
> can be explained as being the result of
> {{{
> sage: bernoulli(1)
> -1/2
> }}}
> since the `bernoulli()` function returns the traditional "first Bernoulli
> numbers".
>
> We should decide which convention to use, and update the documentation if
> necessary.
>
> Discussion on sage-nt: https://groups.google.com/forum/#!topic/sage-
> nt/n5wUmDJHCto
New description:
If `chi` is the trivial Dirichlet character modulo 1, then
`chi.bernoulli(1)` returns different results depending on the algorithm:
{{{
sage: chi = DirichletGroup(1)[0]
sage: chi.bernoulli(1) # algorithm='recurrence'
-1/2
sage: chi.bernoulli(1, algorithm='definition', cache=False)
1/2
}}}
The documentation is consistent with the answer `1/2`. The answer `-1/2`
can be explained as being the result of
{{{
sage: bernoulli(1)
-1/2
}}}
since the `bernoulli()` function returns the traditional "first Bernoulli
numbers".
This ticket changes the method `DirichletCharacter.bernoulli()` so that it
always returns `1/2` in this case, and expands the documentation.
Discussion on sage-nt: https://groups.google.com/forum/#!topic/sage-
nt/n5wUmDJHCto
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17586#comment:2>
Sage <http://www.sagemath.org>
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