#17586: Inconsistency in DirichletGroup(1)[0].bernoulli(1)
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.5
Component: modular | Keywords: Dirichlet character Bernoulli
forms | number
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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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
--
Ticket URL: <http://trac.sagemath.org/ticket/17586>
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