#6018: Confusing behaviour with Dirichlet characters
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Reporter: davidloeffler | Owner: craigcitro
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-4.3.2
Component: modular forms | Keywords: Dirichlet characters
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by davidloeffler):
On reflection, the issue is surprisingly subtle.
Consider taking a Dirichlet group with values in the integers of a
cyclotomic field K, and base_extending to: (1) the complex double field;
(2) the residue field of a prime of K.
In case (1), your example shows that we can't expect the constructor of
the new group to calculate the order of a given zeta. But case (2) shows
that the order of the base-extended zeta might not be the same as the
order of the original zeta, and one can easily get nonsense if one assumes
this.
Case (1) is actually OK if we don't pass zeta as an argument at all,
because we can factor polynomials in CDF. This is more or less what
applying Craig's patch and mine will give: zeta_order is still available
as an argument, but it's not used by the base extension code, which relies
on the base ring supporting *either* polynomial factoring or
{{{multiplicative_order}}}.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6018#comment:13>
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