Ticket #7917 (new enhancement)
[with patch, needs review] make gauss_sum() work for dirichlet characters when the base ring is CC
| Reported by: | bober | Owned by: | was |
|---|---|---|---|
| Priority: | major | Milestone: | sage-5.10 |
| Component: | number theory | Keywords: | dirichlet character gauss sum |
| Cc: | rishi | Work issues: | |
| Report Upstream: | N/A | Reviewers: | |
| Authors: | bober | Merged in: | |
| Dependencies: | Stopgaps: |
Description
This is a pretty small change. We add three lines to gauss_sum_numerical() to make it work when the base ring is a complex field, and change gauss_sum() to call gauss_sum_numerical() when the base ring is a complex field.
Note that it is actually much faster to compute the (approximate) gauss sum when the base ring is CC, as compared to when the base ring is a cyclotomic field.
sage: G = DirichletGroup(2981)
sage: chi = G.0
sage: timeit('chi.gauss_sum_numerical()')
5 loops, best of 3: 1.82 s per loop
sage: G = DirichletGroup(2981, ComplexField(200))
sage: chi = G.0
sage: timeit('chi.gauss_sum_numerical()')
25 loops, best of 3: 23.5 ms per loop
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