#15486: Speed up NumberField_generic.zeta() and DirichletGroup()
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Reporter: elarson3 | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: roots of unity | Merged in:
dirichlet group | Reviewers:
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0bbfc15be4a05287814e0a6068a547549ab96587
u/pbruin/15486-roots_of_unity | Stopgaps:
Dependencies: #15898, #15767 |
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Description changed by pbruin:
Old description:
> The runtime of the Newforms function is unacceptable for large
> conductors.
>
> This is because in the _ _init_ _ method of the ModularFormsAmbient_R
> class (in modular/modform/ambient_R.py), the object attribute _
> _R_character is precomputed. However, this precomputation can be very
> expensive, and is unnecessary when calling many functions (e.g.
> Newforms). Thus, it should be done with lazy evaluation.
>
> For a benchmark --- This reduces the runtime of Newforms(719, names='a')
> to 3--4 sec... from its previous value of over a day (interrupted before
> completion)!
New description:
The runtime of the Newforms function is unacceptable for large conductors.
To fix this, we speed up both the `DirichletGroup` constructor and the
`zeta(n)` method of number fields by avoiding the computation of the group
of all roots of unity or its order.
For a benchmark --- This reduces the runtime of Newforms(719, names='a')
to 3--4 sec... from its previous value of over a day (interrupted before
completion)!
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Ticket URL: <http://trac.sagemath.org/ticket/15486#comment:15>
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