#18663: Speed up computation of twists of newforms
-------------------------------------+-------------------------------------
       Reporter:  davidloeffler      |        Owner:
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.8
      Component:  modular forms      |   Resolution:
       Keywords:                     |    Merged in:
        Authors:                     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/davidloeffler/better_twists      |  480f9516ba7526b13ae34bd8b31dc224f1c62432
   Dependencies:  #18478             |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by pbruin):

 * status:  needs_review => needs_work
 * dependencies:  18478 => #18478


Comment:

 I haven't looked at this in detail, but with both this ticket and #6018
 applied, the example from comment:15:ticket:18086 only takes about a
 second.  However, some long doctests fail even with #18478 merged:
 {{{
 sage -t --long --warn-long 49.1 src/sage/modular/modform/element.py
 **********************************************************************
 File "src/sage/modular/modform/element.py", line 1188, in
 sage.modular.modform.element.Newform.twist
 Failed example:
     Delta.twist(chi, level=3)  # long time
 Expected:
     Traceback (most recent call last):
     ...
     RuntimeError: twist of q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 +
 O(q^6) by Dirichlet character modulo 1 of conductor 1 is not a newform in
 Cuspidal subspace of dimension 3 of Modular Forms space of dimension 5 for
 Congruence Subgroup Gamma0(3) of weight 12 over Cyclotomic Field of order
 1 and degree 1
 Got:
     ...
          raise RuntimeError('twist of %s by %s is not a newform in %s' %
 (self, chi, S))
     UnboundLocalError: local variable 'S' referenced before assignment
 **********************************************************************
 File "src/sage/modular/modform/element.py", line 1192, in
 sage.modular.modform.element.Newform.twist
 Failed example:
     Delta.twist(chi, level=3, check=False)  # long time
 Exception raised:
     ...
          raise RuntimeError('twist of %s by %s is not a newform in %s' %
 (self, chi, S))
     UnboundLocalError: local variable 'S' referenced before assignment
 **********************************************************************
 1 item had failures:
    2 of  17 in sage.modular.modform.element.Newform.twist
     [305 tests, 2 failures, 45.85 s]
 ----------------------------------------------------------------------
 sage -t --long --warn-long 49.1 src/sage/modular/modform/element.py  # 2
 doctests failed
 ----------------------------------------------------------------------
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/18663#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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