#18589: isogeny efficiency improvement
-------------------------+-------------------------------------------------
       Reporter:         |        Owner:
  cremona                |       Status:  needs_review
           Type:         |    Milestone:  sage-6.8
  enhancement            |   Resolution:
       Priority:  major  |    Merged in:
      Component:         |    Reviewers:
  elliptic curves        |  Work issues:
       Keywords:         |       Commit:
  isogeny                |  ad56369f5def8060575b6567342dedb28a447293
        Authors:  John   |     Stopgaps:
  Cremona                |
Report Upstream:  N/A    |
         Branch:         |
  u/cremona/18589        |
   Dependencies:         |
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Comment (by jdemeyer):

 In the current implementation, you are computing
 {{{
     from sage.rings.arith import gcd
     a = _least_semi_primitive(l)
     m = E.multiplication_by_m(a, x_only=True)
     F = psi_l.parent()
     x = F.gen()
     d = F(m.denominator())
     n = F(m.numerator())
 }}}
 even when `factors_by_degree` is empty.

 An easy optimization would be
 {{{
 if all(factors == [] for factors in factors_by_degree):
     return ...
 }}}
 just before that block.

--
Ticket URL: <http://trac.sagemath.org/ticket/18589#comment:38>
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