#17920: Reimplement IntegerLists using Polyhedron.integral_points()
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       Reporter:  jdemeyer           |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  blocker            |    Milestone:  sage-6.6
      Component:  combinatorics      |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Jeroen Demeyer     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/jdemeyer/ticket/17920            |  b0a04aa5a4454766ed9802d8e99abcd7fb3e105b
   Dependencies:  #17937             |     Stopgaps:
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Comment (by nthiery):

 Dear Jeroen,

 Thanks a lot for taking action! It's definitely a good thing to have a
 good connection between ``IntegerListLex`` and ``Polyhedron``, as
 there is some non trivial overlap. The main differences is that
 ``IntegerListLex`` was specifically designed for allowing for
 (essentially) Constant Amortized Time lexicographic Iteration in
 almost constant memory, which is an important feature.

 So I can see a work path along the following lines:

 - Get this ticket in to have a robust implementation of list

 - Completely rewrite the current ``IntegerListLex`` iterator to be
   robust (it's definitely possible); keep the Polyhedron
   implementation for testing purposes as well as for counting, ...

 - Optimize the iterator (Cythonization, using ClonableIntArray, ...).

 Please do not change the enumeration order, at least as default: quite
 some code depends on it (I agree, this should be made explicit in the
 documentation). The proposed generalizations (n in a range, negative
 entries) are fine since the iterator could be made to handle them.

 Cheers,
                        Nicolas

--
Ticket URL: <http://trac.sagemath.org/ticket/17920#comment:39>
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