#14862: Compositions accept any input
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       Reporter:  stumpc5            |        Owner:  sage-combinat
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-5.13
      Component:  combinatorics      |   Resolution:
       Keywords:  composition,       |    Merged in:
  FindStat                           |    Reviewers:
        Authors:                     |  Work issues:  provide a test in the
Report Upstream:  N/A                |  constructor
         Branch:                     |       Commit:
   Dependencies:                     |     Stopgaps:
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Comment (by nbruin):

 Replying to [comment:11 darij]:
 > Why do we need a class for compositions of maps, by the way? Isn't that
 the same as just... maps?

 We don't, and the composition of maps can be obtained using `phi*psi`
 (which will have its own clashes if you want pointwise products for maps
 into a multiplicative group). However, the fact that the slot in the
 global namespace is in principle available doesn't imply it should be used
 for a special notion.

 The title of the ticket already shows the confusion that can arise: The
 ticket complains that `Composition` is too lax with its argument checking
 and at the same time it seems `Composition` doesn't accept inputs that are
 perfectly valid for a mathematically widely accepted meaning of the word.

 Note that the full name is fine:
 {{{
 sage.combinat.composition.Composition
 }}}
 [Note that it is a function, not a class, by the way]. I just think it's
 inappropriate to import it into the global namespace under such a generic
 name. If you make that
 {{{
 from sage.combinat.composition import Composition as IntegerComposition
 }}}
 you should be fine and a lot less ambiguous already. With a system that is
 the scope of sage we really have to be careful with the global namespace.
 It is a very scarce resource.

 I like `IntegerComposition`, by the way, and I don't think `Partition` is
 that problematic. If that becomes problematic, we can probably write a
 generic Partition routine to be imported in the global namespace that
 dispatches to the appropriate routine (!IntegerPartition or !SetPartition
 or whatever) based on type of the input parameters.

--
Ticket URL: <http://trac.sagemath.org/ticket/14862#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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