#8414: lattice -> space in weyl_groups.py
-----------------------------+----------------------------------------------
   Reporter:  bump           |       Owner:  bump        
       Type:  defect         |      Status:  needs_review
   Priority:  major          |   Milestone:  sage-4.3.4  
  Component:  combinatorics  |    Keywords:              
     Author:  Daniel Bump    |    Upstream:  N/A         
   Reviewer:                 |      Merged:              
Work_issues:                 |  
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Changes (by bump):

  * status:  needs_work => needs_review


Old description:

> WeylGroups and WeylGroupElements have a method lattice() and also an
> attribute _lattice. At one time this pointed to the ambient lattice, but
> now it points to the ambient space.
>
> For consistency perhaps the name of the method and attribute should
> therefore be changed to space(). The patch makes this change.
>
> A further change: the reflections() method now has a keys option. This
> method returns
> a dictionary between the reflections in W and the positive roots.
> The default keys="reflections" makes the reflections the keys and the
> roots the values. The option
> keys="values" interchanges these.

New description:

 WeylGroups and WeylGroupElements have a method lattice() and also an
 attribute _lattice. At one time this pointed to the ambient lattice, but
 now it points to the ambient space.

 For consistency perhaps the name of the method and attribute should
 therefore be changed to space(). The patch makes this change.

 The patch also makes reflections of the Weyl group a
 family and adds methods {{{inverse_family}}} and {{{has_key}}} to
 the method family, per Nicolas' suggestion.

--

Comment:

 I have revised the patch taking into account Nicolas' suggestion that
 reflections be a family, and that finite families should have inverse
 families as a method.

 I did not revise the change lattice -> space pending further discussion of
 the matter. As I said in my last message, it seems that
 it might sometimes be a misnomer but still an improvement over calling the
 method "lattice".

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8414#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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