#20656: MixedIntegerLinearProgram: Remove _variables dictionary
---------------------------+----------------------------------
   Reporter:  mkoeppe      |            Owner:
       Type:  enhancement  |           Status:  new
   Priority:  major        |        Milestone:  sage-7.3
  Component:  numerical    |         Keywords:  lp
  Merged in:               |          Authors:
  Reviewers:               |  Report Upstream:  N/A
Work issues:               |           Branch:
     Commit:               |     Dependencies:  #20461, #20462
   Stopgaps:               |
---------------------------+----------------------------------
 The '_variables' attribute dictionary maps a "variable" (an "element" of a
 `MIPVariable` "dictionary") to an index in the backend. This is redundant
 because these "variables" are elements of type `LinearFunction`, and as
 such know their index in the backend already.

 {{{
 sage: p = MixedIntegerLinearProgram(solver='GLPK')
 sage: pv = p.new_variable(nonnegative=True)
 sage: pv[0]
 x_0
 sage: pv[77]
 x_1
 sage: pv[0].dict().keys()
 [0]
 sage: pv[77].dict().keys()
 [1]
 }}}

 See also: #20461, #20602

--
Ticket URL: <http://trac.sagemath.org/ticket/20656>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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