#13976: Problem in the return type of BooleanIdeal.variety()
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   Reporter:  Bouillaguet          |             Owner:  malb    
       Type:  defect               |            Status:  new     
   Priority:  major                |         Milestone:  sage-5.7
  Component:  commutative algebra  |          Keywords:          
Work issues:                       |   Report Upstream:  N/A     
  Reviewers:                       |           Authors:          
  Merged in:                       |      Dependencies:          
   Stopgaps:                       |  
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 One can do:
 {{{
 sage= R.<x,y,z> = GF(2)[]
 sage: I = ideal( [ x*y*z + x*z + y + 1, x+y+z+1] )
 sage: sols = (I+sage.rings.ideal.FieldIdeal(R)).variety()
 sage: sols
 [{y: 1, z: 0, x: 0}, {y: 1, z: 1, x: 1}]

 sage: sols[0][y]
 1
 }}}

 Now the same thing fails in ``!BooleanRing``'s:
 {{{
 sage: R.<x,y,z> = BooleanPolynomialRing()
 sage: I = ideal( [ x*y*z + x*z + y + 1, x+y+z+1] )
 sage: sols = I.variety()
 sage: sols
 [{y: 1, z: 0, x: 0}, {y: 1, z: 1, x: 1}]

 sage: sols[0][y]
 Traceback (most recent call last):
 ...
 KeyError: y
 }}}

 This is caused by an ugly hack (I authored...) in #13103 to make the
 ``variety()`` function work on ``!BooleanIdeal``'s.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13976>
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