#13671: p.lift(...) results are non-deterministic and incoherent for 
multivariate
polynomials
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       Reporter:  Bouillaguet                                    |         
Owner:  malb           
           Type:  defect                                         |        
Status:  positive_review
       Priority:  major                                          |     
Milestone:  sage-5.5       
      Component:  commutative algebra                            |    
Resolution:                 
       Keywords:  polynomial rings, mathematically wrong result  |   Work 
issues:                 
Report Upstream:  N/A                                            |     
Reviewers:  Marco Streng   
        Authors:  Charles Bouillaguet                            |     Merged 
in:                 
   Dependencies:                                                 |      
Stopgaps:                 
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Changes (by mstreng):

  * status:  needs_review => positive_review
  * reviewer:  => Marco Streng


Old description:

> {{{
> sage: R.<x1,x2> = QQ[]
> sage: I = R.ideal(x2**2 + x1 - 2, x1**2 - 1)
> sage: test = I.gen(0) + x2*I.gen(1)
> sage: test.lift(I) # correct
> [1, x2]
> sage: (test+1).lift(I) # invalid input, should give error
> [0, 0]
> sage: test.lift(I) # incorrect
> [0, 0]
> }}}
>
> p.lift(I) should raise an exception "!ValueError: polynomial is not in
> the ideal" instead of returning [0,0,...,0] in the first place...

New description:

 ** Merge together with #13675, circular dependency **

 {{{
 sage: R.<x1,x2> = QQ[]
 sage: I = R.ideal(x2**2 + x1 - 2, x1**2 - 1)
 sage: test = I.gen(0) + x2*I.gen(1)
 sage: test.lift(I) # correct
 [1, x2]
 sage: (test+1).lift(I) # invalid input, should give error
 [0, 0]
 sage: test.lift(I) # incorrect
 [0, 0]
 }}}

 p.lift(I) should raise an exception "!ValueError: polynomial is not in the
 ideal" instead of returning [0,0,...,0] in the first place...

 ** Merge together with #13675, circular dependency **

--

Comment:

 Looks good!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13671#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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