#8586: Integer overflow in vector_space_dimension()
-----------------------------------+----------------------------------------
   Reporter:  malb                 |       Owner:  malb                         
            
       Type:  defect               |      Status:  new                          
            
   Priority:  major                |   Milestone:  sage-4.4                     
            
  Component:  commutative algebra  |    Keywords:                               
            
     Author:                       |    Upstream:  Reported upstream. Little or 
no feedback.
   Reviewer:                       |      Merged:                               
            
Work_issues:                       |  
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 {{{
 #!python
 sage: P.<x> = PolynomialRing(GF(32003),1)
 sage: sage.rings.ideal.FieldIdeal(P).vector_space_dimension()
 32003

 sage: P.<x,y> = PolynomialRing(GF(32003),2)
 sage: sage.rings.ideal.FieldIdeal(P).vector_space_dimension()
 1024192009

 sage: P.<x,y,z> = PolynomialRing(GF(32003),3)
 sage: sage.rings.ideal.FieldIdeal(P).vector_space_dimension()
 -1973539045 # 2^32 - (32003^3) % 2^32 == 1973539045
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8586>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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