#7712: error with polynomial with interval coefficients
--------------------------------+-------------------------------------------
   Reporter:  zimmerma          |       Owner:  AlexGhitza
       Type:  defect            |      Status:  new       
   Priority:  major             |   Milestone:  sage-4.3  
  Component:  basic arithmetic  |    Keywords:            
Work_issues:                    |      Author:            
   Upstream:  N/A               |    Reviewer:            
     Merged:                    |  
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Comment(by zimmerma):

 Here is a more complex example, which shows this is not only a printing
 issue:
 {{{
 def method2(prec):
    n=[0,9,7,8,11,6,3,7,6,6,4,3,4,1,2,2,1,1,1,2,0,0,0,3,0,0,0,0,1]
    R = RealIntervalField(prec)
    P.<xk1,sk1,sk2> = PolynomialRing(R)
    Q.<xk> = PolynomialRing(P)
    C = (sk1-xk)^n[1]*xk^n[2]
    C=C.integral()
    C=C(sk1/2)-C(xk1)
    C=R(10^6)*C.subs(sk1=sk2-xk1)
    C=C.subs(xk1=xk,sk2=sk1)
    for k in range(3,29):
       C=C*xk^n[k]
       C=C.integral()
       C=C(sk1/k)-C(xk1)
       C=R(10^6)*C.subs(sk1=sk2-xk1)
       C=C.subs(xk1=xk,sk2=sk1)
    C=C.subs(xk=R(0),sk1=R(1))
    return C(0,0,0)

 sage: method2(391)
 0
 sage: _.parent()
 Integer Ring

 sage: method2(392)
 1.?e-8
 sage: _.parent()
 Real Interval Field with 392 bits of precision
 }}}
 Normally, both calls should return an object of type "Real Interval
 Field", isn't it?
 (If necessary, I can open a different trac ticket for both issues.)

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7712#comment:3>
Sage <http://www.sagemath.org>
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