#7712: error with polynomial with interval coefficients
--------------------------------+-------------------------------------------
   Reporter:  zimmerma          |       Owner:  AlexGhitza
       Type:  defect            |      Status:  new       
   Priority:  major             |   Milestone:  sage-4.3.4
  Component:  basic arithmetic  |    Keywords:            
     Author:                    |    Upstream:  N/A       
   Reviewer:                    |      Merged:            
Work_issues:                    |  
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Comment(by ylchapuy):

 Here is my point:
 {{{
 sage: 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
 ....:
 sage: C391 = method2(391)
 sage: C391
 0
 sage: type(C391)
 <class
 'sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict'>
 sage: type(C391(0,0,0))
 <type 'sage.rings.integer.Integer'>
 sage: type(C391(GF(17)['z'](0),0,0))
 <type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7712#comment:11>
Sage <http://www.sagemath.org>
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