#14345: newton_sloprs for polynomial over ZpCA requires a prime, and 
newton_polygon
doesn't exist
-------------------------+--------------------------------------------------
   Reporter:  robharron  |             Owner:  roed               
       Type:  defect     |            Status:  new                
   Priority:  minor      |         Milestone:  sage-5.9           
  Component:  padics     |          Keywords:  newton slopes, ZpCA
Work issues:             |   Report Upstream:  N/A                
  Reviewers:             |           Authors:                     
  Merged in:             |      Dependencies:                     
   Stopgaps:             |  
-------------------------+--------------------------------------------------
 Here's the bug:
 {{{
 R = PolynomialRing(ZpCA(5), 'x')
 sage: x = R.gen()
 sage: f = x^2 + 1
 sage: f.newton_slopes()
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)
 <ipython-input-79-687b034aeac7> in <module>()
 ----> 1 f.newton_slopes()

 TypeError: newton_slopes() takes exactly one argument (0 given)
 sage: f.newton_polygon()
 ---------------------------------------------------------------------------
 AttributeError                            Traceback (most recent call
 last)
 <ipython-input-87-e7bcefa164b7> in <module>()
 ----> 1 f.newton_polygon()

 /Users/rharron/Programming/sage/local/lib/python2.7/site-
 packages/sage/structure/element.so in
 sage.structure.element.Element.__getattr__
 (sage/structure/element.c:3527)()

 /Users/rharron/Programming/sage/local/lib/python2.7/site-
 packages/sage/structure/misc.so in
 sage.structure.misc.getattr_from_other_class
 (sage/structure/misc.c:1488)()

 AttributeError: 'Polynomial_padic_flat' object has no attribute
 'newton_polygon'
 }}}

 ZpCR and Qp work fine. The problem appears to be that polynomials over
 ZpCA don't know they're over a p-adic ring.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14345>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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