#9549: InfinitePolynomialRing_sparse.is_field lacks `proof=...` option
-----------------------------------+----------------------------------------
   Reporter:  mmezzarobba          |       Owner:  malb      
       Type:  defect               |      Status:  new       
   Priority:  major                |   Milestone:  sage-4.5.2
  Component:  commutative algebra  |    Keywords:            
     Author:                       |    Upstream:  N/A       
   Reviewer:                       |      Merged:            
Work_issues:                       |  
-----------------------------------+----------------------------------------
 The class `InfinitePolynomialRing_sparse` defines two methods called
 `is_field()`. The second definition rejects keyword arguments. This
 prevents from creating polynomial rings over infinite polynomial rings:
 {{{
 $ ./sage
 ----------------------------------------------------------------------
 | Sage Version 4.5, Release Date: 2010-07-16                         |
 | Type notebook() for the GUI, and license() for information.        |
 ----------------------------------------------------------------------
 sage: InfinitePolynomialRing(QQ, 'a')['x']
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)

 /home/marc/opt/sage-4.5/<ipython console> in <module>()

 /home/marc/opt/sage-4.5/local/lib/python2.6/site-
 packages/sage/rings/ring.so in sage.rings.ring.Ring.__getitem__
 (sage/rings/ring.c:2550)()

 /home/marc/opt/sage-4.5/local/lib/python2.6/site-
 packages/sage/rings/polynomial/polynomial_ring_constructor.pyc in
 PolynomialRing(base_ring, arg1, arg2, sparse, order, names, name,
 implementation)
     341                 raise TypeError, "if second arguments is a string
 with no commas, then there must be no other non-optional arguments"
     342             name = arg1
 --> 343             R = _single_variate(base_ring, name, sparse,
 implementation)
     344         else:
     345             # 2-4. PolynomialRing(base_ring, names,
 order='degrevlex'):

 /home/marc/opt/sage-4.5/local/lib/python2.6/site-
 packages/sage/rings/polynomial/polynomial_ring_constructor.pyc in
 _single_variate(base_ring, name, sparse, implementation)
     420             R =
 m.PolynomialRing_dense_padic_ring_fixed_mod(base_ring, name)
     421
 --> 422         elif base_ring.is_field(proof = False):
     423             R = m.PolynomialRing_field(base_ring, name, sparse,
 implementation=implementation)
     424

 TypeError: is_field() got an unexpected keyword argument 'proof'
 }}}

 There is a similar issue with ``is_integral_domain``, too.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9549>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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