#9980: Deprecate functionality of `PowerSeriesRing` which conflicts with
construction of multivariate power series
-----------------------------------+----------------------------------------
   Reporter:  niles                |       Owner:  malb                         
    
       Type:  defect               |      Status:  new                          
    
   Priority:  major                |   Milestone:                               
    
  Component:  commutative algebra  |    Keywords:  power series, deprecation 
warning
     Author:                       |    Upstream:  N/A                          
    
   Reviewer:                       |      Merged:                               
    
Work_issues:                       |  
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 Multivariate power series are implemented by #1956.  As mentioned on that
 ticket, the existing code for `PowerSeriesRing` did not allow multivariate
 power series rings to be constructed using the same arguments as
 multivariate polynomials accept:

 {{{
 sage: T = PowerSeriesRing(QQ,3,'t'); T
 Multivariate Power Series Ring in t0, t1, t2 over Rational Field

 sage: T = PowerSeriesRing(QQ,'t',3); T
 Power Series Ring in t over Rational Field
 sage: T.default_prec()
 3

 sage: P = PolynomialRing(QQ,'t',3); P
 Multivariate Polynomial Ring in t0, t1, t2 over Rational Field
 }}}

 There is a non-trivial body of code (elliptic curves, and maybe p-adics)
 which makes use of this syntax.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9980>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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