#13327: Allow conversion of strings to iterated polynomial rings
---------------------------------------+------------------------------------
       Reporter:  novoselt             |         Owner:  malb           
           Type:  defect               |        Status:  positive_review
       Priority:  major                |     Milestone:  sage-5.3       
      Component:  commutative algebra  |    Resolution:                 
       Keywords:                       |   Work issues:                 
Report Upstream:  N/A                  |     Reviewers:                 
        Authors:  Andrey Novoseltsev   |     Merged in:                 
   Dependencies:                       |      Stopgaps:                 
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Comment (by novoselt):

 I think this is horrible, as well as
 {{{
 sage: QQ["a"]["a"]
 Univariate Polynomial Ring in a over Univariate Polynomial Ring in a over
 Rational Field
 }}}
 but some people think that it does not matter how something is printing
 and the name is meaningless.

 From my point of view, all generator names should be distinct and
 different from generator names used in the base ring (recursively). Note
 that if this is enforced, then it is not possible to create polynomial
 rings with symbolic coefficients, since "any name is in SR". Since such
 polynomials are important (at least to me), the first step is to have
 symbolic rings with only explicitly specified names allows as variables.
 Then constructors can check for name collisions.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13327#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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