#13433: Lazy power series: fix bad handling of base ring and categorification
-----------------------------------------------+----------------------------
       Reporter:  hivert                       |         Owner:  hivert   
           Type:  defect                       |        Status:  new      
       Priority:  major                        |     Milestone:  sage-5.10
      Component:  combinatorics                |    Resolution:           
       Keywords:  LazyPowerSeries, categories  |   Work issues:           
Report Upstream:  N/A                          |     Reviewers:           
        Authors:  Florent Hivert               |     Merged in:           
   Dependencies:                               |      Stopgaps:           
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Description changed by hivert:

Old description:

> Currently
> {{{
> sage: R = LazyPowerSeriesRing(QQ)
> sage: type(R.gen().coefficient(0))
> <type 'sage.rings.rational.Rational'>
> sage: type(R.gen().coefficient(1))
> <type 'int'>
> sage: type(R.gen().coefficient(2))
> <type 'int'>
> }}}
> it should be always {{{Rational}}}

New description:

 Currently
 {{{
 sage: R = LazyPowerSeriesRing(QQ)
 sage: type(R.gen().coefficient(0))
 <type 'sage.rings.rational.Rational'>
 sage: type(R.gen().coefficient(1))
 <type 'int'>
 sage: type(R.gen().coefficient(2))
 <type 'int'>
 }}}
 it should be always {{{Rational}}}

 I also fixed the following bug:
 {{{
 sage: from sage.combinat.species.series import LazyPowerSeriesRing
 sage: L = LazyPowerSeriesRing(QQ)
 sage: g = L.gen(); z = L.zero()
 sage: s = z+g; s
 Uninitialized lazy power series
 sage: s.coefficients(10)
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 sage: s
 Uninitialized lazy power series
 }}}
 It should be:
 {{{
 sage: s.coefficients(10)
 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
 sage: s
 x + O(x^10)
 }}}

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13433#comment:2>
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