#16201: default precision for symbolic power series from SR.series()
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   Reporter:  rws          |            Owner:
       Type:  enhancement  |           Status:  new
   Priority:  major        |        Milestone:  sage-6.2
  Component:  algebra      |         Keywords:  series precision
  Merged in:               |          Authors:
  Reviewers:               |  Report Upstream:  N/A
Work issues:               |           Branch:
     Commit:               |     Dependencies:
   Stopgaps:               |
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 Both Laurent and power series ring elements have a default precision of
 20. OTOH, symbolic series expansions need the precision set:
 {{{
 sage: R.<t> = LaurentSeriesRing(QQ)
 sage: 1/(1-t)
 1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12
 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19 + O(t^20)
 sage: var('x')
 x
 sage: ex=1/(1-x)
 sage: ex.series(x)
 ...
 TypeError: series() takes exactly 2 positional arguments (1 given)
 }}}
 This ticket proposes to unify the behaviour by allowing the following:
 {{{
 sage: ex.series(x)
 1 + 1*x + 1*x^2 + 1*x^3 + 1*x^4 + 1*x^5 + 1*x^6 + 1*x^7 + 1*x^8 + 1*x^9 +
 1*x^10 + 1*x^11 + 1*x^12 + 1*x^13 + 1*x^14 + 1*x^15 + 1*x^16 + 1*x^17 +
 1*x^18 + 1*x^19 + Order(x^20)
 }}}
 As this is about reducing surprise for the user both algebra and symbolic
 series default precision should have the same value, so the ticket should
 also implement such a global value.

--
Ticket URL: <http://trac.sagemath.org/ticket/16201>
Sage <http://www.sagemath.org>
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