#8158: efficiency problem with polynomials (SymbolicRing vs PolynomialRing)
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       Reporter:  zimmerma             |        Owner:  malb
           Type:  defect               |       Status:  new
       Priority:  major                |    Milestone:  sage-5.12
      Component:  commutative algebra  |   Resolution:
       Keywords:                       |    Merged in:
        Authors:                       |    Reviewers:
Report Upstream:  N/A                  |  Work issues:
         Branch:                       |       Commit:
   Dependencies:                       |     Stopgaps:
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Comment (by zimmerma):

 PolynomialRing is still slower with Sage 5.11, even with integer
 coefficients:
 {{{
 +--------------------------------------------------------------------+
 | Sage Version 5.11, Release Date: 2013-08-13                        |
 | Type "notebook()" for the browser-based notebook interface.        |
 | Type "help()" for help.                                            |
 +--------------------------------------------------------------------+
 sage: var('a,b,c')
 (a, b, c)
 sage: %time d=expand((a+b+c+1)^100)
 CPU times: user 16.35 s, sys: 0.26 s, total: 16.61 s
 Wall time: 18.59 s
 sage: P.<a,b,c> = PolynomialRing(QQ)
 sage: %time d=(a+b+c+1)^100
 CPU times: user 34.35 s, sys: 0.08 s, total: 34.42 s
 Wall time: 35.80 s
 sage: P.<a,b,c> = PolynomialRing(ZZ)
 sage: %time d=(a+b+c+1)^100
 CPU times: user 32.29 s, sys: 0.07 s, total: 32.36 s
 Wall time: 34.89 s
 }}}
 Paul

--
Ticket URL: <http://trac.sagemath.org/ticket/8158#comment:2>
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