#12802: test containment of ideals in class MPolynomialIdeal
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       Reporter:  mariah                          |         Owner:  AlexGhitza  
                  
           Type:  enhancement                     |        Status:  
needs_review                  
       Priority:  minor                           |     Milestone:  sage-5.1    
                  
      Component:  commutative algebra             |    Resolution:              
                  
       Keywords:  sd40.5, groebner bases, ideals  |   Work issues:  cache 
handling                
Report Upstream:  N/A                             |     Reviewers:  Andrey 
Novoseltsev, Simon King
        Authors:  John Perry                      |     Merged in:              
                  
   Dependencies:                                  |      Stopgaps:              
                  
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Changes (by john_perry):

  * status:  needs_info => needs_review


Comment:

 I'm about to upload a new patch that uses Simon's `_gb_by_ordering` idea.
 Here are the timings on the same machine as the other day:
 {{{
 sage: P.<x,y> = QQ[]
 <+ 30*y + 25, 1/400*x^4*y^4 - 1/5*x^5*y^2 - 1/20*x^4*y^3 + 4*x^6 + 2*x^5*y
 + 11/20*x^4*y^2 - 12*x^5 - 3*x^4*y + 9*x^4]*P
 sage: J2 = J.gens()*P
 sage: %timeit J==J2
 5 loops, best of 3: 376 µs per loop
 sage: _ = J.groebner_basis()
 sage: %timeit J==J2
 625 loops, best of 3: 372 µs per loop
 sage: _ = J2.groebner_basis()
 sage: %timeit J==J2
 625 loops, best of 3: 362 µs per loop
 }}}
 A more than 1000-fold increase. :-)

 All tests in sage/rings pass muster, as do the tests in schemes that had
 failed the other day.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12802#comment:37>
Sage <http://www.sagemath.org>
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