#13256: abs floor ceil for quadratic number field
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       Reporter:  vdelecroix                                               |    
     Owner:  vdelecroix  
           Type:  enhancement                                              |    
    Status:  needs_review
       Priority:  major                                                    |    
 Milestone:  sage-5.3    
      Component:  number fields                                            |    
Resolution:              
       Keywords:  absolute value, floor, ceiling, number field, quadratic  |   
Work issues:              
Report Upstream:  N/A                                                      |    
 Reviewers:              
        Authors:  Vincent Delecroix                                        |    
 Merged in:              
   Dependencies:  #7160, #13213                                            |    
  Stopgaps:              
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Changes (by vdelecroix):

  * status:  new => needs_review


Old description:

> Implementation of absolute value (abs), floor (floor) and ceiling (ceil)
> function for elements in quadratic number field. This depends (not very
> much) on comparisons in quadratic number fields implemented in tickects
> #7160 and #13213.
>
> Strangely enough, floor and ceil functions are much faster than abs
> function! The reason is because the comparison in #13213 which is called
> in abs is actually very slow.
> {{{
> sage: sage: K.<sqrt2> = QuadraticField(2, name='sqrt2')
> sage: %timeit abs(sqrt2)
> 125 loops, best of 3: 2.22 ms per loop
> sage: %timeit floor(sqrt2)
> 625 loops, best of 3: 3.37 µs per loop
> }}}

New description:

 Implementation of absolute value (abs), floor (floor) and ceiling (ceil)
 function for elements in quadratic number field.

 The function abs depends on the function sign implemented in tickets #7160
 and #13213.

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13256#comment:1>
Sage <http://www.sagemath.org>
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