#11475: improve prime_pi (speedup + small fixes)
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       Reporter:  rohana                            |         Owner:  was       
                        
           Type:  enhancement                       |        Status:  
positive_review                   
       Priority:  major                             |     Milestone:  sage-5.1  
                        
      Component:  number theory                     |    Resolution:            
                        
       Keywords:  primes, prime counting, prime_pi  |   Work issues:            
                        
Report Upstream:  N/A                               |     Reviewers:  Yann 
Laigle-Chapuy, Leif Leonhardy
        Authors:  R. Andrew Ohana                   |     Merged in:            
                        
   Dependencies:                                    |      Stopgaps:            
                        
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Comment (by kcrisman):

 On the plus side, this fixes some of #6876.  On the down side:
 {{{
 WARNING: we draw the plot of ``prime_pi`` as a stairstep function with
 explicitly drawn vertical lines where the function jumps. Technically
 Technically there should not be any vertical lines, but they make the
 graph look much better, so we include them. Use the option
 ``vertical_lines=False`` to turn these off.
 }}}
 I'm adding a fix for the latter, and a doctest for the former.  Shouldn't
 affect anything.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:60>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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