#7719: Improvements to complex AGM
--------------------------------+-------------------------------------------
   Reporter:  cremona           |       Owner:  AlexGhitza                   
       Type:  enhancement       |      Status:  needs_work                   
   Priority:  major             |   Milestone:  sage-4.3.1                   
  Component:  basic arithmetic  |    Keywords:  complex agm                  
Work_issues:                    |      Author:  John Cremona, Robert Bradshaw
   Upstream:  N/A               |    Reviewer:  Robert Bradshaw, John Cremona
     Merged:                    |  
--------------------------------+-------------------------------------------
Changes (by newvalueoldvalue):

  * status:  new => needs_work
  * reviewer:  => Robert Bradshaw, John Cremona
  * author:  => John Cremona, Robert Bradshaw


Comment:

 Robert: in line 1508 you set required_prec to self.prec -2.  In my code I
 used the precision-2 when testing relative error based on nothing more
 than trial and error (this way it converged while with the same precision
 it did not), since I am hopeless at working this kind of thing out
 properly.

 Before merging this, I'll need to fix some doctests in the elliptic curve
 code -- but before that there's some more work to be done, since the new
 cmp_abs() does not work on my 32-bit machine (and my 64-bit machine has
 crashed...):
 {{{
 sage -t  "devel/sage-cagm/sage/rings/complex_number.pyx"
 **********************************************************************
 File "/home/john/sage-4.3.rc0/devel/sage-
 cagm/sage/rings/complex_number.pyx", line 2190:
     sage: cmp_abs(CC(5), CC(1))
 Expected:
     1
 Got:
     -1
 **********************************************************************
 File "/home/john/sage-4.3.rc0/devel/sage-
 cagm/sage/rings/complex_number.pyx", line 2192:
     sage: cmp_abs(CC(5), CC(4))
 Expected:
     1
 Got:
     -1
 **********************************************************************
 File "/home/john/sage-4.3.rc0/devel/sage-
 cagm/sage/rings/complex_number.pyx", line 2194:
     sage: cmp_abs(CC(5), CC(5))
 Expected:
     0
 Got:
     -1
 **********************************************************************
 File "/home/john/sage-4.3.rc0/devel/sage-
 cagm/sage/rings/complex_number.pyx", line 2200:
     sage: cmp_abs(CC(-100), CC(1))
 Expected:
     1
 Got:
     -1
 **********************************************************************
 File "/home/john/sage-4.3.rc0/devel/sage-
 cagm/sage/rings/complex_number.pyx", line 2202:
     sage: cmp_abs(CC(-100), CC(100))
 Expected:
     0
 Got:
     -1
 **********************************************************************
 File "/home/john/sage-4.3.rc0/devel/sage-
 cagm/sage/rings/complex_number.pyx", line 2206:
     sage: cmp_abs(CC(1,1), CC(1))
 Expected:
     1
 Got:
     -1
 **********************************************************************
 1 items had failures:
    6 of  19 in __main__.example_79
 ***Test Failed*** 6 failures.
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7719#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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