#4214: [with patch, needs work] elliptic_logarithm gives inaccurate answers
---------------------------+------------------------------------------------
 Reporter:  AlexGhitza     |        Owner:  AlexGhitza
     Type:  defect         |       Status:  new       
 Priority:  major          |    Milestone:  sage-3.1.3
Component:  number theory  |   Resolution:            
 Keywords:                 |  
---------------------------+------------------------------------------------
Changes (by GeorgSWeber):

  * summary:  [with patch, needs review] elliptic_logarithm gives
              inaccurate answers => [with patch, needs work]
              elliptic_logarithm gives inaccurate answers

Comment:

 Hi Alex,
 unfortunately, the patch does not work yet. This is what I get before
 applying the patch:
 {{{
 sage -t -long
 
devel/sage/sage/schemes/elliptic_curves/ell_point.py**********************************************************************
 File "/Users/georgweber/Public/sage/sage-3.1.3.alpha3/tmp/ell_point.py",
 line 1103:
     sage: P.elliptic_logarithm(precision=55)
 Expected:
     0.2735052644156991
 Got:
     0.2735052671206336
 **********************************************************************
 File "/Users/georgweber/Public/sage/sage-3.1.3.alpha3/tmp/ell_point.py",
 line 1105:
     sage: P.elliptic_logarithm()  # 100 bits
 Expected:
     0.27656204014107100870071052662
 Got:
     0.27656204014107100870070982517
 **********************************************************************
 1 items had failures:
    2 of  20 in __main__.example_33
 ***Test Failed*** 2 failures.
 For whitespace errors, see the file
 /Users/georgweber/Public/sage/sage-3.1.3.alpha3/tmp/.doctest_ell_point.py
          [35.2 s]
 exit code: 1024

 ----------------------------------------------------------------------
 The following tests failed:


         sage -t -long devel/sage/sage/schemes/elliptic_curves/ell_point.py
 Total time for all tests: 35.2 seconds
 }}}

 But after applying the patch (to vanilla Sage 3.1.3alpha3 on my Intel Mac
 OS X 10.4), I still get:
 {{{
 sage -t -long
 
devel/sage/sage/schemes/elliptic_curves/ell_point.py**********************************************************************
 File "/Users/georgweber/Public/sage/sage-3.1.3.alpha3/tmp/ell_point.py",
 line 1120:
     sage: P.elliptic_logarithm(algorithm='sage')  # 100 bits
 Expected:
     0.27656204014107100870071052662
 Got:
     0.27656204014107100870070982517
 **********************************************************************
 1 items had failures:
    1 of  21 in __main__.example_33
 ***Test Failed*** 1 failures.
 For whitespace errors, see the file
 /Users/georgweber/Public/sage/sage-3.1.3.alpha3/tmp/.doctest_ell_point.py
          [28.4 s]
 exit code: 1024

 ----------------------------------------------------------------------
 The following tests failed:


         sage -t -long devel/sage/sage/schemes/elliptic_curves/ell_point.py
 Total time for all tests: 28.4 seconds
 }}}

 Thus the patch got one failure away, but the other pertains.

 Maybe just use dots for the time being (see the following line) there in
 the doctest,
 as even these fewer digits already display what you want to show (accuracy
 problem
 of the Sage internal algorithm)?

 {{{
 0.2765620401410710087...
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4214#comment:4>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel
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