#18888: failing optional mathematica tests, due to bugs in N() and n()
-------------------------------------+-------------------------------------
       Reporter:  slabbe             |        Owner:
           Type:  defect             |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-7.1
      Component:  interfaces:        |   Resolution:
  optional                           |    Merged in:
       Keywords:  mathematica        |    Reviewers:
        Authors:                     |  Work issues:  fix `N()` and `n()`
Report Upstream:  N/A                |       Commit:
         Branch:  public/18888       |  4fd09adee1cffa4fb7922862d20d2587f7837362
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------

Comment (by dimpase):

 Replying to [comment:25 vbraun]:
 > Whats wrong? With hindsight you need
 > {{{
 > sage: log(3.14 / 0.005, 2)
 > 9.29462074889163
 > }}}
 > bits of precision to know the next decimal digit, and there is probably
 a guard (binary) digit:
 > {{{
 > sage: pi.n(11)
 > 3.14
 > sage: pi.n(digits=10)
 > 3.141592654
 > }}}
 well, I am struggling to understand the error here:
 E.g. how would you explain the following:
 (it sort of works if the precision is specified...)

 {{{
 sage: mathematica('Pi').n()
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)
 <ipython-input-1-0b9c467a05fb> in <module>()
 ----> 1 mathematica('Pi').n()

 /home/scratch/dimpase/sage/sage/src/sage/structure/element.pyx in
 sage.structure.element.Element.numerical_approx
 (build/cythonized/sage/structure/element.c:7330)()
     717         """
     718         from sage.misc.functional import numerical_approx
 --> 719         return numerical_approx(self, prec=prec, digits=digits,
     720                                 algorithm=algorithm)
     721     n = numerical_approx

 /home/scratch/dimpase/sage/sage/local/lib/python2.7/site-
 packages/sage/misc/functional.pyc in numerical_approx(x, prec, digits,
 algorithm)
    1330
    1331     if prec > inprec:
 -> 1332         raise TypeError("cannot approximate to a precision of %s
 bits, use at most %s bits" % (prec, inprec))
    1333
    1334     # The issue is not precision, try conversion instead

 TypeError: cannot approximate to a precision of 53 bits, use at most
 prec[Pi] bits
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/18888#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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