#8734: make sage variables unique in maxima
-------------------------------------+-------------------------------------
       Reporter:  jason              |        Owner:  jason
           Type:  defect             |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.2
      Component:  interfaces         |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Jason Grout, Ralf  |    Reviewers:  Volker Braun
  Stephan                            |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  be9367f966fc76ba6028b57ab4317530cfd1205e
  u/rws/ticket/8734-1                |     Stopgaps:
   Dependencies:                     |
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Comment (by rws):

 As far as I understand now, a `MaximaElementFunction` is a function
 defined within the Maxima process, and so `x` is the parameter name, not a
 registered variable. Thus the output `sin(x)` makes sense. OTOH any
 `_SAGE_VAR_x` that appears in a `MaximaElement` repr refers to a
 registered variable within Maxima that is associated with a registered
 Sage var named `x`. Let's interpret the above output in the light of this.
 > {{{
 > sage: f+g
 > cos(_SAGE_VAR_x)+sin(x)
 > }}}
 Correct but can the user make sense of it?
 > {{{
 > sage: (f+g)(2)
 > cos(_SAGE_VAR_x)+sin(2)
 > }}}
 That is not less correct than
 {{{
 sage: (sin(x)+cos(y))(2)
 cos(y) + sin(2)
 }}}
 and it just seems to be another case of `SR._call_element_()` where is
 stated: "Note that you make get unexpected results when calling symbolic
 expressions and not explicitly giving the variables."

 Moreover, it was a hack that this worked at all in the
 `MaximaAbstractElementFunction._add_()` doctests because
 {{{
 sage: f = maxima.function('z','sin(z)')
 sage: f
 sin(z)
 sage: f(2)
 sin(2)
 sage: (sin(z))(2)
 ---------------------------------------------------------------------------
 NameError                                 Traceback (most recent call
 last)
 NameError: name 'z' is not defined
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/8734#comment:27>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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