#1773: piecewise functions and integration / arithmetic do not play well 
together
----------------------------+------------------------
       Reporter:  was       |        Owner:  gfurnish
           Type:  defect    |       Status:  new
       Priority:  major     |    Milestone:  sage-7.3
      Component:  calculus  |   Resolution:
       Keywords:            |    Merged in:
        Authors:            |    Reviewers:
Report Upstream:  N/A       |  Work issues:
         Branch:            |       Commit:
   Dependencies:  #14801    |     Stopgaps:
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Comment (by rws):

 The problem on first sight here is that operations on `piecewise` do not
 get translated to what is expected, i.e., squaring the pieces. Also it
 seems that Maxima does not convert them, nor is it considering loading
 `pw.mac` without which it simply knows nothing about piecewise functions.
 So we must either load this package when encountering `piecewise` in the
 Maxima interface then convert, or the expression must be simplified, i.e.,
 the operations applied piecewise, probably by Pynac. Or both.

 Of course, the `integral` member function is accessible with pure
 `piecewise` objects:
 {{{
 sage: tri_wave1 = piecewise([ [(-1,1), f1^2], [(1,3), f2^2]])
 sage: tri_wave1.integral(definite=True)
 4/3
 }}}

--
Ticket URL: <https://trac.sagemath.org/ticket/1773#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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