#4721: [with patch; needs review] Indefinite integration for piecewise functions
-------------------------+--------------------------------------------------
 Reporter:  pbutler      |        Owner:  burcin    
     Type:  enhancement  |       Status:  new       
 Priority:  minor        |    Milestone:  sage-3.4.1
Component:  calculus     |   Resolution:            
 Keywords:               |  
-------------------------+--------------------------------------------------
Comment (by wdj):

 The last two patches together (first patch #3 then the "default" patch)
 apply cleanly to 3.3.alpha2. They also pass sage -t.

 A few comments:

 1) You have

 {{{
             sage: f1(y) = (x+3)^2
             sage: f2(y) = x+3
             sage: f3(y) = 3
             sage: f = Piecewise([[(-infinity, -3), f1], [(-3, 0), f2],
 [(0, infinity), f3]])
             sage: f.integral()
             Piecewise defined function with 3 parts, [[(-Infinity, -3),
 (x^3 + 9*x^2 + 27*x)/3 + 9],
             [(-3, 0), (x^2 + 6*x)/2 + 9/2], [(0, +Infinity), 3*x + 9/2]]
 }}}
 in the docstring. Is this mixing of x's and y's intended or a typo? If
 intended, why?

 2) I would have perferred that you add yourself to the AUTHR field at the
 top and add

 {{{
 AUTHOR:
   P Butler
 }}}
 in the docstring of the function itself. Not crutial, but it will help
 others in the future know which part is whose.

 3) You have the comment:


 {{{
             # if this piece starts at negative infinity, we won't
             # try to compute the definite integral of the piece.
 }}}
 yet you have the definite integral
 {{{

             sage: f1(x) = e^(-abs(x))
             sage: f = Piecewise([[(-infinity, infinity), f1]])
             sage: f.integral(definite=True)
             2
 }}}
 Could you explain this please? I think maybe you meant to say
 "...try to compute the indefinite...":
 {{{
 sage: f.integral()
 Piecewise defined function with 1 parts, [[(-Infinity, +Infinity),
 -integrate(e^(-abs(x)), x, x, +Infinity)]]
 }}}
 If so, could you add this example and comment to the docstring please?


 If you agree to all this, could you just make a small patch to go on top
 of the previous 2 so I can just apply it in my clone, run sage -t, and
 give this a positive review?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4721#comment:15>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of 
Reinventing the Wheel
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