> I'm doing numerical minimization on it right now and the only reason I
> want/need it to be a sage function is so I can .subs() real values for
> my parameters.  To get around that, I'm just going to use global
> variables for my parameters.  It's kind of ugly, but it will work.  It
> would be nice to be able to get symbolic derivatives too, but I don't
> need these either.
>   

Something like that ?

class PieceOfFunction(object):
    def __init__(f,interval)
       self.f = f
       self.interval = interval
    def diff():
       return PieceOfFunction(self.diff(),self.interval)

class PiecewiseFunction(object):
    def __init__(listOfPieces):
       self.listOfPieces = listOfPieces

    def diff():
       newList = []
       for f in self.listOfPieces :
          newList.append(f.diff(),f.interval)
       retuen PiecewiseFunction(newList)

I define a piece of function as a pair of a function and an interval, 
and then a piecewise function as a list of pieces of functions.
I'm far from being sure that it is an optimal way, but as far as I 
understand your problem, I would do like that.

Have a good day
Laurent


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