You could try
sage: R.<x> = QQ[]
sage: f1 = x
sage: f2 = R(1)
sage: f = Piecewise([[(0,1),f1],[(1,2),f2]])
sage: f.plot()
sage: f(3/2)
1
or
sage: f1 = lambda x: x
sage: f2 = lambda x: 1
sage: f = Piecewise([[(0,1),f1],[(1,2),f2]])
sage: f(3/2)
1
sage: f.plot()
or
sage: x = var("x")
sage: f1(x) = x
sage: f2(x) = 1
sage: f = Piecewise([[(0,1),f1],[(1,2),f2]])
sage: f(3/2)
1
sage: list_plot([f(x) for x in srange(0, 2, step = 0.1)], plotjoined=True)
Piecewise was written before SR and, as William pointed out,
badly needs to be rewritten so they work together better.
For example, in this case f.plot() will fail with a strange
error.
On Thu, Mar 25, 2010 at 11:08 PM, Dan Drake <dr...@kaist.edu> wrote:
> Hello,
>
> I'm trying to use a piecewise function, and it doesn't seem to work very
> well. If I do
>
> f = Piecewise([((0, 1), x), ((1, 2), 1)], x)
>
> and try to evaluate f(3/2), it complains that Integer objects are not
> callable. The docstring for Piecewise says "if the optional var is
> specified, then any symbolic expressions in the list will be converted
> to symbolic functions using fcn.function(var)" -- shouldn't it also
> try to convert non-symbolic expressions? I can do SR(1), but I don't
> want to get into explaining to my students what that means.
>
> With the above definition, I also can't easily plot the function: if I
> do
>
> plot(f, 0, 2)
>
> I get "ValueError: free variable: x |--> x" and if I do
>
> plot(f(x), x, 0, 2)
>
> it complains "value not defined outside of domain". The only way I could
> get the function to plot is with
>
> plot(lambda x: f(x), 0, 2)
>
> which seems like an unnecessary workaround.
>
> If I define the function with
>
> f = Piecewise([((0,1), x), ((1,2), SR(1))])
>
> I still have problems; when I try to evaluate f(3/2), it says "the
> number of arguments must be less than or equal to 0"!?
>
> I also can't seem to get diff() to work with this function, even though
> f.derivative() works.
>
> Are these known problems? Am I not using Piecewise properly?
>
> Dan
>
> --
> --- Dan Drake
> ----- http://mathsci.kaist.ac.kr/~drake
> -------
>
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>
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> =iu3A
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>
>
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