On Wed, 19 Aug 2009, KvS wrote:
>
> Dear all,
>
> just started exploring Sage (via sagenb.org), I'm very enthousiastic
> about the concept and am very eager to leave 'black box' Mathematica
> asap. One issue however I can't seem to get my head around, namely
> what exactly is the 'right' way to think of and work with Sage-
> functions (as opposed to function constructs in the Python language)?
>
> E.g. when trying to plot a piecewise function, this works:
>
> f1 = lambda x:x
> f2 = lambda x:x^2
> f = Piecewise([[(0,1),f1],[(1,2),f2]])
> P = f.plot()
>
> whereas this (and several modifications of it I tried):
>
> x=var('x')
> f1(x)=x
> f2(x)=x^2
> f(x)=Piecewise([[(0,1),f1(x)],[(1,2),f2(x)]])
> P=f.plot()
>
> throws a TypeError:
>
> File "ring.pyx", line 272, in
> sage.symbolic.ring.SymbolicRing._element_constructor_ (sage/symbolic/
> ring.cpp:4456)
> TypeError
>
> Personally I would prefer the second approach as I would like to use
> only Sage-functions for mathematical functions (so not use lambda:
> etc.) to keep a notion of distinction between the mathematical objects
> on the one hand and the Python code on the other hand that controls
> the program flow. But it seems that I just don't really understand how
> to do that. Why is the second piece of code wrong and what would be
> the 'right' way to do it? Is there a function construct in Sage like
> the concept of a 'pure function' in Mathematica, so something like
> f=Function(x,x^2), where x is only a dummy that has no link with any x
> that might be defined before this command?
>
> Many thanks in advance for your time.
Probably what you want to do is
sage: f(x) = x^2
Note that piecewise functions have a lot of rough edges, so are probably
not the best examples for "how things should work."
- Robert
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