This message is about differences between a Python function and a symbolic function. This is also explained in the Some Common Issues with Functions page in the Sage Tutorial.
In Sage, one may define a symbolic function like:
sage:f(x)=x^2-1
And draw it using one the following way (both works):
sage:plot(f,(x,-10,10))sage:plot(f(x),(x,-10,10))
Here both f and f(x) are symbolic expressions:
sage:type(f)<type'sage.symbolic.expression.Expression'>sage:type(f(x))<type'sage.symbolic.expression.Expression'>
although there are different:
sage:fx|-->x^2-1sage:f(x)x^2-1
Now if f is a Python function defined with a def statement:
sage:deff(x):....:ifx>0:....:returnx....:else:....:return0
It is really a Python function:
sage:f<functionfat0xb933470>sage:type(f)<type'function'>
As above, one can draw the function f:
sage:plot(f,(x,-10,10))
But be carefull, drawing f(x) will not work as expected:
sage:plot(f(x),(x,-10,10))
Why? Because, the python function f gets evaluated on the variable x and this may either raise an exception depending on the definition of f or return some result which might not be a symbolic expression. Here f(x) gets always evaluated to zero because in the definition of f, bool(x > 0) returns False:
sage:xxsage:bool(x>0)Falsesage:f(x)0
Hence the following constant function is drawn:
sage:plot(0,(x,-10,10))
which is not what we want.