All functions support the methods documented below, inherited from sympy.core.function.Function.
Base class for applied mathematical functions.
It also serves as a constructor for undefined function classes.
Examples
First example shows how to use Function as a constructor for undefined function classes:
>>> from sympy import Function, Symbol
>>> x = Symbol('x')
>>> f = Function('f')
>>> g = Function('g')(x)
>>> f
f
>>> f(x)
f(x)
>>> g
g(x)
>>> f(x).diff(x)
Derivative(f(x), x)
>>> g.diff(x)
Derivative(g(x), x)
In the following example Function is used as a base class for my_func that represents a mathematical function my_func. Suppose that it is well known, that my_func(0) is 1 and my_func at infinity goes to 0, so we want those two simplifications to occur automatically. Suppose also that my_func(x) is real exactly when x is real. Here is an implementation that honours those requirements:
>>> from sympy import Function, S, oo, I, sin
>>> class my_func(Function):
...
... nargs = 1
...
... @classmethod
... def eval(cls, x):
... if x.is_Number:
... if x is S.Zero:
... return S.One
... elif x is S.Infinity:
... return S.Zero
...
... def _eval_is_real(self):
... return self.args[0].is_real
...
>>> x = S('x')
>>> my_func(0) + sin(0)
1
>>> my_func(oo)
0
>>> my_func(3.54).n() # Not yet implemented for my_func.
my_func(3.54)
>>> my_func(I).is_real
False
In order for my_func to become useful, several other methods would need to be implemented. See source code of some of the already implemented functions for more complete examples.
Attributes
| nargs |
Returns the method as the 2-tuple (base, exponent).
Returns the first derivative of the function.
Returns whether the functon is commutative.