How to define a mathematical function in SymPy?
Here's your solution:
>>> import sympy
>>> x = sympy.symbols('x')
>>> f = x**2 + 1
>>> sympy.diff(f, x)
2*x
sympy.Function
is for undefined functions. Like if f = Function('f')
then f(x)
remains unevaluated in expressions.
If you want an actual function (like if you do f(1)
it evaluates x**2 + 1
at x=1
, you can use a Python function
def f(x):
return x**2 + 1
Then f(Symbol('x'))
will give a symbolic x**2 + 1
and f(1)
will give 2
.
Or you can assign the expression to a variable
f = x**2 + 1
and use that. If you want to substitute x
for a value, use subs
, like
f.subs(x, 1)
Another possibility (isympy
command prompt):
>>> type(x)
<class 'sympy.core.symbol.Symbol'>
>>> f = Lambda(x, x**2)
>>> f
2
x ↦ x
>>> f(3)
9
Calculating the derivative works like that:
>>> g = Lambda(x, diff(f(x), x))
>>> g
x ↦ 2x
>>> g(3)
6