43

I've been trying this now for hours. I think I don't understand a basic concept, that's why I couldn't answer this question to myself so far.

What I'm trying is to implement a simple mathematical function, like this:

f(x) = x**2 + 1

After that I want to derive that function.

I've defined the symbol and function with:

x = sympy.Symbol('x')
f = sympy.Function('f')(x)

Now I'm struggling with defining the equation to this function f(x). Something like f.exp("x**2 + 1") is not working.

I also wonder how I could get a print out to the console of this function after it's finally defined.

Robin
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6 Answers6

60

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)
asmeurer
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    Thanks for this. Do you still need to do `f = Function('f')` before defining the function or is that implicit from the python function definition? – Bill Sep 10 '19 at 15:04
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    @Bill `def f(...)` sets the variable `f` to be the Python function defined by the def. If you do `f = Function('f')`, that will override the variable `f` to be the SymPy object `Function('f')`. The two options I show here do not use `Function` at all. That is only if you want something that is completely unevaluated. See also the section [in the SymPy tutorial](https://docs.sympy.org/latest/tutorial/gotchas.html#symbols) on symbols. – asmeurer Sep 10 '19 at 19:45
20

Here's your solution:

>>> import sympy
>>> x = sympy.symbols('x')
>>> f = x**2 + 1
>>> sympy.diff(f, x)
2*x
enedil
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6

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
hochl
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1

Have a look to: Sympy how to define variables for functions, integrals and polynomials

You can define it according to ways:

  • a python function with def as describe above
  • a python expression g=x**2 + 1
Nadir SOUALEM
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  • From Review: Hi, while links are great way of sharing knowledge, they won't really answer the question if they get broken in the future. Add to your answer the essential content of the link which answers the question. In case the content is too complex or too big to fit here, describe the general idea of the proposed solution. Remember to always keep a link reference to the original solution's website. See: [How do I write a good answer?](https://stackoverflow.com/help/how-to-answer) – sɐunıɔןɐqɐp Nov 24 '19 at 14:08
0

Creating a Undefined Function:

from sympy import *
f = symbols("f", cls=Function)

Felipe Morelli
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-2

I recommended :

  1. first, define a symbolic variable
x = sympy.symbols('x')
  1. second, define a symbolic function
f = sympy.Function('f')(x)
  1. define a formula
 f = x**x+1

if you have so many variable can use this function

 def symbols_builder(arg):
     globals()[arg]=sp.symbols(str(arg))

if you have so many functions can use this function

def func_build(name, *args):
    globals()[name]=sp.Function(str(name))(args)
amir khatami
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    At step 3 you reassign variable f, meaning step 2 effect is lost. And actually step 2 is not needed, step 3 is enough. – mins Sep 09 '22 at 13:26