CODEWITHSUNDEEP
pythonsympy
weis26
weis26

Reputation: 401

taking symbol in sum [sympy]

For example, I'd like to solve


(source: texify.com)

Here's what I tried:

from sympy import var, solve
x = var('x')
f = lambda N: sum( n**2 for n in range(1,N+1) )
f(x)

# output:
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 1, in <lambda>
TypeError: range() integer end argument expected, got Add.

Upvotes: 2

Views: 4724

Answers (2)

MRocklin
MRocklin

Reputation: 57271

Try the summation function 

In [1]: n = Symbol('n', real=True)

In [2]: N = Symbol('N', real=True)

In [3]: summation(n**2, (n, 1, N)) # sum n**2 taking n from 1 to N
Out[3]: 
 3    2    
N    N    N
── + ── + ─
3    2    6

In [4]: solve(summation(n**2, (n, 1, N)) - 55, N)
Out[4]: [5]

Upvotes: 3

Sven Marnach
Sven Marnach

Reputation: 601599

Python's built-in range() function isn't aware of symbolic evaluation. Try using SymPy's sum() function instead:

>>> from sympy import sum, var, solve
>>> x = var('x')
>>> f = lambda N: sum(n**2, (n, 1, N))
>>> n = var("n")
>>> f(x)
x/6 + x**2/2 + x**3/3

Note that the lambda expression might be unnecessary, depending on you actually want to achieve:

>>> N = var("N")
>>> solve(sum(n**2, (n, 1, N)) - 55, N)
[-13/4 - I*359**(1/2)/4, 5, -13/4 + I*359**(1/2)/4]

You'll still have to ignore the complex results.

Upvotes: 5

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