回吐符號[sympy]

Question

例如，我想解決

http://www.texify.com/img/%5CLARGE%5C%21%5Cdisplayst%5Csum_%7Bn%3D1%7D%5EN%5C%20n%5E2%5C%20%3D%5C%2055.gif

這裏是我的嘗試：

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. 

Answer 1

Python的內置range()功能並不知道的象徵性評估。嘗試使用SymPy的sum()函數：

>>> 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 

注意lambda表達式可能是不必要的，這取決於你真正想實現：

>>> 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] 

你還是要忽略複雜的結果。

Answer 2

嘗試求和函數

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]