如何在同意的情况下解决y =（x + 1）** 3 -2？

Question

I'd like to solve y = (x+1)**3 - 2 for x in sympy to find its inverse function.
I tried using solve , but I didn't get what I expected.

Here's what I wrote in IPython console in cmd (sympy 1.0 on Python 3.5.2):

In [1]: from sympy import *
In [2]: x, y = symbols('x y')
In [3]: n = Eq(y,(x+1)**3 - 2)
In [4]: solve(n,x)
Out [4]: 
[-(-1/2 - sqrt(3)*I/2)*(-27*y/2 + sqrt((-27*y - 54)**2)/2 - 27)**(1/3)/3 - 1,
 -(-1/2 + sqrt(3)*I/2)*(-27*y/2 + sqrt((-27*y - 54)**2)/2 - 27)**(1/3)/3 - 1,
 -(-27*y/2 + sqrt((-27*y - 54)**2)/2 - 27)**(1/3)/3 - 1]

I was looking at the last element in the list in Out [4] , but it doesn't equal x = (y+2)**(1/3) - 1 (which I was expecting).
Why did sympy output the wrong result, and what can I do to make sympy output the solution I was looking for?

I tried using solveset , but I got the same results as using solve .

In [13]: solveset(n,x)
Out[13]: {-(-1/2 - sqrt(3)*I/2)*(-27*y/2 + sqrt((-27*y - 54)**2)/2 - 27)**(1/3)/
3 - 1, -(-1/2 + sqrt(3)*I/2)*(-27*y/2 + sqrt((-27*y - 54)**2)/2 - 27)**(1/3)/3 -
 1, -(-27*y/2 + sqrt((-27*y - 54)**2)/2 - 27)**(1/3)/3 - 1}

Answer 1

Sympy gave you the correct result: your last result is equivalent to (y+2)**(1/3) - 1.

What you're looking for is simplify :

>>> from sympy import symbols, Eq, solve, simplify
>>> x, y = symbols("x y")
>>> n = Eq(y, (x+1)**3 - 2)
>>> s = solve(n, x)
>>> simplify(s[2])
(y + 2)**(1/3) - 1

edit: Worked with sympy 0.7.6.1, after updating to 1.0 it doesn't work anymore.

Answer 2

If you declare that x and y are positive, then there is only one solution:

import sympy as sy
x, y = sy.symbols("x y", positive=True)
n = sy.Eq(y, (x+1)**3 - 2)
s = sy.solve(n, x)
print(s)

yields

[(y + 2)**(1/3) - 1]