[FIXED] solving equation in python with SymPy takes forever

Issue

I tried to solve this equation but still running. I gave the symbol and the equation is "Eq((1-(1+ x )(-60))/ x+32*(1+x)(-60) , 41.81)".

Solution

The way solve and solveset usual work is to split an expression into numerator and denominator, and return solutions for the one that are not in the other.

Let's define a helper function to put the solutions from nsolve into a FiniteSet and one to give the final solution:

>>> from sympy import FiniteSet, nsolve, Add, Eq
>>> from sympy.abc import x
>>> rr = lambda x: FiniteSet(*[i[0] for i in real_roots(x, multiple=False)])
>>> sol = lambda n, d: list(rr(n) - rr(d))
>>> go = lambda eq: sol(*eq.rewrite(Add).as_numer_denom())

Now we try this out on your original expression:

>>> eq = Eq(32/(x + 1)**60 + (1 - 1/(x + 1)**60)/x, 41.81)
>>> fsol = go(eq)  # very slow
>>> [i.n(3) for i in fsol]
[-3.33, -2.56, -1.44, -0.568, -0.228, 0.0220]

If you check those out by substituting into the original expression (written as an expression) you will find that only the last one is valid

>>> expr = eq.rewrite(Add)
>>> [expr.subs(x, i).n(3) for i in fsol]
[-42.1, -42.2, 4.72e+22, 2.64e+23, 1.97e+8, 1.31e-15]

Now let's replace that Float with a Rational and get solutions:

>>> req = nsimplify(eq, rational=True); req
Eq(32/(x + 1)**60 + (1 - 1/(x + 1)**60)/x, 4181/100)
>>> rsol = go(_)  # pretty fast
>>> [i.n(3) for i in rsol]
[-2.00, 0.0220]

We know the 2nd solution is right; let's check the first:

>>> req.subs(x, rsol[0]).rewrite(Add).n(3)
-0.e-114

So both solutions appear to be valid and you don't get any spurious solutions which (by the way) I wasn't expecting from nsolve.

Answered By - smichr