Can sympy solve (1. - (x ** n)) ** (1/n) = y , and similar?

[Stuart Reynolds]

Dear Sympy users,

I'm new to sympy and interested in using it for function design.
I'm curious about what types of things I should be able to expected sympy.solve to solve. In particular, trying to solve:
(1. - (x ** 2)) ** (1. / 2) = 1/2
seems to fail for me:


import sympy
x, one, two = sympy.symbols("x 1 2")

# Equation of circle: y=sqrt(1 - x^2)
# What x is gives 1/2?
f = (one - (x ** two)) ** (one / two)

# Asking sympy to find the analytics solution:
print sympy.solveset(sympy.Eq(f, one/two), x, domain=sympy.Reals)
# ValueError: x**w where w is irrational is not defined for negative x



This equation as a solution:
print sympy.lambdify([], f.subs({x:0.865}))() # 0.501 --- seems pretty close


Did I ask it wrong or is it a limitation of the solver?

Thanks,
- Stuart

[Vishesh Mangla]

 

Can you solve it manually?

Sent from Mail for Windows 10

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[Oscar Benjamin]

On Fri, 8 Mar 2019 at 17:25, Stuart Reynolds <stuart....@gmail.com> wrote:
>
> Dear Sympy users,
>
> I'm new to sympy and interested in using it for function design.
> I'm curious about what types of things I should be able to expected sympy.solve to solve. In particular, trying to solve:
> (1. - (x ** 2)) ** (1. / 2) = 1/2
> seems to fail for me:

You can solve it like this using rational or floats:

In [9]: solve(Eq((1-(x**2))**(S(1)/2), S(1)/2), x)

Out[9]:

⎡-√3 √3⎤

⎢────, ──⎥

⎣ 2 2 ⎦


In [10]: solve(Eq((1.0-(x**2))**0.5, 0.5), x)

Out[10]: [-0.866025403784439, 0.866025403784439]

[Stuart Reynolds]

Ahh -- thank you. I was using solveset. Should have used solve.

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[Aaron Meurer]

solveset should be able to solve equations like this. If it can't,
please open an issue for it. For me it works just fine for
solveset(Eq((1-(x**2))**(S(1)/2), S(1)/2), x). It does have problems
with the general symbolic solveset(Eq((1-(x**n))**(S(1)/n), y), x)
because of domain and assumptions issues.

>>> solveset(Eq((1-x**n)**(1/n), y), x)
ConditionSet(x, Eq(-y + (1 - x**n)**(1/n), 0), Complexes(Reals x Reals, False))
>>> solveset(Eq((1-x**n)**(1/n), y), x, Reals)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "./sympy/solvers/solveset.py", line 1696, in solveset
return solveset(f.xreplace({symbol: r}), r, domain
File "./sympy/solvers/solveset.py", line 1714, in solveset
return _solveset(f, symbol, domain, _check=True)
File "./sympy/solvers/solveset.py", line 916, in _solveset
result = solver(Add(f.lhs, - f.rhs, evaluate=False), symbol, domain)
File "./sympy/solvers/solveset.py", line 883, in <lambda>
solver = lambda f, x, domain=domain: _solveset(f, x, domain)
File "./sympy/solvers/solveset.py", line 931, in _solveset
lhs, rhs_s = inverter(f, 0, symbol)
File "./sympy/solvers/solveset.py", line 884, in <lambda>
inverter = lambda f, rhs, symbol: _invert(f, rhs, symbol, domain)
File "./sympy/solvers/solveset.py", line 156, in _invert
x1, s = _invert_real(f_x, FiniteSet(y), x)
File "./sympy/solvers/solveset.py", line 202, in _invert_real
return _invert_real(h, imageset(Lambda(n, n - g), g_ys), symbol)
File "./sympy/solvers/solveset.py", line 237, in _invert_real
raise ValueError("x**w where w is irrational is not "

ValueError: x**w where w is irrational is not defined for negative x

>>> solve(Eq((1-x**n)**(1/n), y), x)
[(1 - y**n)**(1/n)]

I don't know if this can be improved.

Aaron Meurer

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