Problems finding a numerical root

[Philipp Janert]

Consider the following SymPy session:

>>> from sympy import *
>>> x = Symbol( "x", Real=True )
>>> f = 5*x**(2/3)/243 + x**(-2) - 3/x**4 + 15/x**6 - 1/(9*x**(2/3)) - 1/(3*x**(4/3))
>>> nsolve( f, x, (1,3) )
3.08052599290539 - 0.62790375155299*I

The problem is that f has a real root, very near x=2.09,

as plotting f(x) will reveal immediately. 

If I give tighter bounds, such as: nsolve( f, x, (2,2.2) ),

nsolve fails to converge entirely, "Could not find a root".

True, f(x) blows up as x -> 0, but that's well outside

the specified bounds. 

I understand that SymPy is not a numerical library, 

but this problem seems sufficiently straightforward. 

Is this expected behavior, or a bug, or a user error 

(which is the most probable case)?

Best, 

  Ph.

[Davide Sandona']

Hello Philipp, are you sure you have written down the correct expression? This is what it looks like upon closer inspection:

plot(f, (x, 0, 5), ylim=(-0.1, 1), title="$%s$" % latex(f))

There is no real root! However, nsolve was able to find one of the complex roots. You can see which one from the domain coloring plot below:

plot_complex(f, (x, -2-3j, 4+3j), coloring="b", grid=False, n=500, cmap=colorcet.colorwheel, title="$%s$" % latex(f))

Charts are generated with SymPy Plotting Backends: https://sympy-plot-backends.readthedocs.io/en/latest/index.html

Davide.

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[Philipp Janert]

You are right; I must have made a mistake when transcribing the formula.

I need to look into that.

Sorry about the spam. ;-(