Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Recursion error when computing L² matrix norm #17333

Open
Zaharid opened this issue Aug 2, 2019 · 4 comments
Open

Recursion error when computing L² matrix norm #17333

Zaharid opened this issue Aug 2, 2019 · 4 comments
Labels
matrices

Comments

@Zaharid
Copy link

Zaharid commented Aug 2, 2019

The following script results in a RecursionError

from sympy import Matrix

m = Matrix(
    [
        [1.04880884817015, 0, 0, 0],
        [0.953462589245592, 0.436931448752652, 0, 0],
        [0.953462589245592, 0.20806259464412, 0.384212242932273, 0],
        [0.953462589245592, 0.20806259464412, 0.123939433203959, 0.36367301868042],
    ]
)

print(m.norm(2))
Traceback 
Traceback (most recent call last):
  File "xx.py", line 12, in <module>
    print(m.norm(2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/matrices/matrices.py", line 3923, in norm
    return Max(*self.singular_values())
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 350, in __new__
    args = frozenset(cls._new_args_filter(args))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 522, in _new_args_filter
    not arg.is_comparable):
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/basic.py", line 687, in is_comparable
    for p in self.as_real_imag()]
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 1136, in as_real_imag
    r = self.func(self.func(re, 2) + self.func(im, 2), S.Half)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 637, in eval
    rv = atan2(y, x)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/trigonometric.py", line 2921, in eval
    (x + S.ImaginaryUnit*y)/sqrt(x**2 + y**2))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/miscellaneous.py", line 132, in sqrt
    return Pow(arg, S.Half, evaluate=evaluate)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 286, in __new__
    obj = b._eval_power(e)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/power.py", line 376, in _eval_power
    S.Half - e*arg(b)/(2*S.Pi)))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 458, in __new__
    result = super(Function, cls).__new__(cls, *args, **options)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/function.py", line 277, in __new__
    evaluated = cls.eval(*args)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/functions/elementary/complexes.py", line 627, in eval
    c, arg_ = factor_terms(arg).as_coeff_Mul()
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1202, in factor_terms
    return do(expr)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1177, in do
    list_args = [do(a) for a in Add.make_args(p)]
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1177, in <listcomp>
    list_args = [do(a) for a in Add.make_args(p)]
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1198, in do
    *[do(a) for a in p.args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1198, in <listcomp>
    *[do(a) for a in p.args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1167, in do
    newargs = tuple([do(i) for i in args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1167, in <listcomp>
    newargs = tuple([do(i) for i in args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1177, in do
    list_args = [do(a) for a in Add.make_args(p)]
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1177, in <listcomp>
    list_args = [do(a) for a in Add.make_args(p)]
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1198, in do
    *[do(a) for a in p.args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1198, in <listcomp>
    *[do(a) for a in p.args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1167, in do
    newargs = tuple([do(i) for i in args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1167, in <listcomp>
    newargs = tuple([do(i) for i in args])
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1195, in do
    fraction=fraction).xreplace(special)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 1063, in gcd_terms
    cont, numer, denom = _gcd_terms(terms, isprimitive, fraction)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 937, in _gcd_terms
    terms = list(map(Term, [t for t in terms if t]))
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 837, in __init__
    numer = Factors(numer)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/exprtools.py", line 376, in __init__
    i1 *= k**factors.pop(k)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/numbers.py", line 2046, in __mul__
    return Rational.__mul__(self, other)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/decorators.py", line 91, in __sympifyit_wrapper
    return func(a, b)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/numbers.py", line 1608, in __mul__
    return Number.__mul__(self, other)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/decorators.py", line 91, in __sympifyit_wrapper
    return func(a, b)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/numbers.py", line 664, in __mul__
    return AtomicExpr.__mul__(self, other)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/decorators.py", line 91, in __sympifyit_wrapper
    return func(a, b)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/decorators.py", line 129, in binary_op_wrapper
    return func(self, other)
  File "/home/zah/anaconda3/lib/python3.7/site-packages/sympy/core/expr.py", line 151, in __mul__
    return Mul(self, other)
RecursionError: maximum recursion depth exceeded

This computation should be doauble as this is just the biggest singular value. This is likely to be connected to #17332.
@smichr
Copy link
Member

smichr commented Aug 4, 2019

Nice Traceback inclusion!

Perhaps we should have an issues template that has this in it:

<details>
<summary>Traceback</summary>

```python-traceback
replace_this_with_traceback
```
</details>

@sylee957
Copy link
Member

sylee957 commented Aug 5, 2019

I see this is because of the singular values bloating up.

@iuryt
Copy link

iuryt commented Apr 21, 2020

@sylee957 may have a point.
Maybe it helps the developers to find the problem.
If I create a random symmetric matrix:

from sympy import *
import numpy as np

n = 4
M = np.random.randint(0,3,(n,n))
A = Matrix(np.dot(M,M.T))

A.norm(2)

There are times it works, and others don't.

@sylee957
Copy link
Member

sylee957 commented Apr 21, 2020 •
edited

The original issue is no problem after #18911.
But a test from this example should be added

But I think that another issue comes from #17333 (comment) for comparison.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Assignees
No one assigned
Labels
matrices
Projects
None yet
Milestone
No milestone
Development

No branches or pull requests
5 participants
@smichr @Zaharid @iuryt @sylee957 @sidhantnagpal