Powers and complex numbers

[Paul Royik]

I have the following expresssion:

f=x**(Rational(2,3))

How can I get 1, when substituting (-1) instead of complex number?

For now, I got complex number when run f.subs(x,-1).evalf()

[Aaron Meurer]

You need to use real_root, like

In [3]: real_root(-1, 3)
Out[3]: -1

In [4]: real_root(-1, 3)**2
Out[4]: 1

SymPy, like most math libraries, uses complex roots (i.e., principal
roots) because they have nicer mathematical properties.

Aaron Meurer

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[Paul Royik]

So, there is no way to do it using subs and/or some manipulations?

real_root(-1, 3) is of no help, because I can have arbitrary expression.

[Aaron Meurer]

You can generally do this sort of thing using replace().
Unfortunately, the pattern matcher doesn't recognize rational numbers
as a/b, so you have to do a more manual check. This should work:

e.replace(lambda i: i.is_Pow and i.base == x and i.exp.is_Rational,
lambda i: real_root(-1,
i.exp.as_numer_denom()[1])**i.exp.as_numer_denom()[0])

(replace -1 with whatever value you want to replace). A "cleaner"
solution would be to create a custom Pow subclass that evaluates like
you want, and replace instances of Pow with your class before doing a
substitution.

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/c88261c0-3449-4d7a-abf8-8d28ebdca59d%40googlegroups.com.

[Paul Royik]

Thank you.

[Paul Royik]

I decided to use "cleaner" solution: create a custom Pow subclass that evaluates. What method should I override?

[Aaron Meurer]

You want to override eval. Take a look at
http://docs.sympy.org/latest/guide.html#functions for an example.

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/503d6140-3541-42a5-95d4-9c202f7d8e4e%40googlegroups.com.

[Paul Royik]

Thank you.

How to override behaviour, so that above expression, i.e.(-1)**(2/3).is_real outputs True?

[Aaron Meurer]

I guess you'll want to check if the base is_Number and is_negative and
do the custom logic, otherwise run the superclass eval. Something like
(untested):

@classmethod
def eval(cls, base, exp):
if base.is_Number and base.is_negative:
# Custom logic here
else:
return super().eval(base, exp)

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/2a8b8984-c262-4b64-8c05-80deb5d74700%40googlegroups.com.

[Paul Royik]

Thank you very much.