root of power not simplifying to base of power, e.g. cbrt(x**3) != x

Question

I am trying to simplify expressions containing exponents on SymPy. However, the desired results are not returned.

This is what I have tried thus far:

import sympy as sp

a, b, c, d = sp.symbols("a b c d", real = True, positive = True)

exp1 = (a - b + c)**3
exp2 = (a - b + c)**3 - ((a - b + c)**2 - d)**sp.Rational(3, 2)

Exp1 = exp1**sp.Rational(1, 3)
print(Exp1)
Output[1]: ((a - b + c)**3)**(1/3)

The expected result for Exp1 was a - b + c since I assumsed all the variales are positive.

Exp2 = exp2.subs(d, 0)
print(Exp2)
Output[2]: (a - b + c)**3 - (a - b + c)**2*Abs(a - b + c)

The expected result for Exp2 was 0.

Is there a way of forcing Sympy to return the fully simplified expressions or results when the base of the exponent has more than one variable.

The following answers did not help solve my problem:

The fact that `a`, `b`, and `c` are all positive doesn't mean `a - b + c` will be positive. — user2357112, Dec 10 '22 at 13:54
That said, sympy doesn't seem to recognize that cubing and cube rooting are inverses of each other for real arguments. — user2357112, Dec 10 '22 at 13:58
@user2357112, I've tried taking the absolute value of 'a - b + c', but that didn't help. — Huizar Wilson, Dec 10 '22 at 14:48
Cubing and cube rooting are not inverses over negative numbers if cube root means the principal root e.g. `(-1)**(1/3)`. SymPy provides `real_root` to get the other version of cube root. — Oscar Benjamin, Dec 11 '22 at 01:28
Ah. Even when the symbols are real, it's treating the operation as the complex cube root. — user2357112, Dec 11 '22 at 06:53

score 1 · Answer 1 · answered Dec 10 '22 at 23:47

1

Use the force option:

>>> powdenest(Exp1, force=True)
a - b + c

You can read the docstring for cbrt to get an explanation of how the principle root concept keeps cbrt(x**3) from being returned as x.

answered Dec 10 '22 at 23:47

smichr

1 Answers1