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equality with integer exponents

asked 2019-12-23 10:22:48 -0500

Jingenbl gravatar image

updated 2019-12-23 11:47:54 -0500

eric_g gravatar image

n = var("n",domain = ZZ) assume(n>0) bool(3^(2*n) == (3^2)^n )

reply: False

Why?

Big thangs

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answered 2019-12-23 11:46:33 -0500

eric_g gravatar image

When asked for a Boolean expression, SageMath returns False if it is not capable to evaluate the expression to either true or false (a real false). This is what is happening in the present case; SageMath does not detect the identity:

sage: (3^(2*n) - (3^2)^n).simplify_full()
-9^n + 3^(2*n)

SymPy is more clever:

sage: (3^(2*n) - (3^2)^n)._sympy_().simplify()
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Well, SageMath can get it with canonicalize_radical():

sage: (3^(2*n) - (3^2)^n).canonicalize_radical()
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Indeed. But here I know the answer; in general, it will be necessary to show a lot of experience in the manipulation of symbolic expressions before concluding.

Jingenbl gravatar imageJingenbl ( 2019-12-24 03:09:41 -0500 )edit

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Asked: 2019-12-23 10:22:48 -0500

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Last updated: Dec 23 '19