Re: [Axiom-developer] Testing if (72*a^3*b^5)^(1/2) is equivalent to 6*a*b^2*(2*a*b)^(1/2)

[Martin Rubey]

Ted Kosan <address@hidden> writes:

> I have been experimenting with Axiom to see how it compares to other
> computer algebra systems.
>
> One of the things I tried testing was if Axiom could determine if
> (72*a^3*b^5)^(1/2) was equivalent to 6*a*b^2*(2*a*b)^(1/2):
>
> (2) -> (72*a^3*b^5)^(1/2) - 6*a*b^2*(2*a*b)^(1/2)
>
>          +------+
>          |   3 5        2 +----+
>  (2)  \|72a b   - 6a b \|2a b
>
>
> When I entered this expression into Wolfram Alpha, it returned 0 as a result.
>
> Is Axiom capable of determining if (72*a^3*b^5)^(1/2) is equivalent to
> 6*a*b^2*(2*a*b)^(1/2) ?

It should be.  At least FriCAS is:

(1) -> (72*a^3*b^5)^(1/2) - 6*a*b^2*(2*a*b)^(1/2)

         +------+
         |   3 5        2 +----+
   (1)  \|72a b   - 6a b \|2a b
                                                    Type: Expression(Integer)
(2) -> normalize %

   (2)  0
                                                    Type: Expression(Integer)

Of course, you have to be careful interpreting this result, see
William's answer!

Martin