cubic equation's root transformation

[Shaul Rabinovich]

Hi,
Does anybody know a way (other than typing manually) to (Maple-)transform
p/(-q+(q^2+p^3)^(1/2))^(1/3) to (-q-(q^2+p^3)^(1/2))^(1/3) ?
Thanks

[Edwin Clark]

"Shaul Rabinovich" <sav...@eng.tau.ac.il> wrote in message
news:c50431a3.03123...@posting.google.com...

The two expression are not equal. For example, let p = 1 and q = 0 then the
first is 1 and the second is (-1)^(1/3) which Maple considers as
(1+sqrt(3)*I)/2. If you used surd(-1,3) instead of (-1)^(1/3) you get -1
which is still different from 1.

Or, did you know that and just want to make the transformation anyhow? In
that case the only thing I can think of now is:

> A:=-p/(-q+(q^2+p^3)^(1/2))^(1/3):
> denom(A):
> op([1,1],%)-op([1,2],%):
> %^(1/3);

2 3 1/2 (1/3)
(-q - (q + p ) )

--Edwin Clark

(And Happy New Year!)

[Shaul Rabinovich]

"Edwin Clark" <ecl...@math.usf.edu> wrote in message news:<r%JIb.162230$%h4.1...@twister.tampabay.rr.com>...

> The two expression are not equal. For example, let p = 1 and q = 0 then the
> first is 1 and the second is (-1)^(1/3) which Maple considers as
> (1+sqrt(3)*I)/2. If you used surd(-1,3) instead of (-1)^(1/3) you get -1
> which is still different from 1.

Of course, you are right - I droped the sign while copying. And, of
course, (-1)^(1/3)=-1.

> Or, did you know that and just want to make the transformation anyhow? In
> that case the only thing I can think of now is:
>
> > A:=-p/(-q+(q^2+p^3)^(1/2))^(1/3):
> > denom(A):
> > op([1,1],%)-op([1,2],%):
> > %^(1/3);
>
> 2 3 1/2 (1/3)
> (-q - (q + p ) )

Great! Thank you very much and Happy New Year!

Shaul