       Mathematica confusion

• To: uiucuxc!yoda.ncsa.uiuc.edu!mathgroup
• Subject: Mathematica confusion
• From: uiucuxc!uthvm1.bitnet!AN123651
• Date: Mon, 25 Jun 90 14:54:41 CST

```Thanks to the many people who have responded to my earlier posting.
Let me see if I can be more clear, and refrain from embarassing
myself further.

When I enter the expression

(1/x) (1/x^2)^(1/x^2 -1)

mma simplifies it to

x^(-1 - 2 (-1 + x^(-2)))

Now, consider x = -2 (not -1 as I mistyped previously). In the first
expression, x is squared before any roots are taken, so it is natural
to expect a real answer. In the second case, a root of -2 is taken and
a complex answer is no surprise. mma's simplification effects the
choice of the branch cut.

This is not a bug. The question of branch cuts is difficult. Instead,
let me post this as a query - how can I get mma to take the cut I
want? Note that mma is not entirely consistent on this point:

(1/x) (1/x^2)^(1/x^2 -1) /. x-> -2
and
f[x_] := (1/x) (1/x^2)^(1/x^2 -1)
f[-2]