Exponent function

• To: mathgroup at smc.vnet.net
• Subject: [mg7807] Exponent function
• From: Raya Firsov-Khanin <raya at mech.ed.ac.uk>
• Date: Sat, 12 Jul 1997 02:45:49 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I've noticed the following strange feature of

Exponent[expr, arg, List]

function of Mathematica.  Suppose I want to
find all powers of x in the expression of the type

test = x + x^(1+a) + x^(-1+a) + x^2

then Exponent[test, x, List] gives the correct result

{1, 2, 1-a, -1+a}.

Suppose now, I add x^(-1) to test:

test1 = test + x^(-1)

then

Exponent[test1, x, List] gives a result {-1, -1, 1, 1, 2}.

For expressions like

test2 = test + x^(-n) the result of Exponent[] is correct

{1, 2, 1-a, -1+a, -n}, while for expressions where n is specified,
e.g.  n=1, 2, 3, ...  the result is always wrong.

I need to use Exponent function in a program that
should solve nonlinear problems using Multiple Scale Method. I need to
identify exponential frequencies of different terms in the equations, and
to study under what conditions they become resonant.

Any suggestions on how I can make Exponent function to give correct
results? Or may be there are some other ways to find powers of x in the
expressions of the type written above.
Any help would be appreciated. I already spent a morning trying to solve
this puzzle.
Thanks a lot.
Raya

```

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