RE: Extracting Coefficients and Powers

• To: mathgroup at smc.vnet.net
• Subject: [mg48271] RE: [mg48254] Extracting Coefficients and Powers
• From: "DrBob" <drbob at bigfoot.com>
• Date: Thu, 20 May 2004 04:03:49 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Here's one method:

expr = 5 - 3/x^5.2 + x^3.2 - x^5;
rules = {(a_)?(FreeQ[#1, x] & )*(b_:1) :> {a, b}, b_:1 :> {1, b}};
expr /. Plus -> List
Transpose[Replace[%, rules, 1]]

{5, -(3/x^5.2), x^3.2, -x^5}
{{5, -3, 1, -1}, {1, 1/x^5.2,
x^3.2, x^5}}

If there's no constant term, it requires a little fix-up to get 0 in there.
This might do:

expr = -(3/x^5.2) + x^3.2 - x^5;
rules =
{(a_)?(FreeQ[#1, x] & )*(b_:1) :> {a, b},
b_:1 :> {1, b}};
expr /. Plus -> List
Transpose[Replace[%, rules, 1]]
If[MemberQ[Last[%], 1], %, Transpose[Prepend[Transpose[%], {0, 1}]]]

{-(3/x^5.2), x^3.2, -x^5}
{{-3, 1, -1}, {1/x^5.2, x^3.2, x^5}}
{{0, -3, 1, -1}, {1, 1/x^5.2, x^3.2, x^5}}

DrBob

www.eclecticdreams.net

-----Original Message-----
From: Bruce W. Colletti [mailto:bcolletti at compuserve.com]
To: mathgroup at smc.vnet.net
Subject: [mg48271] [mg48254] Extracting Coefficients and Powers

I have a sum of terms, each of the form "a * x^r" or "a * 1/x^r", where
a and (positive) r are real numbers (if a is missing, it's presumably 1
or -1 and if there is no x-term, r is understood to be 0).

In my application, the complete expression is given by Expand[p], where
p is a product of terms having form a t^b + c t^d (p is actually a
factorial moment generating function).

I want to extract all coefficients into a list (including 1 or -1
coefficients), and exponents into another (to include 0 for any constant
term).  For instance,

x^3.2 + 5 - 3 / x^5.2 - x^5

yields the coefficients' list {1, 5, -3, -1} and exponents' list {3.2,
0, -5.2,5}.

How would I build these lists?  Must Cases[ ] be used or are there
built-in functions?

Thanks.

Bruce

```

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