Re: Extracting Coefficients and Powers

• To: mathgroup at smc.vnet.net
• Subject: [mg48269] Re: [mg48254] Extracting Coefficients and Powers
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 20 May 2004 04:03:45 -0400 (EDT)
• References: <200405190920.FAA15723@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Bruce W. Colletti wrote:
> 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
>

If you are willing to work with rational exponents you can do as below
to get exponent/coefficient list pairs. These can be further processed
in an abvious way to get the separate lists you seek.

In[15]:= InputForm[ipoly = Internal`NestedTermsList[Rationalize[x^3.2 +
5 - 3 / x^5.2 - x^5], x]]
Out[15]//InputForm= {{5, -1}, {16/5, 1}, {0, 5}, {-26/5, -3}}

In[16]:= InputForm[poly = Internal`FromNestedTermsList[ipoly, x]]
Out[16]//InputForm= 5 - 3/x^(26/5) + x^(16/5) - x^5

Daniel Lichtblau
Wolfram Research

```

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