       Re: minimal power

• To: mathgroup at smc.vnet.net
• Subject: [mg50255] Re: minimal power
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Mon, 23 Aug 2004 06:34:21 -0400 (EDT)
• References: <cg96v1\$a3l\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Firstly, it is not a good idea to use D as a variable name because it is
reserved for doing differentiation. The safe bet is to use variable names

Define your series (you can use e rather than f with no problems)

s = a/t^(5/2) + b/t^(3/2) + c/t^2^(-1) + d*t^(1/2) + e*t^(3/2);

If this were a polynomial then CoefficientList[s, t] would extract the
various powers, but here you have to be cleverer. There are lots of ways to
do what you want, but one that will be generally useful here and elsewhere
is to evaluate FullForm[s], which gives

Plus[Times[a, Power[t, Rational[-5, 2]]], Times[b, Power[t, Rational[-3,
2]]],
Times[c, Power[t, Rational[-1, 2]]], Times[d, Power[t, Rational[1, 2]]],
Times[e, Power[t, Rational[3, 2]]]]

This tells you that the various powers of t are represented as Power[t,
Rational[x_, y_]], where x_ and y_ are patterns that match to any arguments
of Rational.

Now use this to extract the various powers of t in s (extracting only the
powers and omitting the base t):

p = Cases[s, Rational[x_, y_], 3];

This gives p as the list {-(5/2), -(3/2), -(1/2), 1/2, 3/2}.

{Min[p],Max[p]} then gives you the minimum and maximum powers of t.

This approach can be generalised. You start by looking at
FullForm[expression] and then design an appropriate Cases expression that
pulls out the pieces that you want.

Steve Luttrell

"Nodar Shubitidze" <shubi at nusun.jinr.ru> wrote in message
news:cg96v1\$a3l\$1 at smc.vnet.net...
> Hi !
>
>    I have for example following expression:
>   S = A t^(-5/2) + B t^(-3/2) + C t^(-1/2) + D t^(1/2) + F t^(3/2);
> Eith command "Exponent[S,t]" I can receive maximal power of S.
>    Why I may calculate minimal power of S ?
>    With best regards
> Nodar Shubitidze
> Joint Institute for Nuclear Research
> Dubna, RUSSIA
>

```

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