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MathGroup Archive 1999

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Re: Re: POLEZERO plots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19168] Re: [mg19069] Re: POLEZERO plots
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Thu, 5 Aug 1999 23:59:10 -0400
  • References: <7o5ilf$rmr@smc.vnet.net> <199908050534.BAA03328@smc.vnet.net.>
  • Sender: owner-wri-mathgroup at wolfram.com

"P.J. Hinton" wrote:
> 
> On 2 Aug 1999, John Cogill wrote:
> ...
> > My Mathematica 4 complains "ivar .. " until I change the zeros to ones
> > in both cases.
> >
> > I feel I must be missing something.
> 
> The problem is with the author's use of the Coefficient[] function, with
> which the "ivar" tag is associated.  Mathematica does not allow you to
> invoke Coefficient[] with an integer (1).
> 
> If you rewrite the assignments for ncoeff and dcoeff so that they use
> CoefficientList[]
> 
> OLD:
> 
> ncoeff = Table[
>         Re[Coefficient[numerator,z^k]],{k,0,Length[zeros]}];
> 
> NEW:
> 
> ncoeff = Map[Re, CoefficientList[numerator,z]];
> ...
> 
> The code works fine.
> ...
> P.J. Hinton
> Mathematica Programming Group           paulh at wolfram.com
> Wolfram Research, Inc.


As noted, CoefficientList is nowadays preferable to use in the situation
indicated above. All the same I thought I'd indicate how to make
Coefficient work because there are other situations in which
CoefficientList is too expensive or not usable.

For example, suppose you want a bunch of coefficients including that for
the zeroeth order term, and the expression will not allow for use of
CoefficientList because it is not a polynomial in the given variable. Or
maybe you don't want all the coefficients of a large polynomial, so
CoefficientList would be too slow. In such cases you might use the
three-argument form of Coefficient, which does not have a problem with
an exponent of zero.

In[12]:=  ee = 1+2*x+3*x^2;

In[13]:= Table[Coefficient[ee, x, k], {k, 0, 2}]
Out[13]= {1, 2, 3}


Daniel Lichtblau
Wolfram Research


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