MathGroup Archive 2001

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Expansion Coefficients in Multivariate Series Expansions?


Daniel Lichtblau wrote:
> 
> "A. E. Siegman" wrote:
> >
> > Given an expression that is the sum of products of integer powers of
> > three variables (say x,y,z) multiplied by numerical coefficients:
> >
> >    f = c000 + c100 x + c010 y + c001 z + c110 x y + c211 x^2 y z + . . .
> >
> > where the  cijk's are all real numbers, and f may or may not be in
> > Normal (or other) form, how do I find the coefficient of a particular
> > term, e.g. c100 for the x term (*not*  c1000 + c110 y), or  ckmn for the
> > x^k y^m z^n term?
> > [...]
> 
> Or you could write your own code. Below is a simple procedural way,
> taking derivatives and setting variables to zero.
> 
> In[64]:= myCoefficient[ee_, vars__] := Module[
>   {len, vlist={vars}, res=ee},
>   Do[
>     res = D[res, vlist[[j]]] /. vlist[[j,1]]->0,
>     {j,Length[vlist]}];
>   res
>   ]
> 
> In[66]:= myCoefficient[f, {x,0}, {y,0}, {z,0}]
> Out[66]= c000
> 
> A functional programming approach might use Fold.
> 
> In[72]:= myCoefficient2[ee_, vars__] := Fold[(D[#1,#2] /. #2[[1]]->0)&,
> f, {vars}]
> 
> In[73]:= myCoefficient2[f, {x,0}, {y,0}, {z,0}]
> Out[73]= c000
> [...]

Oops, forgot to divide by factorials in those last ones. Those should
be:

myCoefficient[ee_, vars__] := Module[
  {len, vlist={vars}, res=ee},
  Do[
    res = D[res, vlist[[j]]] / vlist[[j,2]]! /. vlist[[j,1]]->0,
    {j,Length[vlist]}
	];
    res
  ]

myCoefficient2[ee_, vars__] :=
	Fold[(D[#1,#2]/#2[[2]]! /. #2[[1]]->0)&, f, {vars}]


Daniel Lichtblau
Wolfram Research


  • Prev by Date: Re: Sum of Squares
  • Next by Date: Re: How can I make the output value of Interpolation[] preciser?
  • Previous by thread: Re: Expansion Coefficients in Multivariate Series Expansions?
  • Next by thread: Re: Expansion Coefficients in Multivariate Series Expansions?