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MathGroup Archive 2006

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Construction of Vandermonde equations:

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65166] Construction of Vandermonde equations:
  • From: Gopinath Venkatesan <gopinathv at ou.edu>
  • Date: Wed, 15 Mar 2006 23:59:51 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Mathematica Experts

I have to form Vandermonde equations like this.

A[i,1]*x1^(m-1)+A[i,2]*x2^(m-1)+...+A[i,n]*xn^(m-1)=0 (say).

And in the above, the variables i=1,2,...n, and m=1,2,...n, and m is mu(symbol), and x is an array {x1,x2,x3,...xn}.

So I did this in Mathematica, with n=7, like below.

\!\(\(n = 7;\)\[IndentingNewLine]
  \(x = {0, 1/6, 2/6, 3/6, 4/6, 5/6, 1};\)\[IndentingNewLine]
  \(mat = Array[A, {n, n}];\)\[IndentingNewLine]
  \(S = 0;\)\[IndentingNewLine]
  \(Do[S = S + A[i,
   j]*x[\([j]\)]\^\(μ - 1\), {j, 1, n, 1}];\)\[IndentingNewLine]
  \(SS[i_, μ_] = S;\)\[IndentingNewLine]
  SS[2, p]\)

SS[2,p] is a check to see what we get for that value of i and mu(m).

But I wanted to put the element value of A[i,j] that is A[[i,j]] instead of A[i,j]. When I do that it gives error -- Part specification i is neither an integer or list of integers, as well as, -- Part specification A[[2,1]] is longer than the depth of the object.

Please suggest me what is the correct method to form such Vandermonde equations. Thanks.

Gopinath
Univ of Oklahoma


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