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MathGroup Archive 2006

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Re: Construction of Vandermonde equations:

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65183] Re: [mg65166] Construction of Vandermonde equations:
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 17 Mar 2006 00:13:27 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

x={x1,x2,x3};

n=Length[x];

mat=Array[A,{n,n}];

Thread[mat.x^(m-1)==0]


Bob Hanlon

> 
> From: Gopinath Venkatesan <gopinathv at ou.edu>
To: mathgroup at smc.vnet.net
> Subject: [mg65183] [mg65166] Construction of Vandermonde equations:
> 
> 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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