Subj : Re: Idea - Tensor could be modelled by 2 arrays and a function
To   : alt.math,alt.sci.physics,comp.programming
From : Mr Pixie
Date : Tue Aug 23 2005 07:27 pm


"tadchem" <tadchemNOSPAM@comcast.net> wrote in message 
news:NtmdnZ2dnZ1qA6rdnZ2dnbCnl96dnZ2dRVn-zZ2dnZ0@comcast.com...
>
> "Mr Pixie" <mrpixie@hotmail.com> wrote in message
> news:XxicnQxrrNewiJfeSa8jmA@karoo.co.uk...
>
> <snip>
>
> I used to program extensively in APL.
>
> In APL all variables are treated as arrays.
>
> Matrix inversion and transposition are monadic operators.
>
> I wrote a multivariate linear regression in one line.
>
> What could be simpler?
>
> Go read up on linear algebra.
>
>
> Tom Davidson
> Richmond, VA

I think I may have sussed it - here is the code so far:

function lorentz(A) array[]
{
   ' Lorentz Transformation by Anthony Smales
   ' Array A is the input array
    var B[1]: array;  ' B is the result array

    ' lorentz transformation code

    var input_velocity : real; ' input_velocity is the relative velocity 
from reference frame A to frame B

    var gamma = 1/((1-input_velocity^2)^0.5);

    var transformed_x0_dimension : real;
    var transformed_x1_dimension : real;
    var transformed_x2_dimension : real;
    var transformed_x3_dimension : real;

    var transformed_x0_dimension =  gamma*(A[0,0]) + (-0 * gamma)*(A[0,1]) + 
0*(A[0,2]) + 0*(A[0,3]);
    var transformed_x1_dimension =  gamma*(A[1,0]) + (-0 * gamma)*(A[1,1]) + 
0*(A[1,2]) + 0*(A[1,3]);
    var transformed_x2_dimension =  gamma*(A[2,0]) + (-0 * gamma)*(A[2,1]) + 
0*(A[2,2]) + 0*(A[2,3]);
    var transformed_x3_dimension =  gamma*(A[3,0]) + (-0 * gamma)*(A[3,1]) + 
0*(A[3,2]) + 0*(A[3,3]);

    B[0] = transformed_x0_dimension;
    B[1] = transformed_x1_dimension;
    B[2] = transformed_x2_dimension;
    B[3] = transformed_x3_dimension;
    return B[];
}

I do seem to have abandoned using 3 arrays though - there are now 2 in 
total, - which, I suppose, is what I stated originally...

Note that array A has 4 dimensions, but array B has only 1 dimension... so, 
its like : 'you give me 4 numbers and I give
you one number back' - sounds about right?

So, am I correct in saying that the result array we have here represents the 
dual space?

.