These are instructions for downloading and running the program QD on MATLAB.
Given a homogeneous polynomial and an ellipsoid in n dimensions the program
will produce the harmonic polynomial agreeing with the given polynomial on
the ellipsoid.  

To download the program
1.  Download the package quaddir.zip.  
2.  Unzip the package. The package should contain 11 files and a folder
that in turn contains 10 files.
3.  Put the entire package in a directory where you plan to run MATLAB
(for UNIX users) or after starting MATLAB set the "current directory"
to the place where the files are located (for windows users).
4.  At the prompt, type QD to start the program.  
5.  You will be asked to input the dimension, degree, and coefficients
that determine the ellisoid.  The program will return the solution.

Below is a sample version of the program with output.


%%%%%%%%%%%%%%%%%%%%Sample Execution%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


>> QD
This program will produce a harmonic function with 
boundary data at prescribed by the user on an ellisoid
prescribed by the user.
To begin press any key
What is the dimension of the space?3
What is the degree of the polynomial?4

ans =

Enter the power of x(1)

 1

ans =

Enter the power of x(2)

 2

ans =

Enter the power of x(3)

 1
What is the coefficient?1
Your polynomial is currently;
x(1)*x(2)^2*x(3)
Do you wish to add another term?(y/n)n
Now enter the coefficients which determine the ellipsoid
  a(1)^2x(1)^2+a(2)^2x(2)^2+...+a(n)^2x(n)^2=1 .

ans =

Enter ellipse coefficient a(1)

 2

ans =

Enter ellipse coefficient a(2)

 4

ans =

Enter ellipse coefficient a(3)

 6
The harmonic function agreeing with the given polynomial
on the given ellispe is
 
0.88235*x(1)*x(2)^2*x(3) - 0.029412*x(1)^3x(3) - 0.26471*x(1)x(3)^3
0.0073529*x(1)x(3)
>>