A = [2 1; 1 2];
theta = 0:%pi/50:2*%pi; // %pi is scilab for the constant pi
n = size(theta,2); // theta is a 1 x n row vector
x = zeros(theta); // x and y start as zero vectors
y = zeros(theta);
for i = 1:n,
    angle = theta(i); // this angle
    c = cos(angle);
    s = sin(angle);
    X = [ c, s ];
    r = sqrt(1/abs(X*A*X')); // formula from section 4
    x(i) = r*c; // r cos(theta)
    y(i) = r*s;
end;
plot(x,y,'r*-');
xtitle('Plot of 2x^2 + 2xy + 2y^2 = +/- 1','x','y');