Hey all, I'm running a bit of code to solve for a variable in an equation. Here are the specs:
theta = (2.*pi().*n1.*d1)./y;
a = n0.*n1 + n0.*n2 - n1.^2 - n1.*n2 + n0.*n1.*cos(theta) - n0.*n2.*cos(theta) + (n1.^2).*cos(theta) - n1.*n2.*cos(theta) + n0.*k2.*sin(theta) + n1.*k2.*sin(theta);
b = n1.*k2 - n0.*k2 + n0.*k2.*cos(theta) + n1.*k2.*cos(theta) - n0.*n1.*sin(theta) + n0.*n2.*sin(theta) - (n1.^2).*sin(theta) + n1.*n2.*sin(theta);
c = n0.*n1 + n0.*n2 + n1.^2 + n1.*n2 + n0.*n1.*cos(theta) - n0.*n2.*cos(theta) - (n1.^2).*cos(theta) + n1.*n2.*cos(theta) + n0.*k2.*sin(theta) - n1.*k2.*sin(theta);
d = n0.*k2.*cos(theta) - n1.*k2.*cos(theta) - n0.*k2 - n1.*k2 - n0.*n1.*sin(theta) + n0.*n2.*sin(theta) + (n1.^2).*sin(theta) - n1.*n2.*sin(theta);
[n1] = solve(sqrt((1./((c.^2+d.^2).^2)).*(((a.*c + b.*d).^2) + ((b.*c - a.*d).^2))) - R);
I have defined every variable as a symbolic variable. It is a pretty nasty piece of work, and when I run this, I ask for the solution, calling n1 in the command window. I get this back as a result:
(pi*d1*n1)/atan((n1*(- R^4*k2^4*n0^2 - 2*R^4*k2^2*n0^3*n2 - 2*R^4*k2^2*n0^2*n1^2 - 2*R^4*k2^2*n0^2*n2^2 - 2*R^4*k2^2*n0*n1^2*n2 - R^4*n0^4*n2^2 - 2*R^4*n0^3*n1^2*n2 - 2*R^4*n0^3*n2^3 - R^4*n0^2*n1^4 - 4*R^4*n0^2*n1^2*n2^2 - R^4*n0^2*n2^4 - 2*R^4*n0*n1^4*n2 - 2*R^4*n0*n1^2*n2^3 - R^4*n1^4*n2^2 + 2*R^2*k2^4*n0^2 + 4*R^2*k2^2*n0^2*n1^2 + 4*R^2*k2^2*n0^2*n2^2 + 2*R^2*n0^4*n2^2 + 2*R^2*n0^2*n1^4 - 8*R^2*n0^2*n1^2*n2^2 + 2*R^2*n0^2*n2^4 + 2*R^2*n1^4*n2^2 - k2^4*n0^2 + 2*k2^2*n0^3*n2 - 2*k2^2*n0^2*n1^2 - 2*k2^2*n0^2*n2^2 + 2*k2^2*n0*n1^2*n2 - n0^4*n2^2 + 2*n0^3*n1^2*n2 + 2*n0^3*n2^3 - n0^2*n1^4 - 4*n0^2*n1^2*n2^2 - n0^2*n2^4 + 2*n0*n1^4*n2 + 2*n0*n1^2*n2^3 - n1^4*n2^2)^(1/2) - k2*n1^3 + k2*n0^2*n1 + R^2*k2*n1^3 - R^2*k2*n0^2*n1)/(R^2*k2^2*n0^2 + R^2*n0^2*n2^2 + 2*R^2*n0*n1^2*n2 + R^2*n1^4 - k2^2*n0^2 - n0^2*n2^2 + 2*n0*n1^2*n2 - n1^4))
(pi*d1*n1)/atan((k2^2*n0*n1*i - k2*n0^2*n1 + k2*n1^3 + n0^2*n1*n2*i + n0*n1^3*i + n0*n1*n2^2*i + n1^3*n2*i)/(k2^2*n0^2 + n0^2*n2^2 + 2*n0*n1^2*n2 + n1^4))
and negative versions of the above as well, making 4 solutions. All of these solutions are dependent upon n1 itself. So, my question is this: Is n1 = f(n1), or did I do something wrong?
