# High order equation Solving

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Jack_111 on 11 Oct 2013
Commented: Walter Roberson on 14 Oct 2013
I am doing ray tracing and I have to make intersection between the ray and polynomial so I got the following equation and I have to solve it for t.
A(21).*(Y.^5) + (A(20).*(Y.^4)).*X + A(19).*(Y.^4) + (A(18).*(Y.^3)).*(X.^2) + (A(17).*(Y.^3)).*X + A(16).*(Y.^3) + (A(15).*(Y.^2)).*(X.^3) + (A(14).*(Y.^2)).*(X.^2) + (A(13).*(Y.^2)).*X + A(12).*(Y.^2) + (A(11).*(Y)).*(X.^4) + (A(10).*Y).*(X.^3) + (A(9).*Y).*(X.^2) + (A(8).*Y).*(X) + (A(7).*Y) + A(6).*(X.^5) + A(5).*(X.^4) + A(4).*(X.^3) + A(3).*(X.^2) + A(2).*X + A(1) - Z = 0;*
While:
X = (px +t*dx);
Y = (py +t*dy);
Z = (pz +t*dz);
so I want to get t in respect to the other variables. ( I have all the other variables but I don't know how to calculate it )

sixwwwwww on 12 Oct 2013
Dear Yaman, Here is the solution of your problem in symbolic form:
syms X Y Z p x y z t dx dy dz
A = sym('A%d', [1 21]);
X = p * x + t * dx;
Y = p * y + t * dy;
Z = p * z + t * dz;
equation = A(21) * Y^5 + (A(20) * Y^4) * X + A(19)* Y^4 + (A(18) * Y^3) * X^2 + (A(17) * Y^3) * X + A(16) * Y^3 + (A(15) * Y^2) * X^3 + ...
(A(14) * Y^2) * X^2 + (A(13) * Y^2) * X + A(12) * Y^2 + (A(11) * Y) * X^4 + (A(10) * Y) * X^3 + (A(9) * Y) * X^2 + (A(8) * Y) *X + A(7) * Y +...
A(6) * X^5 + A(5) * X^4 + A(4) * X^3 + A(3) * X^2 + A(2) * X + A(1) - Z;
Solution = solve(equation == 0, t);
Now if you put your know values of A(1)...A(21) and p, x, y, z, dx, dy, dz using "subs" function in "equation" then use last statement
Solution = solve(equation == 0, t);
then you will get your desired solution for "t". For information about "subs" see http://www.mathworks.com/help/symbolic/subs.html . Good luck!
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Walter Roberson on 14 Oct 2013
double(Solution)