How to combine subs and solve correctly?

Dear MATLAB-Central,

Trying to solve the intersection of a circle (param. repr. x=C+R*(1-T^2)/(1+T^2); y=D+R*(2*T)/(1+T^2)) and an ellipse ((x-E)^2/A^2 + (y-F)^2/B^2 = 1), with given but varying positions and radii in the variables a,b,c,d,e,f, I do the following:

• syms A B C D E F R t
• Expr = (C+R*(1-(t*t))/(1+(t*t)) - E)*(C+R*(1-(t*t))/(1+(t*t)) - E)/(A*A) + (D+R*2*t/(1+(t*t)) - F)*(D+R*2*t/(1+(t*t)) - F)/(B*B);
• Expr = subs(Expr,{A,B,C,D,E,F,R},{a,b,c,d,e,f,r});
• Expr = simplify(Expr);
• solve(Expr == 1,t)

This code produces the error message: "Conversion to char from logical is not possible."

How can I solve this problem? I greatly appreciate any help suggestion.

Best regards,

Verena

Answer 1

[Walter Roberson]

The ability to use "==" in solve() was introduced in R2012a. If you are using an earlier version you will have to change your last line to

solve(Expr - 1, t)

[Verena]

Walter,

Thank you very much for your prompt answer and this hint.

But unfortunately, the manner the derived solution is quite hard to compare: The program puts out four intersection points given as giant expressions, like 1/6/(22578481442063296/106741283587350147 + 3^(1/2)*32010144944016589^(1/2)*1280000/3953380873605561*... and much more longer. The simplify-call takes a lot time and does not reveal a better readable expression either.

I'm looking forward for an approximation of the intersection points up to the second position after decimal point. Do you know any routine which will do it?

Thank you very much for your attention,

Verena