MATLAB: I have a problem with the output of solve

solvesym

ello,
I tried to solve an equation
syms x y;
S = solve('x^2 + y^2 = 240^2','x*(s-x)+y*(t-y)-240*sqrt((s-x)^2+(t-y)^2)*0.64279=0')
in this case I get
Warning: Warning, solutions may have been lost
S =
    x: [4x1 sym]
    y: [4x1 sym]
S.x en S.y contains a very long equation that I can not directly convert to a number, but by pasting it in the command window I can find the values
the strange thing is if I replace s en t by their values I get other solutions
syms x y;
S = solve('x^2 + y^2 = 240^2','x*(279.8-x)+y*(-528.05 -y)-240*sqrt((279.8-x)^2+(-528.05 -y)^2)*0.64279=0')
and these are the correct solutions,
x=double(S.x)
y=double(S.y)
x =
      -17.428
       207.85
y =
      -239.37
         -120
so why do I get other solutions if I use s and t as a variable? and even stranger, if I replace 0.64279 by the cosinus of an angle than it thus work at all?
any ideas? probaly I am making a mistake somewhere? So wy is my solutions S.x and S.y not available as a number but as an expression, and how can I convert it?

Best Answer

Because you are sending quoted strings to solve(), x, y, s and t will all be treated as symbolic variables. The S.x, S.y you get out will be symbolic formula in the symbolic variables s and t. You cannot just double() to get values: you have to subs() in values for s and t and then you can double()
The symbolic expression you get out is a quartic (degree 4), so 4 solutions is proper.
x = 154.2671257, y = 183.85226111
x = -238.7563737, y = -24.40069805
x = 207.8465888, y = -119.9991483
x = -17.42811880, y = -239.3663732
MuPAD is known to lose solutions for polynomials in versions up to at least R2010b.
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