I have a problem with the output of solve

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?

Answer 1

[Walter Roberson]

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.