Bug in system solver? why it give wrong answer? here's proof

So i have an equation that i need to solve for Xtest, the rest are constants that have been defined,(T11,T12,R11,L11,L12)

>> T11(counter1,1)

ans =

     4.1346 + 3.7345i

>> T12(counter1,1)

ans =

    -4.8766 - 1.6522i

>> R11(counter1,1)

ans =

    -1.2971 + 3.0915i

>> L11(counter1,1)

ans =

     4.8939 + 0.8988i

>> L12(counter1,1)

ans =

    -1.7834 + 9.5488i

>> S11e(counter1,1)

ans =

     4.7170 + 2.3709i

>> S22e(counter1,1)

ans =

     0.0222 - 0.2871i

>> S12e(counter1,1)

ans =

     0.3975 - 2.3266i

>> syms  Xtest
>> P = ((T11(counter1,1)-L11(counter1,1))/(T12(counter1,1)-(L12(counter1,1)*Xtest)))^2 - ((T12(counter1,1)*Xtest - L12(counter1,1))/(T12(counter1,1)*Xtest - L12(counter1,1)*(Xtest^2)))

P =

- (Xtest*(2745295363781011/562949953421312 + 7440648460943983/4503599627370496*I) - 8031595954485133/4503599627370496 + 335968815892787/35184372088832*I)/(Xtest*(2745295363781011/562949953421312 + 7440648460943983/4503599627370496*I) - Xtest^2*(8031595954485133/4503599627370496 - 335968815892787/35184372088832*I)) - 1/(Xtest*(8031595954485133/4503599627370496 - 335968815892787/35184372088832*I) - 2745295363781011/562949953421312 - 7440648460943983/4503599627370496*I)^2*(591387244714502586985380151581/79228162514264337593543950336 + 2729658162811733403516616363985/633825300114114700748351602688*I)

>> [Xtest] = double(solve (P))

Xtest =

    -0.0750 - 0.5247i
    -0.0844 + 0.5639i
    -0.2597 - 1.7345i

>>

Matlab solve the equation and states that Xtest has 3 values

-0.0750 - 0.5247i

-0.0844 + 0.5639i

-0.2597 - 1.7345i

Xtest(1) is the first value, Xtest(2) is 2nd and Xtest(3)is third. now lets substitude Xtest(1,2&3) into the original equation, it should = to 0, or at least very cose to 0.

but see, only the 2nd and 3rd is =0 the 1st answer is clearly not 0, what went wrong here? is this a bug in matlab?

>> ((T11(counter1,1)-L11(counter1,1))/(T12(counter1,1)-(L12(counter1,1)*Xtest(1))))^2 - ((T12(counter1,1)*Xtest(1) - L12(counter1,1))/(T12(counter1,1)*Xtest(1) - L12(counter1,1)*(Xtest(1)^2)))

ans =

     1.1977 + 0.1702i

>> ((T11(counter1,1)-L11(counter1,1))/(T12(counter1,1)-(L12(counter1,1)*Xtest(2))))^2 - ((T12(counter1,1)*Xtest(2) - L12(counter1,1))/(T12(counter1,1)*Xtest(2) - L12(counter1,1)*(Xtest(2)^2)))

ans =

   -3.5527e-014 -4.9738e-014i

>> ((T11(counter1,1)-L11(counter1,1))/(T12(counter1,1)-(L12(counter1,1)*Xtest(3))))^2 - ((T12(counter1,1)*Xtest(3) - L12(counter1,1))/(T12(counter1,1)*Xtest(3) - L12(counter1,1)*(Xtest(3)^2)))

ans =

    1.7347e-017 -8.6736e-019i

>>

Answer 1

[Walter Roberson]

It does appear to be a bug. That extra point is one of two singularities (the other singularity is its complex conjugate)

[raymond]

I'm sorry, i dont understand you :-(

shouldn't the answer be a one that, if substitude back into the equation, will yield 0?

if it doesn comply to the equation, then it shouldn't be consider an answer,

is there a way to make it, say, ignore the singularities (wrong answer)

[Walter Roberson]

Yes, the answers *should* be ones that substitute back to yield 0. You have correctly identified a bug that is giving back extra answers. The extra answer is at a location where (if you had enough decimal places) the expression would divide by 0. There is no way to make it ignore the wrong answers because it has a bug and does not know they are wrong answers.

Answer 2

[raymond]

how can i make the program not to display the extra singularities?