trying to find all possible roots of the following;
[125/2(1-sqrt(3i))]^1/3
tried the below, but keep getting error;
is not a valid expression or equations_o_l_v_e=double(solve('((125/2)(1-sqrt(3i)))^1/3'));MATLAB: Roots of complex numbers
complex numbers roots
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I'm going to walk through your code and comment on a few things along the way.
%All known or base variables%
Xc = [];Yc = [];e = 5.194469088;f = 5.193588373;a1 = 5.2548;a4 = 0.2271;fi2 = 1.046746555;%All substitute value variables%
P1 = 2 * Xc * f;Because Xc is empty so is P1. P1 is not a function of Xc or anything like that. If it were a function of Xc it would be something like:
P1 = @(Xc) 2*Xc*f;Continuing on with your code:
P2 = e * cos(fi2);Q1 = 2 * Yc * f;Q1 is empty for the same reason P1 is except for Yc instead of Xc.
Q2 = -e * sin(fi2);R1 = Xc.^2 + Yc.^2 + f^2 - a1^2;R2 = Xc -a4;R1 and R2 are empty because they're also functions of the empty matrix Xc. An empty plus or minus a scalar is still empty by scalar "expansion".
%Equation Parts%
Part1 = (R1 * Q2) - (R2 * Q1);Part2 = (P1 * R2) - (P2 * R1);Part3 = (P1 * Q2) - (P2 * Q1);Each of these three parts is also empty.
%Equation and Plot%
eq = @(Xc,Yc) (Part1.^2 + Part2.^2 - Part3.^2);So your "function of Xc and Yc" actually doesn't depend on the inputs Xc and Yc at all. It returns the sum and difference of three empty matrices, which means a simpler way of writing eq is:
eq = @(~, ~) [];So when you call fimplicit:
figure;fimplicit (eq,[-100 100 -100 100]);It passes in something nonempty and receives an empty back. That's why it issues the warning.
You probably want to make Part1, Part2, and Part3 functions of Xc and Yc, which will require making the P#, Q#, and R# lines into functions like I did with P1 (and calling them as functions rather than referring to them as variables.)
R2016b:
>> rts=roots([16 -32 116 0 -100])rts = 0.904997916303652 + 2.626226923351172i 0.904997916303652 - 2.626226923351172i 1.000000000000000 + 0.000000000000000i -0.809995832607303 + 0.000000000000000i>> rts(logical(~imag(rts) & real(rts)>=0 & real(rts)<=1))ans = 1.000000000000000>> num2hex(rts(3))ans =3feffffffffffffc>> polyval([16 -32 116 0 -100],rts(3))ans = -8.526512829121202e-14>> polyval([16 -32 116 0 -100],1)ans = 0R2011a:
>> rts=roots([16 -32 116 0 -100])rts = 0.904997916303650 + 2.626226923351169i 0.904997916303650 - 2.626226923351169i 1.000000000000000 -0.809995832607303 >> rts(logical(~imag(rts) & real(rts)>=0 & real(rts)<=1))ans = Empty matrix: 0-by-1>> num2strexact(rts(3))ans =1.000000000000000444089209850062616169452667236328125>> num2hex(rts(3))ans =3ff0000000000002>> polyval([16 -32 116 0 -100],rts(3))ans = 8.526512829121202e-014>> polyval([16 -32 116 0 -100],1)ans = 0So it looks like the roots function (which uses eig in the background) has different behavior depending on the version. The versions missed being exactly 1.0 by 2-3 least significant bits (one version less than and the other version greater than). You will have to adjust your code to account for this.
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