Question about solving symbolic coupled non-linear equations

5 Dec 2024
1 Answer
Answer Accepted
Updated 6 Dec 2024
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Ran in:
Hi all, I have some questions about solving non-linear coupled equations in symbolic form. My code is as follows:
syms p q a v lambda K C
eqns = [((lambda*(a^4)/2)*p^3 +(3*lambda*v*(a^4)/2)*p^2 + (lambda*(a^4)/2)*p*q^2 + (lambda*v*(a^4)/2)*q^2 + lambda*(a^4)*(v^2)*p + (K/2)*q + C) == 0, (lambda*(a^4)*v*p*q +(lambda*(a^4)/2)*q^3 + (lambda*(a^4)/2)*(p^2)*q -(K/2)*p) == 0 ];
S = solve(eqns,[p q])
S = struct with fields:
p: [3x1 sym] q: [3x1 sym]
disp(S)
p: [3x1 sym] q: [3x1 sym]
It does not return to any symbolic solutions. Does it mean that the solution does not exist or I miss some codes?

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 Accepted Answer

Walter Roberson
Walter Roberson on 5 Dec 2024
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The main issue was that you are displaying a struct, and symbolic variable arrays are not expanded for struct.
The second issue was that the answers use root() constructs to shorten the presentation of the roots of a cubic. You can specify maxdegree to cause the roots of the cubic polynomial to be expanded.
syms p q a v lambda K C
eqns = [((lambda*(a^4)/2)*p^3 +(3*lambda*v*(a^4)/2)*p^2 + (lambda*(a^4)/2)*p*q^2 + (lambda*v*(a^4)/2)*q^2 + lambda*(a^4)*(v^2)*p + (K/2)*q + C) == 0, (lambda*(a^4)*v*p*q +(lambda*(a^4)/2)*q^3 + (lambda*(a^4)/2)*(p^2)*q -(K/2)*p) == 0 ];
S = solve(eqns,[p q], 'maxdegre', 3)
S = struct with fields:
p: [3x1 sym] q: [3x1 sym]
disp(char((S.p)))
[v + (v*(K^2 - 4*C*a^4*lambda*v)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/(2*((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)) - ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)/2 + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (3^(1/2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3))*1i)/2))/(2*C*K) - (a^4*lambda*(4*C^2 + K^2*v^2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/(2*((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)) - ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)/2 + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (3^(1/2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3))*1i)/2)^2)/(2*C*K^2); v + (v*(K^2 - 4*C*a^4*lambda*v)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/(2*((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)) - ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)/2 + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) + (3^(1/2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3))*1i)/2))/(2*C*K) - (a^4*lambda*(4*C^2 + K^2*v^2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/(2*((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)) - ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)/2 + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) + (3^(1/2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3))*1i)/2)^2)/(2*C*K^2); v + (v*(K^2 - 4*C*a^4*lambda*v)*(((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) - ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2))))/(2*C*K) - (a^4*lambda*(4*C^2 + K^2*v^2)*(((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) - ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)))^2)/(2*C*K^2)]
disp(char((S.q)))
[((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/(2*((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)) - ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)/2 + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (3^(1/2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3))*1i)/2; ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/(2*((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)) - ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3)/2 + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) + (3^(1/2)*(((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3))*1i)/2; ((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) - ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))/((((C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) + ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^2 + ((K^4 - 6*C*K^2*a^4*lambda*v)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)) - (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^2/(9*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^3)^(1/2) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)^3/(27*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^3) - (C*K^3)/(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2) - ((2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)*(K^4 - 6*C*K^2*a^4*lambda*v))/(6*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2)^2))^(1/3) + (2*K^3*a^4*lambda*v - 4*C*K*a^8*lambda^2*v^2)/(3*(4*C^2*a^8*lambda^2 + K^2*a^8*lambda^2*v^2))]

4 Comments
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Tsz Tsun
Tsz Tsun on 5 Dec 2024
I also have a question, it says p, q is a [3x1] sym, should I get 3 solutions?
Torsten
Torsten on 5 Dec 2024
Edited: Torsten on 5 Dec 2024
Yes, S.p and S.q are 3x1 vectors. Here, (S.p(i),S.q(i)) are corresponding solutions for p and q (i = 1,2,3).

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