How to make solve stop when a non-trivial solution is first found

Question

Tommi Muller 2020-6-1

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/539315-how-to-make-solve-stop-when-a-non-trivial-solution-is-first-found

回答： Abhisek Pradhan 2020-6-5

I have a system of quadratic equations I would like to solve, something like below:

syms q11 q12 q13 q21 q22 q23 q31 q32 q33
[q11_sol, q12_sol, q13_sol, q21_sol, q22_sol, q23_sol, q31_sol, q32_sol, q33_sol] = ...
    solve(...
    q11*q22 == q12*q21*((T(1,1)*T(2,2))/(T(2,1)*T(1,2))), ...
    q22*q33 == q23*q32*((T(2,2)*T(3,3))/(T(3,2)*T(2,3))), ...
    q11*q33 == q13*q31*((T(1,1)*T(3,3))/(T(3,1)*T(1,3))), ...
    q31^2 + q32^2 + q33^2 == 1, ...
    q21^2 + q22^2 + q23^2 == 1, ...
    q11^2 + q12^2 + q13^2 == 1, ...
    q21*q31 + q22*q32 + q23*q33 == 0, ...
    q11*q31 + q12*q32 + q13*q33 == 0, ...
    q11*q21 + q12*q22 + q13*q23 == 0);

where T is some matrix I defined.

My issue is that solving this system takes a long time, and I just want one non-trivial solution (just one solution that doesn't have 0's or 1's or -1's in it).

Is there a way for me to tell the solve function to stop when a non-trivial solution is first found?

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Star Strider 2020-6-1

Unrecognized function or variable 'T'.

Tommi Muller 2020-6-1

I mentioned that T is some predefined 3x3 matrix, but let's say for example that:

T = [-2/15, 8, 4; 2/5, -6, 6; -1/30, -1, 1/4];

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Answer 1

Abhisek Pradhan 2020-6-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/539315-how-to-make-solve-stop-when-a-non-trivial-solution-is-first-found#answer_446537

solve by default returns one of the many solutions. Now the problem lies in getting a solution which is not trivial. the following, link may help in working with full solution.

https://in.mathworks.com/help/symbolic/solve-an-algebraic-equation.html#buhn64h