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"Warning: Unable to find explicit solution. For options, see help."

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Tatjana
Tatjana 2021 年 1 月 15 日
Trying to solve a system of non-linear equations, but I get the above error message.
Here is my code:
clear all
syms h_1 h_2 h_3 h_4 h_5 h_6 l m_1 m_2 m_3 m_4 m_5 m_6
eq1 = h_6*m_1*m_6+2*h_5*m_1*m_5+h_4*m_1*m_4-2*h_6*(m_3)^2-4*h_5*m_2*m_3-2*h_3*m_1*m_3-2*h_4*(m_2)^2-2*h_2*m_1*m_2-h_1*m_1^2+(h_4*h_6-(h_5)^2)*l == 0;
eq2 = 2*h_6*m_2*m_6-4*h_6*m_3*m_5-4*h_4*m_1*m_5-4*h_5*m_3*m_4-2*h_4*m_2*m_4-4*h_2*m_1*m_4-2*h_1*m_1*m_2+(2*h_3*h_5-2*h_2*h_6)*l == 0;
eq3 = -2*h_6*m_3*m_6-4*h_5*m_2*m_6-4*h_3*m_1*m_6-4*h_4*m_2*m_5-4*h_2*m_1*m_5+2*h_4*m_3*m_4-2*h_1*m_1*m_3+(2*h_2*h_5-2*h_3*h_4)*l == 0;
eq4 = h_6*m_4*m_6-2*h_6*m_5^2-2*h_5*m_4*m_5-4*h_3*m_2*m_5-h_4*m_4^2+2*h_3*m_3*m_4-2*h_2*m_2*m_4+h_1*m_1*m_4-2*h_1*m_2^2+(h_1*h_6-h_3^2)*l == 0;
eq5 = -2*h_6*m_5*m_6-4*h_5*m_4*m_6-4*h_3*m_2*m_6-2*h_4*m_4*m_5+2*h_1*m_1*m_5-4*h_2*m_3*m_4-4*h_1*m_2*m_3+(2*h_2*h_3-2*h_1*h_5)*l == 0;
eq6 = -h_6*m_6^2-2*h_5*m_5*m_6+h_4*m_4*m_6-2*h_4*m_3*m_6+2*h_2*m_2*m_6+h_1*m_1*m_6-2*h_4*m_5^2-4*h_2*m_3*m_5-2*h_1*m_3^2+(h_1*h_4-h_2^2)*l == 0;
eq7 = h_1*h_4*h_6-h_2^2*h_6-h_1*h_5^2+2*h_2*h_3*h_5-h_3^2*h_4-1 == 0;
sols = solve([eq1,eq2,eq3,eq4,eq5,eq6,eq7],[h_1, h_2, h_3, h_4, h_5, h_6, l], 'returnconditions', true)
The m_i are known and I need the solution in terms of the m_i. I know there is a solution but I need to confirm as I cannot solve this by hand.
Is this to hard to solve or is my code wrong? Thanks for any help

  3 件のコメント

Daniel Pollard
Daniel Pollard 2021 年 1 月 15 日
Those equations are massive and very complicated. I'm not in the least bit surprised it found no solutions.
If you're 100% certain there are solutions which it should have found, check your code for errors. If I'd typed that out, even if I was careful, I'm guarunteed a million mistakes.
Tatjana
Tatjana 2021 年 1 月 15 日
Thanks for your answer! Yes they are massive but I pretty much did copy and paste. You see, those h_i are actually entries of a metric and the m_i come from a symmetric matrix. Those eqs come from a function differentiated in different directions. Is there no way I can get a solution for that?
Athrey Ranjith Krishnanunni
Athrey Ranjith Krishnanunni 2021 年 1 月 16 日
It would help to know what the actual mathematical equations are, and the physical context from which they came.

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