How can I find the trivial solution to a polynomial equation?

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MathWorks Support Team 2021-9-24

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https://ww2.mathworks.cn/matlabcentral/answers/1459974-how-can-i-find-the-trivial-solution-to-a-polynomial-equation

回答： MathWorks Support Team 2021-9-24

Given is a polynomial of the folllowing form,

pol = c11 + c12*x + c13*x^2 + c14*x^3 - (c21 + c22*x + c23*x^2 + c34*x^3)

How can I have MATLAB find the trivial roots 'c11 = c21', 'c12 = c22', 'c13 = c23' and 'c14 = c34' by means of the Symbolic Math Toolbox?

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Answer 1

MathWorks Support Team 2021-9-24

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1459974-how-can-i-find-the-trivial-solution-to-a-polynomial-equation#answer_794174

Firstly, function 'coeffs' has to be used in order to factorize the latter expression with respect to the unknown variable 'x', namely,

syms c11 c12 c13 c14 c21 c22 c23 c34 x
pol = c11 + c12*x + c13*x^2 + c14*x^3 - (c21 + c22*x + c23*x^2 + c34*x^3);
pol_c = coeffs(pol,x)

See the following documentation page for more information accordingly,

https://de.mathworks.com/help/symbolic/sym.coeffs.html

This will return a vector of the corresponding factors of the latter polynomial expression with respect to 'x' that has the size of the number of powers of 'x' in the expression, from 0 up to the highest power. Thus, in this case one would obtain a vector 'pol_c' with four symbolic factors, namely,

>> pol_c

pol_c =

[c11 - c21, c12 - c22, c13 - c23, c14 - c34]

Then, please consider using function 'solve' for the symbolic equation that results if you set the latter vector equal to a vector of zeros, namely,

sol = solve(pol_c == zeros(1, length(pol_c)));

In this way, 'sol' is a struct that contains as field names the names of the unknown variables and as fields the corresponding solution for each of the aforementioned equations. For instance,

>> sol.c11

ans =

c21