How to convert non-linear equations to matrix form?

Question

Priyank 2013-4-18

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https://ww2.mathworks.cn/matlabcentral/answers/72641-how-to-convert-non-linear-equations-to-matrix-form

评论： Danek 2017-3-13

Hi, I am trying to represent a algebraic equation into matrix form and came across an function 'equationToMatrix' but it only converts linear equations to matrix also for a particular equation as below (x+1)(x-1) = x^2 - 1, if i want matlab to get the coefficients of the equation matlab function 'coeffs' shows [1,-1] but if i want to respresent 1*(x^2) + 0*x -1, hence the coeeficient [1,0,-1] is there a function which would decompose a equation into ascending/descending order of power and then compute its coefficient

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Answer 1

Iman Ansari 2013-4-18

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https://ww2.mathworks.cn/matlabcentral/answers/72641-how-to-convert-non-linear-equations-to-matrix-form#answer_82739

在 MATLAB Online 中打开

Hi. Maybe sym2poly:

syms x
C=sym2poly(x^3 - 2*x - 5)
poly2sym(C)

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Answer 2

Andy 2017-2-20

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编辑：Andy 2017-2-20

在 MATLAB Online 中打开

I had a similar question, and I wrote a function which operates exactly like equationsToMatrix, but does not complain when the equations are nonlinear in your chosen variables. Hope it helps!

http://stackoverflow.com/a/42334647/5768063

    function [A,b] = equationsToMatrix( eq, x )
    %FACTORMAT equationsToMatrix for nonlinear equations
    %   factors out the vector x from eq such that eq = Ax + b
    %   eq does not need to be linear in x
    %   eq must be a vector of equations, and x must be a vector of symbols
    assert(isa(eq,'sym'), 'Equations must be symbolic')
    assert(isa(x,'sym'), 'Vector x must be symbolic')
    n = numel(eq);
    m = numel(x);
    A = repmat(sym(0),n,m);
    for i = 1:n % loop through equations
        [c,p] = coeffs(eq(i),x); % coefficients, powers of x(1)...x(n)
        for j = 1:m % loop through x(1)...x(n)
            for k = 1:numel(p) % loop through found powers/coefficients
                if has(p(k),x(j)) % if power has the j'th variable
                    A(i,j) = A(i,j) + p(k)*c(k)/x(j); % add the coefficient
                end
            end
        end
    end
    b = simplify(eq - A*x,'ignoreanalyticconstraints',true);
    end

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Danek 2017-3-13

I was trying to use the method you explained. Is there anyway that you can explain how you put in the equations. I tried defining eq= and x= at the top but it's not allowing the program to run at all. Thank you

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