How to plot the symbolic expression given by "root"

Question

MGMKLML 2017-5-24

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编辑： Karan Gill 2017-10-17

Hello.

I want to solve the 3rd degree symbolic equation. I chose "solve" for this purpose. It gives the answer with "root(...)"; For example,

root(z^3 - (9*z^2)/10 + (17*z)/40 - 9/40, z, 1)
root(z^3 - (9*z^2)/10 + (17*z)/40 - 9/40, z, 2)
root(z^3 - (9*z^2)/10 + (17*z)/40 - 9/40, z, 3)

Now I want to plot this function, I mean, z^3 - (9*z^2)/10 + (17*z)/40. The problem is that this expression depends on the coefficients I give to the function. I could copy and paste this equation myself but then I need to do it everytime I change the coefficients which is pretty uncomfortable.

Is it possible to get the symbolic expression or just to make MATLAB plot the function somehow without doing it manually?

The code is here:

function draft14 
clc;
fsys = @(x,y,z,c,mu1,s1,r2,b,s2) [c*y - mu1*x + x*z + s1; ...
                                r2*y*(1 - b*y) - x*y; ...
                                z - x*y + s2];                                               
c = 0.2;
mu1 = 0.5;
s1 = 0.1;
r2 = 0.9;
b = 0.5;
s2 = 0;
par = [c mu1 s1 r2 b s2];
f = @(t,x) fsys(x(1),x(2),x(3),par(1),par(2),par(3),par(4),par(5),par(6));
tspan = 0:0.01:2;
y0 = [0.1 0.9 0.1];
[~,Y] = ode45(f,tspan,y0); 
plot3(Y(:,1),Y(:,2),Y(:,3)); hold on;
plot3(y0(1),y0(2),y0(3), 'o','LineWidth',3);
xlabel('X'); ylabel('Y'); zlabel('Z');
figure;
plot(Y(:,1),Y(:,2)); 
xlabel('X'); ylabel('Y');
cubeq(par);
end
function cubeq(par) %Решает численно кубическое уравнение
c = par(1);
mu1 = par(2);
s1 = par(3);
r2 = par(4);
b = par(5);
s2 = par(6);
syms x
f = x^3 - r2*x^2 + (c + mu1*r2*b)*x - r2*(b*s1 + c);
s = solve(f,x);
disp('Решение кубического уравнения:');
disp(s);
clear x;
end

P.S. In the code above you can see than I set the parameters in the first function and then give it to the "cubeq" function. In the "cubeq" function I need to plot the cubic parabola, on which the roots depend.

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Answer 1

Karan Gill 2017-5-25

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编辑：Karan Gill 2017-10-17

在 MATLAB Online 中打开

If I understand correctly, you're asking " How can I automatically substitute values into a symbolic expression?". Use the subs function: https://www.mathworks.com/help/symbolic/subs.html

Googling " substitute value symbolic matlab " should show " subs " as the first result.

Here, use something like

    params = [c mu1 ...];
    paramValues = [0.2 0.5 ...];
    f = subs(f,params,paramValues)

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MGMKLML 2017-5-25

Not exactly what I meant. I meant to plot the function which is given in the root expression, I mean, what stands under "root(...)"

Karan Gill 2017-5-26

Then use children and fplot as Walter said.

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Answer 2

Star Strider 2017-5-25

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在 MATLAB Online 中打开

See if using vpasolve instead of solve does what you want:

s = vpasolve(f,x);

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Answer 3

Walter Roberson 2017-5-25

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Once you have a root() expression, you can use children() on it to extract the formula, after which you can plot as per usual, either by subs in numeric values or by fplot()