Solve non-linear symbolic equation

i'm trying to find the solution of a non-linear equation using the command solve. the problem is a trigonometric one, where the variables are all dependent of the symbol T.

syms ('T','real');
cth = (1-T^2)/(1+T^2);
sth = 2*T/(1+T^2);

A=[G1 G2; G4 G5]; 
B=[-G3; -G6]; %Gi for i=1:6 is function of T
X = A\B;
x=X(1); %function of T
y=X(2); %function of T

Eq= (x-b1x)^2+(y-b1y)^2 - d^2;
T_values = solve(Eq,T);
T_values = vpa(T_values);
theta = 2*atan(T)

it shows Warning message: Solutions are only valid under certain conditions. To

include parameters and conditions in the solution, specify the

'ReturnConditions' value as 'true'.

then changing to:

T_values = solve(Eq,T,'ReturnConditions',true)

displays the following error: Error using sym>tomupad (line 1539)

Unable to convert 'struct' to 'sym'.

[Torsten]

What do you get using the solve-command without the 'ReturnConditions' == true option ?

[Maneet Kaur Bagga]

Hi Mohamed,

It would be easy to reproduce the code and solve the error if you provide the values of the variables.

[Walter Roberson]

syms ('T','real');
cth = (1-T^2)/(1+T^2);
sth = 2*T/(1+T^2);

A=[G1 G2; G4 G5]; 
B=[-G3; -G6]; %Gi for i=1:6 is function of T
X = A\B;
x=X(1); %function of T
y=X(2); %function of T

Eq= (x-b1x)^2+(y-b1y)^2 - d^2;
sol = solve(Eq,T,'returnconditions', true);
T_values = vpa(sol.T);
theta = 2*atan(T_values)

sol.conditions
vpa(sol.conditions)

We cannot execute because you have not defined the G variables.

Answer 1

[Karan Singh]

Hi Mohamed,

The “solve” function in MATLAB is used to solve equations. By default, it returns all solutions without any conditions. However, in some cases, the solutions are only valid under certain conditions. The warning message you're seeing is MATLAB telling you that the solutions it found might only be valid under certain conditions. By specifying “ReturnConditions”, “true”, you're asking MATLAB to return these conditions along with the solutions.

However, the error message you're seeing is because you're trying to assign the output of “solve” with “ReturnConditions”, “true” to a single variable “T_values”. When you specify “ReturnConditions”, “true”, “solve” returns three outputs: the solutions, the parameters in the solutions, and the conditions on the parameters.

To fix the error, you should assign the output of “solve” to three variables, like this:

[sol, params, conditions] = solve(Eq, T, 'ReturnConditions', true); 

After this, you can use “vpa” to convert “sol” to a numeric approximation:

T_values = vpa(sol); 

Attached below are the documentation links that you may find helpful:

• Equations and systems solver - MATLAB solve (mathworks.com)
• Variable-precision arithmetic (arbitrary-precision arithmetic) - MATLAB vpa (mathworks.com)

Hope this helps!

Karan Singh Khati

[Walter Roberson]

When you specify “ReturnConditions”, “true”, “solve” returns three outputs:

syms p
sol = solve(p^2 > 3, p, 'returnconditions', true)

sol = struct with fields:
             p: [2×1 sym]
    parameters: x
    conditions: [2×1 sym]

sol.p

ans = 

sol.conditions

ans = 

Single output is fine.

However

vpa(sol)

Error using sym>tomupad
Unable to convert 'struct' to 'sym'.

Error in sym (line 273)
S.s = tomupad(x);

Error in vpa (line 46)
ss = sym(s);

That is because vpa() is not defined on a struct. You would need to vpa() something extracted from the struct

vpa(sol.p)

[Karan Singh]

Thanks Walter for the correction!