How to solve symbolic system of equations?

Question

Ali 2011-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/458-how-to-solve-symbolic-system-of-equations

Hello,

I am dynamically generating a system of symbolic linear equations that I trying to figure out how to solve. For example,

syms a b c

Eqs = [3*a + 4*b + 7*c + 11; 5*a + 3*b + 3*c + 4; 7*a + 13*b + 5*c + 9];

Since these equations are dynamically generated based on user parameters, the variables names can change and so forth, so that is why I need to do this symbolically.

If you do:

rref(Eqs)

you get ans =[1; 0; 0] which is weird.

If anyone knows how to solve this, please let me know. I would appreciate it. If anyone can let me know how to parse these symbolic expressions, I would appreciate it too. How to separate and isolate different variables.

Thanks, Ali

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Answer 1

Kenneth Eaton 2011-1-26

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Easy, use the SOLVE function:

>> S = solve(Eqs)
S = 
      a: [1x1 sym]
      b: [1x1 sym]
      c: [1x1 sym]

And you can convert the symbolic results in these fields to numeric values using the functions SUBS or DOUBLE:

>> subs(S.a)
ans =
      0.2773

Or you could convert all the fields to numeric values and place them in a vector with one call to STRUCTFUN:

>> structfun(@subs,S)
ans =
      0.2773  % The value for a
     -0.2455  % The value for b
     -1.5500  % The value for c

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Ali 2011-1-26

Hi Kenneth,

Thanks again. That was a big help.

Now here is another issue that I am having. Sometimes, I have more equations than I have unknowns. I end up with an overly-constrained system.

I might end up with the following:

Eqs = [3*a + 4*b + 7*c + 11;

5*a + 3*b + 3*c + 4;

7*a + 13*b + 5*c + 9;

3*a + 17*b + 13*c + 5];

Is there any way of solving these equations without involving the use of the optimization toolbox and "linprog(...)??" linprog requires explicit "Aeq*x = Beq" type parameter specifications.

Which begs the question, is it possible to parse these symbolic expressions and separate value from variable?

Sorry for the long post. I would appreciate any help you can give me.

Thanks,

Ali

Walter Roberson 2011-1-27

You can use symvar() and coeff() to extract the variables and their coefficients from multinomial systems.

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Answer 2

Paulo Silva 2011-1-27

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%'3*a + 4*b + 7*c + 11=0' -> '3*a + 4*b + 7*c = -11'
%'5*a + 3*b + 3*c + 4=0' ->  '5*a + 3*b + 3*c = -4' 
%'7*a + 13*b + 5*c + 9=0' -> '7*a + 13*b + 5*c = -9'
A=[3 4 7
   5 3 3
   7 13 5];
B=[-11
    -4
    -9];
X=linsolve(A,B); or X=A\B , same results
a=X(1);
b=X(2);
c=X(3);