Symbolic équation factorisation : how to identify automatically the factor in front one variable and put it into a variable

Hello,

I have a system of very long symbolic equations with many different symbolic variables which could be factorized that way:

B1=A11*V1+A12*V2+.....+A1n*Vn
:
Bm=Am1*V1+Am2*V2+.....+Amn*Vn

The coefficients Aij are a sum and multiplication of different symbolic variables and I would like to extra it to put it in a symbolic array. Is there a matlab function that I don,t know of capable of doing this?

Thank you for your time, Rémy

PS: Here is a simple example: The two equations I could have :

a=e*c*V1-c*V2+d*V1+f
b=d*e*V2+e*V1+f*d*V1+e*f*V2+e

I would like to be able to identify automatically the factors in front of Vi and put them into an array such as:

B(1)=a-f
B(2)=b-e
A(1,1)=e*c+d
A(1,2)=-c
A(2,1)=e+f*d
A(2,2)=d*e+e*f

[Walter Roberson]

Your example is confusing, as you define a in terms of c and then define c in term of a, which would requires that a be expanded, and so end up defining c in terms of c . When you do that kind of thing, you are almost certain to end up with nonlinear equations, whereas your B1..Bm form is strictly linear forms.

[Rémy Bretin]

Oh yeah excuse me, I tried to make up a simple example, and I haven't realized that mistake, I will correct it.

Answer 1

[Walter Roberson]

syms a b c d V1 V2 x
E1 = b*c*V1-c*V2+d*V1+b;
E2 = d*x*V2+a*V1+b*d*V1+a*b*V2+a;
E3 = d*b*V2 + c;   %suppose V1 coefficient is 0?
eqns = [E1;E2;E3];
neqns = length(eqns);
vars = [V1;V2];
nvars = length(vars);
A = zeros(neqns, nvars + 1, 'sym');
extvars = [sym(1); vars];
for eqidx = 1 : neqns
  [P,Q] = coeffs(eqns(eqidx), vars);
  [tf, exvidx] = ismember(Q, extvars);
  A(eqidx, exvidx(tf)) = P(tf);
end
B = A(:,1);
A = A(:,2:end);

[Walter Roberson]

Much more simple:

>> [A,B] = equationsToMatrix(eqns,vars)
A =
[ d + b*c,        -c]
[ a + b*d, a*b + d*x]
[       0,       b*d]
B =
 -b
 -a
 -c

[Rémy Bretin]

Thank you a lot for the answer, it does what I wanted.

Have good evening.