For manipulating equations that you have mentioned above, the Symbolic Math Toolbox can be very useful. You can use the 'diff' function to find the partial derivative with respect to 'e', 'f' and 'g' and find the coefficients after simplifying the code using the 'simplify' function.
% Defining variables as symbolic
syms a b c d e f g YAL YBL XA XB YBR
eqn = (a*(YBL*e - YBR*e - YAL*f + YBR*f + YAL*g - YBL*g))/(XB*YBL*e - XB*YBR*e - XB*YAL*f + XA*YBR*f - XA*YBL*g + XB*YAL*g) + (c*(XA - XB)*(YBL - YBR))/(XB*YBL*e - XB*YBR*e - XB*YAL*f + XA*YBR*f - XA*YBL*g + XB*YAL*g) + (b*(XA - XB)*(f - g))/(XB*YBL*e - XB*YBR*e - XB*YAL*f + XA*YBR*f - XA*YBL*g + XB*YAL*g) == 1;
% Getting the numerator and denominator for RHS and LHS
[LN, LD] = numden(lhs(eqn));
[RN, RD] = numden(rhs(eqn));
% Simplifying the equation and creating a new equation with denominator as
% 1
neweqn1 = simplify(LN * RD) - simplify(RN * LD) == 0;
% Finding the co-efficients of e, f and g
v_e = diff(neweqn1, e);
v_f = diff(neweqn1, f);
v_g = diff(neweqn1, g);
% Finding the constant expression to create final form of the equation
constant_expr = simplify(lhs(neweqn1) - lhs(v_e*e+v_f*f+v_g*g));
% Equation with rearranged coefficients
finaleqn = lhs(v_e*e+v_f*f+v_g*g) == constant_expr
Also, you can refer to the following documentation for more information:
- 'simplify': https://www.mathworks.com/help/symbolic/simplify.html
- 'numden': https://www.mathworks.com/help/symbolic/sym.numden.html
- 'diff': https://www.mathworks.com/help/symbolic/diff.html
Hope this helps in resolving your query!
