Solve system of equations when plotting
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Hi,
I'm trying to solve a system of equations below symbolically. The challenge is that it only works symbolically if variables 'phi' and 'psi' are defined with numeric values as opposed to symbolic variables (this makes sense, since when 'phi' and 'psi' are defined, the system becomes a system of 5 equations and 5 unknowns as opposed to 5 equations and 7 unknowns.
This works:
t = 1;
t2 = 1;
k = 1;
k2 = 1;
a1 = 1;
phi = pi/3;
psi = pi/6;
syms a2 a3 b1 b2 b3
S = solve(b1 == a1*t + a2*1j*k,b2 == a1*1j*k + a2*t, b3==a3*t2 + b2*1j*k2*exp(1j*phi), ...
a2 == exp(1j*phi)*(b2*t2*exp(1j*phi)+a3*1j*k2), a3 == b3*exp(2j*psi));
S.b1
This does not
t = 1;
t2 = 1;
k = 1;
k2 = 1;
a1 = 1;
syms a2 a3 b1 b2 b3 phi psi
S = solve(b1 == a1*t + a2*1j*k,b2 == a1*1j*k + a2*t, b3==a3*t2 + b2*1j*k2*exp(1j*phi), ...
a2 == exp(1j*phi)*(b2*t2*exp(1j*phi)+a3*1j*k2), a3 == b3*exp(2j*psi));
S.b1
However, I'd like to try to plot each variable (say, b1) with respect to phi and psi changing. This means that I can't define it before hand. I've hit a bit of a roadblock as to how to do this.
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Answers (1)
Walter Roberson
on 13 Oct 2023
t = 1;
t2 = 1;
k = 1;
k2 = 1;
a1 = 1;
syms a2 a3 b1 b2 b3 phi psi
eqns = [b1 == a1*t + a2*1j*k,b2 == a1*1j*k + a2*t, b3==a3*t2 + b2*1j*k2*exp(1j*phi), ...
a2 == exp(1j*phi)*(b2*t2*exp(1j*phi)+a3*1j*k2), a3 == b3*exp(2j*psi)]
symvar(eqns)
size(eqns)
S = solve(eqns)
S.b1
You have 5 equations in 6 unknowns. solve() is going to guess which variables to solve for
S2 = solve(eqns, [a2 a3 b1 b2 b3])
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