Your belief has preciously little value. Faith in mathematics tends to be a waste of mental energy. Let me expand your equations, looking at them one at a time.
0 < beta_bar
beta_bar < 1
0 < sigma_bar
0 < phi_bar
0 < phi_pi_bar
0 < phi_y_bar
So those are simply lower and upper bounds on the problem. Solve does not understand inequalities, because they never give a unique solution.
syms g_23 phi_y_bar phi_pi_bar theta_bar phi_bar sigma_bar beta_bar
g_23 = solve(g_23^2 - 6835969944064461/9007199254740992 == 0)
g_23 =
That gave us two potential solutions for g_23. One is positive, one negative, but you never said anything about what g_23 should be.
phi_y_bar = solve(phi_y_bar - 3907/20000 == 0)
phi_y_bar =
phi_pi_bar = solve(phi_pi_bar - 14709/10000 == 0)
phi_pi_bar =
Those pair of equations simply assign values to variables. Why would you put lower and upper bounds on something when you then assign it a value?
Next, we see the equation for theta_bar. It has a trivial solution, regardless of the value of g_23.
theta_bar = solve(g_23*theta_bar - (7846842892884325*theta_bar)/9007199254740992 == 0,theta_bar)
Yep. theta_bar is just ZERO. You can see that, if you factor out theta_bar.
Next, we see an equation for phi_bar. I'll tell vpa to just write out the equation itself. Remember, that you told us that phi_bar MUST be positive.
vpa((11137*g_23)/10000 - (7846842892884325*phi_bar)/9007199254740992 + g_23*phi_bar - 1092378616225659/1125899906842624 == 0,5)
ans =
Do you see the first case? That tells us that phi_bar is NEGATIVE. Or the second term offers the possibility that phi_bar is EXACTLY zero. But you told us that phi_bar MUST be positive. Neither of the solutions are valid.
The fact is, we can stop right now. There are NO solutions to your problem.
While I could look at the rest of your problem, there is no need to proceed further. Well, I could write them down. This next one again tells us that phi_bar is NEGATIVE. But since we know it is not allowed to be negative...
(6250*phi_bar)/6197 - (2659174770252075*theta_bar)/1125899906842624 - (12447*phi_bar*theta_bar)/6197 + phi_bar*theta_bar^2 + (11137*theta_bar^2)/10000 + 55685/49576 == 0
ans =
sigma_bar - 11137/10000 == 0
ans =
beta_bar*theta_bar - (6197*theta_bar)/6250 == 0
ans = (11137*beta_bar)/10000 - (6197*phi_bar)/6250 + beta_bar*phi_bar - 1243281529372025/1125899906842624 == 0
ans =
Again, faith is a waste of mental energy. This is simply not a precision problem, but a question of existence at all.