/* MJ-5 Units II-III: dimensional/algebraic residuals. */
kill(all)$
assume(a0>0,A>0)$
a:a0+A*(1-cos(eta))$
cycle_endpoint_residual:trigsimp(subst(2*%pi,eta,a)-subst(0,eta,a))$
print("cycle_endpoint_residual =",cycle_endpoint_residual)$

/* Raman energy bookkeeping: scattered photon plus molecular gain. */
energy_residual:ratsimp(h*nu0-(h*(nu0-num)+h*num))$
print("raman_energy_residual =",energy_residual)$

/* Equivalent algebraic forms of the Bose occupation factor. */
bose_factor_identity_residual:
    ratsimp(exp(beta*(eps-mu))/(exp(beta*(eps-mu))-1)-
            1/(1-exp(-beta*(eps-mu))))$
print("bose_factor_identity_residual =",bose_factor_identity_residual)$

/* Square the Saha prefactor to avoid fractional-power sign assumptions. */
saha_units_residual:ratsimp((mass^3*energy^3/hbar^6)/(length^(-6))-1)$
/* With energy = mass*length^2/time^2 and hbar = mass*length^2/time. */
saha_units_residual:ev(saha_units_residual,
                       energy=mass*length^2/time^2,
                       hbar=mass*length^2/time)$
print("saha_dimensional_residual =",ratsimp(saha_units_residual))$

/* Chandrasekhar scaling: R cancels between relativistic degeneracy and gravity. */
assume(hbar>0,c_light>0,G>0,M>0,mu_e>0,m_u>0,R>0)$
N_e:M/(mu_e*m_u)$
K:hbar*c_light*N_e^(4/3)/R$
W:-G*M^2/R$
M_limit:(hbar*c_light/G)^(3/2)/(mu_e*m_u)^2$
chandrasekhar_balance_residual:radcan(subst(M_limit,M,K+W))$
print("chandrasekhar_balance_residual =",chandrasekhar_balance_residual)$