Table 3. Unit table used for our automated dimensional analysis.

Variables	Units	m	s	kg	T	V
a, g	Acceleration	1	−2	0	0	0
h, ℏ, L, Jz	Angular momentum	2	−1	1	0	0
A	Area	2	0	0	0	0
kb	Boltzmann constant	2	−2	1	−1	0
C	Capacitance	2	−2	1	0	−2
q, q1, q2	Charge	2	−2	1	0	−1
j	Current density	0	−3	1	0	−1
I, I0	Current Intensity	2	−3	1	0	−1
ρ, ρ0	Density	−3	0	1	0	0
θ, θ1, θ2, σ, n	Dimensionless	0	0	0	0	0
g_, kf, γ, χ, β, α	Dimensionless	0	0	0	0	0
pγ, n0, δ, f, μ	Dimensionless	0	0	0	0	0
n0, δ, f, μ, Z1, Z2	Dimensionless	0	0	0	0	0
D	Diffusion coefficient	2	−1	0	0	0
μdrift	Drift velocity constant	0	−1	1	0	0
pd	Electric dipole moment	3	−2	1	0	−1
Ef	Electric field	−1	0	0	0	1
ϵ	Electric permitivity	1	−2	1	0	−2
E, K, U	Energy	2	−2	1	0	0
Eden	Energy density	−1	−2	1	0	0
FE	Energy flux	0	−3	1	0	0
F, Nn	Force	1	−2	1	0	0
ω, ω0	Frequency	0	−1	0	0	0
kG	Grav. coupling (Gm1m2)	3	−2	1	0	0
H	Hubble constant	0	−1	0	0	0
Lind	Inductance	−2	4	−1	0	2
nrho	Inverse volume	−3	0	0	0	0
x, x1, x2, x3	Length	1	0	0	0	0
y, y1, y2, y3	Length	1	0	0	0	0
z, z1, z2, r, r1, r2	Length	1	0	0	0	0
λ, d1, d2, d, ff, af	Length	1	0	0	0	0
I1, I2, I*, I*0	Light intensity	0	−3	1	0	0
B, Bx, By, Bz	Magnetic field	−2	1	0	0	1
μm	Magnetic moment	4	−3	1	0	−1
M	Magnetization	1	−3	1	0	−1
m, m0, m1, m2	Mass	0	0	1	0	0
μe	Mobility	0	1	−1	0	0
p	Momentum	1	−1	1	0	0
G	Newton’s constant	3	−2	−1	0	0
P*	Polarization	0	−2	1	0	−1
P	Power	2	−3	1	0	0
pF	Pressure	−1	−2	1	0	0
R	Resistance	−2	3	−1	0	2
μS	Shear modulus	−1	−2	1	0	0
Lrad	Spectral radiance	0	−2	1	0	0
kspring	Spring constant	0	−2	1	0	0
σden	Surface charge density	0	−2	1	0	−1
T, T1, T2	Temperature	0	0	0	1	0
κ	Thermal conductivity	1	−3	1	−1	0
t, t1	Time	0	1	0	0	0
τ	Torque	2	−2	1	0	0
Avec	Vector potential	−1	1	0	0	1
u, v, v1, c, w	Velocity	1	−1	0	0	0
V, V1, V2	Volume	3	0	0	0	0
ρc, ρc0	Volume charge density	−1	−2	1	0	−1
Ve	Voltage	0	0	0	0	1
k	Wave number	−1	0	0	0	0
Y	Young modulus	−1	−2	1	0	0