Datasets:
RANDMEDIATION
/
PhysicsBabel

Dataset card Data Studio Files
xet
 Community
1
size
int64
2
8
keys
stringlengths
10
106
symbols
stringlengths
3
29
domains
stringclasses
62 values
pi
stringlengths
3
46
equation
stringlengths
10
59
name
stringclasses
19 values
n_const
int64
0
4
n_domains
int64
1
6
max_exp
int64
1
34
exp_l1
int64
2
134
complexity
float64
0
113
score
float64
-104.8
10
plausible
bool
2 classes
exponents
stringlengths
27
177
5
capacitance,current,kin_viscosity,length,mass
m·ℓ·ν·i·C_e
em,mechanics
m·ℓ⁻⁶·ν⁴·i⁻²·C_e
m = k₀ · ℓ⁶·ν⁻⁴·i²·C_e⁻¹
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "-6", "kin_viscosity": "4", "current": "-2", "capacitance": "1"}
5
current,inductance,kin_viscosity,length,mass
m·ℓ·ν·i·L_e
em,mechanics
m·ℓ⁻²·ν²·i⁻²·L_e⁻¹
m = k₀ · ℓ²·ν⁻²·i²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "kin_viscosity": "2", "current": "-2", "inductance": "-1"}
5
current,efield,kin_viscosity,length,mass
m·ℓ·ν·i·E_f
em,mechanics
m·ℓ⁻⁵·ν³·i⁻¹·E_f⁻¹
m = k₀ · ℓ⁵·ν⁻³·i·E_f
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "-5", "kin_viscosity": "3", "current": "-1", "efield": "-1"}
5
bfield,current,kin_viscosity,length,mass
m·ℓ·ν·i·B
em,mechanics
m·ℓ⁻⁴·ν²·i⁻¹·B⁻¹
m = k₀ · ℓ⁴·ν⁻²·i·B
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "-4", "kin_viscosity": "2", "current": "-1", "bfield": "-1"}
5
current,kin_viscosity,length,mag_flux,mass
m·ℓ·ν·i·Φ
em,mechanics
m·ℓ⁻²·ν²·i⁻¹·Φ⁻¹
m = k₀ · ℓ²·ν⁻²·i·Φ
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "kin_viscosity": "2", "current": "-1", "mag_flux": "-1"}
5
current,kin_viscosity,length,mass,permittivity
m·ℓ·ν·i·ε
em,mechanics
m·ℓ⁻⁵·ν⁴·i⁻²·ε
m = k₀ · ℓ⁵·ν⁻⁴·i²·ε⁻¹
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "-5", "kin_viscosity": "4", "current": "-2", "permittivity": "1"}
5
current,kin_viscosity,length,mass,permeability
m·ℓ·ν·i·μ₀
em,mechanics
m·ℓ⁻³·ν²·i⁻²·μ₀⁻¹
m = k₀ · ℓ³·ν⁻²·i²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "kin_viscosity": "2", "current": "-2", "permeability": "-1"}
5
conductivity,current,kin_viscosity,length,mass
m·ℓ·ν·i·σ
em,mechanics
m·ℓ⁻³·ν³·i⁻²·σ
m = k₀ · ℓ³·ν⁻³·i²·σ⁻¹
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-3", "kin_viscosity": "3", "current": "-2", "conductivity": "1"}
5
current,kin_viscosity,length,mass,resistivity
m·ℓ·ν·i·ρ_e
em,mechanics
m·ℓ⁻³·ν³·i⁻²·ρ_e⁻¹
m = k₀ · ℓ³·ν⁻³·i²·ρ_e
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "-3", "kin_viscosity": "3", "current": "-2", "resistivity": "-1"}
5
kin_viscosity,length,mass,resistance,voltage
m·ℓ·ν·U·R
em,mechanics
m·ℓ⁻⁴·ν³·U⁻²·R
m = k₀ · ℓ⁴·ν⁻³·U²·R⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "-4", "kin_viscosity": "3", "voltage": "-2", "resistance": "1"}
5
capacitance,kin_viscosity,length,mass,voltage
m·ℓ·ν·U·C_e
em,mechanics
m·ℓ⁻²·ν²·U⁻²·C_e⁻¹
m = k₀ · ℓ²·ν⁻²·U²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "kin_viscosity": "2", "voltage": "-2", "capacitance": "-1"}
5
inductance,kin_viscosity,length,mass,voltage
m·ℓ·ν·U·L_e
em,mechanics
m·ℓ⁻⁶·ν⁴·U⁻²·L_e
m = k₀ · ℓ⁶·ν⁻⁴·U²·L_e⁻¹
null
0
2
6
14
12.4
-2.9
false
{"mass": "1", "length": "-6", "kin_viscosity": "4", "voltage": "-2", "inductance": "1"}
5
kin_viscosity,length,mass,permittivity,voltage
m·ℓ·ν·U·ε
em,mechanics
m·ℓ⁻³·ν²·U⁻²·ε⁻¹
m = k₀ · ℓ³·ν⁻²·U²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "-3", "kin_viscosity": "2", "voltage": "-2", "permittivity": "-1"}
5
kin_viscosity,length,mass,permeability,voltage
m·ℓ·ν·U·μ₀
em,mechanics
m·ℓ⁻⁵·ν⁴·U⁻²·μ₀
m = k₀ · ℓ⁵·ν⁻⁴·U²·μ₀⁻¹
null
0
2
5
13
11.2
-1.7
false
{"mass": "1", "length": "-5", "kin_viscosity": "4", "voltage": "-2", "permeability": "1"}
5
conductivity,kin_viscosity,length,mass,voltage
m·ℓ·ν·U·σ
em,mechanics
m·ℓ⁻⁵·ν³·U⁻²·σ⁻¹
m = k₀ · ℓ⁵·ν⁻³·U²·σ
null
0
2
5
12
10.5
-1
false
{"mass": "1", "length": "-5", "kin_viscosity": "3", "voltage": "-2", "conductivity": "-1"}
5
kin_viscosity,length,mass,resistivity,voltage
m·ℓ·ν·U·ρ_e
em,mechanics
m·ℓ⁻⁵·ν³·U⁻²·ρ_e
m = k₀ · ℓ⁵·ν⁻³·U²·ρ_e⁻¹
null
0
2
5
12
10.5
-1
false
{"mass": "1", "length": "-5", "kin_viscosity": "3", "voltage": "-2", "resistivity": "1"}
5
elem_charge,kin_viscosity,length,mass,voltage
m·ℓ·ν·U·e
constants,em,mechanics
m·ℓ⁻²·ν²·U⁻¹·e⁻¹
m = k₀ · ℓ²·ν⁻²·U·e
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "-2", "kin_viscosity": "2", "voltage": "-1", "elem_charge": "-1"}
5
efield,kin_viscosity,length,mass,resistance
m·ℓ·ν·R·E_f
em,mechanics
m·ℓ⁻⁶·ν³·R·E_f⁻²
m = k₀ · ℓ⁶·ν⁻³·R⁻¹·E_f²
null
0
2
6
13
11.7
-2.2
false
{"mass": "1", "length": "-6", "kin_viscosity": "3", "resistance": "1", "efield": "-2"}
5
bfield,kin_viscosity,length,mass,resistance
m·ℓ·ν·R·B
em,mechanics
m·ℓ⁻⁴·ν·R·B⁻²
m = k₀ · ℓ⁴·ν⁻¹·R⁻¹·B²
null
0
2
4
9
7.9
1.6
false
{"mass": "1", "length": "-4", "kin_viscosity": "1", "resistance": "1", "bfield": "-2"}
5
capacitance,efield,kin_viscosity,length,mass
m·ℓ·ν·C_e·E_f
em,mechanics
m·ℓ⁻⁴·ν²·C_e⁻¹·E_f⁻²
m = k₀ · ℓ⁴·ν⁻²·C_e·E_f²
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "kin_viscosity": "2", "capacitance": "-1", "efield": "-2"}
5
capacitance,elem_charge,kin_viscosity,length,mass
m·ℓ·ν·C_e·e
constants,em,mechanics
m·ℓ⁻²·ν²·C_e·e⁻²
m = k₀ · ℓ²·ν⁻²·C_e⁻¹·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "-2", "kin_viscosity": "2", "capacitance": "1", "elem_charge": "-2"}
5
efield,inductance,kin_viscosity,length,mass
m·ℓ·ν·L_e·E_f
em,mechanics
m·ℓ⁻⁸·ν⁴·L_e·E_f⁻²
m = k₀ · ℓ⁸·ν⁻⁴·L_e⁻¹·E_f²
null
0
2
8
16
14.8
-5.3
false
{"mass": "1", "length": "-8", "kin_viscosity": "4", "inductance": "1", "efield": "-2"}
5
bfield,inductance,kin_viscosity,length,mass
m·ℓ·ν·L_e·B
em,mechanics
m·ℓ⁻⁶·ν²·L_e·B⁻²
m = k₀ · ℓ⁶·ν⁻²·L_e⁻¹·B²
null
0
2
6
12
11
-1.5
false
{"mass": "1", "length": "-6", "kin_viscosity": "2", "inductance": "1", "bfield": "-2"}
5
inductance,kin_viscosity,length,mag_flux,mass
m·ℓ·ν·L_e·Φ
em,mechanics
m·ℓ⁻²·ν²·L_e·Φ⁻²
m = k₀ · ℓ²·ν⁻²·L_e⁻¹·Φ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "kin_viscosity": "2", "inductance": "1", "mag_flux": "-2"}
5
efield,kin_viscosity,length,mass,permittivity
m·ℓ·ν·E_f·ε
em,mechanics
m·ℓ⁻⁵·ν²·E_f⁻²·ε⁻¹
m = k₀ · ℓ⁵·ν⁻²·E_f²·ε
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "-5", "kin_viscosity": "2", "efield": "-2", "permittivity": "-1"}
5
efield,kin_viscosity,length,mass,permeability
m·ℓ·ν·E_f·μ₀
em,mechanics
m·ℓ⁻⁷·ν⁴·E_f⁻²·μ₀
m = k₀ · ℓ⁷·ν⁻⁴·E_f²·μ₀⁻¹
null
0
2
7
15
13.6
-4.1
false
{"mass": "1", "length": "-7", "kin_viscosity": "4", "efield": "-2", "permeability": "1"}
5
conductivity,efield,kin_viscosity,length,mass
m·ℓ·ν·E_f·σ
em,mechanics
m·ℓ⁻⁷·ν³·E_f⁻²·σ⁻¹
m = k₀ · ℓ⁷·ν⁻³·E_f²·σ
null
0
2
7
14
12.9
-3.4
false
{"mass": "1", "length": "-7", "kin_viscosity": "3", "efield": "-2", "conductivity": "-1"}
5
efield,kin_viscosity,length,mass,resistivity
m·ℓ·ν·E_f·ρ_e
em,mechanics
m·ℓ⁻⁷·ν³·E_f⁻²·ρ_e
m = k₀ · ℓ⁷·ν⁻³·E_f²·ρ_e⁻¹
null
0
2
7
14
12.9
-3.4
false
{"mass": "1", "length": "-7", "kin_viscosity": "3", "efield": "-2", "resistivity": "1"}
5
efield,elem_charge,kin_viscosity,length,mass
m·ℓ·ν·E_f·e
constants,em,mechanics
m·ℓ⁻³·ν²·E_f⁻¹·e⁻¹
m = k₀ · ℓ³·ν⁻²·E_f·e
null
1
3
3
8
7.3
1.7
false
{"mass": "1", "length": "-3", "kin_viscosity": "2", "efield": "-1", "elem_charge": "-1"}
5
bfield,kin_viscosity,length,mass,permeability
m·ℓ·ν·B·μ₀
em,mechanics
m·ℓ⁻⁵·ν²·B⁻²·μ₀
m = k₀ · ℓ⁵·ν⁻²·B²·μ₀⁻¹
null
0
2
5
11
9.8
-0.3
false
{"mass": "1", "length": "-5", "kin_viscosity": "2", "bfield": "-2", "permeability": "1"}
5
bfield,conductivity,kin_viscosity,length,mass
m·ℓ·ν·B·σ
em,mechanics
m·ℓ⁻⁵·ν·B⁻²·σ⁻¹
m = k₀ · ℓ⁵·ν⁻¹·B²·σ
null
0
2
5
10
9.1
0.4
false
{"mass": "1", "length": "-5", "kin_viscosity": "1", "bfield": "-2", "conductivity": "-1"}
5
bfield,kin_viscosity,length,mass,resistivity
m·ℓ·ν·B·ρ_e
em,mechanics
m·ℓ⁻⁵·ν·B⁻²·ρ_e
m = k₀ · ℓ⁵·ν⁻¹·B²·ρ_e⁻¹
null
0
2
5
10
9.1
0.4
false
{"mass": "1", "length": "-5", "kin_viscosity": "1", "bfield": "-2", "resistivity": "1"}
5
bfield,elem_charge,kin_viscosity,length,mass
m·ℓ·ν·B·e
constants,em,mechanics
m·ℓ⁻²·ν·B⁻¹·e⁻¹
m = k₀ · ℓ²·ν⁻¹·B·e
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "-2", "kin_viscosity": "1", "bfield": "-1", "elem_charge": "-1"}
5
kin_viscosity,length,mag_flux,mass,permeability
m·ℓ·ν·Φ·μ₀
em,mechanics
m·ℓ⁻¹·ν²·Φ⁻²·μ₀
m = k₀ · ℓ·ν⁻²·Φ²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "kin_viscosity": "2", "mag_flux": "-2", "permeability": "1"}
5
conductivity,kin_viscosity,length,mag_flux,mass
m·ℓ·ν·Φ·σ
em,mechanics
m·ℓ⁻¹·ν·Φ⁻²·σ⁻¹
m = k₀ · ℓ·ν⁻¹·Φ²·σ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-1", "kin_viscosity": "1", "mag_flux": "-2", "conductivity": "-1"}
5
kin_viscosity,length,mag_flux,mass,resistivity
m·ℓ·ν·Φ·ρ_e
em,mechanics
m·ℓ⁻¹·ν·Φ⁻²·ρ_e
m = k₀ · ℓ·ν⁻¹·Φ²·ρ_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-1", "kin_viscosity": "1", "mag_flux": "-2", "resistivity": "1"}
5
elem_charge,kin_viscosity,length,mass,permittivity
m·ℓ·ν·ε·e
constants,em,mechanics
m·ℓ⁻¹·ν²·ε·e⁻²
m = k₀ · ℓ·ν⁻²·ε⁻¹·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "-1", "kin_viscosity": "2", "permittivity": "1", "elem_charge": "-2"}
5
conductivity,elem_charge,kin_viscosity,length,mass
m·ℓ·ν·σ·e
constants,em,mechanics
m·ℓ·ν·σ·e⁻²
m = k₀ · ℓ⁻¹·ν⁻¹·σ⁻¹·e²
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "1", "kin_viscosity": "1", "conductivity": "1", "elem_charge": "-2"}
5
elem_charge,kin_viscosity,length,mass,resistivity
m·ℓ·ν·ρ_e·e
constants,em,mechanics
m·ℓ·ν·ρ_e⁻¹·e⁻²
m = k₀ · ℓ⁻¹·ν⁻¹·ρ_e·e²
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "1", "kin_viscosity": "1", "resistivity": "-1", "elem_charge": "-2"}
5
amount,kin_viscosity,length,mass,molar_energy
m·ℓ·ν·n·E_m
chemistry,mechanics
m·ℓ⁻²·ν²·n⁻¹·E_m⁻¹
m = k₀ · ℓ²·ν⁻²·n·E_m
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "kin_viscosity": "2", "amount": "-1", "molar_energy": "-1"}
5
cat_activity,kin_viscosity,length,mass,molar_mass
m·ℓ·ν·M_m·z
chemistry,mechanics
m·ℓ⁻²·ν·M_m⁻¹·z⁻¹
m = k₀ · ℓ²·ν⁻¹·M_m·z
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "kin_viscosity": "1", "molar_mass": "-1", "cat_activity": "-1"}
5
concentration,kin_viscosity,length,mass,molar_energy
m·ℓ·ν·c_n·E_m
chemistry,mechanics
m·ℓ⁻⁵·ν²·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ⁵·ν⁻²·c_n·E_m
null
0
2
5
10
9.1
0.4
false
{"mass": "1", "length": "-5", "kin_viscosity": "2", "concentration": "-1", "molar_energy": "-1"}
6
boltzmann,gas_constant,kin_viscosity,length,mass,molar_energy
m·ℓ·ν·E_m·R·k_B
chemistry,constants,mechanics
m·ℓ⁻²·ν²·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ²·ν⁻²·E_m·R⁻¹·k_B
null
1
3
2
8
7.1
1.9
false
{"mass": "1", "length": "-2", "kin_viscosity": "2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
5
cat_activity,kin_viscosity,length,mass,molar_energy
m·ℓ·ν·E_m·z
chemistry,mechanics
m·ℓ⁻⁴·ν³·E_m⁻¹·z⁻¹
m = k₀ · ℓ⁴·ν⁻³·E_m·z
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "-4", "kin_viscosity": "3", "molar_energy": "-1", "cat_activity": "-1"}
5
avogadro,kin_viscosity,length,mass,molar_energy
m·ℓ·ν·E_m·N_A
chemistry,constants,mechanics
m·ℓ⁻²·ν²·E_m⁻¹·N_A
m = k₀ · ℓ²·ν⁻²·E_m·N_A⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "-2", "kin_viscosity": "2", "molar_energy": "-1", "avogadro": "1"}
4
grav_const,kin_viscosity,length,mass
m·ℓ·ν·G
constants,mechanics
m·ℓ·ν⁻²·G
m = k₀ · ℓ⁻¹·ν²·G⁻¹
null
1
2
2
5
3.8
5.7
true
{"mass": "1", "length": "1", "kin_viscosity": "-2", "grav_const": "1"}
5
entropy,length,mass,omega,temperature
m·ℓ·ω·Θ·S_e
mechanics,thermo
m·ℓ²·ω²·Θ⁻¹·S_e⁻¹
m = k₀ · ℓ⁻²·ω⁻²·Θ·S_e
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "2", "temperature": "-1", "entropy": "-1"}
5
heat_capacity,length,mass,omega,temperature
m·ℓ·ω·Θ·C
mechanics,thermo
m·ℓ²·ω²·Θ⁻¹·C⁻¹
m = k₀ · ℓ⁻²·ω⁻²·Θ·C
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "2", "temperature": "-1", "heat_capacity": "-1"}
5
length,mass,omega,temperature,thermal_cond
m·ℓ·ω·Θ·κ
mechanics,thermo
m·ℓ·ω³·Θ⁻¹·κ⁻¹
m = k₀ · ℓ⁻¹·ω⁻³·Θ·κ
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "1", "omega": "3", "temperature": "-1", "thermal_cond": "-1"}
6
amount,gas_constant,length,mass,omega,temperature
m·ℓ·ω·Θ·n·R
chemistry,mechanics,thermo
m·ℓ²·ω²·Θ⁻¹·n⁻¹·R⁻¹
m = k₀ · ℓ⁻²·ω⁻²·Θ·n·R
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "omega": "2", "temperature": "-1", "amount": "-1", "gas_constant": "-1"}
6
concentration,gas_constant,length,mass,omega,temperature
m·ℓ·ω·Θ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻¹·ω²·Θ⁻¹·c_n⁻¹·R⁻¹
m = k₀ · ℓ·ω⁻²·Θ·c_n·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-1", "omega": "2", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,gas_constant,length,mass,omega,temperature
m·ℓ·ω·Θ·R·z
chemistry,mechanics,thermo
m·ℓ²·ω³·Θ⁻¹·R⁻¹·z⁻¹
m = k₀ · ℓ⁻²·ω⁻³·Θ·R·z
null
0
3
3
9
8.3
0.7
false
{"mass": "1", "length": "2", "omega": "3", "temperature": "-1", "gas_constant": "-1", "cat_activity": "-1"}
6
avogadro,gas_constant,length,mass,omega,temperature
m·ℓ·ω·Θ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ²·ω²·Θ⁻¹·R⁻¹·N_A
m = k₀ · ℓ⁻²·ω⁻²·Θ·R·N_A⁻¹
null
1
4
2
8
7.7
0.8
false
{"mass": "1", "length": "2", "omega": "2", "temperature": "-1", "gas_constant": "-1", "avogadro": "1"}
5
boltzmann,length,mass,omega,temperature
m·ℓ·ω·Θ·k_B
constants,mechanics,thermo
m·ℓ²·ω²·Θ⁻¹·k_B⁻¹
m = k₀ · ℓ⁻²·ω⁻²·Θ·k_B
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "omega": "2", "temperature": "-1", "boltzmann": "-1"}
5
entropy,expansion,length,mass,omega
m·ℓ·ω·S_e·β
mechanics,thermo
m·ℓ²·ω²·S_e⁻¹·β
m = k₀ · ℓ⁻²·ω⁻²·S_e·β⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "2", "entropy": "-1", "expansion": "1"}
6
entropy,gas_constant,length,mass,molar_energy,omega
m·ℓ·ω·S_e·E_m·R
chemistry,mechanics,thermo
m·ℓ²·ω²·S_e⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻²·ω⁻²·S_e·E_m·R⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "omega": "2", "entropy": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
expansion,heat_capacity,length,mass,omega
m·ℓ·ω·C·β
mechanics,thermo
m·ℓ²·ω²·C⁻¹·β
m = k₀ · ℓ⁻²·ω⁻²·C·β⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "2", "heat_capacity": "-1", "expansion": "1"}
6
gas_constant,heat_capacity,length,mass,molar_energy,omega
m·ℓ·ω·C·E_m·R
chemistry,mechanics,thermo
m·ℓ²·ω²·C⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻²·ω⁻²·C·E_m·R⁻¹
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "omega": "2", "heat_capacity": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
length,mass,omega,specific_heat,thermal_cond
m·ℓ·ω·c·κ
mechanics,thermo
m·ℓ⁻¹·ω·c·κ⁻¹
m = k₀ · ℓ·ω⁻¹·c⁻¹·κ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "omega": "1", "specific_heat": "1", "thermal_cond": "-1"}
5
expansion,length,mass,omega,thermal_cond
m·ℓ·ω·κ·β
mechanics,thermo
m·ℓ·ω³·κ⁻¹·β
m = k₀ · ℓ⁻¹·ω⁻³·κ·β⁻¹
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "1", "omega": "3", "thermal_cond": "-1", "expansion": "1"}
6
gas_constant,length,mass,molar_mass,omega,thermal_cond
m·ℓ·ω·κ·M_m·R
chemistry,mechanics,thermo
m·ℓ⁻¹·ω·κ⁻¹·M_m⁻¹·R
m = k₀ · ℓ·ω⁻¹·κ·M_m·R⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "-1", "omega": "1", "thermal_cond": "-1", "molar_mass": "-1", "gas_constant": "1"}
6
gas_constant,length,mass,molar_energy,omega,thermal_cond
m·ℓ·ω·κ·E_m·R
chemistry,mechanics,thermo
m·ℓ·ω³·κ⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻¹·ω⁻³·κ·E_m·R⁻¹
null
0
3
3
8
7.6
1.4
false
{"mass": "1", "length": "1", "omega": "3", "thermal_cond": "-1", "molar_energy": "-1", "gas_constant": "1"}
6
amount,expansion,gas_constant,length,mass,omega
m·ℓ·ω·β·n·R
chemistry,mechanics,thermo
m·ℓ²·ω²·β·n⁻¹·R⁻¹
m = k₀ · ℓ⁻²·ω⁻²·β⁻¹·n·R
null
0
3
2
8
7.1
1.9
false
{"mass": "1", "length": "2", "omega": "2", "expansion": "1", "amount": "-1", "gas_constant": "-1"}
6
concentration,expansion,gas_constant,length,mass,omega
m·ℓ·ω·β·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻¹·ω²·β·c_n⁻¹·R⁻¹
m = k₀ · ℓ·ω⁻²·β⁻¹·c_n·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-1", "omega": "2", "expansion": "1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,expansion,gas_constant,length,mass,omega
m·ℓ·ω·β·R·z
chemistry,mechanics,thermo
m·ℓ²·ω³·β·R⁻¹·z⁻¹
m = k₀ · ℓ⁻²·ω⁻³·β⁻¹·R·z
null
0
3
3
9
8.3
0.7
false
{"mass": "1", "length": "2", "omega": "3", "expansion": "1", "gas_constant": "-1", "cat_activity": "-1"}
6
avogadro,expansion,gas_constant,length,mass,omega
m·ℓ·ω·β·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ²·ω²·β·R⁻¹·N_A
m = k₀ · ℓ⁻²·ω⁻²·β⁻¹·R·N_A⁻¹
null
1
4
2
8
7.7
0.8
false
{"mass": "1", "length": "2", "omega": "2", "expansion": "1", "gas_constant": "-1", "avogadro": "1"}
5
boltzmann,expansion,length,mass,omega
m·ℓ·ω·β·k_B
constants,mechanics,thermo
m·ℓ²·ω²·β·k_B⁻¹
m = k₀ · ℓ⁻²·ω⁻²·β⁻¹·k_B
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "omega": "2", "expansion": "1", "boltzmann": "-1"}
5
charge,length,mass,omega,voltage
m·ℓ·ω·q·U
em,mechanics
m·ℓ²·ω²·q⁻¹·U⁻¹
m = k₀ · ℓ⁻²·ω⁻²·q·U
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "2", "charge": "-1", "voltage": "-1"}
5
charge,length,mass,omega,resistance
m·ℓ·ω·q·R
em,mechanics
m·ℓ²·ω·q⁻²·R⁻¹
m = k₀ · ℓ⁻²·ω⁻¹·q²·R
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "1", "charge": "-2", "resistance": "-1"}
5
capacitance,charge,length,mass,omega
m·ℓ·ω·q·C_e
em,mechanics
m·ℓ²·ω²·q⁻²·C_e
m = k₀ · ℓ⁻²·ω⁻²·q²·C_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "omega": "2", "charge": "-2", "capacitance": "1"}
5
charge,efield,length,mass,omega
m·ℓ·ω·q·E_f
em,mechanics
m·ℓ·ω²·q⁻¹·E_f⁻¹
m = k₀ · ℓ⁻¹·ω⁻²·q·E_f
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "omega": "2", "charge": "-1", "efield": "-1"}
5
charge,length,mag_flux,mass,omega
m·ℓ·ω·q·Φ
em,mechanics
m·ℓ²·ω·q⁻¹·Φ⁻¹
m = k₀ · ℓ⁻²·ω⁻¹·q·Φ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "2", "omega": "1", "charge": "-1", "mag_flux": "-1"}
5
charge,length,mass,omega,permittivity
m·ℓ·ω·q·ε
em,mechanics
m·ℓ³·ω²·q⁻²·ε
m = k₀ · ℓ⁻³·ω⁻²·q²·ε⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "3", "omega": "2", "charge": "-2", "permittivity": "1"}
5
charge,conductivity,length,mass,omega
m·ℓ·ω·q·σ
em,mechanics
m·ℓ³·ω·q⁻²·σ
m = k₀ · ℓ⁻³·ω⁻¹·q²·σ⁻¹
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "3", "omega": "1", "charge": "-2", "conductivity": "1"}
5
charge,length,mass,omega,resistivity
m·ℓ·ω·q·ρ_e
em,mechanics
m·ℓ³·ω·q⁻²·ρ_e⁻¹
m = k₀ · ℓ⁻³·ω⁻¹·q²·ρ_e
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "3", "omega": "1", "charge": "-2", "resistivity": "-1"}
5
current,length,mass,omega,voltage
m·ℓ·ω·i·U
em,mechanics
m·ℓ²·ω³·i⁻¹·U⁻¹
m = k₀ · ℓ⁻²·ω⁻³·i·U
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "2", "omega": "3", "current": "-1", "voltage": "-1"}
5
current,length,mass,omega,resistance
m·ℓ·ω·i·R
em,mechanics
m·ℓ²·ω³·i⁻²·R⁻¹
m = k₀ · ℓ⁻²·ω⁻³·i²·R
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "2", "omega": "3", "current": "-2", "resistance": "-1"}
5
capacitance,current,length,mass,omega
m·ℓ·ω·i·C_e
em,mechanics
m·ℓ²·ω⁴·i⁻²·C_e
m = k₀ · ℓ⁻²·ω⁻⁴·i²·C_e⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "omega": "4", "current": "-2", "capacitance": "1"}
5
current,inductance,length,mass,omega
m·ℓ·ω·i·L_e
em,mechanics
m·ℓ²·ω²·i⁻²·L_e⁻¹
m = k₀ · ℓ⁻²·ω⁻²·i²·L_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "omega": "2", "current": "-2", "inductance": "-1"}
5
current,efield,length,mass,omega
m·ℓ·ω·i·E_f
em,mechanics
m·ℓ·ω³·i⁻¹·E_f⁻¹
m = k₀ · ℓ⁻¹·ω⁻³·i·E_f
null
0
2
3
7
6
3.5
true
{"mass": "1", "length": "1", "omega": "3", "current": "-1", "efield": "-1"}
5
current,length,mag_flux,mass,omega
m·ℓ·ω·i·Φ
em,mechanics
m·ℓ²·ω²·i⁻¹·Φ⁻¹
m = k₀ · ℓ⁻²·ω⁻²·i·Φ
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "2", "current": "-1", "mag_flux": "-1"}
5
current,length,mass,omega,permittivity
m·ℓ·ω·i·ε
em,mechanics
m·ℓ³·ω⁴·i⁻²·ε
m = k₀ · ℓ⁻³·ω⁻⁴·i²·ε⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "3", "omega": "4", "current": "-2", "permittivity": "1"}
5
current,length,mass,omega,permeability
m·ℓ·ω·i·μ₀
em,mechanics
m·ℓ·ω²·i⁻²·μ₀⁻¹
m = k₀ · ℓ⁻¹·ω⁻²·i²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "omega": "2", "current": "-2", "permeability": "-1"}
5
conductivity,current,length,mass,omega
m·ℓ·ω·i·σ
em,mechanics
m·ℓ³·ω³·i⁻²·σ
m = k₀ · ℓ⁻³·ω⁻³·i²·σ⁻¹
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "3", "omega": "3", "current": "-2", "conductivity": "1"}
5
current,length,mass,omega,resistivity
m·ℓ·ω·i·ρ_e
em,mechanics
m·ℓ³·ω³·i⁻²·ρ_e⁻¹
m = k₀ · ℓ⁻³·ω⁻³·i²·ρ_e
null
0
2
3
10
8.1
1.4
false
{"mass": "1", "length": "3", "omega": "3", "current": "-2", "resistivity": "-1"}
5
length,mass,omega,resistance,voltage
m·ℓ·ω·U·R
em,mechanics
m·ℓ²·ω³·U⁻²·R
m = k₀ · ℓ⁻²·ω⁻³·U²·R⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "length": "2", "omega": "3", "voltage": "-2", "resistance": "1"}
5
capacitance,length,mass,omega,voltage
m·ℓ·ω·U·C_e
em,mechanics
m·ℓ²·ω²·U⁻²·C_e⁻¹
m = k₀ · ℓ⁻²·ω⁻²·U²·C_e
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "omega": "2", "voltage": "-2", "capacitance": "-1"}
5
inductance,length,mass,omega,voltage
m·ℓ·ω·U·L_e
em,mechanics
m·ℓ²·ω⁴·U⁻²·L_e
m = k₀ · ℓ⁻²·ω⁻⁴·U²·L_e⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "1", "length": "2", "omega": "4", "voltage": "-2", "inductance": "1"}
5
length,mass,omega,permittivity,voltage
m·ℓ·ω·U·ε
em,mechanics
m·ℓ·ω²·U⁻²·ε⁻¹
m = k₀ · ℓ⁻¹·ω⁻²·U²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "omega": "2", "voltage": "-2", "permittivity": "-1"}
5
length,mass,omega,permeability,voltage
m·ℓ·ω·U·μ₀
em,mechanics
m·ℓ³·ω⁴·U⁻²·μ₀
m = k₀ · ℓ⁻³·ω⁻⁴·U²·μ₀⁻¹
null
0
2
4
11
9.3
0.2
false
{"mass": "1", "length": "3", "omega": "4", "voltage": "-2", "permeability": "1"}
5
conductivity,length,mass,omega,voltage
m·ℓ·ω·U·σ
em,mechanics
m·ℓ·ω³·U⁻²·σ⁻¹
m = k₀ · ℓ⁻¹·ω⁻³·U²·σ
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "1", "omega": "3", "voltage": "-2", "conductivity": "-1"}
5
length,mass,omega,resistivity,voltage
m·ℓ·ω·U·ρ_e
em,mechanics
m·ℓ·ω³·U⁻²·ρ_e
m = k₀ · ℓ⁻¹·ω⁻³·U²·ρ_e⁻¹
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "1", "omega": "3", "voltage": "-2", "resistivity": "1"}
5
elem_charge,length,mass,omega,voltage
m·ℓ·ω·U·e
constants,em,mechanics
m·ℓ²·ω²·U⁻¹·e⁻¹
m = k₀ · ℓ⁻²·ω⁻²·U·e
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "omega": "2", "voltage": "-1", "elem_charge": "-1"}
5
bfield,length,mass,omega,resistance
m·ℓ·ω·R·B
em,mechanics
m·ℓ⁻²·ω·R·B⁻²
m = k₀ · ℓ²·ω⁻¹·R⁻¹·B²
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "omega": "1", "resistance": "1", "bfield": "-2"}
5
length,mag_flux,mass,omega,resistance
m·ℓ·ω·R·Φ
em,mechanics
m·ℓ²·ω·R·Φ⁻²
m = k₀ · ℓ⁻²·ω⁻¹·R⁻¹·Φ²
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "omega": "1", "resistance": "1", "mag_flux": "-2"}
5
elem_charge,length,mass,omega,resistance
m·ℓ·ω·R·e
constants,em,mechanics
m·ℓ²·ω·R⁻¹·e⁻²
m = k₀ · ℓ⁻²·ω⁻¹·R·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "omega": "1", "resistance": "-1", "elem_charge": "-2"}
5
capacitance,elem_charge,length,mass,omega
m·ℓ·ω·C_e·e
constants,em,mechanics
m·ℓ²·ω²·C_e·e⁻²
m = k₀ · ℓ⁻²·ω⁻²·C_e⁻¹·e²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "length": "2", "omega": "2", "capacitance": "1", "elem_charge": "-2"}
5
bfield,inductance,length,mass,omega
m·ℓ·ω·L_e·B
em,mechanics
m·ℓ⁻²·ω²·L_e·B⁻²
m = k₀ · ℓ²·ω⁻²·L_e⁻¹·B²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "omega": "2", "inductance": "1", "bfield": "-2"}
5
inductance,length,mag_flux,mass,omega
m·ℓ·ω·L_e·Φ
em,mechanics
m·ℓ²·ω²·L_e·Φ⁻²
m = k₀ · ℓ⁻²·ω⁻²·L_e⁻¹·Φ²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "2", "omega": "2", "inductance": "1", "mag_flux": "-2"}
5
efield,length,mass,omega,permittivity
m·ℓ·ω·E_f·ε
em,mechanics
m·ℓ⁻¹·ω²·E_f⁻²·ε⁻¹
m = k₀ · ℓ·ω⁻²·E_f²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "omega": "2", "efield": "-2", "permittivity": "-1"}