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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
4 | force,length,mass,time | m·ℓ·t·F | mechanics | m·ℓ·t⁻²·F⁻¹ | m = k₀ · ℓ⁻¹·t²·F | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "1", "time": "-2", "force": "-1"} |
4 | energy,length,mass,time | m·ℓ·t·E | mechanics | m·ℓ²·t⁻²·E⁻¹ | m = k₀ · ℓ⁻²·t²·E | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "time": "-2", "energy": "-1"} |
4 | length,mass,time,torque | m·ℓ·t·τ | mechanics | m·ℓ²·t⁻²·τ⁻¹ | m = k₀ · ℓ⁻²·t²·τ | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "2", "time": "-2", "torque": "-1"} |
4 | length,mass,power,time | m·ℓ·t·P | mechanics | m·ℓ²·t⁻³·P⁻¹ | m = k₀ · ℓ⁻²·t³·P | null | 0 | 1 | 3 | 7 | 5.1 | 4.9 | true | {"mass": "1", "length": "2", "time": "-3", "power": "-1"} |
4 | length,mass,momentum,time | m·ℓ·t·p | mechanics | m·ℓ·t⁻¹·p⁻¹ | m = k₀ · ℓ⁻¹·t·p | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "1", "time": "-1", "momentum": "-1"} |
4 | ang_momentum,length,mass,time | m·ℓ·t·Lₐ | mechanics | m·ℓ²·t⁻¹·Lₐ⁻¹ | m = k₀ · ℓ⁻²·t·Lₐ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "2", "time": "-1", "ang_momentum": "-1"} |
4 | action,length,mass,time | m·ℓ·t·S | mechanics | m·ℓ²·t⁻¹·S⁻¹ | m = k₀ · ℓ⁻²·t·S | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "2", "time": "-1", "action": "-1"} |
4 | length,mass,pressure,time | m·ℓ·t·P_p | mechanics | m·ℓ⁻¹·t⁻²·P_p⁻¹ | m = k₀ · ℓ·t²·P_p | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "-1", "time": "-2", "pressure": "-1"} |
4 | length,mass,time,viscosity | m·ℓ·t·μ | mechanics | m·ℓ⁻¹·t⁻¹·μ⁻¹ | m = k₀ · ℓ·t·μ | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "-1", "time": "-1", "viscosity": "-1"} |
5 | entropy,length,mass,temperature,time | m·ℓ·t·Θ·S_e | mechanics,thermo | m·ℓ²·t⁻²·Θ⁻¹·S_e⁻¹ | m = k₀ · ℓ⁻²·t²·Θ·S_e | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "temperature": "-1", "entropy": "-1"} |
5 | heat_capacity,length,mass,temperature,time | m·ℓ·t·Θ·C | mechanics,thermo | m·ℓ²·t⁻²·Θ⁻¹·C⁻¹ | m = k₀ · ℓ⁻²·t²·Θ·C | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "temperature": "-1", "heat_capacity": "-1"} |
5 | length,mass,temperature,thermal_cond,time | m·ℓ·t·Θ·κ | mechanics,thermo | m·ℓ·t⁻³·Θ⁻¹·κ⁻¹ | m = k₀ · ℓ⁻¹·t³·Θ·κ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "1", "time": "-3", "temperature": "-1", "thermal_cond": "-1"} |
6 | amount,gas_constant,length,mass,temperature,time | m·ℓ·t·Θ·n·R | chemistry,mechanics,thermo | m·ℓ²·t⁻²·Θ⁻¹·n⁻¹·R⁻¹ | m = k₀ · ℓ⁻²·t²·Θ·n·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "time": "-2", "temperature": "-1", "amount": "-1", "gas_constant": "-1"} |
6 | concentration,gas_constant,length,mass,temperature,time | m·ℓ·t·Θ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻¹·t⁻²·Θ⁻¹·c_n⁻¹·R⁻¹ | m = k₀ · ℓ·t²·Θ·c_n·R | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "-1", "time": "-2", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"} |
6 | cat_activity,gas_constant,length,mass,temperature,time | m·ℓ·t·Θ·R·z | chemistry,mechanics,thermo | m·ℓ²·t⁻³·Θ⁻¹·R⁻¹·z⁻¹ | m = k₀ · ℓ⁻²·t³·Θ·R·z | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "1", "length": "2", "time": "-3", "temperature": "-1", "gas_constant": "-1", "cat_activity": "-1"} |
6 | avogadro,gas_constant,length,mass,temperature,time | m·ℓ·t·Θ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ²·t⁻²·Θ⁻¹·R⁻¹·N_A | m = k₀ · ℓ⁻²·t²·Θ·R·N_A⁻¹ | null | 1 | 4 | 2 | 8 | 7.7 | 0.8 | false | {"mass": "1", "length": "2", "time": "-2", "temperature": "-1", "gas_constant": "-1", "avogadro": "1"} |
5 | boltzmann,length,mass,temperature,time | m·ℓ·t·Θ·k_B | constants,mechanics,thermo | m·ℓ²·t⁻²·Θ⁻¹·k_B⁻¹ | m = k₀ · ℓ⁻²·t²·Θ·k_B | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "time": "-2", "temperature": "-1", "boltzmann": "-1"} |
5 | entropy,expansion,length,mass,time | m·ℓ·t·S_e·β | mechanics,thermo | m·ℓ²·t⁻²·S_e⁻¹·β | m = k₀ · ℓ⁻²·t²·S_e·β⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "entropy": "-1", "expansion": "1"} |
6 | entropy,gas_constant,length,mass,molar_energy,time | m·ℓ·t·S_e·E_m·R | chemistry,mechanics,thermo | m·ℓ²·t⁻²·S_e⁻¹·E_m⁻¹·R | m = k₀ · ℓ⁻²·t²·S_e·E_m·R⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "time": "-2", "entropy": "-1", "molar_energy": "-1", "gas_constant": "1"} |
5 | expansion,heat_capacity,length,mass,time | m·ℓ·t·C·β | mechanics,thermo | m·ℓ²·t⁻²·C⁻¹·β | m = k₀ · ℓ⁻²·t²·C·β⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "heat_capacity": "-1", "expansion": "1"} |
6 | gas_constant,heat_capacity,length,mass,molar_energy,time | m·ℓ·t·C·E_m·R | chemistry,mechanics,thermo | m·ℓ²·t⁻²·C⁻¹·E_m⁻¹·R | m = k₀ · ℓ⁻²·t²·C·E_m·R⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "time": "-2", "heat_capacity": "-1", "molar_energy": "-1", "gas_constant": "1"} |
5 | length,mass,specific_heat,thermal_cond,time | m·ℓ·t·c·κ | mechanics,thermo | m·ℓ⁻¹·t⁻¹·c·κ⁻¹ | m = k₀ · ℓ·t·c⁻¹·κ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "time": "-1", "specific_heat": "1", "thermal_cond": "-1"} |
5 | expansion,length,mass,thermal_cond,time | m·ℓ·t·κ·β | mechanics,thermo | m·ℓ·t⁻³·κ⁻¹·β | m = k₀ · ℓ⁻¹·t³·κ·β⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "1", "time": "-3", "thermal_cond": "-1", "expansion": "1"} |
6 | gas_constant,length,mass,molar_mass,thermal_cond,time | m·ℓ·t·κ·M_m·R | chemistry,mechanics,thermo | m·ℓ⁻¹·t⁻¹·κ⁻¹·M_m⁻¹·R | m = k₀ · ℓ·t·κ·M_m·R⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "-1", "time": "-1", "thermal_cond": "-1", "molar_mass": "-1", "gas_constant": "1"} |
6 | gas_constant,length,mass,molar_energy,thermal_cond,time | m·ℓ·t·κ·E_m·R | chemistry,mechanics,thermo | m·ℓ·t⁻³·κ⁻¹·E_m⁻¹·R | m = k₀ · ℓ⁻¹·t³·κ·E_m·R⁻¹ | null | 0 | 3 | 3 | 8 | 7.6 | 1.4 | false | {"mass": "1", "length": "1", "time": "-3", "thermal_cond": "-1", "molar_energy": "-1", "gas_constant": "1"} |
6 | amount,expansion,gas_constant,length,mass,time | m·ℓ·t·β·n·R | chemistry,mechanics,thermo | m·ℓ²·t⁻²·β·n⁻¹·R⁻¹ | m = k₀ · ℓ⁻²·t²·β⁻¹·n·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "time": "-2", "expansion": "1", "amount": "-1", "gas_constant": "-1"} |
6 | concentration,expansion,gas_constant,length,mass,time | m·ℓ·t·β·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻¹·t⁻²·β·c_n⁻¹·R⁻¹ | m = k₀ · ℓ·t²·β⁻¹·c_n·R | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "-1", "time": "-2", "expansion": "1", "concentration": "-1", "gas_constant": "-1"} |
6 | cat_activity,expansion,gas_constant,length,mass,time | m·ℓ·t·β·R·z | chemistry,mechanics,thermo | m·ℓ²·t⁻³·β·R⁻¹·z⁻¹ | m = k₀ · ℓ⁻²·t³·β⁻¹·R·z | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "1", "length": "2", "time": "-3", "expansion": "1", "gas_constant": "-1", "cat_activity": "-1"} |
6 | avogadro,expansion,gas_constant,length,mass,time | m·ℓ·t·β·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ²·t⁻²·β·R⁻¹·N_A | m = k₀ · ℓ⁻²·t²·β⁻¹·R·N_A⁻¹ | null | 1 | 4 | 2 | 8 | 7.7 | 0.8 | false | {"mass": "1", "length": "2", "time": "-2", "expansion": "1", "gas_constant": "-1", "avogadro": "1"} |
5 | boltzmann,expansion,length,mass,time | m·ℓ·t·β·k_B | constants,mechanics,thermo | m·ℓ²·t⁻²·β·k_B⁻¹ | m = k₀ · ℓ⁻²·t²·β⁻¹·k_B | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "time": "-2", "expansion": "1", "boltzmann": "-1"} |
5 | charge,length,mass,time,voltage | m·ℓ·t·q·U | em,mechanics | m·ℓ²·t⁻²·q⁻¹·U⁻¹ | m = k₀ · ℓ⁻²·t²·q·U | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "charge": "-1", "voltage": "-1"} |
5 | charge,length,mass,resistance,time | m·ℓ·t·q·R | em,mechanics | m·ℓ²·t⁻¹·q⁻²·R⁻¹ | m = k₀ · ℓ⁻²·t·q²·R | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-1", "charge": "-2", "resistance": "-1"} |
5 | capacitance,charge,length,mass,time | m·ℓ·t·q·C_e | em,mechanics | m·ℓ²·t⁻²·q⁻²·C_e | m = k₀ · ℓ⁻²·t²·q²·C_e⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "time": "-2", "charge": "-2", "capacitance": "1"} |
5 | charge,efield,length,mass,time | m·ℓ·t·q·E_f | em,mechanics | m·ℓ·t⁻²·q⁻¹·E_f⁻¹ | m = k₀ · ℓ⁻¹·t²·q·E_f | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "1", "time": "-2", "charge": "-1", "efield": "-1"} |
5 | charge,length,mag_flux,mass,time | m·ℓ·t·q·Φ | em,mechanics | m·ℓ²·t⁻¹·q⁻¹·Φ⁻¹ | m = k₀ · ℓ⁻²·t·q·Φ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "time": "-1", "charge": "-1", "mag_flux": "-1"} |
5 | charge,length,mass,permittivity,time | m·ℓ·t·q·ε | em,mechanics | m·ℓ³·t⁻²·q⁻²·ε | m = k₀ · ℓ⁻³·t²·q²·ε⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "time": "-2", "charge": "-2", "permittivity": "1"} |
5 | charge,conductivity,length,mass,time | m·ℓ·t·q·σ | em,mechanics | m·ℓ³·t⁻¹·q⁻²·σ | m = k₀ · ℓ⁻³·t·q²·σ⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "3", "time": "-1", "charge": "-2", "conductivity": "1"} |
5 | charge,length,mass,resistivity,time | m·ℓ·t·q·ρ_e | em,mechanics | m·ℓ³·t⁻¹·q⁻²·ρ_e⁻¹ | m = k₀ · ℓ⁻³·t·q²·ρ_e | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "3", "time": "-1", "charge": "-2", "resistivity": "-1"} |
5 | current,length,mass,time,voltage | m·ℓ·t·i·U | em,mechanics | m·ℓ²·t⁻³·i⁻¹·U⁻¹ | m = k₀ · ℓ⁻²·t³·i·U | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "2", "time": "-3", "current": "-1", "voltage": "-1"} |
5 | current,length,mass,resistance,time | m·ℓ·t·i·R | em,mechanics | m·ℓ²·t⁻³·i⁻²·R⁻¹ | m = k₀ · ℓ⁻²·t³·i²·R | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "2", "time": "-3", "current": "-2", "resistance": "-1"} |
5 | capacitance,current,length,mass,time | m·ℓ·t·i·C_e | em,mechanics | m·ℓ²·t⁻⁴·i⁻²·C_e | m = k₀ · ℓ⁻²·t⁴·i²·C_e⁻¹ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "2", "time": "-4", "current": "-2", "capacitance": "1"} |
5 | current,inductance,length,mass,time | m·ℓ·t·i·L_e | em,mechanics | m·ℓ²·t⁻²·i⁻²·L_e⁻¹ | m = k₀ · ℓ⁻²·t²·i²·L_e | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "time": "-2", "current": "-2", "inductance": "-1"} |
5 | current,efield,length,mass,time | m·ℓ·t·i·E_f | em,mechanics | m·ℓ·t⁻³·i⁻¹·E_f⁻¹ | m = k₀ · ℓ⁻¹·t³·i·E_f | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "1", "time": "-3", "current": "-1", "efield": "-1"} |
5 | current,length,mag_flux,mass,time | m·ℓ·t·i·Φ | em,mechanics | m·ℓ²·t⁻²·i⁻¹·Φ⁻¹ | m = k₀ · ℓ⁻²·t²·i·Φ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "current": "-1", "mag_flux": "-1"} |
5 | current,length,mass,permittivity,time | m·ℓ·t·i·ε | em,mechanics | m·ℓ³·t⁻⁴·i⁻²·ε | m = k₀ · ℓ⁻³·t⁴·i²·ε⁻¹ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "3", "time": "-4", "current": "-2", "permittivity": "1"} |
5 | current,length,mass,permeability,time | m·ℓ·t·i·μ₀ | em,mechanics | m·ℓ·t⁻²·i⁻²·μ₀⁻¹ | m = k₀ · ℓ⁻¹·t²·i²·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "time": "-2", "current": "-2", "permeability": "-1"} |
5 | conductivity,current,length,mass,time | m·ℓ·t·i·σ | em,mechanics | m·ℓ³·t⁻³·i⁻²·σ | m = k₀ · ℓ⁻³·t³·i²·σ⁻¹ | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "1", "length": "3", "time": "-3", "current": "-2", "conductivity": "1"} |
5 | current,length,mass,resistivity,time | m·ℓ·t·i·ρ_e | em,mechanics | m·ℓ³·t⁻³·i⁻²·ρ_e⁻¹ | m = k₀ · ℓ⁻³·t³·i²·ρ_e | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "1", "length": "3", "time": "-3", "current": "-2", "resistivity": "-1"} |
5 | length,mass,resistance,time,voltage | m·ℓ·t·U·R | em,mechanics | m·ℓ²·t⁻³·U⁻²·R | m = k₀ · ℓ⁻²·t³·U²·R⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "2", "time": "-3", "voltage": "-2", "resistance": "1"} |
5 | capacitance,length,mass,time,voltage | m·ℓ·t·U·C_e | em,mechanics | m·ℓ²·t⁻²·U⁻²·C_e⁻¹ | m = k₀ · ℓ⁻²·t²·U²·C_e | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "time": "-2", "voltage": "-2", "capacitance": "-1"} |
5 | inductance,length,mass,time,voltage | m·ℓ·t·U·L_e | em,mechanics | m·ℓ²·t⁻⁴·U⁻²·L_e | m = k₀ · ℓ⁻²·t⁴·U²·L_e⁻¹ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "2", "time": "-4", "voltage": "-2", "inductance": "1"} |
5 | length,mass,permittivity,time,voltage | m·ℓ·t·U·ε | em,mechanics | m·ℓ·t⁻²·U⁻²·ε⁻¹ | m = k₀ · ℓ⁻¹·t²·U²·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "time": "-2", "voltage": "-2", "permittivity": "-1"} |
5 | length,mass,permeability,time,voltage | m·ℓ·t·U·μ₀ | em,mechanics | m·ℓ³·t⁻⁴·U⁻²·μ₀ | m = k₀ · ℓ⁻³·t⁴·U²·μ₀⁻¹ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "3", "time": "-4", "voltage": "-2", "permeability": "1"} |
5 | conductivity,length,mass,time,voltage | m·ℓ·t·U·σ | em,mechanics | m·ℓ·t⁻³·U⁻²·σ⁻¹ | m = k₀ · ℓ⁻¹·t³·U²·σ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "1", "time": "-3", "voltage": "-2", "conductivity": "-1"} |
5 | length,mass,resistivity,time,voltage | m·ℓ·t·U·ρ_e | em,mechanics | m·ℓ·t⁻³·U⁻²·ρ_e | m = k₀ · ℓ⁻¹·t³·U²·ρ_e⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "1", "time": "-3", "voltage": "-2", "resistivity": "1"} |
5 | elem_charge,length,mass,time,voltage | m·ℓ·t·U·e | constants,em,mechanics | m·ℓ²·t⁻²·U⁻¹·e⁻¹ | m = k₀ · ℓ⁻²·t²·U·e | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "time": "-2", "voltage": "-1", "elem_charge": "-1"} |
5 | bfield,length,mass,resistance,time | m·ℓ·t·R·B | em,mechanics | m·ℓ⁻²·t⁻¹·R·B⁻² | m = k₀ · ℓ²·t·R⁻¹·B² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-2", "time": "-1", "resistance": "1", "bfield": "-2"} |
5 | length,mag_flux,mass,resistance,time | m·ℓ·t·R·Φ | em,mechanics | m·ℓ²·t⁻¹·R·Φ⁻² | m = k₀ · ℓ⁻²·t·R⁻¹·Φ² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-1", "resistance": "1", "mag_flux": "-2"} |
5 | elem_charge,length,mass,resistance,time | m·ℓ·t·R·e | constants,em,mechanics | m·ℓ²·t⁻¹·R⁻¹·e⁻² | m = k₀ · ℓ⁻²·t·R·e² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "time": "-1", "resistance": "-1", "elem_charge": "-2"} |
5 | capacitance,elem_charge,length,mass,time | m·ℓ·t·C_e·e | constants,em,mechanics | m·ℓ²·t⁻²·C_e·e⁻² | m = k₀ · ℓ⁻²·t²·C_e⁻¹·e² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "1", "length": "2", "time": "-2", "capacitance": "1", "elem_charge": "-2"} |
5 | bfield,inductance,length,mass,time | m·ℓ·t·L_e·B | em,mechanics | m·ℓ⁻²·t⁻²·L_e·B⁻² | m = k₀ · ℓ²·t²·L_e⁻¹·B² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "time": "-2", "inductance": "1", "bfield": "-2"} |
5 | inductance,length,mag_flux,mass,time | m·ℓ·t·L_e·Φ | em,mechanics | m·ℓ²·t⁻²·L_e·Φ⁻² | m = k₀ · ℓ⁻²·t²·L_e⁻¹·Φ² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "time": "-2", "inductance": "1", "mag_flux": "-2"} |
5 | efield,length,mass,permittivity,time | m·ℓ·t·E_f·ε | em,mechanics | m·ℓ⁻¹·t⁻²·E_f⁻²·ε⁻¹ | m = k₀ · ℓ·t²·E_f²·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "time": "-2", "efield": "-2", "permittivity": "-1"} |
5 | efield,length,mass,permeability,time | m·ℓ·t·E_f·μ₀ | em,mechanics | m·ℓ·t⁻⁴·E_f⁻²·μ₀ | m = k₀ · ℓ⁻¹·t⁴·E_f²·μ₀⁻¹ | null | 0 | 2 | 4 | 9 | 7.9 | 1.6 | false | {"mass": "1", "length": "1", "time": "-4", "efield": "-2", "permeability": "1"} |
5 | conductivity,efield,length,mass,time | m·ℓ·t·E_f·σ | em,mechanics | m·ℓ⁻¹·t⁻³·E_f⁻²·σ⁻¹ | m = k₀ · ℓ·t³·E_f²·σ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "-1", "time": "-3", "efield": "-2", "conductivity": "-1"} |
5 | efield,length,mass,resistivity,time | m·ℓ·t·E_f·ρ_e | em,mechanics | m·ℓ⁻¹·t⁻³·E_f⁻²·ρ_e | m = k₀ · ℓ·t³·E_f²·ρ_e⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "-1", "time": "-3", "efield": "-2", "resistivity": "1"} |
5 | efield,elem_charge,length,mass,time | m·ℓ·t·E_f·e | constants,em,mechanics | m·ℓ·t⁻²·E_f⁻¹·e⁻¹ | m = k₀ · ℓ⁻¹·t²·E_f·e | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "1", "length": "1", "time": "-2", "efield": "-1", "elem_charge": "-1"} |
5 | bfield,length,mass,permeability,time | m·ℓ·t·B·μ₀ | em,mechanics | m·ℓ⁻¹·t⁻²·B⁻²·μ₀ | m = k₀ · ℓ·t²·B²·μ₀⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "time": "-2", "bfield": "-2", "permeability": "1"} |
5 | bfield,conductivity,length,mass,time | m·ℓ·t·B·σ | em,mechanics | m·ℓ⁻³·t⁻¹·B⁻²·σ⁻¹ | m = k₀ · ℓ³·t·B²·σ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "-3", "time": "-1", "bfield": "-2", "conductivity": "-1"} |
5 | bfield,length,mass,resistivity,time | m·ℓ·t·B·ρ_e | em,mechanics | m·ℓ⁻³·t⁻¹·B⁻²·ρ_e | m = k₀ · ℓ³·t·B²·ρ_e⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "-3", "time": "-1", "bfield": "-2", "resistivity": "1"} |
5 | length,mag_flux,mass,permeability,time | m·ℓ·t·Φ·μ₀ | em,mechanics | m·ℓ³·t⁻²·Φ⁻²·μ₀ | m = k₀ · ℓ⁻³·t²·Φ²·μ₀⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "time": "-2", "mag_flux": "-2", "permeability": "1"} |
5 | conductivity,length,mag_flux,mass,time | m·ℓ·t·Φ·σ | em,mechanics | m·ℓ·t⁻¹·Φ⁻²·σ⁻¹ | m = k₀ · ℓ⁻¹·t·Φ²·σ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "1", "time": "-1", "mag_flux": "-2", "conductivity": "-1"} |
5 | length,mag_flux,mass,resistivity,time | m·ℓ·t·Φ·ρ_e | em,mechanics | m·ℓ·t⁻¹·Φ⁻²·ρ_e | m = k₀ · ℓ⁻¹·t·Φ²·ρ_e⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "1", "time": "-1", "mag_flux": "-2", "resistivity": "1"} |
5 | elem_charge,length,mag_flux,mass,time | m·ℓ·t·Φ·e | constants,em,mechanics | m·ℓ²·t⁻¹·Φ⁻¹·e⁻¹ | m = k₀ · ℓ⁻²·t·Φ·e | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "1", "length": "2", "time": "-1", "mag_flux": "-1", "elem_charge": "-1"} |
5 | elem_charge,length,mass,permittivity,time | m·ℓ·t·ε·e | constants,em,mechanics | m·ℓ³·t⁻²·ε·e⁻² | m = k₀ · ℓ⁻³·t²·ε⁻¹·e² | null | 1 | 3 | 3 | 9 | 8 | 1 | false | {"mass": "1", "length": "3", "time": "-2", "permittivity": "1", "elem_charge": "-2"} |
5 | conductivity,elem_charge,length,mass,time | m·ℓ·t·σ·e | constants,em,mechanics | m·ℓ³·t⁻¹·σ·e⁻² | m = k₀ · ℓ⁻³·t·σ⁻¹·e² | null | 1 | 3 | 3 | 8 | 7.3 | 1.7 | false | {"mass": "1", "length": "3", "time": "-1", "conductivity": "1", "elem_charge": "-2"} |
5 | elem_charge,length,mass,resistivity,time | m·ℓ·t·ρ_e·e | constants,em,mechanics | m·ℓ³·t⁻¹·ρ_e⁻¹·e⁻² | m = k₀ · ℓ⁻³·t·ρ_e·e² | null | 1 | 3 | 3 | 8 | 7.3 | 1.7 | false | {"mass": "1", "length": "3", "time": "-1", "resistivity": "-1", "elem_charge": "-2"} |
5 | amount,length,mass,molar_energy,time | m·ℓ·t·n·E_m | chemistry,mechanics | m·ℓ²·t⁻²·n⁻¹·E_m⁻¹ | m = k₀ · ℓ⁻²·t²·n·E_m | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "time": "-2", "amount": "-1", "molar_energy": "-1"} |
5 | concentration,length,mass,molar_energy,time | m·ℓ·t·c_n·E_m | chemistry,mechanics | m·ℓ⁻¹·t⁻²·c_n⁻¹·E_m⁻¹ | m = k₀ · ℓ·t²·c_n·E_m | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "-1", "time": "-2", "concentration": "-1", "molar_energy": "-1"} |
6 | boltzmann,gas_constant,length,mass,molar_energy,time | m·ℓ·t·E_m·R·k_B | chemistry,constants,mechanics | m·ℓ²·t⁻²·E_m⁻¹·R·k_B⁻¹ | m = k₀ · ℓ⁻²·t²·E_m·R⁻¹·k_B | null | 1 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "time": "-2", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"} |
5 | cat_activity,length,mass,molar_energy,time | m·ℓ·t·E_m·z | chemistry,mechanics | m·ℓ²·t⁻³·E_m⁻¹·z⁻¹ | m = k₀ · ℓ⁻²·t³·E_m·z | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "2", "time": "-3", "molar_energy": "-1", "cat_activity": "-1"} |
5 | avogadro,length,mass,molar_energy,time | m·ℓ·t·E_m·N_A | chemistry,constants,mechanics | m·ℓ²·t⁻²·E_m⁻¹·N_A | m = k₀ · ℓ⁻²·t²·E_m·N_A⁻¹ | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "time": "-2", "molar_energy": "-1", "avogadro": "1"} |
4 | grav_const,length,mass,time | m·ℓ·t·G | constants,mechanics | m·ℓ⁻³·t²·G | m = k₀ · ℓ³·t⁻²·G⁻¹ | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "1", "length": "-3", "time": "2", "grav_const": "1"} |
4 | length,mass,planck,time | m·ℓ·t·h | constants,mechanics | m·ℓ²·t⁻¹·h⁻¹ | m = k₀ · ℓ⁻²·t·h | null | 1 | 2 | 2 | 5 | 3.8 | 5.7 | true | {"mass": "1", "length": "2", "time": "-1", "planck": "-1"} |
4 | force,length,mass,velocity | m·ℓ·v·F | mechanics | m·ℓ⁻¹·v²·F⁻¹ | m = k₀ · ℓ·v⁻²·F | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "-1", "velocity": "2", "force": "-1"} |
4 | length,mass,power,velocity | m·ℓ·v·P | mechanics | m·ℓ⁻¹·v³·P⁻¹ | m = k₀ · ℓ·v⁻³·P | null | 0 | 1 | 3 | 6 | 4.4 | 5.6 | true | {"mass": "1", "length": "-1", "velocity": "3", "power": "-1"} |
4 | ang_momentum,length,mass,velocity | m·ℓ·v·Lₐ | mechanics | m·ℓ·v·Lₐ⁻¹ | m = k₀ · ℓ⁻¹·v⁻¹·Lₐ | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "1", "velocity": "1", "ang_momentum": "-1"} |
4 | action,length,mass,velocity | m·ℓ·v·S | mechanics | m·ℓ·v·S⁻¹ | m = k₀ · ℓ⁻¹·v⁻¹·S | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "1", "velocity": "1", "action": "-1"} |
4 | length,mass,pressure,velocity | m·ℓ·v·P_p | mechanics | m·ℓ⁻³·v²·P_p⁻¹ | m = k₀ · ℓ³·v⁻²·P_p | null | 0 | 1 | 3 | 7 | 5.1 | 4.9 | true | {"mass": "1", "length": "-3", "velocity": "2", "pressure": "-1"} |
4 | length,mass,velocity,viscosity | m·ℓ·v·μ | mechanics | m·ℓ⁻²·v·μ⁻¹ | m = k₀ · ℓ²·v⁻¹·μ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "-2", "velocity": "1", "viscosity": "-1"} |
4 | length,mass,stiffness,velocity | m·ℓ·v·k | mechanics | m·ℓ⁻²·v²·k⁻¹ | m = k₀ · ℓ²·v⁻²·k | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "-2", "velocity": "2", "stiffness": "-1"} |
4 | length,mass,surf_tension,velocity | m·ℓ·v·γ | mechanics | m·ℓ⁻²·v²·γ⁻¹ | m = k₀ · ℓ²·v⁻²·γ | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "-2", "velocity": "2", "surf_tension": "-1"} |
5 | length,mass,temperature,thermal_cond,velocity | m·ℓ·v·Θ·κ | mechanics,thermo | m·ℓ⁻²·v³·Θ⁻¹·κ⁻¹ | m = k₀ · ℓ²·v⁻³·Θ·κ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "-2", "velocity": "3", "temperature": "-1", "thermal_cond": "-1"} |
6 | concentration,gas_constant,length,mass,temperature,velocity | m·ℓ·v·Θ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻³·v²·Θ⁻¹·c_n⁻¹·R⁻¹ | m = k₀ · ℓ³·v⁻²·Θ·c_n·R | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "1", "length": "-3", "velocity": "2", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"} |
6 | cat_activity,gas_constant,length,mass,temperature,velocity | m·ℓ·v·Θ·R·z | chemistry,mechanics,thermo | m·ℓ⁻¹·v³·Θ⁻¹·R⁻¹·z⁻¹ | m = k₀ · ℓ·v⁻³·Θ·R·z | null | 0 | 3 | 3 | 8 | 7.6 | 1.4 | false | {"mass": "1", "length": "-1", "velocity": "3", "temperature": "-1", "gas_constant": "-1", "cat_activity": "-1"} |
5 | length,mass,specific_heat,thermal_cond,velocity | m·ℓ·v·c·κ | mechanics,thermo | m·ℓ⁻²·v·c·κ⁻¹ | m = k₀ · ℓ²·v⁻¹·c⁻¹·κ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "-2", "velocity": "1", "specific_heat": "1", "thermal_cond": "-1"} |
6 | cat_activity,gas_constant,length,mass,specific_heat,velocity | m·ℓ·v·c·R·z | chemistry,mechanics,thermo | m·ℓ⁻¹·v·c·R⁻¹·z⁻¹ | m = k₀ · ℓ·v⁻¹·c⁻¹·R·z | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "-1", "velocity": "1", "specific_heat": "1", "gas_constant": "-1", "cat_activity": "-1"} |
5 | expansion,length,mass,thermal_cond,velocity | m·ℓ·v·κ·β | mechanics,thermo | m·ℓ⁻²·v³·κ⁻¹·β | m = k₀ · ℓ²·v⁻³·κ·β⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "-2", "velocity": "3", "thermal_cond": "-1", "expansion": "1"} |
6 | gas_constant,length,mass,molar_mass,thermal_cond,velocity | m·ℓ·v·κ·M_m·R | chemistry,mechanics,thermo | m·ℓ⁻²·v·κ⁻¹·M_m⁻¹·R | m = k₀ · ℓ²·v⁻¹·κ·M_m·R⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "-2", "velocity": "1", "thermal_cond": "-1", "molar_mass": "-1", "gas_constant": "1"} |
6 | gas_constant,length,mass,molar_energy,thermal_cond,velocity | m·ℓ·v·κ·E_m·R | chemistry,mechanics,thermo | m·ℓ⁻²·v³·κ⁻¹·E_m⁻¹·R | m = k₀ · ℓ²·v⁻³·κ·E_m·R⁻¹ | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "1", "length": "-2", "velocity": "3", "thermal_cond": "-1", "molar_energy": "-1", "gas_constant": "1"} |
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