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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6 | cat_activity,entropy,gas_constant,length,mass,momentum | m·ℓ·p·S_e·R·z | chemistry,mechanics,thermo | m·ℓ·p⁻¹·S_e⁻¹·R·z | m = k₀ · ℓ⁻¹·p·S_e·R⁻¹·z⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "1", "momentum": "-1", "entropy": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | heat_capacity,length,mass,momentum,thermal_cond | m·ℓ·p·C·κ | mechanics,thermo | m·ℓ²·p⁻¹·C⁻¹·κ | m = k₀ · ℓ⁻²·p·C·κ⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "momentum": "-1", "heat_capacity": "-1", "thermal_cond": "1"} |
6 | cat_activity,gas_constant,heat_capacity,length,mass,momentum | m·ℓ·p·C·R·z | chemistry,mechanics,thermo | m·ℓ·p⁻¹·C⁻¹·R·z | m = k₀ · ℓ⁻¹·p·C·R⁻¹·z⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "1", "momentum": "-1", "heat_capacity": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | expansion,length,mass,momentum,thermal_cond | m·ℓ·p·κ·β | mechanics,thermo | m²·ℓ²·p⁻³·κ·β⁻¹ | κ = k₀ · m⁻²·ℓ⁻²·p³·β | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "length": "2", "momentum": "-3", "thermal_cond": "1", "expansion": "-1"} |
6 | amount,gas_constant,length,mass,momentum,thermal_cond | m·ℓ·p·κ·n·R | chemistry,mechanics,thermo | m·ℓ²·p⁻¹·κ·n⁻¹·R⁻¹ | m = k₀ · ℓ⁻²·p·κ⁻¹·n·R | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "2", "momentum": "-1", "thermal_cond": "1", "amount": "-1", "gas_constant": "-1"} |
6 | concentration,gas_constant,length,mass,momentum,thermal_cond | m·ℓ·p·κ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻¹·p⁻¹·κ·c_n⁻¹·R⁻¹ | m = k₀ · ℓ·p·κ⁻¹·c_n·R | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "-1", "momentum": "-1", "thermal_cond": "1", "concentration": "-1", "gas_constant": "-1"} |
6 | gas_constant,length,mass,molar_energy,momentum,thermal_cond | m·ℓ·p·κ·E_m·R | chemistry,mechanics,thermo | m²·ℓ²·p⁻³·κ·E_m·R⁻¹ | κ = k₀ · m⁻²·ℓ⁻²·p³·E_m⁻¹·R | null | 0 | 3 | 3 | 10 | 9 | 0 | false | {"mass": "2", "length": "2", "momentum": "-3", "thermal_cond": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | avogadro,gas_constant,length,mass,momentum,thermal_cond | m·ℓ·p·κ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ²·p⁻¹·κ·R⁻¹·N_A | m = k₀ · ℓ⁻²·p·κ⁻¹·R·N_A⁻¹ | null | 1 | 4 | 2 | 7 | 7 | 1.5 | false | {"mass": "1", "length": "2", "momentum": "-1", "thermal_cond": "1", "gas_constant": "-1", "avogadro": "1"} |
5 | boltzmann,length,mass,momentum,thermal_cond | m·ℓ·p·κ·k_B | constants,mechanics,thermo | m·ℓ²·p⁻¹·κ·k_B⁻¹ | m = k₀ · ℓ⁻²·p·κ⁻¹·k_B | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "1", "length": "2", "momentum": "-1", "thermal_cond": "1", "boltzmann": "-1"} |
4 | length,mass,momentum,thermal_diff | m·ℓ·p·α | mechanics,thermo | m·ℓ⁻¹·p⁻¹·α | m = k₀ · ℓ·p·α⁻¹ | null | 0 | 2 | 1 | 4 | 2.6 | 6.9 | true | {"mass": "1", "length": "-1", "momentum": "-1", "thermal_diff": "1"} |
6 | concentration,expansion,gas_constant,length,mass,momentum | m·ℓ·p·β·c_n·R | chemistry,mechanics,thermo | m·ℓ³·p⁻²·β⁻¹·c_n·R | m = k₀ · ℓ⁻³·p²·β·c_n⁻¹·R⁻¹ | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "1", "length": "3", "momentum": "-2", "expansion": "-1", "concentration": "1", "gas_constant": "1"} |
6 | cat_activity,expansion,gas_constant,length,mass,momentum | m·ℓ·p·β·R·z | chemistry,mechanics,thermo | m²·ℓ·p⁻³·β⁻¹·R·z | ℓ = k₀ · m⁻²·p³·β·R⁻¹·z⁻¹ | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "2", "length": "1", "momentum": "-3", "expansion": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | charge,current,length,mass,momentum | m·ℓ·p·q·i | em,mechanics | m·ℓ·p⁻¹·q⁻¹·i | m = k₀ · ℓ⁻¹·p·q·i⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "charge": "-1", "current": "1"} |
5 | charge,efield,length,mass,momentum | m·ℓ·p·q·E_f | em,mechanics | m·ℓ·p⁻²·q·E_f | m = k₀ · ℓ⁻¹·p²·q⁻¹·E_f⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "1", "momentum": "-2", "charge": "1", "efield": "1"} |
5 | charge,length,mass,momentum,permittivity | m·ℓ·p·q·ε | em,mechanics | m·ℓ⁻¹·p⁻²·q²·ε⁻¹ | m = k₀ · ℓ·p²·q⁻²·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "momentum": "-2", "charge": "2", "permittivity": "-1"} |
5 | current,length,mass,momentum,voltage | m·ℓ·p·i·U | em,mechanics | m²·ℓ·p⁻³·i·U | ℓ = k₀ · m⁻²·p³·i⁻¹·U⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "2", "length": "1", "momentum": "-3", "current": "1", "voltage": "1"} |
5 | current,length,mass,momentum,resistance | m·ℓ·p·i·R | em,mechanics | m²·ℓ·p⁻³·i²·R | ℓ = k₀ · m⁻²·p³·i⁻²·R⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "length": "1", "momentum": "-3", "current": "2", "resistance": "1"} |
5 | capacitance,current,length,mass,momentum | m·ℓ·p·i·C_e | em,mechanics | m³·ℓ²·p⁻⁴·i²·C_e⁻¹ | C_e = k₀ · m³·ℓ²·p⁻⁴·i² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "3", "length": "2", "momentum": "-4", "current": "2", "capacitance": "-1"} |
5 | current,efield,length,mass,momentum | m·ℓ·p·i·E_f | em,mechanics | m²·ℓ²·p⁻³·i·E_f | i = k₀ · m⁻²·ℓ⁻²·p³·E_f⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "length": "2", "momentum": "-3", "current": "1", "efield": "1"} |
5 | bfield,current,length,mass,momentum | m·ℓ·p·i·B | em,mechanics | m·ℓ²·p⁻²·i·B | m = k₀ · ℓ⁻²·p²·i⁻¹·B⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "momentum": "-2", "current": "1", "bfield": "1"} |
5 | current,length,mass,momentum,permittivity | m·ℓ·p·i·ε | em,mechanics | m³·ℓ·p⁻⁴·i²·ε⁻¹ | ℓ = k₀ · m⁻³·p⁴·i⁻²·ε | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "3", "length": "1", "momentum": "-4", "current": "2", "permittivity": "-1"} |
5 | current,length,mass,momentum,permeability | m·ℓ·p·i·μ₀ | em,mechanics | m·ℓ·p⁻²·i²·μ₀ | m = k₀ · ℓ⁻¹·p²·i⁻²·μ₀⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "momentum": "-2", "current": "2", "permeability": "1"} |
5 | current,elem_charge,length,mass,momentum | m·ℓ·p·i·e | constants,em,mechanics | m·ℓ·p⁻¹·i·e⁻¹ | m = k₀ · ℓ⁻¹·p·i⁻¹·e | null | 1 | 3 | 1 | 5 | 4.2 | 4.8 | false | {"mass": "1", "length": "1", "momentum": "-1", "current": "1", "elem_charge": "-1"} |
5 | length,mass,momentum,resistance,voltage | m·ℓ·p·U·R | em,mechanics | m²·ℓ·p⁻³·U²·R⁻¹ | ℓ = k₀ · m⁻²·p³·U⁻²·R | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "length": "1", "momentum": "-3", "voltage": "2", "resistance": "-1"} |
5 | inductance,length,mass,momentum,voltage | m·ℓ·p·U·L_e | em,mechanics | m³·ℓ²·p⁻⁴·U²·L_e⁻¹ | L_e = k₀ · m³·ℓ²·p⁻⁴·U² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "3", "length": "2", "momentum": "-4", "voltage": "2", "inductance": "-1"} |
5 | bfield,length,mass,momentum,voltage | m·ℓ·p·U·B | em,mechanics | m·ℓ⁻¹·p⁻¹·U·B⁻¹ | m = k₀ · ℓ·p·U⁻¹·B | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "momentum": "-1", "voltage": "1", "bfield": "-1"} |
5 | length,mag_flux,mass,momentum,voltage | m·ℓ·p·U·Φ | em,mechanics | m·ℓ·p⁻¹·U·Φ⁻¹ | m = k₀ · ℓ⁻¹·p·U⁻¹·Φ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "voltage": "1", "mag_flux": "-1"} |
5 | length,mass,momentum,permittivity,voltage | m·ℓ·p·U·ε | em,mechanics | m·ℓ·p⁻²·U²·ε | m = k₀ · ℓ⁻¹·p²·U⁻²·ε⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "momentum": "-2", "voltage": "2", "permittivity": "1"} |
5 | length,mass,momentum,permeability,voltage | m·ℓ·p·U·μ₀ | em,mechanics | m³·ℓ·p⁻⁴·U²·μ₀⁻¹ | ℓ = k₀ · m⁻³·p⁴·U⁻²·μ₀ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "3", "length": "1", "momentum": "-4", "voltage": "2", "permeability": "-1"} |
5 | conductivity,length,mass,momentum,voltage | m·ℓ·p·U·σ | em,mechanics | m²·ℓ²·p⁻³·U²·σ | σ = k₀ · m⁻²·ℓ⁻²·p³·U⁻² | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "2", "length": "2", "momentum": "-3", "voltage": "2", "conductivity": "1"} |
5 | length,mass,momentum,resistivity,voltage | m·ℓ·p·U·ρ_e | em,mechanics | m²·ℓ²·p⁻³·U²·ρ_e⁻¹ | ρ_e = k₀ · m²·ℓ²·p⁻³·U² | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "2", "length": "2", "momentum": "-3", "voltage": "2", "resistivity": "-1"} |
5 | capacitance,length,mass,momentum,resistance | m·ℓ·p·R·C_e | em,mechanics | m·ℓ·p⁻¹·R⁻¹·C_e⁻¹ | m = k₀ · ℓ⁻¹·p·R·C_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "resistance": "-1", "capacitance": "-1"} |
5 | inductance,length,mass,momentum,resistance | m·ℓ·p·R·L_e | em,mechanics | m·ℓ·p⁻¹·R·L_e⁻¹ | m = k₀ · ℓ⁻¹·p·R⁻¹·L_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "resistance": "1", "inductance": "-1"} |
5 | efield,length,mass,momentum,resistance | m·ℓ·p·R·E_f | em,mechanics | m²·ℓ³·p⁻³·R⁻¹·E_f² | R = k₀ · m²·ℓ³·p⁻³·E_f² | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "2", "length": "3", "momentum": "-3", "resistance": "-1", "efield": "2"} |
5 | capacitance,inductance,length,mass,momentum | m·ℓ·p·C_e·L_e | em,mechanics | m²·ℓ²·p⁻²·C_e⁻¹·L_e⁻¹ | C_e = k₀ · m²·ℓ²·p⁻²·L_e⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "momentum": "-2", "capacitance": "-1", "inductance": "-1"} |
5 | capacitance,efield,length,mass,momentum | m·ℓ·p·C_e·E_f | em,mechanics | m·ℓ²·p⁻²·C_e·E_f² | m = k₀ · ℓ⁻²·p²·C_e⁻¹·E_f⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "momentum": "-2", "capacitance": "1", "efield": "2"} |
5 | capacitance,length,mass,momentum,permeability | m·ℓ·p·C_e·μ₀ | em,mechanics | m²·ℓ·p⁻²·C_e⁻¹·μ₀⁻¹ | ℓ = k₀ · m⁻²·p²·C_e·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "length": "1", "momentum": "-2", "capacitance": "-1", "permeability": "-1"} |
5 | capacitance,conductivity,length,mass,momentum | m·ℓ·p·C_e·σ | em,mechanics | m·ℓ²·p⁻¹·C_e⁻¹·σ | m = k₀ · ℓ⁻²·p·C_e·σ⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "momentum": "-1", "capacitance": "-1", "conductivity": "1"} |
5 | capacitance,length,mass,momentum,resistivity | m·ℓ·p·C_e·ρ_e | em,mechanics | m·ℓ²·p⁻¹·C_e⁻¹·ρ_e⁻¹ | m = k₀ · ℓ⁻²·p·C_e·ρ_e | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "momentum": "-1", "capacitance": "-1", "resistivity": "-1"} |
5 | efield,inductance,length,mass,momentum | m·ℓ·p·L_e·E_f | em,mechanics | m³·ℓ⁴·p⁻⁴·L_e⁻¹·E_f² | L_e = k₀ · m³·ℓ⁴·p⁻⁴·E_f² | null | 0 | 2 | 4 | 14 | 11.4 | -1.9 | false | {"mass": "3", "length": "4", "momentum": "-4", "inductance": "-1", "efield": "2"} |
5 | bfield,inductance,length,mass,momentum | m·ℓ·p·L_e·B | em,mechanics | m·ℓ⁴·p⁻²·L_e⁻¹·B² | m = k₀ · ℓ⁻⁴·p²·L_e·B⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "momentum": "-2", "inductance": "-1", "bfield": "2"} |
5 | inductance,length,mass,momentum,permittivity | m·ℓ·p·L_e·ε | em,mechanics | m²·ℓ·p⁻²·L_e⁻¹·ε⁻¹ | ℓ = k₀ · m⁻²·p²·L_e·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "length": "1", "momentum": "-2", "inductance": "-1", "permittivity": "-1"} |
5 | efield,length,mag_flux,mass,momentum | m·ℓ·p·E_f·Φ | em,mechanics | m·ℓ²·p⁻¹·E_f·Φ⁻¹ | m = k₀ · ℓ⁻²·p·E_f⁻¹·Φ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "momentum": "-1", "efield": "1", "mag_flux": "-1"} |
5 | efield,length,mass,momentum,permittivity | m·ℓ·p·E_f·ε | em,mechanics | m·ℓ³·p⁻²·E_f²·ε | m = k₀ · ℓ⁻³·p²·E_f⁻²·ε⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "momentum": "-2", "efield": "2", "permittivity": "1"} |
5 | efield,length,mass,momentum,permeability | m·ℓ·p·E_f·μ₀ | em,mechanics | m³·ℓ³·p⁻⁴·E_f²·μ₀⁻¹ | μ₀ = k₀ · m³·ℓ³·p⁻⁴·E_f² | null | 0 | 2 | 4 | 13 | 10.7 | -1.2 | false | {"mass": "3", "length": "3", "momentum": "-4", "efield": "2", "permeability": "-1"} |
5 | conductivity,efield,length,mass,momentum | m·ℓ·p·E_f·σ | em,mechanics | m²·ℓ⁴·p⁻³·E_f²·σ | σ = k₀ · m⁻²·ℓ⁻⁴·p³·E_f⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "2", "length": "4", "momentum": "-3", "efield": "2", "conductivity": "1"} |
5 | efield,length,mass,momentum,resistivity | m·ℓ·p·E_f·ρ_e | em,mechanics | m²·ℓ⁴·p⁻³·E_f²·ρ_e⁻¹ | ρ_e = k₀ · m²·ℓ⁴·p⁻³·E_f² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "2", "length": "4", "momentum": "-3", "efield": "2", "resistivity": "-1"} |
5 | efield,elem_charge,length,mass,momentum | m·ℓ·p·E_f·e | constants,em,mechanics | m·ℓ·p⁻²·E_f·e | m = k₀ · ℓ⁻¹·p²·E_f⁻¹·e⁻¹ | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "1", "length": "1", "momentum": "-2", "efield": "1", "elem_charge": "1"} |
5 | bfield,length,mass,momentum,permeability | m·ℓ·p·B·μ₀ | em,mechanics | m·ℓ³·p⁻²·B²·μ₀⁻¹ | m = k₀ · ℓ⁻³·p²·B⁻²·μ₀ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "momentum": "-2", "bfield": "2", "permeability": "-1"} |
5 | length,mag_flux,mass,momentum,permeability | m·ℓ·p·Φ·μ₀ | em,mechanics | m·ℓ⁻¹·p⁻²·Φ²·μ₀⁻¹ | m = k₀ · ℓ·p²·Φ⁻²·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "momentum": "-2", "mag_flux": "2", "permeability": "-1"} |
5 | conductivity,length,mass,momentum,permittivity | m·ℓ·p·ε·σ | em,mechanics | m·ℓ·p⁻¹·ε⁻¹·σ | m = k₀ · ℓ⁻¹·p·ε·σ⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "permittivity": "-1", "conductivity": "1"} |
5 | length,mass,momentum,permittivity,resistivity | m·ℓ·p·ε·ρ_e | em,mechanics | m·ℓ·p⁻¹·ε⁻¹·ρ_e⁻¹ | m = k₀ · ℓ⁻¹·p·ε·ρ_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "permittivity": "-1", "resistivity": "-1"} |
5 | elem_charge,length,mass,momentum,permittivity | m·ℓ·p·ε·e | constants,em,mechanics | m·ℓ⁻¹·p⁻²·ε⁻¹·e² | m = k₀ · ℓ·p²·ε·e⁻² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "-1", "momentum": "-2", "permittivity": "-1", "elem_charge": "2"} |
5 | conductivity,length,mass,momentum,permeability | m·ℓ·p·μ₀·σ | em,mechanics | m·ℓ⁻¹·p⁻¹·μ₀⁻¹·σ⁻¹ | m = k₀ · ℓ·p·μ₀·σ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "momentum": "-1", "permeability": "-1", "conductivity": "-1"} |
5 | length,mass,momentum,permeability,resistivity | m·ℓ·p·μ₀·ρ_e | em,mechanics | m·ℓ⁻¹·p⁻¹·μ₀⁻¹·ρ_e | m = k₀ · ℓ·p·μ₀·ρ_e⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "momentum": "-1", "permeability": "-1", "resistivity": "1"} |
5 | amount,cat_activity,length,mass,momentum | m·ℓ·p·n·z | chemistry,mechanics | m·ℓ·p⁻¹·n⁻¹·z | m = k₀ · ℓ⁻¹·p·n·z⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "momentum": "-1", "amount": "-1", "cat_activity": "1"} |
5 | concentration,length,mass,molar_energy,momentum | m·ℓ·p·c_n·E_m | chemistry,mechanics | m·ℓ³·p⁻²·c_n·E_m | m = k₀ · ℓ⁻³·p²·c_n⁻¹·E_m⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "3", "momentum": "-2", "concentration": "1", "molar_energy": "1"} |
5 | cat_activity,concentration,length,mass,momentum | m·ℓ·p·c_n·z | chemistry,mechanics | m·ℓ⁻²·p⁻¹·c_n⁻¹·z | m = k₀ · ℓ²·p·c_n·z⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "-2", "momentum": "-1", "concentration": "-1", "cat_activity": "1"} |
5 | cat_activity,length,mass,molar_energy,momentum | m·ℓ·p·E_m·z | chemistry,mechanics | m²·ℓ·p⁻³·E_m·z | ℓ = k₀ · m⁻²·p³·E_m⁻¹·z⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "2", "length": "1", "momentum": "-3", "molar_energy": "1", "cat_activity": "1"} |
6 | boltzmann,cat_activity,gas_constant,length,mass,momentum | m·ℓ·p·R·z·k_B | chemistry,constants,mechanics | m·ℓ·p⁻¹·R·z·k_B⁻¹ | m = k₀ · ℓ⁻¹·p·R⁻¹·z⁻¹·k_B | null | 1 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "1", "momentum": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"} |
5 | avogadro,cat_activity,length,mass,momentum | m·ℓ·p·z·N_A | chemistry,constants,mechanics | m·ℓ·p⁻¹·z·N_A | m = k₀ · ℓ⁻¹·p·z⁻¹·N_A⁻¹ | null | 1 | 3 | 1 | 5 | 4.2 | 4.8 | false | {"mass": "1", "length": "1", "momentum": "-1", "cat_activity": "1", "avogadro": "1"} |
4 | grav_const,length,mass,momentum | m·ℓ·p·G | constants,mechanics | m³·ℓ⁻¹·p⁻²·G | ℓ = k₀ · m³·p⁻²·G | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "3", "length": "-1", "momentum": "-2", "grav_const": "1"} |
4 | ang_momentum,length,mass,pressure | m·ℓ·Lₐ·P_p | mechanics | m·ℓ⁵·Lₐ⁻²·P_p | m = k₀ · ℓ⁻⁵·Lₐ²·P_p⁻¹ | null | 0 | 1 | 5 | 9 | 7.5 | 2.5 | false | {"mass": "1", "length": "5", "ang_momentum": "-2", "pressure": "1"} |
4 | ang_momentum,length,mass,omega | m·ℓ·Lₐ·ω | mechanics | m·ℓ²·Lₐ⁻¹·ω | m = k₀ · ℓ⁻²·Lₐ·ω⁻¹ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "omega": "1"} |
4 | ang_momentum,frequency,length,mass | m·ℓ·Lₐ·f | mechanics | m·ℓ²·Lₐ⁻¹·f | m = k₀ · ℓ⁻²·Lₐ·f⁻¹ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "frequency": "1"} |
4 | ang_momentum,length,mass,stiffness | m·ℓ·Lₐ·k | mechanics | m·ℓ⁴·Lₐ⁻²·k | m = k₀ · ℓ⁻⁴·Lₐ²·k⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "4", "ang_momentum": "-2", "stiffness": "1"} |
4 | ang_momentum,length,mass,surf_tension | m·ℓ·Lₐ·γ | mechanics | m·ℓ⁴·Lₐ⁻²·γ | m = k₀ · ℓ⁻⁴·Lₐ²·γ⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "4", "ang_momentum": "-2", "surf_tension": "1"} |
4 | ang_momentum,flowrate,length,mass | m·ℓ·Lₐ·Q | mechanics | m·ℓ⁻¹·Lₐ⁻¹·Q | m = k₀ · ℓ·Lₐ·Q⁻¹ | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "-1", "ang_momentum": "-1", "flowrate": "1"} |
5 | ang_momentum,entropy,length,mass,temperature | m·ℓ·Lₐ·Θ·S_e | mechanics,thermo | m·ℓ²·Lₐ⁻²·Θ·S_e | m = k₀ · ℓ⁻²·Lₐ²·Θ⁻¹·S_e⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "temperature": "1", "entropy": "1"} |
5 | ang_momentum,heat_capacity,length,mass,temperature | m·ℓ·Lₐ·Θ·C | mechanics,thermo | m·ℓ²·Lₐ⁻²·Θ·C | m = k₀ · ℓ⁻²·Lₐ²·Θ⁻¹·C⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "temperature": "1", "heat_capacity": "1"} |
5 | ang_momentum,length,mass,specific_heat,temperature | m·ℓ·Lₐ·Θ·c | mechanics,thermo | m²·ℓ²·Lₐ⁻²·Θ·c | Θ = k₀ · m⁻²·ℓ⁻²·Lₐ²·c⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "ang_momentum": "-2", "temperature": "1", "specific_heat": "1"} |
5 | ang_momentum,length,mass,temperature,thermal_cond | m·ℓ·Lₐ·Θ·κ | mechanics,thermo | m²·ℓ⁵·Lₐ⁻³·Θ·κ | Θ = k₀ · m⁻²·ℓ⁻⁵·Lₐ³·κ⁻¹ | null | 0 | 2 | 5 | 12 | 10.5 | -1 | false | {"mass": "2", "length": "5", "ang_momentum": "-3", "temperature": "1", "thermal_cond": "1"} |
6 | amount,ang_momentum,gas_constant,length,mass,temperature | m·ℓ·Lₐ·Θ·n·R | chemistry,mechanics,thermo | m·ℓ²·Lₐ⁻²·Θ·n·R | m = k₀ · ℓ⁻²·Lₐ²·Θ⁻¹·n⁻¹·R⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "temperature": "1", "amount": "1", "gas_constant": "1"} |
6 | ang_momentum,gas_constant,length,mass,molar_mass,temperature | m·ℓ·Lₐ·Θ·M_m·R | chemistry,mechanics,thermo | m²·ℓ²·Lₐ⁻²·Θ·M_m⁻¹·R | Θ = k₀ · m⁻²·ℓ⁻²·Lₐ²·M_m·R⁻¹ | null | 0 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "2", "length": "2", "ang_momentum": "-2", "temperature": "1", "molar_mass": "-1", "gas_constant": "1"} |
6 | ang_momentum,concentration,gas_constant,length,mass,temperature | m·ℓ·Lₐ·Θ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁵·Lₐ⁻²·Θ·c_n·R | m = k₀ · ℓ⁻⁵·Lₐ²·Θ⁻¹·c_n⁻¹·R⁻¹ | null | 0 | 3 | 5 | 11 | 10.7 | -1.7 | false | {"mass": "1", "length": "5", "ang_momentum": "-2", "temperature": "1", "concentration": "1", "gas_constant": "1"} |
6 | ang_momentum,cat_activity,gas_constant,length,mass,temperature | m·ℓ·Lₐ·Θ·R·z | chemistry,mechanics,thermo | m²·ℓ⁴·Lₐ⁻³·Θ·R·z | Θ = k₀ · m⁻²·ℓ⁻⁴·Lₐ³·R⁻¹·z⁻¹ | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "2", "length": "4", "ang_momentum": "-3", "temperature": "1", "gas_constant": "1", "cat_activity": "1"} |
6 | ang_momentum,avogadro,gas_constant,length,mass,temperature | m·ℓ·Lₐ·Θ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ²·Lₐ⁻²·Θ·R·N_A⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·Θ⁻¹·R⁻¹·N_A | null | 1 | 4 | 2 | 8 | 7.7 | 0.8 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "temperature": "1", "gas_constant": "1", "avogadro": "-1"} |
5 | ang_momentum,boltzmann,length,mass,temperature | m·ℓ·Lₐ·Θ·k_B | constants,mechanics,thermo | m·ℓ²·Lₐ⁻²·Θ·k_B | m = k₀ · ℓ⁻²·Lₐ²·Θ⁻¹·k_B⁻¹ | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "temperature": "1", "boltzmann": "1"} |
5 | ang_momentum,entropy,length,mass,thermal_cond | m·ℓ·Lₐ·S_e·κ | mechanics,thermo | m·ℓ³·Lₐ⁻¹·S_e⁻¹·κ | m = k₀ · ℓ⁻³·Lₐ·S_e·κ⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "ang_momentum": "-1", "entropy": "-1", "thermal_cond": "1"} |
5 | ang_momentum,entropy,expansion,length,mass | m·ℓ·Lₐ·S_e·β | mechanics,thermo | m·ℓ²·Lₐ⁻²·S_e·β⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·S_e⁻¹·β | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "entropy": "1", "expansion": "-1"} |
6 | ang_momentum,entropy,gas_constant,length,mass,molar_energy | m·ℓ·Lₐ·S_e·E_m·R | chemistry,mechanics,thermo | m·ℓ²·Lₐ⁻²·S_e·E_m·R⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·S_e⁻¹·E_m⁻¹·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "entropy": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | ang_momentum,cat_activity,entropy,gas_constant,length,mass | m·ℓ·Lₐ·S_e·R·z | chemistry,mechanics,thermo | m·ℓ²·Lₐ⁻¹·S_e⁻¹·R·z | m = k₀ · ℓ⁻²·Lₐ·S_e·R⁻¹·z⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "2", "ang_momentum": "-1", "entropy": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | ang_momentum,heat_capacity,length,mass,thermal_cond | m·ℓ·Lₐ·C·κ | mechanics,thermo | m·ℓ³·Lₐ⁻¹·C⁻¹·κ | m = k₀ · ℓ⁻³·Lₐ·C·κ⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "ang_momentum": "-1", "heat_capacity": "-1", "thermal_cond": "1"} |
5 | ang_momentum,expansion,heat_capacity,length,mass | m·ℓ·Lₐ·C·β | mechanics,thermo | m·ℓ²·Lₐ⁻²·C·β⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·C⁻¹·β | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "heat_capacity": "1", "expansion": "-1"} |
6 | ang_momentum,gas_constant,heat_capacity,length,mass,molar_energy | m·ℓ·Lₐ·C·E_m·R | chemistry,mechanics,thermo | m·ℓ²·Lₐ⁻²·C·E_m·R⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·C⁻¹·E_m⁻¹·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "heat_capacity": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | ang_momentum,cat_activity,gas_constant,heat_capacity,length,mass | m·ℓ·Lₐ·C·R·z | chemistry,mechanics,thermo | m·ℓ²·Lₐ⁻¹·C⁻¹·R·z | m = k₀ · ℓ⁻²·Lₐ·C·R⁻¹·z⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "2", "ang_momentum": "-1", "heat_capacity": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | ang_momentum,expansion,length,mass,specific_heat | m·ℓ·Lₐ·c·β | mechanics,thermo | m²·ℓ²·Lₐ⁻²·c·β⁻¹ | c = k₀ · m⁻²·ℓ⁻²·Lₐ²·β | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "ang_momentum": "-2", "specific_heat": "1", "expansion": "-1"} |
6 | ang_momentum,gas_constant,length,mass,molar_energy,specific_heat | m·ℓ·Lₐ·c·E_m·R | chemistry,mechanics,thermo | m²·ℓ²·Lₐ⁻²·c·E_m·R⁻¹ | c = k₀ · m⁻²·ℓ⁻²·Lₐ²·E_m⁻¹·R | null | 0 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "2", "length": "2", "ang_momentum": "-2", "specific_heat": "1", "molar_energy": "1", "gas_constant": "-1"} |
5 | ang_momentum,expansion,length,mass,thermal_cond | m·ℓ·Lₐ·κ·β | mechanics,thermo | m²·ℓ⁵·Lₐ⁻³·κ·β⁻¹ | κ = k₀ · m⁻²·ℓ⁻⁵·Lₐ³·β | null | 0 | 2 | 5 | 12 | 10.5 | -1 | false | {"mass": "2", "length": "5", "ang_momentum": "-3", "thermal_cond": "1", "expansion": "-1"} |
6 | amount,ang_momentum,gas_constant,length,mass,thermal_cond | m·ℓ·Lₐ·κ·n·R | chemistry,mechanics,thermo | m·ℓ³·Lₐ⁻¹·κ·n⁻¹·R⁻¹ | m = k₀ · ℓ⁻³·Lₐ·κ⁻¹·n·R | null | 0 | 3 | 3 | 8 | 7.6 | 1.4 | false | {"mass": "1", "length": "3", "ang_momentum": "-1", "thermal_cond": "1", "amount": "-1", "gas_constant": "-1"} |
6 | ang_momentum,gas_constant,length,mass,molar_energy,thermal_cond | m·ℓ·Lₐ·κ·E_m·R | chemistry,mechanics,thermo | m²·ℓ⁵·Lₐ⁻³·κ·E_m·R⁻¹ | κ = k₀ · m⁻²·ℓ⁻⁵·Lₐ³·E_m⁻¹·R | null | 0 | 3 | 5 | 13 | 12.1 | -3.1 | false | {"mass": "2", "length": "5", "ang_momentum": "-3", "thermal_cond": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | ang_momentum,avogadro,gas_constant,length,mass,thermal_cond | m·ℓ·Lₐ·κ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ³·Lₐ⁻¹·κ·R⁻¹·N_A | m = k₀ · ℓ⁻³·Lₐ·κ⁻¹·R·N_A⁻¹ | null | 1 | 4 | 3 | 8 | 8.2 | 0.3 | false | {"mass": "1", "length": "3", "ang_momentum": "-1", "thermal_cond": "1", "gas_constant": "-1", "avogadro": "1"} |
5 | ang_momentum,boltzmann,length,mass,thermal_cond | m·ℓ·Lₐ·κ·k_B | constants,mechanics,thermo | m·ℓ³·Lₐ⁻¹·κ·k_B⁻¹ | m = k₀ · ℓ⁻³·Lₐ·κ⁻¹·k_B | null | 1 | 3 | 3 | 7 | 6.6 | 2.4 | false | {"mass": "1", "length": "3", "ang_momentum": "-1", "thermal_cond": "1", "boltzmann": "-1"} |
6 | amount,ang_momentum,expansion,gas_constant,length,mass | m·ℓ·Lₐ·β·n·R | chemistry,mechanics,thermo | m·ℓ²·Lₐ⁻²·β⁻¹·n·R | m = k₀ · ℓ⁻²·Lₐ²·β·n⁻¹·R⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "expansion": "-1", "amount": "1", "gas_constant": "1"} |
6 | ang_momentum,expansion,gas_constant,length,mass,molar_mass | m·ℓ·Lₐ·β·M_m·R | chemistry,mechanics,thermo | m²·ℓ²·Lₐ⁻²·β⁻¹·M_m⁻¹·R | β = k₀ · m²·ℓ²·Lₐ⁻²·M_m⁻¹·R | null | 0 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "2", "length": "2", "ang_momentum": "-2", "expansion": "-1", "molar_mass": "-1", "gas_constant": "1"} |
6 | ang_momentum,concentration,expansion,gas_constant,length,mass | m·ℓ·Lₐ·β·c_n·R | chemistry,mechanics,thermo | m·ℓ⁵·Lₐ⁻²·β⁻¹·c_n·R | m = k₀ · ℓ⁻⁵·Lₐ²·β·c_n⁻¹·R⁻¹ | null | 0 | 3 | 5 | 11 | 10.7 | -1.7 | false | {"mass": "1", "length": "5", "ang_momentum": "-2", "expansion": "-1", "concentration": "1", "gas_constant": "1"} |
6 | ang_momentum,cat_activity,expansion,gas_constant,length,mass | m·ℓ·Lₐ·β·R·z | chemistry,mechanics,thermo | m²·ℓ⁴·Lₐ⁻³·β⁻¹·R·z | β = k₀ · m²·ℓ⁴·Lₐ⁻³·R·z | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "2", "length": "4", "ang_momentum": "-3", "expansion": "-1", "gas_constant": "1", "cat_activity": "1"} |
6 | ang_momentum,avogadro,expansion,gas_constant,length,mass | m·ℓ·Lₐ·β·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ²·Lₐ⁻²·β⁻¹·R·N_A⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·β·R⁻¹·N_A | null | 1 | 4 | 2 | 8 | 7.7 | 0.8 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "expansion": "-1", "gas_constant": "1", "avogadro": "-1"} |
5 | ang_momentum,boltzmann,expansion,length,mass | m·ℓ·Lₐ·β·k_B | constants,mechanics,thermo | m·ℓ²·Lₐ⁻²·β⁻¹·k_B | m = k₀ · ℓ⁻²·Lₐ²·β·k_B⁻¹ | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "expansion": "-1", "boltzmann": "1"} |
5 | ang_momentum,charge,current,length,mass | m·ℓ·Lₐ·q·i | em,mechanics | m·ℓ²·Lₐ⁻¹·q⁻¹·i | m = k₀ · ℓ⁻²·Lₐ·q·i⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "charge": "-1", "current": "1"} |
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