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 | charge,current,length,mass,pressure | m·ℓ·P_p·q·i | em,mechanics | m·ℓ⁻¹·P_p⁻¹·q⁻²·i² | m = k₀ · ℓ·P_p·q²·i⁻² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "charge": "-2", "current": "2"} |
5 | charge,length,mass,pressure,resistance | m·ℓ·P_p·q·R | em,mechanics | m·ℓ⁵·P_p·q⁻⁴·R⁻² | m = k₀ · ℓ⁻⁵·P_p⁻¹·q⁴·R² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "1", "length": "5", "pressure": "1", "charge": "-4", "resistance": "-2"} |
5 | bfield,charge,length,mass,pressure | m·ℓ·P_p·q·B | em,mechanics | m·ℓ·P_p·q⁻²·B⁻² | m = k₀ · ℓ⁻¹·P_p⁻¹·q²·B² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "pressure": "1", "charge": "-2", "bfield": "-2"} |
5 | charge,length,mag_flux,mass,pressure | m·ℓ·P_p·q·Φ | em,mechanics | m·ℓ⁵·P_p·q⁻²·Φ⁻² | m = k₀ · ℓ⁻⁵·P_p⁻¹·q²·Φ² | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "5", "pressure": "1", "charge": "-2", "mag_flux": "-2"} |
5 | charge,conductivity,length,mass,pressure | m·ℓ·P_p·q·σ | em,mechanics | m·ℓ⁷·P_p·q⁻⁴·σ² | m = k₀ · ℓ⁻⁷·P_p⁻¹·q⁴·σ⁻² | null | 0 | 2 | 7 | 15 | 13.6 | -4.1 | false | {"mass": "1", "length": "7", "pressure": "1", "charge": "-4", "conductivity": "2"} |
5 | charge,length,mass,pressure,resistivity | m·ℓ·P_p·q·ρ_e | em,mechanics | m·ℓ⁷·P_p·q⁻⁴·ρ_e⁻² | m = k₀ · ℓ⁻⁷·P_p⁻¹·q⁴·ρ_e² | null | 0 | 2 | 7 | 15 | 13.6 | -4.1 | false | {"mass": "1", "length": "7", "pressure": "1", "charge": "-4", "resistivity": "-2"} |
5 | current,length,mass,pressure,voltage | m·ℓ·P_p·i·U | em,mechanics | m·ℓ⁻⁷·P_p⁻³·i²·U² | m = k₀ · ℓ⁷·P_p³·i⁻²·U⁻² | null | 0 | 2 | 7 | 15 | 13.6 | -4.1 | false | {"mass": "1", "length": "-7", "pressure": "-3", "current": "2", "voltage": "2"} |
5 | current,length,mass,pressure,resistance | m·ℓ·P_p·i·R | em,mechanics | m·ℓ⁻⁷·P_p⁻³·i⁴·R² | m = k₀ · ℓ⁷·P_p³·i⁻⁴·R⁻² | null | 0 | 2 | 7 | 17 | 15 | -5.5 | false | {"mass": "1", "length": "-7", "pressure": "-3", "current": "4", "resistance": "2"} |
5 | capacitance,current,length,mass,pressure | m·ℓ·P_p·i·C_e | em,mechanics | m·ℓ⁻⁴·P_p⁻²·i²·C_e⁻¹ | m = k₀ · ℓ⁴·P_p²·i⁻²·C_e | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "-4", "pressure": "-2", "current": "2", "capacitance": "-1"} |
5 | current,efield,length,mass,pressure | m·ℓ·P_p·i·E_f | em,mechanics | m·ℓ⁻⁵·P_p⁻³·i²·E_f² | m = k₀ · ℓ⁵·P_p³·i⁻²·E_f⁻² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "1", "length": "-5", "pressure": "-3", "current": "2", "efield": "2"} |
5 | current,length,mass,permittivity,pressure | m·ℓ·P_p·i·ε | em,mechanics | m·ℓ⁻⁵·P_p⁻²·i²·ε⁻¹ | m = k₀ · ℓ⁵·P_p²·i⁻²·ε | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "-5", "pressure": "-2", "current": "2", "permittivity": "-1"} |
5 | conductivity,current,length,mass,pressure | m·ℓ·P_p·i·σ | em,mechanics | m·ℓ⁻⁹·P_p⁻³·i⁴·σ⁻² | m = k₀ · ℓ⁹·P_p³·i⁻⁴·σ² | null | 0 | 2 | 9 | 19 | 17.4 | -7.9 | false | {"mass": "1", "length": "-9", "pressure": "-3", "current": "4", "conductivity": "-2"} |
5 | current,length,mass,pressure,resistivity | m·ℓ·P_p·i·ρ_e | em,mechanics | m·ℓ⁻⁹·P_p⁻³·i⁴·ρ_e² | m = k₀ · ℓ⁹·P_p³·i⁻⁴·ρ_e⁻² | null | 0 | 2 | 9 | 19 | 17.4 | -7.9 | false | {"mass": "1", "length": "-9", "pressure": "-3", "current": "4", "resistivity": "2"} |
5 | current,elem_charge,length,mass,pressure | m·ℓ·P_p·i·e | constants,em,mechanics | m·ℓ⁻¹·P_p⁻¹·i²·e⁻² | m = k₀ · ℓ·P_p·i⁻²·e² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "-1", "pressure": "-1", "current": "2", "elem_charge": "-2"} |
5 | length,mass,pressure,resistance,voltage | m·ℓ·P_p·U·R | em,mechanics | m·ℓ⁻⁷·P_p⁻³·U⁴·R⁻² | m = k₀ · ℓ⁷·P_p³·U⁻⁴·R² | null | 0 | 2 | 7 | 17 | 15 | -5.5 | false | {"mass": "1", "length": "-7", "pressure": "-3", "voltage": "4", "resistance": "-2"} |
5 | inductance,length,mass,pressure,voltage | m·ℓ·P_p·U·L_e | em,mechanics | m·ℓ⁻⁴·P_p⁻²·U²·L_e⁻¹ | m = k₀ · ℓ⁴·P_p²·U⁻²·L_e | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "-4", "pressure": "-2", "voltage": "2", "inductance": "-1"} |
5 | bfield,length,mass,pressure,voltage | m·ℓ·P_p·U·B | em,mechanics | m·ℓ⁻⁵·P_p⁻¹·U²·B⁻² | m = k₀ · ℓ⁵·P_p·U⁻²·B² | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "-5", "pressure": "-1", "voltage": "2", "bfield": "-2"} |
5 | length,mag_flux,mass,pressure,voltage | m·ℓ·P_p·U·Φ | em,mechanics | m·ℓ⁻¹·P_p⁻¹·U²·Φ⁻² | m = k₀ · ℓ·P_p·U⁻²·Φ² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "voltage": "2", "mag_flux": "-2"} |
5 | length,mass,permeability,pressure,voltage | m·ℓ·P_p·U·μ₀ | em,mechanics | m·ℓ⁻⁵·P_p⁻²·U²·μ₀⁻¹ | m = k₀ · ℓ⁵·P_p²·U⁻²·μ₀ | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "-5", "pressure": "-2", "voltage": "2", "permeability": "-1"} |
5 | conductivity,length,mass,pressure,voltage | m·ℓ·P_p·U·σ | em,mechanics | m·ℓ⁻⁵·P_p⁻³·U⁴·σ² | m = k₀ · ℓ⁵·P_p³·U⁻⁴·σ⁻² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "1", "length": "-5", "pressure": "-3", "voltage": "4", "conductivity": "2"} |
5 | length,mass,pressure,resistivity,voltage | m·ℓ·P_p·U·ρ_e | em,mechanics | m·ℓ⁻⁵·P_p⁻³·U⁴·ρ_e⁻² | m = k₀ · ℓ⁵·P_p³·U⁻⁴·ρ_e² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "1", "length": "-5", "pressure": "-3", "voltage": "4", "resistivity": "-2"} |
5 | capacitance,length,mass,pressure,resistance | m·ℓ·P_p·R·C_e | em,mechanics | m·ℓ⁻¹·P_p⁻¹·R⁻²·C_e⁻² | m = k₀ · ℓ·P_p·R²·C_e² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "resistance": "-2", "capacitance": "-2"} |
5 | inductance,length,mass,pressure,resistance | m·ℓ·P_p·R·L_e | em,mechanics | m·ℓ⁻¹·P_p⁻¹·R²·L_e⁻² | m = k₀ · ℓ·P_p·R⁻²·L_e² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "resistance": "2", "inductance": "-2"} |
5 | efield,length,mass,pressure,resistance | m·ℓ·P_p·R·E_f | em,mechanics | m·ℓ⁻³·P_p⁻³·R⁻²·E_f⁴ | m = k₀ · ℓ³·P_p³·R²·E_f⁻⁴ | null | 0 | 2 | 4 | 13 | 10.7 | -1.2 | false | {"mass": "1", "length": "-3", "pressure": "-3", "resistance": "-2", "efield": "4"} |
5 | bfield,length,mass,pressure,resistance | m·ℓ·P_p·R·B | em,mechanics | m·ℓ⁻³·P_p·R²·B⁻⁴ | m = k₀ · ℓ³·P_p⁻¹·R⁻²·B⁴ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "-3", "pressure": "1", "resistance": "2", "bfield": "-4"} |
5 | length,mag_flux,mass,pressure,resistance | m·ℓ·P_p·R·Φ | em,mechanics | m·ℓ⁵·P_p·R²·Φ⁻⁴ | m = k₀ · ℓ⁻⁵·P_p⁻¹·R⁻²·Φ⁴ | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "1", "length": "5", "pressure": "1", "resistance": "2", "mag_flux": "-4"} |
5 | length,mass,permittivity,pressure,resistance | m·ℓ·P_p·R·ε | em,mechanics | m·ℓ⁻³·P_p⁻¹·R⁻²·ε⁻² | m = k₀ · ℓ³·P_p·R²·ε² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "pressure": "-1", "resistance": "-2", "permittivity": "-2"} |
5 | length,mass,permeability,pressure,resistance | m·ℓ·P_p·R·μ₀ | em,mechanics | m·ℓ⁻³·P_p⁻¹·R²·μ₀⁻² | m = k₀ · ℓ³·P_p·R⁻²·μ₀² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "pressure": "-1", "resistance": "2", "permeability": "-2"} |
5 | elem_charge,length,mass,pressure,resistance | m·ℓ·P_p·R·e | constants,em,mechanics | m·ℓ⁵·P_p·R⁻²·e⁻⁴ | m = k₀ · ℓ⁻⁵·P_p⁻¹·R²·e⁴ | null | 1 | 3 | 5 | 13 | 11.8 | -2.8 | false | {"mass": "1", "length": "5", "pressure": "1", "resistance": "-2", "elem_charge": "-4"} |
5 | capacitance,inductance,length,mass,pressure | m·ℓ·P_p·C_e·L_e | em,mechanics | m·ℓ⁻¹·P_p⁻¹·C_e⁻¹·L_e⁻¹ | m = k₀ · ℓ·P_p·C_e·L_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "pressure": "-1", "capacitance": "-1", "inductance": "-1"} |
5 | capacitance,length,mass,permeability,pressure | m·ℓ·P_p·C_e·μ₀ | em,mechanics | m·ℓ⁻²·P_p⁻¹·C_e⁻¹·μ₀⁻¹ | m = k₀ · ℓ²·P_p·C_e·μ₀ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "-2", "pressure": "-1", "capacitance": "-1", "permeability": "-1"} |
5 | capacitance,conductivity,length,mass,pressure | m·ℓ·P_p·C_e·σ | em,mechanics | m·ℓ·P_p⁻¹·C_e⁻²·σ² | m = k₀ · ℓ⁻¹·P_p·C_e²·σ⁻² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "pressure": "-1", "capacitance": "-2", "conductivity": "2"} |
5 | capacitance,length,mass,pressure,resistivity | m·ℓ·P_p·C_e·ρ_e | em,mechanics | m·ℓ·P_p⁻¹·C_e⁻²·ρ_e⁻² | m = k₀ · ℓ⁻¹·P_p·C_e²·ρ_e² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "pressure": "-1", "capacitance": "-2", "resistivity": "-2"} |
5 | efield,inductance,length,mass,pressure | m·ℓ·P_p·L_e·E_f | em,mechanics | m·ℓ⁻²·P_p⁻²·L_e⁻¹·E_f² | m = k₀ · ℓ²·P_p²·L_e·E_f⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "-2", "pressure": "-2", "inductance": "-1", "efield": "2"} |
5 | inductance,length,mass,permittivity,pressure | m·ℓ·P_p·L_e·ε | em,mechanics | m·ℓ⁻²·P_p⁻¹·L_e⁻¹·ε⁻¹ | m = k₀ · ℓ²·P_p·L_e·ε | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "-2", "pressure": "-1", "inductance": "-1", "permittivity": "-1"} |
5 | conductivity,inductance,length,mass,pressure | m·ℓ·P_p·L_e·σ | em,mechanics | m·ℓ⁻³·P_p⁻¹·L_e⁻²·σ⁻² | m = k₀ · ℓ³·P_p·L_e²·σ² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "pressure": "-1", "inductance": "-2", "conductivity": "-2"} |
5 | inductance,length,mass,pressure,resistivity | m·ℓ·P_p·L_e·ρ_e | em,mechanics | m·ℓ⁻³·P_p⁻¹·L_e⁻²·ρ_e² | m = k₀ · ℓ³·P_p·L_e²·ρ_e⁻² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "pressure": "-1", "inductance": "-2", "resistivity": "2"} |
5 | bfield,efield,length,mass,pressure | m·ℓ·P_p·E_f·B | em,mechanics | m·ℓ⁻³·P_p⁻¹·E_f²·B⁻² | m = k₀ · ℓ³·P_p·E_f⁻²·B² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "pressure": "-1", "efield": "2", "bfield": "-2"} |
5 | efield,length,mag_flux,mass,pressure | m·ℓ·P_p·E_f·Φ | em,mechanics | m·ℓ·P_p⁻¹·E_f²·Φ⁻² | m = k₀ · ℓ⁻¹·P_p·E_f⁻²·Φ² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "pressure": "-1", "efield": "2", "mag_flux": "-2"} |
5 | efield,length,mass,permeability,pressure | m·ℓ·P_p·E_f·μ₀ | em,mechanics | m·ℓ⁻³·P_p⁻²·E_f²·μ₀⁻¹ | m = k₀ · ℓ³·P_p²·E_f⁻²·μ₀ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "-3", "pressure": "-2", "efield": "2", "permeability": "-1"} |
5 | conductivity,efield,length,mass,pressure | m·ℓ·P_p·E_f·σ | em,mechanics | m·ℓ⁻¹·P_p⁻³·E_f⁴·σ² | m = k₀ · ℓ·P_p³·E_f⁻⁴·σ⁻² | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "-1", "pressure": "-3", "efield": "4", "conductivity": "2"} |
5 | efield,length,mass,pressure,resistivity | m·ℓ·P_p·E_f·ρ_e | em,mechanics | m·ℓ⁻¹·P_p⁻³·E_f⁴·ρ_e⁻² | m = k₀ · ℓ·P_p³·E_f⁻⁴·ρ_e² | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "-1", "pressure": "-3", "efield": "4", "resistivity": "-2"} |
5 | bfield,conductivity,length,mass,pressure | m·ℓ·P_p·B·σ | em,mechanics | m·ℓ⁻⁵·P_p·B⁻⁴·σ⁻² | m = k₀ · ℓ⁵·P_p⁻¹·B⁴·σ² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "1", "length": "-5", "pressure": "1", "bfield": "-4", "conductivity": "-2"} |
5 | bfield,length,mass,pressure,resistivity | m·ℓ·P_p·B·ρ_e | em,mechanics | m·ℓ⁻⁵·P_p·B⁻⁴·ρ_e² | m = k₀ · ℓ⁵·P_p⁻¹·B⁴·ρ_e⁻² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "1", "length": "-5", "pressure": "1", "bfield": "-4", "resistivity": "2"} |
5 | bfield,elem_charge,length,mass,pressure | m·ℓ·P_p·B·e | constants,em,mechanics | m·ℓ·P_p·B⁻²·e⁻² | m = k₀ · ℓ⁻¹·P_p⁻¹·B²·e² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "1", "pressure": "1", "bfield": "-2", "elem_charge": "-2"} |
5 | conductivity,length,mag_flux,mass,pressure | m·ℓ·P_p·Φ·σ | em,mechanics | m·ℓ³·P_p·Φ⁻⁴·σ⁻² | m = k₀ · ℓ⁻³·P_p⁻¹·Φ⁴·σ² | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "3", "pressure": "1", "mag_flux": "-4", "conductivity": "-2"} |
5 | length,mag_flux,mass,pressure,resistivity | m·ℓ·P_p·Φ·ρ_e | em,mechanics | m·ℓ³·P_p·Φ⁻⁴·ρ_e² | m = k₀ · ℓ⁻³·P_p⁻¹·Φ⁴·ρ_e⁻² | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "1", "length": "3", "pressure": "1", "mag_flux": "-4", "resistivity": "2"} |
5 | elem_charge,length,mag_flux,mass,pressure | m·ℓ·P_p·Φ·e | constants,em,mechanics | m·ℓ⁵·P_p·Φ⁻²·e⁻² | m = k₀ · ℓ⁻⁵·P_p⁻¹·Φ²·e² | null | 1 | 3 | 5 | 11 | 10.4 | -1.4 | false | {"mass": "1", "length": "5", "pressure": "1", "mag_flux": "-2", "elem_charge": "-2"} |
5 | length,mass,permeability,permittivity,pressure | m·ℓ·P_p·ε·μ₀ | em,mechanics | m·ℓ⁻³·P_p⁻¹·ε⁻¹·μ₀⁻¹ | m = k₀ · ℓ³·P_p·ε·μ₀ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "-3", "pressure": "-1", "permittivity": "-1", "permeability": "-1"} |
5 | conductivity,length,mass,permittivity,pressure | m·ℓ·P_p·ε·σ | em,mechanics | m·ℓ⁻¹·P_p⁻¹·ε⁻²·σ² | m = k₀ · ℓ·P_p·ε²·σ⁻² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "permittivity": "-2", "conductivity": "2"} |
5 | length,mass,permittivity,pressure,resistivity | m·ℓ·P_p·ε·ρ_e | em,mechanics | m·ℓ⁻¹·P_p⁻¹·ε⁻²·ρ_e⁻² | m = k₀ · ℓ·P_p·ε²·ρ_e² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "permittivity": "-2", "resistivity": "-2"} |
5 | conductivity,length,mass,permeability,pressure | m·ℓ·P_p·μ₀·σ | em,mechanics | m·ℓ⁻⁵·P_p⁻¹·μ₀⁻²·σ⁻² | m = k₀ · ℓ⁵·P_p·μ₀²·σ² | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "-5", "pressure": "-1", "permeability": "-2", "conductivity": "-2"} |
5 | length,mass,permeability,pressure,resistivity | m·ℓ·P_p·μ₀·ρ_e | em,mechanics | m·ℓ⁻⁵·P_p⁻¹·μ₀⁻²·ρ_e² | m = k₀ · ℓ⁵·P_p·μ₀²·ρ_e⁻² | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "-5", "pressure": "-1", "permeability": "-2", "resistivity": "2"} |
5 | conductivity,elem_charge,length,mass,pressure | m·ℓ·P_p·σ·e | constants,em,mechanics | m·ℓ⁷·P_p·σ²·e⁻⁴ | m = k₀ · ℓ⁻⁷·P_p⁻¹·σ⁻²·e⁴ | null | 1 | 3 | 7 | 15 | 14.2 | -5.2 | false | {"mass": "1", "length": "7", "pressure": "1", "conductivity": "2", "elem_charge": "-4"} |
5 | elem_charge,length,mass,pressure,resistivity | m·ℓ·P_p·ρ_e·e | constants,em,mechanics | m·ℓ⁷·P_p·ρ_e⁻²·e⁻⁴ | m = k₀ · ℓ⁻⁷·P_p⁻¹·ρ_e²·e⁴ | null | 1 | 3 | 7 | 15 | 14.2 | -5.2 | false | {"mass": "1", "length": "7", "pressure": "1", "resistivity": "-2", "elem_charge": "-4"} |
5 | amount,cat_activity,length,mass,pressure | m·ℓ·P_p·n·z | chemistry,mechanics | m·ℓ⁻¹·P_p⁻¹·n⁻²·z² | m = k₀ · ℓ·P_p·n²·z⁻² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "-1", "pressure": "-1", "amount": "-2", "cat_activity": "2"} |
5 | length,mass,molar_energy,molar_mass,pressure | m·ℓ·P_p·M_m·E_m | chemistry,mechanics | m·ℓ⁻³·P_p⁻¹·M_m⁻¹·E_m | m = k₀ · ℓ³·P_p·M_m·E_m⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "-3", "pressure": "-1", "molar_mass": "-1", "molar_energy": "1"} |
5 | cat_activity,length,mass,molar_mass,pressure | m·ℓ·P_p·M_m·z | chemistry,mechanics | m·ℓ·P_p·M_m⁻²·z⁻² | m = k₀ · ℓ⁻¹·P_p⁻¹·M_m²·z² | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "pressure": "1", "molar_mass": "-2", "cat_activity": "-2"} |
5 | cat_activity,concentration,length,mass,pressure | m·ℓ·P_p·c_n·z | chemistry,mechanics | m·ℓ⁻⁷·P_p⁻¹·c_n⁻²·z² | m = k₀ · ℓ⁷·P_p·c_n²·z⁻² | null | 0 | 2 | 7 | 13 | 12.2 | -2.7 | false | {"mass": "1", "length": "-7", "pressure": "-1", "concentration": "-2", "cat_activity": "2"} |
5 | cat_activity,length,mass,molar_energy,pressure | m·ℓ·P_p·E_m·z | chemistry,mechanics | m·ℓ⁻⁷·P_p⁻³·E_m²·z² | m = k₀ · ℓ⁷·P_p³·E_m⁻²·z⁻² | null | 0 | 2 | 7 | 15 | 13.6 | -4.1 | false | {"mass": "1", "length": "-7", "pressure": "-3", "molar_energy": "2", "cat_activity": "2"} |
6 | boltzmann,cat_activity,gas_constant,length,mass,pressure | m·ℓ·P_p·R·z·k_B | chemistry,constants,mechanics | m·ℓ⁻¹·P_p⁻¹·R²·z²·k_B⁻² | m = k₀ · ℓ·P_p·R⁻²·z⁻²·k_B² | null | 1 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "1", "length": "-1", "pressure": "-1", "gas_constant": "2", "cat_activity": "2", "boltzmann": "-2"} |
5 | avogadro,cat_activity,length,mass,pressure | m·ℓ·P_p·z·N_A | chemistry,constants,mechanics | m·ℓ⁻¹·P_p⁻¹·z²·N_A² | m = k₀ · ℓ·P_p·z⁻²·N_A⁻² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "-1", "pressure": "-1", "cat_activity": "2", "avogadro": "2"} |
4 | length,light_speed,mass,pressure | m·ℓ·P_p·c₀ | constants,mechanics | m·ℓ⁻³·P_p⁻¹·c₀² | m = k₀ · ℓ³·P_p·c₀⁻² | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "1", "length": "-3", "pressure": "-1", "light_speed": "2"} |
4 | grav_const,length,mass,pressure | m·ℓ·P_p·G | constants,mechanics | m²·ℓ⁻⁴·P_p⁻¹·G | P_p = k₀ · m²·ℓ⁻⁴·G | null | 1 | 2 | 4 | 8 | 6.9 | 2.6 | false | {"mass": "2", "length": "-4", "pressure": "-1", "grav_const": "1"} |
4 | length,mass,planck,pressure | m·ℓ·P_p·h | constants,mechanics | m·ℓ⁵·P_p·h⁻² | m = k₀ · ℓ⁻⁵·P_p⁻¹·h² | null | 1 | 2 | 5 | 9 | 8.1 | 1.4 | false | {"mass": "1", "length": "5", "pressure": "1", "planck": "-2"} |
3 | density,length,mass | m·ℓ·ρ | mechanics | m·ℓ⁻³·ρ⁻¹ | m = k₀ · ℓ³·ρ | null | 0 | 1 | 3 | 5 | 3.4 | 6.6 | true | {"mass": "1", "length": "-3", "density": "-1"} |
4 | kin_viscosity,length,mass,viscosity | m·ℓ·μ·ν | mechanics | m·ℓ⁻³·μ⁻¹·ν | m = k₀ · ℓ³·μ·ν⁻¹ | null | 0 | 1 | 3 | 6 | 4.4 | 5.6 | true | {"mass": "1", "length": "-3", "viscosity": "-1", "kin_viscosity": "1"} |
4 | length,mass,omega,viscosity | m·ℓ·μ·ω | mechanics | m·ℓ⁻¹·μ⁻¹·ω | m = k₀ · ℓ·μ·ω⁻¹ | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "-1", "viscosity": "-1", "omega": "1"} |
4 | frequency,length,mass,viscosity | m·ℓ·μ·f | mechanics | m·ℓ⁻¹·μ⁻¹·f | m = k₀ · ℓ·μ·f⁻¹ | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "-1", "viscosity": "-1", "frequency": "1"} |
4 | length,mass,stiffness,viscosity | m·ℓ·μ·k | mechanics | m·ℓ⁻²·μ⁻²·k | m = k₀ · ℓ²·μ²·k⁻¹ | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "-2", "viscosity": "-2", "stiffness": "1"} |
4 | length,mass,surf_tension,viscosity | m·ℓ·μ·γ | mechanics | m·ℓ⁻²·μ⁻²·γ | m = k₀ · ℓ²·μ²·γ⁻¹ | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "1", "length": "-2", "viscosity": "-2", "surf_tension": "1"} |
4 | flowrate,length,mass,viscosity | m·ℓ·μ·Q | mechanics | m·ℓ⁻⁴·μ⁻¹·Q | m = k₀ · ℓ⁴·μ·Q⁻¹ | null | 0 | 1 | 4 | 7 | 5.6 | 4.4 | false | {"mass": "1", "length": "-4", "viscosity": "-1", "flowrate": "1"} |
5 | entropy,length,mass,temperature,viscosity | m·ℓ·μ·Θ·S_e | mechanics,thermo | m·ℓ⁻⁴·μ⁻²·Θ·S_e | m = k₀ · ℓ⁴·μ²·Θ⁻¹·S_e⁻¹ | null | 0 | 2 | 4 | 9 | 7.9 | 1.6 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "temperature": "1", "entropy": "1"} |
5 | heat_capacity,length,mass,temperature,viscosity | m·ℓ·μ·Θ·C | mechanics,thermo | m·ℓ⁻⁴·μ⁻²·Θ·C | m = k₀ · ℓ⁴·μ²·Θ⁻¹·C⁻¹ | null | 0 | 2 | 4 | 9 | 7.9 | 1.6 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "temperature": "1", "heat_capacity": "1"} |
5 | length,mass,specific_heat,temperature,viscosity | m·ℓ·μ·Θ·c | mechanics,thermo | m²·ℓ⁻⁴·μ⁻²·Θ·c | Θ = k₀ · m⁻²·ℓ⁴·μ²·c⁻¹ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "length": "-4", "viscosity": "-2", "temperature": "1", "specific_heat": "1"} |
5 | length,mass,temperature,thermal_cond,viscosity | m·ℓ·μ·Θ·κ | mechanics,thermo | m²·ℓ⁻⁴·μ⁻³·Θ·κ | Θ = k₀ · m⁻²·ℓ⁴·μ³·κ⁻¹ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "2", "length": "-4", "viscosity": "-3", "temperature": "1", "thermal_cond": "1"} |
6 | amount,gas_constant,length,mass,temperature,viscosity | m·ℓ·μ·Θ·n·R | chemistry,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·Θ·n·R | m = k₀ · ℓ⁴·μ²·Θ⁻¹·n⁻¹·R⁻¹ | null | 0 | 3 | 4 | 10 | 9.5 | -0.5 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "temperature": "1", "amount": "1", "gas_constant": "1"} |
6 | gas_constant,length,mass,molar_mass,temperature,viscosity | m·ℓ·μ·Θ·M_m·R | chemistry,mechanics,thermo | m²·ℓ⁻⁴·μ⁻²·Θ·M_m⁻¹·R | Θ = k₀ · m⁻²·ℓ⁴·μ²·M_m·R⁻¹ | null | 0 | 3 | 4 | 11 | 10.2 | -1.2 | false | {"mass": "2", "length": "-4", "viscosity": "-2", "temperature": "1", "molar_mass": "-1", "gas_constant": "1"} |
6 | concentration,gas_constant,length,mass,temperature,viscosity | m·ℓ·μ·Θ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻¹·μ⁻²·Θ·c_n·R | m = k₀ · ℓ·μ²·Θ⁻¹·c_n⁻¹·R⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "-1", "viscosity": "-2", "temperature": "1", "concentration": "1", "gas_constant": "1"} |
6 | cat_activity,gas_constant,length,mass,temperature,viscosity | m·ℓ·μ·Θ·R·z | chemistry,mechanics,thermo | m²·ℓ⁻⁵·μ⁻³·Θ·R·z | Θ = k₀ · m⁻²·ℓ⁵·μ³·R⁻¹·z⁻¹ | null | 0 | 3 | 5 | 13 | 12.1 | -3.1 | false | {"mass": "2", "length": "-5", "viscosity": "-3", "temperature": "1", "gas_constant": "1", "cat_activity": "1"} |
6 | avogadro,gas_constant,length,mass,temperature,viscosity | m·ℓ·μ·Θ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·Θ·R·N_A⁻¹ | m = k₀ · ℓ⁴·μ²·Θ⁻¹·R⁻¹·N_A | null | 1 | 4 | 4 | 10 | 10.1 | -1.6 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "temperature": "1", "gas_constant": "1", "avogadro": "-1"} |
5 | boltzmann,length,mass,temperature,viscosity | m·ℓ·μ·Θ·k_B | constants,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·Θ·k_B | m = k₀ · ℓ⁴·μ²·Θ⁻¹·k_B⁻¹ | null | 1 | 3 | 4 | 9 | 8.5 | 0.5 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "temperature": "1", "boltzmann": "1"} |
5 | entropy,expansion,length,mass,viscosity | m·ℓ·μ·S_e·β | mechanics,thermo | m·ℓ⁻⁴·μ⁻²·S_e·β⁻¹ | m = k₀ · ℓ⁴·μ²·S_e⁻¹·β | null | 0 | 2 | 4 | 9 | 7.9 | 1.6 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "entropy": "1", "expansion": "-1"} |
6 | entropy,gas_constant,length,mass,molar_energy,viscosity | m·ℓ·μ·S_e·E_m·R | chemistry,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·S_e·E_m·R⁻¹ | m = k₀ · ℓ⁴·μ²·S_e⁻¹·E_m⁻¹·R | null | 0 | 3 | 4 | 10 | 9.5 | -0.5 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "entropy": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | cat_activity,entropy,gas_constant,length,mass,viscosity | m·ℓ·μ·S_e·R·z | chemistry,mechanics,thermo | m·ℓ⁻¹·μ⁻¹·S_e⁻¹·R·z | m = k₀ · ℓ·μ·S_e·R⁻¹·z⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "-1", "viscosity": "-1", "entropy": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | expansion,heat_capacity,length,mass,viscosity | m·ℓ·μ·C·β | mechanics,thermo | m·ℓ⁻⁴·μ⁻²·C·β⁻¹ | m = k₀ · ℓ⁴·μ²·C⁻¹·β | null | 0 | 2 | 4 | 9 | 7.9 | 1.6 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "heat_capacity": "1", "expansion": "-1"} |
6 | gas_constant,heat_capacity,length,mass,molar_energy,viscosity | m·ℓ·μ·C·E_m·R | chemistry,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·C·E_m·R⁻¹ | m = k₀ · ℓ⁴·μ²·C⁻¹·E_m⁻¹·R | null | 0 | 3 | 4 | 10 | 9.5 | -0.5 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "heat_capacity": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | cat_activity,gas_constant,heat_capacity,length,mass,viscosity | m·ℓ·μ·C·R·z | chemistry,mechanics,thermo | m·ℓ⁻¹·μ⁻¹·C⁻¹·R·z | m = k₀ · ℓ·μ·C·R⁻¹·z⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "length": "-1", "viscosity": "-1", "heat_capacity": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | expansion,length,mass,specific_heat,viscosity | m·ℓ·μ·c·β | mechanics,thermo | m²·ℓ⁻⁴·μ⁻²·c·β⁻¹ | c = k₀ · m⁻²·ℓ⁴·μ²·β | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "length": "-4", "viscosity": "-2", "specific_heat": "1", "expansion": "-1"} |
6 | gas_constant,length,mass,molar_energy,specific_heat,viscosity | m·ℓ·μ·c·E_m·R | chemistry,mechanics,thermo | m²·ℓ⁻⁴·μ⁻²·c·E_m·R⁻¹ | c = k₀ · m⁻²·ℓ⁴·μ²·E_m⁻¹·R | null | 0 | 3 | 4 | 11 | 10.2 | -1.2 | false | {"mass": "2", "length": "-4", "viscosity": "-2", "specific_heat": "1", "molar_energy": "1", "gas_constant": "-1"} |
5 | expansion,length,mass,thermal_cond,viscosity | m·ℓ·μ·κ·β | mechanics,thermo | m²·ℓ⁻⁴·μ⁻³·κ·β⁻¹ | κ = k₀ · m⁻²·ℓ⁴·μ³·β | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "2", "length": "-4", "viscosity": "-3", "thermal_cond": "1", "expansion": "-1"} |
6 | concentration,gas_constant,length,mass,thermal_cond,viscosity | m·ℓ·μ·κ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻³·μ⁻¹·κ·c_n⁻¹·R⁻¹ | m = k₀ · ℓ³·μ·κ⁻¹·c_n·R | null | 0 | 3 | 3 | 8 | 7.6 | 1.4 | false | {"mass": "1", "length": "-3", "viscosity": "-1", "thermal_cond": "1", "concentration": "-1", "gas_constant": "-1"} |
6 | gas_constant,length,mass,molar_energy,thermal_cond,viscosity | m·ℓ·μ·κ·E_m·R | chemistry,mechanics,thermo | m²·ℓ⁻⁴·μ⁻³·κ·E_m·R⁻¹ | κ = k₀ · m⁻²·ℓ⁴·μ³·E_m⁻¹·R | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "2", "length": "-4", "viscosity": "-3", "thermal_cond": "1", "molar_energy": "1", "gas_constant": "-1"} |
4 | length,mass,thermal_diff,viscosity | m·ℓ·μ·α | mechanics,thermo | m·ℓ⁻³·μ⁻¹·α | m = k₀ · ℓ³·μ·α⁻¹ | null | 0 | 2 | 3 | 6 | 5 | 4.5 | true | {"mass": "1", "length": "-3", "viscosity": "-1", "thermal_diff": "1"} |
6 | amount,expansion,gas_constant,length,mass,viscosity | m·ℓ·μ·β·n·R | chemistry,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·β⁻¹·n·R | m = k₀ · ℓ⁴·μ²·β·n⁻¹·R⁻¹ | null | 0 | 3 | 4 | 10 | 9.5 | -0.5 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "expansion": "-1", "amount": "1", "gas_constant": "1"} |
6 | expansion,gas_constant,length,mass,molar_mass,viscosity | m·ℓ·μ·β·M_m·R | chemistry,mechanics,thermo | m²·ℓ⁻⁴·μ⁻²·β⁻¹·M_m⁻¹·R | β = k₀ · m²·ℓ⁻⁴·μ⁻²·M_m⁻¹·R | null | 0 | 3 | 4 | 11 | 10.2 | -1.2 | false | {"mass": "2", "length": "-4", "viscosity": "-2", "expansion": "-1", "molar_mass": "-1", "gas_constant": "1"} |
6 | concentration,expansion,gas_constant,length,mass,viscosity | m·ℓ·μ·β·c_n·R | chemistry,mechanics,thermo | m·ℓ⁻¹·μ⁻²·β⁻¹·c_n·R | m = k₀ · ℓ·μ²·β·c_n⁻¹·R⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "-1", "viscosity": "-2", "expansion": "-1", "concentration": "1", "gas_constant": "1"} |
6 | cat_activity,expansion,gas_constant,length,mass,viscosity | m·ℓ·μ·β·R·z | chemistry,mechanics,thermo | m²·ℓ⁻⁵·μ⁻³·β⁻¹·R·z | β = k₀ · m²·ℓ⁻⁵·μ⁻³·R·z | null | 0 | 3 | 5 | 13 | 12.1 | -3.1 | false | {"mass": "2", "length": "-5", "viscosity": "-3", "expansion": "-1", "gas_constant": "1", "cat_activity": "1"} |
6 | avogadro,expansion,gas_constant,length,mass,viscosity | m·ℓ·μ·β·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·β⁻¹·R·N_A⁻¹ | m = k₀ · ℓ⁴·μ²·β·R⁻¹·N_A | null | 1 | 4 | 4 | 10 | 10.1 | -1.6 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "expansion": "-1", "gas_constant": "1", "avogadro": "-1"} |
5 | boltzmann,expansion,length,mass,viscosity | m·ℓ·μ·β·k_B | constants,mechanics,thermo | m·ℓ⁻⁴·μ⁻²·β⁻¹·k_B | m = k₀ · ℓ⁴·μ²·β·k_B⁻¹ | null | 1 | 3 | 4 | 9 | 8.5 | 0.5 | false | {"mass": "1", "length": "-4", "viscosity": "-2", "expansion": "-1", "boltzmann": "1"} |
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