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 | acceleration,cat_activity,gas_constant,mass,momentum,specific_heat | m·a·p·c·R·z | chemistry,mechanics,thermo | m²·a·p⁻¹·c·R⁻¹·z⁻¹ | a = k₀ · m⁻²·p·c⁻¹·R·z | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "2", "acceleration": "1", "momentum": "-1", "specific_heat": "1", "gas_constant": "-1", "cat_activity": "-1"} |
5 | acceleration,expansion,mass,momentum,thermal_cond | m·a·p·κ·β | mechanics,thermo | m²·a²·p⁻¹·κ⁻¹·β | p = k₀ · m²·a²·κ⁻¹·β | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "2", "momentum": "-1", "thermal_cond": "-1", "expansion": "1"} |
6 | acceleration,amount,gas_constant,mass,momentum,thermal_cond | m·a·p·κ·n·R | chemistry,mechanics,thermo | m³·a²·p⁻³·κ⁻¹·n·R | κ = k₀ · m³·a²·p⁻³·n·R | null | 0 | 3 | 3 | 11 | 9.7 | -0.7 | false | {"mass": "3", "acceleration": "2", "momentum": "-3", "thermal_cond": "-1", "amount": "1", "gas_constant": "1"} |
6 | acceleration,gas_constant,mass,molar_mass,momentum,thermal_cond | m·a·p·κ·M_m·R | chemistry,mechanics,thermo | m⁴·a²·p⁻³·κ⁻¹·M_m⁻¹·R | κ = k₀ · m⁴·a²·p⁻³·M_m⁻¹·R | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "4", "acceleration": "2", "momentum": "-3", "thermal_cond": "-1", "molar_mass": "-1", "gas_constant": "1"} |
6 | acceleration,concentration,gas_constant,mass,momentum,thermal_cond | m·a·p·κ·c_n·R | chemistry,mechanics,thermo | m³·a·p⁻³·κ·c_n⁻¹·R⁻¹ | a = k₀ · m⁻³·p³·κ⁻¹·c_n·R | null | 0 | 3 | 3 | 10 | 9 | 0 | false | {"mass": "3", "acceleration": "1", "momentum": "-3", "thermal_cond": "1", "concentration": "-1", "gas_constant": "-1"} |
6 | acceleration,gas_constant,mass,molar_energy,momentum,thermal_cond | m·a·p·κ·E_m·R | chemistry,mechanics,thermo | m²·a²·p⁻¹·κ⁻¹·E_m⁻¹·R | p = k₀ · m²·a²·κ⁻¹·E_m⁻¹·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "2", "acceleration": "2", "momentum": "-1", "thermal_cond": "-1", "molar_energy": "-1", "gas_constant": "1"} |
6 | acceleration,cat_activity,gas_constant,mass,momentum,thermal_cond | m·a·p·κ·R·z | chemistry,mechanics,thermo | m²·a·p⁻²·κ⁻¹·R·z | a = k₀ · m⁻²·p²·κ·R⁻¹·z⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "2", "acceleration": "1", "momentum": "-2", "thermal_cond": "-1", "gas_constant": "1", "cat_activity": "1"} |
6 | acceleration,avogadro,gas_constant,mass,momentum,thermal_cond | m·a·p·κ·R·N_A | chemistry,constants,mechanics,thermo | m³·a²·p⁻³·κ⁻¹·R·N_A⁻¹ | κ = k₀ · m³·a²·p⁻³·R·N_A⁻¹ | null | 1 | 4 | 3 | 11 | 10.3 | -1.8 | false | {"mass": "3", "acceleration": "2", "momentum": "-3", "thermal_cond": "-1", "gas_constant": "1", "avogadro": "-1"} |
5 | acceleration,boltzmann,mass,momentum,thermal_cond | m·a·p·κ·k_B | constants,mechanics,thermo | m³·a²·p⁻³·κ⁻¹·k_B | κ = k₀ · m³·a²·p⁻³·k_B | null | 1 | 3 | 3 | 10 | 8.7 | 0.3 | false | {"mass": "3", "acceleration": "2", "momentum": "-3", "thermal_cond": "-1", "boltzmann": "1"} |
4 | acceleration,mass,momentum,thermal_diff | m·a·p·α | mechanics,thermo | m³·a·p⁻³·α | a = k₀ · m⁻³·p³·α⁻¹ | null | 0 | 2 | 3 | 8 | 6.4 | 3.1 | true | {"mass": "3", "acceleration": "1", "momentum": "-3", "thermal_diff": "1"} |
6 | acceleration,concentration,expansion,gas_constant,mass,momentum | m·a·p·β·c_n·R | chemistry,mechanics,thermo | m⁵·a³·p⁻⁴·β·c_n⁻¹·R⁻¹ | β = k₀ · m⁻⁵·a⁻³·p⁴·c_n·R | null | 0 | 3 | 5 | 15 | 13.5 | -4.5 | false | {"mass": "5", "acceleration": "3", "momentum": "-4", "expansion": "1", "concentration": "-1", "gas_constant": "-1"} |
5 | acceleration,charge,current,mass,momentum | m·a·p·q·i | em,mechanics | m·a·p⁻¹·q·i⁻¹ | m = k₀ · a⁻¹·p·q⁻¹·i | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "charge": "1", "current": "-1"} |
5 | acceleration,charge,mass,momentum,resistance | m·a·p·q·R | em,mechanics | m²·a·p⁻³·q²·R | a = k₀ · m⁻²·p³·q⁻²·R⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "acceleration": "1", "momentum": "-3", "charge": "2", "resistance": "1"} |
5 | acceleration,charge,inductance,mass,momentum | m·a·p·q·L_e | em,mechanics | m³·a²·p⁻⁴·q²·L_e | L_e = k₀ · m⁻³·a⁻²·p⁴·q⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "3", "acceleration": "2", "momentum": "-4", "charge": "2", "inductance": "1"} |
5 | acceleration,bfield,charge,mass,momentum | m·a·p·q·B | em,mechanics | m²·a·p⁻¹·q⁻¹·B⁻¹ | a = k₀ · m⁻²·p·q·B | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "2", "acceleration": "1", "momentum": "-1", "charge": "-1", "bfield": "-1"} |
5 | acceleration,charge,mag_flux,mass,momentum | m·a·p·q·Φ | em,mechanics | m²·a·p⁻³·q·Φ | a = k₀ · m⁻²·p³·q⁻¹·Φ⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "2", "acceleration": "1", "momentum": "-3", "charge": "1", "mag_flux": "1"} |
5 | acceleration,charge,mass,momentum,permittivity | m·a·p·q·ε | em,mechanics | m³·a·p⁻⁴·q²·ε⁻¹ | a = k₀ · m⁻³·p⁴·q⁻²·ε | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "3", "acceleration": "1", "momentum": "-4", "charge": "2", "permittivity": "-1"} |
5 | acceleration,charge,mass,momentum,permeability | m·a·p·q·μ₀ | em,mechanics | m·a·p⁻²·q²·μ₀ | m = k₀ · a⁻¹·p²·q⁻²·μ₀⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "acceleration": "1", "momentum": "-2", "charge": "2", "permeability": "1"} |
5 | acceleration,charge,conductivity,mass,momentum | m·a·p·q·σ | em,mechanics | m⁴·a²·p⁻⁵·q²·σ⁻¹ | σ = k₀ · m⁴·a²·p⁻⁵·q² | null | 0 | 2 | 5 | 14 | 11.9 | -2.4 | false | {"mass": "4", "acceleration": "2", "momentum": "-5", "charge": "2", "conductivity": "-1"} |
5 | acceleration,charge,mass,momentum,resistivity | m·a·p·q·ρ_e | em,mechanics | m⁴·a²·p⁻⁵·q²·ρ_e | ρ_e = k₀ · m⁻⁴·a⁻²·p⁵·q⁻² | null | 0 | 2 | 5 | 14 | 11.9 | -2.4 | false | {"mass": "4", "acceleration": "2", "momentum": "-5", "charge": "2", "resistivity": "1"} |
5 | acceleration,current,efield,mass,momentum | m·a·p·i·E_f | em,mechanics | m²·a²·p⁻¹·i⁻¹·E_f⁻¹ | p = k₀ · m²·a²·i⁻¹·E_f⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "2", "momentum": "-1", "current": "-1", "efield": "-1"} |
5 | acceleration,bfield,current,mass,momentum | m·a·p·i·B | em,mechanics | m³·a²·p⁻²·i⁻¹·B⁻¹ | i = k₀ · m³·a²·p⁻²·B⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "3", "acceleration": "2", "momentum": "-2", "current": "-1", "bfield": "-1"} |
5 | acceleration,current,mass,momentum,permittivity | m·a·p·i·ε | em,mechanics | m·a⁻¹·p⁻²·i²·ε⁻¹ | m = k₀ · a·p²·i⁻²·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "acceleration": "-1", "momentum": "-2", "current": "2", "permittivity": "-1"} |
5 | acceleration,current,elem_charge,mass,momentum | m·a·p·i·e | constants,em,mechanics | m·a·p⁻¹·i⁻¹·e | m = k₀ · a⁻¹·p·i·e⁻¹ | null | 1 | 3 | 1 | 5 | 4.2 | 4.8 | false | {"mass": "1", "acceleration": "1", "momentum": "-1", "current": "-1", "elem_charge": "1"} |
5 | acceleration,efield,mass,momentum,voltage | m·a·p·U·E_f | em,mechanics | m²·a·p⁻²·U·E_f⁻¹ | a = k₀ · m⁻²·p²·U⁻¹·E_f | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "1", "momentum": "-2", "voltage": "1", "efield": "-1"} |
5 | acceleration,bfield,mass,momentum,voltage | m·a·p·U·B | em,mechanics | m³·a·p⁻³·U·B⁻¹ | a = k₀ · m⁻³·p³·U⁻¹·B | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "3", "acceleration": "1", "momentum": "-3", "voltage": "1", "bfield": "-1"} |
5 | acceleration,mag_flux,mass,momentum,voltage | m·a·p·U·Φ | em,mechanics | m·a·p⁻¹·U⁻¹·Φ | m = k₀ · a⁻¹·p·U·Φ⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "voltage": "-1", "mag_flux": "1"} |
5 | acceleration,mass,momentum,permeability,voltage | m·a·p·U·μ₀ | em,mechanics | m·a⁻¹·p⁻²·U²·μ₀⁻¹ | m = k₀ · a·p²·U⁻²·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "acceleration": "-1", "momentum": "-2", "voltage": "2", "permeability": "-1"} |
5 | acceleration,conductivity,mass,momentum,voltage | m·a·p·U·σ | em,mechanics | m²·a²·p⁻¹·U⁻²·σ⁻¹ | p = k₀ · m²·a²·U⁻²·σ⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "acceleration": "2", "momentum": "-1", "voltage": "-2", "conductivity": "-1"} |
5 | acceleration,mass,momentum,resistivity,voltage | m·a·p·U·ρ_e | em,mechanics | m²·a²·p⁻¹·U⁻²·ρ_e | p = k₀ · m²·a²·U⁻²·ρ_e | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "acceleration": "2", "momentum": "-1", "voltage": "-2", "resistivity": "1"} |
5 | acceleration,capacitance,mass,momentum,resistance | m·a·p·R·C_e | em,mechanics | m·a·p⁻¹·R·C_e | m = k₀ · a⁻¹·p·R⁻¹·C_e⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "resistance": "1", "capacitance": "1"} |
5 | acceleration,inductance,mass,momentum,resistance | m·a·p·R·L_e | em,mechanics | m·a·p⁻¹·R⁻¹·L_e | m = k₀ · a⁻¹·p·R·L_e⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "resistance": "-1", "inductance": "1"} |
5 | acceleration,efield,mass,momentum,resistance | m·a·p·R·E_f | em,mechanics | m⁴·a³·p⁻³·R·E_f⁻² | R = k₀ · m⁻⁴·a⁻³·p³·E_f² | null | 0 | 2 | 4 | 13 | 10.7 | -1.2 | false | {"mass": "4", "acceleration": "3", "momentum": "-3", "resistance": "1", "efield": "-2"} |
5 | acceleration,bfield,mass,momentum,resistance | m·a·p·R·B | em,mechanics | m⁶·a³·p⁻⁵·R·B⁻² | R = k₀ · m⁻⁶·a⁻³·p⁵·B² | null | 0 | 2 | 6 | 17 | 14.5 | -5 | false | {"mass": "6", "acceleration": "3", "momentum": "-5", "resistance": "1", "bfield": "-2"} |
5 | acceleration,mag_flux,mass,momentum,resistance | m·a·p·R·Φ | em,mechanics | m²·a·p⁻³·R⁻¹·Φ² | a = k₀ · m⁻²·p³·R·Φ⁻² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "acceleration": "1", "momentum": "-3", "resistance": "-1", "mag_flux": "2"} |
5 | acceleration,conductivity,mass,momentum,resistance | m·a·p·R·σ | em,mechanics | m²·a·p⁻²·R⁻¹·σ⁻¹ | a = k₀ · m⁻²·p²·R·σ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "1", "momentum": "-2", "resistance": "-1", "conductivity": "-1"} |
5 | acceleration,mass,momentum,resistance,resistivity | m·a·p·R·ρ_e | em,mechanics | m²·a·p⁻²·R⁻¹·ρ_e | a = k₀ · m⁻²·p²·R·ρ_e⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "1", "momentum": "-2", "resistance": "-1", "resistivity": "1"} |
5 | acceleration,elem_charge,mass,momentum,resistance | m·a·p·R·e | constants,em,mechanics | m²·a·p⁻³·R·e² | a = k₀ · m⁻²·p³·R⁻¹·e⁻² | null | 1 | 3 | 3 | 9 | 8 | 1 | false | {"mass": "2", "acceleration": "1", "momentum": "-3", "resistance": "1", "elem_charge": "2"} |
5 | acceleration,capacitance,inductance,mass,momentum | m·a·p·C_e·L_e | em,mechanics | m²·a²·p⁻²·C_e·L_e | C_e = k₀ · m⁻²·a⁻²·p²·L_e⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "acceleration": "2", "momentum": "-2", "capacitance": "1", "inductance": "1"} |
5 | acceleration,capacitance,efield,mass,momentum | m·a·p·C_e·E_f | em,mechanics | m³·a²·p⁻²·C_e⁻¹·E_f⁻² | C_e = k₀ · m³·a²·p⁻²·E_f⁻² | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "3", "acceleration": "2", "momentum": "-2", "capacitance": "-1", "efield": "-2"} |
5 | acceleration,bfield,capacitance,mass,momentum | m·a·p·C_e·B | em,mechanics | m⁵·a²·p⁻⁴·C_e⁻¹·B⁻² | C_e = k₀ · m⁵·a²·p⁻⁴·B⁻² | null | 0 | 2 | 5 | 14 | 11.9 | -2.4 | false | {"mass": "5", "acceleration": "2", "momentum": "-4", "capacitance": "-1", "bfield": "-2"} |
5 | acceleration,capacitance,mag_flux,mass,momentum | m·a·p·C_e·Φ | em,mechanics | m³·a²·p⁻⁴·C_e·Φ² | C_e = k₀ · m⁻³·a⁻²·p⁴·Φ⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "3", "acceleration": "2", "momentum": "-4", "capacitance": "1", "mag_flux": "2"} |
5 | acceleration,capacitance,mass,momentum,permittivity | m·a·p·C_e·ε | em,mechanics | m²·a·p⁻²·C_e·ε⁻¹ | a = k₀ · m⁻²·p²·C_e⁻¹·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "1", "momentum": "-2", "capacitance": "1", "permittivity": "-1"} |
5 | acceleration,capacitance,conductivity,mass,momentum | m·a·p·C_e·σ | em,mechanics | m³·a²·p⁻³·C_e·σ⁻¹ | C_e = k₀ · m⁻³·a⁻²·p³·σ | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "3", "acceleration": "2", "momentum": "-3", "capacitance": "1", "conductivity": "-1"} |
5 | acceleration,capacitance,mass,momentum,resistivity | m·a·p·C_e·ρ_e | em,mechanics | m³·a²·p⁻³·C_e·ρ_e | C_e = k₀ · m⁻³·a⁻²·p³·ρ_e⁻¹ | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "3", "acceleration": "2", "momentum": "-3", "capacitance": "1", "resistivity": "1"} |
5 | acceleration,efield,inductance,mass,momentum | m·a·p·L_e·E_f | em,mechanics | m⁵·a⁴·p⁻⁴·L_e·E_f⁻² | L_e = k₀ · m⁻⁵·a⁻⁴·p⁴·E_f² | null | 0 | 2 | 5 | 16 | 13.3 | -3.8 | false | {"mass": "5", "acceleration": "4", "momentum": "-4", "inductance": "1", "efield": "-2"} |
5 | acceleration,bfield,inductance,mass,momentum | m·a·p·L_e·B | em,mechanics | m⁷·a⁴·p⁻⁶·L_e·B⁻² | L_e = k₀ · m⁻⁷·a⁻⁴·p⁶·B² | null | 0 | 2 | 7 | 20 | 17.1 | -7.6 | false | {"mass": "7", "acceleration": "4", "momentum": "-6", "inductance": "1", "bfield": "-2"} |
5 | acceleration,inductance,mass,momentum,permeability | m·a·p·L_e·μ₀ | em,mechanics | m²·a·p⁻²·L_e·μ₀⁻¹ | a = k₀ · m⁻²·p²·L_e⁻¹·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "2", "acceleration": "1", "momentum": "-2", "inductance": "1", "permeability": "-1"} |
5 | acceleration,elem_charge,inductance,mass,momentum | m·a·p·L_e·e | constants,em,mechanics | m³·a²·p⁻⁴·L_e·e² | L_e = k₀ · m⁻³·a⁻²·p⁴·e⁻² | null | 1 | 3 | 4 | 12 | 10.6 | -1.6 | false | {"mass": "3", "acceleration": "2", "momentum": "-4", "inductance": "1", "elem_charge": "2"} |
5 | acceleration,efield,mag_flux,mass,momentum | m·a·p·E_f·Φ | em,mechanics | m³·a²·p⁻³·E_f⁻¹·Φ | E_f = k₀ · m³·a²·p⁻³·Φ | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "3", "acceleration": "2", "momentum": "-3", "efield": "-1", "mag_flux": "1"} |
5 | acceleration,efield,mass,momentum,permittivity | m·a·p·E_f·ε | em,mechanics | m⁵·a³·p⁻⁴·E_f⁻²·ε⁻¹ | ε = k₀ · m⁵·a³·p⁻⁴·E_f⁻² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "5", "acceleration": "3", "momentum": "-4", "efield": "-2", "permittivity": "-1"} |
5 | acceleration,efield,mass,momentum,permeability | m·a·p·E_f·μ₀ | em,mechanics | m³·a³·p⁻²·E_f⁻²·μ₀ | μ₀ = k₀ · m⁻³·a⁻³·p²·E_f² | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "3", "acceleration": "3", "momentum": "-2", "efield": "-2", "permeability": "1"} |
5 | acceleration,conductivity,efield,mass,momentum | m·a·p·E_f·σ | em,mechanics | m⁶·a⁴·p⁻⁵·E_f⁻²·σ⁻¹ | σ = k₀ · m⁶·a⁴·p⁻⁵·E_f⁻² | null | 0 | 2 | 6 | 18 | 15.2 | -5.7 | false | {"mass": "6", "acceleration": "4", "momentum": "-5", "efield": "-2", "conductivity": "-1"} |
5 | acceleration,efield,mass,momentum,resistivity | m·a·p·E_f·ρ_e | em,mechanics | m⁶·a⁴·p⁻⁵·E_f⁻²·ρ_e | ρ_e = k₀ · m⁻⁶·a⁻⁴·p⁵·E_f² | null | 0 | 2 | 6 | 18 | 15.2 | -5.7 | false | {"mass": "6", "acceleration": "4", "momentum": "-5", "efield": "-2", "resistivity": "1"} |
5 | acceleration,bfield,mag_flux,mass,momentum | m·a·p·B·Φ | em,mechanics | m⁴·a²·p⁻⁴·B⁻¹·Φ | B = k₀ · m⁴·a²·p⁻⁴·Φ | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "4", "acceleration": "2", "momentum": "-4", "bfield": "-1", "mag_flux": "1"} |
5 | acceleration,bfield,mass,momentum,permittivity | m·a·p·B·ε | em,mechanics | m⁷·a³·p⁻⁶·B⁻²·ε⁻¹ | ε = k₀ · m⁷·a³·p⁻⁶·B⁻² | null | 0 | 2 | 7 | 19 | 16.4 | -6.9 | false | {"mass": "7", "acceleration": "3", "momentum": "-6", "bfield": "-2", "permittivity": "-1"} |
5 | acceleration,bfield,mass,momentum,permeability | m·a·p·B·μ₀ | em,mechanics | m⁵·a³·p⁻⁴·B⁻²·μ₀ | μ₀ = k₀ · m⁻⁵·a⁻³·p⁴·B² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "5", "acceleration": "3", "momentum": "-4", "bfield": "-2", "permeability": "1"} |
5 | acceleration,bfield,conductivity,mass,momentum | m·a·p·B·σ | em,mechanics | m⁸·a⁴·p⁻⁷·B⁻²·σ⁻¹ | σ = k₀ · m⁸·a⁴·p⁻⁷·B⁻² | null | 0 | 2 | 8 | 22 | 19 | -9.5 | false | {"mass": "8", "acceleration": "4", "momentum": "-7", "bfield": "-2", "conductivity": "-1"} |
5 | acceleration,bfield,mass,momentum,resistivity | m·a·p·B·ρ_e | em,mechanics | m⁸·a⁴·p⁻⁷·B⁻²·ρ_e | ρ_e = k₀ · m⁻⁸·a⁻⁴·p⁷·B² | null | 0 | 2 | 8 | 22 | 19 | -9.5 | false | {"mass": "8", "acceleration": "4", "momentum": "-7", "bfield": "-2", "resistivity": "1"} |
5 | acceleration,bfield,elem_charge,mass,momentum | m·a·p·B·e | constants,em,mechanics | m²·a·p⁻¹·B⁻¹·e⁻¹ | a = k₀ · m⁻²·p·B·e | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "2", "acceleration": "1", "momentum": "-1", "bfield": "-1", "elem_charge": "-1"} |
5 | acceleration,mag_flux,mass,momentum,permittivity | m·a·p·Φ·ε | em,mechanics | m·a·p⁻²·Φ²·ε | m = k₀ · a⁻¹·p²·Φ⁻²·ε⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "acceleration": "1", "momentum": "-2", "mag_flux": "2", "permittivity": "1"} |
5 | acceleration,mag_flux,mass,momentum,permeability | m·a·p·Φ·μ₀ | em,mechanics | m³·a·p⁻⁴·Φ²·μ₀⁻¹ | a = k₀ · m⁻³·p⁴·Φ⁻²·μ₀ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "3", "acceleration": "1", "momentum": "-4", "mag_flux": "2", "permeability": "-1"} |
5 | acceleration,elem_charge,mag_flux,mass,momentum | m·a·p·Φ·e | constants,em,mechanics | m²·a·p⁻³·Φ·e | a = k₀ · m⁻²·p³·Φ⁻¹·e⁻¹ | null | 1 | 3 | 3 | 8 | 7.3 | 1.7 | false | {"mass": "2", "acceleration": "1", "momentum": "-3", "mag_flux": "1", "elem_charge": "1"} |
5 | acceleration,conductivity,mass,momentum,permittivity | m·a·p·ε·σ | em,mechanics | m·a·p⁻¹·ε·σ⁻¹ | m = k₀ · a⁻¹·p·ε⁻¹·σ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "permittivity": "1", "conductivity": "-1"} |
5 | acceleration,mass,momentum,permittivity,resistivity | m·a·p·ε·ρ_e | em,mechanics | m·a·p⁻¹·ε·ρ_e | m = k₀ · a⁻¹·p·ε⁻¹·ρ_e⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "permittivity": "1", "resistivity": "1"} |
5 | acceleration,elem_charge,mass,momentum,permittivity | m·a·p·ε·e | constants,em,mechanics | m³·a·p⁻⁴·ε⁻¹·e² | a = k₀ · m⁻³·p⁴·ε·e⁻² | null | 1 | 3 | 4 | 11 | 9.9 | -0.9 | false | {"mass": "3", "acceleration": "1", "momentum": "-4", "permittivity": "-1", "elem_charge": "2"} |
5 | acceleration,conductivity,mass,momentum,permeability | m·a·p·μ₀·σ | em,mechanics | m³·a·p⁻³·μ₀⁻¹·σ⁻¹ | a = k₀ · m⁻³·p³·μ₀·σ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "3", "acceleration": "1", "momentum": "-3", "permeability": "-1", "conductivity": "-1"} |
5 | acceleration,mass,momentum,permeability,resistivity | m·a·p·μ₀·ρ_e | em,mechanics | m³·a·p⁻³·μ₀⁻¹·ρ_e | a = k₀ · m⁻³·p³·μ₀·ρ_e⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "3", "acceleration": "1", "momentum": "-3", "permeability": "-1", "resistivity": "1"} |
5 | acceleration,elem_charge,mass,momentum,permeability | m·a·p·μ₀·e | constants,em,mechanics | m·a·p⁻²·μ₀·e² | m = k₀ · a⁻¹·p²·μ₀⁻¹·e⁻² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "acceleration": "1", "momentum": "-2", "permeability": "1", "elem_charge": "2"} |
5 | acceleration,conductivity,elem_charge,mass,momentum | m·a·p·σ·e | constants,em,mechanics | m⁴·a²·p⁻⁵·σ⁻¹·e² | σ = k₀ · m⁴·a²·p⁻⁵·e² | null | 1 | 3 | 5 | 14 | 12.5 | -3.5 | false | {"mass": "4", "acceleration": "2", "momentum": "-5", "conductivity": "-1", "elem_charge": "2"} |
5 | acceleration,elem_charge,mass,momentum,resistivity | m·a·p·ρ_e·e | constants,em,mechanics | m⁴·a²·p⁻⁵·ρ_e·e² | ρ_e = k₀ · m⁻⁴·a⁻²·p⁵·e⁻² | null | 1 | 3 | 5 | 14 | 12.5 | -3.5 | false | {"mass": "4", "acceleration": "2", "momentum": "-5", "resistivity": "1", "elem_charge": "2"} |
5 | acceleration,amount,concentration,mass,momentum | m·a·p·n·c_n | chemistry,mechanics | m⁶·a³·p⁻⁶·n·c_n⁻¹ | n = k₀ · m⁻⁶·a⁻³·p⁶·c_n | null | 0 | 2 | 6 | 17 | 14.5 | -5 | false | {"mass": "6", "acceleration": "3", "momentum": "-6", "amount": "1", "concentration": "-1"} |
5 | acceleration,amount,cat_activity,mass,momentum | m·a·p·n·z | chemistry,mechanics | m·a·p⁻¹·n·z⁻¹ | m = k₀ · a⁻¹·p·n⁻¹·z | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "acceleration": "1", "momentum": "-1", "amount": "1", "cat_activity": "-1"} |
5 | acceleration,concentration,mass,molar_mass,momentum | m·a·p·M_m·c_n | chemistry,mechanics | m⁷·a³·p⁻⁶·M_m⁻¹·c_n⁻¹ | M_m = k₀ · m⁷·a³·p⁻⁶·c_n⁻¹ | null | 0 | 2 | 7 | 18 | 15.7 | -6.2 | false | {"mass": "7", "acceleration": "3", "momentum": "-6", "molar_mass": "-1", "concentration": "-1"} |
5 | acceleration,cat_activity,mass,molar_mass,momentum | m·a·p·M_m·z | chemistry,mechanics | m²·a·p⁻¹·M_m⁻¹·z⁻¹ | a = k₀ · m⁻²·p·M_m·z | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "2", "acceleration": "1", "momentum": "-1", "molar_mass": "-1", "cat_activity": "-1"} |
5 | acceleration,concentration,mass,molar_energy,momentum | m·a·p·c_n·E_m | chemistry,mechanics | m⁵·a³·p⁻⁴·c_n⁻¹·E_m⁻¹ | c_n = k₀ · m⁵·a³·p⁻⁴·E_m⁻¹ | null | 0 | 2 | 5 | 14 | 11.9 | -2.4 | false | {"mass": "5", "acceleration": "3", "momentum": "-4", "concentration": "-1", "molar_energy": "-1"} |
6 | acceleration,boltzmann,concentration,gas_constant,mass,momentum | m·a·p·c_n·R·k_B | chemistry,constants,mechanics | m⁶·a³·p⁻⁶·c_n⁻¹·R⁻¹·k_B | c_n = k₀ · m⁶·a³·p⁻⁶·R⁻¹·k_B | null | 1 | 3 | 6 | 18 | 16.1 | -7.1 | false | {"mass": "6", "acceleration": "3", "momentum": "-6", "concentration": "-1", "gas_constant": "-1", "boltzmann": "1"} |
5 | acceleration,cat_activity,concentration,mass,momentum | m·a·p·c_n·z | chemistry,mechanics | m⁵·a²·p⁻⁵·c_n⁻¹·z | c_n = k₀ · m⁵·a²·p⁻⁵·z | null | 0 | 2 | 5 | 14 | 11.9 | -2.4 | false | {"mass": "5", "acceleration": "2", "momentum": "-5", "concentration": "-1", "cat_activity": "1"} |
5 | acceleration,avogadro,concentration,mass,momentum | m·a·p·c_n·N_A | chemistry,constants,mechanics | m⁶·a³·p⁻⁶·c_n⁻¹·N_A⁻¹ | c_n = k₀ · m⁶·a³·p⁻⁶·N_A⁻¹ | null | 1 | 3 | 6 | 17 | 15.1 | -6.1 | false | {"mass": "6", "acceleration": "3", "momentum": "-6", "concentration": "-1", "avogadro": "-1"} |
6 | acceleration,boltzmann,cat_activity,gas_constant,mass,momentum | m·a·p·R·z·k_B | chemistry,constants,mechanics | m·a·p⁻¹·R⁻¹·z⁻¹·k_B | m = k₀ · a⁻¹·p·R·z·k_B⁻¹ | null | 1 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "acceleration": "1", "momentum": "-1", "gas_constant": "-1", "cat_activity": "-1", "boltzmann": "1"} |
5 | acceleration,avogadro,cat_activity,mass,momentum | m·a·p·z·N_A | chemistry,constants,mechanics | m·a·p⁻¹·z⁻¹·N_A⁻¹ | m = k₀ · a⁻¹·p·z·N_A | null | 1 | 3 | 1 | 5 | 4.2 | 4.8 | false | {"mass": "1", "acceleration": "1", "momentum": "-1", "cat_activity": "-1", "avogadro": "-1"} |
5 | acceleration,illuminance,lum_intensity,mass,momentum | m·a·p·I_v·E_v | mechanics,photometry | m⁴·a²·p⁻⁴·I_v·E_v⁻¹ | I_v = k₀ · m⁻⁴·a⁻²·p⁴·E_v | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "4", "acceleration": "2", "momentum": "-4", "lum_intensity": "1", "illuminance": "-1"} |
5 | acceleration,lum_intensity,luminance,mass,momentum | m·a·p·I_v·L_v | mechanics,photometry | m⁴·a²·p⁻⁴·I_v·L_v⁻¹ | I_v = k₀ · m⁻⁴·a⁻²·p⁴·L_v | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "4", "acceleration": "2", "momentum": "-4", "lum_intensity": "1", "luminance": "-1"} |
4 | acceleration,grav_const,mass,momentum | m·a·p·G | constants,mechanics | m⁵·a·p⁻⁴·G | a = k₀ · m⁻⁵·p⁴·G⁻¹ | null | 1 | 2 | 5 | 11 | 9.5 | 0 | false | {"mass": "5", "acceleration": "1", "momentum": "-4", "grav_const": "1"} |
4 | acceleration,mass,momentum,planck | m·a·p·h | constants,mechanics | m²·a·p⁻³·h | a = k₀ · m⁻²·p³·h⁻¹ | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "2", "acceleration": "1", "momentum": "-3", "planck": "1"} |
4 | acceleration,ang_momentum,inertia,mass | m·a·Lₐ·J | mechanics | m·a²·Lₐ⁻⁴·J³ | m = k₀ · a⁻²·Lₐ⁴·J⁻³ | null | 0 | 1 | 4 | 10 | 7.7 | 2.3 | false | {"mass": "1", "acceleration": "2", "ang_momentum": "-4", "inertia": "3"} |
4 | acceleration,ang_momentum,mass,pressure | m·a·Lₐ·P_p | mechanics | m⁷·a⁵·Lₐ⁻⁴·P_p⁻³ | P_p = k₀ · m⁷ᐟ³·a⁵ᐟ³·Lₐ⁻⁴ᐟ³ | null | 0 | 1 | 7 | 19 | 15.5 | -5.5 | false | {"mass": "7", "acceleration": "5", "ang_momentum": "-4", "pressure": "-3"} |
4 | acceleration,ang_momentum,density,mass | m·a·Lₐ·ρ | mechanics | m³·a·Lₐ⁻²·ρ⁻¹ | a = k₀ · m⁻³·Lₐ²·ρ | null | 0 | 1 | 3 | 7 | 5.1 | 4.9 | true | {"mass": "3", "acceleration": "1", "ang_momentum": "-2", "density": "-1"} |
4 | acceleration,ang_momentum,mass,viscosity | m·a·Lₐ·μ | mechanics | m²·a·Lₐ⁻¹·μ⁻¹ | a = k₀ · m⁻²·Lₐ·μ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "2", "acceleration": "1", "ang_momentum": "-1", "viscosity": "-1"} |
4 | acceleration,ang_momentum,mass,omega | m·a·Lₐ·ω | mechanics | m·a²·Lₐ⁻¹·ω⁻³ | m = k₀ · a⁻²·Lₐ·ω³ | null | 0 | 1 | 3 | 7 | 5.1 | 4.9 | true | {"mass": "1", "acceleration": "2", "ang_momentum": "-1", "omega": "-3"} |
4 | acceleration,ang_momentum,frequency,mass | m·a·Lₐ·f | mechanics | m·a²·Lₐ⁻¹·f⁻³ | m = k₀ · a⁻²·Lₐ·f³ | null | 0 | 1 | 3 | 7 | 5.1 | 4.9 | true | {"mass": "1", "acceleration": "2", "ang_momentum": "-1", "frequency": "-3"} |
4 | acceleration,ang_momentum,mass,stiffness | m·a·Lₐ·k | mechanics | m⁵·a⁴·Lₐ⁻²·k⁻³ | Lₐ = k₀ · m⁵ᐟ²·a²·k⁻³ᐟ² | null | 0 | 1 | 5 | 14 | 11 | -1 | false | {"mass": "5", "acceleration": "4", "ang_momentum": "-2", "stiffness": "-3"} |
4 | acceleration,ang_momentum,mass,surf_tension | m·a·Lₐ·γ | mechanics | m⁵·a⁴·Lₐ⁻²·γ⁻³ | Lₐ = k₀ · m⁵ᐟ²·a²·γ⁻³ᐟ² | null | 0 | 1 | 5 | 14 | 11 | -1 | false | {"mass": "5", "acceleration": "4", "ang_momentum": "-2", "surf_tension": "-3"} |
4 | acceleration,ang_momentum,area,mass | m·a·Lₐ·A | mechanics | m⁴·a²·Lₐ⁻⁴·A³ | a = k₀ · m⁻²·Lₐ²·A⁻³ᐟ² | null | 0 | 1 | 4 | 13 | 9.8 | 0.2 | false | {"mass": "4", "acceleration": "2", "ang_momentum": "-4", "area": "3"} |
4 | acceleration,ang_momentum,mass,volume | m·a·Lₐ·V | mechanics | m²·a·Lₐ⁻²·V | a = k₀ · m⁻²·Lₐ²·V⁻¹ | null | 0 | 1 | 2 | 6 | 3.9 | 6.1 | true | {"mass": "2", "acceleration": "1", "ang_momentum": "-2", "volume": "1"} |
4 | acceleration,ang_momentum,flowrate,mass | m·a·Lₐ·Q | mechanics | m⁵·a·Lₐ⁻⁵·Q³ | a = k₀ · m⁻⁵·Lₐ⁵·Q⁻³ | null | 0 | 1 | 5 | 14 | 11 | -1 | false | {"mass": "5", "acceleration": "1", "ang_momentum": "-5", "flowrate": "3"} |
5 | acceleration,ang_momentum,entropy,mass,temperature | m·a·Lₐ·Θ·S_e | mechanics,thermo | m·a²·Lₐ²·Θ⁻³·S_e⁻³ | m = k₀ · a⁻²·Lₐ⁻²·Θ³·S_e³ | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "1", "acceleration": "2", "ang_momentum": "2", "temperature": "-3", "entropy": "-3"} |
5 | acceleration,ang_momentum,heat_capacity,mass,temperature | m·a·Lₐ·Θ·C | mechanics,thermo | m·a²·Lₐ²·Θ⁻³·C⁻³ | m = k₀ · a⁻²·Lₐ⁻²·Θ³·C³ | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "1", "acceleration": "2", "ang_momentum": "2", "temperature": "-3", "heat_capacity": "-3"} |
5 | acceleration,ang_momentum,mass,specific_heat,temperature | m·a·Lₐ·Θ·c | mechanics,thermo | m²·a⁻²·Lₐ⁻²·Θ³·c³ | m = k₀ · a·Lₐ·Θ⁻³ᐟ²·c⁻³ᐟ² | null | 0 | 2 | 3 | 12 | 9.5 | 0 | false | {"mass": "2", "acceleration": "-2", "ang_momentum": "-2", "temperature": "3", "specific_heat": "3"} |
5 | acceleration,ang_momentum,mass,temperature,thermal_cond | m·a·Lₐ·Θ·κ | mechanics,thermo | m⁴·a⁵·Lₐ⁻¹·Θ⁻³·κ⁻³ | Lₐ = k₀ · m⁴·a⁵·Θ⁻³·κ⁻³ | null | 0 | 2 | 5 | 16 | 13.3 | -3.8 | false | {"mass": "4", "acceleration": "5", "ang_momentum": "-1", "temperature": "-3", "thermal_cond": "-3"} |
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