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 | concentration,force,gas_constant,mass,temperature,velocity | m·v·F·Θ·c_n·R | chemistry,mechanics,thermo | m²·v⁴·F⁻³·Θ·c_n·R | Θ = k₀ · m⁻²·v⁻⁴·F³·c_n⁻¹·R⁻¹ | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "2", "velocity": "4", "force": "-3", "temperature": "1", "concentration": "1", "gas_constant": "1"} |
5 | entropy,force,mass,thermal_cond,velocity | m·v·F·S_e·κ | mechanics,thermo | m²·v³·F⁻²·S_e⁻¹·κ | S_e = k₀ · m²·v³·F⁻²·κ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-2", "entropy": "-1", "thermal_cond": "1"} |
6 | concentration,entropy,force,gas_constant,mass,velocity | m·v·F·S_e·c_n·R | chemistry,mechanics,thermo | m³·v⁶·F⁻³·S_e⁻¹·c_n·R | S_e = k₀ · m³·v⁶·F⁻³·c_n·R | null | 0 | 3 | 6 | 15 | 14 | -5 | false | {"mass": "3", "velocity": "6", "force": "-3", "entropy": "-1", "concentration": "1", "gas_constant": "1"} |
6 | cat_activity,entropy,force,gas_constant,mass,velocity | m·v·F·S_e·R·z | chemistry,mechanics,thermo | m·v·F⁻¹·S_e⁻¹·R·z | m = k₀ · v⁻¹·F·S_e·R⁻¹·z⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "velocity": "1", "force": "-1", "entropy": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | force,heat_capacity,mass,thermal_cond,velocity | m·v·F·C·κ | mechanics,thermo | m²·v³·F⁻²·C⁻¹·κ | C = k₀ · m²·v³·F⁻²·κ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-2", "heat_capacity": "-1", "thermal_cond": "1"} |
6 | concentration,force,gas_constant,heat_capacity,mass,velocity | m·v·F·C·c_n·R | chemistry,mechanics,thermo | m³·v⁶·F⁻³·C⁻¹·c_n·R | C = k₀ · m³·v⁶·F⁻³·c_n·R | null | 0 | 3 | 6 | 15 | 14 | -5 | false | {"mass": "3", "velocity": "6", "force": "-3", "heat_capacity": "-1", "concentration": "1", "gas_constant": "1"} |
6 | cat_activity,force,gas_constant,heat_capacity,mass,velocity | m·v·F·C·R·z | chemistry,mechanics,thermo | m·v·F⁻¹·C⁻¹·R·z | m = k₀ · v⁻¹·F·C·R⁻¹·z⁻¹ | null | 0 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "velocity": "1", "force": "-1", "heat_capacity": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | force,mass,specific_heat,thermal_cond,velocity | m·v·F·c·κ | mechanics,thermo | m·v³·F⁻²·c⁻¹·κ | m = k₀ · v⁻³·F²·c·κ⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "velocity": "3", "force": "-2", "specific_heat": "-1", "thermal_cond": "1"} |
6 | concentration,force,gas_constant,mass,specific_heat,velocity | m·v·F·c·c_n·R | chemistry,mechanics,thermo | m²·v⁶·F⁻³·c⁻¹·c_n·R | c = k₀ · m²·v⁶·F⁻³·c_n·R | null | 0 | 3 | 6 | 14 | 13.3 | -4.3 | false | {"mass": "2", "velocity": "6", "force": "-3", "specific_heat": "-1", "concentration": "1", "gas_constant": "1"} |
5 | expansion,force,mass,thermal_cond,velocity | m·v·F·κ·β | mechanics,thermo | m·v·F⁻²·κ·β⁻¹ | m = k₀ · v⁻¹·F²·κ⁻¹·β | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "1", "force": "-2", "thermal_cond": "1", "expansion": "-1"} |
6 | amount,force,gas_constant,mass,thermal_cond,velocity | m·v·F·κ·n·R | chemistry,mechanics,thermo | m²·v³·F⁻²·κ·n⁻¹·R⁻¹ | κ = k₀ · m⁻²·v⁻³·F²·n·R | null | 0 | 3 | 3 | 10 | 9 | 0 | false | {"mass": "2", "velocity": "3", "force": "-2", "thermal_cond": "1", "amount": "-1", "gas_constant": "-1"} |
6 | force,gas_constant,mass,molar_mass,thermal_cond,velocity | m·v·F·κ·M_m·R | chemistry,mechanics,thermo | m·v³·F⁻²·κ·M_m·R⁻¹ | m = k₀ · v⁻³·F²·κ⁻¹·M_m⁻¹·R | null | 0 | 3 | 3 | 9 | 8.3 | 0.7 | false | {"mass": "1", "velocity": "3", "force": "-2", "thermal_cond": "1", "molar_mass": "1", "gas_constant": "-1"} |
6 | concentration,force,gas_constant,mass,thermal_cond,velocity | m·v·F·κ·c_n·R | chemistry,mechanics,thermo | m·v³·F⁻¹·κ⁻¹·c_n·R | m = k₀ · v⁻³·F·κ·c_n⁻¹·R⁻¹ | null | 0 | 3 | 3 | 8 | 7.6 | 1.4 | false | {"mass": "1", "velocity": "3", "force": "-1", "thermal_cond": "-1", "concentration": "1", "gas_constant": "1"} |
6 | force,gas_constant,mass,molar_energy,thermal_cond,velocity | m·v·F·κ·E_m·R | chemistry,mechanics,thermo | m·v·F⁻²·κ·E_m·R⁻¹ | m = k₀ · v⁻¹·F²·κ⁻¹·E_m⁻¹·R | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "velocity": "1", "force": "-2", "thermal_cond": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | cat_activity,force,gas_constant,mass,thermal_cond,velocity | m·v·F·κ·R·z | chemistry,mechanics,thermo | m·v²·F⁻¹·κ·R⁻¹·z⁻¹ | m = k₀ · v⁻²·F·κ⁻¹·R·z | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "velocity": "2", "force": "-1", "thermal_cond": "1", "gas_constant": "-1", "cat_activity": "-1"} |
6 | avogadro,force,gas_constant,mass,thermal_cond,velocity | m·v·F·κ·R·N_A | chemistry,constants,mechanics,thermo | m²·v³·F⁻²·κ·R⁻¹·N_A | κ = k₀ · m⁻²·v⁻³·F²·R·N_A⁻¹ | null | 1 | 4 | 3 | 10 | 9.6 | -1.1 | false | {"mass": "2", "velocity": "3", "force": "-2", "thermal_cond": "1", "gas_constant": "-1", "avogadro": "1"} |
5 | boltzmann,force,mass,thermal_cond,velocity | m·v·F·κ·k_B | constants,mechanics,thermo | m²·v³·F⁻²·κ·k_B⁻¹ | κ = k₀ · m⁻²·v⁻³·F²·k_B | null | 1 | 3 | 3 | 9 | 8 | 1 | false | {"mass": "2", "velocity": "3", "force": "-2", "thermal_cond": "1", "boltzmann": "-1"} |
4 | force,mass,thermal_diff,velocity | m·v·F·α | mechanics,thermo | m·v³·F⁻¹·α⁻¹ | m = k₀ · v⁻³·F·α | null | 0 | 2 | 3 | 6 | 5 | 4.5 | true | {"mass": "1", "velocity": "3", "force": "-1", "thermal_diff": "-1"} |
6 | concentration,expansion,force,gas_constant,mass,velocity | m·v·F·β·c_n·R | chemistry,mechanics,thermo | m²·v⁴·F⁻³·β⁻¹·c_n·R | β = k₀ · m²·v⁴·F⁻³·c_n·R | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "2", "velocity": "4", "force": "-3", "expansion": "-1", "concentration": "1", "gas_constant": "1"} |
5 | charge,current,force,mass,velocity | m·v·F·q·i | em,mechanics | m·v·F⁻¹·q⁻¹·i | m = k₀ · v⁻¹·F·q·i⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "charge": "-1", "current": "1"} |
5 | charge,force,mass,resistance,velocity | m·v·F·q·R | em,mechanics | m²·v³·F⁻¹·q⁻²·R⁻¹ | F = k₀ · m²·v³·q⁻²·R⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-1", "charge": "-2", "resistance": "-1"} |
5 | charge,force,inductance,mass,velocity | m·v·F·q·L_e | em,mechanics | m³·v⁴·F⁻²·q⁻²·L_e⁻¹ | L_e = k₀ · m³·v⁴·F⁻²·q⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "3", "velocity": "4", "force": "-2", "charge": "-2", "inductance": "-1"} |
5 | charge,force,mag_flux,mass,velocity | m·v·F·q·Φ | em,mechanics | m²·v³·F⁻¹·q⁻¹·Φ⁻¹ | F = k₀ · m²·v³·q⁻¹·Φ⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "2", "velocity": "3", "force": "-1", "charge": "-1", "mag_flux": "-1"} |
5 | charge,force,mass,permittivity,velocity | m·v·F·q·ε | em,mechanics | m²·v⁴·F⁻¹·q⁻²·ε | F = k₀ · m²·v⁴·q⁻²·ε | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "velocity": "4", "force": "-1", "charge": "-2", "permittivity": "1"} |
5 | charge,force,mass,permeability,velocity | m·v·F·q·μ₀ | em,mechanics | m²·v²·F⁻¹·q⁻²·μ₀⁻¹ | F = k₀ · m²·v²·q⁻²·μ₀⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "velocity": "2", "force": "-1", "charge": "-2", "permeability": "-1"} |
5 | charge,conductivity,force,mass,velocity | m·v·F·q·σ | em,mechanics | m³·v⁵·F⁻²·q⁻²·σ | σ = k₀ · m⁻³·v⁻⁵·F²·q² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "3", "velocity": "5", "force": "-2", "charge": "-2", "conductivity": "1"} |
5 | charge,force,mass,resistivity,velocity | m·v·F·q·ρ_e | em,mechanics | m³·v⁵·F⁻²·q⁻²·ρ_e⁻¹ | ρ_e = k₀ · m³·v⁵·F⁻²·q⁻² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "3", "velocity": "5", "force": "-2", "charge": "-2", "resistivity": "-1"} |
5 | current,efield,force,mass,velocity | m·v·F·i·E_f | em,mechanics | m·v·F⁻²·i·E_f | m = k₀ · v⁻¹·F²·i⁻¹·E_f⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "1", "force": "-2", "current": "1", "efield": "1"} |
5 | bfield,current,force,mass,velocity | m·v·F·i·B | em,mechanics | m·v²·F⁻²·i·B | m = k₀ · v⁻²·F²·i⁻¹·B⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "velocity": "2", "force": "-2", "current": "1", "bfield": "1"} |
5 | current,elem_charge,force,mass,velocity | m·v·F·i·e | constants,em,mechanics | m·v·F⁻¹·i·e⁻¹ | m = k₀ · v⁻¹·F·i⁻¹·e | null | 1 | 3 | 1 | 5 | 4.2 | 4.8 | false | {"mass": "1", "velocity": "1", "force": "-1", "current": "1", "elem_charge": "-1"} |
5 | efield,force,mass,velocity,voltage | m·v·F·U·E_f | em,mechanics | m·v²·F⁻¹·U⁻¹·E_f | m = k₀ · v⁻²·F·U·E_f⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "2", "force": "-1", "voltage": "-1", "efield": "1"} |
5 | bfield,force,mass,velocity,voltage | m·v·F·U·B | em,mechanics | m·v³·F⁻¹·U⁻¹·B | m = k₀ · v⁻³·F·U·B⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "velocity": "3", "force": "-1", "voltage": "-1", "bfield": "1"} |
5 | force,mag_flux,mass,velocity,voltage | m·v·F·U·Φ | em,mechanics | m·v·F⁻¹·U·Φ⁻¹ | m = k₀ · v⁻¹·F·U⁻¹·Φ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "voltage": "1", "mag_flux": "-1"} |
5 | conductivity,force,mass,velocity,voltage | m·v·F·U·σ | em,mechanics | m·v·F⁻²·U²·σ | m = k₀ · v⁻¹·F²·U⁻²·σ⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "velocity": "1", "force": "-2", "voltage": "2", "conductivity": "1"} |
5 | force,mass,resistivity,velocity,voltage | m·v·F·U·ρ_e | em,mechanics | m·v·F⁻²·U²·ρ_e⁻¹ | m = k₀ · v⁻¹·F²·U⁻²·ρ_e | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "velocity": "1", "force": "-2", "voltage": "2", "resistivity": "-1"} |
5 | capacitance,force,mass,resistance,velocity | m·v·F·R·C_e | em,mechanics | m·v·F⁻¹·R⁻¹·C_e⁻¹ | m = k₀ · v⁻¹·F·R·C_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "resistance": "-1", "capacitance": "-1"} |
5 | force,inductance,mass,resistance,velocity | m·v·F·R·L_e | em,mechanics | m·v·F⁻¹·R·L_e⁻¹ | m = k₀ · v⁻¹·F·R⁻¹·L_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "resistance": "1", "inductance": "-1"} |
5 | efield,force,mass,resistance,velocity | m·v·F·R·E_f | em,mechanics | m²·v³·F⁻³·R⁻¹·E_f² | R = k₀ · m²·v³·F⁻³·E_f² | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "2", "velocity": "3", "force": "-3", "resistance": "-1", "efield": "2"} |
5 | bfield,force,mass,resistance,velocity | m·v·F·R·B | em,mechanics | m²·v⁵·F⁻³·R⁻¹·B² | R = k₀ · m²·v⁵·F⁻³·B² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "2", "velocity": "5", "force": "-3", "resistance": "-1", "bfield": "2"} |
5 | force,mag_flux,mass,resistance,velocity | m·v·F·R·Φ | em,mechanics | m²·v³·F⁻¹·R·Φ⁻² | F = k₀ · m²·v³·R·Φ⁻² | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-1", "resistance": "1", "mag_flux": "-2"} |
5 | conductivity,force,mass,resistance,velocity | m·v·F·R·σ | em,mechanics | m·v²·F⁻¹·R·σ | m = k₀ · v⁻²·F·R⁻¹·σ⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "2", "force": "-1", "resistance": "1", "conductivity": "1"} |
5 | force,mass,resistance,resistivity,velocity | m·v·F·R·ρ_e | em,mechanics | m·v²·F⁻¹·R·ρ_e⁻¹ | m = k₀ · v⁻²·F·R⁻¹·ρ_e | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "2", "force": "-1", "resistance": "1", "resistivity": "-1"} |
5 | elem_charge,force,mass,resistance,velocity | m·v·F·R·e | constants,em,mechanics | m²·v³·F⁻¹·R⁻¹·e⁻² | F = k₀ · m²·v³·R⁻¹·e⁻² | null | 1 | 3 | 3 | 9 | 8 | 1 | false | {"mass": "2", "velocity": "3", "force": "-1", "resistance": "-1", "elem_charge": "-2"} |
5 | capacitance,force,inductance,mass,velocity | m·v·F·C_e·L_e | em,mechanics | m²·v²·F⁻²·C_e⁻¹·L_e⁻¹ | C_e = k₀ · m²·v²·F⁻²·L_e⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "velocity": "2", "force": "-2", "capacitance": "-1", "inductance": "-1"} |
5 | capacitance,efield,force,mass,velocity | m·v·F·C_e·E_f | em,mechanics | m·v²·F⁻²·C_e·E_f² | m = k₀ · v⁻²·F²·C_e⁻¹·E_f⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "velocity": "2", "force": "-2", "capacitance": "1", "efield": "2"} |
5 | bfield,capacitance,force,mass,velocity | m·v·F·C_e·B | em,mechanics | m·v⁴·F⁻²·C_e·B² | m = k₀ · v⁻⁴·F²·C_e⁻¹·B⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "velocity": "4", "force": "-2", "capacitance": "1", "bfield": "2"} |
5 | capacitance,force,mag_flux,mass,velocity | m·v·F·C_e·Φ | em,mechanics | m³·v⁴·F⁻²·C_e⁻¹·Φ⁻² | C_e = k₀ · m³·v⁴·F⁻²·Φ⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "3", "velocity": "4", "force": "-2", "capacitance": "-1", "mag_flux": "-2"} |
5 | capacitance,force,mass,permittivity,velocity | m·v·F·C_e·ε | em,mechanics | m·v²·F⁻¹·C_e⁻¹·ε | m = k₀ · v⁻²·F·C_e·ε⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "2", "force": "-1", "capacitance": "-1", "permittivity": "1"} |
5 | capacitance,conductivity,force,mass,velocity | m·v·F·C_e·σ | em,mechanics | m²·v³·F⁻²·C_e⁻¹·σ | C_e = k₀ · m²·v³·F⁻²·σ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-2", "capacitance": "-1", "conductivity": "1"} |
5 | capacitance,force,mass,resistivity,velocity | m·v·F·C_e·ρ_e | em,mechanics | m²·v³·F⁻²·C_e⁻¹·ρ_e⁻¹ | C_e = k₀ · m²·v³·F⁻²·ρ_e⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-2", "capacitance": "-1", "resistivity": "-1"} |
5 | efield,force,inductance,mass,velocity | m·v·F·L_e·E_f | em,mechanics | m³·v⁴·F⁻⁴·L_e⁻¹·E_f² | L_e = k₀ · m³·v⁴·F⁻⁴·E_f² | null | 0 | 2 | 4 | 14 | 11.4 | -1.9 | false | {"mass": "3", "velocity": "4", "force": "-4", "inductance": "-1", "efield": "2"} |
5 | bfield,force,inductance,mass,velocity | m·v·F·L_e·B | em,mechanics | m³·v⁶·F⁻⁴·L_e⁻¹·B² | L_e = k₀ · m³·v⁶·F⁻⁴·B² | null | 0 | 2 | 6 | 16 | 13.8 | -4.3 | false | {"mass": "3", "velocity": "6", "force": "-4", "inductance": "-1", "bfield": "2"} |
5 | force,inductance,mass,permeability,velocity | m·v·F·L_e·μ₀ | em,mechanics | m·v²·F⁻¹·L_e⁻¹·μ₀ | m = k₀ · v⁻²·F·L_e·μ₀⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "velocity": "2", "force": "-1", "inductance": "-1", "permeability": "1"} |
5 | elem_charge,force,inductance,mass,velocity | m·v·F·L_e·e | constants,em,mechanics | m³·v⁴·F⁻²·L_e⁻¹·e⁻² | L_e = k₀ · m³·v⁴·F⁻²·e⁻² | null | 1 | 3 | 4 | 12 | 10.6 | -1.6 | false | {"mass": "3", "velocity": "4", "force": "-2", "inductance": "-1", "elem_charge": "-2"} |
5 | efield,force,mag_flux,mass,velocity | m·v·F·E_f·Φ | em,mechanics | m²·v³·F⁻²·E_f·Φ⁻¹ | E_f = k₀ · m⁻²·v⁻³·F²·Φ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "velocity": "3", "force": "-2", "efield": "1", "mag_flux": "-1"} |
5 | efield,force,mass,permittivity,velocity | m·v·F·E_f·ε | em,mechanics | m²·v⁴·F⁻³·E_f²·ε | ε = k₀ · m⁻²·v⁻⁴·F³·E_f⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "2", "velocity": "4", "force": "-3", "efield": "2", "permittivity": "1"} |
5 | efield,force,mass,permeability,velocity | m·v·F·E_f·μ₀ | em,mechanics | m²·v²·F⁻³·E_f²·μ₀⁻¹ | μ₀ = k₀ · m²·v²·F⁻³·E_f² | null | 0 | 2 | 3 | 10 | 8.1 | 1.4 | false | {"mass": "2", "velocity": "2", "force": "-3", "efield": "2", "permeability": "-1"} |
5 | conductivity,efield,force,mass,velocity | m·v·F·E_f·σ | em,mechanics | m³·v⁵·F⁻⁴·E_f²·σ | σ = k₀ · m⁻³·v⁻⁵·F⁴·E_f⁻² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "3", "velocity": "5", "force": "-4", "efield": "2", "conductivity": "1"} |
5 | efield,force,mass,resistivity,velocity | m·v·F·E_f·ρ_e | em,mechanics | m³·v⁵·F⁻⁴·E_f²·ρ_e⁻¹ | ρ_e = k₀ · m³·v⁵·F⁻⁴·E_f² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "3", "velocity": "5", "force": "-4", "efield": "2", "resistivity": "-1"} |
5 | bfield,force,mag_flux,mass,velocity | m·v·F·B·Φ | em,mechanics | m²·v⁴·F⁻²·B·Φ⁻¹ | B = k₀ · m⁻²·v⁻⁴·F²·Φ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "velocity": "4", "force": "-2", "bfield": "1", "mag_flux": "-1"} |
5 | bfield,force,mass,permittivity,velocity | m·v·F·B·ε | em,mechanics | m²·v⁶·F⁻³·B²·ε | ε = k₀ · m⁻²·v⁻⁶·F³·B⁻² | null | 0 | 2 | 6 | 14 | 12.4 | -2.9 | false | {"mass": "2", "velocity": "6", "force": "-3", "bfield": "2", "permittivity": "1"} |
5 | bfield,force,mass,permeability,velocity | m·v·F·B·μ₀ | em,mechanics | m²·v⁴·F⁻³·B²·μ₀⁻¹ | μ₀ = k₀ · m²·v⁴·F⁻³·B² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "2", "velocity": "4", "force": "-3", "bfield": "2", "permeability": "-1"} |
5 | bfield,conductivity,force,mass,velocity | m·v·F·B·σ | em,mechanics | m³·v⁷·F⁻⁴·B²·σ | σ = k₀ · m⁻³·v⁻⁷·F⁴·B⁻² | null | 0 | 2 | 7 | 17 | 15 | -5.5 | false | {"mass": "3", "velocity": "7", "force": "-4", "bfield": "2", "conductivity": "1"} |
5 | bfield,force,mass,resistivity,velocity | m·v·F·B·ρ_e | em,mechanics | m³·v⁷·F⁻⁴·B²·ρ_e⁻¹ | ρ_e = k₀ · m³·v⁷·F⁻⁴·B² | null | 0 | 2 | 7 | 17 | 15 | -5.5 | false | {"mass": "3", "velocity": "7", "force": "-4", "bfield": "2", "resistivity": "-1"} |
5 | force,mag_flux,mass,permittivity,velocity | m·v·F·Φ·ε | em,mechanics | m²·v²·F⁻¹·Φ⁻²·ε⁻¹ | F = k₀ · m²·v²·Φ⁻²·ε⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "velocity": "2", "force": "-1", "mag_flux": "-2", "permittivity": "-1"} |
5 | force,mag_flux,mass,permeability,velocity | m·v·F·Φ·μ₀ | em,mechanics | m²·v⁴·F⁻¹·Φ⁻²·μ₀ | F = k₀ · m²·v⁴·Φ⁻²·μ₀ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "velocity": "4", "force": "-1", "mag_flux": "-2", "permeability": "1"} |
5 | elem_charge,force,mag_flux,mass,velocity | m·v·F·Φ·e | constants,em,mechanics | m²·v³·F⁻¹·Φ⁻¹·e⁻¹ | F = k₀ · m²·v³·Φ⁻¹·e⁻¹ | null | 1 | 3 | 3 | 8 | 7.3 | 1.7 | false | {"mass": "2", "velocity": "3", "force": "-1", "mag_flux": "-1", "elem_charge": "-1"} |
5 | conductivity,force,mass,permittivity,velocity | m·v·F·ε·σ | em,mechanics | m·v·F⁻¹·ε⁻¹·σ | m = k₀ · v⁻¹·F·ε·σ⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "permittivity": "-1", "conductivity": "1"} |
5 | force,mass,permittivity,resistivity,velocity | m·v·F·ε·ρ_e | em,mechanics | m·v·F⁻¹·ε⁻¹·ρ_e⁻¹ | m = k₀ · v⁻¹·F·ε·ρ_e | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "permittivity": "-1", "resistivity": "-1"} |
5 | elem_charge,force,mass,permittivity,velocity | m·v·F·ε·e | constants,em,mechanics | m²·v⁴·F⁻¹·ε·e⁻² | F = k₀ · m²·v⁴·ε·e⁻² | null | 1 | 3 | 4 | 10 | 9.2 | -0.2 | false | {"mass": "2", "velocity": "4", "force": "-1", "permittivity": "1", "elem_charge": "-2"} |
5 | conductivity,force,mass,permeability,velocity | m·v·F·μ₀·σ | em,mechanics | m·v³·F⁻¹·μ₀·σ | m = k₀ · v⁻³·F·μ₀⁻¹·σ⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "velocity": "3", "force": "-1", "permeability": "1", "conductivity": "1"} |
5 | force,mass,permeability,resistivity,velocity | m·v·F·μ₀·ρ_e | em,mechanics | m·v³·F⁻¹·μ₀·ρ_e⁻¹ | m = k₀ · v⁻³·F·μ₀⁻¹·ρ_e | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "velocity": "3", "force": "-1", "permeability": "1", "resistivity": "-1"} |
5 | elem_charge,force,mass,permeability,velocity | m·v·F·μ₀·e | constants,em,mechanics | m²·v²·F⁻¹·μ₀⁻¹·e⁻² | F = k₀ · m²·v²·μ₀⁻¹·e⁻² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "2", "velocity": "2", "force": "-1", "permeability": "-1", "elem_charge": "-2"} |
5 | conductivity,elem_charge,force,mass,velocity | m·v·F·σ·e | constants,em,mechanics | m³·v⁵·F⁻²·σ·e⁻² | σ = k₀ · m⁻³·v⁻⁵·F²·e² | null | 1 | 3 | 5 | 13 | 11.8 | -2.8 | false | {"mass": "3", "velocity": "5", "force": "-2", "conductivity": "1", "elem_charge": "-2"} |
5 | elem_charge,force,mass,resistivity,velocity | m·v·F·ρ_e·e | constants,em,mechanics | m³·v⁵·F⁻²·ρ_e⁻¹·e⁻² | ρ_e = k₀ · m³·v⁵·F⁻²·e⁻² | null | 1 | 3 | 5 | 13 | 11.8 | -2.8 | false | {"mass": "3", "velocity": "5", "force": "-2", "resistivity": "-1", "elem_charge": "-2"} |
5 | amount,concentration,force,mass,velocity | m·v·F·n·c_n | chemistry,mechanics | m³·v⁶·F⁻³·n⁻¹·c_n | n = k₀ · m³·v⁶·F⁻³·c_n | null | 0 | 2 | 6 | 14 | 12.4 | -2.9 | false | {"mass": "3", "velocity": "6", "force": "-3", "amount": "-1", "concentration": "1"} |
5 | amount,cat_activity,force,mass,velocity | m·v·F·n·z | chemistry,mechanics | m·v·F⁻¹·n⁻¹·z | m = k₀ · v⁻¹·F·n·z⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "velocity": "1", "force": "-1", "amount": "-1", "cat_activity": "1"} |
5 | concentration,force,mass,molar_mass,velocity | m·v·F·M_m·c_n | chemistry,mechanics | m²·v⁶·F⁻³·M_m·c_n | M_m = k₀ · m⁻²·v⁻⁶·F³·c_n⁻¹ | null | 0 | 2 | 6 | 13 | 11.7 | -2.2 | false | {"mass": "2", "velocity": "6", "force": "-3", "molar_mass": "1", "concentration": "1"} |
5 | concentration,force,mass,molar_energy,velocity | m·v·F·c_n·E_m | chemistry,mechanics | m²·v⁴·F⁻³·c_n·E_m | c_n = k₀ · m⁻²·v⁻⁴·F³·E_m⁻¹ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "2", "velocity": "4", "force": "-3", "concentration": "1", "molar_energy": "1"} |
6 | boltzmann,concentration,force,gas_constant,mass,velocity | m·v·F·c_n·R·k_B | chemistry,constants,mechanics | m³·v⁶·F⁻³·c_n·R·k_B⁻¹ | c_n = k₀ · m⁻³·v⁻⁶·F³·R⁻¹·k_B | null | 1 | 3 | 6 | 15 | 14 | -5 | false | {"mass": "3", "velocity": "6", "force": "-3", "concentration": "1", "gas_constant": "1", "boltzmann": "-1"} |
5 | cat_activity,concentration,force,mass,velocity | m·v·F·c_n·z | chemistry,mechanics | m²·v⁵·F⁻²·c_n·z⁻¹ | c_n = k₀ · m⁻²·v⁻⁵·F²·z | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "2", "velocity": "5", "force": "-2", "concentration": "1", "cat_activity": "-1"} |
5 | avogadro,concentration,force,mass,velocity | m·v·F·c_n·N_A | chemistry,constants,mechanics | m³·v⁶·F⁻³·c_n·N_A | c_n = k₀ · m⁻³·v⁻⁶·F³·N_A⁻¹ | null | 1 | 3 | 6 | 14 | 13 | -4 | false | {"mass": "3", "velocity": "6", "force": "-3", "concentration": "1", "avogadro": "1"} |
6 | boltzmann,cat_activity,force,gas_constant,mass,velocity | m·v·F·R·z·k_B | chemistry,constants,mechanics | m·v·F⁻¹·R·z·k_B⁻¹ | m = k₀ · v⁻¹·F·R⁻¹·z⁻¹·k_B | null | 1 | 3 | 1 | 6 | 5.2 | 3.8 | false | {"mass": "1", "velocity": "1", "force": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"} |
5 | avogadro,cat_activity,force,mass,velocity | m·v·F·z·N_A | chemistry,constants,mechanics | m·v·F⁻¹·z·N_A | m = k₀ · v⁻¹·F·z⁻¹·N_A⁻¹ | null | 1 | 3 | 1 | 5 | 4.2 | 4.8 | false | {"mass": "1", "velocity": "1", "force": "-1", "cat_activity": "1", "avogadro": "1"} |
5 | force,illuminance,lum_intensity,mass,velocity | m·v·F·I_v·E_v | mechanics,photometry | m²·v⁴·F⁻²·I_v⁻¹·E_v | I_v = k₀ · m²·v⁴·F⁻²·E_v | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "velocity": "4", "force": "-2", "lum_intensity": "-1", "illuminance": "1"} |
5 | force,lum_intensity,luminance,mass,velocity | m·v·F·I_v·L_v | mechanics,photometry | m²·v⁴·F⁻²·I_v⁻¹·L_v | I_v = k₀ · m²·v⁴·F⁻²·L_v | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "velocity": "4", "force": "-2", "lum_intensity": "-1", "luminance": "1"} |
4 | force,mass,planck,velocity | m·v·F·h | constants,mechanics | m²·v³·F⁻¹·h⁻¹ | F = k₀ · m²·v³·h⁻¹ | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "2", "velocity": "3", "force": "-1", "planck": "-1"} |
3 | energy,mass,velocity | m·v·E | mechanics | m·v²·E⁻¹ | m = k₀ · v⁻²·E | kinetic energy | 0 | 1 | 2 | 4 | 2.2 | 7.8 | true | {"mass": "1", "velocity": "2", "energy": "-1"} |
3 | mass,torque,velocity | m·v·τ | mechanics | m·v²·τ⁻¹ | m = k₀ · v⁻²·τ | null | 0 | 1 | 2 | 4 | 2.2 | 7.8 | true | {"mass": "1", "velocity": "2", "torque": "-1"} |
4 | ang_momentum,mass,power,velocity | m·v·P·Lₐ | mechanics | m²·v⁴·P⁻¹·Lₐ⁻¹ | P = k₀ · m²·v⁴·Lₐ⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "2", "velocity": "4", "power": "-1", "ang_momentum": "-1"} |
4 | action,mass,power,velocity | m·v·P·S | mechanics | m²·v⁴·P⁻¹·S⁻¹ | P = k₀ · m²·v⁴·S⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "2", "velocity": "4", "power": "-1", "action": "-1"} |
4 | inertia,mass,power,velocity | m·v·P·J | mechanics | m³·v⁶·P⁻²·J⁻¹ | J = k₀ · m³·v⁶·P⁻² | null | 0 | 1 | 6 | 12 | 10.1 | -0.1 | false | {"mass": "3", "velocity": "6", "power": "-2", "inertia": "-1"} |
4 | mass,power,pressure,velocity | m·v·P·P_p | mechanics | m²·v⁷·P⁻³·P_p | P_p = k₀ · m⁻²·v⁻⁷·P³ | null | 0 | 1 | 7 | 13 | 11.3 | -1.3 | false | {"mass": "2", "velocity": "7", "power": "-3", "pressure": "1"} |
4 | density,mass,power,velocity | m·v·P·ρ | mechanics | m²·v⁹·P⁻³·ρ | ρ = k₀ · m⁻²·v⁻⁹·P³ | null | 0 | 1 | 9 | 15 | 13.7 | -3.7 | false | {"mass": "2", "velocity": "9", "power": "-3", "density": "1"} |
4 | mass,power,velocity,viscosity | m·v·P·μ | mechanics | m·v⁵·P⁻²·μ | m = k₀ · v⁻⁵·P²·μ⁻¹ | null | 0 | 1 | 5 | 9 | 7.5 | 2.5 | false | {"mass": "1", "velocity": "5", "power": "-2", "viscosity": "1"} |
4 | kin_viscosity,mass,power,velocity | m·v·P·ν | mechanics | m·v⁴·P⁻¹·ν⁻¹ | m = k₀ · v⁻⁴·P·ν | null | 0 | 1 | 4 | 7 | 5.6 | 4.4 | false | {"mass": "1", "velocity": "4", "power": "-1", "kin_viscosity": "-1"} |
4 | mass,omega,power,velocity | m·v·P·ω | mechanics | m·v²·P⁻¹·ω | m = k₀ · v⁻²·P·ω⁻¹ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "velocity": "2", "power": "-1", "omega": "1"} |
4 | frequency,mass,power,velocity | m·v·P·f | mechanics | m·v²·P⁻¹·f | m = k₀ · v⁻²·P·f⁻¹ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "velocity": "2", "power": "-1", "frequency": "1"} |
4 | mass,power,stiffness,velocity | m·v·P·k | mechanics | m·v⁴·P⁻²·k | m = k₀ · v⁻⁴·P²·k⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "velocity": "4", "power": "-2", "stiffness": "1"} |
4 | mass,power,surf_tension,velocity | m·v·P·γ | mechanics | m·v⁴·P⁻²·γ | m = k₀ · v⁻⁴·P²·γ⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "velocity": "4", "power": "-2", "surf_tension": "1"} |
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