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 | ang_momentum,charge,length,mass,voltage | m·ℓ·Lₐ·q·U | em,mechanics | m·ℓ²·Lₐ⁻²·q·U | m = k₀ · ℓ⁻²·Lₐ²·q⁻¹·U⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "charge": "1", "voltage": "1"} |
5 | ang_momentum,capacitance,charge,length,mass | m·ℓ·Lₐ·q·C_e | em,mechanics | m·ℓ²·Lₐ⁻²·q²·C_e⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·q⁻²·C_e | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "charge": "2", "capacitance": "-1"} |
5 | ang_momentum,charge,efield,length,mass | m·ℓ·Lₐ·q·E_f | em,mechanics | m·ℓ³·Lₐ⁻²·q·E_f | m = k₀ · ℓ⁻³·Lₐ²·q⁻¹·E_f⁻¹ | null | 0 | 2 | 3 | 8 | 6.7 | 2.8 | true | {"mass": "1", "length": "3", "ang_momentum": "-2", "charge": "1", "efield": "1"} |
5 | ang_momentum,charge,length,mass,permittivity | m·ℓ·Lₐ·q·ε | em,mechanics | m·ℓ·Lₐ⁻²·q²·ε⁻¹ | m = k₀ · ℓ⁻¹·Lₐ²·q⁻²·ε | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "ang_momentum": "-2", "charge": "2", "permittivity": "-1"} |
5 | ang_momentum,current,length,mass,voltage | m·ℓ·Lₐ·i·U | em,mechanics | m²·ℓ⁴·Lₐ⁻³·i·U | i = k₀ · m⁻²·ℓ⁻⁴·Lₐ³·U⁻¹ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "2", "length": "4", "ang_momentum": "-3", "current": "1", "voltage": "1"} |
5 | ang_momentum,current,length,mass,resistance | m·ℓ·Lₐ·i·R | em,mechanics | m²·ℓ⁴·Lₐ⁻³·i²·R | R = k₀ · m⁻²·ℓ⁻⁴·Lₐ³·i⁻² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "2", "length": "4", "ang_momentum": "-3", "current": "2", "resistance": "1"} |
5 | ang_momentum,capacitance,current,length,mass | m·ℓ·Lₐ·i·C_e | em,mechanics | m³·ℓ⁶·Lₐ⁻⁴·i²·C_e⁻¹ | C_e = k₀ · m³·ℓ⁶·Lₐ⁻⁴·i² | null | 0 | 2 | 6 | 16 | 13.8 | -4.3 | false | {"mass": "3", "length": "6", "ang_momentum": "-4", "current": "2", "capacitance": "-1"} |
5 | ang_momentum,current,inductance,length,mass | m·ℓ·Lₐ·i·L_e | em,mechanics | m·ℓ²·Lₐ⁻²·i²·L_e | m = k₀ · ℓ⁻²·Lₐ²·i⁻²·L_e⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "current": "2", "inductance": "1"} |
5 | ang_momentum,current,efield,length,mass | m·ℓ·Lₐ·i·E_f | em,mechanics | m²·ℓ⁵·Lₐ⁻³·i·E_f | i = k₀ · m⁻²·ℓ⁻⁵·Lₐ³·E_f⁻¹ | null | 0 | 2 | 5 | 12 | 10.5 | -1 | false | {"mass": "2", "length": "5", "ang_momentum": "-3", "current": "1", "efield": "1"} |
5 | ang_momentum,bfield,current,length,mass | m·ℓ·Lₐ·i·B | em,mechanics | m·ℓ⁴·Lₐ⁻²·i·B | m = k₀ · ℓ⁻⁴·Lₐ²·i⁻¹·B⁻¹ | null | 0 | 2 | 4 | 9 | 7.9 | 1.6 | false | {"mass": "1", "length": "4", "ang_momentum": "-2", "current": "1", "bfield": "1"} |
5 | ang_momentum,current,length,mag_flux,mass | m·ℓ·Lₐ·i·Φ | em,mechanics | m·ℓ²·Lₐ⁻²·i·Φ | m = k₀ · ℓ⁻²·Lₐ²·i⁻¹·Φ⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "current": "1", "mag_flux": "1"} |
5 | ang_momentum,current,length,mass,permittivity | m·ℓ·Lₐ·i·ε | em,mechanics | m³·ℓ⁵·Lₐ⁻⁴·i²·ε⁻¹ | ε = k₀ · m³·ℓ⁵·Lₐ⁻⁴·i² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "3", "length": "5", "ang_momentum": "-4", "current": "2", "permittivity": "-1"} |
5 | ang_momentum,current,length,mass,permeability | m·ℓ·Lₐ·i·μ₀ | em,mechanics | m·ℓ³·Lₐ⁻²·i²·μ₀ | m = k₀ · ℓ⁻³·Lₐ²·i⁻²·μ₀⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "ang_momentum": "-2", "current": "2", "permeability": "1"} |
5 | ang_momentum,conductivity,current,length,mass | m·ℓ·Lₐ·i·σ | em,mechanics | m²·ℓ³·Lₐ⁻³·i²·σ⁻¹ | σ = k₀ · m²·ℓ³·Lₐ⁻³·i² | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "2", "length": "3", "ang_momentum": "-3", "current": "2", "conductivity": "-1"} |
5 | ang_momentum,current,length,mass,resistivity | m·ℓ·Lₐ·i·ρ_e | em,mechanics | m²·ℓ³·Lₐ⁻³·i²·ρ_e | ρ_e = k₀ · m⁻²·ℓ⁻³·Lₐ³·i⁻² | null | 0 | 2 | 3 | 11 | 8.8 | 0.7 | false | {"mass": "2", "length": "3", "ang_momentum": "-3", "current": "2", "resistivity": "1"} |
5 | ang_momentum,current,elem_charge,length,mass | m·ℓ·Lₐ·i·e | constants,em,mechanics | m·ℓ²·Lₐ⁻¹·i·e⁻¹ | m = k₀ · ℓ⁻²·Lₐ·i⁻¹·e | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "1", "length": "2", "ang_momentum": "-1", "current": "1", "elem_charge": "-1"} |
5 | ang_momentum,length,mass,resistance,voltage | m·ℓ·Lₐ·U·R | em,mechanics | m²·ℓ⁴·Lₐ⁻³·U²·R⁻¹ | R = k₀ · m²·ℓ⁴·Lₐ⁻³·U² | null | 0 | 2 | 4 | 12 | 10 | -0.5 | false | {"mass": "2", "length": "4", "ang_momentum": "-3", "voltage": "2", "resistance": "-1"} |
5 | ang_momentum,capacitance,length,mass,voltage | m·ℓ·Lₐ·U·C_e | em,mechanics | m·ℓ²·Lₐ⁻²·U²·C_e | m = k₀ · ℓ⁻²·Lₐ²·U⁻²·C_e⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "voltage": "2", "capacitance": "1"} |
5 | ang_momentum,inductance,length,mass,voltage | m·ℓ·Lₐ·U·L_e | em,mechanics | m³·ℓ⁶·Lₐ⁻⁴·U²·L_e⁻¹ | L_e = k₀ · m³·ℓ⁶·Lₐ⁻⁴·U² | null | 0 | 2 | 6 | 16 | 13.8 | -4.3 | false | {"mass": "3", "length": "6", "ang_momentum": "-4", "voltage": "2", "inductance": "-1"} |
5 | ang_momentum,length,mag_flux,mass,voltage | m·ℓ·Lₐ·U·Φ | em,mechanics | m·ℓ²·Lₐ⁻¹·U·Φ⁻¹ | m = k₀ · ℓ⁻²·Lₐ·U⁻¹·Φ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "voltage": "1", "mag_flux": "-1"} |
5 | ang_momentum,length,mass,permittivity,voltage | m·ℓ·Lₐ·U·ε | em,mechanics | m·ℓ³·Lₐ⁻²·U²·ε | m = k₀ · ℓ⁻³·Lₐ²·U⁻²·ε⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "1", "length": "3", "ang_momentum": "-2", "voltage": "2", "permittivity": "1"} |
5 | ang_momentum,length,mass,permeability,voltage | m·ℓ·Lₐ·U·μ₀ | em,mechanics | m³·ℓ⁵·Lₐ⁻⁴·U²·μ₀⁻¹ | μ₀ = k₀ · m³·ℓ⁵·Lₐ⁻⁴·U² | null | 0 | 2 | 5 | 15 | 12.6 | -3.1 | false | {"mass": "3", "length": "5", "ang_momentum": "-4", "voltage": "2", "permeability": "-1"} |
5 | ang_momentum,conductivity,length,mass,voltage | m·ℓ·Lₐ·U·σ | em,mechanics | m²·ℓ⁵·Lₐ⁻³·U²·σ | σ = k₀ · m⁻²·ℓ⁻⁵·Lₐ³·U⁻² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "2", "length": "5", "ang_momentum": "-3", "voltage": "2", "conductivity": "1"} |
5 | ang_momentum,length,mass,resistivity,voltage | m·ℓ·Lₐ·U·ρ_e | em,mechanics | m²·ℓ⁵·Lₐ⁻³·U²·ρ_e⁻¹ | ρ_e = k₀ · m²·ℓ⁵·Lₐ⁻³·U² | null | 0 | 2 | 5 | 13 | 11.2 | -1.7 | false | {"mass": "2", "length": "5", "ang_momentum": "-3", "voltage": "2", "resistivity": "-1"} |
5 | ang_momentum,elem_charge,length,mass,voltage | m·ℓ·Lₐ·U·e | constants,em,mechanics | m·ℓ²·Lₐ⁻²·U·e | m = k₀ · ℓ⁻²·Lₐ²·U⁻¹·e⁻¹ | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "voltage": "1", "elem_charge": "1"} |
5 | ang_momentum,capacitance,length,mass,resistance | m·ℓ·Lₐ·R·C_e | em,mechanics | m·ℓ²·Lₐ⁻¹·R⁻¹·C_e⁻¹ | m = k₀ · ℓ⁻²·Lₐ·R·C_e | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "resistance": "-1", "capacitance": "-1"} |
5 | ang_momentum,inductance,length,mass,resistance | m·ℓ·Lₐ·R·L_e | em,mechanics | m·ℓ²·Lₐ⁻¹·R·L_e⁻¹ | m = k₀ · ℓ⁻²·Lₐ·R⁻¹·L_e | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "resistance": "1", "inductance": "-1"} |
5 | ang_momentum,efield,length,mass,resistance | m·ℓ·Lₐ·R·E_f | em,mechanics | m²·ℓ⁶·Lₐ⁻³·R⁻¹·E_f² | R = k₀ · m²·ℓ⁶·Lₐ⁻³·E_f² | null | 0 | 2 | 6 | 14 | 12.4 | -2.9 | false | {"mass": "2", "length": "6", "ang_momentum": "-3", "resistance": "-1", "efield": "2"} |
5 | ang_momentum,length,mass,permittivity,resistance | m·ℓ·Lₐ·R·ε | em,mechanics | m·ℓ·Lₐ⁻¹·R⁻¹·ε⁻¹ | m = k₀ · ℓ⁻¹·Lₐ·R·ε | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "ang_momentum": "-1", "resistance": "-1", "permittivity": "-1"} |
5 | ang_momentum,length,mass,permeability,resistance | m·ℓ·Lₐ·R·μ₀ | em,mechanics | m·ℓ·Lₐ⁻¹·R·μ₀⁻¹ | m = k₀ · ℓ⁻¹·Lₐ·R⁻¹·μ₀ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "ang_momentum": "-1", "resistance": "1", "permeability": "-1"} |
5 | ang_momentum,capacitance,inductance,length,mass | m·ℓ·Lₐ·C_e·L_e | em,mechanics | m²·ℓ⁴·Lₐ⁻²·C_e⁻¹·L_e⁻¹ | C_e = k₀ · m²·ℓ⁴·Lₐ⁻²·L_e⁻¹ | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "2", "length": "4", "ang_momentum": "-2", "capacitance": "-1", "inductance": "-1"} |
5 | ang_momentum,capacitance,efield,length,mass | m·ℓ·Lₐ·C_e·E_f | em,mechanics | m·ℓ⁴·Lₐ⁻²·C_e·E_f² | m = k₀ · ℓ⁻⁴·Lₐ²·C_e⁻¹·E_f⁻² | null | 0 | 2 | 4 | 10 | 8.6 | 0.9 | false | {"mass": "1", "length": "4", "ang_momentum": "-2", "capacitance": "1", "efield": "2"} |
5 | ang_momentum,capacitance,length,mass,permeability | m·ℓ·Lₐ·C_e·μ₀ | em,mechanics | m²·ℓ³·Lₐ⁻²·C_e⁻¹·μ₀⁻¹ | C_e = k₀ · m²·ℓ³·Lₐ⁻²·μ₀⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "length": "3", "ang_momentum": "-2", "capacitance": "-1", "permeability": "-1"} |
5 | ang_momentum,capacitance,conductivity,length,mass | m·ℓ·Lₐ·C_e·σ | em,mechanics | m·ℓ³·Lₐ⁻¹·C_e⁻¹·σ | m = k₀ · ℓ⁻³·Lₐ·C_e·σ⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "ang_momentum": "-1", "capacitance": "-1", "conductivity": "1"} |
5 | ang_momentum,capacitance,length,mass,resistivity | m·ℓ·Lₐ·C_e·ρ_e | em,mechanics | m·ℓ³·Lₐ⁻¹·C_e⁻¹·ρ_e⁻¹ | m = k₀ · ℓ⁻³·Lₐ·C_e·ρ_e | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "ang_momentum": "-1", "capacitance": "-1", "resistivity": "-1"} |
5 | ang_momentum,capacitance,elem_charge,length,mass | m·ℓ·Lₐ·C_e·e | constants,em,mechanics | m·ℓ²·Lₐ⁻²·C_e⁻¹·e² | m = k₀ · ℓ⁻²·Lₐ²·C_e·e⁻² | null | 1 | 3 | 2 | 8 | 6.8 | 2.2 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "capacitance": "-1", "elem_charge": "2"} |
5 | ang_momentum,efield,inductance,length,mass | m·ℓ·Lₐ·L_e·E_f | em,mechanics | m³·ℓ⁸·Lₐ⁻⁴·L_e⁻¹·E_f² | L_e = k₀ · m³·ℓ⁸·Lₐ⁻⁴·E_f² | null | 0 | 2 | 8 | 18 | 16.2 | -6.7 | false | {"mass": "3", "length": "8", "ang_momentum": "-4", "inductance": "-1", "efield": "2"} |
5 | ang_momentum,bfield,inductance,length,mass | m·ℓ·Lₐ·L_e·B | em,mechanics | m·ℓ⁶·Lₐ⁻²·L_e⁻¹·B² | m = k₀ · ℓ⁻⁶·Lₐ²·L_e·B⁻² | null | 0 | 2 | 6 | 12 | 11 | -1.5 | false | {"mass": "1", "length": "6", "ang_momentum": "-2", "inductance": "-1", "bfield": "2"} |
5 | ang_momentum,inductance,length,mag_flux,mass | m·ℓ·Lₐ·L_e·Φ | em,mechanics | m·ℓ²·Lₐ⁻²·L_e⁻¹·Φ² | m = k₀ · ℓ⁻²·Lₐ²·L_e·Φ⁻² | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "inductance": "-1", "mag_flux": "2"} |
5 | ang_momentum,inductance,length,mass,permittivity | m·ℓ·Lₐ·L_e·ε | em,mechanics | m²·ℓ³·Lₐ⁻²·L_e⁻¹·ε⁻¹ | L_e = k₀ · m²·ℓ³·Lₐ⁻²·ε⁻¹ | null | 0 | 2 | 3 | 9 | 7.4 | 2.1 | false | {"mass": "2", "length": "3", "ang_momentum": "-2", "inductance": "-1", "permittivity": "-1"} |
5 | ang_momentum,conductivity,inductance,length,mass | m·ℓ·Lₐ·L_e·σ | em,mechanics | m·ℓ·Lₐ⁻¹·L_e⁻¹·σ⁻¹ | m = k₀ · ℓ⁻¹·Lₐ·L_e·σ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "ang_momentum": "-1", "inductance": "-1", "conductivity": "-1"} |
5 | ang_momentum,inductance,length,mass,resistivity | m·ℓ·Lₐ·L_e·ρ_e | em,mechanics | m·ℓ·Lₐ⁻¹·L_e⁻¹·ρ_e | m = k₀ · ℓ⁻¹·Lₐ·L_e·ρ_e⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "ang_momentum": "-1", "inductance": "-1", "resistivity": "1"} |
5 | ang_momentum,bfield,efield,length,mass | m·ℓ·Lₐ·E_f·B | em,mechanics | m·ℓ·Lₐ⁻¹·E_f·B⁻¹ | m = k₀ · ℓ⁻¹·Lₐ·E_f⁻¹·B | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "1", "ang_momentum": "-1", "efield": "1", "bfield": "-1"} |
5 | ang_momentum,efield,length,mag_flux,mass | m·ℓ·Lₐ·E_f·Φ | em,mechanics | m·ℓ³·Lₐ⁻¹·E_f·Φ⁻¹ | m = k₀ · ℓ⁻³·Lₐ·E_f⁻¹·Φ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "ang_momentum": "-1", "efield": "1", "mag_flux": "-1"} |
5 | ang_momentum,efield,length,mass,permittivity | m·ℓ·Lₐ·E_f·ε | em,mechanics | m·ℓ⁵·Lₐ⁻²·E_f²·ε | m = k₀ · ℓ⁻⁵·Lₐ²·E_f⁻²·ε⁻¹ | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "5", "ang_momentum": "-2", "efield": "2", "permittivity": "1"} |
5 | ang_momentum,efield,length,mass,permeability | m·ℓ·Lₐ·E_f·μ₀ | em,mechanics | m³·ℓ⁷·Lₐ⁻⁴·E_f²·μ₀⁻¹ | μ₀ = k₀ · m³·ℓ⁷·Lₐ⁻⁴·E_f² | null | 0 | 2 | 7 | 17 | 15 | -5.5 | false | {"mass": "3", "length": "7", "ang_momentum": "-4", "efield": "2", "permeability": "-1"} |
5 | ang_momentum,conductivity,efield,length,mass | m·ℓ·Lₐ·E_f·σ | em,mechanics | m²·ℓ⁷·Lₐ⁻³·E_f²·σ | σ = k₀ · m⁻²·ℓ⁻⁷·Lₐ³·E_f⁻² | null | 0 | 2 | 7 | 15 | 13.6 | -4.1 | false | {"mass": "2", "length": "7", "ang_momentum": "-3", "efield": "2", "conductivity": "1"} |
5 | ang_momentum,efield,length,mass,resistivity | m·ℓ·Lₐ·E_f·ρ_e | em,mechanics | m²·ℓ⁷·Lₐ⁻³·E_f²·ρ_e⁻¹ | ρ_e = k₀ · m²·ℓ⁷·Lₐ⁻³·E_f² | null | 0 | 2 | 7 | 15 | 13.6 | -4.1 | false | {"mass": "2", "length": "7", "ang_momentum": "-3", "efield": "2", "resistivity": "-1"} |
5 | ang_momentum,efield,elem_charge,length,mass | m·ℓ·Lₐ·E_f·e | constants,em,mechanics | m·ℓ³·Lₐ⁻²·E_f·e | m = k₀ · ℓ⁻³·Lₐ²·E_f⁻¹·e⁻¹ | null | 1 | 3 | 3 | 8 | 7.3 | 1.7 | false | {"mass": "1", "length": "3", "ang_momentum": "-2", "efield": "1", "elem_charge": "1"} |
5 | ang_momentum,bfield,length,mass,permeability | m·ℓ·Lₐ·B·μ₀ | em,mechanics | m·ℓ⁵·Lₐ⁻²·B²·μ₀⁻¹ | m = k₀ · ℓ⁻⁵·Lₐ²·B⁻²·μ₀ | null | 0 | 2 | 5 | 11 | 9.8 | -0.3 | false | {"mass": "1", "length": "5", "ang_momentum": "-2", "bfield": "2", "permeability": "-1"} |
5 | ang_momentum,length,mag_flux,mass,permeability | m·ℓ·Lₐ·Φ·μ₀ | em,mechanics | m·ℓ·Lₐ⁻²·Φ²·μ₀⁻¹ | m = k₀ · ℓ⁻¹·Lₐ²·Φ⁻²·μ₀ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "1", "ang_momentum": "-2", "mag_flux": "2", "permeability": "-1"} |
5 | ang_momentum,length,mass,permeability,permittivity | m·ℓ·Lₐ·ε·μ₀ | em,mechanics | m²·ℓ²·Lₐ⁻²·ε⁻¹·μ₀⁻¹ | ε = k₀ · m²·ℓ²·Lₐ⁻²·μ₀⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "ang_momentum": "-2", "permittivity": "-1", "permeability": "-1"} |
5 | ang_momentum,conductivity,length,mass,permittivity | m·ℓ·Lₐ·ε·σ | em,mechanics | m·ℓ²·Lₐ⁻¹·ε⁻¹·σ | m = k₀ · ℓ⁻²·Lₐ·ε·σ⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "permittivity": "-1", "conductivity": "1"} |
5 | ang_momentum,length,mass,permittivity,resistivity | m·ℓ·Lₐ·ε·ρ_e | em,mechanics | m·ℓ²·Lₐ⁻¹·ε⁻¹·ρ_e⁻¹ | m = k₀ · ℓ⁻²·Lₐ·ε·ρ_e | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "permittivity": "-1", "resistivity": "-1"} |
5 | ang_momentum,elem_charge,length,mass,permittivity | m·ℓ·Lₐ·ε·e | constants,em,mechanics | m·ℓ·Lₐ⁻²·ε⁻¹·e² | m = k₀ · ℓ⁻¹·Lₐ²·ε·e⁻² | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "1", "ang_momentum": "-2", "permittivity": "-1", "elem_charge": "2"} |
5 | amount,ang_momentum,length,mass,molar_energy | m·ℓ·Lₐ·n·E_m | chemistry,mechanics | m·ℓ²·Lₐ⁻²·n·E_m | m = k₀ · ℓ⁻²·Lₐ²·n⁻¹·E_m⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "ang_momentum": "-2", "amount": "1", "molar_energy": "1"} |
5 | amount,ang_momentum,cat_activity,length,mass | m·ℓ·Lₐ·n·z | chemistry,mechanics | m·ℓ²·Lₐ⁻¹·n⁻¹·z | m = k₀ · ℓ⁻²·Lₐ·n·z⁻¹ | null | 0 | 2 | 2 | 6 | 4.8 | 4.7 | true | {"mass": "1", "length": "2", "ang_momentum": "-1", "amount": "-1", "cat_activity": "1"} |
5 | ang_momentum,length,mass,molar_energy,molar_mass | m·ℓ·Lₐ·M_m·E_m | chemistry,mechanics | m²·ℓ²·Lₐ⁻²·M_m⁻¹·E_m | M_m = k₀ · m²·ℓ²·Lₐ⁻²·E_m | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "ang_momentum": "-2", "molar_mass": "-1", "molar_energy": "1"} |
5 | ang_momentum,concentration,length,mass,molar_energy | m·ℓ·Lₐ·c_n·E_m | chemistry,mechanics | m·ℓ⁵·Lₐ⁻²·c_n·E_m | m = k₀ · ℓ⁻⁵·Lₐ²·c_n⁻¹·E_m⁻¹ | null | 0 | 2 | 5 | 10 | 9.1 | 0.4 | false | {"mass": "1", "length": "5", "ang_momentum": "-2", "concentration": "1", "molar_energy": "1"} |
5 | ang_momentum,cat_activity,concentration,length,mass | m·ℓ·Lₐ·c_n·z | chemistry,mechanics | m·ℓ⁻¹·Lₐ⁻¹·c_n⁻¹·z | m = k₀ · ℓ·Lₐ·c_n·z⁻¹ | null | 0 | 2 | 1 | 5 | 3.6 | 5.9 | true | {"mass": "1", "length": "-1", "ang_momentum": "-1", "concentration": "-1", "cat_activity": "1"} |
6 | ang_momentum,boltzmann,gas_constant,length,mass,molar_energy | m·ℓ·Lₐ·E_m·R·k_B | chemistry,constants,mechanics | m·ℓ²·Lₐ⁻²·E_m·R⁻¹·k_B | m = k₀ · ℓ⁻²·Lₐ²·E_m⁻¹·R·k_B⁻¹ | null | 1 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1"} |
5 | ang_momentum,cat_activity,length,mass,molar_energy | m·ℓ·Lₐ·E_m·z | chemistry,mechanics | m²·ℓ⁴·Lₐ⁻³·E_m·z | E_m = k₀ · m⁻²·ℓ⁻⁴·Lₐ³·z⁻¹ | null | 0 | 2 | 4 | 11 | 9.3 | 0.2 | false | {"mass": "2", "length": "4", "ang_momentum": "-3", "molar_energy": "1", "cat_activity": "1"} |
5 | ang_momentum,avogadro,length,mass,molar_energy | m·ℓ·Lₐ·E_m·N_A | chemistry,constants,mechanics | m·ℓ²·Lₐ⁻²·E_m·N_A⁻¹ | m = k₀ · ℓ⁻²·Lₐ²·E_m⁻¹·N_A | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "ang_momentum": "-2", "molar_energy": "1", "avogadro": "-1"} |
6 | ang_momentum,boltzmann,cat_activity,gas_constant,length,mass | m·ℓ·Lₐ·R·z·k_B | chemistry,constants,mechanics | m·ℓ²·Lₐ⁻¹·R·z·k_B⁻¹ | m = k₀ · ℓ⁻²·Lₐ·R⁻¹·z⁻¹·k_B | null | 1 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "2", "ang_momentum": "-1", "gas_constant": "1", "cat_activity": "1", "boltzmann": "-1"} |
5 | ang_momentum,avogadro,cat_activity,length,mass | m·ℓ·Lₐ·z·N_A | chemistry,constants,mechanics | m·ℓ²·Lₐ⁻¹·z·N_A | m = k₀ · ℓ⁻²·Lₐ·z⁻¹·N_A⁻¹ | null | 1 | 3 | 2 | 6 | 5.4 | 3.6 | false | {"mass": "1", "length": "2", "ang_momentum": "-1", "cat_activity": "1", "avogadro": "1"} |
4 | ang_momentum,length,light_speed,mass | m·ℓ·Lₐ·c₀ | constants,mechanics | m·ℓ·Lₐ⁻¹·c₀ | m = k₀ · ℓ⁻¹·Lₐ·c₀⁻¹ | null | 1 | 2 | 1 | 4 | 2.6 | 6.9 | true | {"mass": "1", "length": "1", "ang_momentum": "-1", "light_speed": "1"} |
4 | ang_momentum,grav_const,length,mass | m·ℓ·Lₐ·G | constants,mechanics | m³·ℓ·Lₐ⁻²·G | ℓ = k₀ · m⁻³·Lₐ²·G⁻¹ | null | 1 | 2 | 3 | 7 | 5.7 | 3.8 | true | {"mass": "3", "length": "1", "ang_momentum": "-2", "grav_const": "1"} |
4 | action,length,mass,pressure | m·ℓ·S·P_p | mechanics | m·ℓ⁵·S⁻²·P_p | m = k₀ · ℓ⁻⁵·S²·P_p⁻¹ | null | 0 | 1 | 5 | 9 | 7.5 | 2.5 | false | {"mass": "1", "length": "5", "action": "-2", "pressure": "1"} |
4 | action,length,mass,omega | m·ℓ·S·ω | mechanics | m·ℓ²·S⁻¹·ω | m = k₀ · ℓ⁻²·S·ω⁻¹ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "2", "action": "-1", "omega": "1"} |
4 | action,frequency,length,mass | m·ℓ·S·f | mechanics | m·ℓ²·S⁻¹·f | m = k₀ · ℓ⁻²·S·f⁻¹ | null | 0 | 1 | 2 | 5 | 3.2 | 6.8 | true | {"mass": "1", "length": "2", "action": "-1", "frequency": "1"} |
4 | action,length,mass,stiffness | m·ℓ·S·k | mechanics | m·ℓ⁴·S⁻²·k | m = k₀ · ℓ⁻⁴·S²·k⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "4", "action": "-2", "stiffness": "1"} |
4 | action,length,mass,surf_tension | m·ℓ·S·γ | mechanics | m·ℓ⁴·S⁻²·γ | m = k₀ · ℓ⁻⁴·S²·γ⁻¹ | null | 0 | 1 | 4 | 8 | 6.3 | 3.7 | false | {"mass": "1", "length": "4", "action": "-2", "surf_tension": "1"} |
4 | action,flowrate,length,mass | m·ℓ·S·Q | mechanics | m·ℓ⁻¹·S⁻¹·Q | m = k₀ · ℓ·S·Q⁻¹ | null | 0 | 1 | 1 | 4 | 2 | 8 | true | {"mass": "1", "length": "-1", "action": "-1", "flowrate": "1"} |
5 | action,entropy,length,mass,temperature | m·ℓ·S·Θ·S_e | mechanics,thermo | m·ℓ²·S⁻²·Θ·S_e | m = k₀ · ℓ⁻²·S²·Θ⁻¹·S_e⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "action": "-2", "temperature": "1", "entropy": "1"} |
5 | action,heat_capacity,length,mass,temperature | m·ℓ·S·Θ·C | mechanics,thermo | m·ℓ²·S⁻²·Θ·C | m = k₀ · ℓ⁻²·S²·Θ⁻¹·C⁻¹ | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "action": "-2", "temperature": "1", "heat_capacity": "1"} |
5 | action,length,mass,specific_heat,temperature | m·ℓ·S·Θ·c | mechanics,thermo | m²·ℓ²·S⁻²·Θ·c | Θ = k₀ · m⁻²·ℓ⁻²·S²·c⁻¹ | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "action": "-2", "temperature": "1", "specific_heat": "1"} |
5 | action,length,mass,temperature,thermal_cond | m·ℓ·S·Θ·κ | mechanics,thermo | m²·ℓ⁵·S⁻³·Θ·κ | Θ = k₀ · m⁻²·ℓ⁻⁵·S³·κ⁻¹ | null | 0 | 2 | 5 | 12 | 10.5 | -1 | false | {"mass": "2", "length": "5", "action": "-3", "temperature": "1", "thermal_cond": "1"} |
6 | action,amount,gas_constant,length,mass,temperature | m·ℓ·S·Θ·n·R | chemistry,mechanics,thermo | m·ℓ²·S⁻²·Θ·n·R | m = k₀ · ℓ⁻²·S²·Θ⁻¹·n⁻¹·R⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "action": "-2", "temperature": "1", "amount": "1", "gas_constant": "1"} |
6 | action,gas_constant,length,mass,molar_mass,temperature | m·ℓ·S·Θ·M_m·R | chemistry,mechanics,thermo | m²·ℓ²·S⁻²·Θ·M_m⁻¹·R | Θ = k₀ · m⁻²·ℓ⁻²·S²·M_m·R⁻¹ | null | 0 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "2", "length": "2", "action": "-2", "temperature": "1", "molar_mass": "-1", "gas_constant": "1"} |
6 | action,concentration,gas_constant,length,mass,temperature | m·ℓ·S·Θ·c_n·R | chemistry,mechanics,thermo | m·ℓ⁵·S⁻²·Θ·c_n·R | m = k₀ · ℓ⁻⁵·S²·Θ⁻¹·c_n⁻¹·R⁻¹ | null | 0 | 3 | 5 | 11 | 10.7 | -1.7 | false | {"mass": "1", "length": "5", "action": "-2", "temperature": "1", "concentration": "1", "gas_constant": "1"} |
6 | action,cat_activity,gas_constant,length,mass,temperature | m·ℓ·S·Θ·R·z | chemistry,mechanics,thermo | m²·ℓ⁴·S⁻³·Θ·R·z | Θ = k₀ · m⁻²·ℓ⁻⁴·S³·R⁻¹·z⁻¹ | null | 0 | 3 | 4 | 12 | 10.9 | -1.9 | false | {"mass": "2", "length": "4", "action": "-3", "temperature": "1", "gas_constant": "1", "cat_activity": "1"} |
6 | action,avogadro,gas_constant,length,mass,temperature | m·ℓ·S·Θ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ²·S⁻²·Θ·R·N_A⁻¹ | m = k₀ · ℓ⁻²·S²·Θ⁻¹·R⁻¹·N_A | null | 1 | 4 | 2 | 8 | 7.7 | 0.8 | false | {"mass": "1", "length": "2", "action": "-2", "temperature": "1", "gas_constant": "1", "avogadro": "-1"} |
5 | action,boltzmann,length,mass,temperature | m·ℓ·S·Θ·k_B | constants,mechanics,thermo | m·ℓ²·S⁻²·Θ·k_B | m = k₀ · ℓ⁻²·S²·Θ⁻¹·k_B⁻¹ | null | 1 | 3 | 2 | 7 | 6.1 | 2.9 | false | {"mass": "1", "length": "2", "action": "-2", "temperature": "1", "boltzmann": "1"} |
5 | action,entropy,length,mass,thermal_cond | m·ℓ·S·S_e·κ | mechanics,thermo | m·ℓ³·S⁻¹·S_e⁻¹·κ | m = k₀ · ℓ⁻³·S·S_e·κ⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "action": "-1", "entropy": "-1", "thermal_cond": "1"} |
5 | action,entropy,expansion,length,mass | m·ℓ·S·S_e·β | mechanics,thermo | m·ℓ²·S⁻²·S_e·β⁻¹ | m = k₀ · ℓ⁻²·S²·S_e⁻¹·β | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "action": "-2", "entropy": "1", "expansion": "-1"} |
6 | action,entropy,gas_constant,length,mass,molar_energy | m·ℓ·S·S_e·E_m·R | chemistry,mechanics,thermo | m·ℓ²·S⁻²·S_e·E_m·R⁻¹ | m = k₀ · ℓ⁻²·S²·S_e⁻¹·E_m⁻¹·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "action": "-2", "entropy": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | action,cat_activity,entropy,gas_constant,length,mass | m·ℓ·S·S_e·R·z | chemistry,mechanics,thermo | m·ℓ²·S⁻¹·S_e⁻¹·R·z | m = k₀ · ℓ⁻²·S·S_e·R⁻¹·z⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "2", "action": "-1", "entropy": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | action,heat_capacity,length,mass,thermal_cond | m·ℓ·S·C·κ | mechanics,thermo | m·ℓ³·S⁻¹·C⁻¹·κ | m = k₀ · ℓ⁻³·S·C·κ⁻¹ | null | 0 | 2 | 3 | 7 | 6 | 3.5 | true | {"mass": "1", "length": "3", "action": "-1", "heat_capacity": "-1", "thermal_cond": "1"} |
5 | action,expansion,heat_capacity,length,mass | m·ℓ·S·C·β | mechanics,thermo | m·ℓ²·S⁻²·C·β⁻¹ | m = k₀ · ℓ⁻²·S²·C⁻¹·β | null | 0 | 2 | 2 | 7 | 5.5 | 4 | true | {"mass": "1", "length": "2", "action": "-2", "heat_capacity": "1", "expansion": "-1"} |
6 | action,gas_constant,heat_capacity,length,mass,molar_energy | m·ℓ·S·C·E_m·R | chemistry,mechanics,thermo | m·ℓ²·S⁻²·C·E_m·R⁻¹ | m = k₀ · ℓ⁻²·S²·C⁻¹·E_m⁻¹·R | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "action": "-2", "heat_capacity": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | action,cat_activity,gas_constant,heat_capacity,length,mass | m·ℓ·S·C·R·z | chemistry,mechanics,thermo | m·ℓ²·S⁻¹·C⁻¹·R·z | m = k₀ · ℓ⁻²·S·C·R⁻¹·z⁻¹ | null | 0 | 3 | 2 | 7 | 6.4 | 2.6 | false | {"mass": "1", "length": "2", "action": "-1", "heat_capacity": "-1", "gas_constant": "1", "cat_activity": "1"} |
5 | action,expansion,length,mass,specific_heat | m·ℓ·S·c·β | mechanics,thermo | m²·ℓ²·S⁻²·c·β⁻¹ | c = k₀ · m⁻²·ℓ⁻²·S²·β | null | 0 | 2 | 2 | 8 | 6.2 | 3.3 | true | {"mass": "2", "length": "2", "action": "-2", "specific_heat": "1", "expansion": "-1"} |
6 | action,gas_constant,length,mass,molar_energy,specific_heat | m·ℓ·S·c·E_m·R | chemistry,mechanics,thermo | m²·ℓ²·S⁻²·c·E_m·R⁻¹ | c = k₀ · m⁻²·ℓ⁻²·S²·E_m⁻¹·R | null | 0 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "2", "length": "2", "action": "-2", "specific_heat": "1", "molar_energy": "1", "gas_constant": "-1"} |
5 | action,expansion,length,mass,thermal_cond | m·ℓ·S·κ·β | mechanics,thermo | m²·ℓ⁵·S⁻³·κ·β⁻¹ | κ = k₀ · m⁻²·ℓ⁻⁵·S³·β | null | 0 | 2 | 5 | 12 | 10.5 | -1 | false | {"mass": "2", "length": "5", "action": "-3", "thermal_cond": "1", "expansion": "-1"} |
6 | action,amount,gas_constant,length,mass,thermal_cond | m·ℓ·S·κ·n·R | chemistry,mechanics,thermo | m·ℓ³·S⁻¹·κ·n⁻¹·R⁻¹ | m = k₀ · ℓ⁻³·S·κ⁻¹·n·R | null | 0 | 3 | 3 | 8 | 7.6 | 1.4 | false | {"mass": "1", "length": "3", "action": "-1", "thermal_cond": "1", "amount": "-1", "gas_constant": "-1"} |
6 | action,gas_constant,length,mass,molar_energy,thermal_cond | m·ℓ·S·κ·E_m·R | chemistry,mechanics,thermo | m²·ℓ⁵·S⁻³·κ·E_m·R⁻¹ | κ = k₀ · m⁻²·ℓ⁻⁵·S³·E_m⁻¹·R | null | 0 | 3 | 5 | 13 | 12.1 | -3.1 | false | {"mass": "2", "length": "5", "action": "-3", "thermal_cond": "1", "molar_energy": "1", "gas_constant": "-1"} |
6 | action,avogadro,gas_constant,length,mass,thermal_cond | m·ℓ·S·κ·R·N_A | chemistry,constants,mechanics,thermo | m·ℓ³·S⁻¹·κ·R⁻¹·N_A | m = k₀ · ℓ⁻³·S·κ⁻¹·R·N_A⁻¹ | null | 1 | 4 | 3 | 8 | 8.2 | 0.3 | false | {"mass": "1", "length": "3", "action": "-1", "thermal_cond": "1", "gas_constant": "-1", "avogadro": "1"} |
5 | action,boltzmann,length,mass,thermal_cond | m·ℓ·S·κ·k_B | constants,mechanics,thermo | m·ℓ³·S⁻¹·κ·k_B⁻¹ | m = k₀ · ℓ⁻³·S·κ⁻¹·k_B | null | 1 | 3 | 3 | 7 | 6.6 | 2.4 | false | {"mass": "1", "length": "3", "action": "-1", "thermal_cond": "1", "boltzmann": "-1"} |
6 | action,amount,expansion,gas_constant,length,mass | m·ℓ·S·β·n·R | chemistry,mechanics,thermo | m·ℓ²·S⁻²·β⁻¹·n·R | m = k₀ · ℓ⁻²·S²·β·n⁻¹·R⁻¹ | null | 0 | 3 | 2 | 8 | 7.1 | 1.9 | false | {"mass": "1", "length": "2", "action": "-2", "expansion": "-1", "amount": "1", "gas_constant": "1"} |
6 | action,expansion,gas_constant,length,mass,molar_mass | m·ℓ·S·β·M_m·R | chemistry,mechanics,thermo | m²·ℓ²·S⁻²·β⁻¹·M_m⁻¹·R | β = k₀ · m²·ℓ²·S⁻²·M_m⁻¹·R | null | 0 | 3 | 2 | 9 | 7.8 | 1.2 | false | {"mass": "2", "length": "2", "action": "-2", "expansion": "-1", "molar_mass": "-1", "gas_constant": "1"} |
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