{"feynman-i.8.14": {"dataset_class_key": "FeynmanICh8Eq14", "sympy_eq_str": "sqrt((x0 - x1)**2 + (x2 - x3)**2)", "sympy_eq_srepr": "Pow(Add(Pow(Add(Symbol('x0', real=True), Mul(Integer(-1), Symbol('x1', real=True))), Integer(2)), Pow(Add(Symbol('x2', real=True), Mul(Integer(-1), Symbol('x3', real=True))), Integer(2))), Rational(1, 2))", "symbols": ["$d$", "$x_2$", "$x_1$", "$y_2$", "$y_1$"], "symbols_descs": ["Distance", "Position", "Position", "Position", "Position"], "si-derived_units": ["$m$", "$m$", "$m$", "$m$", "$m$"], "si_units": ["$m$", "$m$", "$m$", "$m$", "$m$"], "properties": ["V, F, NN", "V, F", "V, F", "V, F", "V, F"]}, "feynman-i.10.7": {"dataset_class_key": "FeynmanICh10Eq7", "sympy_eq_str": "x0/sqrt(1 - 1.11265005605362e-17*x1**2)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Pow(Add(Integer(1), Mul(Integer(-1), Float('1.1126500560536185e-17', precision=53), Pow(Symbol('x1', real=True), Integer(2)))), Rational(-1, 2)))", "symbols": ["$m$", "$m_0$", "$v$", "$c$"], "symbols_descs": ["Mass", "Invariant mass", "Velocity", "Speed of light"], "si-derived_units": ["$kg$", "$kg$", "$m/s$", "$m/s$"], "si_units": ["$kg$", "$kg$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F, P", "V, F, P", "V, F, P", "C, F, P"]}, "feynman-i.11.19": {"dataset_class_key": "FeynmanICh11Eq19", "sympy_eq_str": "x0*x1 + x2*x3 + x4*x5", "sympy_eq_srepr": "Add(Mul(Symbol('x0', real=True), Symbol('x1', real=True)), Mul(Symbol('x2', real=True), Symbol('x3', real=True)), Mul(Symbol('x4', real=True), Symbol('x5', real=True)))", "symbols": ["$A$", "$x_1$", "$y_1$", "$x_2$", "$y_2$", "$x_3$", "$y_3$"], "symbols_descs": ["Inner product", "Element of a vector", "Element of a vector", "Element of a vector", "Element of a vector", "Element of a vector", "Element of a vector"], "si-derived_units": ["$1$", "$1$", "$1$", "$1$", "$1$", "$1$", "$1$"], "si_units": ["$1$", "$1$", "$1$", "$1$", "$1$", "$1$", "$1$"], "properties": ["V, F", "V, F", "V, F", "V, F", "V, F", "V, F", "V, F"]}, "feynman-i.12.2": {"dataset_class_key": "FeynmanICh12Eq2", "sympy_eq_str": "28235825615.541*x0*x1/(pi*x2**2)", "sympy_eq_srepr": "Mul(Float('28235825615.541', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Symbol('x1', real=True), Pow(Symbol('x2', real=True), Integer(-2)))", "symbols": ["$F$", "$q_1$", "$q_2$", "$r$", "$\\epsilon$"], "symbols_descs": ["Electrostatic force", "Electric charge", "Electric charge", "Distance", "Vacuum permittivity"], "si-derived_units": ["$N$", "$C$", "$C$", "$m$", "$F/m$"], "si_units": ["$kg \\cdot m \\cdot s^{-2}$", "$s \\cdot A$", "$s \\cdot A$", "$m$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$"], "properties": ["V, F", "V, F", "V, F", "V, F, P", "C, F, P"]}, "feynman-i.12.11": {"dataset_class_key": "FeynmanICh12Eq11", "sympy_eq_str": "x0*(x1 + x2*x3*sin(x4))", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Add(Symbol('x1', real=True), Mul(Symbol('x2', real=True), Symbol('x3', real=True), sin(Symbol('x4', real=True)))))", "symbols": ["$F$", "$q$", "$E$", "$B$", "$v$", "$\\theta$"], "symbols_descs": ["Force", "Electric charge", "Electric field", "Magnetic field strength", "Velocity", "Angle"], "si-derived_units": ["$N$", "$C$", "$V/m$", "$T$", "$m/s$", "$rad$"], "si_units": ["$kg \\cdot m \\cdot s^{-2}$", "$s \\cdot A$", "$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$", "$kg \\cdot s^{-2} \\cdot A^{-1}$", "$m \\cdot s^{-1}$", "$1$"], "properties": ["V, F", "V, F", "V, F", "V, F, P", "V, F, P", "V, F, NN"]}, "feynman-i.13.4": {"dataset_class_key": "FeynmanICh13Eq4", "sympy_eq_str": "0.5*x0*(x1**2 + x2**2 + x3**2)", "sympy_eq_srepr": "Mul(Float('0.5', precision=53), Symbol('x0', real=True), Add(Pow(Symbol('x1', real=True), Integer(2)), Pow(Symbol('x2', real=True), Integer(2)), Pow(Symbol('x3', real=True), Integer(2))))", "symbols": ["$K$", "$m$", "$v$", "$u$", "$w$"], "symbols_descs": ["Kinetic energy", "Mass", "Element of velocity", "Element of velocity", "Element of velocity"], "si-derived_units": ["$J$", "$kg$", "$m/s$", "$m/s$", "$m/s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg$", "$m \\cdot s{-1}$", "$m \\cdot s{-1}$", "$m \\cdot s{-1}$"], "properties": ["V, F, P", "V, F, P", "V, F, P", "V, F, P", "V, F, P"]}, "feynman-i.13.12": {"dataset_class_key": "FeynmanICh13Eq12", "sympy_eq_str": "6.6743e-11*x0*x1*(-1/x3 + 1/x2)", "sympy_eq_srepr": "Mul(Float('6.6742999999999994e-11', precision=53), Symbol('x0', real=True), Symbol('x1', real=True), Add(Mul(Integer(-1), Pow(Symbol('x3', real=True), Integer(-1))), Pow(Symbol('x2', real=True), Integer(-1))))", "symbols": ["$U$", "$G$", "$m_1$", "$m_2$", "$r_2$", "$r_1$"], "symbols_descs": ["Potential energy", "Gravitational constant", "Mass (The Earth)", "Mass", "Distance", "Distance"], "si-derived_units": ["$J$", "$m^3 \\cdot kg^{-1} \\cdot s^{-2}$", "$kg$", "$kg$", "$m$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg^{-1} \\cdot m^3 \\cdot s^{-2}$", "$kg$", "$kg$", "$m$", "$m$"], "properties": ["V, F, P", "C, F, P", "V, F, P", "V, F, P", "V, F, P", "V, F, P"]}, "feynman-i.15.10": {"dataset_class_key": "FeynmanICh15Eq10", "sympy_eq_str": "x0*x1/sqrt(1 - 1.11265005605362e-17*x1**2)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True), Pow(Add(Integer(1), Mul(Integer(-1), Float('1.1126500560536185e-17', precision=53), Pow(Symbol('x1', real=True), Integer(2)))), Rational(-1, 2)))", "symbols": ["$p$", "$m_0$", "$v$", "$c$"], "symbols_descs": ["Relativistic momentum", "Rest Mass", "Velocity", "Speed of light"], "si-derived_units": ["$kg \\cdot m/s$", "$kg$", "$m/s$", "$m/s$"], "si_units": ["$kg \\cdot m \\cdot s^{-1}$", "$kg$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F, P", "V, F, P", "V, F", "C, F, P"]}, "feynman-i.16.6": {"dataset_class_key": "FeynmanICh16Eq6", "sympy_eq_str": "(x0 + x1)/(1.11265005605362e-17*x0*x1 + 1)", "sympy_eq_srepr": "Mul(Add(Symbol('x0', real=True), Symbol('x1', real=True)), Pow(Add(Mul(Float('1.1126500560536185e-17', precision=53), Symbol('x0', real=True), Symbol('x1', real=True)), Integer(1)), Integer(-1)))", "symbols": ["$v_1$", "$u$", "$v$", "$c$"], "symbols_descs": ["Velocity", "Velocity", "Velocity", "Speed of light"], "si-derived_units": ["$m/s$", "$m/s$", "$m/s$", "$m/s$"], "si_units": ["$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F", "V, F", "V, F", "C, F, P"]}, "feynman-i.18.4": {"dataset_class_key": "FeynmanICh18Eq4", "sympy_eq_str": "(x0*x1 + x2*x3)/(x0 + x2)", "sympy_eq_srepr": "Mul(Pow(Add(Symbol('x0', real=True), Symbol('x2', real=True)), Integer(-1)), Add(Mul(Symbol('x0', real=True), Symbol('x1', real=True)), Mul(Symbol('x2', real=True), Symbol('x3', real=True))))", "symbols": ["$r$", "$m_1$", "$r_1$", "$m_2$", "$r_2$"], "symbols_descs": ["Center of gravity", "Mass", "Position", "Mass", "Position"], "si-derived_units": ["$m$", "$kg$", "$m$", "$kg$", "$m$"], "si_units": ["$m$", "$kg$", "$m$", "$kg$", "$m$"], "properties": ["V, F", "V, F, P", "V, F", "V, F, P", "V, F"]}, "feynman-i.24.6": {"dataset_class_key": "FeynmanICh24Eq6", "sympy_eq_str": "0.25*x0*x3**2*(x1**2 + x2**2)", "sympy_eq_srepr": "Mul(Float('0.25', precision=53), Symbol('x0', real=True), Pow(Symbol('x3', real=True), Integer(2)), Add(Pow(Symbol('x1', real=True), Integer(2)), Pow(Symbol('x2', real=True), Integer(2))))", "symbols": ["$E$", "$m$", "$\\omega$", "$\\omega_0$", "$x$"], "symbols_descs": ["Energy", "Mass", "Angular velocity", "Angular velocity", "Position"], "si-derived_units": ["$J$", "$kg$", "$rad/s$", "$rad/s$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg$", "$s^{-1}$", "$s^{-1}$", "$m$"], "properties": ["V, F, P", "V, F, P", "V, F", "V, F", "V, F"]}, "feynman-i.29.4": {"dataset_class_key": "FeynmanICh29Eq4", "sympy_eq_str": "3.33564095198152e-9*x0", "sympy_eq_srepr": "Mul(Float('3.3356409519815204e-9', precision=53), Symbol('x0', real=True))", "symbols": ["$k$", "$\\omega$", "$c$"], "symbols_descs": ["Wavenumber", "Frequency of electromagnetic waves", "Speed of light"], "si-derived_units": ["$1/m$", "$rad/s$", "$m/s$"], "si_units": ["$m^{-1}$", "$s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F, P", "V, F, P", "C, F, P"]}, "feynman-i.32.5": {"dataset_class_key": "FeynmanICh32Eq5", "sympy_eq_str": "6.9862982685735e-16*x0**2*x1**2/pi", "sympy_eq_srepr": "Mul(Float('6.9862982685734964e-16', precision=53), Pow(pi, Integer(-1)), Pow(Symbol('x0', real=True), Integer(2)), Pow(Symbol('x1', real=True), Integer(2)))", "symbols": ["$P$", "$q$", "$a$", "$\\epsilon$", "$c$"], "symbols_descs": ["Radiant energy", "Electric charge", "Magnitude of direction vector", "Vacuum permittivity", "Speed of light"], "si-derived_units": ["$W$", "$C$", "$m/s^2$", "$F/m$", "$m/s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-3}$", "$s \\cdot A$", "$m \\cdot s^{-2}$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m \\cdot s^{-1}$"], "properties": ["V, F, P", "V, F", "V, F, P", "C, F, P", "C, F, P"]}, "feynman-i.34.8": {"dataset_class_key": "FeynmanICh34Eq8", "sympy_eq_str": "x0*x1*x2/x3", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True), Symbol('x2', real=True), Pow(Symbol('x3', real=True), Integer(-1)))", "symbols": ["$\\omega$", "$q$", "$v$", "$B$", "$p$"], "symbols_descs": ["Angular velocity", "Electric charge", "Velocity", "Magnetic field", "Angular momentum"], "si-derived_units": ["$rad/s$", "$C$", "$m/s$", "$T$", "$J \\cdot s$"], "si_units": ["$s^{-1}$", "$s \\cdot A$", "$m \\cdot s^{-1}$", "$kg \\cdot s^{-2} \\cdot A^{-1}$", "$kg \\cdot m^2 \\cdot s^{-1}$"], "properties": ["V, F", "V, F", "V, F", "V, F", "V, F"]}, "feynman-i.34.10": {"dataset_class_key": "FeynmanICh34Eq10", "sympy_eq_str": "x0/(1 - 3.33564095198152e-9*x1)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Pow(Add(Integer(1), Mul(Integer(-1), Float('3.3356409519815204e-9', precision=53), Symbol('x1', real=True))), Integer(-1)))", "symbols": ["$\\omega$", "$\\omega_0$", "$v$", "$c$"], "symbols_descs": ["Frequency of electromagnetic waves", "Frequency of electromagnetic waves", "Velocity", "Speed of light"], "si-derived_units": ["$rad/s$", "$rad/s$", "$m/s$", "$m/s$"], "si_units": ["$s^{-1}$", "$s^{-1}$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F, P", "V, F, P", "V, F", "C, F, P"]}, "feynman-i.34.27": {"dataset_class_key": "FeynmanICh34Eq27", "sympy_eq_str": "3.313e-34*x0/pi", "sympy_eq_srepr": "Mul(Float('3.3129999999999999e-34', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True))", "symbols": ["$W$", "$h$", "$\\omega$"], "symbols_descs": ["Energy", "Planck constant", "Frequency of electromagnetic waves"], "si-derived_units": ["$J$", "$J \\cdot s$", "$1/s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$s^{-1}$"], "properties": ["V, F, P", "C, F, P", "V, F, P"]}, "feynman-i.38.12": {"dataset_class_key": "FeynmanICh38Eq12", "sympy_eq_str": "3.88724918104e-78/(pi*x0*x1**2)", "sympy_eq_srepr": "Mul(Float('3.8872491810399996e-78', precision=53), Pow(pi, Integer(-1)), Pow(Symbol('x0', real=True), Integer(-1)), Pow(Symbol('x1', real=True), Integer(-2)))", "symbols": ["$r$", "$\\epsilon$", "$h$", "$m$", "$q$"], "symbols_descs": ["Bohr radius", "Vacuum permittivity", "Planck constant", "Mass", "Electric charge"], "si-derived_units": ["$m$", "$F/m$", "$J \\cdot s$", "$kg$", "$C$"], "si_units": ["$m$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$kg$", "$s \\cdot A$"], "properties": ["V, F, P", "C, F, P", "C, F, P", "V, F, P", "V, F"]}, "feynman-i.39.10": {"dataset_class_key": "FeynmanICh39Eq10", "sympy_eq_str": "1.5*x0*x1", "sympy_eq_srepr": "Mul(Float('1.5', precision=53), Symbol('x0', real=True), Symbol('x1', real=True))", "symbols": ["$U$", "$P$", "$V$"], "symbols_descs": ["Internal energy", "Pressure", "Volume"], "si-derived_units": ["$J$", "$Pa$", "$m^3$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg \\cdot m^{-1} \\cdot s^{-2}$", "$m^3$"], "properties": ["V, F, P", "V, F, P", "V, F, P"]}, "feynman-i.39.11": {"dataset_class_key": "FeynmanICh39Eq11", "sympy_eq_str": "x1*x2/(x0 - 1)", "sympy_eq_srepr": "Mul(Symbol('x1', real=True), Symbol('x2', real=True), Pow(Add(Symbol('x0', real=True), Integer(-1)), Integer(-1)))", "symbols": ["$U$", "$\\gamma$", "$P$", "$V$"], "symbols_descs": ["Energy", "Heat capacity ratio", "Pressure", "Volume"], "si-derived_units": ["$J$", "$1$", "$Pa$", "$m^3$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$1$", "$kg \\cdot m^{-1} \\cdot s^{-2}$", "$m^3$"], "properties": ["V, F", "V, F, P", "V, F, P", "V, F, P"]}, "feynman-i.43.31": {"dataset_class_key": "FeynmanICh43Eq31", "sympy_eq_str": "1.380649e-23*x0*x1", "sympy_eq_srepr": "Mul(Float('1.3806490000000001e-23', precision=53), Symbol('x0', real=True), Symbol('x1', real=True))", "symbols": ["$D$", "$\\mu$", "$k$", "$T$"], "symbols_descs": ["Diffusion coefficient", "Viscosity", "Boltzmann constant", "Temperature"], "si-derived_units": ["$m^2/s$", "$Pa \\cdot s$", "$J/K$", "$K$"], "si_units": ["$m^2 \\cdot s^{-1}$", "$kg \\cdot m^{-1} \\cdot s^{-1}$", "$kg \\cdot m^2 \\cdot s^{-2} \\cdot K^{-1}$", "$K$"], "properties": ["V, F, P", "V, F, P", "C, F, P", "V, F, P"]}, "feynman-i.43.43": {"dataset_class_key": "FeynmanICh43Eq43", "sympy_eq_str": "1.380649e-23*x1/(x2*(x0 - 1))", "sympy_eq_srepr": "Mul(Float('1.3806490000000001e-23', precision=53), Symbol('x1', real=True), Pow(Symbol('x2', real=True), Integer(-1)), Pow(Add(Symbol('x0', real=True), Integer(-1)), Integer(-1)))", "symbols": ["$\\kappa$", "$\\gamma$", "$k$", "$v$", "$\\sigma_c$"], "symbols_descs": ["Thermal conductivity", "Heat capacity ratio", "Boltzmann constant", "Velocity", "Molecular collision cross section"], "si-derived_units": ["$W/(m \\cdot K)$", "$1$", "$J/K$", "$m/s$", "$m^2$"], "si_units": ["$kg \\cdot m \\cdot s^{-3} \\cdot K^{-1}$", "$1$", "$kg \\cdot m^2 \\cdot s^{-2} \\cdot K^{-1}$", "$m \\cdot s^{-1}$", "$m^2$"], "properties": ["V, F, P", "V, F, P", "C, F, P", "V, F, P", "V, F, P"]}, "feynman-i.48.2": {"dataset_class_key": "FeynmanICh48Eq2", "sympy_eq_str": "8.98755178736818e+16*x0/sqrt(1 - 1.11265005605362e-17*x1**2)", "sympy_eq_srepr": "Mul(Float('89875517873681760.0', precision=53), Symbol('x0', real=True), Pow(Add(Integer(1), Mul(Integer(-1), Float('1.1126500560536185e-17', precision=53), Pow(Symbol('x1', real=True), Integer(2)))), Rational(-1, 2)))", "symbols": ["$E$", "$m$", "$c$", "$v$"], "symbols_descs": ["Energy", "Mass", "Speed of light", "Velocity"], "si-derived_units": ["$J$", "$kg$", "$m/s$", "$m/s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F, P", "V, F, P", "C, F, P", "V, F, P"]}, "feynman-ii.6.11": {"dataset_class_key": "FeynmanIICh6Eq11", "sympy_eq_str": "28235825615.541*x0*cos(x1)/(pi*x2**2)", "sympy_eq_srepr": "Mul(Float('28235825615.541', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x2', real=True), Integer(-2)), cos(Symbol('x1', real=True)))", "symbols": ["$\\phi$", "$\\epsilon$", "$p$", "$\\theta$", "$r$"], "symbols_descs": ["Electric potential", "Vacuum permittivity", "Electric dipole moment", "Angle", "Distance"], "si-derived_units": ["$V$", "$F/m$", "$C \\cdot m$", "$rad$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-3} \\cdot A^{-1}$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m \\cdot s \\cdot A$", "$1$", "$m$"], "properties": ["V, F", "C, F, P", "V, F", "V, F, NN", "V, F, P"]}, "feynman-ii.8.7": {"dataset_class_key": "FeynmanIICh8Eq7", "sympy_eq_str": "16941495369.3246*x0**2/(pi*x1)", "sympy_eq_srepr": "Mul(Float('16941495369.3246', precision=53), Pow(pi, Integer(-1)), Pow(Symbol('x0', real=True), Integer(2)), Pow(Symbol('x1', real=True), Integer(-1)))", "symbols": ["$U$", "$Q$", "$\\epsilon$", "$a$"], "symbols_descs": ["Energy", "Electric charge", "Vacuum permittivity", "Radius"], "si-derived_units": ["$J$", "$C$", "$F/m$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$s \\cdot A$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m$"], "properties": ["V, F", "V, F", "C, F, P", "V, F, P"]}, "feynman-ii.11.3": {"dataset_class_key": "FeynmanIICh11Eq3", "sympy_eq_str": "x0*x1/(x2*(x3**2 - x4**2))", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True), Pow(Symbol('x2', real=True), Integer(-1)), Pow(Add(Pow(Symbol('x3', real=True), Integer(2)), Mul(Integer(-1), Pow(Symbol('x4', real=True), Integer(2)))), Integer(-1)))", "symbols": ["$x$", "$q$", "$E$", "$m$", "$\\omega_0$", "$\\omega$"], "symbols_descs": ["Position", "Electric charge", "Magnitude of electric field", "Mass", "Angular velocity", "Angular velocity"], "si-derived_units": ["$m$", "$C$", "$V/m$", "$kg$", "$rad/s$", "$rad/s$"], "si_units": ["$m$", "$s \\cdot A$", "$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$", "$kg$", "$s^{-1}$", "$s^{-1}$"], "properties": ["V, F", "V, F", "V, F, P", "V, F, P", "V, F", "V, F"]}, "feynman-ii.21.32": {"dataset_class_key": "FeynmanIICh21Eq32", "sympy_eq_str": "28235825615.541*x0/(pi*x1*(1 - 3.33564095198152e-9*x2))", "sympy_eq_srepr": "Mul(Float('28235825615.541', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)), Pow(Add(Integer(1), Mul(Integer(-1), Float('3.3356409519815204e-9', precision=53), Symbol('x2', real=True))), Integer(-1)))", "symbols": ["$\\phi$", "$q$", "$\\epsilon$", "$r$", "$v$", "$c$"], "symbols_descs": ["Electric potential", "Electric charge", "Vacuum permittivity", "Distance", "Velocity", "Speed of light"], "si-derived_units": ["$V$", "$C$", "$F/m$", "$m$", "$m/s$", "$m/s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-3} \\cdot A^{-1}$", "$s \\cdot A$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m$", "$m \\cdot s^{-1}$", "$m \\cdot s^{-1}$"], "properties": ["V, F", "V, F", "C, F, P", "V, F, P", "V, F, P", "C, F, P"]}, "feynman-ii.34.2": {"dataset_class_key": "FeynmanIICh34Eq2", "sympy_eq_str": "x0*x1*x2/2", "sympy_eq_srepr": "Mul(Rational(1, 2), Symbol('x0', real=True), Symbol('x1', real=True), Symbol('x2', real=True))", "symbols": ["$\\mu$", "$q$", "$v$", "$r$"], "symbols_descs": ["Magnetic moment", "Electric charge", "Velocity", "Radius"], "si-derived_units": ["$J/T$", "$C$", "$m/s$", "$m$"], "si_units": ["$m^2 \\cdot A$", "$s \\cdot A$", "$m \\cdot s^{-1}$", "$m$"], "properties": ["V, F", "V, F", "V, F", "V, F, P"]}, "feynman-ii.34.2a": {"dataset_class_key": "FeynmanIICh34Eq2a", "sympy_eq_str": "x0*x1/(2*pi*x2)", "sympy_eq_srepr": "Mul(Rational(1, 2), Pow(pi, Integer(-1)), Symbol('x0', real=True), Symbol('x1', real=True), Pow(Symbol('x2', real=True), Integer(-1)))", "symbols": ["$I$", "$q$", "$v$", "$r$"], "symbols_descs": ["Electric Current", "Electric charge", "Velocity", "Radius"], "si-derived_units": ["$A$", "$C$", "$m/s$", "$m$"], "si_units": ["$A$", "$s \\cdot A$", "$m \\cdot s^{-1}$", "$m$"], "properties": ["V, F", "V, F", "V, F", "V, F, P"]}, "feynman-ii.34.29a": {"dataset_class_key": "FeynmanIICh34Eq29a", "sympy_eq_str": "1.6565e-34*x0/(pi*x1)", "sympy_eq_srepr": "Mul(Float('1.6565e-34', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)))", "symbols": ["$\\mu$", "$q$", "$h$", "$m$"], "symbols_descs": ["Bohr magneton", "Electric charge", "Planck constant", "Mass"], "si-derived_units": ["$J/T$", "$C$", "$J \\cdot s$", "$kg$"], "si_units": ["$m^2 \\cdot A$", "$s \\cdot A$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$kg$"], "properties": ["V, F", "V, F", "C, F, P", "V, F, P"]}, "feynman-ii.37.1": {"dataset_class_key": "FeynmanIICh37Eq1", "sympy_eq_str": "x0*x2*(x1 + 1)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x2', real=True), Add(Symbol('x1', real=True), Integer(1)))", "symbols": ["$E$", "$\\mu$", "$\\chi$", "$B$"], "symbols_descs": ["Energy of magnetic field", "Magnetic moment", "Volume magnetic susceptibility", "Magnetic field strength"], "si-derived_units": ["$J$", "$J/T$", "$1$", "$T$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$m^2 \\cdot A$", "$1$", "$kg \\cdot s^{-2} \\cdot A^{-1}$"], "properties": ["V, F", "V, F", "V, F", "V, F"]}, "feynman-iii.4.32": {"dataset_class_key": "FeynmanIIICh4Eq32", "sympy_eq_str": "1/(exp(2.39959613196403e-11*x0/(pi*x1)) - 1)", "sympy_eq_srepr": "Pow(Add(exp(Mul(Float('2.3995961319640253e-11', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)))), Integer(-1)), Integer(-1))", "symbols": ["$n$", "$h$", "$\\omega$", "$k$", "$T$"], "symbols_descs": ["Average number of photons", "Planck constant", "Frequency", "Boltzmann constant", "Temperature"], "si-derived_units": ["$1$", "$J \\cdot s$", "$rad/s$", "$J/K$", "$K$"], "si_units": ["$1$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$s^{-1}$", "$kg \\cdot m^2 \\cdot s^{-2} \\cdot K^{-1}$", "$K$"], "properties": ["V, F, P", "C, F, P", "V, F, P", "C, F, P", "V, F, P"]}, "feynman-iii.8.54": {"dataset_class_key": "FeynmanIIICh8Eq54", "sympy_eq_str": "sin(3018412315122245888053292650463232*pi*x0*x1)**2", "sympy_eq_srepr": "Pow(sin(Mul(Integer(3018412315122245888053292650463232), pi, Symbol('x0', real=True), Symbol('x1', real=True))), Integer(2))", "symbols": ["$|C|^2$", "$A$", "$t$", "$h$"], "symbols_descs": ["Probability", "Energy", "Time", "Planck constant"], "si-derived_units": ["$1$", "$J$", "$s$", "$J \\cdot s$"], "si_units": ["$1$", "$kg \\cdot m^2 \\cdot s^{-2}$", "$s$", "$kg \\cdot m^2 \\cdot s^{-1}$"], "properties": ["V, F, NN", "V, F", "V, F, NN", "C, F, P"]}, "feynman-iii.13.18": {"dataset_class_key": "FeynmanIIICh13Eq18", "sympy_eq_str": "6.03682463024449e+33*pi*x0*x1**2*x2", "sympy_eq_srepr": "Mul(Float('6.0368246302444918e+33', precision=53), pi, Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(2)), Symbol('x2', real=True))", "symbols": ["$v$", "$A$", "$b$", "$k$", "$h$"], "symbols_descs": ["Speed of the waves", "Energy", "Lattice constant", "Wavenumber", "Planck constant"], "si-derived_units": ["$m/s$", "$J$", "$m$", "$1/m$", "$J \\cdot s$"], "si_units": ["$m \\cdot s^{-1}$", "$kg \\cdot m^2 \\cdot s^{-2}$", "$m$", "$m^{-1}$", "$kg \\cdot m^2 \\cdot s^{-1}$"], "properties": ["V, F", "V, F", "V, F, P", "V, F, P", "C, F, P"]}, "feynman-iii.14.14": {"dataset_class_key": "FeynmanIIICh14Eq14", "sympy_eq_str": "x0*(exp(7.24297051603992e+22*x1*x2/x3) - 1)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Add(exp(Mul(Float('7.2429705160399199e+22', precision=53), Symbol('x1', real=True), Symbol('x2', real=True), Pow(Symbol('x3', real=True), Integer(-1)))), Integer(-1)))", "symbols": ["$I$", "$I_0$", "$q$", "$\\Delta V$", "$\\kappa$", "$T$"], "symbols_descs": ["Electric Current", "Electric current", "Electric charge", "Voltage", "Boltzmann constant", "Temperature"], "si-derived_units": ["$A$", "$A$", "$C$", "$V$", "$J/K$", "$K$"], "si_units": ["$A$", "$A$", "$s \\cdot A$", "$kg \\cdot m^2 \\cdot s^{-3} \\cdot A^{-1}$", "$kg \\cdot m^2 \\cdot s^{-2} \\cdot K^{-1}$", "$K$"], "properties": ["V, F", "V, F", "V, F, P", "V, F", "C, F, P", "V, F, P"]}, "feynman-iii.15.12": {"dataset_class_key": "FeynmanIIICh15Eq12", "sympy_eq_str": "2*x0*(1 - cos(x1*x2))", "sympy_eq_srepr": "Mul(Integer(2), Symbol('x0', real=True), Add(Integer(1), Mul(Integer(-1), cos(Mul(Symbol('x1', real=True), Symbol('x2', real=True))))))", "symbols": ["$E$", "$A$", "$k$", "$d$"], "symbols_descs": ["Energy", "Amplitude", "Propagation coefficient", "Lattice constant"], "si-derived_units": ["$J$", "$J$", "$1/m$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg \\cdot m^2 \\cdot s^{-2}$", "$m^{-1}$", "$m$"], "properties": ["V, F, P", "V, F, P", "V, F, P", "V, F, P"]}, "feynman-iii.15.14": {"dataset_class_key": "FeynmanIIICh15Eq14", "sympy_eq_str": "5.4879845e-68/(pi**2*x0*x1**2)", "sympy_eq_srepr": "Mul(Float('5.4879844999999998e-68', precision=53), Pow(pi, Integer(-2)), Pow(Symbol('x0', real=True), Integer(-1)), Pow(Symbol('x1', real=True), Integer(-2)))", "symbols": ["$m$", "$h$", "$A$", "$b$"], "symbols_descs": ["Effective mass", "Planck constant", "Amplitude", "Lattice constant"], "si-derived_units": ["$kg$", "$J \\cdot s$", "$m/s$", "$m$"], "si_units": ["$kg$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$m \\cdot s^{-1}$", "$m$"], "properties": ["V, F, P", "C, F, P", "V, F, P", "V, F, P"]}, "feynman-iii.17.37": {"dataset_class_key": "FeynmanIIICh17Eq37", "sympy_eq_str": "x0*(x1*cos(x2) + 1)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Add(Mul(Symbol('x1', real=True), cos(Symbol('x2', real=True))), Integer(1)))", "symbols": ["$f$", "$\\beta$", "$\\alpha$", "$\\theta$"], "symbols_descs": ["Distribution", "Variable", "Variable", "Angle"], "si-derived_units": ["$1$", "$1$", "$1$", "$rad$"], "si_units": ["$1$", "$1$", "$1$", "$1$"], "properties": ["V, F", "V, F, P", "V, F", "V, F, NN"]}, "feynman-iii.19.51": {"dataset_class_key": "FeynmanIIICh19Eq51", "sympy_eq_str": "-3.63185176721637e+87*x0*x1**4/x2**2", "sympy_eq_srepr": "Mul(Integer(-1), Float('3.6318517672163677e+87', precision=53), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(4)), Pow(Symbol('x2', real=True), Integer(-2)))", "symbols": ["$E$", "$m$", "$q$", "$\\epsilon$", "$h$", "$n$"], "symbols_descs": ["Energy", "Mass", "Electric charge", "Vacuum permittivity", "Planck constant", "Number of protons"], "si-derived_units": ["$J$", "$kg$", "$C$", "$F/m$", "$J \\cdot s$", "$1$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg$", "$s \\cdot A$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$1$"], "properties": ["V, F, P", "V, F, P", "V, F", "C, F, P", "C, F, P", "V, I,P"]}, "feynman-bonus.8": {"dataset_class_key": "FeynmanBonus8", "sympy_eq_str": "x0/(12214328760283.5*x0*(1 - cos(x1)) + 1)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Pow(Add(Mul(Float('12214328760283.518', precision=53), Symbol('x0', real=True), Add(Integer(1), Mul(Integer(-1), cos(Symbol('x1', real=True))))), Integer(1)), Integer(-1)))", "symbols": ["$U$", "$E$", "$m$", "$c$", "$\\theta$"], "symbols_descs": ["Energy", "Electromagnetic energy", "Electron mass", "Speed of light", "Incidence angle"], "si-derived_units": ["$J$", "$J$", "$kg$", "$m/s$", "$rad$"], "si_units": ["$J$", "$kg \\cdot m^2 \\cdot s^{-2}$", "$kg$", "$m \\cdot s^{-1}$", "$1$"], "properties": ["V, F, P", "V, F, P", "C, F, P", "C, F, P", "V, F"]}, "feynman-bonus.18": {"dataset_class_key": "FeynmanBonus18", "sympy_eq_str": "5618566741.08146*(8.98755178736818e+16*x0/x1**2 + x2**2)/pi", "sympy_eq_srepr": "Mul(Float('5618566741.0814629', precision=53), Pow(pi, Integer(-1)), Add(Mul(Float('89875517873681760.0', precision=53), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-2))), Pow(Symbol('x2', real=True), Integer(2))))", "symbols": ["$\\rho$", "$G$", "$c$", "$k_\\text{f}$", "$a_\\text{f}$", "$H$"], "symbols_descs": ["Density", "Gravitational constant", "Speed of light", "Curvature of the Universe", "Distance", "Hubble's constant"], "si-derived_units": ["$kg/m^3$", "$m^3 \\cdot kg^{-1} \\cdot s^{-2}$", "$m/s$", "$1/m^2$", "$m$", "$1/s$"], "si_units": ["$kg \\cdot m^{-3}$", "$kg^{-1} \\cdot m^3 \\cdot s^{-2}$", "$m \\cdot s^{-1}$", "$m^{-2}$", "$m$", "$s^{-1}$"], "properties": ["V, F", "C, F, P", "C, F, P", "V, F", "V, F, P", "V, F"]}} |