Datasets:

yoshitomo-matsubara
/

srsd-feynman_easy

{"feynman-i.12.1": {"dataset_class_key": "FeynmanICh12Eq1", "sympy_eq_str": "x0*x1", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True))", "symbols": ["$F$", "$\\mu$", "$N_\\text{n}$"], "symbols_descs": ["Force of friction", "Coefficient of friction", "Normal force"], "si-derived_units": ["$N$", "$1$", "$N$"], "si_units": ["$kg \\cdot m \\cdot s^{-2}$", "$1$", "$kg \\cdot m \\cdot s^{-2}$"], "properties": ["V, F, P", "V, F, P", "V, F, P"]}, "feynman-i.12.4": {"dataset_class_key": "FeynmanICh12Eq4", "sympy_eq_str": "28235825615.541*x0/(pi*x1**2)", "sympy_eq_srepr": "Mul(Float('28235825615.541', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-2)))", "symbols": ["$E$", "$q_1$", "$r$", "$\\epsilon$"], "symbols_descs": ["Magnitude of electric field", "Electric charge", "Distance", "Vacuum permittivity"], "si-derived_units": ["$V/m$", "$C$", "$m$", "$F/m$"], "si_units": ["$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$", "$s \\cdot A$", "$m$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$"], "properties": ["V, F", "V, F", "V, F, P", "C, F, P"]}, "feynman-i.12.5": {"dataset_class_key": "FeynmanICh12Eq5", "sympy_eq_str": "x0*x1", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True))", "symbols": ["$F$", "$q_2$", "$E$"], "symbols_descs": ["Force", "Electric charge", "Electric field"], "si-derived_units": ["$N$", "$C$", "$V/m$"], "si_units": ["$kg \\cdot m \\cdot s^{-2}$", "$s \\cdot A$", "$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$"], "properties": ["V, F", "V, F", "V, F"]}, "feynman-i.14.3": {"dataset_class_key": "FeynmanICh14Eq3", "sympy_eq_str": "9.80665*x0*x1", "sympy_eq_srepr": "Mul(Float('9.8066499999999994', precision=53), Symbol('x0', real=True), Symbol('x1', real=True))", "symbols": ["$U$", "$m$", "$g$", "$z$"], "symbols_descs": ["Potential energy", "Mass", "Gravitational acceleration", "Height"], "si-derived_units": ["$J$", "$kg$", "$m/s^2$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg$", "$m \\cdot s^{-2}$", "$m$"], "properties": ["V, F", "V, F, P", "C, F, P", "V, F"]}, "feynman-i.14.4": {"dataset_class_key": "FeynmanICh14Eq4", "sympy_eq_str": "0.5*x0*x1**2", "sympy_eq_srepr": "Mul(Float('0.5', precision=53), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(2)))", "symbols": ["$U$", "$k_\\text{spring}$", "$x$"], "symbols_descs": ["Elastic energy", "Spring constant", "Position"], "si-derived_units": ["$J$", "$N/m$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg \\cdot s^{-2}$", "$m$"], "properties": ["V, F, P", "V, F, P", "V, F"]}, "feynman-i.18.12": {"dataset_class_key": "FeynmanICh18Eq12", "sympy_eq_str": "x0*x1*sin(x2)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True), sin(Symbol('x2', real=True)))", "symbols": ["$\\tau$", "$r$", "$F$", "$\\theta$"], "symbols_descs": ["Torque", "Distance", "Force", "Angle"], "si-derived_units": ["$N \\cdot m$", "$m$", "$N$", "$rad$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$m$", "$kg \\cdot m \\cdot s^{-2}$", "$1$"], "properties": ["V, F", "V, F, P", "V, F, P", "V, F, NN"]}, "feynman-i.18.16": {"dataset_class_key": "FeynmanICh18Eq16", "sympy_eq_str": "x0*x1*x2*sin(x3)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x1', real=True), Symbol('x2', real=True), sin(Symbol('x3', real=True)))", "symbols": ["$L$", "$m$", "$r$", "$v$", "$\\theta$"], "symbols_descs": ["Angular momentum", "Mass", "Distance", "Velocity", "Angle"], "si-derived_units": ["$kg \\cdot m^2/s$", "$kg$", "$m$", "$m/s$", "$rad$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-1}$", "$kg$", "$m$", "$m \\cdot s^{-1}$", "$1$"], "properties": ["V, F", "V, F, P", "V, F, P", "V, F, P", "V, F, NN"]}, "feynman-i.25.13": {"dataset_class_key": "FeynmanICh25Eq13", "sympy_eq_str": "x0/x1", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)))", "symbols": ["$V$", "$q$", "$C$"], "symbols_descs": ["Voltage", "Electric charge", "Electrostatic Capacitance"], "si-derived_units": ["$V$", "$C$", "$F$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-3} \\cdot A^{-1}$", "$s \\cdot A$", "$kg^{-1} \\cdot m^{-2} \\cdot s^4 \\cdot A^2$"], "properties": ["V, F", "V, F", "V, F, P"]}, "feynman-i.26.2": {"dataset_class_key": "FeynmanICh26Eq2", "sympy_eq_str": "sin(x0)/sin(x1)", "sympy_eq_srepr": "Mul(sin(Symbol('x0', real=True)), Pow(sin(Symbol('x1', real=True)), Integer(-1)))", "symbols": ["$n$", "$\\theta_1$", "$\\theta_2$"], "symbols_descs": ["Relative refractive index", "Refraction angle 1", "Refraction angle 2"], "si-derived_units": ["$1$", "$rad$", "$rad$"], "si_units": ["$1$", "$1$", "$1$"], "properties": ["V, F, P", "V, F, NN", "V, F, NN"]}, "feynman-i.27.6": {"dataset_class_key": "FeynmanICh27Eq6", "sympy_eq_str": "1/(x1/x2 + 1/x0)", "sympy_eq_srepr": "Pow(Add(Mul(Symbol('x1', real=True), Pow(Symbol('x2', real=True), Integer(-1))), Pow(Symbol('x0', real=True), Integer(-1))), Integer(-1))", "symbols": ["$f$", "$d_1$", "$n$", "$d_2$"], "symbols_descs": ["Focal length", "Distance", "Refractive index", "Distance"], "si-derived_units": ["$m$", "$m$", "$1$", "$m$"], "si_units": ["$m$", "$m$", "$1$", "$m$"], "properties": ["V, F, P", "V, F, P", "V, F, P,", "V, F, P"]}, "feynman-i.30.5": {"dataset_class_key": "FeynmanICh30Eq5", "sympy_eq_str": "x0/(x1*sin(x2))", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)), Pow(sin(Symbol('x2', real=True)), Integer(-1)))", "symbols": ["$d$", "$\\lambda$", "$n$", "$\\theta$"], "symbols_descs": ["Interplanar distance", "Wavelength of X-ray", "Number of phase difference", "Incidence/Reflection angle"], "si-derived_units": ["$m$", "$m$", "$1$", "$rad$"], "si_units": ["$m$", "$m$", "$1$", "$1$"], "properties": ["V, F, P", "V, F, P", "V, I, P", "V, F, NN"]}, "feynman-i.43.16": {"dataset_class_key": "FeynmanICh43Eq16", "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": ["$v$", "$\\mu$", "$q$", "$V$", "$d$"], "symbols_descs": ["Velocity", "Ionic conductivity", "Electric charge of ions", "Voltage", "Distance"], "si-derived_units": ["$m/s$", "$s/kg$", "$C$", "$V$", "$m$"], "si_units": ["$m \\cdot s^{-1}$", "$kg^{-1} \\cdot s$", "$s \\cdot A$", "$kg \\cdot m^2 \\cdot s^{-3} \\cdot A^{-1}$", "$m$"], "properties": ["V, F", "V, F", "V, F", "V, F", "V, F, P"]}, "feynman-i.47.23": {"dataset_class_key": "FeynmanICh47Eq23", "sympy_eq_str": "sqrt(x0*x1/x2)", "sympy_eq_srepr": "Pow(Mul(Symbol('x0', real=True), Symbol('x1', real=True), Pow(Symbol('x2', real=True), Integer(-1))), Rational(1, 2))", "symbols": ["$c$", "$\\gamma$", "$P$", "$\\rho$"], "symbols_descs": ["Velocity of sound", "Heat capacity ratio", "Atmospheric pressure", "Density of air"], "si-derived_units": ["$m/s$", "$1$", "$Pa$", "$kg \\cdot m^{-3}$"], "si_units": ["$m \\cdot s^{-1}$", "$1$", "$kg \\cdot m^{-1} \\cdot s^{-2}$", "$kg \\cdot m^{-3}$"], "properties": ["V, F, P", "V, F, P", "V, F, P", "V, F, P"]}, "feynman-ii.2.42": {"dataset_class_key": "FeynmanIICh2Eq42", "sympy_eq_str": "x0*x3*(x1 - x2)/x4", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Symbol('x3', real=True), Pow(Symbol('x4', real=True), Integer(-1)), Add(Symbol('x1', real=True), Mul(Integer(-1), Symbol('x2', real=True))))", "symbols": ["$J$", "$\\kappa$", "$T_2$", "$T_1$", "$A$", "$d$"], "symbols_descs": ["Rate of heat flow", "Thermal conductivity", "Temperature", "Temperature", "Area", "Length"], "si-derived_units": ["$W$", "$W/(m \\cdot K)$", "$K$", "$K$", "$m^2$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-3}$", "$kg \\cdot m \\cdot s^{-3} \\cdot K^{-1}$", "$K$", "$K$", "$m^2$", "$m$"], "properties": ["V, F", "V, F, P", "V, F, P", "V, F, P", "V, F, P", "V, F, P"]}, "feynman-ii.3.24": {"dataset_class_key": "FeynmanIICh3Eq24", "sympy_eq_str": "x0/(4*pi*x1**2)", "sympy_eq_srepr": "Mul(Rational(1, 4), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-2)))", "symbols": ["$h$", "$W$", "$r$"], "symbols_descs": ["Heat flux", "Work", "Distance"], "si-derived_units": ["$J/m^2$", "$J$", "$m$"], "si_units": ["$kg \\cdot s^{-2}$", "$kg \\cdot m^2 \\cdot s^{-2}$", "$m$"], "properties": ["V, F", "V, F", "V, F, P"]}, "feynman-ii.4.23": {"dataset_class_key": "FeynmanIICh4Eq23", "sympy_eq_str": "28235825615.541*x0/(pi*x1)", "sympy_eq_srepr": "Mul(Float('28235825615.541', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)))", "symbols": ["$\\phi$", "$q$", "$\\epsilon$", "$r$"], "symbols_descs": ["Electric potential", "Electric charge", "Vacuum permittivity", "Distance"], "si-derived_units": ["$V$", "$C$", "$F/m$", "$m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-3} \\cdot A^{-1}$", "$s \\cdot A$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m$"], "properties": ["V, F", "V, F", "C, F, P", "V, F, P"]}, "feynman-ii.8.31": {"dataset_class_key": "FeynmanIICh8Eq31", "sympy_eq_str": "4.427e-12*x0**2", "sympy_eq_srepr": "Mul(Float('4.4269999999999996e-12', precision=53), Pow(Symbol('x0', real=True), Integer(2)))", "symbols": ["$u$", "$\\epsilon$", "$E$"], "symbols_descs": ["Energy", "Vacuum permittivity", "Magnitude of electric field"], "si-derived_units": ["$J$", "$F/m$", "$V/m$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$"], "properties": ["V, F, P", "C, F, P", "V, F, P"]}, "feynman-ii.10.9": {"dataset_class_key": "FeynmanIICh10Eq9", "sympy_eq_str": "112943302462.164*x0/(x1 + 1)", "sympy_eq_srepr": "Mul(Float('112943302462.164', precision=53), Symbol('x0', real=True), Pow(Add(Symbol('x1', real=True), Integer(1)), Integer(-1)))", "symbols": ["$E$", "$\\sigma_\\text{free}$", "$\\epsilon$", "$\\chi$"], "symbols_descs": ["Electric field", "Surface charge", "Vacuum permittivity", "Electric susceptibility"], "si-derived_units": ["$V/m$", "$C/m^2$", "$F/m$", "$1$"], "si_units": ["$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$", "$m \\cdot ^{-2} \\cdot s \\cdot A$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$1$"], "properties": ["V, F", "V, F", "C, F, P", "V, F, P"]}, "feynman-ii.13.17": {"dataset_class_key": "FeynmanIICh13Eq17", "sympy_eq_str": "6.28331859077038e-7*x0/(pi*x1)", "sympy_eq_srepr": "Mul(Float('6.2833185907703779e-7', precision=53), Pow(pi, Integer(-1)), Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)))", "symbols": ["$B$", "$\\epsilon$", "$c$", "$I$", "$r$"], "symbols_descs": ["Magnitude of the magnetic field", "Vacuum permittivity", "Speed of light", "Electric current", "Radius"], "si-derived_units": ["$T$", "$F/m$", "$m/s$", "$A$", "$m$"], "si_units": ["$kg \\cdot s^{-2} \\cdot A^{-1}$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m \\cdot s^{-1}$", "$A$", "$m$"], "properties": ["V, F", "C, F, P", "C, F, P", "V, F", "V, F, P"]}, "feynman-ii.15.4": {"dataset_class_key": "FeynmanIICh15Eq4", "sympy_eq_str": "-x0*x1*cos(x2)", "sympy_eq_srepr": "Mul(Integer(-1), Symbol('x0', real=True), Symbol('x1', real=True), cos(Symbol('x2', real=True)))", "symbols": ["$U$", "$\\mu$", "$B$", "$\\theta$"], "symbols_descs": ["Energy from magnetic field", "Magnetic dipole moment", "Magnetic field strength", "Angle"], "si-derived_units": ["$J$", "$J/T$", "$T$", "$rad$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$m^2 \\cdot A$", "$kg \\cdot s^{-2} \\cdot A^{-1}$", "$1$"], "properties": ["V, F", "V, F", "V, F", "V, F, NN"]}, "feynman-ii.15.5": {"dataset_class_key": "FeynmanIICh15Eq5", "sympy_eq_str": "-x0*x1*cos(x2)", "sympy_eq_srepr": "Mul(Integer(-1), Symbol('x0', real=True), Symbol('x1', real=True), cos(Symbol('x2', real=True)))", "symbols": ["$U$", "$p$", "$E$", "$\\theta$"], "symbols_descs": ["Energy", "Electric dipole moment", "Magnitude of electric field", "Angle"], "si-derived_units": ["$J$", "$C \\cdot m$", "$V/m$", "$rad$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$m \\cdot s \\cdot A$", "$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$", "$1$"], "properties": ["V, F", "V, F", "V, F", "V, F, NN"]}, "feynman-ii.27.16": {"dataset_class_key": "FeynmanIICh27Eq16", "sympy_eq_str": "0.002654362423132*x0**2", "sympy_eq_srepr": "Mul(Float('0.0026543624231319999', precision=53), Pow(Symbol('x0', real=True), Integer(2)))", "symbols": ["$L$", "$\\epsilon$", "$c$", "$E$"], "symbols_descs": ["Radiance", "Vacuum permittivity", "Speed of light", "Magnitude of electric field"], "si-derived_units": ["$W/(sr \\cdot m^2)$", "$F/m$", "$m/s$", "$V/m$"], "si_units": ["$kg \\cdot s^{-3}$", "$kg^{-1} \\cdot m^{-3} \\cdot s^4 \\cdot A^2$", "$m \\cdot s^{-1}$", "$kg \\cdot m \\cdot s^{-3} \\cdot A^{-1}$"], "properties": ["V, F", "C, F, P", "C, F, P", "V, F, P"]}, "feynman-ii.27.18": {"dataset_class_key": "FeynmanIICh27Eq18", "sympy_eq_str": "8.854e-12*x0**2", "sympy_eq_srepr": "Mul(Float('8.8539999999999992e-12', precision=53), Pow(Symbol('x0', real=True), 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P", "V, F", "V, F", "V, F", "V, F, P"]}, "feynman-ii.34.29b": {"dataset_class_key": "FeynmanIICh34Eq29b", "sympy_eq_str": "27992786230.9085*pi*x0*x1*x2", "sympy_eq_srepr": "Mul(Float('27992786230.908546', precision=53), pi, Symbol('x0', real=True), Symbol('x1', real=True), Symbol('x2', real=True))", "symbols": ["$U$", "$g$", "$\\mu$", "$B$", "$J_z$", "$h$"], "symbols_descs": ["Energy", "g-factor", "Bohr magneton", "Magnetic field strength", "Element of angular momentum", "Planck constant"], "si-derived_units": ["$J$", "$1$", "$J/T$", "$T$", "$J \\cdot s$", "$J \\cdot s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-2}$", "$1$", "$m^2 \\cdot A$", "$kg \\cdot s^{-2} \\cdot A^{-1}$", "$kg \\cdot m^2 \\cdot s^{-1}$", "$kg \\cdot m^2 \\cdot s^{-1}$"], "properties": ["V, F", "V, F", "C, F, P", "V, F", "V, F", "C, F, P"]}, "feynman-ii.38.3": {"dataset_class_key": "FeynmanIICh38Eq3", "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": ["$F$", "$Y$", "$A$", "$\\delta l$", "$l$"], "symbols_descs": ["Force", "Young's modulus", "Area", "Displacement", "Length"], "si-derived_units": ["$N$", "$Pa$", "$m^2$", "$m$", "$m$"], "si_units": ["$kg \\cdot m \\cdot s^{-2}$", "$kg \\cdot m^{-1} \\cdot s^{-2}$", "$m^2$", "$m$", "$m$"], "properties": ["V, F", "V, F, P", "V, F, P", "V, F", "V, F, P"]}, "feynman-ii.38.14": {"dataset_class_key": "FeynmanIICh38Eq14", "sympy_eq_str": "x0/(2*x1 + 2)", "sympy_eq_srepr": "Mul(Symbol('x0', real=True), Pow(Add(Mul(Integer(2), Symbol('x1', real=True)), Integer(2)), Integer(-1)))", "symbols": ["$\\mu$", "$Y$", "$\\sigma$"], "symbols_descs": ["Rigidity modulus", "Young's modulus", "Poisson coefficient"], "si-derived_units": ["$Pa$", "$Pa$", "$1$"], "si_units": ["$kg \\cdot m^{-1} \\cdot s^{-2}$", "$kg \\cdot m^{-1} \\cdot s^{-2}$", "$1$"], "properties": ["V, F, P", "V, F, P", "V, F, P"]}, "feynman-iii.7.38": {"dataset_class_key": "FeynmanIIICh7Eq38", "sympy_eq_str": "6.03682463024449e+33*pi*x0*x1", "sympy_eq_srepr": "Mul(Float('6.0368246302444918e+33', precision=53), pi, Symbol('x0', real=True), Symbol('x1', real=True))", "symbols": ["$\\omega$", "$\\mu$", "$B$", "$h$"], "symbols_descs": ["Precession frequency", "Magnetic moment", "Magnetic flux density", "Planck constant"], "si-derived_units": ["$rad$", "$J/T$", "$T$", "$J \\cdot s$"], "si_units": ["$1$", "$m^2 \\cdot A$", "$kg \\cdot s^{-2} \\cdot A^{-1}$", "$kg \\cdot m^2 \\cdot s^{-1}$"], "properties": ["V, F", "V, F", "V, F", "C, F, P"]}, "feynman-iii.12.43": {"dataset_class_key": "FeynmanIIICh12Eq43", "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": ["$J$", "$m$", "$h$"], "symbols_descs": ["Spin magnetic moment", "Spin state", "Planck constant"], "si-derived_units": ["$J \\cdot s$", "$1$", "$J \\cdot s$"], "si_units": ["$kg \\cdot m^2 \\cdot s^{-1}$", "$1$", "$kg \\cdot m^2 \\cdot s^{-1}$"], "properties": ["V, F, P", "V, I, NN", "C, F, P"]}, "feynman-iii.15.27": {"dataset_class_key": "FeynmanIIICh15Eq27", "sympy_eq_str": "2*pi*x0/(x1*x2)", "sympy_eq_srepr": "Mul(Integer(2), pi, Symbol('x0', real=True), Pow(Symbol('x1', real=True), Integer(-1)), Pow(Symbol('x2', real=True), Integer(-1)))", "symbols": ["$k$", "$s$", "$N$", "$b$"], "symbols_descs": ["Wavenumber", "Parameter of state", "Number of atoms", "Lattice constant"], "si-derived_units": ["$m^{-1}$", "$1$", "$1$", "$m$"], "si_units": ["$m^{-1}$", "$1$", "$1$", "$m$"], "properties": ["V, F", "V, I", "V, I, P", "V, F, P"]}}