remove equations with repetitive skeletons

equations.jsonl

@@ -1,31 +1,21 @@
-{"name": "II.24.17_1_0", "symbols": ["c", "k", "omega", "d"], "symbol_descs": ["the speed of the wave", "the wave number", "the angular frequency", "the diameter or thickness of the waveguide or medium"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-d*omega*sqrt(1/(d**2*k**2 + pi**2))", "symbol_ranges": [null, [1.5988699087132785, 5.868821422051696], [4.0, 6.0], [2.0, 4.0]]}
 {"name": "II.6.15b_1_0", "symbols": ["p_d", "Ef", "epsilon", "theta", "r"], "symbol_descs": ["the dipole moment", "the electric field", "the electric constant or permittivity of the medium", "the angle between the dipole axis and the position vector", "the distance from the dipole to the point where the electric field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "8*pi*Ef*epsilon*r**3/(3*sin(2*theta))", "symbol_ranges": [null, [-0.17796760168839998, 0.103798930323723], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "II.24.17_0_0", "symbols": ["omega", "k", "c", "d"], "symbol_descs": ["the angular frequency", "the wave number", "the speed of the wave", "the diameter or thickness of the waveguide or medium"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-c*sqrt(d**2*k**2 + pi**2)/d", "symbol_ranges": [null, [1.5988699087132785, 5.868821422051696], [1.0, 2.0], [2.0, 4.0]]}
-{"name": "I.16.6_0_0", "symbols": ["c", "v1", "v", "u"], "symbol_descs": ["the speed of light", "the resultant velocity of two objects after a relativistic addition", "the velocity of one of the objects", "the velocity of the other object"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-sqrt(u*v*v1/(u + v - v1))", "symbol_ranges": [null, [0.40069679605367, 4.975182551848956], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.6.15a_1_0", "symbols": ["p_d", "Ef", "epsilon", "r", "x", "y", "z"], "symbol_descs": ["the electric dipole moment", "the electric field strength at a point", "the electric constant (permittivity of free space)", "the distance from the dipole to the point where the field is being measured", "the x-coordinate of the point where the field is being measured", "the y-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "4*pi*Ef*epsilon*r**5/(3*z*sqrt(x**2 + y**2))", "symbol_ranges": [null, [0.0011930972073398915, 3.654440850903496], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "I.32.17_5_2", "symbols": ["omega_0", "Pwr", "epsilon", "c", "Ef", "r", "omega"], "symbol_descs": ["the natural frequency of the oscillator or resonant frequency", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the frequency of the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "-sqrt(3)*sqrt(2*sqrt(3)*sqrt(pi)*Ef*omega**2*r*sqrt(Pwr*c*epsilon)/Pwr + 3*omega**2)/3", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0]]}
-{"name": "I.37.4_0_0", "symbols": ["I1", "Int", "I2", "delta"], "symbol_descs": ["the intensity of the first wave source", "the resultant intensity of two wave sources", "the intensity of the second wave source", "the phase difference between the two wave sources"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*I2*cos(delta)**2 + I2 + Int - 2*sqrt(I2*(I2*cos(delta)**2 + I2 + Int))*cos(delta)", "symbol_ranges": [null, [0.0027163447847069477, 13.60662800081353], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.36.38_1_0", "symbols": ["H", "f", "mom", "kb", "T", "alpha", "epsilon", "c", "M"], "symbol_descs": ["the magnetic field strength", "the resultant value of the function", "the momentum of an object or particle", "the Boltzmann constant", "the temperature in Kelvin", "the polarizability of a medium or molecule", "the electric permittivity of a medium", "the speed of light in vacuum", "the magnetization of a material"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "M*alpha/(c**2*epsilon) + T*f*kb/mom", "symbol_ranges": [null, [0.1886648613106507, 11.236770740165767], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.15.5_0_0", "symbols": ["p_d", "E_n", "Ef", "theta"], "symbol_descs": ["the dipole moment per unit area", "the normal component of the electric field at the surface", "the external electric field", "the angle between the dipole moment and the external electric field"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-E_n/(Ef*cos(theta))", "symbol_ranges": [null, [-10.57903779497229, 23.62245117792713], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.48.2_1_0", "symbols": ["v", "E_n", "m", "c"], "symbol_descs": ["the object's velocity", "the total energy of an object", "the relativistic mass of an object", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-c*sqrt(1 - c**4*m**2/E_n**2)", "symbol_ranges": [null, [12.33980490912196, 500.70511898733184], [1.0, 5.0], [3.0, 10.0]]}
 {"name": "II.35.21_2_1", "symbols": ["B", "M", "n_rho", "mom", "kb", "T"], "symbol_descs": ["the magnetic field strength", "the magnetization of a material", "the density of magnetic moments", "the magnetic moment of a particle", "the Boltzmann constant", "the temperature in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "T*kb*log(sqrt(-(M + mom*n_rho)/(M - mom*n_rho)))/mom", "symbol_ranges": [null, [0.1057610677641476, 23.521766000937422], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.35.18_0_0", "symbols": ["n_0", "n", "kb", "T", "mom", "B"], "symbol_descs": ["the number of particles at equilibrium", "the number of particles in a given state", "the Boltzmann constant", "the temperature of the system", "the magnetic moment of a particle", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "n*exp(B*mom/(T*kb)) + n*exp(-B*mom/(T*kb))", "symbol_ranges": [null, [0.006709112588478311, 1.4581675020057816], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "I.24.6_2_0", "symbols": ["omega_0", "E_n", "m", "omega", "x"], "symbol_descs": ["the natural angular frequency", "the quantum mechanical energy of the nth state", "the mass of the object", "the angular frequency of the perturbation", "the displacement from the equilibrium position"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(4*E_n/m - omega**2*x**2)/x", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "III.15.14_1_0", "symbols": ["E_n", "m", "h", "d"], "symbol_descs": ["the nth energy level of the system", "the mass of a particle in a quantum mechanical system", "the Planck constant", "the width or distance between the boundaries of the quantum well"], "symbol_properties": ["O", "V", "V", "V"], "expression": "h**2/(8*pi**2*d**2*m)", "symbol_ranges": [null, [0.00013405297967021765, 0.16840723156123433], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.6.15a_2_0", "symbols": ["r", "Ef", "epsilon", "p_d", "x", "y", "z"], "symbol_descs": ["the distance from the dipole to the point where the field is being measured", "the electric field strength at a point", "the electric constant (permittivity of free space)", "the electric dipole moment", "the x-coordinate of the point where the field is being measured", "the y-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "2**(3/5)*3**(1/5)*(p_d*z*sqrt(x**2 + y**2)/(Ef*epsilon))**(1/5)/(2*pi**(1/5))", "symbol_ranges": [null, [0.0011930972073398915, 3.654440850903496], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.13.23_1_0", "symbols": ["v", "rho_c", "rho_c_0", "c"], "symbol_descs": ["the velocity of the object or frame of reference", "the critical density of the universe at a given velocity", "the critical density of the universe at rest", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-c*sqrt(1 - rho_c_0**2/rho_c**2)", "symbol_ranges": [null, [1.0171198727704565, 5.971656782546941], [1.0, 5.0], [3.0, 10.0]]}
 {"name": "I.24.6_3_1", "symbols": ["x", "E_n", "m", "omega", "omega_0"], "symbol_descs": ["the displacement from the equilibrium position", "the quantum mechanical energy of the nth state", "the mass of the object", "the angular frequency of the perturbation", "the natural angular frequency"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "2*sqrt(E_n/(m*(omega**2 + omega_0**2)))", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "I.24.6_3_0", "symbols": ["x", "E_n", "m", "omega", "omega_0"], "symbol_descs": ["the displacement from the equilibrium position", "the quantum mechanical energy of the nth state", "the mass of the object", "the angular frequency of the perturbation", "the natural angular frequency"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-2*sqrt(E_n/(m*(omega**2 + omega_0**2)))", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "I.32.17_3_1", "symbols": ["r", "Pwr", "epsilon", "c", "Ef", "omega", "omega_0"], "symbol_descs": ["the radius of the scattering object or atom", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the frequency of the external electric field", "the natural frequency of the oscillator or resonant frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(3)*sqrt(Pwr/(c*epsilon))*(omega - omega_0)*(omega + omega_0)/(2*sqrt(pi)*Ef*omega**2)", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 5.0]]}
 {"name": "I.32.5_1_1", "symbols": ["a", "Pwr", "q", "epsilon", "c"], "symbol_descs": ["the acceleration of the charged particle", "the power of an electromagnetic wave", "the charge of a particle", "the electric constant or permittivity of free space", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(6)*sqrt(pi)*sqrt(Pwr*c**3*epsilon)/q", "symbol_ranges": [null, [0.00022359931628901765, 8.699813613754754], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.32.5_0_1", "symbols": ["q", "Pwr", "a", "epsilon", "c"], "symbol_descs": ["the charge of a particle", "the power of an electromagnetic wave", "the acceleration of the charged particle", "the electric constant or permittivity of free space", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(6)*sqrt(pi)*sqrt(Pwr*c**3*epsilon)/a", "symbol_ranges": [null, [0.00022359931628901765, 8.699813613754754], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "III.9.52_0_0", "symbols": ["p_d", "prob", "Ef", "t", "h", "omega", "omega_0"], "symbol_descs": ["the dipole moment of the transition", "the transition probability of an atomic system", "the amplitude of the external electric field", "the interaction time between the atomic system and the external field", "the Planck constant", "the frequency of the external field", "the resonant frequency of the atomic transition"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "h*prob*t*(omega - omega_0)**2/(4*pi*Ef*(1 - cos(t*(omega - omega_0))))", "symbol_ranges": [null, [7.678126964405091e-05, 109.69273649259692], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "II.11.20_1_0", "symbols": ["p_d", "Pol", "n_rho", "Ef", "kb", "T"], "symbol_descs": ["the dipole moment of a molecule", "the polarization of a medium", "the density of molecules or dipoles", "the external electric field strength", "the Boltzmann constant", "the temperature in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-sqrt(3)*sqrt(Pol*T*kb/(Ef*n_rho))", "symbol_ranges": [null, [0.043722934612498036, 61.65709083651663], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "III.19.51_1_0", "symbols": ["q", "E_n", "m", "h", "n", "epsilon"], "symbol_descs": ["the elementary charge", "the energy of the nth energy level", "the mass of the electron", "the Planck constant", "the principal quantum number", "the electric constant (permittivity of free space)"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-2**(3/4)*(-E_n*epsilon**2*h**2*n**2/m)**(1/4)", "symbol_ranges": [null, [-45.25115748167385, -5.8291901757498e-05], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.27.18_1_0", "symbols": ["Ef", "E_den", "epsilon"], "symbol_descs": ["the electric field strength", "the energy density", "the electric permittivity"], "symbol_properties": ["O", "V", "V"], "expression": "-sqrt(E_den/epsilon)", "symbol_ranges": [null, [1.2962182386994536, 119.07281588315959], [1.0, 5.0]]}
 {"name": "II.37.1_0_0", "symbols": ["mom", "E_n", "B", "chi"], "symbol_descs": ["the magnetic moment", "the nth energy level", "the magnetic field strength", "the magnetic susceptibility"], "symbol_properties": ["O", "V", "V", "V"], "expression": "E_n/(B*(chi + 1))", "symbol_ranges": [null, [3.225301161323166, 132.48590574989166], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.43.43_0_0", "symbols": ["gamma", "kappa", "kb", "A", "v"], "symbol_descs": ["the adiabatic index", "the isentropic expansion factor", "Boltzmann's constant", "a constant area", "the velocity"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1 + kb*v/(A*kappa)", "symbol_ranges": [null, [0.06749211830306556, 13.205911610827933], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "II.6.15a_3_0", "symbols": ["x", "Ef", "epsilon", "p_d", "r", "y", "z"], "symbol_descs": ["the x-coordinate of the point where the field is being measured", "the electric field strength at a point", "the electric constant (permittivity of free space)", "the electric dipole moment", "the distance from the dipole to the point where the field is being measured", "the y-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "-sqrt(16*pi**2*Ef**2*epsilon**2*r**10/(p_d**2*z**2) - 9*y**2)/3", "symbol_ranges": [null, [0.0011930972073398915, 3.654440850903496], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.24.6_1_1", "symbols": ["omega", "E_n", "m", "omega_0", "x"], "symbol_descs": ["the angular frequency of the perturbation", "the quantum mechanical energy of the nth state", "the mass of the object", "the natural angular frequency", "the displacement from the equilibrium position"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(4*E_n/m - omega_0**2*x**2)/x", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.24.17_0_1", "symbols": ["omega", "k", "c", "d"], "symbol_descs": ["the angular frequency", "the wave number", "the speed of the wave", "the diameter or thickness of the waveguide or medium"], "symbol_properties": ["O", "V", "V", "V"], "expression": "c*sqrt(d**2*k**2 + pi**2)/d", "symbol_ranges": [null, [1.5988699087132785, 5.868821422051696], [1.0, 2.0], [2.0, 4.0]]}
 {"name": "II.36.38_7_0", "symbols": ["M", "f", "mom", "H", "kb", "T", "alpha", "epsilon", "c"], "symbol_descs": ["the magnetization of a material", "the resultant value of the function", "the momentum of an object or particle", "the magnetic field strength", "the Boltzmann constant", "the temperature in Kelvin", "the polarizability of a medium or molecule", "the electric permittivity of a medium", "the speed of light in vacuum"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "c**2*epsilon*(H*mom - T*f*kb)/(alpha*mom)", "symbol_ranges": [null, [0.1886648613106507, 11.236770740165767], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
@@ -36,11 +26,9 @@
 {"name": "I.12.4_2_0", "symbols": ["r", "Ef", "q1", "epsilon"], "symbol_descs": ["the distance from the charge to the point where the electric field is being measured", "the electric field at a given point", "the charge of the object generating the electric field", "the electric constant (permittivity of free space)"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-sqrt(q1/(Ef*epsilon))/(2*sqrt(pi))", "symbol_ranges": [null, [0.0008475473883141839, 0.26838468642326563], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.24.6_2_1", "symbols": ["omega_0", "E_n", "m", "omega", "x"], "symbol_descs": ["the natural angular frequency", "the quantum mechanical energy of the nth state", "the mass of the object", "the angular frequency of the perturbation", "the displacement from the equilibrium position"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(4*E_n/m - omega**2*x**2)/x", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.43.43_3_0", "symbols": ["v", "kappa", "gamma", "kb", "A"], "symbol_descs": ["the velocity", "the isentropic expansion factor", "the adiabatic index", "Boltzmann's constant", "a constant area"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "A*kappa*(gamma - 1)/kb", "symbol_ranges": [null, [0.06749211830306556, 13.205911610827933], [2.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "III.13.18_1_0", "symbols": ["d", "v", "E_n", "k", "h"], "symbol_descs": ["the distance between particles or the diameter of a nanoparticle", "the velocity of a particle or wave", "the nth energy level of a quantum system", "Boltzmann's constant, relating energy to temperature", "the Planck constant, relating energy to frequency"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(h*v/(E_n*k))/(2*sqrt(pi))", "symbol_ranges": [null, [6.2068148190537045, 5492.805849998013], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "III.15.12_0_0", "symbols": ["U", "E_n", "k", "d"], "symbol_descs": ["the characteristic potential energy", "the n-th energy level", "the wave number", "the distance between potential energy wells"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-E_n/(2*cos(d*k) - 2)", "symbol_ranges": [null, [9.217599913903162e-07, 19.816237029971756], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.37.1_2_0", "symbols": ["chi", "E_n", "mom", "B"], "symbol_descs": ["the magnetic susceptibility", "the nth energy level", "the magnetic moment", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-1 + E_n/(B*mom)", "symbol_ranges": [null, [3.225301161323166, 132.48590574989166], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.34.29a_2_0", "symbols": ["m", "mom", "q", "h"], "symbol_descs": ["the mass of a particle", "the momentum of a particle", "the charge of a particle", "the Planck constant"], "symbol_properties": ["O", "V", "V", "V"], "expression": "h*q/(4*pi*mom)", "symbol_ranges": [null, [0.024820648324816643, 1.7205798409397295], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "III.10.19_1_0", "symbols": ["Bx", "E_n", "mom", "By", "Bz"], "symbol_descs": ["the x-component of the magnetic field", "the energy of a particle in a magnetic field", "the magnetic moment of the particle", "the y-component of the magnetic field", "the z-component of the magnetic field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(-By**2 - Bz**2 + E_n**2/mom**2)", "symbol_ranges": [null, [3.4048848628776556, 41.058200383882884], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.21.32_2_0", "symbols": ["r", "Volt", "q", "epsilon", "v", "c"], "symbol_descs": ["the distance from the charge", "the electric potential", "the electric charge", "the electric constant (permittivity of free space)", "the velocity of the charge", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "c*q/(4*pi*Volt*epsilon*(c - v))", "symbol_ranges": [null, [0.004959674953354889, 0.38694954458871633], [1.0, 5.0], [1.0, 5.0], [1.0, 2.0], [3.0, 10.0]]}
 {"name": "II.24.17_2_1", "symbols": ["d", "k", "omega", "c"], "symbol_descs": ["the diameter or thickness of the waveguide or medium", "the wave number", "the angular frequency", "the speed of the wave"], "symbol_properties": ["O", "V", "V", "V"], "expression": "pi*c*sqrt(-1/((c*k - omega)*(c*k + omega)))", "symbol_ranges": [null, [1.5988699087132785, 5.868821422051696], [4.0, 6.0], [1.0, 2.0]]}
 {"name": "I.32.17_4_3", "symbols": ["omega", "Pwr", "epsilon", "c", "Ef", "r", "omega_0"], "symbol_descs": ["the frequency of the external electric field", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the natural frequency of the oscillator or resonant frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(2*sqrt(3)*sqrt(pi)*Ef*omega_0**2*r*sqrt(Pwr*c*epsilon)/(4*pi*Ef**2*c*epsilon*r**2 - 3*Pwr) - 3*Pwr*omega_0**2/(4*pi*Ef**2*c*epsilon*r**2 - 3*Pwr))", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 5.0]]}
@@ -52,7 +40,6 @@
 {"name": "II.13.34_1_0", "symbols": ["v", "j", "rho_c_0", "c"], "symbol_descs": ["the object's velocity", "the current density of a charged object", "the object's rest charge density", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-c*j*sqrt(1/(c**2*rho_c_0**2 + j**2))", "symbol_ranges": [null, [1.09826134448646, 11.762331082663536], [1.0, 5.0], [3.0, 10.0]]}
 {"name": "II.11.27_0_0", "symbols": ["n", "Pol", "alpha", "epsilon", "Ef"], "symbol_descs": ["the number density of polarizable units", "the polarization of a material", "the polarizability of a unit", "the permittivity of free space or a constant", "the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "3*Pol/(alpha*(3*Ef*epsilon + Pol))", "symbol_ranges": [null, [0.00014473174629744197, 5.04333483437795], [0.0, 1.0], [1.0, 2.0], [1.0, 2.0]]}
 {"name": "I.29.16_0_0", "symbols": ["x1", "x", "x2", "theta1", "theta2"], "symbol_descs": ["the magnitude of the first vector", "the distance between two points", "the magnitude of the second vector", "the angle of the first vector", "the angle of the second vector"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "x2*cos(theta1 - theta2) - sqrt(x**2 + x2**2*cos(theta1 - theta2)**2 - x2**2)", "symbol_ranges": [null, [0.11471601544235527, 9.412228054660888], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "III.10.19_2_0", "symbols": ["By", "E_n", "mom", "Bx", "Bz"], "symbol_descs": ["the y-component of the magnetic field", "the energy of a particle in a magnetic field", "the magnetic moment of the particle", "the x-component of the magnetic field", "the z-component of the magnetic field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(-Bx**2 - Bz**2 + E_n**2/mom**2)", "symbol_ranges": [null, [3.4048848628776556, 41.058200383882884], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.24.17_1_1", "symbols": ["c", "k", "omega", "d"], "symbol_descs": ["the speed of the wave", "the wave number", "the angular frequency", "the diameter or thickness of the waveguide or medium"], "symbol_properties": ["O", "V", "V", "V"], "expression": "d*omega*sqrt(1/(d**2*k**2 + pi**2))", "symbol_ranges": [null, [1.5988699087132785, 5.868821422051696], [4.0, 6.0], [2.0, 4.0]]}
 {"name": "II.6.15a_3_1", "symbols": ["x", "Ef", "epsilon", "p_d", "r", "y", "z"], "symbol_descs": ["the x-coordinate of the point where the field is being measured", "the electric field strength at a point", "the electric constant (permittivity of free space)", "the electric dipole moment", "the distance from the dipole to the point where the field is being measured", "the y-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(16*pi**2*Ef**2*epsilon**2*r**10/(p_d**2*z**2) - 9*y**2)/3", "symbol_ranges": [null, [0.0011930972073398915, 3.654440850903496], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "III.12.43_0_0", "symbols": ["n", "L", "h"], "symbol_descs": ["a quantum number representing the energy level", "the angular momentum of an object", "the Planck constant"], "symbol_properties": ["O", "V", "V"], "expression": "2*pi*L/h", "symbol_ranges": [null, [0.1821224832518985, 3.846426391831527], [1.0, 5.0]]}
@@ -64,29 +51,23 @@
 {"name": "I.15.1_1_0", "symbols": ["v", "p", "m_0", "c"], "symbol_descs": ["the object's velocity", "the relativistic momentum of an object", "the object's rest mass", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-c*p*sqrt(1/(c**2*m_0**2 + p**2))", "symbol_ranges": [null, [1.0519873444493597, 11.661403633940267], [1.0, 5.0], [3.0, 10.0]]}
 {"name": "III.13.18_1_1", "symbols": ["d", "v", "E_n", "k", "h"], "symbol_descs": ["the distance between particles or the diameter of a nanoparticle", "the velocity of a particle or wave", "the nth energy level of a quantum system", "Boltzmann's constant, relating energy to temperature", "the Planck constant, relating energy to frequency"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(h*v/(E_n*k))/(2*sqrt(pi))", "symbol_ranges": [null, [6.2068148190537045, 5492.805849998013], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.35.18_3_1", "symbols": ["mom", "n", "n_0", "kb", "T", "B"], "symbol_descs": ["the magnetic moment of a particle", "the number of particles in a given state", "the number of particles at equilibrium", "the Boltzmann constant", "the temperature of the system", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "T*kb*log((n_0 + sqrt(-4*n**2 + n_0**2))/(2*n))/B", "symbol_ranges": [null, [0.006709112588478311, 1.4581675020057816], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "II.35.18_2_0", "symbols": ["T", "n", "n_0", "kb", "mom", "B"], "symbol_descs": ["the temperature of the system", "the number of particles in a given state", "the number of particles at equilibrium", "the Boltzmann constant", "the magnetic moment of a particle", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "B*mom/(kb*log((n_0 - sqrt(-4*n**2 + n_0**2))/(2*n)))", "symbol_ranges": [null, [0.006709112588478311, 1.4581675020057816], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.36.38_3_0", "symbols": ["T", "f", "mom", "H", "kb", "alpha", "epsilon", "c", "M"], "symbol_descs": ["the temperature in Kelvin", "the resultant value of the function", "the momentum of an object or particle", "the magnetic field strength", "the Boltzmann constant", "the polarizability of a medium or molecule", "the electric permittivity of a medium", "the speed of light in vacuum", "the magnetization of a material"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "mom*(H*c**2*epsilon - M*alpha)/(c**2*epsilon*f*kb)", "symbol_ranges": [null, [0.1886648613106507, 11.236770740165767], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.13.12_3_0", "symbols": ["r2", "U", "m1", "m2", "r1", "G"], "symbol_descs": ["the final distance between the two objects", "the potential energy of two objects", "the mass of the first object", "the mass of the second object", "the initial distance between the two objects", "the gravitational constant"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "G*m1*m2*r1/(G*m1*m2 + U*r1)", "symbol_ranges": [null, [-46.91653390035222, 53.856019963163504], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.32.17_5_3", "symbols": ["omega_0", "Pwr", "epsilon", "c", "Ef", "r", "omega"], "symbol_descs": ["the natural frequency of the oscillator or resonant frequency", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the frequency of the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(3)*sqrt(2*sqrt(3)*sqrt(pi)*Ef*omega**2*r*sqrt(Pwr*c*epsilon)/Pwr + 3*omega**2)/3", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0]]}
-{"name": "II.35.18_4_0", "symbols": ["B", "n", "n_0", "kb", "T", "mom"], "symbol_descs": ["the magnetic field strength", "the number of particles in a given state", "the number of particles at equilibrium", "the Boltzmann constant", "the temperature of the system", "the magnetic moment of a particle"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "T*kb*log((n_0 - sqrt(-4*n**2 + n_0**2))/(2*n))/mom", "symbol_ranges": [null, [0.006709112588478311, 1.4581675020057816], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.29.16_1_0", "symbols": ["x2", "x", "x1", "theta1", "theta2"], "symbol_descs": ["the magnitude of the second vector", "the distance between two points", "the magnitude of the first vector", "the angle of the first vector", "the angle of the second vector"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "x1*cos(theta1 - theta2) - sqrt(x**2 + x1**2*cos(theta1 - theta2)**2 - x1**2)", "symbol_ranges": [null, [0.11471601544235527, 9.412228054660888], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "III.17.37_1_0", "symbols": ["alpha", "f", "beta", "theta"], "symbol_descs": ["a coefficient modifying the cosine term", "the resultant value of the function", "a scaling factor", "the angle in radians"], "symbol_properties": ["O", "V", "V", "V"], "expression": "(-beta + f)/(beta*cos(theta))", "symbol_ranges": [null, [-17.993846130660476, 18.008238963633936], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.6.15a_4_1", "symbols": ["y", "Ef", "epsilon", "p_d", "r", "x", "z"], "symbol_descs": ["the y-coordinate of the point where the field is being measured", "the electric field strength at a point", "the electric constant (permittivity of free space)", "the electric dipole moment", "the distance from the dipole to the point where the field is being measured", "the x-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(16*pi**2*Ef**2*epsilon**2*r**10/(p_d**2*z**2) - 9*x**2)/3", "symbol_ranges": [null, [0.0011930972073398915, 3.654440850903496], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "I.32.17_5_1", "symbols": ["omega_0", "Pwr", "epsilon", "c", "Ef", "r", "omega"], "symbol_descs": ["the natural frequency of the oscillator or resonant frequency", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the frequency of the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(3)*sqrt(-2*sqrt(3)*sqrt(pi)*Ef*omega**2*r*sqrt(Pwr*c*epsilon)/Pwr + 3*omega**2)/3", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0]]}
 {"name": "I.11.19_4_0", "symbols": ["y2", "A", "x1", "x2", "x3", "y1", "y3"], "symbol_descs": ["the second variable or value", "the resulting sum of products", "the first coefficient", "the second coefficient", "the third coefficient", "the first variable or value", "the third variable or value"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(-A + x1*y1 - x3*y3)/x2", "symbol_ranges": [null, [8.3997264282878, 58.02378770462634], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.35.18_2_1", "symbols": ["T", "n", "n_0", "kb", "mom", "B"], "symbol_descs": ["the temperature of the system", "the number of particles in a given state", "the number of particles at equilibrium", "the Boltzmann constant", "the magnetic moment of a particle", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "B*mom/(kb*log((n_0 + sqrt(-4*n**2 + n_0**2))/(2*n)))", "symbol_ranges": [null, [0.006709112588478311, 1.4581675020057816], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.11.20_1_1", "symbols": ["p_d", "Pol", "n_rho", "Ef", "kb", "T"], "symbol_descs": ["the dipole moment of a molecule", "the polarization of a medium", "the density of molecules or dipoles", "the external electric field strength", "the Boltzmann constant", "the temperature in Kelvin"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "sqrt(3)*sqrt(Pol*T*kb/(Ef*n_rho))", "symbol_ranges": [null, [0.043722934612498036, 61.65709083651663], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "II.24.17_2_0", "symbols": ["d", "k", "omega", "c"], "symbol_descs": ["the diameter or thickness of the waveguide or medium", "the wave number", "the angular frequency", "the speed of the wave"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-pi*c*sqrt(-1/((c*k - omega)*(c*k + omega)))", "symbol_ranges": [null, [1.5988699087132785, 5.868821422051696], [4.0, 6.0], [1.0, 2.0]]}
 {"name": "II.11.17_5_0", "symbols": ["Ef", "n", "n_0", "kb", "T", "theta", "p_d"], "symbol_descs": ["the electric field strength", "the carrier density", "the equilibrium carrier density", "the Boltzmann constant", "the temperature in Kelvin", "the angle between the electric field and the carrier movement direction", "the dipole moment of the carrier"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "T*kb*(n - n_0)/(n_0*p_d*cos(theta))", "symbol_ranges": [null, [-9.144469948055056, 8.334506483608134], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.44.4_4_0", "symbols": ["V2", "E_n", "n", "kb", "T", "V1"], "symbol_descs": ["the final volume of the gas", "the energy change of an ideal gas", "the number of moles of the gas", "the Boltzmann constant", "the temperature of the gas in Kelvin", "the initial volume of the gas"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "V1*exp(E_n/(T*kb*n))", "symbol_ranges": [null, [-122.59845948152238, 97.96308803656285], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.34.29b_3_0", "symbols": ["mom", "E_n", "g_", "h", "Jz", "B"], "symbol_descs": ["the magnetic moment of the particle or atom", "the energy of the nth state", "the g-factor of the particle or atom", "the Planck constant", "the z-component of the total angular momentum", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "E_n*h/(2*pi*B*Jz*g_)", "symbol_ranges": [null, [6.736957826456598, 2591.027254399127], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.27.16_2_0", "symbols": ["Ef", "flux", "epsilon", "c"], "symbol_descs": ["the magnitude of the electric field", "the energy flux density", "the electric constant or permittivity of free space", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-sqrt(flux/(c*epsilon))", "symbol_ranges": [null, [2.236204467279266, 511.4096794100542], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "II.11.3_3_0", "symbols": ["omega_0", "x", "q", "Ef", "m", "omega"], "symbol_descs": ["the natural angular frequency of the oscillation", "the displacement of an object from its equilibrium position", "the electric charge of the object", "the external electric field strength", "the mass of the object", "the angular frequency of the external force"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-sqrt(Ef*q/(m*x) + omega**2)", "symbol_ranges": [null, [0.02116443013176181, 1.0360796152433274], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 2.0]]}
 {"name": "II.34.29b_0_0", "symbols": ["g_", "E_n", "h", "Jz", "mom", "B"], "symbol_descs": ["the g-factor of the particle or atom", "the energy of the nth state", "the Planck constant", "the z-component of the total angular momentum", "the magnetic moment of the particle or atom", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "E_n*h/(2*pi*B*Jz*mom)", "symbol_ranges": [null, [6.736957826456598, 2591.027254399127], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.11.19_0_0", "symbols": ["x1", "A", "x2", "x3", "y1", "y2", "y3"], "symbol_descs": ["the first coefficient", "the resulting sum of products", "the second coefficient", "the third coefficient", "the first variable or value", "the second variable or value", "the third variable or value"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(A + x2*y2 + x3*y3)/y1", "symbol_ranges": [null, [8.3997264282878, 58.02378770462634], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "III.10.19_2_1", "symbols": ["By", "E_n", "mom", "Bx", "Bz"], "symbol_descs": ["the y-component of the magnetic field", "the energy of a particle in a magnetic field", "the magnetic moment of the particle", "the x-component of the magnetic field", "the z-component of the magnetic field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(-Bx**2 - Bz**2 + E_n**2/mom**2)", "symbol_ranges": [null, [3.4048848628776556, 41.058200383882884], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.8.31_1_0", "symbols": ["Ef", "E_den", "epsilon"], "symbol_descs": ["the electric field strength", "the energy density", "the electric permittivity"], "symbol_properties": ["O", "V", "V"], "expression": "-sqrt(2)*sqrt(E_den/epsilon)", "symbol_ranges": [null, [0.5680592170269461, 60.38864631827431], [1.0, 5.0]]}
-{"name": "I.32.17_4_2", "symbols": ["omega", "Pwr", "epsilon", "c", "Ef", "r", "omega_0"], "symbol_descs": ["the frequency of the external electric field", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the natural frequency of the oscillator or resonant frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "-sqrt(2*sqrt(3)*sqrt(pi)*Ef*omega_0**2*r*sqrt(Pwr*c*epsilon)/(4*pi*Ef**2*c*epsilon*r**2 - 3*Pwr) - 3*Pwr*omega_0**2/(4*pi*Ef**2*c*epsilon*r**2 - 3*Pwr))", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 5.0]]}
 {"name": "II.11.17_4_0", "symbols": ["p_d", "n", "n_0", "kb", "T", "theta", "Ef"], "symbol_descs": ["the dipole moment of the carrier", "the carrier density", "the equilibrium carrier density", "the Boltzmann constant", "the temperature in Kelvin", "the angle between the electric field and the carrier movement direction", "the electric field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "T*kb*(n - n_0)/(Ef*n_0*cos(theta))", "symbol_ranges": [null, [-9.144469948055056, 8.334506483608134], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.36.38_4_0", "symbols": ["alpha", "f", "mom", "H", "kb", "T", "epsilon", "c", "M"], "symbol_descs": ["the polarizability of a medium or molecule", "the resultant value of the function", "the momentum of an object or particle", "the magnetic field strength", "the Boltzmann constant", "the temperature in Kelvin", "the electric permittivity of a medium", "the speed of light in vacuum", "the magnetization of a material"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "c**2*epsilon*(H*mom - T*f*kb)/(M*mom)", "symbol_ranges": [null, [0.1886648613106507, 11.236770740165767], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.6.15b_3_0", "symbols": ["r", "Ef", "epsilon", "p_d", "theta"], "symbol_descs": ["the distance from the dipole to the point where the electric field is being measured", "the electric field", "the electric constant or permittivity of the medium", "the dipole moment", "the angle between the dipole axis and the position vector"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "6**(1/3)*(p_d*sin(theta)*cos(theta)/(Ef*epsilon))**(1/3)/(2*pi**(1/3))", "symbol_ranges": [null, [-0.17796760168839998, 0.103798930323723], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
@@ -97,13 +78,10 @@
 {"name": "I.10.7_1_0", "symbols": ["v", "m", "m_0", "c"], "symbol_descs": ["the object's velocity", "the relativistic mass of an object", "the object's rest mass", "the speed of light"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-c*sqrt(1 - m_0**2/m**2)", "symbol_ranges": [null, [1.014734117935586, 6.354799431835959], [1.0, 5.0], [3.0, 10.0]]}
 {"name": "II.11.27_1_0", "symbols": ["alpha", "Pol", "n", "epsilon", "Ef"], "symbol_descs": ["the polarizability of a unit", "the polarization of a material", "the number density of polarizable units", "the permittivity of free space or a constant", "the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "3*Pol/(n*(3*Ef*epsilon + Pol))", "symbol_ranges": [null, [0.00014473174629744197, 5.04333483437795], [0.0, 1.0], [1.0, 2.0], [1.0, 2.0]]}
 {"name": "I.44.4_2_0", "symbols": ["T", "E_n", "n", "kb", "V1", "V2"], "symbol_descs": ["the temperature of the gas in Kelvin", "the energy change of an ideal gas", "the number of moles of the gas", "the Boltzmann constant", "the initial volume of the gas", "the final volume of the gas"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "E_n/(kb*n*log(V2/V1))", "symbol_ranges": [null, [-122.59845948152238, 97.96308803656285], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "II.35.18_3_0", "symbols": ["mom", "n", "n_0", "kb", "T", "B"], "symbol_descs": ["the magnetic moment of a particle", "the number of particles in a given state", "the number of particles at equilibrium", "the Boltzmann constant", "the temperature of the system", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "T*kb*log((n_0 - sqrt(-4*n**2 + n_0**2))/(2*n))/B", "symbol_ranges": [null, [0.006709112588478311, 1.4581675020057816], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "I.32.5_1_0", "symbols": ["a", "Pwr", "q", "epsilon", "c"], "symbol_descs": ["the acceleration of the charged particle", "the power of an electromagnetic wave", "the charge of a particle", "the electric constant or permittivity of free space", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(6)*sqrt(pi)*sqrt(Pwr*c**3*epsilon)/q", "symbol_ranges": [null, [0.00022359931628901765, 8.699813613754754], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.34.1_2_0", "symbols": ["omega_0", "omega", "c", "v"], "symbol_descs": ["the object's proper angular frequency (at rest)", "the relativistic angular frequency of an object", "the speed of light", "the object's velocity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "omega*(c - v)/c", "symbol_ranges": [null, [1.1779071869463607, 11.881660366764937], [3.0, 10.0], [1.0, 2.0]]}
 {"name": "I.37.4_0_1", "symbols": ["I1", "Int", "I2", "delta"], "symbol_descs": ["the intensity of the first wave source", "the resultant intensity of two wave sources", "the intensity of the second wave source", "the phase difference between the two wave sources"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*I2*cos(delta)**2 + I2 + Int + 2*sqrt(I2*(I2*cos(delta)**2 + I2 + Int))*cos(delta)", "symbol_ranges": [null, [0.0027163447847069477, 13.60662800081353], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.11.19_3_0", "symbols": ["y1", "A", "x1", "x2", "x3", "y2", "y3"], "symbol_descs": ["the first variable or value", "the resulting sum of products", "the first coefficient", "the second coefficient", "the third coefficient", "the second variable or value", "the third variable or value"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(A + x2*y2 + x3*y3)/x1", "symbol_ranges": [null, [8.3997264282878, 58.02378770462634], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.11.27_3_0", "symbols": ["Ef", "Pol", "n", "alpha", "epsilon"], "symbol_descs": ["the external electric field", "the polarization of a material", "the number density of polarizable units", "the polarizability of a unit", "the permittivity of free space or a constant"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-Pol/(3*epsilon) + Pol/(alpha*epsilon*n)", "symbol_ranges": [null, [0.00014473174629744197, 5.04333483437795], [0.0, 1.0], [0.0, 1.0], [1.0, 2.0]]}
-{"name": "II.11.3_4_0", "symbols": ["omega", "x", "q", "Ef", "m", "omega_0"], "symbol_descs": ["the angular frequency of the external force", "the displacement of an object from its equilibrium position", "the electric charge of the object", "the external electric field strength", "the mass of the object", "the natural angular frequency of the oscillation"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-sqrt(-Ef*q/(m*x) + omega_0**2)", "symbol_ranges": [null, [0.02116443013176181, 1.0360796152433274], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [3.0, 5.0]]}
 {"name": "III.21.20_3_0", "symbols": ["m", "j", "rho_c_0", "q", "A_vec"], "symbol_descs": ["the mass of a charge carrier", "the current density", "the charge carrier density", "the elementary charge", "the vector potential"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-A_vec*q*rho_c_0/j", "symbol_ranges": [null, [-87.5834868720019, -0.43341100149525336], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "III.13.18_0_0", "symbols": ["E_n", "v", "d", "k", "h"], "symbol_descs": ["the nth energy level of a quantum system", "the velocity of a particle or wave", "the distance between particles or the diameter of a nanoparticle", "Boltzmann's constant, relating energy to temperature", "the Planck constant, relating energy to frequency"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "h*v/(4*pi*d**2*k)", "symbol_ranges": [null, [6.2068148190537045, 5492.805849998013], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.27.6_2_0", "symbols": ["n", "foc", "d1", "d2"], "symbol_descs": ["the refractive index of the medium between the two optical components", "the focal length of a combination of two optical components", "the distance from the first optical component to the object", "the distance from the second optical component to the image"], "symbol_properties": ["O", "V", "V", "V"], "expression": "d2/foc - d2/d1", "symbol_ranges": [null, [0.19334600838248958, 2.216827384181275], [1.0, 5.0], [1.0, 5.0]]}
@@ -111,7 +89,6 @@
 {"name": "I.11.19_1_0", "symbols": ["x2", "A", "x1", "x3", "y1", "y2", "y3"], "symbol_descs": ["the second coefficient", "the resulting sum of products", "the first coefficient", "the third coefficient", "the first variable or value", "the second variable or value", "the third variable or value"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(-A + x1*y1 - x3*y3)/y2", "symbol_ranges": [null, [8.3997264282878, 58.02378770462634], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.37.1_1_0", "symbols": ["B", "E_n", "mom", "chi"], "symbol_descs": ["the magnetic field strength", "the nth energy level", "the magnetic moment", "the magnetic susceptibility"], "symbol_properties": ["O", "V", "V", "V"], "expression": "E_n/(mom*(chi + 1))", "symbol_ranges": [null, [3.225301161323166, 132.48590574989166], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.36.38_0_0", "symbols": ["mom", "f", "H", "kb", "T", "alpha", "epsilon", "c", "M"], "symbol_descs": ["the momentum of an object or particle", "the resultant value of the function", "the magnetic field strength", "the Boltzmann constant", "the temperature in Kelvin", "the polarizability of a medium or molecule", "the electric permittivity of a medium", "the speed of light in vacuum", "the magnetization of a material"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "T*c**2*epsilon*f*kb/(H*c**2*epsilon - M*alpha)", "symbol_ranges": [null, [0.1886648613106507, 11.236770740165767], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
-{"name": "II.6.15a_4_0", "symbols": ["y", "Ef", "epsilon", "p_d", "r", "x", "z"], "symbol_descs": ["the y-coordinate of the point where the field is being measured", "the electric field strength at a point", "the electric constant (permittivity of free space)", "the electric dipole moment", "the distance from the dipole to the point where the field is being measured", "the x-coordinate of the point where the field is being measured", "the z-coordinate of the point where the field is being measured"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "-sqrt(16*pi**2*Ef**2*epsilon**2*r**10/(p_d**2*z**2) - 9*x**2)/3", "symbol_ranges": [null, [0.0011930972073398915, 3.654440850903496], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "III.9.52_1_0", "symbols": ["Ef", "prob", "p_d", "t", "h", "omega", "omega_0"], "symbol_descs": ["the amplitude of the external electric field", "the transition probability of an atomic system", "the dipole moment of the transition", "the interaction time between the atomic system and the external field", "the Planck constant", "the frequency of the external field", "the resonant frequency of the atomic transition"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "h*prob*t*(omega - omega_0)**2/(4*pi*p_d*(1 - cos(t*(omega - omega_0))))", "symbol_ranges": [null, [7.678126964405091e-05, 109.69273649259692], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.11.3_2_0", "symbols": ["m", "x", "q", "Ef", "omega_0", "omega"], "symbol_descs": ["the mass of the object", "the displacement of an object from its equilibrium position", "the electric charge of the object", "the external electric field strength", "the natural angular frequency of the oscillation", "the angular frequency of the external force"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-Ef*q/(x*(omega**2 - omega_0**2))", "symbol_ranges": [null, [0.02116443013176181, 1.0360796152433274], [1.0, 3.0], [1.0, 3.0], [3.0, 5.0], [1.0, 2.0]]}
 {"name": "I.34.14_2_0", "symbols": ["omega_0", "omega", "c", "v"], "symbol_descs": ["the object's rest angular frequency", "the relativistic angular frequency", "the speed of light", "the object's velocity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "c*omega*sqrt(1 - v**2/c**2)/(c + v)", "symbol_ranges": [null, [1.1531244964596823, 10.259297894054416], [3.0, 10.0], [1.0, 2.0]]}
@@ -120,21 +97,15 @@
 {"name": "III.15.27_2_0", "symbols": ["d", "k", "alpha", "n"], "symbol_descs": ["the diameter or a characteristic length", "the spring constant or a proportionality constant", "a material-dependent constant or a dimensionless parameter", "the number of turns or a dimensionless quantity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*pi*alpha/(k*n)", "symbol_ranges": [null, [0.30874056747990736, 26.02235270815693], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.34.29b_2_0", "symbols": ["Jz", "E_n", "g_", "h", "mom", "B"], "symbol_descs": ["the z-component of the total angular momentum", "the energy of the nth state", "the g-factor of the particle or atom", "the Planck constant", "the magnetic moment of the particle or atom", "the magnetic field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "E_n*h/(2*pi*B*g_*mom)", "symbol_ranges": [null, [6.736957826456598, 2591.027254399127], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "II.3.24_1_0", "symbols": ["r", "flux", "Pwr"], "symbol_descs": ["the distance from the object", "the radiant flux of an object", "the power emitted by the object"], "symbol_properties": ["O", "V", "V"], "expression": "-sqrt(Pwr/flux)/(2*sqrt(pi))", "symbol_ranges": [null, [0.0033230907768000517, 0.3633117109385513], [1.0, 5.0]]}
-{"name": "I.37.4_1_0", "symbols": ["I2", "Int", "I1", "delta"], "symbol_descs": ["the intensity of the second wave source", "the resultant intensity of two wave sources", "the intensity of the first wave source", "the phase difference between the two wave sources"], "symbol_properties": ["O", "V", "V", "V"], "expression": "2*I1*cos(delta)**2 + I1 - Int - 2*sqrt(I1*(I1*cos(delta)**2 + I1 - Int))*cos(delta)", "symbol_ranges": [null, [0.0027163447847069477, 13.60662800081353], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "I.24.6_1_0", "symbols": ["omega", "E_n", "m", "omega_0", "x"], "symbol_descs": ["the angular frequency of the perturbation", "the quantum mechanical energy of the nth state", "the mass of the object", "the natural angular frequency", "the displacement from the equilibrium position"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(4*E_n/m - omega_0**2*x**2)/x", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.11.17_2_0", "symbols": ["T", "n", "n_0", "kb", "theta", "p_d", "Ef"], "symbol_descs": ["the temperature in Kelvin", "the carrier density", "the equilibrium carrier density", "the Boltzmann constant", "the angle between the electric field and the carrier movement direction", "the dipole moment of the carrier", "the electric field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "Ef*n_0*p_d*cos(theta)/(kb*(n - n_0))", "symbol_ranges": [null, [-9.144469948055056, 8.334506483608134], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.50.26_3_0", "symbols": ["alpha", "x", "x1", "omega", "t"], "symbol_descs": ["the non-linearity coefficient", "the resulting displacement", "the initial amplitude", "the angular frequency", "the time"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(x/cos(omega*t) - x1)/(x1*cos(omega*t))", "symbol_ranges": [null, [-0.6919201144862417, 10.927955005614129], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.32.17_3_0", "symbols": ["r", "Pwr", "epsilon", "c", "Ef", "omega", "omega_0"], "symbol_descs": ["the radius of the scattering object or atom", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the frequency of the external electric field", "the natural frequency of the oscillator or resonant frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(3)*sqrt(Pwr/(c*epsilon))*(-omega**2 + omega_0**2)/(2*sqrt(pi)*Ef*omega**2)", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 5.0]]}
-{"name": "I.32.17_2_1", "symbols": ["Ef", "Pwr", "epsilon", "c", "r", "omega", "omega_0"], "symbol_descs": ["the strength of the external electric field", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the radius of the scattering object or atom", "the frequency of the external electric field", "the natural frequency of the oscillator or resonant frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "sqrt(3)*sqrt(Pwr/(c*epsilon))*(omega - omega_0)*(omega + omega_0)/(2*sqrt(pi)*omega**2*r)", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 5.0]]}
 {"name": "III.19.51_3_0", "symbols": ["n", "E_n", "m", "q", "h", "epsilon"], "symbol_descs": ["the principal quantum number", "the energy of the nth energy level", "the mass of the electron", "the elementary charge", "the Planck constant", "the electric constant (permittivity of free space)"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "-sqrt(2)*q**2*sqrt(-m/E_n)/(4*epsilon*h)", "symbol_ranges": [null, [-45.25115748167385, -5.8291901757498e-05], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.40.1_4_0", "symbols": ["g", "n", "n_0", "m", "x", "T", "kb"], "symbol_descs": ["the acceleration due to gravity", "the density of particles at a given point", "the density of particles at the reference point", "the mass of a particle", "the height or distance from the reference point", "the temperature in Kelvin", "the Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "T*kb*log(n_0/n)/(m*x)", "symbol_ranges": [null, [6.331108462377704e-23, 4.531836594598494], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "I.32.5_0_0", "symbols": ["q", "Pwr", "a", "epsilon", "c"], "symbol_descs": ["the charge of a particle", "the power of an electromagnetic wave", "the acceleration of the charged particle", "the electric constant or permittivity of free space", "the speed of light"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(6)*sqrt(pi)*sqrt(Pwr*c**3*epsilon)/a", "symbol_ranges": [null, [0.00022359931628901765, 8.699813613754754], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "III.10.19_3_0", "symbols": ["Bz", "E_n", "mom", "Bx", "By"], "symbol_descs": ["the z-component of the magnetic field", "the energy of a particle in a magnetic field", "the magnetic moment of the particle", "the x-component of the magnetic field", "the y-component of the magnetic field"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "-sqrt(-Bx**2 - By**2 + E_n**2/mom**2)", "symbol_ranges": [null, [3.4048848628776556, 41.058200383882884], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.15.3t_0_0", "symbols": ["x", "t1", "c", "u", "t"], "symbol_descs": ["the position of the event in the observer's frame", "the relativistic time in the observer's frame", "the speed of light", "the relative velocity between the observer's frame and the object's frame", "the time of the event in the object's frame"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "c**2*(t - t1*sqrt((c**2 - u**2)/c**2))/u", "symbol_ranges": [null, [0.3503236042134061, 5.4910234521431915], [3.0, 10.0], [1.0, 2.0], [1.0, 5.0]]}
 {"name": "II.15.5_1_0", "symbols": ["Ef", "E_n", "p_d", "theta"], "symbol_descs": ["the external electric field", "the normal component of the electric field at the surface", "the dipole moment per unit area", "the angle between the dipole moment and the external electric field"], "symbol_properties": ["O", "V", "V", "V"], "expression": "-E_n/(p_d*cos(theta))", "symbol_ranges": [null, [-10.57903779497229, 23.62245117792713], [1.0, 5.0], [1.0, 5.0]]}
 {"name": "I.50.26_0_0", "symbols": ["x1", "x", "omega", "t", "alpha"], "symbol_descs": ["the initial amplitude", "the resulting displacement", "the angular frequency", "the time", "the non-linearity coefficient"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "x/(alpha*cos(omega*t)**2 + cos(omega*t))", "symbol_ranges": [null, [-0.6919201144862417, 10.927955005614129], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "III.17.37_0_0", "symbols": ["beta", "f", "alpha", "theta"], "symbol_descs": ["a scaling factor", "the resultant value of the function", "a coefficient modifying the cosine term", "the angle in radians"], "symbol_properties": ["O", "V", "V", "V"], "expression": "f/(alpha*cos(theta) + 1)", "symbol_ranges": [null, [-17.993846130660476, 18.008238963633936], [1.0, 5.0], [1.0, 5.0]]}
-{"name": "I.32.17_5_0", "symbols": ["omega_0", "Pwr", "epsilon", "c", "Ef", "r", "omega"], "symbol_descs": ["the natural frequency of the oscillator or resonant frequency", "the power of the scattered radiation", "the electric constant (permittivity of free space)", "the speed of light", "the strength of the external electric field", "the radius of the scattering object or atom", "the frequency of the external electric field"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "-sqrt(3)*sqrt(-2*sqrt(3)*sqrt(pi)*Ef*omega**2*r*sqrt(Pwr*c*epsilon)/Pwr + 3*omega**2)/3", "symbol_ranges": [null, [0.024877445150521406, 80.4297055337143], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0]]}
 {"name": "II.11.17_0_0", "symbols": ["n_0", "n", "kb", "T", "theta", "p_d", "Ef"], "symbol_descs": ["the equilibrium carrier density", "the carrier density", "the Boltzmann constant", "the temperature in Kelvin", "the angle between the electric field and the carrier movement direction", "the dipole moment of the carrier", "the electric field strength"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "T*kb*n/(Ef*p_d*cos(theta) + T*kb)", "symbol_ranges": [null, [-9.144469948055056, 8.334506483608134], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "I.24.6_0_0", "symbols": ["m", "E_n", "omega", "omega_0", "x"], "symbol_descs": ["the mass of the object", "the quantum mechanical energy of the nth state", "the angular frequency of the perturbation", "the natural angular frequency", "the displacement from the equilibrium position"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "4*E_n/(x**2*(omega**2 + omega_0**2))", "symbol_ranges": [null, [0.9473864624578928, 90.57929739954962], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
 {"name": "II.11.3_0_0", "symbols": ["q", "x", "Ef", "m", "omega_0", "omega"], "symbol_descs": ["the electric charge of the object", "the displacement of an object from its equilibrium position", "the external electric field strength", "the mass of the object", "the natural angular frequency of the oscillation", "the angular frequency of the external force"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "m*x*(-omega**2 + omega_0**2)/Ef", "symbol_ranges": [null, [0.02116443013176181, 1.0360796152433274], [1.0, 3.0], [1.0, 3.0], [3.0, 5.0], [1.0, 2.0]]}