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FeynmanEquations.csv ADDED
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1
+ Filename,Number,Output,Formula,# variables,v1_name,v1_low,v1_high,v2_name,v2_low,v2_high,v3_name,v3_low,v3_high,v4_name,v4_low,v4_high,v5_name,v5_low,v5_high,v6_name,v6_low,v6_high,v7_name,v7_low,v7_high,v8_name,v8_low,v8_high,v9_name,v9_low,v9_high,v10_name,v10_low,v10_high
2
+ I.6.2a,1,f,exp(-theta**2/2)/sqrt(2*pi),1,theta,1,3,,,,,,,,,,,,,,,,,,,,,,,,,,,
3
+ I.6.2,2,f,exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma),2,sigma,1,3,theta,1,3,,,,,,,,,,,,,,,,,,,,,,,,
4
+ I.6.2b,3,f,exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma),3,sigma,1,3,theta,1,3,theta1,1,3,,,,,,,,,,,,,,,,,,,,,
5
+ I.8.14,4,d,sqrt((x2-x1)**2+(y2-y1)**2),4,x1,1,5,x2,1,5,y1,1,5,y2,1,5,,,,,,,,,,,,,,,,,,
6
+ I.9.18,5,F,G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2),9,m1,1,2,m2,1,2,G,1,2,x1,3,4,x2,1,2,y1,3,4,y2,1,2,z1,3,4,z2,1,2,,,
7
+ I.10.7,6,m,m_0/sqrt(1-v**2/c**2),3,m_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
8
+ I.11.19,7,A,x1*y1+x2*y2+x3*y3,6,x1,1,5,x2,1,5,x3,1,5,y1,1,5,y2,1,5,y3,1,5,,,,,,,,,,,,
9
+ I.12.1,8,F,mu*Nn,2,mu,1,5,Nn,1,5,,,,,,,,,,,,,,,,,,,,,,,,
10
+ I.12.2,10,F,q1*q2*r/(4*pi*epsilon*r**3),4,q1,1,5,q2,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,
11
+ I.12.4,11,Ef,q1*r/(4*pi*epsilon*r**3),3,q1,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
12
+ I.12.5,12,F,q2*Ef,2,q2,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
13
+ I.12.11,13,F,q*(Ef+B*v*sin(theta)),5,q,1,5,Ef,1,5,B,1,5,v,1,5,theta,1,5,,,,,,,,,,,,,,,
14
+ I.13.4,9,K,1/2*m*(v**2+u**2+w**2),4,m,1,5,v,1,5,u,1,5,w,1,5,,,,,,,,,,,,,,,,,,
15
+ I.13.12,14,U,G*m1*m2*(1/r2-1/r1),5,m1,1,5,m2,1,5,r1,1,5,r2,1,5,G,1,5,,,,,,,,,,,,,,,
16
+ I.14.3,15,U,m*g*z,3,m,1,5,g,1,5,z,1,5,,,,,,,,,,,,,,,,,,,,,
17
+ I.14.4,16,U,1/2*k_spring*x**2,2,k_spring,1,5,x,1,5,,,,,,,,,,,,,,,,,,,,,,,,
18
+ I.15.3x,17,x1,(x-u*t)/sqrt(1-u**2/c**2),4,x,5,10,u,1,2,c,3,20,t,1,2,,,,,,,,,,,,,,,,,,
19
+ I.15.3t,18,t1,(t-u*x/c**2)/sqrt(1-u**2/c**2),4,x,1,5,c,3,10,u,1,2,t,1,5,,,,,,,,,,,,,,,,,,
20
+ I.15.1,19,p,m_0*v/sqrt(1-v**2/c**2),3,m_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
21
+ I.16.6,20,v1,(u+v)/(1+u*v/c**2),3,c,1,5,v,1,5,u,1,5,,,,,,,,,,,,,,,,,,,,,
22
+ I.18.4,21,r,(m1*r1+m2*r2)/(m1+m2),4,m1,1,5,m2,1,5,r1,1,5,r2,1,5,,,,,,,,,,,,,,,,,,
23
+ I.18.12,22,tau,r*F*sin(theta),3,r,1,5,F,1,5,theta,0,5,,,,,,,,,,,,,,,,,,,,,
24
+ I.18.14,23,L,m*r*v*sin(theta),4,m,1,5,r,1,5,v,1,5,theta,1,5,,,,,,,,,,,,,,,,,,
25
+ I.24.6,24,E_n,1/2*m*(omega**2+omega_0**2)*1/2*x**2,4,m,1,3,omega,1,3,omega_0,1,3,x,1,3,,,,,,,,,,,,,,,,,,
26
+ I.25.13,25,Volt,q/C,2,q,1,5,C,1,5,,,,,,,,,,,,,,,,,,,,,,,,
27
+ I.26.2,26,theta1,arcsin(n*sin(theta2)),2,n,0,1,theta2,1,5,,,,,,,,,,,,,,,,,,,,,,,,
28
+ I.27.6,27,foc,1/(1/d1+n/d2),3,d1,1,5,d2,1,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
29
+ I.29.4,28,k,omega/c,2,omega,1,10,c,1,10,,,,,,,,,,,,,,,,,,,,,,,,
30
+ I.29.16,29,x,sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2)),4,x1,1,5,x2,1,5,theta1,1,5,theta2,1,5,,,,,,,,,,,,,,,,,,
31
+ I.30.3,30,Int,Int_0*sin(n*theta/2)**2/sin(theta/2)**2,3,Int_0,1,5,theta,1,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
32
+ I.30.5,31,theta,arcsin(lambd/(n*d)),3,lambd,1,2,d,2,5,n,1,5,,,,,,,,,,,,,,,,,,,,,
33
+ I.32.5,32,Pwr,q**2*a**2/(6*pi*epsilon*c**3),4,q,1,5,a,1,5,epsilon,1,5,c,1,5,,,,,,,,,,,,,,,,,,
34
+ I.32.17,33,Pwr,(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2),6,epsilon,1,2,c,1,2,Ef,1,2,r,1,2,omega,1,2,omega_0,3,5,,,,,,,,,,,,
35
+ I.34.8,34,omega,q*v*B/p,4,q,1,5,v,1,5,B,1,5,p,1,5,,,,,,,,,,,,,,,,,,
36
+ I.34.1,35,omega,omega_0/(1-v/c),3,c,3,10,v,1,2,omega_0,1,5,,,,,,,,,,,,,,,,,,,,,
37
+ I.34.14,36,omega,(1+v/c)/sqrt(1-v**2/c**2)*omega_0,3,c,3,10,v,1,2,omega_0,1,5,,,,,,,,,,,,,,,,,,,,,
38
+ I.34.27,37,E_n,(h/(2*pi))*omega,2,omega,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,,,,
39
+ I.37.4,38,Int,I1+I2+2*sqrt(I1*I2)*cos(delta),3,I1,1,5,I2,1,5,delta,1,5,,,,,,,,,,,,,,,,,,,,,
40
+ I.38.12,39,r,4*pi*epsilon*(h/(2*pi))**2/(m*q**2),4,m,1,5,q,1,5,h,1,5,epsilon,1,5,,,,,,,,,,,,,,,,,,
41
+ I.39.1,40,E_n,3/2*pr*V,2,pr,1,5,V,1,5,,,,,,,,,,,,,,,,,,,,,,,,
42
+ I.39.11,41,E_n,1/(gamma-1)*pr*V,3,gamma,2,5,pr,1,5,V,1,5,,,,,,,,,,,,,,,,,,,,,
43
+ I.39.22,42,pr,n*kb*T/V,4,n,1,5,T,1,5,V,1,5,kb,1,5,,,,,,,,,,,,,,,,,,
44
+ I.40.1,43,n,n_0*exp(-m*g*x/(kb*T)),6,n_0,1,5,m,1,5,x,1,5,T,1,5,g,1,5,kb,1,5,,,,,,,,,,,,
45
+ I.41.16,44,L_rad,h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1)),5,omega,1,5,T,1,5,h,1,5,kb,1,5,c,1,5,,,,,,,,,,,,,,,
46
+ I.43.16,45,v,mu_drift*q*Volt/d,4,mu_drift,1,5,q,1,5,Volt,1,5,d,1,5,,,,,,,,,,,,,,,,,,
47
+ I.43.31,46,D,mob*kb*T,3,mob,1,5,T,1,5,kb,1,5,,,,,,,,,,,,,,,,,,,,,
48
+ I.43.43,47,kappa,1/(gamma-1)*kb*v/A,4,gamma,2,5,kb,1,5,A,1,5,v,1,5,,,,,,,,,,,,,,,,,,
49
+ I.44.4,48,E_n,n*kb*T*ln(V2/V1),5,n,1,5,kb,1,5,T,1,5,V1,1,5,V2,1,5,,,,,,,,,,,,,,,
50
+ I.47.23,49,c,sqrt(gamma*pr/rho),3,gamma,1,5,pr,1,5,rho,1,5,,,,,,,,,,,,,,,,,,,,,
51
+ I.48.2,50,E_n,m*c**2/sqrt(1-v**2/c**2),3,m,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
52
+ I.50.26,51,x,x1*(cos(omega*t)+alpha*cos(omega*t)**2),4,x1,1,3,omega,1,3,t,1,3,alpha,1,3,,,,,,,,,,,,,,,,,,
53
+ II.2.42,52,Pwr,kappa*(T2-T1)*A/d,5,kappa,1,5,T1,1,5,T2,1,5,A,1,5,d,1,5,,,,,,,,,,,,,,,
54
+ II.3.24,53,flux,Pwr/(4*pi*r**2),2,Pwr,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,,,,
55
+ II.4.23,54,Volt,q/(4*pi*epsilon*r),3,q,1,5,epsilon,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
56
+ II.6.11,55,Volt,1/(4*pi*epsilon)*p_d*cos(theta)/r**2,4,epsilon,1,3,p_d,1,3,theta,1,3,r,1,3,,,,,,,,,,,,,,,,,,
57
+ II.6.15a,56,Ef,p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2),6,epsilon,1,3,p_d,1,3,r,1,3,x,1,3,y,1,3,z,1,3,,,,,,,,,,,,
58
+ II.6.15b,57,Ef,p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3,4,epsilon,1,3,p_d,1,3,theta,1,3,r,1,3,,,,,,,,,,,,,,,,,,
59
+ II.8.7,58,E_n,3/5*q**2/(4*pi*epsilon*d),3,q,1,5,epsilon,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
60
+ II.8.31,59,E_den,epsilon*Ef**2/2,2,epsilon,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
61
+ II.10.9,60,Ef,sigma_den/epsilon*1/(1+chi),3,sigma_den,1,5,epsilon,1,5,chi,1,5,,,,,,,,,,,,,,,,,,,,,
62
+ II.11.3,61,x,q*Ef/(m*(omega_0**2-omega**2)),5,q,1,3,Ef,1,3,m,1,3,omega_0,3,5,omega,1,2,,,,,,,,,,,,,,,
63
+ II.11.17,62,n,n_0*(1+p_d*Ef*cos(theta)/(kb*T)),6,n_0,1,3,kb,1,3,T,1,3,theta,1,3,p_d,1,3,Ef,1,3,,,,,,,,,,,,
64
+ II.11.20,63,Pol,n_rho*p_d**2*Ef/(3*kb*T),5,n_rho,1,5,p_d,1,5,Ef,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,
65
+ II.11.27,64,Pol,n*alpha/(1-(n*alpha/3))*epsilon*Ef,4,n,0,1,alpha,0,1,epsilon,1,2,Ef,1,2,,,,,,,,,,,,,,,,,,
66
+ II.11.28,65,theta,1+n*alpha/(1-(n*alpha/3)),2,n,0,1,alpha,0,1,,,,,,,,,,,,,,,,,,,,,,,,
67
+ II.13.17,66,B,1/(4*pi*epsilon*c**2)*2*I/r,4,epsilon,1,5,c,1,5,I,1,5,r,1,5,,,,,,,,,,,,,,,,,,
68
+ II.13.23,67,rho_c,rho_c_0/sqrt(1-v**2/c**2),3,rho_c_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
69
+ II.13.34,68,j,rho_c_0*v/sqrt(1-v**2/c**2),3,rho_c_0,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,,,,,,,
70
+ II.15.4,69,E_n,-mom*B*cos(theta),3,mom,1,5,B,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
71
+ II.15.5,70,E_n,-p_d*Ef*cos(theta),3,p_d,1,5,Ef,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
72
+ II.21.32,71,Volt,q/(4*pi*epsilon*r*(1-v/c)),5,q,1,5,epsilon,1,5,r,1,5,v,1,2,c,3,10,,,,,,,,,,,,,,,
73
+ II.24.17,72,k,sqrt(omega**2/c**2-pi**2/d**2),3,omega,4,6,c,1,2,d,2,4,,,,,,,,,,,,,,,,,,,,,
74
+ II.27.16,73,flux,epsilon*c*Ef**2,3,epsilon,1,5,c,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,
75
+ II.27.18,74,E_den,epsilon*Ef**2,2,epsilon,1,5,Ef,1,5,,,,,,,,,,,,,,,,,,,,,,,,
76
+ II.34.2a,75,I,q*v/(2*pi*r),3,q,1,5,v,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
77
+ II.34.2,76,mom,q*v*r/2,3,q,1,5,v,1,5,r,1,5,,,,,,,,,,,,,,,,,,,,,
78
+ II.34.11,77,omega,g_*q*B/(2*m),4,g_,1,5,q,1,5,B,1,5,m,1,5,,,,,,,,,,,,,,,,,,
79
+ II.34.29a,78,mom,q*h/(4*pi*m),3,q,1,5,h,1,5,m,1,5,,,,,,,,,,,,,,,,,,,,,
80
+ II.34.29b,79,E_n,g_*mom*B*Jz/(h/(2*pi)),5,g_,1,5,h,1,5,Jz,1,5,mom,1,5,B,1,5,,,,,,,,,,,,,,,
81
+ II.35.18,80,n,n_0/(exp(mom*B/(kb*T))+exp(-mom*B/(kb*T))),5,n_0,1,3,kb,1,3,T,1,3,mom,1,3,B,1,3,,,,,,,,,,,,,,,
82
+ II.35.21,81,M,n_rho*mom*tanh(mom*B/(kb*T)),5,n_rho,1,5,mom,1,5,B,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,
83
+ II.36.38,82,f,mom*H/(kb*T)+(mom*alpha)/(epsilon*c**2*kb*T)*M,8,mom,1,3,H,1,3,kb,1,3,T,1,3,alpha,1,3,epsilon,1,3,c,1,3,M,1,3,,,,,,
84
+ II.37.1,83,E_n,mom*(1+chi)*B,3,mom,1,5,B,1,5,chi,1,5,,,,,,,,,,,,,,,,,,,,,
85
+ II.38.3,84,F,Y*A*x/d,4,Y,1,5,A,1,5,d,1,5,x,1,5,,,,,,,,,,,,,,,,,,
86
+ II.38.14,85,mu_S,Y/(2*(1+sigma)),2,Y,1,5,sigma,1,5,,,,,,,,,,,,,,,,,,,,,,,,
87
+ III.4.32,86,n,1/(exp((h/(2*pi))*omega/(kb*T))-1),4,h,1,5,omega,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,,,,
88
+ III.4.33,87,E_n,(h/(2*pi))*omega/(exp((h/(2*pi))*omega/(kb*T))-1),4,h,1,5,omega,1,5,kb,1,5,T,1,5,,,,,,,,,,,,,,,,,,
89
+ III.7.38,88,omega,2*mom*B/(h/(2*pi)),3,mom,1,5,B,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,
90
+ III.8.54,89,prob,sin(E_n*t/(h/(2*pi)))**2,3,E_n,1,2,t,1,2,h,1,4,,,,,,,,,,,,,,,,,,,,,
91
+ III.9.52,90,prob,(p_d*Ef*t/(h/(2*pi)))*sin((omega-omega_0)*t/2)**2/((omega-omega_0)*t/2)**2,6,p_d,1,3,Ef,1,3,t,1,3,h,1,3,omega,1,5,omega_0,1,5,,,,,,,,,,,,
92
+ III.10.19,91,E_n,mom*sqrt(Bx**2+By**2+Bz**2),4,mom,1,5,Bx,1,5,By,1,5,Bz,1,5,,,,,,,,,,,,,,,,,,
93
+ III.12.43,92,L,n*(h/(2*pi)),2,n,1,5,h,1,5,,,,,,,,,,,,,,,,,,,,,,,,
94
+ III.13.18,93,v,2*E_n*d**2*k/(h/(2*pi)),4,E_n,1,5,d,1,5,k,1,5,h,1,5,,,,,,,,,,,,,,,,,,
95
+ III.14.14,94,I,I_0*(exp(q*Volt/(kb*T))-1),5,I_0,1,5,q,1,2,Volt,1,2,kb,1,2,T,1,2,,,,,,,,,,,,,,,
96
+ III.15.12,95,E_n,2*U*(1-cos(k*d)),3,U,1,5,k,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
97
+ III.15.14,96,m,(h/(2*pi))**2/(2*E_n*d**2),3,h,1,5,E_n,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
98
+ III.15.27,97,k,2*pi*alpha/(n*d),3,alpha,1,5,n,1,5,d,1,5,,,,,,,,,,,,,,,,,,,,,
99
+ III.17.37,98,f,beta*(1+alpha*cos(theta)),3,beta,1,5,alpha,1,5,theta,1,5,,,,,,,,,,,,,,,,,,,,,
100
+ III.19.51,99,E_n,-m*q**4/(2*(4*pi*epsilon)**2*(h/(2*pi))**2)*(1/n**2),5,m,1,5,q,1,5,h,1,5,n,1,5,epsilon,1,5,,,,,,,,,,,,,,,
101
+ III.21.20,100,j,-rho_c_0*q*A_vec/m,4,rho_c_0,1,5,q,1,5,A_vec,1,5,m,1,5,,,,,,,,,,,,,,,,,,
102
+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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+ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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equations.jsonl ADDED
@@ -0,0 +1,100 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {"name": "I.6.2a", "symbols": ["f", "theta"], "symbol_descs": ["Dimensionless", "Dimensionless"], "symbol_properties": ["O", "V"], "expression": "exp(-theta**2/2)/sqrt(2*pi)", "symbol_ranges": [null, [1.0, 3.0]]}
2
+ {"name": "I.6.2", "symbols": ["f", "sigma", "theta"], "symbol_descs": ["Dimensionless", "Dimensionless", "Dimensionless"], "symbol_properties": ["O", "V", "V"], "expression": "exp(-(theta/sigma)**2/2)/(sqrt(2*pi)*sigma)", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0]]}
3
+ {"name": "I.6.2b", "symbols": ["f", "sigma", "theta", "theta1"], "symbol_descs": ["Dimensionless", "Dimensionless", "Dimensionless", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V"], "expression": "exp(-((theta-theta1)/sigma)**2/2)/(sqrt(2*pi)*sigma)", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
4
+ {"name": "I.8.14", "symbols": ["d", "x1", "x2", "y1", "y2"], "symbol_descs": ["Length", "Length", "Length", "Length", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt((x2-x1)**2+(y2-y1)**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
5
+ {"name": "I.9.18", "symbols": ["F", "m1", "m2", "G", "x1", "x2", "y1", "y2", "z1", "z2"], "symbol_descs": ["Force", "Mass", "Mass", "Newton's constant", "Length", "Length", "Length", "Length", "Length", "Length"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V", "V", "V", "V"], "expression": "G*m1*m2/((x2-x1)**2+(y2-y1)**2+(z2-z1)**2)", "symbol_ranges": [null, [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 4.0], [1.0, 2.0], [3.0, 4.0], [1.0, 2.0], [3.0, 4.0], [1.0, 2.0]]}
6
+ {"name": "I.10.7", "symbols": ["m", "m_0", "v", "c"], "symbol_descs": ["Mass", "Mass", "Velocity", "Velocity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m_0/sqrt(1-v**2/c**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 2.0], [3.0, 10.0]]}
7
+ {"name": "I.11.19", "symbols": ["A", "x1", "x2", "x3", "y1", "y2", "y3"], "symbol_descs": ["Area", "Length", "Length", "Length", "Length", "Length", "Length"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "x1*y1+x2*y2+x3*y3", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
8
+ {"name": "I.12.1", "symbols": ["F", "mu", "Nn"], "symbol_descs": ["Force", "Dimensionless", "Force"], "symbol_properties": ["O", "V", "V"], "expression": "mu*Nn", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
9
+ {"name": "I.12.2", "symbols": ["F", "q1", "q2", "epsilon", "r"], "symbol_descs": ["Force", "Charge", "Charge", "Electric permitivity", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "q1*q2*r/(4*pi*epsilon*r**3)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
10
+ {"name": "I.12.4", "symbols": ["Ef", "q1", "epsilon", "r"], "symbol_descs": ["Electric field", "Charge", "Electric permitivity", "Length"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q1*r/(4*pi*epsilon*r**3)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
11
+ {"name": "I.12.5", "symbols": ["F", "q2", "Ef"], "symbol_descs": ["Force", "Charge", "Electric field"], "symbol_properties": ["O", "V", "V"], "expression": "q2*Ef", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
12
+ {"name": "I.12.11", "symbols": ["F", "q", "Ef", "B", "v", "theta"], "symbol_descs": ["Force", "Charge", "Electric field", "Magnetic field", "Velocity", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "q*(Ef+B*v*sin(theta))", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
13
+ {"name": "I.13.4", "symbols": ["K", "m", "v", "u", "w"], "symbol_descs": ["Energy", "Mass", "Velocity", "Velocity", "Velocity"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/2*m*(v**2+u**2+w**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
14
+ {"name": "I.13.12", "symbols": ["U", "m1", "m2", "r1", "r2", "G"], "symbol_descs": ["Energy", "Mass", "Mass", "Length", "Length", "Newton's constant"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "G*m1*m2*(1/r2-1/r1)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
15
+ {"name": "I.14.3", "symbols": ["U", "m", "g", "z"], "symbol_descs": ["Energy", "Mass", "Acceleration", "Length"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m*g*z", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
16
+ {"name": "I.14.4", "symbols": ["U", "k_spring", "x"], "symbol_descs": ["Energy", "Spring constant", "Length"], "symbol_properties": ["O", "V", "V"], "expression": "1/2*k_spring*x**2", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
17
+ {"name": "I.15.3x", "symbols": ["x1", "x", "u", "c", "t"], "symbol_descs": ["Length", "Length", "Velocity", "Velocity", "\u03a4ime"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(x-u*t)/sqrt(1-u**2/c**2)", "symbol_ranges": [null, [5.0, 10.0], [1.0, 2.0], [3.0, 20.0], [1.0, 2.0]]}
18
+ {"name": "I.15.3t", "symbols": ["t1", "x", "c", "u", "t"], "symbol_descs": ["\u03a4ime", "Length", "Velocity", "Velocity", "\u03a4ime"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(t-u*x/c**2)/sqrt(1-u**2/c**2)", "symbol_ranges": [null, [1.0, 5.0], [3.0, 10.0], [1.0, 2.0], [1.0, 5.0]]}
19
+ {"name": "I.15.1", "symbols": ["p", "m_0", "v", "c"], "symbol_descs": ["Momentum", "Mass", "Velocity", "Velocity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m_0*v/sqrt(1-v**2/c**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 2.0], [3.0, 10.0]]}
20
+ {"name": "I.16.6", "symbols": ["v1", "c", "v", "u"], "symbol_descs": ["Velocity", "Velocity", "Velocity", "Velocity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "(u+v)/(1+u*v/c**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
21
+ {"name": "I.18.4", "symbols": ["r", "m1", "m2", "r1", "r2"], "symbol_descs": ["Length", "Mass", "Mass", "Length", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "(m1*r1+m2*r2)/(m1+m2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
22
+ {"name": "I.18.12", "symbols": ["tau", "r", "F", "theta"], "symbol_descs": ["Torque", "Length", "Force", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V"], "expression": "r*F*sin(theta)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [0.0, 5.0]]}
23
+ {"name": "I.18.14", "symbols": ["L", "m", "r", "v", "theta"], "symbol_descs": ["Angular momentum", "Mass", "Length", "Velocity", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "m*r*v*sin(theta)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
24
+ {"name": "I.24.6", "symbols": ["E_n", "m", "omega", "omega_0", "x"], "symbol_descs": ["Energy", "Mass", "Frequency", "Frequency", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/2*m*(omega**2+omega_0**2)*1/2*x**2", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
25
+ {"name": "I.25.13", "symbols": ["Volt", "q", "C"], "symbol_descs": ["Voltage", "Charge", "Capacitance"], "symbol_properties": ["O", "V", "V"], "expression": "q/C", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
26
+ {"name": "I.26.2", "symbols": ["theta1", "n", "theta2"], "symbol_descs": ["Dimensionless", "Dimensionless", "Dimensionless"], "symbol_properties": ["O", "V", "V"], "expression": "arcsin(n*sin(theta2))", "symbol_ranges": [null, [0.0, 1.0], [1.0, 5.0]]}
27
+ {"name": "I.27.6", "symbols": ["foc", "d1", "d2", "n"], "symbol_descs": ["Length", "Length", "Length", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V"], "expression": "1/(1/d1+n/d2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
28
+ {"name": "I.29.4", "symbols": ["k", "omega", "c"], "symbol_descs": ["Wave number", "Frequency", "Velocity"], "symbol_properties": ["O", "V", "V"], "expression": "omega/c", "symbol_ranges": [null, [1.0, 10.0], [1.0, 10.0]]}
29
+ {"name": "I.29.16", "symbols": ["x", "x1", "x2", "theta1", "theta2"], "symbol_descs": ["Length", "Length", "Length", "Dimensionless", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "sqrt(x1**2+x2**2-2*x1*x2*cos(theta1-theta2))", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
30
+ {"name": "I.30.3", "symbols": ["Int", "Int_0", "theta", "n"], "symbol_descs": ["Light intensity", "Light intensity", "Dimensionless", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V"], "expression": "Int_0*sin(n*theta/2)**2/sin(theta/2)**2", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
31
+ {"name": "I.30.5", "symbols": ["theta", "lambd", "d", "n"], "symbol_descs": ["Dimensionless", "Length", "Length", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V"], "expression": "arcsin(lambd/(n*d))", "symbol_ranges": [null, [1.0, 2.0], [2.0, 5.0], [1.0, 5.0]]}
32
+ {"name": "I.32.5", "symbols": ["Pwr", "q", "a", "epsilon", "c"], "symbol_descs": ["Power", "Charge", "Acceleration", "Electric permitivity", "Velocity"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "q**2*a**2/(6*pi*epsilon*c**3)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
33
+ {"name": "I.32.17", "symbols": ["Pwr", "epsilon", "c", "Ef", "r", "omega", "omega_0"], "symbol_descs": ["Power", "Electric permitivity", "Velocity", "Electric field", "Length", "Frequency", "Frequency"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "(1/2*epsilon*c*Ef**2)*(8*pi*r**2/3)*(omega**4/(omega**2-omega_0**2)**2)", "symbol_ranges": [null, [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [1.0, 2.0], [3.0, 5.0]]}
34
+ {"name": "I.34.8", "symbols": ["omega", "q", "v", "B", "p"], "symbol_descs": ["Frequency", "Charge", "Velocity", "Magnetic field", "Momentum"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "q*v*B/p", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
35
+ {"name": "I.34.1", "symbols": ["omega", "c", "v", "omega_0"], "symbol_descs": ["Frequency", "Velocity", "Velocity", "Frequency"], "symbol_properties": ["O", "V", "V", "V"], "expression": "omega_0/(1-v/c)", "symbol_ranges": [null, [3.0, 10.0], [1.0, 2.0], [1.0, 5.0]]}
36
+ {"name": "I.34.14", "symbols": ["omega", "c", "v", "omega_0"], "symbol_descs": ["Frequency", "Velocity", "Velocity", "Frequency"], "symbol_properties": ["O", "V", "V", "V"], "expression": "(1+v/c)/sqrt(1-v**2/c**2)*omega_0", "symbol_ranges": [null, [3.0, 10.0], [1.0, 2.0], [1.0, 5.0]]}
37
+ {"name": "I.34.27", "symbols": ["E_n", "omega", "h"], "symbol_descs": ["Energy", "Frequency", "Angular momentum"], "symbol_properties": ["O", "V", "V"], "expression": "(h/(2*pi))*omega", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
38
+ {"name": "I.37.4", "symbols": ["Int", "I1", "I2", "delta"], "symbol_descs": ["Light intensity", "Light intensity", "Light intensity", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V"], "expression": "I1+I2+2*sqrt(I1*I2)*cos(delta)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
39
+ {"name": "I.38.12", "symbols": ["r", "m", "q", "h", "epsilon"], "symbol_descs": ["Length", "Mass", "Charge", "Angular momentum", "Electric permitivity"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "4*pi*epsilon*(h/(2*pi))**2/(m*q**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
40
+ {"name": "I.39.1", "symbols": ["E_n", "pr", "V"], "symbol_descs": ["Energy", "Pressure", "volume"], "symbol_properties": ["O", "V", "V"], "expression": "3/2*pr*V", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
41
+ {"name": "I.39.11", "symbols": ["E_n", "gamma", "pr", "V"], "symbol_descs": ["Energy", "Dimensionless", "Pressure", "volume"], "symbol_properties": ["O", "V", "V", "V"], "expression": "1/(gamma-1)*pr*V", "symbol_ranges": [null, [2.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
42
+ {"name": "I.39.22", "symbols": ["pr", "n", "T", "V", "kb"], "symbol_descs": ["Pressure", "Dimensionless", "Temperature", "volume", "Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "n*kb*T/V", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
43
+ {"name": "I.40.1", "symbols": ["n", "n_0", "m", "x", "T", "g", "kb"], "symbol_descs": ["Dimensionless", "Dimensionless", "Mass", "Length", "Temperature", "Acceleration", "Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "n_0*exp(-m*g*x/(kb*T))", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
44
+ {"name": "I.41.16", "symbols": ["L_rad", "omega", "T", "h", "kb", "c"], "symbol_descs": ["Spectral radiance", "Frequency", "Temperature", "Angular momentum", "Boltzmann constant", "Velocity"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "h/(2*pi)*omega**3/(pi**2*c**2*(exp((h/(2*pi))*omega/(kb*T))-1))", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
45
+ {"name": "I.43.16", "symbols": ["v", "mu_drift", "q", "Volt", "d"], "symbol_descs": ["Velocity", "Drift velocity constant", "Charge", "Voltage", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "mu_drift*q*Volt/d", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
46
+ {"name": "I.43.31", "symbols": ["D", "mob", "T", "kb"], "symbol_descs": ["Diffusion coefficient", "Mobility", "Temperature", "Boltzmann constant"], "symbol_properties": ["O", "V", "V", "V"], "expression": "mob*kb*T", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
47
+ {"name": "I.43.43", "symbols": ["kappa", "gamma", "kb", "A", "v"], "symbol_descs": ["Thermal conductivity", "Dimensionless", "Boltzmann constant", "Area", "Velocity"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/(gamma-1)*kb*v/A", "symbol_ranges": [null, [2.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
48
+ {"name": "I.44.4", "symbols": ["E_n", "n", "kb", "T", "V1", "V2"], "symbol_descs": ["Energy", "Dimensionless", "Boltzmann constant", "Temperature", "volume", "volume"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "n*kb*T*ln(V2/V1)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
49
+ {"name": "I.47.23", "symbols": ["c", "gamma", "pr", "rho"], "symbol_descs": ["Velocity", "Dimensionless", "Pressure", "Density"], "symbol_properties": ["O", "V", "V", "V"], "expression": "sqrt(gamma*pr/rho)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
50
+ {"name": "I.48.2", "symbols": ["E_n", "m", "v", "c"], "symbol_descs": ["Energy", "Mass", "Velocity", "Velocity"], "symbol_properties": ["O", "V", "V", "V"], "expression": "m*c**2/sqrt(1-v**2/c**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 2.0], [3.0, 10.0]]}
51
+ {"name": "I.50.26", "symbols": ["x", "x1", "omega", "t", "alpha"], "symbol_descs": ["Length", "Length", "Frequency", "\u03a4ime", "Dimensionless"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "x1*(cos(omega*t)+alpha*cos(omega*t)**2)", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
52
+ {"name": "II.2.42", "symbols": ["Pwr", "kappa", "T1", "T2", "A", "d"], "symbol_descs": ["Power", "Thermal conductivity", "Temperature", "Temperature", "Area", "Length"], "symbol_properties": ["O", "V", "V", "V", "V", "V"], "expression": "kappa*(T2-T1)*A/d", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
53
+ {"name": "II.3.24", "symbols": ["flux", "Pwr", "r"], "symbol_descs": ["Energy flux", "Power", "Length"], "symbol_properties": ["O", "V", "V"], "expression": "Pwr/(4*pi*r**2)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
54
+ {"name": "II.4.23", "symbols": ["Volt", "q", "epsilon", "r"], "symbol_descs": ["Voltage", "Charge", "Electric permitivity", "Length"], "symbol_properties": ["O", "V", "V", "V"], "expression": "q/(4*pi*epsilon*r)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
55
+ {"name": "II.6.11", "symbols": ["Volt", "epsilon", "p_d", "theta", "r"], "symbol_descs": ["Voltage", "Electric permitivity", "Electric dipole moment", "Dimensionless", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "1/(4*pi*epsilon)*p_d*cos(theta)/r**2", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
56
+ {"name": "II.6.15a", "symbols": ["Ef", "epsilon", "p_d", "r", "x", "y", "z"], "symbol_descs": ["Electric field", "Electric permitivity", "Electric dipole moment", "Length", "Length", "Length", "Length"], "symbol_properties": ["O", "V", "V", "V", "V", "V", "V"], "expression": "p_d/(4*pi*epsilon)*3*z/r**5*sqrt(x**2+y**2)", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
57
+ {"name": "II.6.15b", "symbols": ["Ef", "epsilon", "p_d", "theta", "r"], "symbol_descs": ["Electric field", "Electric permitivity", "Electric dipole moment", "Dimensionless", "Length"], "symbol_properties": ["O", "V", "V", "V", "V"], "expression": "p_d/(4*pi*epsilon)*3*cos(theta)*sin(theta)/r**3", "symbol_ranges": [null, [1.0, 3.0], [1.0, 3.0], [1.0, 3.0], [1.0, 3.0]]}
58
+ {"name": "II.8.7", "symbols": ["E_n", "q", "epsilon", "d"], "symbol_descs": ["Energy", "Charge", "Electric permitivity", "Length"], "symbol_properties": ["O", "V", "V", "V"], "expression": "3/5*q**2/(4*pi*epsilon*d)", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0], [1.0, 5.0]]}
59
+ {"name": "II.8.31", "symbols": ["E_den", "epsilon", "Ef"], "symbol_descs": ["Energy density", "Electric permitivity", "Electric field"], "symbol_properties": ["O", "V", "V"], "expression": "epsilon*Ef**2/2", "symbol_ranges": [null, [1.0, 5.0], [1.0, 5.0]]}
60
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