Minimal order cross-section 

fr > Section:=[x=0,u[0]=0,v[0]=0,u[1]=0,v[1]=0,v[2]=0]:
 

fr > C , Invariantizations := dmf (LieAlg,Section, fr, [op(Section), u[2]=kappa, v[3]=kappa*tau]):
 

"Section :" 

[v[2] = 0, v[1] = 0, u[1] = 0, v[0] = 0, u[0] = 0, x = 0] 

"Transversality condition :"   u[2]
"Invariantizations:" 

x = 0, u[0] = 0, v[0] = 0, u[1] = 0, v[1] = 0, v[2] = 0, u[2] = kappa, v[3] = kappa*tau, u[3] = y1 

"Commutation rules" 

 

"Syzygies" 

[kappa[1]-y1[0], -1+y0[0]*kappa[0]] 

"Syzygies with attempt to eliminate the y's" 

y0[0] = 1/kappa[0] 

y1[0] = kappa[1] 

fr > Invariantizations;
 

[x = 0, u[0] = 0, v[0] = 0, u[1] = 0, v[1] = 0, v[2] = 0, u[2] = kappa[0], v[3] = kappa[0]*tau[0], u[3] = kappa[1], u[4] = 3*kappa[0]^3-kappa[0]*tau[0]^2+kappa[2], v[4] = 2*kappa[1]*tau[0]+kappa[0]*ta...
[x = 0, u[0] = 0, v[0] = 0, u[1] = 0, v[1] = 0, v[2] = 0, u[2] = kappa[0], v[3] = kappa[0]*tau[0], u[3] = kappa[1], u[4] = 3*kappa[0]^3-kappa[0]*tau[0]^2+kappa[2], v[4] = 2*kappa[1]*tau[0]+kappa[0]*ta... 

fr > rewrite_rules(C);
 

[[y0[0] = 1/kappa[0], y1[0] = kappa[1]]]