Euclidean surfaces : retrieve the Codazzi equation. 

in collaboration with I. Kogan. 

>	coord_frame([x,y],[u],fr);

 

fr>	LieAlg:=[[1,0,0],[0,1,0],[0,0,1],[-u[0,0],0,x],[0,-u[0,0],y],[-y,x,0]]: LieAlg:=map( V-> v_zip(V,frameJetVariables(fr,0)[1..3],plus, vect), LieAlg);

 

fr >	Section:=[x=0,y=0,u[0,0]=0,u[1,0]=0,u[0,1]=0,u[1,1]=0]: stair(Section);

 

fr >	C, Invariantizations :=dmf(LieAlg,Section, fr, [op(Section), u[2,0]=kappa1, u[0,2]=kappa2], com):

 

"Section :" 

"Transversality condition :"   -u[2   0]+u[0   2]
"Invariantizations:" 

"Commutation rules" 

"Syzygies" 

"Syzygies with attempt to eliminate the y's" 

Recognize Codazzi equation in the differential syzygies ideal: 

fr >	collect(equations(C[1])[-1], [kappa2[2,0],kappa1[0,2]]);