%-----------------------------------------------------------------
%programm for generation curvature equations of movig curve 27 08 97
%-----------------------------------------------------------------

%off nat;
dim:=3;


DIM := 3


%--------------curvature matrix------------------------
%for all ii, jj let k(ii,jj) = - k(jj,ii);

procedure delta(ii,jj);begin if ii eq jj then return 1 else return 0; end;


DELTA


%--------------frenet frame ------------------------
%noncom f;
operator f;


operator k;




for all ii such that ii<1 or ii>(dim-1) let k(ii)=0;



for all ii,xxx,yyy let f(ii,xxx*yyy) = f(ii,xxx)*yyy + xxx*f(ii,yyy);


for all ii,xxx,yyy let f(ii,xxx + yyy) = f(ii,xxx) + f(ii,yyy);


for all ii,xxx let f(ii,-xxx) = - f(ii,xxx);



f(1,f(2)*k(1));


F(2)*F(1,K(1)) + F(1,F(2))*K(1)


for all ii let f(1,f(ii,ar)) = k(ii)*f(ii+1,ar) - k(ii-1)*f(ii-1,ar);



for ii:=1:dim do write f(1,f(ii,ar));


F(2,AR)*K(1)

F(3,AR)*K(2) - F(1,AR)*K(1)

 - F(2,AR)*K(2)


%--------------evolution frame ------------------------
operator x;


antisymmetric M;


for ii:=1:dim do for jj:=1:dim do write M(ii,jj);


*** M declared operator 

0

 - M(2,1)

 - M(3,1)

M(2,1)

0

 - M(3,2)

M(3,1)

M(3,2)

0


for all xxx,yyy let XX(xxx*yyy) = XX(xxx)*yyy + xxx*XX(yyy);


*** XX declared operator 

for all xxx,yyy let XX(xxx + yyy) = XX(xxx) + XX(yyy);


for all ii,xxx let XX(-xxx) = - XX(xxx);



for ii:=1:dim do XX(f(ii,ar)):=for jj:=1:dim sum M(ii,jj)*f(jj,ar);




for ii:=1:dim do write ("XX(f(",ii,",ar)):=", XX(f(ii,ar)));


XX(f(1,ar)):= - (F(3,AR)*M(3,1) + F(2,AR)*M(2,1))

XX(f(2,ar)):= - F(3,AR)*M(3,2) + F(1,AR)*M(2,1)

XX(f(3,ar)):=F(2,AR)*M(3,2) + F(1,AR)*M(3,1)


%--------------compatibility ------------------------
%factor f;
%for all ii factor f(ii,ar);
for ii:=1:dim do factor f(ii,ar);




XX(f(1,f(1,ar)));


F(1,AR)*K(1)*M(2,1) + F(2,AR)*XX(K(1)) - F(3,AR)*K(1)*M(3,2)

F(1,XX(f(1,ar)));


F(1,AR)*K(1)*M(2,1) + F(2,AR)*( - F(1,M(2,1)) + K(2)*M(3,1))

 - F(3,AR)*(F(1,M(3,1)) + K(2)*M(2,1))


for ii:=1:dim do write("row", ii,"  ",  XX(f(1,f(ii,ar))) - F(1,XX(f(ii,ar))) );


row1  F(2,AR)*(F(1,M(2,1)) - K(2)*M(3,1) + XX(K(1)))

       + F(3,AR)*(F(1,M(3,1)) + K(2)*M(2,1) - K(1)*M(3,2))

row2  F(1,AR)*( - F(1,M(2,1)) + K(2)*M(3,1) - XX(K(1)))

       + F(3,AR)*(F(1,M(3,2)) + K(1)*M(3,1) + XX(K(2)))

row3  F(1,AR)*( - F(1,M(3,1)) - K(2)*M(2,1) + K(1)*M(3,2))

       - F(2,AR)*(F(1,M(3,2)) + K(1)*M(3,1) + XX(K(2)))


%----------------- setting of the first row of matrix M 
%                 via condition [XX, f(1,ar)] = ro*f(1,ar)

operator c;


for all ii such that ii<1 or ii>(dim) let c(ii)=0;



vf1:= ro*f(1,ar) 
+ for ii:=1:dim sum (f(1,c(ii)) + c(ii-1)*k(ii-1) - c(ii+1)*k(ii) )*f(ii,ar);


VF1 := F(1,AR)*( - C(2)*K(1) + F(1,C(1)) + RO)

        + F(2,AR)*( - C(3)*K(2) + C(1)*K(1) + F(1,C(2)))

        + F(3,AR)*(C(2)*K(2) + F(1,C(3)))


ro:= - f(1,c(1)) + c(2)*k(1);


RO := C(2)*K(1) - F(1,C(1))

vf1;


F(2,AR)*( - C(3)*K(2) + C(1)*K(1) + F(1,C(2)))

 + F(3,AR)*(C(2)*K(2) + F(1,C(3)))

off nat;


for jj:=2:dim do M(1,jj):=coeffn(vf1,f(jj,ar),1);


for ii:=1:dim do for jj:=1:dim do write M(ii,jj);


0$

 - C(3)*K(2) + C(1)*K(1) + F(1,C(2))$

C(2)*K(2) + F(1,C(3))$

C(3)*K(2) - C(1)*K(1) - F(1,C(2))$

0$

 - M(3,2)$

 - (C(2)*K(2) + F(1,C(3)))$

M(3,2)$

0$

for ii:=1:dim do <<roww(ii) := XX(f(1,f(ii,ar))) - F(1,XX(f(ii,ar))) 
                               - ro*f(1,f(ii,ar));

			write("roww(", ii,"):=",roww(ii));
                 >>;


roww(1):=F(2,AR)*(C(3)*F(1,K(2)) + C(2)*K(2)**2 - C(2)*K(1)**2 - C(1)
*F(1,K(1)) + 2*F(1,C(3))*K(2) - F(1,F(1,C(2))) + XX(K(1))) + F(3,
AR)*(C(3)*K(2)**2 - C(2)*F(1,K(2)) - C(1)*K(2)*K(1) - 2*F(1,C(2))*
K(2) - F(1,F(1,C(3))) - K(1)*M(3,2))$

roww(2):=F(1,AR)*( - C(3)*F(1,K(2)) - C(2)*K(2)**2 + C(2)*K(1)**2 + C
(1)*F(1,K(1)) - 2*F(1,C(3))*K(2) + F(1,F(1,C(2))) - XX(K(1))) + F(
3,AR)*( - 2*C(2)*K(2)*K(1) - F(1,C(3))*K(1) + F(1,C(1))*K(2) + F(1
,M(3,2)) + XX(K(2)))$

roww(3):=F(1,AR)*( - C(3)*K(2)**2 + C(2)*F(1,K(2)) + C(1)*K(2)*K(1) +
 2*F(1,C(2))*K(2) + F(1,F(1,C(3))) + K(1)*M(3,2)) + F(2,AR)*(2*C(2
)*K(2)*K(1) + F(1,C(3))*K(1) - F(1,C(1))*K(2) - F(1,M(3,2)) - XX(K
(2)))$


for ii:=1:dim do for jj:=1:dim do write(coeffn(roww(ii),f(jj,ar),1));


0$

C(3)*F(1,K(2)) + C(2)*K(2)**2 - C(2)*K(1)**2 - C(1)*F(1,K(1)) + 2*F(1
,C(3))*K(2) - F(1,F(1,C(2))) + XX(K(1))$

C(3)*K(2)**2 - C(2)*F(1,K(2)) - C(1)*K(2)*K(1) - 2*F(1,C(2))*K(2) - F
(1,F(1,C(3))) - K(1)*M(3,2)$

 - C(3)*F(1,K(2)) - C(2)*K(2)**2 + C(2)*K(1)**2 + C(1)*F(1,K(1)) - 2*
F(1,C(3))*K(2) + F(1,F(1,C(2))) - XX(K(1))$

0$

 - 2*C(2)*K(2)*K(1) - F(1,C(3))*K(1) + F(1,C(1))*K(2) + F(1,M(3,2)) +
 XX(K(2))$

 - C(3)*K(2)**2 + C(2)*F(1,K(2)) + C(1)*K(2)*K(1) + 2*F(1,C(2))*K(2) 
+ F(1,F(1,C(3))) + K(1)*M(3,2)$

2*C(2)*K(2)*K(1) + F(1,C(3))*K(1) - F(1,C(1))*K(2) - F(1,M(3,2)) - XX
(K(2))$

0$




shut ff1;