rreducparautommodg6_6N5.r generic derivation : delta:= [ 0 xi(1,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [xi(3,1) xi(3,2) 0 0 0 0 ] [ ] [xi(4,1) xi(4,2) xi(4,3) 0 0 0 ] [ ] [xi(5,1) xi(5,2) xi(5,3) - xi(4,1) 0 xi(4,3)] [ ] [xi(6,1) xi(6,2) xi(6,3) - xi(3,1) 0 0 ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx1 := [ ] [0 1 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx2 := [ ] [-1 0 0 0 0 0] [ ] [0 0 0 1 0 0] [ ] [0 0 1 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx3 := [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 -1 0 0 0 0] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] [ ] [0 0 0 0 0 0] adx4 := [ ] [0 0 0 0 0 0] [ ] [0 -1 0 0 0 0] [ ] [0 0 0 0 0 0] by subtracting adjoints one then may suppose: xi(4,1):=0,xi(4,2):=0,xi(5,1):=0,xi(6,2):=0 delta:= [ 0 xi(1,2) 0 0 0 0 ] [ ] [ 0 0 0 0 0 0 ] [ ] [xi(3,1) xi(3,2) 0 0 0 0 ] [ ] [ 0 0 xi(4,3) 0 0 0 ] [ ] [xi(5,1) 0 xi(5,3) 0 0 xi(4,3)] [ ] [xi(6,1) 0 xi(6,3) - xi(3,1) 0 0 ] We denote this delta by the shortform shortformdelta:={xi(1,2), ss, xi(3,1), xi(3,2), ss, xi(4,3), ss, xi(5,1), xi(5,3), ss, xi(6,1), xi(6,3)} paramindexeslist:={{1,2},{3,1},{3,2},{4,3},{5,1},{5,3},{6,1},{6,3}} With the generic automorphism one gets$ shortformdeltaprimemodadg:={(b(1,1)*xi(1,2))/b(2,2), ss, (b(3,3)*xi(3,1))/b(1,1), ( - b(3,3)*b(1,2)*xi(3,1) + b(3,3)*b(1,1)*xi(3,2) + b(3,1)*b(1,1)*xi(1,2))/(b(2, 2)*b(1,1)), ss, (b(2,2)*b(1,1)*xi(4,3))/b(3,3), ss, (b(6,3)*b(3,1)*b(2,2)*b(1,1)**2*xi(4,3) - b(6,1)*b(3,3)*b(2,2)*b(1,1)**2*xi(4,3) + b(5,3)*b(3,3)**2*b(1,1)*xi(3,1) - b(4,3)**2*b(3,3)*b(3,1)*xi(3,1) + b(4,3)*b( 4,1)*b(3,3)**2*xi(3,1) + b(4,3)*b(3,3)**2*b(2,2)*b(1,1)*xi(6,1) - b(4,3)*b(3,3)* b(3,1)*b(2,2)*b(1,1)*xi(6,3) + b(4,3)*b(3,1)**2*b(2,2)*b(1,1)*xi(4,3) + b(3,3)** 2*b(2,2)**2*b(1,1)**2*xi(5,1) - b(3,3)*b(3,1)*b(2,2)**2*b(1,1)**2*xi(5,3))/(b(3, 3)**2*b(1,1)**2), ( - b(6,3)*b(2,2)*b(1,1)**2*xi(4,3) + b(4,3)**2*b(3,3)*xi(3,1) + b(4,3)*b(3,3)*b (2,2)*b(1,1)*xi(6,3) - b(4,3)*b(3,1)*b(2,2)*b(1,1)*xi(4,3) - b(4,1)*b(3,3)*b(2,2 )*b(1,1)*xi(4,3) + b(3,3)*b(2,2)**2*b(1,1)**2*xi(5,3))/(b(3,3)**2*b(1,1)), ss, (b(6,3)*b(3,3)*b(1,1)*xi(3,1) - b(4,3)*b(3,3)*b(3,1)*xi(3,1) + b(4,1)*b(3,3)**2* xi(3,1) + b(3,3)**2*b(2,2)*b(1,1)*xi(6,1) - b(3,3)*b(3,1)*b(2,2)*b(1,1)*xi(6,3) + b(3,1)**2*b(2,2)*b(1,1)*xi(4,3))/(b(3,3)*b(1,1)**2), (2*b(4,3)*b(3,3)*xi(3,1) + b(3,3)*b(2,2)*b(1,1)*xi(6,3) - 2*b(3,1)*b(2,2)*b(1,1) *xi(4,3))/(b(3,3)*b(1,1))}$ deltaprimemodg(1,2):=(b(1,1)*xi(1,2))/b(2,2)$ deltaprimemodg(3,1):=(b(3,3)*xi(3,1))/b(1,1)$ deltaprimemodg(3,2):=( - b(3,3)*b(1,2)*xi(3,1) + b(3,3)*b(1,1)*xi(3,2) + b(3,1)* b(1,1)*xi(1,2))/(b(2,2)*b(1,1))$ deltaprimemodg(4,3):=(b(2,2)*b(1,1)*xi(4,3))/b(3,3)$ deltaprimemodg(5,1):=(b(6,3)*b(3,1)*b(2,2)*b(1,1)**2*xi(4,3) - b(6,1)*b(3,3)*b(2 ,2)*b(1,1)**2*xi(4,3) + b(5,3)*b(3,3)**2*b(1,1)*xi(3,1) - b(4,3)**2*b(3,3)*b(3,1 )*xi(3,1) + b(4,3)*b(4,1)*b(3,3)**2*xi(3,1) + b(4,3)*b(3,3)**2*b(2,2)*b(1,1)*xi( 6,1) - b(4,3)*b(3,3)*b(3,1)*b(2,2)*b(1,1)*xi(6,3) + b(4,3)*b(3,1)**2*b(2,2)*b(1, 1)*xi(4,3) + b(3,3)**2*b(2,2)**2*b(1,1)**2*xi(5,1) - b(3,3)*b(3,1)*b(2,2)**2*b(1 ,1)**2*xi(5,3))/(b(3,3)**2*b(1,1)**2)$ deltaprimemodg(5,3):=( - b(6,3)*b(2,2)*b(1,1)**2*xi(4,3) + b(4,3)**2*b(3,3)*xi(3 ,1) + b(4,3)*b(3,3)*b(2,2)*b(1,1)*xi(6,3) - b(4,3)*b(3,1)*b(2,2)*b(1,1)*xi(4,3) - b(4,1)*b(3,3)*b(2,2)*b(1,1)*xi(4,3) + b(3,3)*b(2,2)**2*b(1,1)**2*xi(5,3))/(b(3 ,3)**2*b(1,1))$ deltaprimemodg(6,1):=(b(6,3)*b(3,3)*b(1,1)*xi(3,1) - b(4,3)*b(3,3)*b(3,1)*xi(3,1 ) + b(4,1)*b(3,3)**2*xi(3,1) + b(3,3)**2*b(2,2)*b(1,1)*xi(6,1) - b(3,3)*b(3,1)*b (2,2)*b(1,1)*xi(6,3) + b(3,1)**2*b(2,2)*b(1,1)*xi(4,3))/(b(3,3)*b(1,1)**2)$ deltaprimemodg(6,3):=(2*b(4,3)*b(3,3)*xi(3,1) + b(3,3)*b(2,2)*b(1,1)*xi(6,3) - 2 *b(3,1)*b(2,2)*b(1,1)*xi(4,3))/(b(3,3)*b(1,1))$ det(AUTOM):=b(3,3)**2*b(2,2)**5*b(1,1)**3$ DELTAPRIMEMODADG:= b(1,1)*xi(1,2) mat((0,----------------,0,0,0,0), b(2,2) (0,0,0,0,0,0), b(3,3)*xi(3,1) (----------------, b(1,1) - ((b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(3,3) - b(3,1)*b(1,1)*xi(1,2)) -----------------------------------------------------------------------,0,0 b(2,2)*b(1,1) ,0,0), b(2,2)*b(1,1)*xi(4,3) (0,0,-----------------------,0,0,0), b(3,3) 2 2 ((((b(3,3)*xi(5,1) - b(3,1)*xi(5,3))*b(2,2) *b(1,1) 2 - b(4,3) *b(3,1)*xi(3,1) + b(5,3)*b(3,3)*b(1,1)*xi(3,1) 2 - b(6,1)*b(2,2)*b(1,1) *xi(4,3))*b(3,3) 2 + b(6,3)*b(3,1)*b(2,2)*b(1,1) *xi(4,3) + ( 2 2 (b(3,3) *xi(6,1) - b(3,3)*b(3,1)*xi(6,3) + b(3,1) *xi(4,3))*b(2,2) 2 2 2 *b(1,1) + b(4,1)*b(3,3) *xi(3,1))*b(4,3))/(b(3,3) *b(1,1) ),0,( - (( (b(4,1)*xi(4,3) - b(2,2)*b(1,1)*xi(5,3))*b(2,2)*b(1,1) 2 2 - b(4,3) *xi(3,1))*b(3,3) + b(6,3)*b(2,2)*b(1,1) *xi(4,3) 2 - (b(3,3)*xi(6,3) - b(3,1)*xi(4,3))*b(4,3)*b(2,2)*b(1,1)))/(b(3,3) b(2,2)*b(1,1)*xi(4,3) *b(1,1)),0,0,-----------------------), b(3,3) 2 2 (((b(3,3) *xi(6,1) - b(3,3)*b(3,1)*xi(6,3) + b(3,1) *xi(4,3))*b(2,2)*b(1,1) 2 + b(4,1)*b(3,3) *xi(3,1) - b(4,3)*b(3,3)*b(3,1)*xi(3,1) 2 + b(6,3)*b(3,3)*b(1,1)*xi(3,1))/(b(3,3)*b(1,1) ),0,( (b(3,3)*xi(6,3) - 2*b(3,1)*xi(4,3))*b(2,2)*b(1,1) - b(3,3)*xi(3,1) + 2*b(4,3)*b(3,3)*xi(3,1))/(b(3,3)*b(1,1)),-------------------,0,0)) b(1,1) ******* Suppose xi(1,2) = 0$ xi(1,2):=0$ ***********SUBCASE : xi(4,3) = 0.$ xi(4,3):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, (b(3,3)*xi(3,1))/b(1,1), (b(3,3)*( - b(1,2)*xi(3,1) + b(1,1)*xi(3,2)))/(b(2,2)*b(1,1)), ss, 0, ss, (b(5,3)*b(3,3)*b(1,1)*xi(3,1) - b(4,3)**2*b(3,1)*xi(3,1) + b(4,3)*b(4,1)*b(3,3)* xi(3,1) + b(4,3)*b(3,3)*b(2,2)*b(1,1)*xi(6,1) - b(4,3)*b(3,1)*b(2,2)*b(1,1)*xi(6 ,3) + b(3,3)*b(2,2)**2*b(1,1)**2*xi(5,1) - b(3,1)*b(2,2)**2*b(1,1)**2*xi(5,3))/( b(3,3)*b(1,1)**2), (b(4,3)**2*xi(3,1) + b(4,3)*b(2,2)*b(1,1)*xi(6,3) + b(2,2)**2*b(1,1)**2*xi(5,3)) /(b(3,3)*b(1,1)), ss, (b(6,3)*b(1,1)*xi(3,1) - b(4,3)*b(3,1)*xi(3,1) + b(4,1)*b(3,3)*xi(3,1) + b(3,3)* b(2,2)*b(1,1)*xi(6,1) - b(3,1)*b(2,2)*b(1,1)*xi(6,3))/b(1,1)**2, (2*b(4,3)*xi(3,1) + b(2,2)*b(1,1)*xi(6,3))/b(1,1)}$ deltaprimemodg(1,2):=0$ deltaprimemodg(3,1):=(b(3,3)*xi(3,1))/b(1,1)$ deltaprimemodg(3,2):=(b(3,3)*( - b(1,2)*xi(3,1) + b(1,1)*xi(3,2)))/(b(2,2)*b(1,1 ))$ deltaprimemodg(4,3):=0$ deltaprimemodg(5,1):=(b(5,3)*b(3,3)*b(1,1)*xi(3,1) - b(4,3)**2*b(3,1)*xi(3,1) + b(4,3)*b(4,1)*b(3,3)*xi(3,1) + b(4,3)*b(3,3)*b(2,2)*b(1,1)*xi(6,1) - b(4,3)*b(3, 1)*b(2,2)*b(1,1)*xi(6,3) + b(3,3)*b(2,2)**2*b(1,1)**2*xi(5,1) - b(3,1)*b(2,2)**2 *b(1,1)**2*xi(5,3))/(b(3,3)*b(1,1)**2)$ deltaprimemodg(5,3):=(b(4,3)**2*xi(3,1) + b(4,3)*b(2,2)*b(1,1)*xi(6,3) + b(2,2) **2*b(1,1)**2*xi(5,3))/(b(3,3)*b(1,1))$ deltaprimemodg(6,1):=(b(6,3)*b(1,1)*xi(3,1) - b(4,3)*b(3,1)*xi(3,1) + b(4,1)*b(3 ,3)*xi(3,1) + b(3,3)*b(2,2)*b(1,1)*xi(6,1) - b(3,1)*b(2,2)*b(1,1)*xi(6,3))/b(1,1 )**2$ deltaprimemodg(6,3):=(2*b(4,3)*xi(3,1) + b(2,2)*b(1,1)*xi(6,3))/b(1,1)$ det(AUTOM):=b(3,3)**2*b(2,2)**5*b(1,1)**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), b(3,3)*xi(3,1) - (b(1,2)*xi(3,1) - b(1,1)*xi(3,2))*b(3,3) (----------------,---------------------------------------------,0,0,0,0), b(1,1) b(2,2)*b(1,1) (0,0,0,0,0,0), 2 2 2 (((b(3,3)*xi(5,1) - b(3,1)*xi(5,3))*b(2,2) *b(1,1) - b(4,3) *b(3,1)*xi(3,1) + b(5,3)*b(3,3)*b(1,1)*xi(3,1) + ((b(3,3)*xi(6,1) - b(3,1)*xi(6,3))*b(2,2)*b(1,1) + b(4,1)*b(3,3)*xi(3,1)) 2 *b(4,3))/(b(3,3)*b(1,1) ),0, 2 2 2 b(4,3) *xi(3,1) + b(4,3)*b(2,2)*b(1,1)*xi(6,3) + b(2,2) *b(1,1) *xi(5,3) --------------------------------------------------------------------------, b(3,3)*b(1,1) 0,0,0), (((b(3,3)*xi(6,1) - b(3,1)*xi(6,3))*b(2,2)*b(1,1) + b(4,1)*b(3,3)*xi(3,1) 2 - b(4,3)*b(3,1)*xi(3,1) + b(6,3)*b(1,1)*xi(3,1))/b(1,1) ,0, 2*b(4,3)*xi(3,1) + b(2,2)*b(1,1)*xi(6,3) - b(3,3)*xi(3,1) ------------------------------------------,-------------------,0,0)) b(1,1) b(1,1) *********SUBSUBCASE : xi(3,1) = 0.$ xi(3,1):=0$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, 0, (b(3,3)*xi(3,2))/b(2,2), ss, 0, ss, (b(2,2)*(b(4,3)*b(3,3)*xi(6,1) - b(4,3)*b(3,1)*xi(6,3) + b(3,3)*b(2,2)*b(1,1)*xi (5,1) - b(3,1)*b(2,2)*b(1,1)*xi(5,3)))/(b(3,3)*b(1,1)), (b(2,2)*(b(4,3)*xi(6,3) + b(2,2)*b(1,1)*xi(5,3)))/b(3,3), ss, (b(2,2)*(b(3,3)*xi(6,1) - b(3,1)*xi(6,3)))/b(1,1), b(2,2)*xi(6,3)}$ deltaprimemodg(1,2):=0$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=(b(3,3)*xi(3,2))/b(2,2)$ deltaprimemodg(4,3):=0$ deltaprimemodg(5,1):=(b(2,2)*(b(4,3)*b(3,3)*xi(6,1) - b(4,3)*b(3,1)*xi(6,3) + b( 3,3)*b(2,2)*b(1,1)*xi(5,1) - b(3,1)*b(2,2)*b(1,1)*xi(5,3)))/(b(3,3)*b(1,1))$ deltaprimemodg(5,3):=(b(2,2)*(b(4,3)*xi(6,3) + b(2,2)*b(1,1)*xi(5,3)))/b(3,3)$ deltaprimemodg(6,1):=(b(2,2)*(b(3,3)*xi(6,1) - b(3,1)*xi(6,3)))/b(1,1)$ deltaprimemodg(6,3):=b(2,2)*xi(6,3)$ det(AUTOM):=b(3,3)**2*b(2,2)**5*b(1,1)**3$ DELTAPRIMEMODADG:= mat((0,0,0,0,0,0), (0,0,0,0,0,0), b(3,3)*xi(3,2) (0,----------------,0,0,0,0), b(2,2) (0,0,0,0,0,0), ((((b(3,3)*xi(6,1) - b(3,1)*xi(6,3))*b(4,3) + (b(3,3)*xi(5,1) - b(3,1)*xi(5,3))*b(2,2)*b(1,1))*b(2,2))/(b(3,3) (b(4,3)*xi(6,3) + b(2,2)*b(1,1)*xi(5,3))*b(2,2) *b(1,1)),0,-------------------------------------------------,0,0,0), b(3,3) (b(3,3)*xi(6,1) - b(3,1)*xi(6,3))*b(2,2) (------------------------------------------,0,b(2,2)*xi(6,3),0,0,0)) b(1,1) *********SUBSUBSUBCASE : xi(6,3) NEQ 0.$ Then on may suppose xi(6,3):=1$ xi(6,3):=1$ and one keeps deltaprime(6,3):=k by taking$ b(2,2):=k$ and we get deltaprime(5,3)=0 if we take$ b(4,3):= - b(1,1)*xi(5,3)*k$ and we get deltaprime(6,1)=0 if we take$ b(3,1):=b(3,3)*xi(6,1)$ With the generic automorphism one gets$ shortformdeltaprimemodadg:={0, ss, 0, (b(3,3)*xi(3,2))/k, ss, 0, ss, k**2*( - xi(6,1)*xi(5,3) + xi(5,1)), 0, ss, 0, k}$ deltaprimemodg(1,2):=0$ deltaprimemodg(3,1):=0$ deltaprimemodg(3,2):=(b(3,3)*xi(3,2))/k$ deltaprimemodg(4,3):=0$ deltaprimemodg(5,1):=k**2*( - xi(6,1)*xi(5,3) + xi(5,1))$ deltaprimemodg(5,3):=0$ deltaprimemodg(6,1):=0$ deltaprimemodg(6,3):=k$ det(AUTOM):=b(3,3)**2*b(1,1)**3*k**5$ DELTAPRIMEMODADG:= [ 0 0 0 0 0 0] [ ] [ 0 0 0 0 0 0] [ ] [ b(3,3)*xi(3,2) ] [ 0 ---------------- 0 0 0 0] [ k ] [ ] [ 0 0 0 0 0 0] [ ] [ 2 ] [ - (xi(6,1)*xi(5,3) - xi(5,1))*k 0 0 0 0 0] [ ] [ 0 0 k 0 0 0] Thus , for xi(6,3) neq 0 , we are reduced to:$ shortformdeltaprime ={0,SS,0,epsilon,SS,0,SS,eta,0,SS,0,1}$ where epsilon = xi(3,2) = 0,1 ,eta = xi(5,1) = 0,1.$