known_4i := {P(2,2,2,4) = -2*(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[4]+(P(2,4,4,4
)-6*P(2,4)*P(4,4))*lambda[3]+6*P(3,3)*lambda[4]*lambda[3]+6*P(3,3)*lambda[2]-6
*P(1,2,4,4)+12*P(1,2)*P(4,4)+24*P(1,4)*P(2,4)+6*P(2,2)*P(2,4), P(1,4,4,4) = 3/
2*P(3,3)*lambda[3]+6*P(1,4)*P(4,4)-1/2*P(2,3,3,3)+3*P(2,3)*P(3,3), P(1,3,3,4)
= 2*P(1,3)*lambda[4]+3/2*P(2,3)*lambda[3]+2*P(3,4)*lambda[2]+lambda[4]*lambda[
2]+4*P(1,3)*P(3,4)+2*P(1,4)*P(3,3)-1/2*P(2,2,3,3)+P(2,2)*P(3,3)+2*P(2,3)^2, P(
1,1,2,2) = 2*P(3,3)*lambda[3]*lambda[1]+8*P(3,3)*lambda[4]*lambda[0]-2/3*(P(2,
3,3,3)-6*P(2,3)*P(3,3))*lambda[4]*lambda[2]-2*(P(1,2,4,4)-2*P(1,2)*P(4,4)-4*P(
1,4)*P(2,4))*lambda[2]+2*(P(2,4,4,4)-6*P(2,4)*P(4,4))*lambda[0]+2*P(1,1)*P(2,2
)+4*P(1,2)^2+2*P(3,3)*lambda[4]*lambda[3]*lambda[2]-1/3*(P(2,3,3,3)-6*P(2,3)*P
(3,3))*lambda[1], P(1,1,3,4) = 2*P(1,4)*lambda[2]-P(2,4)*lambda[1]+2*P(1,1)*P(
3,4)+4*P(1,3)*P(1,4), P(1,1,2,3) = 2*P(1,2)*lambda[2]-6*P(2,4)*lambda[0]-P(2,2
)*lambda[1]+4*P(1,4)*lambda[1]+2*P(1,1)*P(2,3)+4*P(1,2)*P(1,3), P(1,1,3,3) = 2
*P(1,1)*P(3,3)+4*P(1,3)^2+2*P(1,3)*lambda[2]-P(2,3)*lambda[1]+6*P(3,4)*lambda[
0], P(3,3,3,4) = -P(2,4,4,4)+6*P(2,4)*P(4,4)+6*P(3,3)*P(3,4), P(2,2,4,4) = 2/3
*(P(2,4,4,4)-6*P(2,4)*P(4,4))*lambda[4]+2*P(3,3)*lambda[3]+2*P(2,2)*P(4,4)+4*P
(2,4)^2-1/3*P(2,3,3,3)+2*P(2,3)*P(3,3), P(2,2,3,4) = -2*P(1,2)+4*P(1,4)*lambda
[4]+3*P(2,4)*lambda[3]-2*P(4,4)*lambda[2]+2*P(2,2)*P(3,4)+4*P(2,3)*P(2,4), P(2
,3,3,4) = 2*P(1,3)+3*P(3,4)*lambda[3]+lambda[2]+4*P(2,3)*P(3,4)+2*P(2,4)*P(3,3
), P(1,3,4,4) = -P(1,2)+2*P(1,4)*lambda[4]+2*P(1,3)*P(4,4)+4*P(1,4)*P(3,4), P(
2,2,2,2) = -12*(P(1,2,4,4)-2*P(1,2)*P(4,4)-4*P(1,4)*P(2,4))*lambda[4]-4*(P(2,3
,3,3)-6*P(2,3)*P(3,3))*lambda[4]^2-(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[3]+4*(P
(2,4,4,4)-6*P(2,4)*P(4,4))*lambda[2]+12*P(3,3)*lambda[4]^2*lambda[3]+12*P(3,3)
*lambda[4]*lambda[2]+24*P(3,3)*lambda[1]-6*P(1,2,2,4)+24*P(1,2)*P(2,4)+12*P(1,
4)*P(2,2)+6*P(2,2)^2, P(1,2,3,3) = 3*P(1,3)*lambda[3]+2*P(3,4)*lambda[1]+
lambda[4]*lambda[1]-3*lambda[0]+2*P(1,2)*P(3,3)+4*P(1,3)*P(2,3), P(1,3,3,3) =
(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[4]-3*P(3,3)*lambda[4]*lambda[3]+3*P(1,2,4,
4)-6*P(1,2)*P(4,4)-12*P(1,4)*P(2,4)+6*P(1,3)*P(3,3), P(3,3,4,4) = -P(2,3)+2*P(
3,4)*lambda[4]+2*P(3,3)*P(4,4)+4*P(3,4)^2, P(4,4,4,4) = -3*P(3,3)+6*P(4,4)^2,
P(3,4,4,4) = 3*P(2,4)+6*P(3,4)*P(4,4), P(1,1,4,4) = -1/2*(P(2,3,3,3)-6*P(2,3)*
P(3,3))*lambda[3]+3/2*P(3,3)*lambda[3]^2+3*P(3,3)*lambda[1]+2*P(1,1)*P(4,4)+4*
P(1,4)^2-P(1,2,2,4)+4*P(1,2)*P(2,4)+2*P(1,4)*P(2,2), P(1,2,2,2) = -3*(P(1,2,4,
4)-2*P(1,2)*P(4,4)-4*P(1,4)*P(2,4))*lambda[3]-(P(2,3,3,3)-6*P(2,3)*P(3,3))*
lambda[4]*lambda[3]+2*(P(2,4,4,4)-6*P(2,4)*P(4,4))*lambda[1]+3*P(3,3)*lambda[4
]*lambda[3]^2+6*P(3,3)*lambda[4]*lambda[1]+6*P(3,3)*lambda[0]+6*P(1,2)*P(2,2),
P(1,2,2,3) = -2*P(1,1)*lambda[4]+3*P(1,2)*lambda[3]+4*P(1,4)*lambda[2]-2*P(2,4
)*lambda[1]-6*P(4,4)*lambda[0]+4*P(1,2)*P(2,3)+2*P(1,3)*P(2,2), P(2,2,2,3) = -\
6*P(1,1)+6*P(1,4)*lambda[3]+3*P(2,2)*lambda[3]-6*P(4,4)*lambda[1]+6*P(2,2)*P(2
,3), P(1,1,2,4) = -1/3*(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[2]-1/3*(P(2,4,4,4)-\
6*P(2,4)*P(4,4))*lambda[1]+P(3,3)*lambda[3]*lambda[2]+4*P(3,3)*lambda[0]+2*P(1
,1)*P(2,4)+4*P(1,2)*P(1,4), P(1,2,3,4) = -P(1,1)+3*P(1,4)*lambda[3]-P(4,4)*
lambda[1]+2*P(1,2)*P(3,4)+2*P(1,3)*P(2,4)+2*P(1,4)*P(2,3), P(2,3,4,4) = 4*P(1,
4)-P(2,2)+2*P(2,4)*lambda[4]+2*P(2,3)*P(4,4)+4*P(2,4)*P(3,4), P(3,3,3,3) = 12*
P(1,4)-3*P(2,2)+6*P(3,3)^2, P(1,1,1,4) = 3/2*P(3,3)*lambda[3]*lambda[1]-2*(P(2
,4,4,4)-6*P(2,4)*P(4,4))*lambda[0]+6*P(1,1)*P(1,4)-1/2*(P(2,3,3,3)-6*P(2,3)*P(
3,3))*lambda[1], P(1,1,1,1) = -3*P(3,3)*lambda[1]^2+12*P(3,3)*lambda[4]*lambda
[3]*lambda[0]+6*P(1,1)^2-4*(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[4]*lambda[0]+12
*P(3,3)*lambda[2]*lambda[0]-12*(P(1,2,4,4)-2*P(1,2)*P(4,4)-4*P(1,4)*P(2,4))*
lambda[0], P(1,1,1,3) = 6*P(1,1)*P(1,3)-6*P(2,2)*lambda[0]+6*P(1,4)*lambda[0]+
3*P(1,2)*lambda[1], P(1,1,1,2) = -(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[0]+3*P(3
,3)*lambda[4]*lambda[3]*lambda[1]-(P(2,3,3,3)-6*P(2,3)*P(3,3))*lambda[4]*
lambda[1]+6*P(1,1)*P(1,2)-3*(P(1,2,4,4)-2*P(1,2)*P(4,4)-4*P(1,4)*P(2,4))*
lambda[1]+9*P(3,3)*lambda[3]*lambda[0]};