known_q := {

P(6,6,6)^2 = 4*P(6,6)^3-7*P(5,6)^2+4*P(4,6)*P(6,6)-8*P(5,5)*P(6,6)-4*P(6,6)*lambda[4]+4*P(4,4)+2*P(5,5,6,6), 

P(4,6,6)*P(5,6,6) = 1/3*P(4,5,5,5)-\2*P(2,5)+2/3*P(3,4)+4*P(6,6)*P(4,6)*P(5,6)+2*P(6,6)*P(5,5)*P(5,6)-P(5,5,6,6)*P(5,6)+4*P(5,6)*P(6,6)*lambda[4]
+4*P(5,6)^3-2*P(4,4)*P(5,6)-2*P(4,5)*P(4,6)-P(4,5)*P(5,5)-4/3*P(4,5)*lambda[4], 

P(5,5,5)*P(6,6,6) = 10*P(5,6)^3+12*P(6,6)*P(5,5)*P(5,6)+4*P(4,5)*P(4,6)+8/3*P(4,5)*lambda[4]-4*P(4,4)*P(5,6)-3*P(5,5,6,6)*P(5,6)+8*P(3,6)*P(6,6)
-4/3*P(3,4)-2/3*P(4,5,5,5)+8*P(5,6)*P(6,6)*lambda[4], 

P(4,5,6)*P(6,6,6) = -2*P(5,6)^3+2*P(6,6)*P(4,6)*P(5,6)-P(6,6)*P(5,5)*P(5,6)+2*P(4,5)*P(6,6)^2+2*P(4,5)*P(4,6)+4/3*P(4,5)*lambda[4]+2*P(4,4)*P(5,6)
+1/2*P(5,5,6,6)*P(5,6)+2*P(3,6)*P(6,6)-2/3*P(3,4)-1/3*P(4,5,5,5), 

P(5,5,6)*P(5,6,6) = P(5,5,6,6)*P(5,6)-2*P(5,6)^3-4/3*P(4,5)*lambda[4]-2*P(4,5)*P(5,5)+1/3*P(4,5,5,5)-4/3*P(3,4), 

P(5,6,6)*P(6,6,6) = 4*P(6,6)^2*P(5,6)+2*P(4,6)*P(5,6)-P(5,5)*P(5,6)-\2*P(4,5)*P(6,6)+2*P(3,6), 

P(4,6,6)*P(6,6,6) = 4*P(5,6)^2*P(6,6)+4*P(4,6)*P(6,6)^2+2*P(5,5)*P(6,6)^2+4*P(6,6)^2*lambda[4]+2*P(4,6)^2-4*P(4,6)*P(5,5)-2*P(5,5)*lambda[4]-3*P(4,5)*P(5,6)
-2*P(4,4)*P(6,6)-P(5,5,6,6)*P(6,6)-2*P(2,6)-2*P(3,5)-2*lambda[3]+P(4,5,5,6), 

P(5,5,6)*P(6,6,6) = -2*P(5,6)^2*P(6,6)-2*P(4,6)*P(5,5)-2*P(5,5)^2-4*P(5,5)*lambda[4]-6*P(4,5)*P(5,6)+P(5,5,6,6)*P(6,6)-4*P(2,6)-2*P(3,5)-4*lambda[3]
+2*P(4,5,5,6), 

P(5,6,6)^2 = 8*P(2,6)+4*P(5,5)*lambda[4]+4*lambda[3]-2*P(4,5,5,6)+4*P(4,5)*P(5,6)+4*P(4,6)*P(5,5)+4*P(5,6)^2*P(6,6)+P(5,5)^2

};