//datetime();

ring r = (0,lambda(0..3)),(X(10),X(8..1)),dp;

poly k12 = 2*lambda(0) -3*X(4)*X(2)*lambda(3)*X(3)
+3*X(3)*X(6)*lambda(3) -4*X(2)*X(4)*lambda(2) -2* X(4)*X(2)*X(3)^2
+3*X(2)*lambda(3)*X(7) +4*X(2)*X(3)*X(7) +2*X(6)*lambda(2)
+X(3)^2*lambda(2) +4*X(6)*X(3)^ 2 +lambda(3)*X(3)^3 +lambda(1)*X(3)
-lambda(3)^2*X(2)^3 +4*lambda(2)*X(2)^3 +X(2)^2*X(4)^2 -2*X(2) *X(10)
+X(4)*X(8) -4/3*X(2)^2*X(8) -X(4)^3 +X(3)^4 +2*X(6)^2;

poly k14 = -16/3*X(6)*X(8) -8*X(2)*X(6)^2 +8*X(2)^2*X(10)
+4*X(4)^2*X(6) -8*X(2)*lambda(0) -4*X(2)*lambda(1)*X(3)
+8*X(2)*X(6)*lambda(2) -4*X(4)*X(7)*X(3) -4*X(7)^2
+4*X(6)*X(2)*lambda(3)*X(3) +4/3*X(2)*X(4)*X(8)
-4*X(2)^2*lambda(3)*X(7) -4/3*X(3)^2*X(8);

poly k15 = -4*X(6)*lambda(3)*X(4)*X(2) +12*X(6)^2*X(3)
-4*X(3)*lambda(0) +4/3*X(7)*X(8) +8*X(7)*X(6)*X(2) +8*X(6)^2*lambda(3)
+8*X(6)*lambda(1) -4*X(7)*X(4)^2 +4*X(3)*X(6)*lambda(2)
+4*X(3)*X(2)*X(10) -8*X(2)* lambda(1)*X(4) -4*X(4)*X(3)*X(2)*X(6)
-4*X(2)*lambda(3)*X(3)*X(7) -4/3*X(4)*X(3)*X(8)
-4/3*X(2)^2*lambda(3)*X(8) -4*X(2)*X(3)^2*X(7)
+4*X(6)*lambda(3)*X(3)^2 +4*X(3)^3*X(6) +8*lambda(1)*X(2)^3
+4*X(2)^2*X(4)*X(7) ;

poly k16a = 4/9*( -9*lambda(3)^2 +18*lambda(2))*X(2)^2*X(6)
-4*X(4)*X(3)^2*X(6) -4*X(6)^2*X(4) +4/3* X(8)*X(3)^2*X(2)
-4/3*X(8)*X(4)*X(2)^2 +8*X(6)^2*X(2)^2 -8*X(10)*X(2)^3 +4*X(7)^2*X(2)
+8*X(7)*X(3)*X(6) +4*X(3)^3* X(7) +4/9*(18*lambda(0)
-9*lambda(3)*lambda(1))*X(2)^2 +4*lambda(1)*X(7) +4*X(2)*X(10)*X(4)
-4* X(6)*lambda(2)*X(4) -4*lambda(0)*X(4) -4*X(3)*X(6)*lambda(3)*X(4)
-4*X(2)*lambda(3)*X(7)*X(4) -8/9* X(8)^2 -4*X(6)*X(3)*X(2)^2*lambda(3)
+4/3*lambda(3)*X(2)*X(8)*X(3) +4/3*X(8)*X(4)^2 +4*X(6)*lambda(3)* X(7)
+4*X(7)*X(2)^3*lambda(3) +8/3*lambda(2)*X(8)*X(2)
-4*lambda(1)*X(3)*X(2)^2 +4*lambda(2)*X(7)* X(3)
+4*X(7)*lambda(3)*X(3)^2;

poly k16b = -4*X(3)^2*X(10) -4*lambda(1)*X(7) +12*lambda(0)*X(4)
+4/3*( -12*lambda(0) +3* lambda(3)*lambda(1))*X(2)^2
+4*X(4)*X(3)*lambda(1) -4*X(6)*lambda(2)*X(4) +12*X(6)*lambda(3)* X(7)
-8/3*lambda(2)*X(8)*X(2) -4*X(6)^2*X(4) -4*X(7)^2*X(2)
-4*lambda(2)*X(7)*X(3) +8*X(7)*X(3)*X(6) -16*X(10) *X(6)
+4*X(2)*X(10)*X(4) +4/3*X(8)^2; 

poly k17b = -4*X(10)*X(4)*X(3)
-4/3*X(8)*lambda(1) +12*lambda(3)*lambda(0)*X(2) +4/3*(
-3*lambda(3)*lambda(2) -6*lambda(1))*X(6)*X(2)
-8*lambda(2)*X(3)*X(2)*X(6) +4/3*(12*lambda(0)
+3*lambda(3)*lambda(1))*X(3)*X(2) +4*lambda(3)*X(6)^2*X(2)
-4*lambda(3)*X(2)^2*X(10) +4*lambda (3)*X(8)*X(6) +12*lambda(3)*X(7)^2
+4*X(4)^2*lambda(1) +8*lambda(2)*X(7)*X(2)^2 -4*lambda(1)* X(4)*X(2)^2
+4*lambda(1)*X(2)*X(3)^2 -8*X(7)*X(6)*X(4) +8/3*X(6)*X(8)*X(3)
-8*X(4)*X(7)*lambda(2) -4/3* lambda(2)*X(8)*X(3) +12*X(3)*X(7)^2
-8/3*X(8)*X(7)*X(2) -8*X(10)*X(7);

poly k18b = 8*(3*lambda(1) -lambda(3)*lambda(2))*X(6)*X(3)
+4*(2*lambda(1) +lambda(3)* lambda(2))*X(7)*X(2) -4*X(10)*X(4)^2
-8*lambda(0)*lambda(2) +4*lambda(1)^2 +4*X(7)^2*X(4) -8*X(2)
*lambda(3)*X(7)*X(6) -4*X(2)*lambda(1)*X(4)*X(3)
+12*X(3)*X(6)^2*lambda(3) -8*X(3)^2*lambda(2)*X(6) +16*X(2)*X(10)*X(6)
+8/3*X(4)*X(8)*X(6) -8/3*X(7)*X(8)*X(3) -16*X(6)^3
+8*lambda(2)*X(2)*X(3)*X(7) -4*lambda(3)*X(3)*X(2)*X(10)
-4*lambda(3)*X(2)*lambda(1)*X(4) -8*lambda(2)*X(2)*X(10)
-4*(4*lambda(0) - lambda(3)*lambda(1))*X(3)^2 -12*(2*lambda(2)
-lambda(3)^2)*X(6)^2 -4*(3*lambda(3)* lambda(0)
-lambda(1)*lambda(2))*X(3) -8*(2*lambda(0) -2*lambda(3)*lambda(1)
+lambda(2)^2)*X(6) -4*lambda(3)*X(7)*X(8) +4/3*X(4)*X(8)*lambda(2)
+16/3*X(10)*X(8) +4*X(3)^3*lambda(1);

ideal J = (k12, k14, k15, k16a, k16b, k17b, k18b);
option(prot);  //display some information on ongoing calc
//int t=timer; ideal GB = groebner(J); timer-t;

LIB "sing.lib";

int t=timer; 
ideal GBR = radical(J); 
timer-t;

write(":w SingGBR34.txt",GBR); 

quit;