QL - SYSTEM

using Baricentricas Package

L1={1,0,0};L2={0,1,0};L3={0,0,1};L4={l,m,n};
S12=Punto[L1,L2];S13=Punto[L1,L3];S14=Punto[L1,L4];
S21=Punto[L2,L1];S23=Punto[L2,L3];S24=Punto[L2,L4];
S31=Punto[L3,L1];S32=Punto[L3,L2];S34=Punto[L3,L4];
S41=Punto[L4,L1];S42=Punto[L4,L2];S43=Punto[L4,L3];
M12=Medio[L1,L2];M23=Medio[L2,L3];M34=Medio[L3,L4];M41=Medio[L4,L1];
DTL1=Recta[Punto[L4,L1],Punto[L2,L3]];DTL2=Recta[Punto[L4,L2],Punto[L1,L3]];DTL3=Recta[Punto[L4,L3],Punto[L1,L2]];
DT1=Punto[DTL2,DTL3];DT2=Punto[DTL3,DTL1];DT3=Punto[DTL1,DTL2];

QL - Points

Registered Points

QLP1={(a^2) (l-m) m (l-n) n,-(b^2) l (l-m) (m-n) n,(c^2) l m (l-n) (m-n)};     (* Miquel Point *)
QLP2={-(c^4) (l-m) (l-2 n) (m-n)-(b^4) (l-2 m) (l-n) (m-n)+(a^4) l (2 l-m-n) (m-n)+(b^2) (c^2) (m-n) (2 (l^2)-3 l m-3 l n+4 m n)+(a^2) ((c^2) ((l^2) m+(l^2) n-5 l m n+2 (m^2) n+l (n^2))+(b^2) (-(l^2) m-l (m^2)-(l^2) n+5 l m n-2 m (n^2))),-(c^4) (l-m) (m-2 n) (l-n)-(a^4) (2 l-m) (l-n) (m-n)-(b^4) m (l-n) (-l+2 m-n)+(b^2) (c^2) (-l (m^2)-2 (l^2) n+5 l m n-(m^2) n-m (n^2))+(a^2) ((c^2) (l-n) (3 l m-2 (m^2)-4 l n+3 m n)+(b^2) ((l^2) m+l (m^2)-5 l m n+(m^2) n+2 l (n^2))),-(a^4) (l-m) (2 l-n) (m-n)-(b^4) (l-m) (l-n) (2 m-n)-(c^4) (l-m) (l+m-2 n) n+(b^2) (c^2) (2 (l^2) m-5 l m n+(m^2) n+l (n^2)+m (n^2))+(a^2) ((b^2) (l-m) (4 l m-3 l n-3 m n+2 (n^2))+(c^2) (-2 l (m^2)-(l^2) n+5 l m n-l (n^2)-m (n^2)))};     (* Morley Point *)
QLP3={-(a^2) (l-m) (l-n) ((c^2) m-(b^2) n)+((b^2)-(c^2)) (m-n) ((c^2) m (l-n)+(b^2) (-l+m) n),(c^2) l ((b^2) (-l+m)+(c^2) (l-n)) (m-n)-(a^4) (l-m) (l-n) n+(a^2) ((b^2) (l-m) (m-n) n-(c^2) (l-n) (l (m-2 n)+m n)),(a^4) (l-m) m (l-n)+(b^2) l (m-n) ((b^2) (l-m)+(c^2) (-l+n))+(a^2) ((c^2) m (l-n) (m-n)-(b^2) (l-m) (2 l m-l n-m n))};     (* Kantor-Hervey Point *)
QLP4={(a^2) (-(a^2) (l-m) (l-n) (m-n)+(b^2) ((l^2) m+m (2 m-n) n+l (-(m^2)-2 m n+(n^2)))+(c^2) (-(l^2) n+m (m-2 n) n+l (-(m^2)+2 m n+(n^2)))),(b^2) (-(m-n) ((b^2) (l-m) (l-n)-(c^2) ((l^2)-2 l n+m n))+(a^2) ((l^2) (m-2 n)-m (n^2)+l (-(m^2)+2 m n+(n^2)))),(c^2) ((m-n) (-(c^2) (l-m) (l-n)+(b^2) ((l^2)-2 l m+m n))+(a^2) ((l^2) (2 m-n)+(m^2) n+l (-(m^2)-2 m n+(n^2))))};     (* Miquel CircumCenter *)
QLP5={-(m-n) ((a^2) (-(b^2) (l-m) (l-2 n)-(c^2) (l-2 m) (l-n))+(a^4) (l-m) (l-n)-((b^2)-(c^2)) ((b^2) (l-m) n+(c^2) m (-l+n))),(l-n) (-((b^2)-(c^2)) (-(c^2) l+(b^2) (l-m)) (m-n)+(a^4) (l-m) n+(a^2) ((b^2) (l-m) (m-2 n)+(c^2) (l m-2 l n+m n))),-(l-m) ((a^4) m (l-n)+((b^2)-(c^2)) (m-n) ((b^2) l+(c^2) (-l+n))+(a^2) ((c^2) (l-n) (-2 m+n)+(b^2) (m n+l (-2 m+n))))};     (* Clawson Center *)
QLP6={3 (a^4) (l-m) (l-n) (m-n)+(b-c) (b+c) (m-n) ((c^2) m (l-n)+(b^2) (-l+m) n)+(a^2) ((c^2) (l-n) (-l m+4 (m^2)+3 l n-6 m n)-(b^2) (l-m) (3 l m-(l+6 m) n+4 (n^2))),-(a^4) (l-m) (l-n) n-(a^2) ((c^2) (l-n) (l (m-2 n)+m n)+(b^2) (l-m) (3 l m-(6 l+m) n+4 (n^2)))+(m-n) ((c^4) l (l-n)+3 (b^4) (l-m) (l-n)+(b^2) (c^2) (-4 (l^2)-3 m n+l (m+6 n))),(a^4) (l-m) m (l-n)+(m-n) ((b^4) l (l-m)+3 (c^4) (l-m) (l-n)+(b^2) (c^2) (-4 (l^2)+6 l m+l n-3 m n))+(a^2) ((c^2) (l-n) (-6 l m+4 (m^2)+3 l n-m n)-(b^2) (l-m) (2 l m-(l+m) n))};     (* Dimidium Point *)
QLP7={((b^2)-(c^2)) l (m-n) (-3 m n+l (m+n))+(a^2) (-(l^2) (((m-n))^2)-2 (m^2) (n^2)+l m n (m+n)),(a^2) m (l-n) (l (m-3 n)+m n)-(c^2) m (l-n) (l (m-3 n)+m n)+(b^2) (-(m^2) (n^2)+l m n (2 m+n)-(l^2) ((m^2)-m n+2 (n^2))),-((a^2)-(b^2)) (l-m) n (3 l m-l n-m n)+(c^2) (-(m^2) (n^2)+l m n (m+2 n)-(l^2) (2 (m^2)-m n+(n^2)))};
QLP8={m n (-(l^2) (m^2)+2 (l^2) m n-2 l (m^2) n-(l^2) (n^2)-2 l m (n^2)+3 (m^2) (n^2)),l n (-(l^2) (m^2)-2 (l^2) m n+2 l (m^2) n+3 (l^2) (n^2)-2 l m (n^2)-(m^2) (n^2)),l m (3 (l^2) (m^2)-2 (l^2) m n-2 l (m^2) n-(l^2) (n^2)+2 l m (n^2)-(m^2) (n^2))};     (* Centroid DT *)
QLP9={m n ((a^4) ((m^2) (n^2)+2 (l^3) (m+n)-(l^2) (((m+n))^2))-((b^2)-(c^2)) ((b^2) ((l^2) (((m-n))^2)+2 l (m^2) n-(m^2) (n^2))-(c^2) ((l^2) (((m-n))^2)+2 l m (n^2)-(m^2) (n^2)))+2 (a^2) ((c^2) (l-n) (l m (m-n)+(m^2) n+(l^2) (-m+n))+(b^2) ((l^3) (m-n)+l (m^2) n-(m^2) (n^2)+(l^2) (-(m^2)+(n^2))))),l n (2 (b^2) (c^2) (m-n) ((m^2) n+(l^2) (m+n)-l m (m+n))-(b^4) (-2 l (m^2) (m-n)+(m^2) n (-2 m+n)+(l^2) ((m^2)-(n^2)))-(c^4) ((m^2) (n^2)+2 l m n (-m+n)+(l^2) ((m^2)-(n^2)))-(a^4) (-2 l (m^2) n+(m^2) (n^2)+(l^2) ((m^2)+2 m n-(n^2)))-2 (a^2) (-(c^2) ((m^2) (n^2)+l m n (-2 m+n)+(l^2) ((m^2)+m n-(n^2)))+(b^2) (-l (m^3)+(m^2) (m-n) n+(l^2) ((m^2)-m n+(n^2))))),l m (-2 (b^2) (c^2) (m-n) (m (n^2)+(l^2) (m+n)-l n (m+n))+(b^4) (-(m^2) (n^2)+2 l m n (-m+n)+(l^2) ((m^2)-(n^2)))+(c^4) (-m (m-2 n) (n^2)+2 l (n^2) (-m+n)+(l^2) ((m^2)-(n^2)))+(a^4) (2 l m (n^2)-(m^2) (n^2)+(l^2) ((m^2)-2 m n-(n^2)))-2 (a^2) ((b^2) (-l m (m-2 n) n-(m^2) (n^2)+(l^2) ((m^2)-m n-(n^2)))+(c^2) (-l (n^3)+m (n^2) (-m+n)+(l^2) ((m^2)-m n+(n^2)))))};     (* CircumCenter DT *)
QLP10={m n (-4 (a^4) (l^3) m-4 (a^2) (b^2) (l^3) m+4 (a^2) (c^2) (l^3) m+(a^4) (l^2) (m^2)+6 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-4 (a^4) (l^3) n+4 (a^2) (b^2) (l^3) n-4 (a^2) (c^2) (l^3) n+6 (a^4) (l^2) m n-4 (a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n-4 (a^2) (c^2) (l^2) m n+4 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n-2 (a^4) l (m^2) n+2 (b^4) l (m^2) n+4 (a^2) (c^2) l (m^2) n-2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)+6 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+4 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+2 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)),l n ((a^4) (l^2) (m^2)+6 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-4 (a^2) (b^2) l (m^3)-4 (b^4) l (m^3)+4 (b^2) (c^2) l (m^3)+2 (a^4) (l^2) m n-2 (b^4) (l^2) m n+4 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n-2 (a^4) l (m^2) n-4 (a^2) (b^2) l (m^2) n+6 (b^4) l (m^2) n+4 (a^2) (c^2) l (m^2) n-4 (b^2) (c^2) l (m^2) n-2 (c^4) l (m^2) n+4 (a^2) (b^2) (m^3) n-4 (b^4) (m^3) n-4 (b^2) (c^2) (m^3) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+4 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+2 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)+6 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)),l m ((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)+2 (a^4) (l^2) m n-2 (b^4) (l^2) m n+4 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n-2 (a^4) l (m^2) n+2 (b^4) l (m^2) n+4 (a^2) (c^2) l (m^2) n-2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)+6 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+4 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)-4 (a^2) (c^2) l m (n^2)-4 (b^2) (c^2) l m (n^2)+6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)+6 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)-4 (a^2) (c^2) l (n^3)+4 (b^2) (c^2) l (n^3)-4 (c^4) l (n^3)+4 (a^2) (c^2) m (n^3)-4 (b^2) (c^2) m (n^3)-4 (c^4) m (n^3))};     (* OrthoCenter DT *)
QLP11={m n (-((b^2)-(c^2)) m n ((b^2) (l-m) n+(c^2) m (-l+n))-(a^4) (-2 (l^2) m n-(m^2) (n^2)+(l^3) (m+n)+l m n (m+n))+(a^2) ((c^2) ((l^3) (m-n)-2 (m^2) (n^2)+2 (l^2) n (-m+n)+l m n (2 m+n))+(b^2) (2 (l^2) m (m-n)-2 (m^2) (n^2)+(l^3) (-m+n)+l m n (m+2 n)))),l n (-(c^4) (l^2) (m-n) n+(a^4) l (l-m) (n^2)-(b^4) (l m (((m-n))^2)+(m^3) n+(l^2) (m-n) n)+(b^2) (c^2) (l m (((m-n))^2)-(m^2) (m-2 n) n+2 (l^2) (m-n) n)+(a^2) ((c^2) l n (l (m-2 n)+m n)+(b^2) ((m^3) n+(l^2) (2 (m^2)+m n-2 (n^2))-l m ((m^2)+2 m n-2 (n^2))))),l m ((a^4) l (m^2) (l-n)+(b^4) (l^2) m (m-n)+(b^2) (c^2) (-2 (l^2) m (m-n)+l (((m-n))^2) n+m (2 m-n) (n^2))+(c^4) ((l^2) m (m-n)-l (((m-n))^2) n-m (n^3))+(a^2) ((b^2) l m (m n+l (-2 m+n))+(c^2) (m (n^3)-l n (-2 (m^2)+2 m n+(n^2))+(l^2) (-2 (m^2)+m n+2 (n^2)))))};     (* NinePointCenter DT *)
QLP12={(m-n) ((l^2)-2 l m-2 l n+3 m n),-(l-n) (-2 l m+(m^2)+3 l n-2 m n),(-l+m) (-3 l m+2 l n+2 m n-(n^2))}; (* Lateral Centroid *)
QLP13={m n (-l m-l n+3 m n),l n (-l m+3 l n-m n),l m (3 l m-l n-m n)}; (* Lateral Harmonic Center *)
QLP14={-(m-n) (2 (l^5) (m^3)-4 (l^4) (m^4)-2 (l^5) (m^2) n-(l^4) (m^3) n+9 (l^3) (m^4) n-2 (l^5) m (n^2)+10 (l^4) (m^2) (n^2)-9 (l^3) (m^3) (n^2)-3 (l^2) (m^4) (n^2)+2 (l^5) (n^3)-(l^4) m (n^3)-9 (l^3) (m^2) (n^3)+13 (l^2) (m^3) (n^3)-5 l (m^4) (n^3)-4 (l^4) (n^4)+9 (l^3) m (n^4)-3 (l^2) (m^2) (n^4)-5 l (m^3) (n^4)+3 (m^4) (n^4)),-(-l+n) (-4 (l^4) (m^4)+2 (l^3) (m^5)+9 (l^4) (m^3) n-(l^3) (m^4) n-2 (l^2) (m^5) n-3 (l^4) (m^2) (n^2)-9 (l^3) (m^3) (n^2)+10 (l^2) (m^4) (n^2)-2 l (m^5) (n^2)-5 (l^4) m (n^3)+13 (l^3) (m^2) (n^3)-9 (l^2) (m^3) (n^3)-l (m^4) (n^3)+2 (m^5) (n^3)+3 (l^4) (n^4)-5 (l^3) m (n^4)-3 (l^2) (m^2) (n^4)+9 l (m^3) (n^4)-4 (m^4) (n^4)),-(-l+m) (-3 (l^4) (m^4)+5 (l^4) (m^3) n+5 (l^3) (m^4) n+3 (l^4) (m^2) (n^2)-13 (l^3) (m^3) (n^2)+3 (l^2) (m^4) (n^2)-9 (l^4) m (n^3)+9 (l^3) (m^2) (n^3)+9 (l^2) (m^3) (n^3)-9 l (m^4) (n^3)+4 (l^4) (n^4)+(l^3) m (n^4)-10 (l^2) (m^2) (n^4)+l (m^3) (n^4)+4 (m^4) (n^4)-2 (l^3) (n^5)+2 (l^2) m (n^5)+2 l (m^2) (n^5)-2 (m^3) (n^5))}; (* QL-1st Quasi Centroid = Centroid 1st Quasi Centroid (QG-P4) Triangle *)
QLP15={(m-n) ((l^5) (m^3)-2 (l^4) (m^4)-(l^5) (m^2) n-2 (l^4) (m^3) n+6 (l^3) (m^4) n-(l^5) m (n^2)+8 (l^4) (m^2) (n^2)-9 (l^3) (m^3) (n^2)+(l^5) (n^3)-2 (l^4) m (n^3)-9 (l^3) (m^2) (n^3)+20 (l^2) (m^3) (n^3)-10 l (m^4) (n^3)-2 (l^4) (n^4)+6 (l^3) m (n^4)-10 l (m^3) (n^4)+6 (m^4) (n^4)),(l-n) (2 (l^4) (m^4)-(l^3) (m^5)-6 (l^4) (m^3) n+2 (l^3) (m^4) n+(l^2) (m^5) n+9 (l^3) (m^3) (n^2)-8 (l^2) (m^4) (n^2)+l (m^5) (n^2)+10 (l^4) m (n^3)-20 (l^3) (m^2) (n^3)+9 (l^2) (m^3) (n^3)+2 l (m^4) (n^3)-(m^5) (n^3)-6 (l^4) (n^4)+10 (l^3) m (n^4)-6 l (m^3) (n^4)+2 (m^4) (n^4)),(l-m) (6 (l^4) (m^4)-10 (l^4) (m^3) n-10 (l^3) (m^4) n+20 (l^3) (m^3) (n^2)+6 (l^4) m (n^3)-9 (l^3) (m^2) (n^3)-9 (l^2) (m^3) (n^3)+6 l (m^4) (n^3)-2 (l^4) (n^4)-2 (l^3) m (n^4)+8 (l^2) (m^2) (n^4)-2 l (m^3) (n^4)-2 (m^4) (n^4)+(l^3) (n^5)-(l^2) m (n^5)-l (m^2) (n^5)+(m^3) (n^5))}; (* QL-2nd Quasi Centroid = Centroid 2nd Quasi Centroid (QG-P8) Triangle *)
QLP16={m n (2 (a^2) (a-b-c) (a+b-c) (a-b+c) (a+b+c) (l-m) (l-n) (l (m-n)+m n) (l m-(l+m) n) (-m n+l (m+n))-((c^2) l m (l-n) (m-n)+(l-m) n ((a^2) m (l-n)+(b^2) l (-m+n))) (-(a^4) (4 (l^2)+m n-l (m+n)) (-m n+l (m+n))+(b-c) (b+c) ((b^2) (((l (m-n)+m n))^2)-(((c l m-c (l+m) n))^2))-2 (a^2) ((b^2) ((l^2) (2 l-3 m) m+2 (l^2) (-l+m) n+(((l-m))^2) (n^2))+(c^2) (-2 l (m^2) n+(m^2) (n^2)+2 (l^3) (-m+n)+(l^2) (m-n) (m+3 n))))),l n (-2 (b^2) (a-b-c) (a+b-c) (a-b+c) (a+b+c) (l-m) (m-n) (l (m-n)+m n) (l m-(l+m) n) (-m n+l (m+n))-((c^2) l m (l-n) (m-n)+(l-m) n ((a^2) m (l-n)+(b^2) l (-m+n))) ((c^4) (((l m-(l+m) n))^2)+(a^2) (-2 l (m^2) ((c^2) l+(b^2) (-3 l+2 m))+4 (m^2) ((c^2) l+(b^2) (-l+m)) n-2 ((b^2) (((l-m))^2)+(c^2) ((l^2)+(m^2))) (n^2))+(b^4) (l (m-n)+m n) (l (m-n)+m (-4 m+n))-2 (b^2) (c^2) ((l^2) (((m-n))^2)+(m^2) (2 m-3 n) n+2 l (m^2) (-m+n))+(a^4) (((m n-l (m+n)))^2))),l m (-2 (a-b-c) (a+b-c) (c^2) (a-b+c) (a+b+c) (l-n) (-m+n) (l (m-n)+m n) (l m-(l+m) n) (-m n+l (m+n))-((c^2) l m (l-n) (m-n)+(l-m) n ((a^2) m (l-n)+(b^2) l (-m+n))) ((b^4) (((l (m-n)+m n))^2)+(c^4) (l m-(l+m) n) (l m-(l+m) n+4 (n^2))+(a^4) (((m n-l (m+n)))^2)-2 (b^2) (c^2) ((l^2) (((m-n))^2)+2 l (m-n) (n^2)+m (n^2) (-3 m+2 n))-2 (a^2) ((b^2) ((l^2) (m^2)+(((l-m))^2) (n^2))+(c^2) (m (m-2 n) (n^2)+(l^2) ((m^2)-3 (n^2))+2 l n (-(m^2)+m n+(n^2))))))}; (* QL-QuasiCircumcenter *)
QLP17={m n (-(a^2) (l-m) (l-n) (2 (l^2) (((m-n))^2)-(m^2) (n^2)+l m n (m+n))-l (m-n) ((b^2) (l-m) n (3 l m-l n-m n)+(c^2) m (l-n) (l (m-3 n)+m n))),l n ((b^2) (l-m) (m-n) (2 (m^2) (n^2)+l m n (-4 m+n)+(l^2) (2 (m^2)+m n-(n^2)))-m (l-n) (-(a^2) (l-m) n (3 l m-l n-m n)+(c^2) l (m-n) (-3 m n+l (m+n)))),l m (-(c^2) (l-n) (m-n) (l m (m-4 n) n+2 (m^2) (n^2)+(l^2) (-(m^2)+m n+2 (n^2)))-(l-m) n ((a^2) m (l-n) (l (m-3 n)+m n)-(b^2) l (m-n) (-3 m n+l (m+n))))}; (* QL-Adjunct QuasiCircumcenter *)
QLP18={(l^2) (m-n) ((l^3) (m^3)-2 (l^2) (m^4)-(l^3) (m^2) n+4 l (m^4) n-(l^3) m (n^2)+4 (l^2) (m^2) (n^2)-3 l (m^3) (n^2)-2 (m^4) (n^2)+(l^3) (n^3)-3 l (m^2) (n^3)+2 (m^3) (n^3)-2 (l^2) (n^4)+4 l m (n^4)-2 (m^2) (n^4)),-(m^2) (l-n) (-2 (l^4) (m^2)+(l^3) (m^3)+4 (l^4) m n-(l^2) (m^3) n-2 (l^4) (n^2)-3 (l^3) m (n^2)+4 (l^2) (m^2) (n^2)-l (m^3) (n^2)+2 (l^3) (n^3)-3 (l^2) m (n^3)+(m^3) (n^3)-2 (l^2) (n^4)+4 l m (n^4)-2 (m^2) (n^4)),-(l-m) (n^2) (2 (l^4) (m^2)-2 (l^3) (m^3)+2 (l^2) (m^4)-4 (l^4) m n+3 (l^3) (m^2) n+3 (l^2) (m^3) n-4 l (m^4) n+2 (l^4) (n^2)-4 (l^2) (m^2) (n^2)+2 (m^4) (n^2)-(l^3) (n^3)+(l^2) m (n^3)+l (m^2) (n^3)-(m^3) (n^3))}; (* Reflection QL-P8 in QL-P12 *)
QLP19={-(-l m-l n+3 m n) (-(a^2) l m+(b^2) l m-(c^2) l m-(a^2) l n-(b^2) l n+(c^2) l n+2 (a^2) m n),(l m-3 l n+m n) ((a^2) l m-(b^2) l m-(c^2) l m+2 (b^2) l n-(a^2) m n-(b^2) m n+(c^2) m n),-(3 l m-l n-m n) (2 (c^2) l m+(a^2) l n-(b^2) l n-(c^2) l n-(a^2) m n+(b^2) m n-(c^2) m n)}; (* Midpoint QL-P1 and QL-P7 *)
QLP20={-(m-n) (-(a^4) (l^2)+(b^4) (l^2)-2 (b^2) (c^2) (l^2)+(c^4) (l^2)+2 (a^2) (b^2) l m-2 (b^4) l m+2 (b^2) (c^2) l m+2 (a^2) (c^2) l n+2 (b^2) (c^2) l n-2 (c^4) l n+(a^4) m n-2 (a^2) (b^2) m n+(b^4) m n-2 (a^2) (c^2) m n-2 (b^2) (c^2) m n+(c^4) m n),(l-n) (-2 (a^4) l m+2 (a^2) (b^2) l m+2 (a^2) (c^2) l m+(a^4) (m^2)-(b^4) (m^2)-2 (a^2) (c^2) (m^2)+(c^4) (m^2)+(a^4) l n-2 (a^2) (b^2) l n+(b^4) l n-2 (a^2) (c^2) l n-2 (b^2) (c^2) l n+(c^4) l n+2 (a^2) (c^2) m n+2 (b^2) (c^2) m n-2 (c^4) m n),-(l-m) ((a^4) l m-2 (a^2) (b^2) l m+(b^4) l m-2 (a^2) (c^2) l m-2 (b^2) (c^2) l m+(c^4) l m-2 (a^4) l n+2 (a^2) (b^2) l n+2 (a^2) (c^2) l n+2 (a^2) (b^2) m n-2 (b^4) m n+2 (b^2) (c^2) m n+(a^4) (n^2)-2 (a^2) (b^2) (n^2)+(b^4) (n^2)-(c^4) (n^2))}; (* Orthocenter Homothetic Center *)
QLP21={(1/2) (2 (a^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (((l-m))^2) m (((l-n))^2) (m-n) n+2 (-m+n) ((c^2) l m (l-n) (m-n)+(a^2) (l-m) m (l-n) n-(b^2) l (l-m) (m-n) n) (2 (a^2) ((b^2) m (l-n)+(c^2) (l-m) n)+(a^4) (-(l^2)+m n)+((b^2)-(c^2)) ((b^2) ((l^2)-2 l m+m n)-(c^2) ((l^2)-2 l n+m n)))),(l-n) (-(b^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) l (((l-m))^2) (((m-n))^2) n+((c^2) l m (l-n) (m-n)+(a^2) (l-m) m (l-n) n-(b^2) l (l-m) (m-n) n) (2 (a^2) ((b^2) l+(c^2) (l-m)) (m-n)+(a^4) ((m^2)+l (-2 m+n))-((b^2)-(c^2)) ((b^2) ((m^2)-l n)+(c^2) ((m^2)+l n-2 m n)))),(1/2) (2 (c^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) l (l-m) m (((l-n))^2) (((m-n))^2)+2 (-l+m) ((c^2) l m (l-n) (m-n)+(a^2) (l-m) m (l-n) n-(b^2) l (l-m) (m-n) n) (-2 (a^2) ((c^2) l+(b^2) (l-n)) (m-n)+(a^4) (l (m-2 n)+(n^2))+((b^2)-(c^2)) ((c^2) (-l m+(n^2))+(b^2) (l m-2 m n+(n^2)))))};(* Adjunct Orthocenter Homothetic Center *)
QLP22={(m-n) (-(a^2) (b^2) (l^2)+(b^4) (l^2)-(a^2) (c^2) (l^2)-2 (b^2) (c^2) (l^2)+(c^4) (l^2)-(a^4) l m+3 (a^2) (b^2) l m-2 (b^4) l m+2 (a^2) (c^2) l m+3 (b^2) (c^2) l m-(c^4) l m-(a^4) l n+2 (a^2) (b^2) l n-(b^4) l n+3 (a^2) (c^2) l n+3 (b^2) (c^2) l n-2 (c^4) l n+2 (a^4) m n-4 (a^2) (b^2) m n+2 (b^4) m n-4 (a^2) (c^2) m n-4 (b^2) (c^2) m n+2 (c^4) m n),-(l-n) (-2 (a^4) l m+3 (a^2) (b^2) l m-(b^4) l m+3 (a^2) (c^2) l m+2 (b^2) (c^2) l m-(c^4) l m+(a^4) (m^2)-(a^2) (b^2) (m^2)-2 (a^2) (c^2) (m^2)-(b^2) (c^2) (m^2)+(c^4) (m^2)+2 (a^4) l n-4 (a^2) (b^2) l n+2 (b^4) l n-4 (a^2) (c^2) l n-4 (b^2) (c^2) l n+2 (c^4) l n-(a^4) m n+2 (a^2) (b^2) m n-(b^4) m n+3 (a^2) (c^2) m n+3 (b^2) (c^2) m n-2 (c^4) m n),(l-m) (2 (a^4) l m-4 (a^2) (b^2) l m+2 (b^4) l m-4 (a^2) (c^2) l m-4 (b^2) (c^2) l m+2 (c^4) l m-2 (a^4) l n+3 (a^2) (b^2) l n-(b^4) l n+3 (a^2) (c^2) l n+2 (b^2) (c^2) l n-(c^4) l n-(a^4) m n+3 (a^2) (b^2) m n-2 (b^4) m n+2 (a^2) (c^2) m n+3 (b^2) (c^2) m n-(c^4) m n+(a^4) (n^2)-2 (a^2) (b^2) (n^2)+(b^4) (n^2)-(a^2) (c^2) (n^2)-(b^2) (c^2) (n^2))};(* QL-Nine-point Homothetic Center *)

QLP23={l (m-n) ((l^2) (m^2)-2 (l^2) m n+2 l (m^2) n+(l^2) (n^2)+2 l m (n^2)-3 (m^2) (n^2)),-m (l-n) ((l^2) (m^2)+2 (l^2) m n-2 l (m^2) n-3 (l^2) (n^2)+2 l m (n^2)+(m^2) (n^2)),-(l-m) n (3 (l^2) (m^2)-2 (l^2) m n-2 l (m^2) n-(l^2) (n^2)+2 l m (n^2)-(m^2) (n^2))};(* Center Midline Conic *)
QLP24={m n ((a^4) (l-m) (l-n) (4 (l^4) (((m-n))^2)-(m^3) (n^3)-3 (l^3) (((m-n))^2) (m+n)-l (m^2) (n^2) (m+n)+(l^2) m n (5 (m^2)-6 m n+5 (n^2)))+(m-n) ((l^2) (((m-n))^2)-3 (m^2) (n^2)+2 l m n (m+n)) (-2 (b^2) (c^2) (l-m) (l-n) (m-n)+(b^4) (l-m) (l (m-n)+m n)-(c^4) (l-n) (m n+l (-m+n)))-2 (a^2) (l-m) (l-n) ((c^2) (-2 (l^3) (((m-n))^3)+2 l m (((m-n))^2) (n^2)+(m^2) (n^3) (-2 m+n)+(l^2) n (2 (m^3)-3 (m^2) n+4 m (n^2)-3 (n^3)))+(b^2) (2 (l^3) (((m-n))^3)+2 l (m^2) (((m-n))^2) n+(m^3) (m-2 n) (n^2)+(l^2) m (-3 (m^3)+4 (m^2) n-3 m (n^2)+2 (n^3))))),l n (-(a^4) (l-m) (l-n) (l (m^2) (3 m-n) (n^2)-(m^3) (n^3)+(l^2) m n (-3 (m^2)-2 m n+5 (n^2))+(l^3) ((m^3)+3 (m^2) n-m (n^2)-3 (n^3)))-2 (a^2) (l-m) (m-n) (-(c^2) (((l-n))^2) ((m^2) (n^2)+2 l m n (-m+n)+(l^2) ((m^2)+2 m n-3 (n^2)))+(b^2) (2 (m^3) (n^3)-2 l (m^2) (n^2) (3 m+n)+(l^2) m n (6 (m^2)+3 m n-2 (n^2))+(l^4) (3 (m^2)-2 m n-(n^2))-2 (l^3) ((m^3)+2 (m^2) n-2 m (n^2)-(n^3))))+(m-n) ((c^4) (l-n) (3 l (m^2) (m-n) (n^2)-(m^3) (n^3)+(l^3) (((m-n))^2) (m+3 n)+(l^2) m n (-3 (m^2)+2 m n+(n^2)))+(b^4) (l-m) ((l^3) (((m-n))^2) (3 m+n)+(m^3) (n^2) (-4 m+3 n)+l (m^2) n (8 (m^2)-3 m n-5 (n^2))+(l^2) m (-4 (m^3)-3 (m^2) n+6 m (n^2)+(n^3)))-2 (b^2) (c^2) ((m^3) (2 m-3 n) (n^3)+2 (l^4) (((m-n))^2) (m+n)+l (m^2) (n^2) (-6 (m^2)+2 m n+5 (n^2))+(l^2) m n (6 (m^3)+3 (m^2) n-8 m (n^2)-(n^3))-(l^3) (2 (m^4)+4 (m^3) n-5 (m^2) (n^2)-2 m (n^3)+(n^4))))),l m ((a^4) (l-m) (l-n) (l (m^2) (m-3 n) (n^2)+(m^3) (n^3)+(l^2) m n (-5 (m^2)+2 m n+3 (n^2))+(l^3) (3 (m^3)+(m^2) n-3 m (n^2)-(n^3)))+2 (a^2) (l-n) (-m+n) (-(b^2) (((l-m))^2) (-(m^2) (n^2)+2 l m n (-m+n)+(l^2) (3 (m^2)-2 m n-(n^2)))+(c^2) (-2 (m^3) (n^3)+2 l (m^2) (n^2) (m+3 n)+(l^2) m n (2 (m^2)-3 m n-6 (n^2))+(l^4) ((m^2)+2 m n-3 (n^2))-2 (l^3) ((m^3)+2 (m^2) n-2 m (n^2)-(n^3))))-(m-n) ((b^4) (l-m) (-(m^3) (n^3)+3 l (m^2) (n^2) (-m+n)+(l^3) (((m-n))^2) (3 m+n)+(l^2) m n ((m^2)+2 m n-3 (n^2)))+(c^4) (l-n) ((m^2) (3 m-4 n) (n^3)+(l^3) (((m-n))^2) (m+3 n)+l m (n^2) (-5 (m^2)-3 m n+8 (n^2))+(l^2) n ((m^3)+6 (m^2) n-3 m (n^2)-4 (n^3)))-2 (b^2) (c^2) (2 (l^4) (((m-n))^2) (m+n)+(m^3) (n^3) (-3 m+2 n)+l (m^2) (n^2) (5 (m^2)+2 m n-6 (n^2))-(l^2) m n ((m^3)+8 (m^2) n-3 m (n^2)-6 (n^3))-(l^3) ((m^4)-2 (m^3) n-5 (m^2) (n^2)+4 m (n^3)+2 (n^4)))))};(*Intersection QL-P1.QL-P8 ^ QL-P13.QL-P17*)
QLP25={(l-m) m (l-n) n (-4 l (m^2) (m-n) (n^2) ((b^2) (l-m) n (3 l m-l n-m n)+(c^2) m (l-n) (l (m-3 n)+m n))+(a^2) ((l^4) m (((m-n))^4) n+(m^5) (n^5)+(l^5) (((m-n))^4) (m+n)-3 l (m^4) (n^4) (m+n)-2 (l^2) (m^3) (n^3) ((m^2)-8 m n+(n^2))+2 (l^3) (m^2) (n^2) ((m^3)-3 (m^2) n-3 m (n^2)+(n^3)))),-l (l-m) (m-n) n ((b^2) (2 (l^2) (m^3) (((m-n))^2) (n^3)+(m^5) (n^5)+l (m^4) (n^4) (-3 m+n)+2 (l^3) (m^2) (n^2) ((m^3)+3 (m^2) n-3 m (n^2)-(n^3))-(l^4) m n (3 (m^4)+4 (m^3) n+6 (m^2) (n^2)-16 m (n^3)+3 (n^4))+(l^5) ((m^5)+(m^4) n+2 (m^3) (n^2)-2 (m^2) (n^3)-3 m (n^4)+(n^5)))-4 (l^2) m (l-n) (n^2) (-(a^2) (l-m) n (3 l m-l n-m n)+(c^2) l (m-n) (-3 m n+l (m+n)))),l m (l-n) (m-n) ((c^2) (2 (l^2) (m^3) (((m-n))^2) (n^3)+l (m^4) (m-3 n) (n^4)+(m^5) (n^5)+2 (l^3) (m^2) (n^2) (-(m^3)-3 (m^2) n+3 m (n^2)+(n^3))-(l^4) m n (3 (m^4)-16 (m^3) n+6 (m^2) (n^2)+4 m (n^3)+3 (n^4))+(l^5) ((m^5)-3 (m^4) n-2 (m^3) (n^2)+2 (m^2) (n^3)+m (n^4)+(n^5)))-4 (l^2) (l-m) (m^2) n ((a^2) m (l-n) (l (m-3 n)+m n)-(b^2) l (m-n) (-3 m n+l (m+n))))}; (* Focus 2nd QL-Parabola *)
QLP26={(a^2) ((a^2) (l-m) (l-n)+(c^2) (m-2 n) (l-n)-(b^2) (l-m) (2 m-n)),(b^2) ((a^2) (l-m) (2 l-n)+((b^2) (-l+m)+(c^2) (l-2 n)) (m-n)),(c^2) ((a^2) (2 l-m) (l-n)+(-(b^2) (l-2 m)+(c^2) (l-n)) (m-n))}; (* Least Square Distances Point *)
QLP27={-2 (a^4) (l-m) (l-n) (m-n)+((b^2)-(c^2)) (m-n) ((b^2) (l-m) n+(c^2) m (-l+n))+(a^2) ((c^2) ((l^2) (m-2 n)+m (3 m-4 n) n+l (-3 (m^2)+3 m n+2 (n^2)))+(b^2) ((l^2) (2 m-n)+m (4 m-3 n) n+l (-2 (m^2)-3 m n+3 (n^2)))),(a^4) (l-m) (l-n) n-(m-n) ((c^4) l (l-n)+2 (b^4) (l-m) (l-n)+(b^2) (c^2) (-3 (l^2)-2 m n+l (m+4 n)))+(a^2) ((c^2) (l-n) (l (m-2 n)+m n)+(b^2) (2 (l^2) (m-2 n)+m (m-3 n) n+l (-2 (m^2)+3 m n+3 (n^2)))),-(a^4) (l-m) m (l-n)+(m-n) ((b^4) l (-l+m)-2 (c^4) (l-m) (l-n)+(b^2) (c^2) (3 (l^2)+2 m n-l (4 m+n)))+(a^2) ((b^2) (l-m) (2 l m-l n-m n)+(c^2) ((l^2) (4 m-2 n)+m (3 m-n) n+l (-3 (m^2)-3 m n+2 (n^2))))};   (* Nine-point Homothetic Center QL-X(3) Quadrangle *)
QLP28={(a^2) (-(a^6) (l-m) (l-n) (2 l-m-n) (m-n)+(b^4) (c^2) (9 l (m^2) n+(l^3) (2 m+n)-3 (l^2) m (m+2 n)+m n (-(m^2)-3 m n+(n^2)))+(b^2) (c^4) (-9 l m (n^2)+3 (l^2) n (2 m+n)-(l^3) (m+2 n)+m n (-(m^2)+3 m n+(n^2)))-(b^6) ((l^3) m-3 (l^2) (m^2)-m n (3 (m^2)-3 m n+(n^2))+l (2 (m^3)+3 (m^2) n-3 m (n^2)+(n^3)))+(c^6) ((l^3) n-3 (l^2) (n^2)-m n ((m^2)-3 m n+3 (n^2))+l ((m^3)-3 (m^2) n+3 m (n^2)+2 (n^3)))-(a^2) (m-n) (3 (b^4) (l-m) (l-n) (m-n)-3 (c^4) (l-m) (l-n) (m-n)+(b^2) (c^2) ((l^3)+9 l m n-3 (l^2) (m+n)-2 m n (m+n)))+(a^4) ((b^2) ((l^3) (3 m-2 n)-m n ((m^2)+3 m n-3 (n^2))-3 (l^2) ((m^2)+2 m n-2 (n^2))-3 l n (-3 (m^2)+m n+(n^2)))+(c^2) ((l^3) (2 m-3 n)+3 l m ((m^2)+m n-3 (n^2))+m n (-3 (m^2)+3 m n+(n^2))+(l^2) (-6 (m^2)+6 m n+3 (n^2))))),(b^2) ((a^6) ((l^3) (2 m-3 n)+m (n^3)+3 (l^2) (-(m^2)+m n+(n^2))+l ((m^3)-3 m (n^2)-(n^3)))+((b^2)-(c^2)) (m-n) ((b^4) (l-m) (l-n) (l-2 m+n)+(c^4) ((l^3)-3 (l^2) n+m (m-2 n) n+3 l (n^2))+(b^2) (c^2) (-2 (l^3)-6 l m n+3 (l^2) (m+n)+m n (m+n)))+(a^4) (-3 (b^2) (l-m) (((l-n))^2) (m-n)+(c^2) ((l^3) n-(m^3) n+3 (l^2) ((m^2)-3 m n+(n^2))-l (2 (m^3)-6 (m^2) n+(n^3))))+(a^2) ((c^4) ((l^3) n+(m^2) (2 m-3 n) n-3 (l^2) (n^2)+l ((m^3)-6 (m^2) n+9 m (n^2)-(n^3)))+(b^4) ((l^3) n+3 (l^2) ((m^2)-3 m n+(n^2))+m n (2 (m^2)-6 m n+3 (n^2))-3 l ((m^3)-2 (m^2) n-m (n^2)+(n^3)))+(b^2) (c^2) (-3 (l^2) m (m-3 n)-2 (l^3) n-(m^2) (m-3 n) n+l ((m^3)-9 m (n^2)+2 (n^3))))),(c^2) ((a^6) ((l^3) (3 m-2 n)-(m^3) n-3 (l^2) ((m^2)+m n-(n^2))+l ((m^3)+3 (m^2) n-(n^3)))-((b^2)-(c^2)) (m-n) ((c^4) (l-m) (l+m-2 n) (l-n)+(b^4) ((l^3)-3 (l^2) m+3 l (m^2)+m n (-2 m+n))+(b^2) (c^2) (-2 (l^3)-6 l m n+3 (l^2) (m+n)+m n (m+n)))-(a^2) ((b^2) (c^2) (-2 (l^3) m+3 (l^2) (3 m-n) n+m (3 m-n) (n^2)+l (2 (m^3)-9 (m^2) n+(n^3)))+(b^4) ((l^3) m-3 (l^2) (m^2)+m (n^2) (-3 m+2 n)+l (-(m^3)+9 (m^2) n-6 m (n^2)+(n^3)))+(c^4) ((l^3) m+3 (l^2) ((m^2)-3 m n+(n^2))+m n (3 (m^2)-6 m n+2 (n^2))-3 l ((m^3)-(m^2) n-2 m (n^2)+(n^3))))+(a^4) (-3 (c^2) (((l-m))^2) (l-n) (m-n)+(b^2) (-(l^3) m+m (n^3)-3 (l^2) ((m^2)-3 m n+(n^2))+l ((m^3)-6 m (n^2)+2 (n^3)))))};  (* Center of the Circle through the 4 X(186)-versions of QL-ComponentTriangles *)
QLP29={(a^4) l (-2 l m+(m^2)+2 l n-(n^2))+((b^2)-(c^2)) (m-n) ((b^2) ((l^2)-2 l m+m n)-(c^2) ((l^2)-2 l n+m n))+(a^2) (-(c^2) ((l^2) n+(m^2) n+l ((m^2)-4 m n+(n^2)))+(b^2) ((l^2) m+m (n^2)+l ((m^2)-4 m n+(n^2)))),-(b^4) m (l-n) (l-2 m+n)+(b^2) (c^2) (-4 l m n+(l^2) (m+n)+m n (m+n))+(a^4) ((l^2) (2 m-n)+(m^2) n+l (-(m^2)-2 m n+(n^2)))+(c^4) (-(l^2) n+m (m-2 n) n+l (-(m^2)+2 m n+(n^2)))-(a^2) (2 (c^2) (l-m) (l-n) (m-n)+(b^2) ((l^2) m+m (n^2)+l ((m^2)-4 m n+(n^2)))),(c^4) (l-m) (l+m-2 n) n-(b^2) (c^2) (-4 l m n+(l^2) (m+n)+m n (m+n))+(b^4) ((l^2) m+m (2 m-n) n+l (-(m^2)-2 m n+(n^2)))+(a^4) ((l^2) (m-2 n)-m (n^2)+l (-(m^2)+2 m n+(n^2)))+(a^2) (-2 (b^2) (l-m) (l-n) (m-n)+(c^2) ((l^2) n+(m^2) n+l ((m^2)-4 m n+(n^2))))};  (* Circumcenter QL-X(265)-Quadrangle *)
QLP30={((b^2)-(c^2)) (-(c^2) (l-m) (l-2 n)+(b^2) (l-2 m) (l-n)) (m-n)+(a^4) (m-n) (-(l^2)+m n)+(a^2) ((c^2) (-(l^2) m+m n (-3 m+2 n)+l ((m^2)+3 m n-2 (n^2)))+(b^2) ((l^2) n+m n (-2 m+3 n)+l (2 (m^2)-3 m n-(n^2)))),(c^4) (l-m) (m-2 n) (l-n)+(a^4) (2 l-m) (l-n) (m-n)+(a^2) ((c^2) (l-n) (-3 l m+2 (m^2)+4 l n-3 m n)-(b^2) (m-n) (2 (l^2)-3 l n+m n))+(b^2) (c^2) (-(l^2) (m-3 n)+2 m (n^2)+l ((m^2)-3 m n-2 (n^2)))+(b^4) (-(l^2) n-(m^2) n+l ((m^2)+(n^2))),(a^4) (l-m) (2 l-n) (m-n)+(b^4) (l-m) (l-n) (2 m-n)+(b^2) (c^2) (l-n) (2 (m^2)+l (-3 m+n))+(c^4) ((l^2) m+m (n^2)-l ((m^2)+(n^2)))+(a^2) (-(c^2) (m-n) (2 (l^2)-3 l m+m n)+(b^2) (m n (-3 m+2 n)+(l^2) (-4 m+3 n)+l (4 (m^2)-2 (n^2))))};  (* Morley's Second Circle Center *)

Other Points

QL2P1a={((a^4) (l^2) m-2 (a^2) (b^2) (l^2) m+(b^4) (l^2) m-2 (a^2) (c^2) (l^2) m-2 (b^2) (c^2) (l^2) m+(c^4) (l^2) m-3 (a^4) (l^2) n+2 (a^2) (b^2) (l^2) n+(b^4) (l^2) n+2 (a^2) (c^2) (l^2) n-2 (b^2) (c^2) (l^2) n+(c^4) (l^2) n+4 (a^2) (b^2) l m n-4 (b^4) l m n+4 (b^2) (c^2) l m n+(a^4) l (n^2)-2 (a^2) (b^2) l (n^2)+(b^4) l (n^2)+2 (a^2) (c^2) l (n^2)+2 (b^2) (c^2) l (n^2)-3 (c^4) l (n^2)+(a^4) m (n^2)-2 (a^2) (b^2) m (n^2)+(b^4) m (n^2)-2 (a^2) (c^2) m (n^2)-2 (b^2) (c^2) m (n^2)+(c^4) m (n^2)-(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) l √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2))+(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) n √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)))/(2 ((a^2)-(b^2)-(c^2)) l n ((a^2) l-(b^2) l+(c^2) l-(a^2) m+(b^2) m+(c^2) m-2 (c^2) n)),((a^4) l (m^2)-2 (a^2) (b^2) l (m^2)+(b^4) l (m^2)-2 (a^2) (c^2) l (m^2)-2 (b^2) (c^2) l (m^2)+(c^4) l (m^2)-4 (a^4) l m n+4 (a^2) (b^2) l m n+4 (a^2) (c^2) l m n+(a^4) (m^2) n+2 (a^2) (b^2) (m^2) n-3 (b^4) (m^2) n-2 (a^2) (c^2) (m^2) n+2 (b^2) (c^2) (m^2) n+(c^4) (m^2) n+(a^4) l (n^2)-2 (a^2) (b^2) l (n^2)+(b^4) l (n^2)-2 (a^2) (c^2) l (n^2)-2 (b^2) (c^2) l (n^2)+(c^4) l (n^2)+(a^4) m (n^2)-2 (a^2) (b^2) m (n^2)+(b^4) m (n^2)+2 (a^2) (c^2) m (n^2)+2 (b^2) (c^2) m (n^2)-3 (c^4) m (n^2)-(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) m √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2))+(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) n √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)))/(2 ((a^2)-(b^2)+(c^2)) m n (-(a^2) l+(b^2) l-(c^2) l+(a^2) m-(b^2) m-(c^2) m+2 (c^2) n)),1}; (* 1st Pluecker Point *)
QL2P1b={((a^4) (l^2) m-2 (a^2) (b^2) (l^2) m+(b^4) (l^2) m-2 (a^2) (c^2) (l^2) m-2 (b^2) (c^2) (l^2) m+(c^4) (l^2) m-3 (a^4) (l^2) n+2 (a^2) (b^2) (l^2) n+(b^4) (l^2) n+2 (a^2) (c^2) (l^2) n-2 (b^2) (c^2) (l^2) n+(c^4) (l^2) n+4 (a^2) (b^2) l m n-4 (b^4) l m n+4 (b^2) (c^2) l m n+(a^4) l (n^2)-2 (a^2) (b^2) l (n^2)+(b^4) l (n^2)+2 (a^2) (c^2) l (n^2)+2 (b^2) (c^2) l (n^2)-3 (c^4) l (n^2)+(a^4) m (n^2)-2 (a^2) (b^2) m (n^2)+(b^4) m (n^2)-2 (a^2) (c^2) m (n^2)-2 (b^2) (c^2) m (n^2)+(c^4) m (n^2)+(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) l √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2))-(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) n √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)))/(2 ((a^2)-(b^2)-(c^2)) l n ((a^2) l-(b^2) l+(c^2) l-(a^2) m+(b^2) m+(c^2) m-2 (c^2) n)),((a^4) l (m^2)-2 (a^2) (b^2) l (m^2)+(b^4) l (m^2)-2 (a^2) (c^2) l (m^2)-2 (b^2) (c^2) l (m^2)+(c^4) l (m^2)-4 (a^4) l m n+4 (a^2) (b^2) l m n+4 (a^2) (c^2) l m n+(a^4) (m^2) n+2 (a^2) (b^2) (m^2) n-3 (b^4) (m^2) n-2 (a^2) (c^2) (m^2) n+2 (b^2) (c^2) (m^2) n+(c^4) (m^2) n+(a^4) l (n^2)-2 (a^2) (b^2) l (n^2)+(b^4) l (n^2)-2 (a^2) (c^2) l (n^2)-2 (b^2) (c^2) l (n^2)+(c^4) l (n^2)+(a^4) m (n^2)-2 (a^2) (b^2) m (n^2)+(b^4) m (n^2)+2 (a^2) (c^2) m (n^2)+2 (b^2) (c^2) m (n^2)-3 (c^4) m (n^2)+(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) m √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2))-(Sqrt[(a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)]) n √((a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-6 (a^4) (l^2) m n+4 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+4 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n+2 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-6 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+4 (a^2) (c^2) l m (n^2)+4 (b^2) (c^2) l m (n^2)-6 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)))/(2 ((a^2)-(b^2)+(c^2)) m n (-(a^2) l+(b^2) l-(c^2) l+(a^2) m-(b^2) m-(c^2) m+2 (c^2) n)),1}; (* 2nd Pluecker Point *)
QL2P2a={(l (m-n)+m n) ((a^2) (l^2) (m^2)-(b^2) (l^2) (m^2)+(c^2) (l^2) (m^2)+2 (a^2) (l^2) m n+2 (b^2) (l^2) m n-2 (c^2) (l^2) m n-2 (a^2) l (m^2) n-2 (b^2) l (m^2) n-2 (c^2) l (m^2) n+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)+(c^2) (l^2) (n^2)-2 (a^2) l m (n^2)+2 (b^2) l m (n^2)+2 (c^2) l m (n^2)+(a^2) (m^2) (n^2)-(b^2) (m^2) (n^2)+(c^2) (m^2) (n^2)+(Sqrt[-4 (b^2) (c^2) ((((l^2) (((m-n))^2)-(m^2) (n^2)))^2)+((((b^2) (((l (m-n)+m n))^2)+(c^2) (((m n+l (-m+n)))^2)-(a^2) (((m n-l (m+n)))^2)))^2)])),-(-m n+l (m+n)) ((a^2) (l^2) (m^2)-(b^2) (l^2) (m^2)-(c^2) (l^2) (m^2)+2 (a^2) (l^2) m n+2 (b^2) (l^2) m n+2 (c^2) (l^2) m n-2 (a^2) l (m^2) n-2 (b^2) l (m^2) n+2 (c^2) l (m^2) n+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)-(c^2) (l^2) (n^2)-2 (a^2) l m (n^2)+2 (b^2) l m (n^2)-2 (c^2) l m (n^2)+(a^2) (m^2) (n^2)-(b^2) (m^2) (n^2)-(c^2) (m^2) (n^2)+(Sqrt[-4 (b^2) (c^2) ((((l^2) (((m-n))^2)-(m^2) (n^2)))^2)+((((b^2) (((l (m-n)+m n))^2)+(c^2) (((m n+l (-m+n)))^2)-(a^2) (((m n-l (m+n)))^2)))^2)])),2 (c^2) (l (m-n)-m n) (l (m-n)+m n) (-m n+l (m+n))};  (* 1st NewtonLine Isogonal Invariant Point *)
QL2P2b={(l (m-n)+m n) ((a^2) (l^2) (m^2)-(b^2) (l^2) (m^2)+(c^2) (l^2) (m^2)+2 (a^2) (l^2) m n+2 (b^2) (l^2) m n-2 (c^2) (l^2) m n-2 (a^2) l (m^2) n-2 (b^2) l (m^2) n-2 (c^2) l (m^2) n+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)+(c^2) (l^2) (n^2)-2 (a^2) l m (n^2)+2 (b^2) l m (n^2)+2 (c^2) l m (n^2)+(a^2) (m^2) (n^2)-(b^2) (m^2) (n^2)+(c^2) (m^2) (n^2)-(Sqrt[-4 (b^2) (c^2) ((((l^2) (((m-n))^2)-(m^2) (n^2)))^2)+((((b^2) (((l (m-n)+m n))^2)+(c^2) (((m n+l (-m+n)))^2)-(a^2) (((m n-l (m+n)))^2)))^2)])),-(-m n+l (m+n)) ((a^2) (l^2) (m^2)-(b^2) (l^2) (m^2)-(c^2) (l^2) (m^2)+2 (a^2) (l^2) m n+2 (b^2) (l^2) m n+2 (c^2) (l^2) m n-2 (a^2) l (m^2) n-2 (b^2) l (m^2) n+2 (c^2) l (m^2) n+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)-(c^2) (l^2) (n^2)-2 (a^2) l m (n^2)+2 (b^2) l m (n^2)-2 (c^2) l m (n^2)+(a^2) (m^2) (n^2)-(b^2) (m^2) (n^2)-(c^2) (m^2) (n^2)-(Sqrt[-4 (b^2) (c^2) ((((l^2) (((m-n))^2)-(m^2) (n^2)))^2)+((((b^2) (((l (m-n)+m n))^2)+(c^2) (((m n+l (-m+n)))^2)-(a^2) (((m n-l (m+n)))^2)))^2)])),2 (c^2) (l (m-n)-m n) (l (m-n)+m n) (-m n+l (m+n))};  (* 2nd NewtonLine Isogonal Invariant Point *)
(* QL2P2a& QL2P2b are also the Foci of the Conic tangential to L1,L2,L3,L4 and with center QL-P9014 *)

Circular Points at Infinity

CI1={-(a^2)+(b^2)-(c^2)-(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),(a^2)-(b^2)-(c^2)+(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),2 (c^2)};    (* 1st CircularPointAtInfinity *)
CI2={-(a^2)+(b^2)-(c^2)+(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),(a^2)-(b^2)-(c^2)-(Sqrt[-4 (b^2) (c^2)+(((-(a^2)+(b^2)+(c^2)))^2)]),2 (c^2)} ;   (* 2nd CircularPointAtInfinity *)

QG - Points in a QL-Quadrigon

QGP1={-m n,l n,-l m};    (* QG-P1:Diagonal Crosspoint *)
QGP2={-n,l-n,l};    (* QG-P2:Midpoint of the 3rd QA-Diagonal *)
QGP3={(m^2) (l-n) n,(l^2) (n^2),-l (m^2) (l-n)};    (* QG-P3:Midpoint of the 3rd QL-Diagonal *)
QGP4={(m-n) (-(l^2) m+2 l (m^2)+(l^2) n-2 l m n+(m^2) n),-(l^2) (m^2)+2 (l^2) m n-l (m^2) n-(l^2) (n^2)+2 l m (n^2)-(m^2) (n^2),-(l-m) (l (m^2)-2 l m n+2 (m^2) n+l (n^2)-m (n^2))};    (* QG-P4:1st Quasi Centroid *)
QGP5={(a^4) (l^2) (m^2)-(a^2) (b^2) (l^2) (m^2)-(a^2) (c^2) (l^2) (m^2)-(a^4) l (m^3)+(a^2) (b^2) l (m^3)+2 (a^2) (c^2) l (m^3)+(b^2) (c^2) l (m^3)-(c^4) l (m^3)+2 (a^2) (b^2) (l^2) m n+2 (a^2) (c^2) (l^2) m n-4 (a^2) (b^2) l (m^2) n-2 (a^2) (c^2) l (m^2) n-2 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+2 (a^2) (b^2) (m^3) n+(a^4) (l^2) (n^2)-(a^2) (b^2) (l^2) (n^2)-(a^2) (c^2) (l^2) (n^2)-2 (a^4) l m (n^2)+2 (a^2) (b^2) l m (n^2)+(a^2) (c^2) l m (n^2)+(b^2) (c^2) l m (n^2)-(c^4) l m (n^2)+(a^4) (m^2) (n^2)-(a^2) (b^2) (m^2) (n^2)-(a^2) (c^2) (m^2) (n^2),-(a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-(b^2) (c^2) (l^2) (m^2)+(a^2) (b^2) l (m^3)-(b^4) l (m^3)-(b^2) (c^2) l (m^3)-(a^4) (l^2) m n+(a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n+(a^2) (c^2) (l^2) m n+2 (b^2) (c^2) (l^2) m n+(a^4) l (m^2) n+3 (b^4) l (m^2) n-2 (a^2) (c^2) l (m^2) n+(c^4) l (m^2) n-(a^2) (b^2) (m^3) n-(b^4) (m^3) n+(b^2) (c^2) (m^3) n-(a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-(b^2) (c^2) (l^2) (n^2)+2 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+(a^2) (c^2) l m (n^2)+(b^2) (c^2) l m (n^2)-(c^4) l m (n^2)-(a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-(b^2) (c^2) (m^2) (n^2),-(a^2) (c^2) (l^2) (m^2)-(b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)+2 (b^2) (c^2) l (m^3)-(a^4) (l^2) m n+(a^2) (b^2) (l^2) m n+(a^2) (c^2) (l^2) m n+2 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n+2 (a^4) l (m^2) n-2 (a^2) (b^2) l (m^2) n-2 (a^2) (c^2) l (m^2) n-4 (b^2) (c^2) l (m^2) n-(a^4) (m^3) n+(a^2) (b^2) (m^3) n+2 (a^2) (c^2) (m^3) n+(b^2) (c^2) (m^3) n-(c^4) (m^3) n-(a^2) (c^2) (l^2) (n^2)-(b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^2) (c^2) l m (n^2)+2 (b^2) (c^2) l m (n^2)-(a^2) (c^2) (m^2) (n^2)-(b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2)};    (* QG-P5:1st Quasi Circumcenter *)
QGP6={-(a^4) (l^2) (m^2)+(b^4) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)+2 (a^2) (b^2) l (m^3)-2 (b^4) l (m^3)+2 (b^2) (c^2) l (m^3)-2 (a^4) (l^2) m n-2 (b^4) (l^2) m n+4 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n+4 (a^4) l (m^2) n+4 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n-4 (b^2) (c^2) l (m^2) n-(a^4) (m^3) n-2 (a^2) (b^2) (m^3) n-(b^4) (m^3) n+2 (a^2) (c^2) (m^3) n+2 (b^2) (c^2) (m^3) n-(c^4) (m^3) n-(a^4) (l^2) (n^2)+(b^4) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-2 (b^4) l m (n^2)+2 (a^2) (c^2) l m (n^2)+2 (b^2) (c^2) l m (n^2)-(a^4) (m^2) (n^2)+(b^4) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2),(a^4) (l^2) (m^2)-(b^4) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-2 (a^2) (b^2) l (m^3)+2 (b^4) l (m^3)+2 (b^2) (c^2) l (m^3)+2 (a^2) (b^2) (l^2) m n+2 (b^4) (l^2) m n+2 (a^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n-(a^4) l (m^2) n-2 (a^2) (b^2) l (m^2) n-5 (b^4) l (m^2) n+2 (a^2) (c^2) l (m^2) n-2 (b^2) (c^2) l (m^2) n-(c^4) l (m^2) n+2 (a^2) (b^2) (m^3) n+2 (b^4) (m^3) n-2 (b^2) (c^2) (m^3) n+(a^4) (l^2) (n^2)-(b^4) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+2 (b^4) l m (n^2)+2 (a^2) (c^2) l m (n^2)+2 (b^2) (c^2) l m (n^2)+(a^4) (m^2) (n^2)-(b^4) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2),(a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-(c^4) (l^2) (m^2)-(a^4) l (m^3)+2 (a^2) (b^2) l (m^3)-(b^4) l (m^3)+2 (a^2) (c^2) l (m^3)-2 (b^2) (c^2) l (m^3)-(c^4) l (m^3)+2 (a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n+2 (a^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n-4 (a^2) (b^2) l (m^2) n+4 (b^4) l (m^2) n-4 (a^2) (c^2) l (m^2) n+4 (c^4) l (m^2) n+2 (a^2) (b^2) (m^3) n-2 (b^4) (m^3) n+2 (b^2) (c^2) (m^3) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+4 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)-2 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-(c^4) (m^2) (n^2)};    (* QG-P6:1st Quasi Orthocenter *)
QGP7={-(a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-(a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-(a^4) l (m^3)+3 (a^2) (b^2) l (m^3)-2 (b^4) l (m^3)+2 (a^2) (c^2) l (m^3)+3 (b^2) (c^2) l (m^3)-(c^4) l (m^3)-2 (a^4) (l^2) m n+2 (a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n+2 (a^2) (c^2) (l^2) m n+4 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n+4 (a^4) l (m^2) n-4 (a^2) (b^2) l (m^2) n+4 (b^4) l (m^2) n-6 (a^2) (c^2) l (m^2) n-6 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n-(a^4) (m^3) n-(b^4) (m^3) n+2 (a^2) (c^2) (m^3) n+2 (b^2) (c^2) (m^3) n-(c^4) (m^3) n-(a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-(a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+3 (a^2) (c^2) l m (n^2)+3 (b^2) (c^2) l m (n^2)-(c^4) l m (n^2)-(a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-(a^2) (c^2) (m^2) (n^2)-2 (b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2),(a^4) (l^2) (m^2)-(a^2) (b^2) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-(b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-(a^2) (b^2) l (m^3)+(b^4) l (m^3)+(b^2) (c^2) l (m^3)-(a^4) (l^2) m n+3 (a^2) (b^2) (l^2) m n+3 (a^2) (c^2) (l^2) m n+2 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n-2 (a^2) (b^2) l (m^2) n-2 (b^4) l (m^2) n-2 (b^2) (c^2) l (m^2) n+(a^2) (b^2) (m^3) n+(b^4) (m^3) n-(b^2) (c^2) (m^3) n+(a^4) (l^2) (n^2)-(a^2) (b^2) (l^2) (n^2)-2 (a^2) (c^2) (l^2) (n^2)-(b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+2 (a^2) (b^2) l m (n^2)+3 (a^2) (c^2) l m (n^2)+3 (b^2) (c^2) l m (n^2)-(c^4) l m (n^2)+(a^4) (m^2) (n^2)-(a^2) (b^2) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-(b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2),(a^4) (l^2) (m^2)-2 (a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-(a^2) (c^2) (l^2) (m^2)-(b^2) (c^2) (l^2) (m^2)-(a^4) l (m^3)+2 (a^2) (b^2) l (m^3)-(b^4) l (m^3)+2 (a^2) (c^2) l (m^3)-(c^4) l (m^3)-(a^4) (l^2) m n+3 (a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n+3 (a^2) (c^2) (l^2) m n+2 (b^2) (c^2) (l^2) m n+2 (a^4) l (m^2) n-6 (a^2) (b^2) l (m^2) n+4 (b^4) l (m^2) n-6 (a^2) (c^2) l (m^2) n-4 (b^2) (c^2) l (m^2) n+4 (c^4) l (m^2) n-(a^4) (m^3) n+3 (a^2) (b^2) (m^3) n-2 (b^4) (m^3) n+2 (a^2) (c^2) (m^3) n+3 (b^2) (c^2) (m^3) n-(c^4) (m^3) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-(a^2) (c^2) (l^2) (n^2)-(b^2) (c^2) (l^2) (n^2)-2 (a^4) l m (n^2)+4 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+2 (a^2) (c^2) l m (n^2)+2 (b^2) (c^2) l m (n^2)-2 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-(a^2) (c^2) (m^2) (n^2)-(b^2) (c^2) (m^2) (n^2)};    (* QG-P7:1st Quasi Nine-point Center *)
QGP8={(m-n) (-(l^2) m+2 l (m^2)+(l^2) n-5 l m n+4 (m^2) n),-(l^2) (m^2)+5 (l^2) m n-4 l (m^2) n-4 (l^2) (n^2)+5 l m (n^2)-(m^2) (n^2),-(l-m) (4 l (m^2)-5 l m n+2 (m^2) n+l (n^2)-m (n^2))};    (* QG-P8:2nd Quasi Centroid *)
QGP9={-(a^4) (l^2) (m^2)+(a^2) (b^2) (l^2) (m^2)+(a^2) (c^2) (l^2) (m^2)+(a^4) l (m^3)-(a^2) (b^2) l (m^3)-2 (a^2) (c^2) l (m^3)-(b^2) (c^2) l (m^3)+(c^4) l (m^3)-2 (a^2) (b^2) (l^2) m n-2 (a^2) (c^2) (l^2) m n-(a^4) l (m^2) n+6 (a^2) (b^2) l (m^2) n-(b^4) l (m^2) n+4 (a^2) (c^2) l (m^2) n+4 (b^2) (c^2) l (m^2) n-3 (c^4) l (m^2) n+(a^4) (m^3) n-4 (a^2) (b^2) (m^3) n+(b^4) (m^3) n-2 (a^2) (c^2) (m^3) n-2 (b^2) (c^2) (m^3) n+(c^4) (m^3) n-(a^4) (l^2) (n^2)+(a^2) (b^2) (l^2) (n^2)+(a^2) (c^2) (l^2) (n^2)+3 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+(b^4) l m (n^2)-3 (a^2) (c^2) l m (n^2)-3 (b^2) (c^2) l m (n^2)+2 (c^4) l m (n^2)-2 (a^4) (m^2) (n^2)+3 (a^2) (b^2) (m^2) (n^2)-(b^4) (m^2) (n^2)+3 (a^2) (c^2) (m^2) (n^2)+2 (b^2) (c^2) (m^2) (n^2)-(c^4) (m^2) (n^2),(a^2) (b^2) (l^2) (m^2)-(b^4) (l^2) (m^2)+(b^2) (c^2) (l^2) (m^2)-(a^2) (b^2) l (m^3)+(b^4) l (m^3)+(b^2) (c^2) l (m^3)+2 (a^4) (l^2) m n-3 (a^2) (b^2) (l^2) m n+3 (b^4) (l^2) m n-3 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+(c^4) (l^2) m n-2 (a^4) l (m^2) n+2 (a^2) (b^2) l (m^2) n-4 (b^4) l (m^2) n+4 (a^2) (c^2) l (m^2) n+2 (b^2) (c^2) l (m^2) n-2 (c^4) l (m^2) n+(a^2) (b^2) (m^3) n+(b^4) (m^3) n-(b^2) (c^2) (m^3) n-(a^4) (l^2) (n^2)+3 (a^2) (b^2) (l^2) (n^2)-2 (b^4) (l^2) (n^2)+2 (a^2) (c^2) (l^2) (n^2)+3 (b^2) (c^2) (l^2) (n^2)-(c^4) (l^2) (n^2)+(a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+3 (b^4) l m (n^2)-3 (a^2) (c^2) l m (n^2)-3 (b^2) (c^2) l m (n^2)+2 (c^4) l m (n^2)+(a^2) (b^2) (m^2) (n^2)-(b^4) (m^2) (n^2)+(b^2) (c^2) (m^2) (n^2),-(a^4) (l^2) (m^2)+2 (a^2) (b^2) (l^2) (m^2)-(b^4) (l^2) (m^2)+3 (a^2) (c^2) (l^2) (m^2)+3 (b^2) (c^2) (l^2) (m^2)-2 (c^4) (l^2) (m^2)+(a^4) l (m^3)-2 (a^2) (b^2) l (m^3)+(b^4) l (m^3)-2 (a^2) (c^2) l (m^3)-4 (b^2) (c^2) l (m^3)+(c^4) l (m^3)+2 (a^4) (l^2) m n-3 (a^2) (b^2) (l^2) m n+(b^4) (l^2) m n-3 (a^2) (c^2) (l^2) m n-4 (b^2) (c^2) (l^2) m n+3 (c^4) (l^2) m n-3 (a^4) l (m^2) n+4 (a^2) (b^2) l (m^2) n-(b^4) l (m^2) n+4 (a^2) (c^2) l (m^2) n+6 (b^2) (c^2) l (m^2) n-(c^4) l (m^2) n+(a^4) (m^3) n-(a^2) (b^2) (m^3) n-2 (a^2) (c^2) (m^3) n-(b^2) (c^2) (m^3) n+(c^4) (m^3) n+(a^2) (c^2) (l^2) (n^2)+(b^2) (c^2) (l^2) (n^2)-(c^4) (l^2) (n^2)-2 (a^2) (c^2) l m (n^2)-2 (b^2) (c^2) l m (n^2)+(a^2) (c^2) (m^2) (n^2)+(b^2) (c^2) (m^2) (n^2)-(c^4) (m^2) (n^2)};    (* QG-P9:2nd Quasi Circumcenter *)
QGP10={(a^4) (l^2) (m^2)-(b^4) (l^2) (m^2)+2 (b^2) (c^2) (l^2) (m^2)-(c^4) (l^2) (m^2)-2 (a^2) (b^2) l (m^3)+2 (b^4) l (m^3)-2 (b^2) (c^2) l (m^3)+2 (a^4) (l^2) m n+2 (b^4) (l^2) m n-4 (b^2) (c^2) (l^2) m n+2 (c^4) (l^2) m n-5 (a^4) l (m^2) n+2 (a^2) (b^2) l (m^2) n-5 (b^4) l (m^2) n+6 (a^2) (c^2) l (m^2) n+6 (b^2) (c^2) l (m^2) n-(c^4) l (m^2) n+2 (a^4) (m^3) n+2 (b^4) (m^3) n-4 (a^2) (c^2) (m^3) n-4 (b^2) (c^2) (m^3) n+2 (c^4) (m^3) n+(a^4) (l^2) (n^2)-(b^4) (l^2) (n^2)+2 (b^2) (c^2) (l^2) (n^2)-(c^4) (l^2) (n^2)-(a^4) l m (n^2)-2 (a^2) (b^2) l m (n^2)+3 (b^4) l m (n^2)-4 (a^2) (c^2) l m (n^2)-4 (b^2) (c^2) l m (n^2)+(c^4) l m (n^2)+2 (a^2) (b^2) (m^2) (n^2)-2 (b^4) (m^2) (n^2)+2 (a^2) (c^2) (m^2) (n^2)+4 (b^2) (c^2) (m^2) (n^2)-2 (c^4) (m^2) (n^2),-(a^4) (l^2) (m^2)+(b^4) (l^2) (m^2)+2 (a^2) (c^2) (l^2) (m^2)-(c^4) (l^2) (m^2)+2 (a^2) (b^2) l (m^3)-2 (b^4) l (m^3)-2 (b^2) (c^2) l (m^3)+(a^4) (l^2) m n-4 (a^2) (b^2) (l^2) m n-(b^4) (l^2) m n-4 (a^2) (c^2) (l^2) m n-2 (b^2) (c^2) (l^2) m n+3 (c^4) (l^2) m n+4 (a^2) (b^2) l (m^2) n+4 (b^4) l (m^2) n+4 (b^2) (c^2) l (m^2) n-2 (a^2) (b^2) (m^3) n-2 (b^4) (m^3) n+2 (b^2) (c^2) (m^3) n-2 (a^4) (l^2) (n^2)+2 (a^2) (b^2) (l^2) (n^2)+4 (a^2) (c^2) (l^2) (n^2)+2 (b^2) (c^2) (l^2) (n^2)-2 (c^4) (l^2) (n^2)+3 (a^4) l m (n^2)-2 (a^2) (b^2) l m (n^2)-(b^4) l m (n^2)-4 (a^2) (c^2) l m (n^2)-4 (b^2) (c^2) l m (n^2)+(c^4) l m (n^2)-(a^4) (m^2) (n^2)+(b^4) (m^2) (n^2)+2 (a^2) (c^2) (m^2) (n^2)-(c^4) (m^2) (n^2),-2 (a^4) (l^2) (m^2)+4 (a^2) (b^2) (l^2) (m^2)-2 (b^4) (l^2) (m^2)+2 (a^2) (c^2) (l^2) (m^2)+2 (b^2) (c^2) (l^2) (m^2)+2 (a^4) l (m^3)-4 (a^2) (b^2) l (m^3)+2 (b^4) l (m^3)-4 (a^2) (c^2) l (m^3)+2 (c^4) l (m^3)+(a^4) (l^2) m n-4 (a^2) (b^2) (l^2) m n+3 (b^4) (l^2) m n-4 (a^2) (c^2) (l^2) m n-2 (b^2) (c^2) (l^2) m n-(c^4) (l^2) m n-(a^4) l (m^2) n+6 (a^2) (b^2) l (m^2) n-5 (b^4) l (m^2) n+6 (a^2) (c^2) l (m^2) n+2 (b^2) (c^2) l (m^2) n-5 (c^4) l (m^2) n-2 (a^2) (b^2) (m^3) n+2 (b^4) (m^3) n-2 (b^2) (c^2) (m^3) n-(a^4) (l^2) (n^2)+2 (a^2) (b^2) (l^2) (n^2)-(b^4) (l^2) (n^2)+(c^4) (l^2) (n^2)+2 (a^4) l m (n^2)-4 (a^2) (b^2) l m (n^2)+2 (b^4) l m (n^2)+2 (c^4) l m (n^2)-(a^4) (m^2) (n^2)+2 (a^2) (b^2) (m^2) (n^2)-(b^4) (m^2) (n^2)+(c^4) (m^2) (n^2)};    (* QG-P10:2nd Quasi Orthocenter *)
QGP11={-(a^2) (b^2) (l^2) (m^2)+(b^4) (l^2) (m^2)-(a^2) (c^2) (l^2) (m^2)-2 (b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-(a^4) l (m^3)+3 (a^2) (b^2) l (m^3)-2 (b^4) l (m^3)+2 (a^2) (c^2) l (m^3)+3 (b^2) (c^2) l (m^3)-(c^4) l (m^3)-2 (a^4) (l^2) m n+2 (a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n+2 (a^2) (c^2) (l^2) m n+4 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n+6 (a^4) l (m^2) n-8 (a^2) (b^2) l (m^2) n+6 (b^4) l (m^2) n-10 (a^2) (c^2) l (m^2) n-10 (b^2) (c^2) l (m^2) n+4 (c^4) l (m^2) n-3 (a^4) (m^3) n+4 (a^2) (b^2) (m^3) n-3 (b^4) (m^3) n+6 (a^2) (c^2) (m^3) n+6 (b^2) (c^2) (m^3) n-3 (c^4) (m^3) n-(a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-(a^2) (c^2) (l^2) (n^2)-2 (b^2) (c^2) (l^2) (n^2)+(c^4) (l^2) (n^2)-2 (a^4) l m (n^2)+6 (a^2) (b^2) l m (n^2)-4 (b^4) l m (n^2)+7 (a^2) (c^2) l m (n^2)+7 (b^2) (c^2) l m (n^2)-3 (c^4) l m (n^2)+2 (a^4) (m^2) (n^2)-5 (a^2) (b^2) (m^2) (n^2)+3 (b^4) (m^2) (n^2)-5 (a^2) (c^2) (m^2) (n^2)-6 (b^2) (c^2) (m^2) (n^2)+3 (c^4) (m^2) (n^2),(a^4) (l^2) (m^2)-(a^2) (b^2) (l^2) (m^2)-2 (a^2) (c^2) (l^2) (m^2)-(b^2) (c^2) (l^2) (m^2)+(c^4) (l^2) (m^2)-(a^2) (b^2) l (m^3)+(b^4) l (m^3)+(b^2) (c^2) l (m^3)-3 (a^4) (l^2) m n+7 (a^2) (b^2) (l^2) m n-2 (b^4) (l^2) m n+7 (a^2) (c^2) (l^2) m n+6 (b^2) (c^2) (l^2) m n-4 (c^4) (l^2) m n+2 (a^4) l (m^2) n-6 (a^2) (b^2) l (m^2) n-4 (a^2) (c^2) l (m^2) n-6 (b^2) (c^2) l (m^2) n+2 (c^4) l (m^2) n+(a^2) (b^2) (m^3) n+(b^4) (m^3) n-(b^2) (c^2) (m^3) n+3 (a^4) (l^2) (n^2)-5 (a^2) (b^2) (l^2) (n^2)+2 (b^4) (l^2) (n^2)-6 (a^2) (c^2) (l^2) (n^2)-5 (b^2) (c^2) (l^2) (n^2)+3 (c^4) (l^2) (n^2)-4 (a^4) l m (n^2)+6 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+7 (a^2) (c^2) l m (n^2)+7 (b^2) (c^2) l m (n^2)-3 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-(a^2) (b^2) (m^2) (n^2)-2 (a^2) (c^2) (m^2) (n^2)-(b^2) (c^2) (m^2) (n^2)+(c^4) (m^2) (n^2),3 (a^4) (l^2) (m^2)-6 (a^2) (b^2) (l^2) (m^2)+3 (b^4) (l^2) (m^2)-5 (a^2) (c^2) (l^2) (m^2)-5 (b^2) (c^2) (l^2) (m^2)+2 (c^4) (l^2) (m^2)-3 (a^4) l (m^3)+6 (a^2) (b^2) l (m^3)-3 (b^4) l (m^3)+6 (a^2) (c^2) l (m^3)+4 (b^2) (c^2) l (m^3)-3 (c^4) l (m^3)-3 (a^4) (l^2) m n+7 (a^2) (b^2) (l^2) m n-4 (b^4) (l^2) m n+7 (a^2) (c^2) (l^2) m n+6 (b^2) (c^2) (l^2) m n-2 (c^4) (l^2) m n+4 (a^4) l (m^2) n-10 (a^2) (b^2) l (m^2) n+6 (b^4) l (m^2) n-10 (a^2) (c^2) l (m^2) n-8 (b^2) (c^2) l (m^2) n+6 (c^4) l (m^2) n-(a^4) (m^3) n+3 (a^2) (b^2) (m^3) n-2 (b^4) (m^3) n+2 (a^2) (c^2) (m^3) n+3 (b^2) (c^2) (m^3) n-(c^4) (m^3) n+(a^4) (l^2) (n^2)-2 (a^2) (b^2) (l^2) (n^2)+(b^4) (l^2) (n^2)-(a^2) (c^2) (l^2) (n^2)-(b^2) (c^2) (l^2) (n^2)-2 (a^4) l m (n^2)+4 (a^2) (b^2) l m (n^2)-2 (b^4) l m (n^2)+2 (a^2) (c^2) l m (n^2)+2 (b^2) (c^2) l m (n^2)-2 (c^4) l m (n^2)+(a^4) (m^2) (n^2)-2 (a^2) (b^2) (m^2) (n^2)+(b^4) (m^2) (n^2)-(a^2) (c^2) (m^2) (n^2)-(b^2) (c^2) (m^2) (n^2)};    (* QG-P11:2nd Quasi Nine-point Center *)
QGP12={2 m-n,-l-n,-l+2 m};     (* QG-P12:Inscribed Harmonic Conic Center *)
QGP13={-m n (m n+l (-3 m+n)),-l n (m n+l (m+n)),-l m (-3 m n+l (m+n))};    (* QG-P13:Circumscribed Harmonic Conic Center *)
QGP14={-l n (-2 l (m^2)+l m n+2 (m^2) n+l (n^2)-m (n^2)),m (l-n) ((l^2) m-(l^2) n-2 l m n-l (n^2)+m (n^2)),l n (-(l^2) m+2 l (m^2)+(l^2) n+l m n-2 (m^2) n)};    (* QG-P3:Center of the M3D Hyperbola *)
QGP15={l (m-n) (l m-2 (m^2)-l n+m n),m ((l^2) m-(l^2) n-l (n^2)+m (n^2)),-(l-m) n (l m-2 (m^2)-l n+m n)};  (* Kirikami Center *)

Quadrilateral Lines

QLL1=NewtonLine={-l m-l n+m n,-l m+l n-m n,l m-l n-m n};
QLL2=SteinerLine={((a^2)-(b^2)-(c^2)) l (m-n),((a^2)-(b^2)+(c^2)) m (l-n),-((a^2)+(b^2)-(c^2)) (l-m) n};
QLL3=PedalLine={l (m-n) (2 (c^2) l m+(a^2) l n-(b^2) l n-(c^2) l n-(a^2) m n+(b^2) m n-(c^2) m n) ((a^2) l m-(b^2) l m-(c^2) l m+2 (b^2) l n-(a^2) m n-(b^2) m n+(c^2) m n),m (l-n) ((a^2) l m-(b^2) l m+(c^2) l m+(a^2) l n+(b^2) l n-(c^2) l n-2 (a^2) m n) (2 (c^2) l m+(a^2) l n-(b^2) l n-(c^2) l n-(a^2) m n+(b^2) m n-(c^2) m n),-(l-m) n ((a^2) l m-(b^2) l m+(c^2) l m+(a^2) l n+(b^2) l n-(c^2) l n-2 (a^2) m n) ((a^2) l m-(b^2) l m-(c^2) l m+2 (b^2) l n-(a^2) m n-(b^2) m n+(c^2) m n)};
QLL4=MorleyLine={-(a^4) (l-m) (l-n) (m-n) (-m n+l (m+n))-l (m-n) ((b^4) (l-m) m (l-n)+(c^4) (l-m) (l-n) n-(b^2) (c^2) (-4 l m n+(l^2) (m+n)+m n (m+n)))+(a^2) ((b^2) ((l^3) m (2 m-n)+(m^2) (n^2) (-2 m+n)+l m n (3 (m^2)+2 m n-2 (n^2))+(l^2) (-2 (m^3)-2 (m^2) n+(n^3)))+(c^2) ((l^3) (m-2 n) n-(m^2) (m-2 n) (n^2)+l m n (2 (m^2)-2 m n-3 (n^2))+(l^2) (-(m^3)+2 m (n^2)+2 (n^3)))),-(a^4) l (l-m) m (l-n) (m-n)-(m-n) ((c^4) (l-m) m (l-n) n+(b^4) (l-m) (l-n) (l (m-n)+m n)+(b^2) (c^2) (-2 (l^2) (n^2)-2 (m^2) (n^2)+(l^3) (-m+n)+l m n (m+3 n)))+(a^2) (-(c^2) m (l-n) ((l^2) n+(m^2) n+l ((m^2)-4 m n+(n^2)))+(b^2) (-(m^2) (n^3)+l m n ((m^2)+2 (n^2))+(l^3) (2 (m^2)-3 m n+2 (n^2))-(l^2) (2 (m^3)-2 (m^2) n+2 m (n^2)+(n^3)))),-(a^4) l (l-m) (l-n) (m-n) n-(m-n) ((b^4) (l-m) m (l-n) n-(c^4) (l-m) (l-n) (l (m-n)-m n)+(b^2) (c^2) (-2 (l^2) (m^2)+(l^3) (m-n)-2 (m^2) (n^2)+l m n (3 m+n)))+(a^2) ((b^2) (l-m) n ((l^2) m+m (n^2)+l ((m^2)-4 m n+(n^2)))+(c^2) (-l+n) ((m^3) n-l m ((m^2)+(n^2))+(l^2) (2 (m^2)-3 m n+2 (n^2))))};
QLL5={-l (m-n) ((b^4) (((l-m))^2) (n^2) (3 l m-l n-m n)-(c^4) (m^2) (((l-n))^2) (l (m-3 n)+m n)+(a^2) (-(b^2) (((l-m))^2) (n^2) (3 l m-l n-m n)+(c^2) (m^2) (((l-n))^2) (l (m-3 n)+m n))-(b^2) (c^2) (-2 (m^3) (n^3)+4 l (m^2) (n^2) (m+n)-5 (l^2) m n ((m^2)+(n^2))+(l^3) ((m^3)+(m^2) n+m (n^2)+(n^3)))),-m (l-n) (-(a^4) (((l-m))^2) (n^2) (3 l m-l n-m n)+(c^2) (-(b^2)+(c^2)) (l^2) (((m-n))^2) (-3 m n+l (m+n))+(a^2) ((b^2) (((l-m))^2) (n^2) (3 l m-l n-m n)+(c^2) (l (m^2) (m-5 n) (n^2)+(m^3) (n^3)+(l^2) m n ((m^2)+4 (n^2))+(l^3) ((m^3)-5 (m^2) n+4 m (n^2)-2 (n^3))))),(l-m) n ((a^4) (m^2) (((l-n))^2) (l (m-3 n)+m n)+(b^2) ((b^2)-(c^2)) (l^2) (((m-n))^2) (-3 m n+l (m+n))+(a^2) (-(c^2) (m^2) (((l-n))^2) (l (m-3 n)+m n)+(b^2) ((m^3) (n^3)+l (m^2) (n^2) (-5 m+n)+(l^2) m n (4 (m^2)+(n^2))+(l^3) (-2 (m^3)+4 (m^2) n-5 m (n^2)+(n^3)))))};  (* NSM Line *)
QLL6={l ((a^2) (m-n) (m n-l (m+n))+(c^2) (-m (m-3 n) n+l ((m^2)-2 m n-(n^2)))+(b^2) (m n (-3 m+n)+l ((m^2)+2 m n-(n^2)))),m ((b^2) (l-n) (l (m-n)+m n)+(c^2) (l (2 m-3 n) n+m (n^2)+(l^2) (-m+n))-(a^2) ((l^2) (m-3 n)-m (n^2)+l n (2 m+n))),n ((c^2) (l-m) (l (m-n)-m n)-(b^2) ((l^2) (m-n)+(m^2) n+l m (-3 m+2 n))+(a^2) (-(m^2) n+(l^2) (-3 m+n)+l m (m+2 n)))};   (* Quasi-OrthoLine *)
QLL7={l ((a^4) (l^4) (m^4)+4 (a^2) (b^2) (l^4) (m^4)+(b^4) (l^4) (m^4)-2 (a^2) (c^2) (l^4) (m^4)-2 (b^2) (c^2) (l^4) (m^4)+(c^4) (l^4) (m^4)-3 (a^2) (b^2) (l^3) (m^5)-3 (b^4) (l^3) (m^5)+3 (b^2) (c^2) (l^3) (m^5)+2 (a^4) (l^4) (m^3) n-4 (a^2) (b^2) (l^4) (m^3) n-2 (b^4) (l^4) (m^3) n+4 (b^2) (c^2) (l^4) (m^3) n-2 (c^4) (l^4) (m^3) n-3 (a^4) (l^3) (m^4) n-3 (a^2) (b^2) (l^3) (m^4) n+6 (b^4) (l^3) (m^4) n+6 (a^2) (c^2) (l^3) (m^4) n-3 (b^2) (c^2) (l^3) (m^4) n-3 (c^4) (l^3) (m^4) n+5 (a^2) (b^2) (l^2) (m^5) n-(b^4) (l^2) (m^5) n-5 (b^2) (c^2) (l^2) (m^5) n-2 (a^2) (b^2) (l^4) (m^2) (n^2)+2 (a^2) (c^2) (l^4) (m^2) (n^2)-3 (a^4) (l^3) (m^3) (n^2)+9 (a^2) (b^2) (l^3) (m^3) (n^2)-3 (a^2) (c^2) (l^3) (m^3) (n^2)-6 (b^2) (c^2) (l^3) (m^3) (n^2)+6 (c^4) (l^3) (m^3) (n^2)+3 (a^4) (l^2) (m^4) (n^2)-6 (a^2) (b^2) (l^2) (m^4) (n^2)-3 (b^4) (l^2) (m^4) (n^2)-6 (a^2) (c^2) (l^2) (m^4) (n^2)+12 (b^2) (c^2) (l^2) (m^4) (n^2)+3 (c^4) (l^2) (m^4) (n^2)-(a^2) (b^2) l (m^5) (n^2)+3 (b^4) l (m^5) (n^2)+(b^2) (c^2) l (m^5) (n^2)-2 (a^4) (l^4) m (n^3)+2 (b^4) (l^4) m (n^3)+4 (a^2) (c^2) (l^4) m (n^3)-4 (b^2) (c^2) (l^4) m (n^3)+2 (c^4) (l^4) m (n^3)+3 (a^4) (l^3) (m^2) (n^3)+3 (a^2) (b^2) (l^3) (m^2) (n^3)-6 (b^4) (l^3) (m^2) (n^3)-9 (a^2) (c^2) (l^3) (m^2) (n^3)+6 (b^2) (c^2) (l^3) (m^2) (n^3)-7 (a^2) (b^2) (l^2) (m^3) (n^3)+7 (b^4) (l^2) (m^3) (n^3)+7 (a^2) (c^2) (l^2) (m^3) (n^3)-7 (c^4) (l^2) (m^3) (n^3)-(a^4) l (m^4) (n^3)+5 (a^2) (b^2) l (m^4) (n^3)-4 (b^4) l (m^4) (n^3)+2 (a^2) (c^2) l (m^4) (n^3)-7 (b^2) (c^2) l (m^4) (n^3)-(c^4) l (m^4) (n^3)-(a^2) (b^2) (m^5) (n^3)+(b^4) (m^5) (n^3)+(b^2) (c^2) (m^5) (n^3)-(a^4) (l^4) (n^4)+2 (a^2) (b^2) (l^4) (n^4)-(b^4) (l^4) (n^4)-4 (a^2) (c^2) (l^4) (n^4)+2 (b^2) (c^2) (l^4) (n^4)-(c^4) (l^4) (n^4)+3 (a^4) (l^3) m (n^4)-6 (a^2) (b^2) (l^3) m (n^4)+3 (b^4) (l^3) m (n^4)+3 (a^2) (c^2) (l^3) m (n^4)+3 (b^2) (c^2) (l^3) m (n^4)-6 (c^4) (l^3) m (n^4)-3 (a^4) (l^2) (m^2) (n^4)+6 (a^2) (b^2) (l^2) (m^2) (n^4)-3 (b^4) (l^2) (m^2) (n^4)+6 (a^2) (c^2) (l^2) (m^2) (n^4)-12 (b^2) (c^2) (l^2) (m^2) (n^4)+3 (c^4) (l^2) (m^2) (n^4)+(a^4) l (m^3) (n^4)-2 (a^2) (b^2) l (m^3) (n^4)+(b^4) l (m^3) (n^4)-5 (a^2) (c^2) l (m^3) (n^4)+7 (b^2) (c^2) l (m^3) (n^4)+4 (c^4) l (m^3) (n^4)+3 (a^2) (c^2) (l^3) (n^5)-3 (b^2) (c^2) (l^3) (n^5)+3 (c^4) (l^3) (n^5)-5 (a^2) (c^2) (l^2) m (n^5)+5 (b^2) (c^2) (l^2) m (n^5)+(c^4) (l^2) m (n^5)+(a^2) (c^2) l (m^2) (n^5)-(b^2) (c^2) l (m^2) (n^5)-3 (c^4) l (m^2) (n^5)+(a^2) (c^2) (m^3) (n^5)-(b^2) (c^2) (m^3) (n^5)-(c^4) (m^3) (n^5)),-m (-3 (a^4) (l^5) (m^3)-3 (a^2) (b^2) (l^5) (m^3)+3 (a^2) (c^2) (l^5) (m^3)+(a^4) (l^4) (m^4)+4 (a^2) (b^2) (l^4) (m^4)+(b^4) (l^4) (m^4)-2 (a^2) (c^2) (l^4) (m^4)-2 (b^2) (c^2) (l^4) (m^4)+(c^4) (l^4) (m^4)-(a^4) (l^5) (m^2) n+5 (a^2) (b^2) (l^5) (m^2) n-5 (a^2) (c^2) (l^5) (m^2) n+6 (a^4) (l^4) (m^3) n-3 (a^2) (b^2) (l^4) (m^3) n-3 (b^4) (l^4) (m^3) n-3 (a^2) (c^2) (l^4) (m^3) n+6 (b^2) (c^2) (l^4) (m^3) n-3 (c^4) (l^4) (m^3) n-2 (a^4) (l^3) (m^4) n-4 (a^2) (b^2) (l^3) (m^4) n+2 (b^4) (l^3) (m^4) n+4 (a^2) (c^2) (l^3) (m^4) n-2 (c^4) (l^3) (m^4) n+3 (a^4) (l^5) m (n^2)-(a^2) (b^2) (l^5) m (n^2)+(a^2) (c^2) (l^5) m (n^2)-3 (a^4) (l^4) (m^2) (n^2)-6 (a^2) (b^2) (l^4) (m^2) (n^2)+3 (b^4) (l^4) (m^2) (n^2)+12 (a^2) (c^2) (l^4) (m^2) (n^2)-6 (b^2) (c^2) (l^4) (m^2) (n^2)+3 (c^4) (l^4) (m^2) (n^2)+9 (a^2) (b^2) (l^3) (m^3) (n^2)-3 (b^4) (l^3) (m^3) (n^2)-6 (a^2) (c^2) (l^3) (m^3) (n^2)-3 (b^2) (c^2) (l^3) (m^3) (n^2)+6 (c^4) (l^3) (m^3) (n^2)-2 (a^2) (b^2) (l^2) (m^4) (n^2)+2 (b^2) (c^2) (l^2) (m^4) (n^2)+(a^4) (l^5) (n^3)-(a^2) (b^2) (l^5) (n^3)+(a^2) (c^2) (l^5) (n^3)-4 (a^4) (l^4) m (n^3)+5 (a^2) (b^2) (l^4) m (n^3)-(b^4) (l^4) m (n^3)-7 (a^2) (c^2) (l^4) m (n^3)+2 (b^2) (c^2) (l^4) m (n^3)-(c^4) (l^4) m (n^3)+7 (a^4) (l^3) (m^2) (n^3)-7 (a^2) (b^2) (l^3) (m^2) (n^3)+7 (b^2) (c^2) (l^3) (m^2) (n^3)-7 (c^4) (l^3) (m^2) (n^3)-6 (a^4) (l^2) (m^3) (n^3)+3 (a^2) (b^2) (l^2) (m^3) (n^3)+3 (b^4) (l^2) (m^3) (n^3)+6 (a^2) (c^2) (l^2) (m^3) (n^3)-9 (b^2) (c^2) (l^2) (m^3) (n^3)+2 (a^4) l (m^4) (n^3)-2 (b^4) l (m^4) (n^3)-4 (a^2) (c^2) l (m^4) (n^3)+4 (b^2) (c^2) l (m^4) (n^3)+2 (c^4) l (m^4) (n^3)+(a^4) (l^3) m (n^4)-2 (a^2) (b^2) (l^3) m (n^4)+(b^4) (l^3) m (n^4)+7 (a^2) (c^2) (l^3) m (n^4)-5 (b^2) (c^2) (l^3) m (n^4)+4 (c^4) (l^3) m (n^4)-3 (a^4) (l^2) (m^2) (n^4)+6 (a^2) (b^2) (l^2) (m^2) (n^4)-3 (b^4) (l^2) (m^2) (n^4)-12 (a^2) (c^2) (l^2) (m^2) (n^4)+6 (b^2) (c^2) (l^2) (m^2) (n^4)+3 (c^4) (l^2) (m^2) (n^4)+3 (a^4) l (m^3) (n^4)-6 (a^2) (b^2) l (m^3) (n^4)+3 (b^4) l (m^3) (n^4)+3 (a^2) (c^2) l (m^3) (n^4)+3 (b^2) (c^2) l (m^3) (n^4)-6 (c^4) l (m^3) (n^4)-(a^4) (m^4) (n^4)+2 (a^2) (b^2) (m^4) (n^4)-(b^4) (m^4) (n^4)+2 (a^2) (c^2) (m^4) (n^4)-4 (b^2) (c^2) (m^4) (n^4)-(c^4) (m^4) (n^4)-(a^2) (c^2) (l^3) (n^5)+(b^2) (c^2) (l^3) (n^5)-(c^4) (l^3) (n^5)-(a^2) (c^2) (l^2) m (n^5)+(b^2) (c^2) (l^2) m (n^5)-3 (c^4) (l^2) m (n^5)+5 (a^2) (c^2) l (m^2) (n^5)-5 (b^2) (c^2) l (m^2) (n^5)+(c^4) l (m^2) (n^5)-3 (a^2) (c^2) (m^3) (n^5)+3 (b^2) (c^2) (m^3) (n^5)+3 (c^4) (m^3) (n^5)),n ((a^4) (l^5) (m^3)+(a^2) (b^2) (l^5) (m^3)-(a^2) (c^2) (l^5) (m^3)-(a^2) (b^2) (l^3) (m^5)-(b^4) (l^3) (m^5)+(b^2) (c^2) (l^3) (m^5)+3 (a^4) (l^5) (m^2) n+(a^2) (b^2) (l^5) (m^2) n-(a^2) (c^2) (l^5) (m^2) n-4 (a^4) (l^4) (m^3) n-7 (a^2) (b^2) (l^4) (m^3) n-(b^4) (l^4) (m^3) n+5 (a^2) (c^2) (l^4) (m^3) n+2 (b^2) (c^2) (l^4) (m^3) n-(c^4) (l^4) (m^3) n+(a^4) (l^3) (m^4) n+7 (a^2) (b^2) (l^3) (m^4) n+4 (b^4) (l^3) (m^4) n-2 (a^2) (c^2) (l^3) (m^4) n-5 (b^2) (c^2) (l^3) (m^4) n+(c^4) (l^3) (m^4) n-(a^2) (b^2) (l^2) (m^5) n-3 (b^4) (l^2) (m^5) n+(b^2) (c^2) (l^2) (m^5) n-(a^4) (l^5) m (n^2)-5 (a^2) (b^2) (l^5) m (n^2)+5 (a^2) (c^2) (l^5) m (n^2)-3 (a^4) (l^4) (m^2) (n^2)+12 (a^2) (b^2) (l^4) (m^2) (n^2)+3 (b^4) (l^4) (m^2) (n^2)-6 (a^2) (c^2) (l^4) (m^2) (n^2)-6 (b^2) (c^2) (l^4) (m^2) (n^2)+3 (c^4) (l^4) (m^2) (n^2)+7 (a^4) (l^3) (m^3) (n^2)-7 (b^4) (l^3) (m^3) (n^2)-7 (a^2) (c^2) (l^3) (m^3) (n^2)+7 (b^2) (c^2) (l^3) (m^3) (n^2)-3 (a^4) (l^2) (m^4) (n^2)-12 (a^2) (b^2) (l^2) (m^4) (n^2)+3 (b^4) (l^2) (m^4) (n^2)+6 (a^2) (c^2) (l^2) (m^4) (n^2)+6 (b^2) (c^2) (l^2) (m^4) (n^2)-3 (c^4) (l^2) (m^4) (n^2)+5 (a^2) (b^2) l (m^5) (n^2)+(b^4) l (m^5) (n^2)-5 (b^2) (c^2) l (m^5) (n^2)-3 (a^4) (l^5) (n^3)+3 (a^2) (b^2) (l^5) (n^3)-3 (a^2) (c^2) (l^5) (n^3)+6 (a^4) (l^4) m (n^3)-3 (a^2) (b^2) (l^4) m (n^3)-3 (b^4) (l^4) m (n^3)-3 (a^2) (c^2) (l^4) m (n^3)+6 (b^2) (c^2) (l^4) m (n^3)-3 (c^4) (l^4) m (n^3)-6 (a^2) (b^2) (l^3) (m^2) (n^3)+6 (b^4) (l^3) (m^2) (n^3)+9 (a^2) (c^2) (l^3) (m^2) (n^3)-3 (b^2) (c^2) (l^3) (m^2) (n^3)-3 (c^4) (l^3) (m^2) (n^3)-6 (a^4) (l^2) (m^3) (n^3)+6 (a^2) (b^2) (l^2) (m^3) (n^3)+3 (a^2) (c^2) (l^2) (m^3) (n^3)-9 (b^2) (c^2) (l^2) (m^3) (n^3)+3 (c^4) (l^2) (m^3) (n^3)+3 (a^4) l (m^4) (n^3)+3 (a^2) (b^2) l (m^4) (n^3)-6 (b^4) l (m^4) (n^3)-6 (a^2) (c^2) l (m^4) (n^3)+3 (b^2) (c^2) l (m^4) (n^3)+3 (c^4) l (m^4) (n^3)-3 (a^2) (b^2) (m^5) (n^3)+3 (b^4) (m^5) (n^3)+3 (b^2) (c^2) (m^5) (n^3)+(a^4) (l^4) (n^4)-2 (a^2) (b^2) (l^4) (n^4)+(b^4) (l^4) (n^4)+4 (a^2) (c^2) (l^4) (n^4)-2 (b^2) (c^2) (l^4) (n^4)+(c^4) (l^4) (n^4)-2 (a^4) (l^3) m (n^4)+4 (a^2) (b^2) (l^3) m (n^4)-2 (b^4) (l^3) m (n^4)-4 (a^2) (c^2) (l^3) m (n^4)+2 (c^4) (l^3) m (n^4)-2 (a^2) (c^2) (l^2) (m^2) (n^4)+2 (b^2) (c^2) (l^2) (m^2) (n^4)+2 (a^4) l (m^3) (n^4)-4 (a^2) (b^2) l (m^3) (n^4)+2 (b^4) l (m^3) (n^4)+4 (b^2) (c^2) l (m^3) (n^4)-2 (c^4) l (m^3) (n^4)-(a^4) (m^4) (n^4)+2 (a^2) (b^2) (m^4) (n^4)-(b^4) (m^4) (n^4)+2 (a^2) (c^2) (m^4) (n^4)-4 (b^2) (c^2) (m^4) (n^4)-(c^4) (m^4) (n^4))};   (* Eulerline DT *)
QLL8={l ((m^3) (n^3) ((m^2)-4 m n+(n^2))-2 (l^4) (((m-n))^2) (3 (m^2)+m n+3 (n^2))+l (m^2) (n^2) ((m^3)+(m^2) n+m (n^2)+(n^3))+(l^3) (((m-n))^2) (3 (m^3)+11 (m^2) n+11 m (n^2)+3 (n^3))+(l^2) m n (-5 (m^4)+4 (m^3) n+4 m (n^3)-5 (n^4))),m (3 (m^3) (n^4) (-2 m+n)+(l^5) (((m-n))^2) (3 m+n)+5 l (m^2) (n^3) (2 (m^2)+m n-(n^2))-(l^4) (((m-n))^2) (6 (m^2)+7 m n+4 (n^2))+(l^2) m (n^2) (-8 (m^3)-8 (m^2) n+4 m (n^2)+(n^3))+(l^3) n (10 (m^4)-8 (m^3) n+m (n^3)+(n^4))),n (3 (m^4) (m-2 n) (n^3)+(l^5) (((m-n))^2) (m+3 n)+5 l (m^3) (n^2) (-(m^2)+m n+2 (n^2))-(l^4) (((m-n))^2) (4 (m^2)+7 m n+6 (n^2))+(l^2) (m^2) n ((m^3)+4 (m^2) n-8 m (n^2)-8 (n^3))+(l^3) m ((m^4)+(m^3) n-8 m (n^3)+10 (n^4)))};(* Centroids Line *)
QLL9={-m n (2 (l^2)-l m-l n+m n),-l n (-l m+2 (m^2)+l n-m n),-l m (l m-l n-m n+2 (n^2))};(* M3D Line *)

QL - Transformations

QLTf1[{u_,v_,w_}]:=Simplificar[{(a^2) m n ((a^2) (l-m) (l-n) v w+(c^2) (l-n) v (l u+m v+m w)+(b^2) (l-m) w (l u+n v+n w)),
(b^2) l n ((b^2) (m-l) (m-n) u w+(c^2) (m-n) u (l u+m v+l w)+(a^2) (m-l) w (n u+m v+n w)),
(c^2) l m ((c^2) (n-l) (n-m) u v+(b^2) (n-m) u (l u+l v+n w)+(a^2) (n-l) v (m u+m v+n w))}]    (* QL-Tf1:Clawson-Schmidt Conjugate *)
QLTf2[{e_,f_,g_}]:={e (g l m+f l n-e m n),f (g l m-f l n+e m n),g (-g l m+f l n+e m n)}  (* QL-Tf2:QL-Line Isoconjugate *)
QLTf3[{x_,y_,z_}]:={-(a^2) m n ((a^4) (l^2)-(a^2) (b^2) (l^2)-(a^2) (c^2) (l^2)-(a^4) l m+(a^2) (b^2) l m+2 (a^2) (c^2) l m+(b^2) (c^2) l m-(c^4) l m-(a^4) l n+2 (a^2) (b^2) l n-(b^4) l n+(a^2) (c^2) l n+(b^2) (c^2) l n+(a^4) m n-2 (a^2) (b^2) m n+(b^4) m n-2 (a^2) (c^2) m n-2 (b^2) (c^2) m n+(c^4) m n) x-(a^2) (b^2) l m n (-(a^2) l+(b^2) l-(c^2) l+(a^2) m-(b^2) m-(c^2) m+2 (c^2) n) y-(a^2) (c^2) l m n (-(a^2) l-(b^2) l+(c^2) l+2 (b^2) m+(a^2) n-(b^2) n-(c^2) n) z,-(a^2) (b^2) l m n (-(a^2) l+(b^2) l-(c^2) l+(a^2) m-(b^2) m-(c^2) m+2 (c^2) n) x-(b^2) l n ((a^2) (b^2) l m-(b^4) l m+(a^2) (c^2) l m+2 (b^2) (c^2) l m-(c^4) l m-(a^2) (b^2) (m^2)+(b^4) (m^2)-(b^2) (c^2) (m^2)+(a^4) l n-2 (a^2) (b^2) l n+(b^4) l n-2 (a^2) (c^2) l n-2 (b^2) (c^2) l n+(c^4) l n-(a^4) m n+2 (a^2) (b^2) m n-(b^4) m n+(a^2) (c^2) m n+(b^2) (c^2) m n) y-(b^2) (c^2) l m n (2 (a^2) l-(a^2) m-(b^2) m+(c^2) m-(a^2) n+(b^2) n-(c^2) n) z,-(a^2) (c^2) l m n (-(a^2) l-(b^2) l+(c^2) l+2 (b^2) m+(a^2) n-(b^2) n-(c^2) n) x-(b^2) (c^2) l m n (2 (a^2) l-(a^2) m-(b^2) m+(c^2) m-(a^2) n+(b^2) n-(c^2) n) y-(c^2) l m ((a^4) l m-2 (a^2) (b^2) l m+(b^4) l m-2 (a^2) (c^2) l m-2 (b^2) (c^2) l m+(c^4) l m+(a^2) (b^2) l n-(b^4) l n+(a^2) (c^2) l n+2 (b^2) (c^2) l n-(c^4) l n-(a^4) m n+(a^2) (b^2) m n+2 (a^2) (c^2) m n+(b^2) (c^2) m n-(c^4) m n-(a^2) (c^2) (n^2)-(b^2) (c^2) (n^2)+(c^4) (n^2)) z}   (* QL-Tf3:CSCe Transformation *)
QLTf4[{x_,y_,z_}]:= {2 (a^2) ((a^2)+(b^2)-(c^2)) ((a^2)-(b^2)+(c^2)) l (m-n) (2 (a^2) l-(a^2) m-(b^2) m+(c^2) m-(a^2) n+(b^2) n-(c^2) n) (x^4)+2 (b^2) ((a^2)+(b^2)-(c^2)) (l-n) ((a^4) l m-(b^4) l m+2 (b^2) (c^2) l m-(c^4) l m-2 (a^2) (b^2) (m^2)+2 (b^4) (m^2)-2 (b^2) (c^2) (m^2)+(a^4) l n-2 (a^2) (b^2) l n+(b^4) l n-2 (a^2) (c^2) l n-2 (b^2) (c^2) l n+(c^4) l n-2 (a^4) m n+4 (a^2) (b^2) m n-2 (b^4) m n+2 (a^2) (c^2) m n+2 (b^2) (c^2) m n) (y^4)+((a^8) (l^2) m+2 (a^6) (b^2) (l^2) m-4 (a^4) (b^4) (l^2) m-2 (a^2) (b^6) (l^2) m+3 (b^8) (l^2) m-2 (a^6) (c^2) (l^2) m+12 (a^4) (b^2) (c^2) (l^2) m+14 (a^2) (b^4) (c^2) (l^2) m-8 (b^6) (c^2) (l^2) m-14 (a^2) (b^2) (c^4) (l^2) m+6 (b^4) (c^4) (l^2) m+2 (a^2) (c^6) (l^2) m-(c^8) (l^2) m-2 (a^6) (b^2) l (m^2)-2 (a^4) (b^4) l (m^2)+10 (a^2) (b^6) l (m^2)-6 (b^8) l (m^2)-2 (a^4) (b^2) (c^2) l (m^2)-20 (a^2) (b^4) (c^2) l (m^2)+6 (b^6) (c^2) l (m^2)+10 (a^2) (b^2) (c^4) l (m^2)+6 (b^4) (c^4) l (m^2)-6 (b^2) (c^6) l (m^2)+(a^8) (l^2) n-4 (a^6) (b^2) (l^2) n-6 (a^4) (b^4) (l^2) n+12 (a^2) (b^6) (l^2) n-3 (b^8) (l^2) n-4 (a^6) (c^2) (l^2) n+8 (a^4) (b^2) (c^2) (l^2) n-4 (a^2) (b^4) (c^2) (l^2) n+8 (b^6) (c^2) (l^2) n+6 (a^4) (c^4) (l^2) n-4 (a^2) (b^2) (c^4) (l^2) n-6 (b^4) (c^4) (l^2) n-4 (a^2) (c^6) (l^2) n+(c^8) (l^2) n-3 (a^8) l m n+4 (a^6) (b^2) l m n+18 (a^4) (b^4) l m n-20 (a^2) (b^6) l m n+(b^8) l m n+8 (a^6) (c^2) l m n-36 (a^4) (b^2) (c^2) l m n-8 (a^2) (b^4) (c^2) l m n+4 (b^6) (c^2) l m n-6 (a^4) (c^4) l m n+28 (a^2) (b^2) (c^4) l m n-10 (b^4) (c^4) l m n+4 (b^2) (c^6) l m n+(c^8) l m n-8 (a^2) (b^6) (m^2) n+8 (b^8) (m^2) n+8 (a^4) (b^2) (c^2) (m^2) n+24 (a^2) (b^4) (c^2) (m^2) n-8 (b^6) (c^2) (m^2) n-16 (a^2) (b^2) (c^4) (m^2) n-8 (b^4) (c^4) (m^2) n+8 (b^2) (c^6) (m^2) n-(a^8) l (n^2)+2 (a^6) (b^2) l (n^2)+4 (a^4) (b^4) l (n^2)-10 (a^2) (b^6) l (n^2)+5 (b^8) l (n^2)+4 (a^6) (c^2) l (n^2)-2 (a^4) (b^2) (c^2) l (n^2)+8 (a^2) (b^4) (c^2) l (n^2)-10 (b^6) (c^2) l (n^2)-6 (a^4) (c^4) l (n^2)-2 (a^2) (b^2) (c^4) l (n^2)+4 (b^4) (c^4) l (n^2)+4 (a^2) (c^6) l (n^2)+2 (b^2) (c^6) l (n^2)-(c^8) l (n^2)+2 (a^8) m (n^2)-2 (a^6) (b^2) m (n^2)-10 (a^4) (b^4) m (n^2)+18 (a^2) (b^6) m (n^2)-8 (b^8) m (n^2)-6 (a^6) (c^2) m (n^2)+12 (a^4) (b^2) (c^2) m (n^2)-14 (a^2) (b^4) (c^2) m (n^2)+8 (b^6) (c^2) m (n^2)+6 (a^4) (c^4) m (n^2)-2 (a^2) (b^2) (c^4) m (n^2)+8 (b^4) (c^4) m (n^2)-2 (a^2) (c^6) m (n^2)-8 (b^2) (c^6) m (n^2)) (y^3) z+(8 (a^6) (c^2) (l^2) m+8 (a^4) (b^2) (c^2) (l^2) m-16 (a^2) (b^4) (c^2) (l^2) m-16 (a^4) (c^4) (l^2) m+8 (a^2) (b^2) (c^4) (l^2) m+8 (a^2) (c^6) (l^2) m+(a^8) l (m^2)-4 (a^6) (b^2) l (m^2)+6 (a^4) (b^4) l (m^2)-4 (a^2) (b^6) l (m^2)+(b^8) l (m^2)-6 (a^6) (c^2) l (m^2)-6 (a^4) (b^2) (c^2) l (m^2)+6 (a^2) (b^4) (c^2) l (m^2)+6 (b^6) (c^2) l (m^2)+12 (a^4) (c^4) l (m^2)+8 (a^2) (b^2) (c^4) l (m^2)-12 (b^4) (c^4) l (m^2)-10 (a^2) (c^6) l (m^2)+2 (b^2) (c^6) l (m^2)+3 (c^8) l (m^2)-8 (a^6) (b^2) (l^2) n+16 (a^4) (b^4) (l^2) n-8 (a^2) (b^6) (l^2) n-8 (a^4) (b^2) (c^2) (l^2) n-8 (a^2) (b^4) (c^2) (l^2) n+16 (a^2) (b^2) (c^4) (l^2) n+14 (a^6) (b^2) l m n-26 (a^4) (b^4) l m n+10 (a^2) (b^6) l m n+2 (b^8) l m n-14 (a^6) (c^2) l m n+50 (a^2) (b^4) (c^2) l m n-4 (b^6) (c^2) l m n+26 (a^4) (c^4) l m n-50 (a^2) (b^2) (c^4) l m n-10 (a^2) (c^6) l m n+4 (b^2) (c^6) l m n-2 (c^8) l m n-2 (a^8) (m^2) n+2 (a^6) (b^2) (m^2) n-2 (a^4) (b^4) (m^2) n+6 (a^2) (b^6) (m^2) n-4 (b^8) (m^2) n+10 (a^6) (c^2) (m^2) n+4 (a^4) (b^2) (c^2) (m^2) n-22 (a^2) (b^4) (c^2) (m^2) n-8 (b^6) (c^2) (m^2) n-18 (a^4) (c^4) (m^2) n+2 (a^2) (b^2) (c^4) (m^2) n+24 (b^4) (c^4) (m^2) n+14 (a^2) (c^6) (m^2) n-8 (b^2) (c^6) (m^2) n-4 (c^8) (m^2) n-(a^8) l (n^2)+6 (a^6) (b^2) l (n^2)-12 (a^4) (b^4) l (n^2)+10 (a^2) (b^6) l (n^2)-3 (b^8) l (n^2)+4 (a^6) (c^2) l (n^2)+6 (a^4) (b^2) (c^2) l (n^2)-8 (a^2) (b^4) (c^2) l (n^2)-2 (b^6) (c^2) l (n^2)-6 (a^4) (c^4) l (n^2)-6 (a^2) (b^2) (c^4) l (n^2)+12 (b^4) (c^4) l (n^2)+4 (a^2) (c^6) l (n^2)-6 (b^2) (c^6) l (n^2)-(c^8) l (n^2)+2 (a^8) m (n^2)-10 (a^6) (b^2) m (n^2)+18 (a^4) (b^4) m (n^2)-14 (a^2) (b^6) m (n^2)+4 (b^8) m (n^2)-2 (a^6) (c^2) m (n^2)-4 (a^4) (b^2) (c^2) m (n^2)-2 (a^2) (b^4) (c^2) m (n^2)+8 (b^6) (c^2) m (n^2)+2 (a^4) (c^4) m (n^2)+22 (a^2) (b^2) (c^4) m (n^2)-24 (b^4) (c^4) m (n^2)-6 (a^2) (c^6) m (n^2)+8 (b^2) (c^6) m (n^2)+4 (c^8) m (n^2)) (y^2) (z^2)+(-(a^8) (l^2) m+4 (a^6) (b^2) (l^2) m-6 (a^4) (b^4) (l^2) m+4 (a^2) (b^6) (l^2) m-(b^8) (l^2) m+4 (a^6) (c^2) (l^2) m-8 (a^4) (b^2) (c^2) (l^2) m+4 (a^2) (b^4) (c^2) (l^2) m+6 (a^4) (c^4) (l^2) m+4 (a^2) (b^2) (c^4) (l^2) m+6 (b^4) (c^4) (l^2) m-12 (a^2) (c^6) (l^2) m-8 (b^2) (c^6) (l^2) m+3 (c^8) (l^2) m+(a^8) l (m^2)-4 (a^6) (b^2) l (m^2)+6 (a^4) (b^4) l (m^2)-4 (a^2) (b^6) l (m^2)+(b^8) l (m^2)-2 (a^6) (c^2) l (m^2)+2 (a^4) (b^2) (c^2) l (m^2)+2 (a^2) (b^4) (c^2) l (m^2)-2 (b^6) (c^2) l (m^2)-4 (a^4) (c^4) l (m^2)-8 (a^2) (b^2) (c^4) l (m^2)-4 (b^4) (c^4) l (m^2)+10 (a^2) (c^6) l (m^2)+10 (b^2) (c^6) l (m^2)-5 (c^8) l (m^2)-(a^8) (l^2) n+2 (a^6) (b^2) (l^2) n-2 (a^2) (b^6) (l^2) n+(b^8) (l^2) n-2 (a^6) (c^2) (l^2) n-12 (a^4) (b^2) (c^2) (l^2) n+14 (a^2) (b^4) (c^2) (l^2) n+4 (a^4) (c^4) (l^2) n-14 (a^2) (b^2) (c^4) (l^2) n-6 (b^4) (c^4) (l^2) n+2 (a^2) (c^6) (l^2) n+8 (b^2) (c^6) (l^2) n-3 (c^8) (l^2) n+3 (a^8) l m n-8 (a^6) (b^2) l m n+6 (a^4) (b^4) l m n-(b^8) l m n-4 (a^6) (c^2) l m n+36 (a^4) (b^2) (c^2) l m n-28 (a^2) (b^4) (c^2) l m n-4 (b^6) (c^2) l m n-18 (a^4) (c^4) l m n+8 (a^2) (b^2) (c^4) l m n+10 (b^4) (c^4) l m n+20 (a^2) (c^6) l m n-4 (b^2) (c^6) l m n-(c^8) l m n-2 (a^8) (m^2) n+6 (a^6) (b^2) (m^2) n-6 (a^4) (b^4) (m^2) n+2 (a^2) (b^6) (m^2) n+2 (a^6) (c^2) (m^2) n-12 (a^4) (b^2) (c^2) (m^2) n+2 (a^2) (b^4) (c^2) (m^2) n+8 (b^6) (c^2) (m^2) n+10 (a^4) (c^4) (m^2) n+14 (a^2) (b^2) (c^4) (m^2) n-8 (b^4) (c^4) (m^2) n-18 (a^2) (c^6) (m^2) n-8 (b^2) (c^6) (m^2) n+8 (c^8) (m^2) n+2 (a^6) (c^2) l (n^2)+2 (a^4) (b^2) (c^2) l (n^2)-10 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)+2 (a^4) (c^4) l (n^2)+20 (a^2) (b^2) (c^4) l (n^2)-6 (b^4) (c^4) l (n^2)-10 (a^2) (c^6) l (n^2)-6 (b^2) (c^6) l (n^2)+6 (c^8) l (n^2)-8 (a^4) (b^2) (c^2) m (n^2)+16 (a^2) (b^4) (c^2) m (n^2)-8 (b^6) (c^2) m (n^2)-24 (a^2) (b^2) (c^4) m (n^2)+8 (b^4) (c^4) m (n^2)+8 (a^2) (c^6) m (n^2)+8 (b^2) (c^6) m (n^2)-8 (c^8) m (n^2)) y (z^3)-2 (c^2) ((a^2)-(b^2)+(c^2)) (l-m) ((a^4) l m-2 (a^2) (b^2) l m+(b^4) l m-2 (a^2) (c^2) l m-2 (b^2) (c^2) l m+(c^4) l m+(a^4) l n-(b^4) l n+2 (b^2) (c^2) l n-(c^4) l n-2 (a^4) m n+2 (a^2) (b^2) m n+4 (a^2) (c^2) m n+2 (b^2) (c^2) m n-2 (c^4) m n-2 (a^2) (c^2) (n^2)-2 (b^2) (c^2) (n^2)+2 (c^4) (n^2)) (z^4)+(x^3) ((-8 (a^8) (l^2) m-12 (a^6) (b^2) (l^2) m+16 (a^4) (b^4) (l^2) m+4 (a^2) (b^6) (l^2) m+4 (a^6) (c^2) (l^2) m-24 (a^4) (b^2) (c^2) (l^2) m-12 (a^2) (b^4) (c^2) (l^2) m+8 (a^4) (c^4) (l^2) m+12 (a^2) (b^2) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m+3 (a^8) l (m^2)+12 (a^6) (b^2) l (m^2)-2 (a^4) (b^4) l (m^2)-12 (a^2) (b^6) l (m^2)-(b^8) l (m^2)-4 (a^6) (c^2) l (m^2)+4 (a^4) (b^2) (c^2) l (m^2)+28 (a^2) (b^4) (c^2) l (m^2)+4 (b^6) (c^2) l (m^2)-2 (a^4) (c^4) l (m^2)-20 (a^2) (b^2) (c^4) l (m^2)-6 (b^4) (c^4) l (m^2)+4 (a^2) (c^6) l (m^2)+4 (b^2) (c^6) l (m^2)-(c^8) l (m^2)+4 (a^8) (l^2) n+12 (a^6) (b^2) (l^2) n-12 (a^4) (b^4) (l^2) n-4 (a^2) (b^6) (l^2) n-4 (a^6) (c^2) (l^2) n+16 (a^4) (b^2) (c^2) (l^2) n+12 (a^2) (b^4) (c^2) (l^2) n-4 (a^4) (c^4) (l^2) n-12 (a^2) (b^2) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n+6 (a^8) l m n-8 (a^6) (b^2) l m n-16 (a^4) (b^4) l m n+16 (a^2) (b^6) l m n+2 (b^8) l m n+8 (a^6) (c^2) l m n+32 (a^4) (b^2) (c^2) l m n-32 (a^2) (b^4) (c^2) l m n-8 (b^6) (c^2) l m n-16 (a^4) (c^4) l m n+16 (a^2) (b^2) (c^4) l m n+12 (b^4) (c^4) l m n-8 (b^2) (c^6) l m n+2 (c^8) l m n-4 (a^6) (b^2) (m^2) n+4 (a^2) (b^6) (m^2) n-4 (a^6) (c^2) (m^2) n-8 (a^4) (b^2) (c^2) (m^2) n-12 (a^2) (b^4) (c^2) (m^2) n+8 (a^4) (c^4) (m^2) n+12 (a^2) (b^2) (c^4) (m^2) n-4 (a^2) (c^6) (m^2) n-(a^8) l (n^2)-4 (a^6) (b^2) l (n^2)+10 (a^4) (b^4) l (n^2)-4 (a^2) (b^6) l (n^2)-(b^8) l (n^2)-4 (a^6) (c^2) l (n^2)-20 (a^4) (b^2) (c^2) l (n^2)+4 (a^2) (b^4) (c^2) l (n^2)+4 (b^6) (c^2) l (n^2)+10 (a^4) (c^4) l (n^2)+4 (a^2) (b^2) (c^4) l (n^2)-6 (b^4) (c^4) l (n^2)-4 (a^2) (c^6) l (n^2)+4 (b^2) (c^6) l (n^2)-(c^8) l (n^2)-4 (a^8) m (n^2)+4 (a^6) (b^2) m (n^2)+4 (a^4) (b^4) m (n^2)-4 (a^2) (b^6) m (n^2)+4 (a^6) (c^2) m (n^2)+12 (a^2) (b^4) (c^2) m (n^2)-4 (a^4) (c^4) m (n^2)-12 (a^2) (b^2) (c^4) m (n^2)+4 (a^2) (c^6) m (n^2)) y+(-4 (a^8) (l^2) m+4 (a^6) (b^2) (l^2) m+4 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m-12 (a^6) (c^2) (l^2) m-16 (a^4) (b^2) (c^2) (l^2) m+12 (a^2) (b^4) (c^2) (l^2) m+12 (a^4) (c^4) (l^2) m-12 (a^2) (b^2) (c^4) (l^2) m+4 (a^2) (c^6) (l^2) m+(a^8) l (m^2)+4 (a^6) (b^2) l (m^2)-10 (a^4) (b^4) l (m^2)+4 (a^2) (b^6) l (m^2)+(b^8) l (m^2)+4 (a^6) (c^2) l (m^2)+20 (a^4) (b^2) (c^2) l (m^2)-4 (a^2) (b^4) (c^2) l (m^2)-4 (b^6) (c^2) l (m^2)-10 (a^4) (c^4) l (m^2)-4 (a^2) (b^2) (c^4) l (m^2)+6 (b^4) (c^4) l (m^2)+4 (a^2) (c^6) l (m^2)-4 (b^2) (c^6) l (m^2)+(c^8) l (m^2)+8 (a^8) (l^2) n-4 (a^6) (b^2) (l^2) n-8 (a^4) (b^4) (l^2) n+4 (a^2) (b^6) (l^2) n+12 (a^6) (c^2) (l^2) n+24 (a^4) (b^2) (c^2) (l^2) n-12 (a^2) (b^4) (c^2) (l^2) n-16 (a^4) (c^4) (l^2) n+12 (a^2) (b^2) (c^4) (l^2) n-4 (a^2) (c^6) (l^2) n-6 (a^8) l m n-8 (a^6) (b^2) l m n+16 (a^4) (b^4) l m n-2 (b^8) l m n+8 (a^6) (c^2) l m n-32 (a^4) (b^2) (c^2) l m n-16 (a^2) (b^4) (c^2) l m n+8 (b^6) (c^2) l m n+16 (a^4) (c^4) l m n+32 (a^2) (b^2) (c^4) l m n-12 (b^4) (c^4) l m n-16 (a^2) (c^6) l m n+8 (b^2) (c^6) l m n-2 (c^8) l m n+4 (a^8) (m^2) n-4 (a^6) (b^2) (m^2) n+4 (a^4) (b^4) (m^2) n-4 (a^2) (b^6) (m^2) n-4 (a^6) (c^2) (m^2) n+12 (a^2) (b^4) (c^2) (m^2) n-4 (a^4) (c^4) (m^2) n-12 (a^2) (b^2) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n-3 (a^8) l (n^2)+4 (a^6) (b^2) l (n^2)+2 (a^4) (b^4) l (n^2)-4 (a^2) (b^6) l (n^2)+(b^8) l (n^2)-12 (a^6) (c^2) l (n^2)-4 (a^4) (b^2) (c^2) l (n^2)+20 (a^2) (b^4) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)+2 (a^4) (c^4) l (n^2)-28 (a^2) (b^2) (c^4) l (n^2)+6 (b^4) (c^4) l (n^2)+12 (a^2) (c^6) l (n^2)-4 (b^2) (c^6) l (n^2)+(c^8) l (n^2)+4 (a^6) (b^2) m (n^2)-8 (a^4) (b^4) m (n^2)+4 (a^2) (b^6) m (n^2)+4 (a^6) (c^2) m (n^2)+8 (a^4) (b^2) (c^2) m (n^2)-12 (a^2) (b^4) (c^2) m (n^2)+12 (a^2) (b^2) (c^4) m (n^2)-4 (a^2) (c^6) m (n^2)) z)+(x^2) ((5 (a^8) (l^2) m+22 (a^6) (b^2) (l^2) m-12 (a^4) (b^4) (l^2) m-14 (a^2) (b^6) (l^2) m-(b^8) (l^2) m-6 (a^6) (c^2) (l^2) m+16 (a^4) (b^2) (c^2) (l^2) m+34 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m-4 (a^4) (c^4) (l^2) m-26 (a^2) (b^2) (c^4) (l^2) m-6 (b^4) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m+4 (b^2) (c^6) (l^2) m-(c^8) (l^2) m-(a^8) l (m^2)-14 (a^6) (b^2) l (m^2)-12 (a^4) (b^4) l (m^2)+22 (a^2) (b^6) l (m^2)+5 (b^8) l (m^2)+2 (a^6) (c^2) l (m^2)+4 (a^4) (b^2) (c^2) l (m^2)-38 (a^2) (b^4) (c^2) l (m^2)-16 (b^6) (c^2) l (m^2)+18 (a^2) (b^2) (c^4) l (m^2)+18 (b^4) (c^4) l (m^2)-2 (a^2) (c^6) l (m^2)-8 (b^2) (c^6) l (m^2)+(c^8) l (m^2)+(a^8) (l^2) n-12 (a^6) (b^2) (l^2) n-2 (a^4) (b^4) (l^2) n+12 (a^2) (b^6) (l^2) n+(b^8) (l^2) n-4 (a^6) (c^2) (l^2) n-4 (a^4) (b^2) (c^2) (l^2) n-28 (a^2) (b^4) (c^2) (l^2) n-4 (b^6) (c^2) (l^2) n+6 (a^4) (c^4) (l^2) n+20 (a^2) (b^2) (c^4) (l^2) n+6 (b^4) (c^4) (l^2) n-4 (a^2) (c^6) (l^2) n-4 (b^2) (c^6) (l^2) n+(c^8) (l^2) n-9 (a^8) l m n-10 (a^6) (b^2) l m n+40 (a^4) (b^4) l m n-14 (a^2) (b^6) l m n-7 (b^8) l m n+10 (a^6) (c^2) l m n-48 (a^4) (b^2) (c^2) l m n+2 (a^2) (b^4) (c^2) l m n+20 (b^6) (c^2) l m n+8 (a^4) (c^4) l m n+22 (a^2) (b^2) (c^4) l m n-18 (b^4) (c^4) l m n-10 (a^2) (c^6) l m n+4 (b^2) (c^6) l m n+(c^8) l m n+6 (a^6) (b^2) (m^2) n+10 (a^4) (b^4) (m^2) n-14 (a^2) (b^6) (m^2) n-2 (b^8) (m^2) n+2 (a^6) (c^2) (m^2) n+12 (a^4) (b^2) (c^2) (m^2) n+34 (a^2) (b^4) (c^2) (m^2) n+8 (b^6) (c^2) (m^2) n-6 (a^4) (c^4) (m^2) n-26 (a^2) (b^2) (c^4) (m^2) n-12 (b^4) (c^4) (m^2) n+6 (a^2) (c^6) (m^2) n+8 (b^2) (c^6) (m^2) n-2 (c^8) (m^2) n-2 (a^8) l (n^2)+4 (a^6) (b^2) l (n^2)-4 (a^2) (b^6) l (n^2)+2 (b^8) l (n^2)+8 (a^6) (c^2) l (n^2)+20 (a^4) (b^2) (c^2) l (n^2)+24 (a^2) (b^4) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)-12 (a^4) (c^4) l (n^2)-28 (a^2) (b^2) (c^4) l (n^2)+8 (a^2) (c^6) l (n^2)+4 (b^2) (c^6) l (n^2)-2 (c^8) l (n^2)+6 (a^8) m (n^2)+4 (a^6) (b^2) m (n^2)-24 (a^4) (b^4) m (n^2)+12 (a^2) (b^6) m (n^2)+2 (b^8) m (n^2)-12 (a^6) (c^2) m (n^2)-28 (a^2) (b^4) (c^2) m (n^2)-8 (b^6) (c^2) m (n^2)+8 (a^4) (c^4) m (n^2)+20 (a^2) (b^2) (c^4) m (n^2)+12 (b^4) (c^4) m (n^2)-4 (a^2) (c^6) m (n^2)-8 (b^2) (c^6) m (n^2)+2 (c^8) m (n^2)) (y^2)+(8 (a^8) (l^2) m-2 (a^6) (b^2) (l^2) m-18 (a^4) (b^4) (l^2) m+10 (a^2) (b^6) (l^2) m+2 (b^8) (l^2) m+18 (a^6) (c^2) (l^2) m+52 (a^4) (b^2) (c^2) (l^2) m-14 (a^2) (b^4) (c^2) (l^2) m-8 (b^6) (c^2) (l^2) m-34 (a^4) (c^4) (l^2) m-2 (a^2) (b^2) (c^4) (l^2) m+12 (b^4) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m-8 (b^2) (c^6) (l^2) m+2 (c^8) (l^2) m-(a^8) l (m^2)-14 (a^6) (b^2) l (m^2)+24 (a^4) (b^4) l (m^2)-2 (a^2) (b^6) l (m^2)-7 (b^8) l (m^2)-10 (a^6) (c^2) l (m^2)-32 (a^4) (b^2) (c^2) l (m^2)-26 (a^2) (b^4) (c^2) l (m^2)+20 (b^6) (c^2) l (m^2)+24 (a^4) (c^4) l (m^2)+42 (a^2) (b^2) (c^4) l (m^2)-18 (b^4) (c^4) l (m^2)-14 (a^2) (c^6) l (m^2)+4 (b^2) (c^6) l (m^2)+(c^8) l (m^2)-8 (a^8) (l^2) n-18 (a^6) (b^2) (l^2) n+34 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n-2 (b^8) (l^2) n+2 (a^6) (c^2) (l^2) n-52 (a^4) (b^2) (c^2) (l^2) n+2 (a^2) (b^4) (c^2) (l^2) n+8 (b^6) (c^2) (l^2) n+18 (a^4) (c^4) (l^2) n+14 (a^2) (b^2) (c^4) (l^2) n-12 (b^4) (c^4) (l^2) n-10 (a^2) (c^6) (l^2) n+8 (b^2) (c^6) (l^2) n-2 (c^8) (l^2) n+44 (a^6) (b^2) l m n-32 (a^4) (b^4) l m n-20 (a^2) (b^6) l m n+8 (b^8) l m n-44 (a^6) (c^2) l m n+92 (a^2) (b^4) (c^2) l m n-16 (b^6) (c^2) l m n+32 (a^4) (c^4) l m n-92 (a^2) (b^2) (c^4) l m n+20 (a^2) (c^6) l m n+16 (b^2) (c^6) l m n-8 (c^8) l m n-6 (a^8) (m^2) n+6 (a^6) (b^2) (m^2) n-14 (a^4) (b^4) (m^2) n+10 (a^2) (b^6) (m^2) n+4 (b^8) (m^2) n+26 (a^6) (c^2) (m^2) n+12 (a^4) (b^2) (c^2) (m^2) n-14 (a^2) (b^4) (c^2) (m^2) n-16 (b^6) (c^2) (m^2) n-30 (a^4) (c^4) (m^2) n-2 (a^2) (b^2) (c^4) (m^2) n+24 (b^4) (c^4) (m^2) n+6 (a^2) (c^6) (m^2) n-16 (b^2) (c^6) (m^2) n+4 (c^8) (m^2) n+(a^8) l (n^2)+10 (a^6) (b^2) l (n^2)-24 (a^4) (b^4) l (n^2)+14 (a^2) (b^6) l (n^2)-(b^8) l (n^2)+14 (a^6) (c^2) l (n^2)+32 (a^4) (b^2) (c^2) l (n^2)-42 (a^2) (b^4) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)-24 (a^4) (c^4) l (n^2)+26 (a^2) (b^2) (c^4) l (n^2)+18 (b^4) (c^4) l (n^2)+2 (a^2) (c^6) l (n^2)-20 (b^2) (c^6) l (n^2)+7 (c^8) l (n^2)+6 (a^8) m (n^2)-26 (a^6) (b^2) m (n^2)+30 (a^4) (b^4) m (n^2)-6 (a^2) (b^6) m (n^2)-4 (b^8) m (n^2)-6 (a^6) (c^2) m (n^2)-12 (a^4) (b^2) (c^2) m (n^2)+2 (a^2) (b^4) (c^2) m (n^2)+16 (b^6) (c^2) m (n^2)+14 (a^4) (c^4) m (n^2)+14 (a^2) (b^2) (c^4) m (n^2)-24 (b^4) (c^4) m (n^2)-10 (a^2) (c^6) m (n^2)+16 (b^2) (c^6) m (n^2)-4 (c^8) m (n^2)) y z+(-(a^8) (l^2) m+4 (a^6) (b^2) (l^2) m-6 (a^4) (b^4) (l^2) m+4 (a^2) (b^6) (l^2) m-(b^8) (l^2) m+12 (a^6) (c^2) (l^2) m+4 (a^4) (b^2) (c^2) (l^2) m-20 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m+2 (a^4) (c^4) (l^2) m+28 (a^2) (b^2) (c^4) (l^2) m-6 (b^4) (c^4) (l^2) m-12 (a^2) (c^6) (l^2) m+4 (b^2) (c^6) (l^2) m-(c^8) (l^2) m+2 (a^8) l (m^2)-8 (a^6) (b^2) l (m^2)+12 (a^4) (b^4) l (m^2)-8 (a^2) (b^6) l (m^2)+2 (b^8) l (m^2)-4 (a^6) (c^2) l (m^2)-20 (a^4) (b^2) (c^2) l (m^2)+28 (a^2) (b^4) (c^2) l (m^2)-4 (b^6) (c^2) l (m^2)-24 (a^2) (b^2) (c^4) l (m^2)+4 (a^2) (c^6) l (m^2)+4 (b^2) (c^6) l (m^2)-2 (c^8) l (m^2)-5 (a^8) (l^2) n+6 (a^6) (b^2) (l^2) n+4 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n+(b^8) (l^2) n-22 (a^6) (c^2) (l^2) n-16 (a^4) (b^2) (c^2) (l^2) n+26 (a^2) (b^4) (c^2) (l^2) n-4 (b^6) (c^2) (l^2) n+12 (a^4) (c^4) (l^2) n-34 (a^2) (b^2) (c^4) (l^2) n+6 (b^4) (c^4) (l^2) n+14 (a^2) (c^6) (l^2) n-4 (b^2) (c^6) (l^2) n+(c^8) (l^2) n+9 (a^8) l m n-10 (a^6) (b^2) l m n-8 (a^4) (b^4) l m n+10 (a^2) (b^6) l m n-(b^8) l m n+10 (a^6) (c^2) l m n+48 (a^4) (b^2) (c^2) l m n-22 (a^2) (b^4) (c^2) l m n-4 (b^6) (c^2) l m n-40 (a^4) (c^4) l m n-2 (a^2) (b^2) (c^4) l m n+18 (b^4) (c^4) l m n+14 (a^2) (c^6) l m n-20 (b^2) (c^6) l m n+7 (c^8) l m n-6 (a^8) (m^2) n+12 (a^6) (b^2) (m^2) n-8 (a^4) (b^4) (m^2) n+4 (a^2) (b^6) (m^2) n-2 (b^8) (m^2) n-4 (a^6) (c^2) (m^2) n-20 (a^2) (b^4) (c^2) (m^2) n+8 (b^6) (c^2) (m^2) n+24 (a^4) (c^4) (m^2) n+28 (a^2) (b^2) (c^4) (m^2) n-12 (b^4) (c^4) (m^2) n-12 (a^2) (c^6) (m^2) n+8 (b^2) (c^6) (m^2) n-2 (c^8) (m^2) n+(a^8) l (n^2)-2 (a^6) (b^2) l (n^2)+2 (a^2) (b^6) l (n^2)-(b^8) l (n^2)+14 (a^6) (c^2) l (n^2)-4 (a^4) (b^2) (c^2) l (n^2)-18 (a^2) (b^4) (c^2) l (n^2)+8 (b^6) (c^2) l (n^2)+12 (a^4) (c^4) l (n^2)+38 (a^2) (b^2) (c^4) l (n^2)-18 (b^4) (c^4) l (n^2)-22 (a^2) (c^6) l (n^2)+16 (b^2) (c^6) l (n^2)-5 (c^8) l (n^2)-2 (a^6) (b^2) m (n^2)+6 (a^4) (b^4) m (n^2)-6 (a^2) (b^6) m (n^2)+2 (b^8) m (n^2)-6 (a^6) (c^2) m (n^2)-12 (a^4) (b^2) (c^2) m (n^2)+26 (a^2) (b^4) (c^2) m (n^2)-8 (b^6) (c^2) m (n^2)-10 (a^4) (c^4) m (n^2)-34 (a^2) (b^2) (c^4) m (n^2)+12 (b^4) (c^4) m (n^2)+14 (a^2) (c^6) m (n^2)-8 (b^2) (c^6) m (n^2)+2 (c^8) m (n^2)) (z^2))+x ((-(a^8) (l^2) m-12 (a^6) (b^2) (l^2) m-2 (a^4) (b^4) (l^2) m+12 (a^2) (b^6) (l^2) m+3 (b^8) (l^2) m+2 (a^6) (c^2) (l^2) m+2 (a^4) (b^2) (c^2) (l^2) m-26 (a^2) (b^4) (c^2) (l^2) m-10 (b^6) (c^2) (l^2) m+16 (a^2) (b^2) (c^4) (l^2) m+12 (b^4) (c^4) (l^2) m-2 (a^2) (c^6) (l^2) m-6 (b^2) (c^6) (l^2) m+(c^8) (l^2) m+4 (a^6) (b^2) l (m^2)+16 (a^4) (b^4) l (m^2)-12 (a^2) (b^6) l (m^2)-8 (b^8) l (m^2)-4 (a^4) (b^2) (c^2) l (m^2)+16 (a^2) (b^4) (c^2) l (m^2)+20 (b^6) (c^2) l (m^2)-4 (a^2) (b^2) (c^4) l (m^2)-16 (b^4) (c^4) l (m^2)+4 (b^2) (c^6) l (m^2)-(a^8) (l^2) n-2 (a^6) (b^2) (l^2) n+12 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n-3 (b^8) (l^2) n+4 (a^6) (c^2) (l^2) n+10 (a^4) (b^2) (c^2) (l^2) n+16 (a^2) (b^4) (c^2) (l^2) n+10 (b^6) (c^2) (l^2) n-6 (a^4) (c^4) (l^2) n-14 (a^2) (b^2) (c^4) (l^2) n-12 (b^4) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n+6 (b^2) (c^6) (l^2) n-(c^8) (l^2) n+3 (a^8) l m n+20 (a^6) (b^2) l m n-26 (a^4) (b^4) l m n-4 (a^2) (b^6) l m n+7 (b^8) l m n-8 (a^6) (c^2) l m n-4 (a^4) (b^2) (c^2) l m n+24 (a^2) (b^4) (c^2) l m n-12 (b^6) (c^2) l m n+6 (a^4) (c^4) l m n-20 (a^2) (b^2) (c^4) l m n+2 (b^4) (c^4) l m n+4 (b^2) (c^6) l m n-(c^8) l m n-2 (a^6) (b^2) (m^2) n-14 (a^4) (b^4) (m^2) n+10 (a^2) (b^6) (m^2) n+6 (b^8) (m^2) n-2 (a^4) (b^2) (c^2) (m^2) n-20 (a^2) (b^4) (c^2) (m^2) n-18 (b^6) (c^2) (m^2) n+10 (a^2) (b^2) (c^4) (m^2) n+18 (b^4) (c^4) (m^2) n-6 (b^2) (c^6) (m^2) n+(a^8) l (n^2)+4 (a^6) (b^2) l (n^2)-10 (a^4) (b^4) l (n^2)+4 (a^2) (b^6) l (n^2)+(b^8) l (n^2)-4 (a^6) (c^2) l (n^2)-16 (a^4) (b^2) (c^2) l (n^2)-20 (a^2) (b^4) (c^2) l (n^2)-8 (b^6) (c^2) l (n^2)+6 (a^4) (c^4) l (n^2)+20 (a^2) (b^2) (c^4) l (n^2)+14 (b^4) (c^4) l (n^2)-4 (a^2) (c^6) l (n^2)-8 (b^2) (c^6) l (n^2)+(c^8) l (n^2)-2 (a^8) m (n^2)-12 (a^6) (b^2) m (n^2)+24 (a^4) (b^4) m (n^2)-4 (a^2) (b^6) m (n^2)-6 (b^8) m (n^2)+6 (a^6) (c^2) m (n^2)+14 (a^4) (b^2) (c^2) m (n^2)+10 (a^2) (b^4) (c^2) m (n^2)+18 (b^6) (c^2) m (n^2)-6 (a^4) (c^4) m (n^2)-8 (a^2) (b^2) (c^4) m (n^2)-18 (b^4) (c^4) m (n^2)+2 (a^2) (c^6) m (n^2)+6 (b^2) (c^6) m (n^2)) (y^3)+(-5 (a^8) (l^2) m-4 (a^6) (b^2) (l^2) m+18 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m-5 (b^8) (l^2) m-2 (a^6) (c^2) (l^2) m-54 (a^4) (b^2) (c^2) (l^2) m-6 (a^2) (b^4) (c^2) (l^2) m+14 (b^6) (c^2) (l^2) m+20 (a^4) (c^4) (l^2) m+24 (a^2) (b^2) (c^4) (l^2) m-12 (b^4) (c^4) (l^2) m-14 (a^2) (c^6) (l^2) m+2 (b^2) (c^6) (l^2) m+(c^8) (l^2) m+12 (a^6) (b^2) l (m^2)-12 (a^4) (b^4) l (m^2)-12 (a^2) (b^6) l (m^2)+12 (b^8) l (m^2)+4 (a^6) (c^2) l (m^2)+20 (a^4) (b^2) (c^2) l (m^2)+44 (a^2) (b^4) (c^2) l (m^2)-20 (b^6) (c^2) l (m^2)-12 (a^4) (c^4) l (m^2)-44 (a^2) (b^2) (c^4) l (m^2)+12 (a^2) (c^6) l (m^2)+12 (b^2) (c^6) l (m^2)-4 (c^8) l (m^2)-(a^8) (l^2) n+26 (a^6) (b^2) (l^2) n-20 (a^4) (b^4) (l^2) n-10 (a^2) (b^6) (l^2) n+5 (b^8) (l^2) n+4 (a^6) (c^2) (l^2) n-6 (a^4) (b^2) (c^2) (l^2) n+24 (a^2) (b^4) (c^2) (l^2) n-14 (b^6) (c^2) (l^2) n-6 (a^4) (c^4) (l^2) n-18 (a^2) (b^2) (c^4) (l^2) n+12 (b^4) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n-2 (b^2) (c^6) (l^2) n-(c^8) (l^2) n+9 (a^8) l m n-40 (a^6) (b^2) l m n-2 (a^4) (b^4) l m n+40 (a^2) (b^6) l m n-7 (b^8) l m n+4 (a^6) (c^2) l m n+108 (a^4) (b^2) (c^2) l m n-76 (a^2) (b^4) (c^2) l m n-4 (b^6) (c^2) l m n-34 (a^4) (c^4) l m n+16 (a^2) (b^2) (c^4) l m n+30 (b^4) (c^4) l m n+20 (a^2) (c^6) l m n-20 (b^2) (c^6) l m n+(c^8) l m n+2 (a^8) (m^2) n-2 (a^6) (b^2) (m^2) n+10 (a^4) (b^4) (m^2) n+2 (a^2) (b^6) (m^2) n-12 (b^8) (m^2) n-12 (a^6) (c^2) (m^2) n-34 (a^4) (b^2) (c^2) (m^2) n-24 (a^2) (b^4) (c^2) (m^2) n+30 (b^6) (c^2) (m^2) n+24 (a^4) (c^4) (m^2) n+42 (a^2) (b^2) (c^4) (m^2) n-18 (b^4) (c^4) (m^2) n-20 (a^2) (c^6) (m^2) n-6 (b^2) (c^6) (m^2) n+6 (c^8) (m^2) n+3 (a^8) l (n^2)-16 (a^6) (b^2) l (n^2)+18 (a^4) (b^4) l (n^2)-5 (b^8) l (n^2)-12 (a^6) (c^2) l (n^2)-8 (a^4) (b^2) (c^2) l (n^2)-4 (a^2) (b^4) (c^2) l (n^2)+24 (b^6) (c^2) l (n^2)+18 (a^4) (c^4) l (n^2)+16 (a^2) (b^2) (c^4) l (n^2)-30 (b^4) (c^4) l (n^2)-12 (a^2) (c^6) l (n^2)+8 (b^2) (c^6) l (n^2)+3 (c^8) l (n^2)-8 (a^8) m (n^2)+24 (a^6) (b^2) m (n^2)-12 (a^4) (b^4) m (n^2)-16 (a^2) (b^6) m (n^2)+12 (b^8) m (n^2)+14 (a^6) (c^2) m (n^2)-26 (a^4) (b^2) (c^2) m (n^2)+42 (a^2) (b^4) (c^2) m (n^2)-30 (b^6) (c^2) m (n^2)-10 (a^4) (c^4) m (n^2)-36 (a^2) (b^2) (c^4) m (n^2)+18 (b^4) (c^4) m (n^2)+10 (a^2) (c^6) m (n^2)+6 (b^2) (c^6) m (n^2)-6 (c^8) m (n^2)) (y^2) z+((a^8) (l^2) m-4 (a^6) (b^2) (l^2) m+6 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m+(b^8) (l^2) m-26 (a^6) (c^2) (l^2) m+6 (a^4) (b^2) (c^2) (l^2) m+18 (a^2) (b^4) (c^2) (l^2) m+2 (b^6) (c^2) (l^2) m+20 (a^4) (c^4) (l^2) m-24 (a^2) (b^2) (c^4) (l^2) m-12 (b^4) (c^4) (l^2) m+10 (a^2) (c^6) (l^2) m+14 (b^2) (c^6) (l^2) m-5 (c^8) (l^2) m-3 (a^8) l (m^2)+12 (a^6) (b^2) l (m^2)-18 (a^4) (b^4) l (m^2)+12 (a^2) (b^6) l (m^2)-3 (b^8) l (m^2)+16 (a^6) (c^2) l (m^2)+8 (a^4) (b^2) (c^2) l (m^2)-16 (a^2) (b^4) (c^2) l (m^2)-8 (b^6) (c^2) l (m^2)-18 (a^4) (c^4) l (m^2)+4 (a^2) (b^2) (c^4) l (m^2)+30 (b^4) (c^4) l (m^2)-24 (b^2) (c^6) l (m^2)+5 (c^8) l (m^2)+5 (a^8) (l^2) n+2 (a^6) (b^2) (l^2) n-20 (a^4) (b^4) (l^2) n+14 (a^2) (b^6) (l^2) n-(b^8) (l^2) n+4 (a^6) (c^2) (l^2) n+54 (a^4) (b^2) (c^2) (l^2) n-24 (a^2) (b^4) (c^2) (l^2) n-2 (b^6) (c^2) (l^2) n-18 (a^4) (c^4) (l^2) n+6 (a^2) (b^2) (c^4) (l^2) n+12 (b^4) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n-14 (b^2) (c^6) (l^2) n+5 (c^8) (l^2) n-9 (a^8) l m n-4 (a^6) (b^2) l m n+34 (a^4) (b^4) l m n-20 (a^2) (b^6) l m n-(b^8) l m n+40 (a^6) (c^2) l m n-108 (a^4) (b^2) (c^2) l m n-16 (a^2) (b^4) (c^2) l m n+20 (b^6) (c^2) l m n+2 (a^4) (c^4) l m n+76 (a^2) (b^2) (c^4) l m n-30 (b^4) (c^4) l m n-40 (a^2) (c^6) l m n+4 (b^2) (c^6) l m n+7 (c^8) l m n+8 (a^8) (m^2) n-14 (a^6) (b^2) (m^2) n+10 (a^4) (b^4) (m^2) n-10 (a^2) (b^6) (m^2) n+6 (b^8) (m^2) n-24 (a^6) (c^2) (m^2) n+26 (a^4) (b^2) (c^2) (m^2) n+36 (a^2) (b^4) (c^2) (m^2) n-6 (b^6) (c^2) (m^2) n+12 (a^4) (c^4) (m^2) n-42 (a^2) (b^2) (c^4) (m^2) n-18 (b^4) (c^4) (m^2) n+16 (a^2) (c^6) (m^2) n+30 (b^2) (c^6) (m^2) n-12 (c^8) (m^2) n-4 (a^6) (b^2) l (n^2)+12 (a^4) (b^4) l (n^2)-12 (a^2) (b^6) l (n^2)+4 (b^8) l (n^2)-12 (a^6) (c^2) l (n^2)-20 (a^4) (b^2) (c^2) l (n^2)+44 (a^2) (b^4) (c^2) l (n^2)-12 (b^6) (c^2) l (n^2)+12 (a^4) (c^4) l (n^2)-44 (a^2) (b^2) (c^4) l (n^2)+12 (a^2) (c^6) l (n^2)+20 (b^2) (c^6) l (n^2)-12 (c^8) l (n^2)-2 (a^8) m (n^2)+12 (a^6) (b^2) m (n^2)-24 (a^4) (b^4) m (n^2)+20 (a^2) (b^6) m (n^2)-6 (b^8) m (n^2)+2 (a^6) (c^2) m (n^2)+34 (a^4) (b^2) (c^2) m (n^2)-42 (a^2) (b^4) (c^2) m (n^2)+6 (b^6) (c^2) m (n^2)-10 (a^4) (c^4) m (n^2)+24 (a^2) (b^2) (c^4) m (n^2)+18 (b^4) (c^4) m (n^2)-2 (a^2) (c^6) m (n^2)-30 (b^2) (c^6) m (n^2)+12 (c^8) m (n^2)) y (z^2)+((a^8) (l^2) m-4 (a^6) (b^2) (l^2) m+6 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m+(b^8) (l^2) m+2 (a^6) (c^2) (l^2) m-10 (a^4) (b^2) (c^2) (l^2) m+14 (a^2) (b^4) (c^2) (l^2) m-6 (b^6) (c^2) (l^2) m-12 (a^4) (c^4) (l^2) m-16 (a^2) (b^2) (c^4) (l^2) m+12 (b^4) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m-10 (b^2) (c^6) (l^2) m+3 (c^8) (l^2) m-(a^8) l (m^2)+4 (a^6) (b^2) l (m^2)-6 (a^4) (b^4) l (m^2)+4 (a^2) (b^6) l (m^2)-(b^8) l (m^2)-4 (a^6) (c^2) l (m^2)+16 (a^4) (b^2) (c^2) l (m^2)-20 (a^2) (b^4) (c^2) l (m^2)+8 (b^6) (c^2) l (m^2)+10 (a^4) (c^4) l (m^2)+20 (a^2) (b^2) (c^4) l (m^2)-14 (b^4) (c^4) l (m^2)-4 (a^2) (c^6) l (m^2)+8 (b^2) (c^6) l (m^2)-(c^8) l (m^2)+(a^8) (l^2) n-2 (a^6) (b^2) (l^2) n+2 (a^2) (b^6) (l^2) n-(b^8) (l^2) n+12 (a^6) (c^2) (l^2) n-2 (a^4) (b^2) (c^2) (l^2) n-16 (a^2) (b^4) (c^2) (l^2) n+6 (b^6) (c^2) (l^2) n+2 (a^4) (c^4) (l^2) n+26 (a^2) (b^2) (c^4) (l^2) n-12 (b^4) (c^4) (l^2) n-12 (a^2) (c^6) (l^2) n+10 (b^2) (c^6) (l^2) n-3 (c^8) (l^2) n-3 (a^8) l m n+8 (a^6) (b^2) l m n-6 (a^4) (b^4) l m n+(b^8) l m n-20 (a^6) (c^2) l m n+4 (a^4) (b^2) (c^2) l m n+20 (a^2) (b^4) (c^2) l m n-4 (b^6) (c^2) l m n+26 (a^4) (c^4) l m n-24 (a^2) (b^2) (c^4) l m n-2 (b^4) (c^4) l m n+4 (a^2) (c^6) l m n+12 (b^2) (c^6) l m n-7 (c^8) l m n+2 (a^8) (m^2) n-6 (a^6) (b^2) (m^2) n+6 (a^4) (b^4) (m^2) n-2 (a^2) (b^6) (m^2) n+12 (a^6) (c^2) (m^2) n-14 (a^4) (b^2) (c^2) (m^2) n+8 (a^2) (b^4) (c^2) (m^2) n-6 (b^6) (c^2) (m^2) n-24 (a^4) (c^4) (m^2) n-10 (a^2) (b^2) (c^4) (m^2) n+18 (b^4) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n-18 (b^2) (c^6) (m^2) n+6 (c^8) (m^2) n-4 (a^6) (c^2) l (n^2)+4 (a^4) (b^2) (c^2) l (n^2)+4 (a^2) (b^4) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)-16 (a^4) (c^4) l (n^2)-16 (a^2) (b^2) (c^4) l (n^2)+16 (b^4) (c^4) l (n^2)+12 (a^2) (c^6) l (n^2)-20 (b^2) (c^6) l (n^2)+8 (c^8) l (n^2)+2 (a^6) (c^2) m (n^2)+2 (a^4) (b^2) (c^2) m (n^2)-10 (a^2) (b^4) (c^2) m (n^2)+6 (b^6) (c^2) m (n^2)+14 (a^4) (c^4) m (n^2)+20 (a^2) (b^2) (c^4) m (n^2)-18 (b^4) (c^4) m (n^2)-10 (a^2) (c^6) m (n^2)+18 (b^2) (c^6) m (n^2)-6 (c^8) m (n^2)) (z^3)),-2 (a^2) ((a^2)+(b^2)-(c^2)) (m-n) (2 (a^4) (l^2)-2 (a^2) (b^2) (l^2)-2 (a^2) (c^2) (l^2)-(a^4) l m+(b^4) l m+2 (a^2) (c^2) l m-(c^4) l m-2 (a^4) l n+4 (a^2) (b^2) l n-2 (b^4) l n+2 (a^2) (c^2) l n+2 (b^2) (c^2) l n+(a^4) m n-2 (a^2) (b^2) m n+(b^4) m n-2 (a^2) (c^2) m n-2 (b^2) (c^2) m n+(c^4) m n) (x^4)-2 (b^2) ((a^2)-(b^2)-(c^2)) ((a^2)+(b^2)-(c^2)) m (l-n) ((a^2) l+(b^2) l-(c^2) l-2 (b^2) m-(a^2) n+(b^2) n+(c^2) n) (y^4)+(-(a^8) (l^2) m-4 (a^6) (b^2) (l^2) m+10 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m-(b^8) (l^2) m+4 (a^6) (c^2) (l^2) m+4 (a^4) (b^2) (c^2) (l^2) m-20 (a^2) (b^4) (c^2) (l^2) m-4 (b^6) (c^2) (l^2) m-6 (a^4) (c^4) (l^2) m+4 (a^2) (b^2) (c^4) (l^2) m+10 (b^4) (c^4) (l^2) m+4 (a^2) (c^6) (l^2) m-4 (b^2) (c^6) (l^2) m-(c^8) (l^2) m+4 (a^6) (b^2) l (m^2)-4 (a^4) (b^4) l (m^2)-4 (a^2) (b^6) l (m^2)+4 (b^8) l (m^2)-12 (a^4) (b^2) (c^2) l (m^2)+16 (a^2) (b^4) (c^2) l (m^2)+12 (b^6) (c^2) l (m^2)+12 (a^2) (b^2) (c^4) l (m^2)-12 (b^4) (c^4) l (m^2)-4 (b^2) (c^6) l (m^2)+4 (a^6) (b^2) (l^2) n-4 (a^4) (b^4) (l^2) n+4 (a^2) (b^6) (l^2) n-4 (b^8) (l^2) n-12 (a^4) (b^2) (c^2) (l^2) n+4 (b^6) (c^2) (l^2) n+12 (a^2) (b^2) (c^4) (l^2) n+4 (b^4) (c^4) (l^2) n-4 (b^2) (c^6) (l^2) n+2 (a^8) l m n-16 (a^4) (b^4) l m n+8 (a^2) (b^6) l m n+6 (b^8) l m n-8 (a^6) (c^2) l m n+16 (a^4) (b^2) (c^2) l m n+32 (a^2) (b^4) (c^2) l m n-8 (b^6) (c^2) l m n+12 (a^4) (c^4) l m n-32 (a^2) (b^2) (c^4) l m n-16 (b^4) (c^4) l m n-8 (a^2) (c^6) l m n+16 (b^2) (c^6) l m n+2 (c^8) l m n-4 (a^6) (b^2) (m^2) n+8 (a^4) (b^4) (m^2) n+4 (a^2) (b^6) (m^2) n-8 (b^8) (m^2) n+12 (a^4) (b^2) (c^2) (m^2) n-24 (a^2) (b^4) (c^2) (m^2) n-12 (b^6) (c^2) (m^2) n-12 (a^2) (b^2) (c^4) (m^2) n+16 (b^4) (c^4) (m^2) n+4 (b^2) (c^6) (m^2) n-4 (a^6) (b^2) l (n^2)+8 (a^4) (b^4) l (n^2)-4 (a^2) (b^6) l (n^2)+12 (a^4) (b^2) (c^2) l (n^2)-8 (a^2) (b^4) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)-12 (a^2) (b^2) (c^4) l (n^2)+4 (b^2) (c^6) l (n^2)-(a^8) m (n^2)+4 (a^6) (b^2) m (n^2)-2 (a^4) (b^4) m (n^2)-4 (a^2) (b^6) m (n^2)+3 (b^8) m (n^2)+4 (a^6) (c^2) m (n^2)-20 (a^4) (b^2) (c^2) m (n^2)+4 (a^2) (b^4) (c^2) m (n^2)+12 (b^6) (c^2) m (n^2)-6 (a^4) (c^4) m (n^2)+28 (a^2) (b^2) (c^4) m (n^2)-2 (b^4) (c^4) m (n^2)+4 (a^2) (c^6) m (n^2)-12 (b^2) (c^6) m (n^2)-(c^8) m (n^2)) (y^3) z+(-2 (a^8) (l^2) m+8 (a^6) (b^2) (l^2) m-12 (a^4) (b^4) (l^2) m+8 (a^2) (b^6) (l^2) m-2 (b^8) (l^2) m+4 (a^6) (c^2) (l^2) m-28 (a^4) (b^2) (c^2) (l^2) m+20 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m+24 (a^2) (b^2) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m-4 (b^2) (c^6) (l^2) m+2 (c^8) (l^2) m+(a^8) l (m^2)-4 (a^6) (b^2) l (m^2)+6 (a^4) (b^4) l (m^2)-4 (a^2) (b^6) l (m^2)+(b^8) l (m^2)-4 (a^6) (c^2) l (m^2)+20 (a^4) (b^2) (c^2) l (m^2)-4 (a^2) (b^4) (c^2) l (m^2)-12 (b^6) (c^2) l (m^2)+6 (a^4) (c^4) l (m^2)-28 (a^2) (b^2) (c^4) l (m^2)-2 (b^4) (c^4) l (m^2)-4 (a^2) (c^6) l (m^2)+12 (b^2) (c^6) l (m^2)+(c^8) l (m^2)+2 (a^8) (l^2) n-4 (a^6) (b^2) (l^2) n+8 (a^4) (b^4) (l^2) n-12 (a^2) (b^6) (l^2) n+6 (b^8) (l^2) n-8 (a^6) (c^2) (l^2) n+20 (a^4) (b^2) (c^2) (l^2) n+4 (b^6) (c^2) (l^2) n+12 (a^4) (c^4) (l^2) n-28 (a^2) (b^2) (c^4) (l^2) n-24 (b^4) (c^4) (l^2) n-8 (a^2) (c^6) (l^2) n+12 (b^2) (c^6) (l^2) n+2 (c^8) (l^2) n+(a^8) l m n-10 (a^6) (b^2) l m n+8 (a^4) (b^4) l m n+10 (a^2) (b^6) l m n-9 (b^8) l m n+4 (a^6) (c^2) l m n+22 (a^4) (b^2) (c^2) l m n-48 (a^2) (b^4) (c^2) l m n-10 (b^6) (c^2) l m n-18 (a^4) (c^4) l m n+2 (a^2) (b^2) (c^4) l m n+40 (b^4) (c^4) l m n+20 (a^2) (c^6) l m n-14 (b^2) (c^6) l m n-7 (c^8) l m n-(a^8) (m^2) n+6 (a^6) (b^2) (m^2) n-4 (a^4) (b^4) (m^2) n-6 (a^2) (b^6) (m^2) n+5 (b^8) (m^2) n+4 (a^6) (c^2) (m^2) n-26 (a^4) (b^2) (c^2) (m^2) n+16 (a^2) (b^4) (c^2) (m^2) n+22 (b^6) (c^2) (m^2) n-6 (a^4) (c^4) (m^2) n+34 (a^2) (b^2) (c^4) (m^2) n-12 (b^4) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n-14 (b^2) (c^6) (m^2) n-(c^8) (m^2) n-2 (a^8) l (n^2)+6 (a^6) (b^2) l (n^2)-6 (a^4) (b^4) l (n^2)+2 (a^2) (b^6) l (n^2)+8 (a^6) (c^2) l (n^2)-26 (a^4) (b^2) (c^2) l (n^2)+12 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)-12 (a^4) (c^4) l (n^2)+34 (a^2) (b^2) (c^4) l (n^2)+10 (b^4) (c^4) l (n^2)+8 (a^2) (c^6) l (n^2)-14 (b^2) (c^6) l (n^2)-2 (c^8) l (n^2)+(a^8) m (n^2)-2 (a^6) (b^2) m (n^2)+2 (a^2) (b^6) m (n^2)-(b^8) m (n^2)-8 (a^6) (c^2) m (n^2)+18 (a^4) (b^2) (c^2) m (n^2)+4 (a^2) (b^4) (c^2) m (n^2)-14 (b^6) (c^2) m (n^2)+18 (a^4) (c^4) m (n^2)-38 (a^2) (b^2) (c^4) m (n^2)-12 (b^4) (c^4) m (n^2)-16 (a^2) (c^6) m (n^2)+22 (b^2) (c^6) m (n^2)+5 (c^8) m (n^2)) (y^2) (z^2)+((a^8) (l^2) m-4 (a^6) (b^2) (l^2) m+6 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m+(b^8) (l^2) m-8 (a^6) (c^2) (l^2) m+20 (a^4) (b^2) (c^2) (l^2) m-16 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m+14 (a^4) (c^4) (l^2) m-20 (a^2) (b^2) (c^4) (l^2) m-10 (b^4) (c^4) (l^2) m-8 (a^2) (c^6) (l^2) m+4 (b^2) (c^6) (l^2) m+(c^8) (l^2) m-(a^8) l (m^2)+4 (a^6) (b^2) l (m^2)-6 (a^4) (b^4) l (m^2)+4 (a^2) (b^6) l (m^2)-(b^8) l (m^2)+6 (a^6) (c^2) l (m^2)-14 (a^4) (b^2) (c^2) l (m^2)+10 (a^2) (b^4) (c^2) l (m^2)-2 (b^6) (c^2) l (m^2)-12 (a^4) (c^4) l (m^2)+16 (a^2) (b^2) (c^4) l (m^2)+12 (b^4) (c^4) l (m^2)+10 (a^2) (c^6) l (m^2)-6 (b^2) (c^6) l (m^2)-3 (c^8) l (m^2)+2 (a^6) (b^2) (l^2) n-6 (a^4) (b^4) (l^2) n+6 (a^2) (b^6) (l^2) n-2 (b^8) (l^2) n+6 (a^6) (c^2) (l^2) n-8 (a^4) (b^2) (c^2) (l^2) n+14 (a^2) (b^4) (c^2) (l^2) n-12 (b^6) (c^2) (l^2) n-18 (a^4) (c^4) (l^2) n+10 (a^2) (b^2) (c^4) (l^2) n+24 (b^4) (c^4) (l^2) n+18 (a^2) (c^6) (l^2) n-4 (b^2) (c^6) (l^2) n-6 (c^8) (l^2) n-(a^8) l m n+6 (a^4) (b^4) l m n-8 (a^2) (b^6) l m n+3 (b^8) l m n+4 (a^6) (c^2) l m n-20 (a^4) (b^2) (c^2) l m n-4 (a^2) (b^4) (c^2) l m n+20 (b^6) (c^2) l m n+2 (a^4) (c^4) l m n+24 (a^2) (b^2) (c^4) l m n-26 (b^4) (c^4) l m n-12 (a^2) (c^6) l m n-4 (b^2) (c^6) l m n+7 (c^8) l m n+(a^8) (m^2) n-2 (a^6) (b^2) (m^2) n+2 (a^2) (b^6) (m^2) n-(b^8) (m^2) n-6 (a^6) (c^2) (m^2) n+16 (a^4) (b^2) (c^2) (m^2) n+2 (a^2) (b^4) (c^2) (m^2) n-12 (b^6) (c^2) (m^2) n+12 (a^4) (c^4) (m^2) n-26 (a^2) (b^2) (c^4) (m^2) n-2 (b^4) (c^4) (m^2) n-10 (a^2) (c^6) (m^2) n+12 (b^2) (c^6) (m^2) n+3 (c^8) (m^2) n-6 (a^6) (c^2) l (n^2)+10 (a^4) (b^2) (c^2) l (n^2)-2 (a^2) (b^4) (c^2) l (n^2)-2 (b^6) (c^2) l (n^2)+18 (a^4) (c^4) l (n^2)-20 (a^2) (b^2) (c^4) l (n^2)-14 (b^4) (c^4) l (n^2)-18 (a^2) (c^6) l (n^2)+10 (b^2) (c^6) l (n^2)+6 (c^8) l (n^2)+4 (a^6) (c^2) m (n^2)-4 (a^4) (b^2) (c^2) m (n^2)-4 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)-16 (a^4) (c^4) m (n^2)+16 (a^2) (b^2) (c^4) m (n^2)+16 (b^4) (c^4) m (n^2)+20 (a^2) (c^6) m (n^2)-12 (b^2) (c^6) m (n^2)-8 (c^8) m (n^2)) y (z^3)+2 (c^2) ((a^2)-(b^2)-(c^2)) (l-m) ((a^4) l m-2 (a^2) (b^2) l m+(b^4) l m-2 (a^2) (c^2) l m-2 (b^2) (c^2) l m+(c^4) l m+2 (a^2) (b^2) l n-2 (b^4) l n+2 (a^2) (c^2) l n+4 (b^2) (c^2) l n-2 (c^4) l n-(a^4) m n+(b^4) m n+2 (a^2) (c^2) m n-(c^4) m n-2 (a^2) (c^2) (n^2)-2 (b^2) (c^2) (n^2)+2 (c^4) (n^2)) (z^4)+(x^3) ((8 (a^8) (l^2) m+12 (a^6) (b^2) (l^2) m-16 (a^4) (b^4) (l^2) m-4 (a^2) (b^6) (l^2) m-20 (a^6) (c^2) (l^2) m-16 (a^4) (b^2) (c^2) (l^2) m+4 (a^2) (b^4) (c^2) (l^2) m+16 (a^4) (c^4) (l^2) m+4 (a^2) (b^2) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m-3 (a^8) l (m^2)-12 (a^6) (b^2) l (m^2)+2 (a^4) (b^4) l (m^2)+12 (a^2) (b^6) l (m^2)+(b^8) l (m^2)+10 (a^6) (c^2) l (m^2)+26 (a^4) (b^2) (c^2) l (m^2)-2 (a^2) (b^4) (c^2) l (m^2)-2 (b^6) (c^2) l (m^2)-12 (a^4) (c^4) l (m^2)-16 (a^2) (b^2) (c^4) l (m^2)+6 (a^2) (c^6) l (m^2)+2 (b^2) (c^6) l (m^2)-(c^8) l (m^2)-6 (a^8) (l^2) n-10 (a^6) (b^2) (l^2) n+14 (a^4) (b^4) (l^2) n+2 (a^2) (b^6) (l^2) n+18 (a^6) (c^2) (l^2) n+20 (a^4) (b^2) (c^2) (l^2) n+2 (a^2) (b^4) (c^2) (l^2) n-18 (a^4) (c^4) (l^2) n-10 (a^2) (b^2) (c^4) (l^2) n+6 (a^2) (c^6) (l^2) n-7 (a^8) l m n+4 (a^6) (b^2) l m n+26 (a^4) (b^4) l m n-20 (a^2) (b^6) l m n-3 (b^8) l m n+12 (a^6) (c^2) l m n-24 (a^4) (b^2) (c^2) l m n+4 (a^2) (b^4) (c^2) l m n+8 (b^6) (c^2) l m n-2 (a^4) (c^4) l m n+20 (a^2) (b^2) (c^4) l m n-6 (b^4) (c^4) l m n-4 (a^2) (c^6) l m n+(c^8) l m n+3 (a^8) (m^2) n+6 (a^6) (b^2) (m^2) n-12 (a^4) (b^4) (m^2) n+2 (a^2) (b^6) (m^2) n+(b^8) (m^2) n-10 (a^6) (c^2) (m^2) n-16 (a^4) (b^2) (c^2) (m^2) n-10 (a^2) (b^4) (c^2) (m^2) n-4 (b^6) (c^2) (m^2) n+12 (a^4) (c^4) (m^2) n+14 (a^2) (b^2) (c^4) (m^2) n+6 (b^4) (c^4) (m^2) n-6 (a^2) (c^6) (m^2) n-4 (b^2) (c^6) (m^2) n+(c^8) (m^2) n+6 (a^8) l (n^2)+4 (a^6) (b^2) l (n^2)-24 (a^4) (b^4) l (n^2)+12 (a^2) (b^6) l (n^2)+2 (b^8) l (n^2)-18 (a^6) (c^2) l (n^2)-10 (a^4) (b^2) (c^2) l (n^2)-14 (a^2) (b^4) (c^2) l (n^2)-6 (b^6) (c^2) l (n^2)+18 (a^4) (c^4) l (n^2)+8 (a^2) (b^2) (c^4) l (n^2)+6 (b^4) (c^4) l (n^2)-6 (a^2) (c^6) l (n^2)-2 (b^2) (c^6) l (n^2)-(a^8) m (n^2)-4 (a^6) (b^2) m (n^2)+10 (a^4) (b^4) m (n^2)-4 (a^2) (b^6) m (n^2)-(b^8) m (n^2)+8 (a^6) (c^2) m (n^2)+20 (a^4) (b^2) (c^2) m (n^2)+16 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)-14 (a^4) (c^4) m (n^2)-20 (a^2) (b^2) (c^4) m (n^2)-6 (b^4) (c^4) m (n^2)+8 (a^2) (c^6) m (n^2)+4 (b^2) (c^6) m (n^2)-(c^8) m (n^2)) y+(6 (a^8) (l^2) m-10 (a^6) (b^2) (l^2) m+2 (a^4) (b^4) (l^2) m+2 (a^2) (b^6) (l^2) m-6 (a^6) (c^2) (l^2) m+20 (a^4) (b^2) (c^2) (l^2) m+2 (a^2) (b^4) (c^2) (l^2) m-6 (a^4) (c^4) (l^2) m-10 (a^2) (b^2) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m-3 (a^8) l (m^2)+2 (a^6) (b^2) l (m^2)+4 (a^4) (b^4) l (m^2)-2 (a^2) (b^6) l (m^2)-(b^8) l (m^2)+8 (a^6) (c^2) l (m^2)-14 (a^4) (b^2) (c^2) l (m^2)-12 (a^2) (b^4) (c^2) l (m^2)+2 (b^6) (c^2) l (m^2)-6 (a^4) (c^4) l (m^2)+14 (a^2) (b^2) (c^4) l (m^2)-2 (b^2) (c^6) l (m^2)+(c^8) l (m^2)-8 (a^8) (l^2) n+8 (a^6) (b^2) (l^2) n+8 (a^6) (c^2) (l^2) n-24 (a^4) (b^2) (c^2) (l^2) n-8 (a^2) (b^4) (c^2) (l^2) n+8 (a^4) (c^4) (l^2) n+16 (a^2) (b^2) (c^4) (l^2) n-8 (a^2) (c^6) (l^2) n-(a^8) l m n+20 (a^6) (b^2) l m n-18 (a^4) (b^4) l m n-4 (a^2) (b^6) l m n+3 (b^8) l m n-4 (a^6) (c^2) l m n+8 (a^4) (b^2) (c^2) l m n+36 (a^2) (b^4) (c^2) l m n-8 (b^6) (c^2) l m n+10 (a^4) (c^4) l m n-28 (a^2) (b^2) (c^4) l m n+6 (b^4) (c^4) l m n-4 (a^2) (c^6) l m n-(c^8) l m n+3 (a^8) (m^2) n-12 (a^6) (b^2) (m^2) n+6 (a^4) (b^4) (m^2) n+4 (a^2) (b^6) (m^2) n-(b^8) (m^2) n-8 (a^6) (c^2) (m^2) n+4 (a^4) (b^2) (c^2) (m^2) n-8 (a^2) (b^4) (c^2) (m^2) n+4 (b^6) (c^2) (m^2) n+6 (a^4) (c^4) (m^2) n+4 (a^2) (b^2) (c^4) (m^2) n-6 (b^4) (c^4) (m^2) n+4 (b^2) (c^6) (m^2) n-(c^8) (m^2) n+8 (a^8) l (n^2)-18 (a^6) (b^2) l (n^2)+10 (a^4) (b^4) l (n^2)+2 (a^2) (b^6) l (n^2)-2 (b^8) l (n^2)-8 (a^6) (c^2) l (n^2)+14 (a^4) (b^2) (c^2) l (n^2)-12 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)-8 (a^4) (c^4) l (n^2)+2 (a^2) (b^2) (c^4) l (n^2)-6 (b^4) (c^4) l (n^2)+8 (a^2) (c^6) l (n^2)+2 (b^2) (c^6) l (n^2)-5 (a^8) m (n^2)+10 (a^6) (b^2) m (n^2)-4 (a^4) (b^4) m (n^2)-2 (a^2) (b^6) m (n^2)+(b^8) m (n^2)+10 (a^6) (c^2) m (n^2)-8 (a^4) (b^2) (c^2) m (n^2)+2 (a^2) (b^4) (c^2) m (n^2)-4 (b^6) (c^2) m (n^2)-4 (a^4) (c^4) m (n^2)+2 (a^2) (b^2) (c^4) m (n^2)+6 (b^4) (c^4) m (n^2)-2 (a^2) (c^6) m (n^2)-4 (b^2) (c^6) m (n^2)+(c^8) m (n^2)) z)+(x^2) ((-5 (a^8) (l^2) m-22 (a^6) (b^2) (l^2) m+12 (a^4) (b^4) (l^2) m+14 (a^2) (b^6) (l^2) m+(b^8) (l^2) m+16 (a^6) (c^2) (l^2) m+38 (a^4) (b^2) (c^2) (l^2) m-4 (a^2) (b^4) (c^2) (l^2) m-2 (b^6) (c^2) (l^2) m-18 (a^4) (c^4) (l^2) m-18 (a^2) (b^2) (c^4) (l^2) m+8 (a^2) (c^6) (l^2) m+2 (b^2) (c^6) (l^2) m-(c^8) (l^2) m+(a^8) l (m^2)+14 (a^6) (b^2) l (m^2)+12 (a^4) (b^4) l (m^2)-22 (a^2) (b^6) l (m^2)-5 (b^8) l (m^2)-4 (a^6) (c^2) l (m^2)-34 (a^4) (b^2) (c^2) l (m^2)-16 (a^2) (b^4) (c^2) l (m^2)+6 (b^6) (c^2) l (m^2)+6 (a^4) (c^4) l (m^2)+26 (a^2) (b^2) (c^4) l (m^2)+4 (b^4) (c^4) l (m^2)-4 (a^2) (c^6) l (m^2)-6 (b^2) (c^6) l (m^2)+(c^8) l (m^2)+2 (a^8) (l^2) n+14 (a^6) (b^2) (l^2) n-10 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n-8 (a^6) (c^2) (l^2) n-34 (a^4) (b^2) (c^2) (l^2) n-12 (a^2) (b^4) (c^2) (l^2) n-2 (b^6) (c^2) (l^2) n+12 (a^4) (c^4) (l^2) n+26 (a^2) (b^2) (c^4) (l^2) n+6 (b^4) (c^4) (l^2) n-8 (a^2) (c^6) (l^2) n-6 (b^2) (c^6) (l^2) n+2 (c^8) (l^2) n+7 (a^8) l m n+14 (a^6) (b^2) l m n-40 (a^4) (b^4) l m n+10 (a^2) (b^6) l m n+9 (b^8) l m n-20 (a^6) (c^2) l m n-2 (a^4) (b^2) (c^2) l m n+48 (a^2) (b^4) (c^2) l m n-10 (b^6) (c^2) l m n+18 (a^4) (c^4) l m n-22 (a^2) (b^2) (c^4) l m n-8 (b^4) (c^4) l m n-4 (a^2) (c^6) l m n+10 (b^2) (c^6) l m n-(c^8) l m n-(a^8) (m^2) n-12 (a^6) (b^2) (m^2) n+2 (a^4) (b^4) (m^2) n+12 (a^2) (b^6) (m^2) n-(b^8) (m^2) n+4 (a^6) (c^2) (m^2) n+28 (a^4) (b^2) (c^2) (m^2) n+4 (a^2) (b^4) (c^2) (m^2) n+4 (b^6) (c^2) (m^2) n-6 (a^4) (c^4) (m^2) n-20 (a^2) (b^2) (c^4) (m^2) n-6 (b^4) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n+4 (b^2) (c^6) (m^2) n-(c^8) (m^2) n-2 (a^8) l (n^2)-12 (a^6) (b^2) l (n^2)+24 (a^4) (b^4) l (n^2)-4 (a^2) (b^6) l (n^2)-6 (b^8) l (n^2)+8 (a^6) (c^2) l (n^2)+28 (a^4) (b^2) (c^2) l (n^2)+12 (b^6) (c^2) l (n^2)-12 (a^4) (c^4) l (n^2)-20 (a^2) (b^2) (c^4) l (n^2)-8 (b^4) (c^4) l (n^2)+8 (a^2) (c^6) l (n^2)+4 (b^2) (c^6) l (n^2)-2 (c^8) l (n^2)-2 (a^8) m (n^2)+4 (a^6) (b^2) m (n^2)-4 (a^2) (b^6) m (n^2)+2 (b^8) m (n^2)+4 (a^6) (c^2) m (n^2)-24 (a^4) (b^2) (c^2) m (n^2)-20 (a^2) (b^4) (c^2) m (n^2)-8 (b^6) (c^2) m (n^2)+28 (a^2) (b^2) (c^4) m (n^2)+12 (b^4) (c^4) m (n^2)-4 (a^2) (c^6) m (n^2)-8 (b^2) (c^6) m (n^2)+2 (c^8) m (n^2)) (y^2)+(-12 (a^8) (l^2) m+12 (a^6) (b^2) (l^2) m+12 (a^4) (b^4) (l^2) m-12 (a^2) (b^6) (l^2) m+20 (a^6) (c^2) (l^2) m-44 (a^4) (b^2) (c^2) (l^2) m-20 (a^2) (b^4) (c^2) (l^2) m-4 (b^6) (c^2) (l^2) m+44 (a^2) (b^2) (c^4) (l^2) m+12 (b^4) (c^4) (l^2) m-12 (a^2) (c^6) (l^2) m-12 (b^2) (c^6) (l^2) m+4 (c^8) (l^2) m+5 (a^8) l (m^2)+4 (a^6) (b^2) l (m^2)-18 (a^4) (b^4) l (m^2)+4 (a^2) (b^6) l (m^2)+5 (b^8) l (m^2)-14 (a^6) (c^2) l (m^2)+6 (a^4) (b^2) (c^2) l (m^2)+54 (a^2) (b^4) (c^2) l (m^2)+2 (b^6) (c^2) l (m^2)+12 (a^4) (c^4) l (m^2)-24 (a^2) (b^2) (c^4) l (m^2)-20 (b^4) (c^4) l (m^2)-2 (a^2) (c^6) l (m^2)+14 (b^2) (c^6) l (m^2)-(c^8) l (m^2)+12 (a^8) (l^2) n-2 (a^6) (b^2) (l^2) n-10 (a^4) (b^4) (l^2) n+2 (a^2) (b^6) (l^2) n-2 (b^8) (l^2) n-30 (a^6) (c^2) (l^2) n+24 (a^4) (b^2) (c^2) (l^2) n+34 (a^2) (b^4) (c^2) (l^2) n+12 (b^6) (c^2) (l^2) n+18 (a^4) (c^4) (l^2) n-42 (a^2) (b^2) (c^4) (l^2) n-24 (b^4) (c^4) (l^2) n+6 (a^2) (c^6) (l^2) n+20 (b^2) (c^6) (l^2) n-6 (c^8) (l^2) n+7 (a^8) l m n-40 (a^6) (b^2) l m n+2 (a^4) (b^4) l m n+40 (a^2) (b^6) l m n-9 (b^8) l m n+4 (a^6) (c^2) l m n+76 (a^4) (b^2) (c^2) l m n-108 (a^2) (b^4) (c^2) l m n-4 (b^6) (c^2) l m n-30 (a^4) (c^4) l m n-16 (a^2) (b^2) (c^4) l m n+34 (b^4) (c^4) l m n+20 (a^2) (c^6) l m n-20 (b^2) (c^6) l m n-(c^8) l m n-5 (a^8) (m^2) n+10 (a^6) (b^2) (m^2) n+20 (a^4) (b^4) (m^2) n-26 (a^2) (b^6) (m^2) n+(b^8) (m^2) n+14 (a^6) (c^2) (m^2) n-24 (a^4) (b^2) (c^2) (m^2) n+6 (a^2) (b^4) (c^2) (m^2) n-4 (b^6) (c^2) (m^2) n-12 (a^4) (c^4) (m^2) n+18 (a^2) (b^2) (c^4) (m^2) n+6 (b^4) (c^4) (m^2) n+2 (a^2) (c^6) (m^2) n-4 (b^2) (c^6) (m^2) n+(c^8) (m^2) n-12 (a^8) l (n^2)+16 (a^6) (b^2) l (n^2)+12 (a^4) (b^4) l (n^2)-24 (a^2) (b^6) l (n^2)+8 (b^8) l (n^2)+30 (a^6) (c^2) l (n^2)-42 (a^4) (b^2) (c^2) l (n^2)+26 (a^2) (b^4) (c^2) l (n^2)-14 (b^6) (c^2) l (n^2)-18 (a^4) (c^4) l (n^2)+36 (a^2) (b^2) (c^4) l (n^2)+10 (b^4) (c^4) l (n^2)-6 (a^2) (c^6) l (n^2)-10 (b^2) (c^6) l (n^2)+6 (c^8) l (n^2)+5 (a^8) m (n^2)-18 (a^4) (b^4) m (n^2)+16 (a^2) (b^6) m (n^2)-3 (b^8) m (n^2)-24 (a^6) (c^2) m (n^2)+4 (a^4) (b^2) (c^2) m (n^2)+8 (a^2) (b^4) (c^2) m (n^2)+12 (b^6) (c^2) m (n^2)+30 (a^4) (c^4) m (n^2)-16 (a^2) (b^2) (c^4) m (n^2)-18 (b^4) (c^4) m (n^2)-8 (a^2) (c^6) m (n^2)+12 (b^2) (c^6) m (n^2)-3 (c^8) m (n^2)) y z+(-(a^8) (l^2) m+4 (a^6) (b^2) (l^2) m-6 (a^4) (b^4) (l^2) m+4 (a^2) (b^6) (l^2) m-(b^8) (l^2) m-6 (a^6) (c^2) (l^2) m-6 (a^4) (b^2) (c^2) (l^2) m+6 (a^2) (b^4) (c^2) (l^2) m+6 (b^6) (c^2) (l^2) m+12 (a^4) (c^4) (l^2) m-8 (a^2) (b^2) (c^4) (l^2) m-12 (b^4) (c^4) (l^2) m-2 (a^2) (c^6) (l^2) m+10 (b^2) (c^6) (l^2) m-3 (c^8) (l^2) m+16 (a^4) (b^2) (c^2) l (m^2)-8 (a^2) (b^4) (c^2) l (m^2)-8 (b^6) (c^2) l (m^2)-8 (a^2) (b^2) (c^4) l (m^2)+16 (b^4) (c^4) l (m^2)-8 (b^2) (c^6) l (m^2)+4 (a^8) (l^2) n-6 (a^6) (b^2) (l^2) n+2 (a^4) (b^4) (l^2) n-2 (a^2) (b^6) (l^2) n+2 (b^8) (l^2) n+8 (a^6) (c^2) (l^2) n+22 (a^4) (b^2) (c^2) (l^2) n-4 (a^2) (b^4) (c^2) (l^2) n-10 (b^6) (c^2) (l^2) n-24 (a^4) (c^4) (l^2) n-2 (a^2) (b^2) (c^4) (l^2) n+18 (b^4) (c^4) (l^2) n+8 (a^2) (c^6) (l^2) n-14 (b^2) (c^6) (l^2) n+4 (c^8) (l^2) n-2 (a^8) l m n-10 (a^6) (b^2) l m n+26 (a^4) (b^4) l m n-14 (a^2) (b^6) l m n+4 (a^6) (c^2) l m n-50 (a^4) (b^2) (c^2) l m n+14 (b^6) (c^2) l m n+50 (a^2) (b^2) (c^4) l m n-26 (b^4) (c^4) l m n-4 (a^2) (c^6) l m n+10 (b^2) (c^6) l m n+2 (c^8) l m n+8 (a^6) (b^2) (m^2) n-16 (a^4) (b^4) (m^2) n+8 (a^2) (b^6) (m^2) n+8 (a^4) (b^2) (c^2) (m^2) n+8 (a^2) (b^4) (c^2) (m^2) n-16 (a^2) (b^2) (c^4) (m^2) n-4 (a^8) l (n^2)+14 (a^6) (b^2) l (n^2)-18 (a^4) (b^4) l (n^2)+10 (a^2) (b^6) l (n^2)-2 (b^8) l (n^2)-8 (a^6) (c^2) l (n^2)+2 (a^4) (b^2) (c^2) l (n^2)+4 (a^2) (b^4) (c^2) l (n^2)+2 (b^6) (c^2) l (n^2)+24 (a^4) (c^4) l (n^2)-22 (a^2) (b^2) (c^4) l (n^2)-2 (b^4) (c^4) l (n^2)-8 (a^2) (c^6) l (n^2)+6 (b^2) (c^6) l (n^2)-4 (c^8) l (n^2)+3 (a^8) m (n^2)-10 (a^6) (b^2) m (n^2)+12 (a^4) (b^4) m (n^2)-6 (a^2) (b^6) m (n^2)+(b^8) m (n^2)+2 (a^6) (c^2) m (n^2)+8 (a^4) (b^2) (c^2) m (n^2)-6 (a^2) (b^4) (c^2) m (n^2)-4 (b^6) (c^2) m (n^2)-12 (a^4) (c^4) m (n^2)+6 (a^2) (b^2) (c^4) m (n^2)+6 (b^4) (c^4) m (n^2)+6 (a^2) (c^6) m (n^2)-4 (b^2) (c^6) m (n^2)+(c^8) m (n^2)) (z^2))+x (((a^8) (l^2) m+12 (a^6) (b^2) (l^2) m+2 (a^4) (b^4) (l^2) m-12 (a^2) (b^6) (l^2) m-3 (b^8) (l^2) m-4 (a^6) (c^2) (l^2) m-28 (a^4) (b^2) (c^2) (l^2) m-4 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m+6 (a^4) (c^4) (l^2) m+20 (a^2) (b^2) (c^4) (l^2) m+2 (b^4) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m-4 (b^2) (c^6) (l^2) m+(c^8) (l^2) m-4 (a^6) (b^2) l (m^2)-16 (a^4) (b^4) l (m^2)+12 (a^2) (b^6) l (m^2)+8 (b^8) l (m^2)+12 (a^4) (b^2) (c^2) l (m^2)+24 (a^2) (b^4) (c^2) l (m^2)-4 (b^6) (c^2) l (m^2)-12 (a^2) (b^2) (c^4) l (m^2)-8 (b^4) (c^4) l (m^2)+4 (b^2) (c^6) l (m^2)-4 (a^6) (b^2) (l^2) n+4 (a^2) (b^6) (l^2) n+12 (a^4) (b^2) (c^2) (l^2) n+8 (a^2) (b^4) (c^2) (l^2) n+4 (b^6) (c^2) (l^2) n-12 (a^2) (b^2) (c^4) (l^2) n-8 (b^4) (c^4) (l^2) n+4 (b^2) (c^6) (l^2) n-2 (a^8) l m n-16 (a^6) (b^2) l m n+16 (a^4) (b^4) l m n+8 (a^2) (b^6) l m n-6 (b^8) l m n+8 (a^6) (c^2) l m n+32 (a^4) (b^2) (c^2) l m n-32 (a^2) (b^4) (c^2) l m n-8 (b^6) (c^2) l m n-12 (a^4) (c^4) l m n-16 (a^2) (b^2) (c^4) l m n+16 (b^4) (c^4) l m n+8 (a^2) (c^6) l m n-2 (c^8) l m n+4 (a^6) (b^2) (m^2) n+12 (a^4) (b^4) (m^2) n-12 (a^2) (b^6) (m^2) n-4 (b^8) (m^2) n-12 (a^4) (b^2) (c^2) (m^2) n-16 (a^2) (b^4) (c^2) (m^2) n+4 (b^6) (c^2) (m^2) n+12 (a^2) (b^2) (c^4) (m^2) n+4 (b^4) (c^4) (m^2) n-4 (b^2) (c^6) (m^2) n+4 (a^6) (b^2) l (n^2)-4 (a^4) (b^4) l (n^2)-4 (a^2) (b^6) l (n^2)+4 (b^8) l (n^2)-12 (a^4) (b^2) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)+12 (a^2) (b^2) (c^4) l (n^2)+4 (b^4) (c^4) l (n^2)-4 (b^2) (c^6) l (n^2)+(a^8) m (n^2)+4 (a^6) (b^2) m (n^2)-10 (a^4) (b^4) m (n^2)+4 (a^2) (b^6) m (n^2)+(b^8) m (n^2)-4 (a^6) (c^2) m (n^2)-4 (a^4) (b^2) (c^2) m (n^2)+20 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)+6 (a^4) (c^4) m (n^2)-4 (a^2) (b^2) (c^4) m (n^2)-10 (b^4) (c^4) m (n^2)-4 (a^2) (c^6) m (n^2)+4 (b^2) (c^6) m (n^2)+(c^8) m (n^2)) (y^3)+(7 (a^8) (l^2) m+2 (a^6) (b^2) (l^2) m-24 (a^4) (b^4) (l^2) m+14 (a^2) (b^6) (l^2) m+(b^8) (l^2) m-20 (a^6) (c^2) (l^2) m+26 (a^4) (b^2) (c^2) (l^2) m+32 (a^2) (b^4) (c^2) (l^2) m+10 (b^6) (c^2) (l^2) m+18 (a^4) (c^4) (l^2) m-42 (a^2) (b^2) (c^4) (l^2) m-24 (b^4) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m+14 (b^2) (c^6) (l^2) m-(c^8) (l^2) m-2 (a^8) l (m^2)-10 (a^6) (b^2) l (m^2)+18 (a^4) (b^4) l (m^2)+2 (a^2) (b^6) l (m^2)-8 (b^8) l (m^2)+8 (a^6) (c^2) l (m^2)+14 (a^4) (b^2) (c^2) l (m^2)-52 (a^2) (b^4) (c^2) l (m^2)-18 (b^6) (c^2) l (m^2)-12 (a^4) (c^4) l (m^2)+2 (a^2) (b^2) (c^4) l (m^2)+34 (b^4) (c^4) l (m^2)+8 (a^2) (c^6) l (m^2)-6 (b^2) (c^6) l (m^2)-2 (c^8) l (m^2)-4 (a^8) (l^2) n-10 (a^6) (b^2) (l^2) n+14 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n+6 (b^8) (l^2) n+16 (a^6) (c^2) (l^2) n+14 (a^4) (b^2) (c^2) (l^2) n-12 (a^2) (b^4) (c^2) (l^2) n-26 (b^6) (c^2) (l^2) n-24 (a^4) (c^4) (l^2) n+2 (a^2) (b^2) (c^4) (l^2) n+30 (b^4) (c^4) (l^2) n+16 (a^2) (c^6) (l^2) n-6 (b^2) (c^6) (l^2) n-4 (c^8) (l^2) n-8 (a^8) l m n+20 (a^6) (b^2) l m n+32 (a^4) (b^4) l m n-44 (a^2) (b^6) l m n+16 (a^6) (c^2) l m n-92 (a^4) (b^2) (c^2) l m n+44 (b^6) (c^2) l m n+92 (a^2) (b^2) (c^4) l m n-32 (b^4) (c^4) l m n-16 (a^2) (c^6) l m n-20 (b^2) (c^6) l m n+8 (c^8) l m n+2 (a^8) (m^2) n+6 (a^6) (b^2) (m^2) n-34 (a^4) (b^4) (m^2) n+18 (a^2) (b^6) (m^2) n+8 (b^8) (m^2) n-8 (a^6) (c^2) (m^2) n-2 (a^4) (b^2) (c^2) (m^2) n+52 (a^2) (b^4) (c^2) (m^2) n-2 (b^6) (c^2) (m^2) n+12 (a^4) (c^4) (m^2) n-14 (a^2) (b^2) (c^4) (m^2) n-18 (b^4) (c^4) (m^2) n-8 (a^2) (c^6) (m^2) n+10 (b^2) (c^6) (m^2) n+2 (c^8) (m^2) n+4 (a^8) l (n^2)+6 (a^6) (b^2) l (n^2)-30 (a^4) (b^4) l (n^2)+26 (a^2) (b^6) l (n^2)-6 (b^8) l (n^2)-16 (a^6) (c^2) l (n^2)-2 (a^4) (b^2) (c^2) l (n^2)+12 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)+24 (a^4) (c^4) l (n^2)-14 (a^2) (b^2) (c^4) l (n^2)-14 (b^4) (c^4) l (n^2)-16 (a^2) (c^6) l (n^2)+10 (b^2) (c^6) l (n^2)+4 (c^8) l (n^2)+(a^8) m (n^2)-14 (a^6) (b^2) m (n^2)+24 (a^4) (b^4) m (n^2)-10 (a^2) (b^6) m (n^2)-(b^8) m (n^2)+4 (a^6) (c^2) m (n^2)+42 (a^4) (b^2) (c^2) m (n^2)-32 (a^2) (b^4) (c^2) m (n^2)-14 (b^6) (c^2) m (n^2)-18 (a^4) (c^4) m (n^2)-26 (a^2) (b^2) (c^4) m (n^2)+24 (b^4) (c^4) m (n^2)+20 (a^2) (c^6) m (n^2)-2 (b^2) (c^6) m (n^2)-7 (c^8) m (n^2)) (y^2) z+(3 (a^8) (l^2) m-12 (a^6) (b^2) (l^2) m+18 (a^4) (b^4) (l^2) m-12 (a^2) (b^6) (l^2) m+3 (b^8) (l^2) m+8 (a^6) (c^2) (l^2) m+16 (a^4) (b^2) (c^2) (l^2) m-8 (a^2) (b^4) (c^2) (l^2) m-16 (b^6) (c^2) (l^2) m-30 (a^4) (c^4) (l^2) m-4 (a^2) (b^2) (c^4) (l^2) m+18 (b^4) (c^4) (l^2) m+24 (a^2) (c^6) (l^2) m-5 (c^8) (l^2) m-(a^8) l (m^2)+4 (a^6) (b^2) l (m^2)-6 (a^4) (b^4) l (m^2)+4 (a^2) (b^6) l (m^2)-(b^8) l (m^2)-2 (a^6) (c^2) l (m^2)-18 (a^4) (b^2) (c^2) l (m^2)-6 (a^2) (b^4) (c^2) l (m^2)+26 (b^6) (c^2) l (m^2)+12 (a^4) (c^4) l (m^2)+24 (a^2) (b^2) (c^4) l (m^2)-20 (b^4) (c^4) l (m^2)-14 (a^2) (c^6) l (m^2)-10 (b^2) (c^6) l (m^2)+5 (c^8) l (m^2)-6 (a^8) (l^2) n+10 (a^6) (b^2) (l^2) n-10 (a^4) (b^4) (l^2) n+14 (a^2) (b^6) (l^2) n-8 (b^8) (l^2) n+6 (a^6) (c^2) (l^2) n-36 (a^4) (b^2) (c^2) (l^2) n-26 (a^2) (b^4) (c^2) (l^2) n+24 (b^6) (c^2) (l^2) n+18 (a^4) (c^4) (l^2) n+42 (a^2) (b^2) (c^4) (l^2) n-12 (b^4) (c^4) (l^2) n-30 (a^2) (c^6) (l^2) n-16 (b^2) (c^6) (l^2) n+12 (c^8) (l^2) n+(a^8) l m n+20 (a^6) (b^2) l m n-34 (a^4) (b^4) l m n+4 (a^2) (b^6) l m n+9 (b^8) l m n-20 (a^6) (c^2) l m n+16 (a^4) (b^2) (c^2) l m n+108 (a^2) (b^4) (c^2) l m n-40 (b^6) (c^2) l m n+30 (a^4) (c^4) l m n-76 (a^2) (b^2) (c^4) l m n-2 (b^4) (c^4) l m n-4 (a^2) (c^6) l m n+40 (b^2) (c^6) l m n-7 (c^8) l m n+(a^8) (m^2) n-14 (a^6) (b^2) (m^2) n+20 (a^4) (b^4) (m^2) n-2 (a^2) (b^6) (m^2) n-5 (b^8) (m^2) n+2 (a^6) (c^2) (m^2) n+24 (a^4) (b^2) (c^2) (m^2) n-54 (a^2) (b^4) (c^2) (m^2) n-4 (b^6) (c^2) (m^2) n-12 (a^4) (c^4) (m^2) n-6 (a^2) (b^2) (c^4) (m^2) n+18 (b^4) (c^4) (m^2) n+14 (a^2) (c^6) (m^2) n-4 (b^2) (c^6) (m^2) n-5 (c^8) (m^2) n+6 (a^8) l (n^2)-20 (a^6) (b^2) l (n^2)+24 (a^4) (b^4) l (n^2)-12 (a^2) (b^6) l (n^2)+2 (b^8) l (n^2)-6 (a^6) (c^2) l (n^2)+42 (a^4) (b^2) (c^2) l (n^2)-34 (a^2) (b^4) (c^2) l (n^2)-2 (b^6) (c^2) l (n^2)-18 (a^4) (c^4) l (n^2)-24 (a^2) (b^2) (c^4) l (n^2)+10 (b^4) (c^4) l (n^2)+30 (a^2) (c^6) l (n^2)+2 (b^2) (c^6) l (n^2)-12 (c^8) l (n^2)-4 (a^8) m (n^2)+12 (a^6) (b^2) m (n^2)-12 (a^4) (b^4) m (n^2)+4 (a^2) (b^6) m (n^2)+12 (a^6) (c^2) m (n^2)-44 (a^4) (b^2) (c^2) m (n^2)+20 (a^2) (b^4) (c^2) m (n^2)+12 (b^6) (c^2) m (n^2)+44 (a^2) (b^2) (c^4) m (n^2)-12 (b^4) (c^4) m (n^2)-20 (a^2) (c^6) m (n^2)-12 (b^2) (c^6) m (n^2)+12 (c^8) m (n^2)) y (z^2)+(-(a^8) (l^2) m+4 (a^6) (b^2) (l^2) m-6 (a^4) (b^4) (l^2) m+4 (a^2) (b^6) (l^2) m-(b^8) (l^2) m+2 (a^6) (c^2) (l^2) m-2 (a^4) (b^2) (c^2) (l^2) m-2 (a^2) (b^4) (c^2) (l^2) m+2 (b^6) (c^2) (l^2) m+4 (a^4) (c^4) (l^2) m+8 (a^2) (b^2) (c^4) (l^2) m+4 (b^4) (c^4) (l^2) m-10 (a^2) (c^6) (l^2) m-10 (b^2) (c^6) (l^2) m+5 (c^8) (l^2) m+(a^8) l (m^2)-4 (a^6) (b^2) l (m^2)+6 (a^4) (b^4) l (m^2)-4 (a^2) (b^6) l (m^2)+(b^8) l (m^2)-4 (a^4) (b^2) (c^2) l (m^2)+8 (a^2) (b^4) (c^2) l (m^2)-4 (b^6) (c^2) l (m^2)-6 (a^4) (c^4) l (m^2)-4 (a^2) (b^2) (c^4) l (m^2)-6 (b^4) (c^4) l (m^2)+8 (a^2) (c^6) l (m^2)+12 (b^2) (c^6) l (m^2)-3 (c^8) l (m^2)-2 (a^6) (b^2) (l^2) n+6 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n+2 (b^8) (l^2) n-8 (a^6) (c^2) (l^2) n-2 (a^4) (b^2) (c^2) (l^2) n+12 (a^2) (b^4) (c^2) (l^2) n-2 (b^6) (c^2) (l^2) n+8 (a^4) (c^4) (l^2) n-14 (a^2) (b^2) (c^4) (l^2) n-10 (b^4) (c^4) (l^2) n+8 (a^2) (c^6) (l^2) n+18 (b^2) (c^6) (l^2) n-8 (c^8) (l^2) n+(a^8) l m n-6 (a^4) (b^4) l m n+8 (a^2) (b^6) l m n-3 (b^8) l m n+4 (a^6) (c^2) l m n+28 (a^4) (b^2) (c^2) l m n-36 (a^2) (b^4) (c^2) l m n+4 (b^6) (c^2) l m n-10 (a^4) (c^4) l m n-8 (a^2) (b^2) (c^4) l m n+18 (b^4) (c^4) l m n+4 (a^2) (c^6) l m n-20 (b^2) (c^6) l m n+(c^8) l m n-(a^8) (m^2) n+2 (a^6) (b^2) (m^2) n-2 (a^2) (b^6) (m^2) n+(b^8) (m^2) n-14 (a^4) (b^2) (c^2) (m^2) n+12 (a^2) (b^4) (c^2) (m^2) n+2 (b^6) (c^2) (m^2) n+6 (a^4) (c^4) (m^2) n+14 (a^2) (b^2) (c^4) (m^2) n-4 (b^4) (c^4) (m^2) n-8 (a^2) (c^6) (m^2) n-2 (b^2) (c^6) (m^2) n+3 (c^8) (m^2) n+8 (a^6) (c^2) l (n^2)-16 (a^4) (b^2) (c^2) l (n^2)+8 (a^2) (b^4) (c^2) l (n^2)-8 (a^4) (c^4) l (n^2)+24 (a^2) (b^2) (c^4) l (n^2)-8 (a^2) (c^6) l (n^2)-8 (b^2) (c^6) l (n^2)+8 (c^8) l (n^2)-6 (a^6) (c^2) m (n^2)+10 (a^4) (b^2) (c^2) m (n^2)-2 (a^2) (b^4) (c^2) m (n^2)-2 (b^6) (c^2) m (n^2)+6 (a^4) (c^4) m (n^2)-20 (a^2) (b^2) (c^4) m (n^2)-2 (b^4) (c^4) m (n^2)+6 (a^2) (c^6) m (n^2)+10 (b^2) (c^6) m (n^2)-6 (c^8) m (n^2)) (z^3)),-2 (a^2) ((a^2)-(b^2)+(c^2)) (m-n) (2 (a^4) (l^2)-2 (a^2) (b^2) (l^2)-2 (a^2) (c^2) (l^2)-2 (a^4) l m+2 (a^2) (b^2) l m+4 (a^2) (c^2) l m+2 (b^2) (c^2) l m-2 (c^4) l m-(a^4) l n+2 (a^2) (b^2) l n-(b^4) l n+(c^4) l n+(a^4) m n-2 (a^2) (b^2) m n+(b^4) m n-2 (a^2) (c^2) m n-2 (b^2) (c^2) m n+(c^4) m n) (x^4)-2 (b^2) ((a^2)-(b^2)-(c^2)) (l-n) (2 (a^2) (b^2) l m-2 (b^4) l m+2 (a^2) (c^2) l m+4 (b^2) (c^2) l m-2 (c^4) l m-2 (a^2) (b^2) (m^2)+2 (b^4) (m^2)-2 (b^2) (c^2) (m^2)+(a^4) l n-2 (a^2) (b^2) l n+(b^4) l n-2 (a^2) (c^2) l n-2 (b^2) (c^2) l n+(c^4) l n-(a^4) m n+2 (a^2) (b^2) m n-(b^4) m n+(c^4) m n) (y^4)+(-6 (a^6) (b^2) (l^2) m+18 (a^4) (b^4) (l^2) m-18 (a^2) (b^6) (l^2) m+6 (b^8) (l^2) m-2 (a^6) (c^2) (l^2) m+8 (a^4) (b^2) (c^2) (l^2) m-10 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m+6 (a^4) (c^4) (l^2) m-14 (a^2) (b^2) (c^4) (l^2) m-24 (b^4) (c^4) (l^2) m-6 (a^2) (c^6) (l^2) m+12 (b^2) (c^6) (l^2) m+2 (c^8) (l^2) m+6 (a^6) (b^2) l (m^2)-18 (a^4) (b^4) l (m^2)+18 (a^2) (b^6) l (m^2)-6 (b^8) l (m^2)-10 (a^4) (b^2) (c^2) l (m^2)+20 (a^2) (b^4) (c^2) l (m^2)-10 (b^6) (c^2) l (m^2)+2 (a^2) (b^2) (c^4) l (m^2)+14 (b^4) (c^4) l (m^2)+2 (b^2) (c^6) l (m^2)-(a^8) (l^2) n+8 (a^6) (b^2) (l^2) n-14 (a^4) (b^4) (l^2) n+8 (a^2) (b^6) (l^2) n-(b^8) (l^2) n+4 (a^6) (c^2) (l^2) n-20 (a^4) (b^2) (c^2) (l^2) n+20 (a^2) (b^4) (c^2) (l^2) n-4 (b^6) (c^2) (l^2) n-6 (a^4) (c^4) (l^2) n+16 (a^2) (b^2) (c^4) (l^2) n+10 (b^4) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n-4 (b^2) (c^6) (l^2) n-(c^8) (l^2) n+(a^8) l m n-4 (a^6) (b^2) l m n-2 (a^4) (b^4) l m n+12 (a^2) (b^6) l m n-7 (b^8) l m n+20 (a^4) (b^2) (c^2) l m n-24 (a^2) (b^4) (c^2) l m n+4 (b^6) (c^2) l m n-6 (a^4) (c^4) l m n+4 (a^2) (b^2) (c^4) l m n+26 (b^4) (c^4) l m n+8 (a^2) (c^6) l m n-20 (b^2) (c^6) l m n-3 (c^8) l m n-4 (a^6) (b^2) (m^2) n+16 (a^4) (b^4) (m^2) n-20 (a^2) (b^6) (m^2) n+8 (b^8) (m^2) n+4 (a^4) (b^2) (c^2) (m^2) n-16 (a^2) (b^4) (c^2) (m^2) n+12 (b^6) (c^2) (m^2) n+4 (a^2) (b^2) (c^4) (m^2) n-16 (b^4) (c^4) (m^2) n-4 (b^2) (c^6) (m^2) n+(a^8) l (n^2)-6 (a^6) (b^2) l (n^2)+12 (a^4) (b^4) l (n^2)-10 (a^2) (b^6) l (n^2)+3 (b^8) l (n^2)-4 (a^6) (c^2) l (n^2)+14 (a^4) (b^2) (c^2) l (n^2)-16 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)+6 (a^4) (c^4) l (n^2)-10 (a^2) (b^2) (c^4) l (n^2)-12 (b^4) (c^4) l (n^2)-4 (a^2) (c^6) l (n^2)+2 (b^2) (c^6) l (n^2)+(c^8) l (n^2)-(a^8) m (n^2)+6 (a^6) (b^2) m (n^2)-12 (a^4) (b^4) m (n^2)+10 (a^2) (b^6) m (n^2)-3 (b^8) m (n^2)+2 (a^6) (c^2) m (n^2)-16 (a^4) (b^2) (c^2) m (n^2)+26 (a^2) (b^4) (c^2) m (n^2)-12 (b^6) (c^2) m (n^2)-2 (a^2) (b^2) (c^4) m (n^2)+2 (b^4) (c^4) m (n^2)-2 (a^2) (c^6) m (n^2)+12 (b^2) (c^6) m (n^2)+(c^8) m (n^2)) (y^3) z+(-2 (a^8) (l^2) m+8 (a^6) (b^2) (l^2) m-12 (a^4) (b^4) (l^2) m+8 (a^2) (b^6) (l^2) m-2 (b^8) (l^2) m+4 (a^6) (c^2) (l^2) m-20 (a^4) (b^2) (c^2) (l^2) m+28 (a^2) (b^4) (c^2) (l^2) m-12 (b^6) (c^2) (l^2) m-8 (a^4) (c^4) (l^2) m+24 (b^4) (c^4) (l^2) m+12 (a^2) (c^6) (l^2) m-4 (b^2) (c^6) (l^2) m-6 (c^8) (l^2) m+2 (a^8) l (m^2)-8 (a^6) (b^2) l (m^2)+12 (a^4) (b^4) l (m^2)-8 (a^2) (b^6) l (m^2)+2 (b^8) l (m^2)-6 (a^6) (c^2) l (m^2)+26 (a^4) (b^2) (c^2) l (m^2)-34 (a^2) (b^4) (c^2) l (m^2)+14 (b^6) (c^2) l (m^2)+6 (a^4) (c^4) l (m^2)-12 (a^2) (b^2) (c^4) l (m^2)-10 (b^4) (c^4) l (m^2)-2 (a^2) (c^6) l (m^2)-6 (b^2) (c^6) l (m^2)+2 (a^8) (l^2) n-4 (a^6) (b^2) (l^2) n+4 (a^2) (b^6) (l^2) n-2 (b^8) (l^2) n-8 (a^6) (c^2) (l^2) n+28 (a^4) (b^2) (c^2) (l^2) n-24 (a^2) (b^4) (c^2) (l^2) n+4 (b^6) (c^2) (l^2) n+12 (a^4) (c^4) (l^2) n-20 (a^2) (b^2) (c^4) (l^2) n-8 (a^2) (c^6) (l^2) n-4 (b^2) (c^6) (l^2) n+2 (c^8) (l^2) n-(a^8) l m n-4 (a^6) (b^2) l m n+18 (a^4) (b^4) l m n-20 (a^2) (b^6) l m n+7 (b^8) l m n+10 (a^6) (c^2) l m n-22 (a^4) (b^2) (c^2) l m n-2 (a^2) (b^4) (c^2) l m n+14 (b^6) (c^2) l m n-8 (a^4) (c^4) l m n+48 (a^2) (b^2) (c^4) l m n-40 (b^4) (c^4) l m n-10 (a^2) (c^6) l m n+10 (b^2) (c^6) l m n+9 (c^8) l m n-(a^8) (m^2) n+8 (a^6) (b^2) (m^2) n-18 (a^4) (b^4) (m^2) n+16 (a^2) (b^6) (m^2) n-5 (b^8) (m^2) n+2 (a^6) (c^2) (m^2) n-18 (a^4) (b^2) (c^2) (m^2) n+38 (a^2) (b^4) (c^2) (m^2) n-22 (b^6) (c^2) (m^2) n-4 (a^2) (b^2) (c^4) (m^2) n+12 (b^4) (c^4) (m^2) n-2 (a^2) (c^6) (m^2) n+14 (b^2) (c^6) (m^2) n+(c^8) (m^2) n-(a^8) l (n^2)+4 (a^6) (b^2) l (n^2)-6 (a^4) (b^4) l (n^2)+4 (a^2) (b^6) l (n^2)-(b^8) l (n^2)+4 (a^6) (c^2) l (n^2)-20 (a^4) (b^2) (c^2) l (n^2)+28 (a^2) (b^4) (c^2) l (n^2)-12 (b^6) (c^2) l (n^2)-6 (a^4) (c^4) l (n^2)+4 (a^2) (b^2) (c^4) l (n^2)+2 (b^4) (c^4) l (n^2)+4 (a^2) (c^6) l (n^2)+12 (b^2) (c^6) l (n^2)-(c^8) l (n^2)+(a^8) m (n^2)-4 (a^6) (b^2) m (n^2)+6 (a^4) (b^4) m (n^2)-4 (a^2) (b^6) m (n^2)+(b^8) m (n^2)-6 (a^6) (c^2) m (n^2)+26 (a^4) (b^2) (c^2) m (n^2)-34 (a^2) (b^4) (c^2) m (n^2)+14 (b^6) (c^2) m (n^2)+4 (a^4) (c^4) m (n^2)-16 (a^2) (b^2) (c^4) m (n^2)+12 (b^4) (c^4) m (n^2)+6 (a^2) (c^6) m (n^2)-22 (b^2) (c^6) m (n^2)-5 (c^8) m (n^2)) (y^2) (z^2)+(-4 (a^6) (c^2) (l^2) m+12 (a^4) (b^2) (c^2) (l^2) m-12 (a^2) (b^4) (c^2) (l^2) m+4 (b^6) (c^2) (l^2) m+4 (a^4) (c^4) (l^2) m-4 (b^4) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m-4 (b^2) (c^6) (l^2) m+4 (c^8) (l^2) m+4 (a^6) (c^2) l (m^2)-12 (a^4) (b^2) (c^2) l (m^2)+12 (a^2) (b^4) (c^2) l (m^2)-4 (b^6) (c^2) l (m^2)-8 (a^4) (c^4) l (m^2)+8 (a^2) (b^2) (c^4) l (m^2)+4 (a^2) (c^6) l (m^2)+4 (b^2) (c^6) l (m^2)+(a^8) (l^2) n-4 (a^6) (b^2) (l^2) n+6 (a^4) (b^4) (l^2) n-4 (a^2) (b^6) (l^2) n+(b^8) (l^2) n+4 (a^6) (c^2) (l^2) n-4 (a^4) (b^2) (c^2) (l^2) n-4 (a^2) (b^4) (c^2) (l^2) n+4 (b^6) (c^2) (l^2) n-10 (a^4) (c^4) (l^2) n+20 (a^2) (b^2) (c^4) (l^2) n-10 (b^4) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n+4 (b^2) (c^6) (l^2) n+(c^8) (l^2) n-2 (a^8) l m n+8 (a^6) (b^2) l m n-12 (a^4) (b^4) l m n+8 (a^2) (b^6) l m n-2 (b^8) l m n-16 (a^4) (b^2) (c^2) l m n+32 (a^2) (b^4) (c^2) l m n-16 (b^6) (c^2) l m n+16 (a^4) (c^4) l m n-32 (a^2) (b^2) (c^4) l m n+16 (b^4) (c^4) l m n-8 (a^2) (c^6) l m n+8 (b^2) (c^6) l m n-6 (c^8) l m n+(a^8) (m^2) n-4 (a^6) (b^2) (m^2) n+6 (a^4) (b^4) (m^2) n-4 (a^2) (b^6) (m^2) n+(b^8) (m^2) n-4 (a^6) (c^2) (m^2) n+20 (a^4) (b^2) (c^2) (m^2) n-28 (a^2) (b^4) (c^2) (m^2) n+12 (b^6) (c^2) (m^2) n+2 (a^4) (c^4) (m^2) n-4 (a^2) (b^2) (c^4) (m^2) n+2 (b^4) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n-12 (b^2) (c^6) (m^2) n-3 (c^8) (m^2) n-4 (a^6) (c^2) l (n^2)+12 (a^4) (b^2) (c^2) l (n^2)-12 (a^2) (b^4) (c^2) l (n^2)+4 (b^6) (c^2) l (n^2)+4 (a^4) (c^4) l (n^2)-16 (a^2) (b^2) (c^4) l (n^2)+12 (b^4) (c^4) l (n^2)+4 (a^2) (c^6) l (n^2)-12 (b^2) (c^6) l (n^2)-4 (c^8) l (n^2)+4 (a^6) (c^2) m (n^2)-12 (a^4) (b^2) (c^2) m (n^2)+12 (a^2) (b^4) (c^2) m (n^2)-4 (b^6) (c^2) m (n^2)-8 (a^4) (c^4) m (n^2)+24 (a^2) (b^2) (c^4) m (n^2)-16 (b^4) (c^4) m (n^2)-4 (a^2) (c^6) m (n^2)+12 (b^2) (c^6) m (n^2)+8 (c^8) m (n^2)) y (z^3)+2 (c^2) ((a^2)-(b^2)-(c^2)) ((a^2)-(b^2)+(c^2)) (l-m) n ((a^2) l-(b^2) l+(c^2) l-(a^2) m+(b^2) m+(c^2) m-2 (c^2) n) (z^4)+(x^3) ((8 (a^8) (l^2) m-8 (a^6) (b^2) (l^2) m-8 (a^4) (b^4) (l^2) m+8 (a^2) (b^6) (l^2) m-8 (a^6) (c^2) (l^2) m+24 (a^4) (b^2) (c^2) (l^2) m-16 (a^2) (b^4) (c^2) (l^2) m+8 (a^2) (b^2) (c^4) (l^2) m-8 (a^8) l (m^2)+8 (a^6) (b^2) l (m^2)+8 (a^4) (b^4) l (m^2)-8 (a^2) (b^6) l (m^2)+18 (a^6) (c^2) l (m^2)-14 (a^4) (b^2) (c^2) l (m^2)-2 (a^2) (b^4) (c^2) l (m^2)-2 (b^6) (c^2) l (m^2)-10 (a^4) (c^4) l (m^2)+12 (a^2) (b^2) (c^4) l (m^2)+6 (b^4) (c^4) l (m^2)-2 (a^2) (c^6) l (m^2)-6 (b^2) (c^6) l (m^2)+2 (c^8) l (m^2)-6 (a^8) (l^2) n+6 (a^6) (b^2) (l^2) n+6 (a^4) (b^4) (l^2) n-6 (a^2) (b^6) (l^2) n+10 (a^6) (c^2) (l^2) n-20 (a^4) (b^2) (c^2) (l^2) n+10 (a^2) (b^4) (c^2) (l^2) n-2 (a^4) (c^4) (l^2) n-2 (a^2) (b^2) (c^4) (l^2) n-2 (a^2) (c^6) (l^2) n+(a^8) l m n+4 (a^6) (b^2) l m n-10 (a^4) (b^4) l m n+4 (a^2) (b^6) l m n+(b^8) l m n-20 (a^6) (c^2) l m n-8 (a^4) (b^2) (c^2) l m n+28 (a^2) (b^4) (c^2) l m n+18 (a^4) (c^4) l m n-36 (a^2) (b^2) (c^4) l m n-6 (b^4) (c^4) l m n+4 (a^2) (c^6) l m n+8 (b^2) (c^6) l m n-3 (c^8) l m n+5 (a^8) (m^2) n-10 (a^6) (b^2) (m^2) n+4 (a^4) (b^4) (m^2) n+2 (a^2) (b^6) (m^2) n-(b^8) (m^2) n-10 (a^6) (c^2) (m^2) n+8 (a^4) (b^2) (c^2) (m^2) n-2 (a^2) (b^4) (c^2) (m^2) n+4 (b^6) (c^2) (m^2) n+4 (a^4) (c^4) (m^2) n-2 (a^2) (b^2) (c^4) (m^2) n-6 (b^4) (c^4) (m^2) n+2 (a^2) (c^6) (m^2) n+4 (b^2) (c^6) (m^2) n-(c^8) (m^2) n+3 (a^8) l (n^2)-8 (a^6) (b^2) l (n^2)+6 (a^4) (b^4) l (n^2)-(b^8) l (n^2)-2 (a^6) (c^2) l (n^2)+14 (a^4) (b^2) (c^2) l (n^2)-14 (a^2) (b^4) (c^2) l (n^2)+2 (b^6) (c^2) l (n^2)-4 (a^4) (c^4) l (n^2)+12 (a^2) (b^2) (c^4) l (n^2)+2 (a^2) (c^6) l (n^2)-2 (b^2) (c^6) l (n^2)+(c^8) l (n^2)-3 (a^8) m (n^2)+8 (a^6) (b^2) m (n^2)-6 (a^4) (b^4) m (n^2)+(b^8) m (n^2)+12 (a^6) (c^2) m (n^2)-4 (a^4) (b^2) (c^2) m (n^2)-4 (a^2) (b^4) (c^2) m (n^2)-4 (b^6) (c^2) m (n^2)-6 (a^4) (c^4) m (n^2)+8 (a^2) (b^2) (c^4) m (n^2)+6 (b^4) (c^4) m (n^2)-4 (a^2) (c^6) m (n^2)-4 (b^2) (c^6) m (n^2)+(c^8) m (n^2)) y+(6 (a^8) (l^2) m-18 (a^6) (b^2) (l^2) m+18 (a^4) (b^4) (l^2) m-6 (a^2) (b^6) (l^2) m+10 (a^6) (c^2) (l^2) m-20 (a^4) (b^2) (c^2) (l^2) m+10 (a^2) (b^4) (c^2) (l^2) m-14 (a^4) (c^4) (l^2) m-2 (a^2) (b^2) (c^4) (l^2) m-2 (a^2) (c^6) (l^2) m-6 (a^8) l (m^2)+18 (a^6) (b^2) l (m^2)-18 (a^4) (b^4) l (m^2)+6 (a^2) (b^6) l (m^2)-4 (a^6) (c^2) l (m^2)+10 (a^4) (b^2) (c^2) l (m^2)-8 (a^2) (b^4) (c^2) l (m^2)+2 (b^6) (c^2) l (m^2)+24 (a^4) (c^4) l (m^2)+14 (a^2) (b^2) (c^4) l (m^2)-6 (b^4) (c^4) l (m^2)-12 (a^2) (c^6) l (m^2)+6 (b^2) (c^6) l (m^2)-2 (c^8) l (m^2)-8 (a^8) (l^2) n+20 (a^6) (b^2) (l^2) n-16 (a^4) (b^4) (l^2) n+4 (a^2) (b^6) (l^2) n-12 (a^6) (c^2) (l^2) n+16 (a^4) (b^2) (c^2) (l^2) n-4 (a^2) (b^4) (c^2) (l^2) n+16 (a^4) (c^4) (l^2) n-4 (a^2) (b^2) (c^4) (l^2) n+4 (a^2) (c^6) (l^2) n+7 (a^8) l m n-12 (a^6) (b^2) l m n+2 (a^4) (b^4) l m n+4 (a^2) (b^6) l m n-(b^8) l m n-4 (a^6) (c^2) l m n+24 (a^4) (b^2) (c^2) l m n-20 (a^2) (b^4) (c^2) l m n-26 (a^4) (c^4) l m n-4 (a^2) (b^2) (c^4) l m n+6 (b^4) (c^4) l m n+20 (a^2) (c^6) l m n-8 (b^2) (c^6) l m n+3 (c^8) l m n+(a^8) (m^2) n-8 (a^6) (b^2) (m^2) n+14 (a^4) (b^4) (m^2) n-8 (a^2) (b^6) (m^2) n+(b^8) (m^2) n+4 (a^6) (c^2) (m^2) n-20 (a^4) (b^2) (c^2) (m^2) n+20 (a^2) (b^4) (c^2) (m^2) n-4 (b^6) (c^2) (m^2) n-10 (a^4) (c^4) (m^2) n-16 (a^2) (b^2) (c^4) (m^2) n+6 (b^4) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n-4 (b^2) (c^6) (m^2) n+(c^8) (m^2) n+3 (a^8) l (n^2)-10 (a^6) (b^2) l (n^2)+12 (a^4) (b^4) l (n^2)-6 (a^2) (b^6) l (n^2)+(b^8) l (n^2)+12 (a^6) (c^2) l (n^2)-26 (a^4) (b^2) (c^2) l (n^2)+16 (a^2) (b^4) (c^2) l (n^2)-2 (b^6) (c^2) l (n^2)-2 (a^4) (c^4) l (n^2)+2 (a^2) (b^2) (c^4) l (n^2)-12 (a^2) (c^6) l (n^2)+2 (b^2) (c^6) l (n^2)-(c^8) l (n^2)-3 (a^8) m (n^2)+10 (a^6) (b^2) m (n^2)-12 (a^4) (b^4) m (n^2)+6 (a^2) (b^6) m (n^2)-(b^8) m (n^2)-6 (a^6) (c^2) m (n^2)+16 (a^4) (b^2) (c^2) m (n^2)-14 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)+12 (a^4) (c^4) m (n^2)+10 (a^2) (b^2) (c^4) m (n^2)-6 (b^4) (c^4) m (n^2)-2 (a^2) (c^6) m (n^2)+4 (b^2) (c^6) m (n^2)-(c^8) m (n^2)) z)+(x^2) ((-4 (a^8) (l^2) m-8 (a^6) (b^2) (l^2) m+24 (a^4) (b^4) (l^2) m-8 (a^2) (b^6) (l^2) m-4 (b^8) (l^2) m+6 (a^6) (c^2) (l^2) m-22 (a^4) (b^2) (c^2) (l^2) m+2 (a^2) (b^4) (c^2) (l^2) m+14 (b^6) (c^2) (l^2) m-2 (a^4) (c^4) (l^2) m+4 (a^2) (b^2) (c^4) (l^2) m-18 (b^4) (c^4) (l^2) m+2 (a^2) (c^6) (l^2) m+10 (b^2) (c^6) (l^2) m-2 (c^8) (l^2) m+4 (a^8) l (m^2)+8 (a^6) (b^2) l (m^2)-24 (a^4) (b^4) l (m^2)+8 (a^2) (b^6) l (m^2)+4 (b^8) l (m^2)-14 (a^6) (c^2) l (m^2)-2 (a^4) (b^2) (c^2) l (m^2)+22 (a^2) (b^4) (c^2) l (m^2)-6 (b^6) (c^2) l (m^2)+18 (a^4) (c^4) l (m^2)-4 (a^2) (b^2) (c^4) l (m^2)+2 (b^4) (c^4) l (m^2)-10 (a^2) (c^6) l (m^2)-2 (b^2) (c^6) l (m^2)+2 (c^8) l (m^2)+(a^8) (l^2) n+6 (a^6) (b^2) (l^2) n-12 (a^4) (b^4) (l^2) n+2 (a^2) (b^6) (l^2) n+3 (b^8) (l^2) n-4 (a^6) (c^2) (l^2) n+6 (a^4) (b^2) (c^2) (l^2) n+8 (a^2) (b^4) (c^2) (l^2) n-10 (b^6) (c^2) (l^2) n+6 (a^4) (c^4) (l^2) n-6 (a^2) (b^2) (c^4) (l^2) n+12 (b^4) (c^4) (l^2) n-4 (a^2) (c^6) (l^2) n-6 (b^2) (c^6) (l^2) n+(c^8) (l^2) n+2 (a^8) l m n-4 (a^6) (b^2) l m n+4 (a^2) (b^6) l m n-2 (b^8) l m n+10 (a^6) (c^2) l m n+50 (a^4) (b^2) (c^2) l m n-50 (a^2) (b^4) (c^2) l m n-10 (b^6) (c^2) l m n-26 (a^4) (c^4) l m n+26 (b^4) (c^4) l m n+14 (a^2) (c^6) l m n-14 (b^2) (c^6) l m n-3 (a^8) (m^2) n-2 (a^6) (b^2) (m^2) n+12 (a^4) (b^4) (m^2) n-6 (a^2) (b^6) (m^2) n-(b^8) (m^2) n+10 (a^6) (c^2) (m^2) n-8 (a^4) (b^2) (c^2) (m^2) n-6 (a^2) (b^4) (c^2) (m^2) n+4 (b^6) (c^2) (m^2) n-12 (a^4) (c^4) (m^2) n+6 (a^2) (b^2) (c^4) (m^2) n-6 (b^4) (c^4) (m^2) n+6 (a^2) (c^6) (m^2) n+4 (b^2) (c^6) (m^2) n-(c^8) (m^2) n-16 (a^4) (b^2) (c^2) l (n^2)+8 (a^2) (b^4) (c^2) l (n^2)+8 (b^6) (c^2) l (n^2)+8 (a^2) (b^2) (c^4) l (n^2)-16 (b^4) (c^4) l (n^2)+8 (b^2) (c^6) l (n^2)-8 (a^6) (c^2) m (n^2)-8 (a^4) (b^2) (c^2) m (n^2)+16 (a^2) (b^4) (c^2) m (n^2)+16 (a^4) (c^4) m (n^2)-8 (a^2) (b^2) (c^4) m (n^2)-8 (a^2) (c^6) m (n^2)) (y^2)+(-12 (a^8) (l^2) m+30 (a^6) (b^2) (l^2) m-18 (a^4) (b^4) (l^2) m-6 (a^2) (b^6) (l^2) m+6 (b^8) (l^2) m+2 (a^6) (c^2) (l^2) m-24 (a^4) (b^2) (c^2) (l^2) m+42 (a^2) (b^4) (c^2) (l^2) m-20 (b^6) (c^2) (l^2) m+10 (a^4) (c^4) (l^2) m-34 (a^2) (b^2) (c^4) (l^2) m+24 (b^4) (c^4) (l^2) m-2 (a^2) (c^6) (l^2) m-12 (b^2) (c^6) (l^2) m+2 (c^8) (l^2) m+12 (a^8) l (m^2)-30 (a^6) (b^2) l (m^2)+18 (a^4) (b^4) l (m^2)+6 (a^2) (b^6) l (m^2)-6 (b^8) l (m^2)-16 (a^6) (c^2) l (m^2)+42 (a^4) (b^2) (c^2) l (m^2)-36 (a^2) (b^4) (c^2) l (m^2)+10 (b^6) (c^2) l (m^2)-12 (a^4) (c^4) l (m^2)-26 (a^2) (b^2) (c^4) l (m^2)-10 (b^4) (c^4) l (m^2)+24 (a^2) (c^6) l (m^2)+14 (b^2) (c^6) l (m^2)-8 (c^8) l (m^2)+12 (a^8) (l^2) n-20 (a^6) (b^2) (l^2) n+12 (a^2) (b^6) (l^2) n-4 (b^8) (l^2) n-12 (a^6) (c^2) (l^2) n+44 (a^4) (b^2) (c^2) (l^2) n-44 (a^2) (b^4) (c^2) (l^2) n+12 (b^6) (c^2) (l^2) n-12 (a^4) (c^4) (l^2) n+20 (a^2) (b^2) (c^4) (l^2) n-12 (b^4) (c^4) (l^2) n+12 (a^2) (c^6) (l^2) n+4 (b^2) (c^6) (l^2) n-7 (a^8) l m n-4 (a^6) (b^2) l m n+30 (a^4) (b^4) l m n-20 (a^2) (b^6) l m n+(b^8) l m n+40 (a^6) (c^2) l m n-76 (a^4) (b^2) (c^2) l m n+16 (a^2) (b^4) (c^2) l m n+20 (b^6) (c^2) l m n-2 (a^4) (c^4) l m n+108 (a^2) (b^2) (c^4) l m n-34 (b^4) (c^4) l m n-40 (a^2) (c^6) l m n+4 (b^2) (c^6) l m n+9 (c^8) l m n-5 (a^8) (m^2) n+24 (a^6) (b^2) (m^2) n-30 (a^4) (b^4) (m^2) n+8 (a^2) (b^6) (m^2) n+3 (b^8) (m^2) n-4 (a^4) (b^2) (c^2) (m^2) n+16 (a^2) (b^4) (c^2) (m^2) n-12 (b^6) (c^2) (m^2) n+18 (a^4) (c^4) (m^2) n-8 (a^2) (b^2) (c^4) (m^2) n+18 (b^4) (c^4) (m^2) n-16 (a^2) (c^6) (m^2) n-12 (b^2) (c^6) (m^2) n+3 (c^8) (m^2) n-5 (a^8) l (n^2)+14 (a^6) (b^2) l (n^2)-12 (a^4) (b^4) l (n^2)+2 (a^2) (b^6) l (n^2)+(b^8) l (n^2)-4 (a^6) (c^2) l (n^2)-6 (a^4) (b^2) (c^2) l (n^2)+24 (a^2) (b^4) (c^2) l (n^2)-14 (b^6) (c^2) l (n^2)+18 (a^4) (c^4) l (n^2)-54 (a^2) (b^2) (c^4) l (n^2)+20 (b^4) (c^4) l (n^2)-4 (a^2) (c^6) l (n^2)-2 (b^2) (c^6) l (n^2)-5 (c^8) l (n^2)+5 (a^8) m (n^2)-14 (a^6) (b^2) m (n^2)+12 (a^4) (b^4) m (n^2)-2 (a^2) (b^6) m (n^2)-(b^8) m (n^2)-10 (a^6) (c^2) m (n^2)+24 (a^4) (b^2) (c^2) m (n^2)-18 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)-20 (a^4) (c^4) m (n^2)-6 (a^2) (b^2) (c^4) m (n^2)-6 (b^4) (c^4) m (n^2)+26 (a^2) (c^6) m (n^2)+4 (b^2) (c^6) m (n^2)-(c^8) m (n^2)) y z+(-2 (a^8) (l^2) m+8 (a^6) (b^2) (l^2) m-12 (a^4) (b^4) (l^2) m+8 (a^2) (b^6) (l^2) m-2 (b^8) (l^2) m-14 (a^6) (c^2) (l^2) m+34 (a^4) (b^2) (c^2) (l^2) m-26 (a^2) (b^4) (c^2) (l^2) m+6 (b^6) (c^2) (l^2) m+10 (a^4) (c^4) (l^2) m+12 (a^2) (b^2) (c^4) (l^2) m-6 (b^4) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m+2 (b^2) (c^6) (l^2) m+2 (a^8) l (m^2)-8 (a^6) (b^2) l (m^2)+12 (a^4) (b^4) l (m^2)-8 (a^2) (b^6) l (m^2)+2 (b^8) l (m^2)+12 (a^6) (c^2) l (m^2)-28 (a^4) (b^2) (c^2) l (m^2)+20 (a^2) (b^4) (c^2) l (m^2)-4 (b^6) (c^2) l (m^2)-24 (a^4) (c^4) l (m^2)+8 (b^4) (c^4) l (m^2)+4 (a^2) (c^6) l (m^2)-12 (b^2) (c^6) l (m^2)+6 (c^8) l (m^2)+5 (a^8) (l^2) n-16 (a^6) (b^2) (l^2) n+18 (a^4) (b^4) (l^2) n-8 (a^2) (b^6) (l^2) n+(b^8) (l^2) n+22 (a^6) (c^2) (l^2) n-38 (a^4) (b^2) (c^2) (l^2) n+18 (a^2) (b^4) (c^2) (l^2) n-2 (b^6) (c^2) (l^2) n-12 (a^4) (c^4) (l^2) n+4 (a^2) (b^2) (c^4) (l^2) n-14 (a^2) (c^6) (l^2) n+2 (b^2) (c^6) (l^2) n-(c^8) (l^2) n-7 (a^8) l m n+20 (a^6) (b^2) l m n-18 (a^4) (b^4) l m n+4 (a^2) (b^6) l m n+(b^8) l m n-14 (a^6) (c^2) l m n+2 (a^4) (b^2) (c^2) l m n+22 (a^2) (b^4) (c^2) l m n-10 (b^6) (c^2) l m n+40 (a^4) (c^4) l m n-48 (a^2) (b^2) (c^4) l m n+8 (b^4) (c^4) l m n-10 (a^2) (c^6) l m n+10 (b^2) (c^6) l m n-9 (c^8) l m n+2 (a^8) (m^2) n-4 (a^6) (b^2) (m^2) n+4 (a^2) (b^6) (m^2) n-2 (b^8) (m^2) n-4 (a^6) (c^2) (m^2) n+24 (a^4) (b^2) (c^2) (m^2) n-28 (a^2) (b^4) (c^2) (m^2) n+8 (b^6) (c^2) (m^2) n+20 (a^2) (b^2) (c^4) (m^2) n-12 (b^4) (c^4) (m^2) n+4 (a^2) (c^6) (m^2) n+8 (b^2) (c^6) (m^2) n-2 (c^8) (m^2) n-(a^8) l (n^2)+4 (a^6) (b^2) l (n^2)-6 (a^4) (b^4) l (n^2)+4 (a^2) (b^6) l (n^2)-(b^8) l (n^2)-14 (a^6) (c^2) l (n^2)+34 (a^4) (b^2) (c^2) l (n^2)-26 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)-12 (a^4) (c^4) l (n^2)+16 (a^2) (b^2) (c^4) l (n^2)-4 (b^4) (c^4) l (n^2)+22 (a^2) (c^6) l (n^2)-6 (b^2) (c^6) l (n^2)+5 (c^8) l (n^2)+(a^8) m (n^2)-4 (a^6) (b^2) m (n^2)+6 (a^4) (b^4) m (n^2)-4 (a^2) (b^6) m (n^2)+(b^8) m (n^2)+12 (a^6) (c^2) m (n^2)-28 (a^4) (b^2) (c^2) m (n^2)+20 (a^2) (b^4) (c^2) m (n^2)-4 (b^6) (c^2) m (n^2)-2 (a^4) (c^4) m (n^2)-4 (a^2) (b^2) (c^4) m (n^2)+6 (b^4) (c^4) m (n^2)-12 (a^2) (c^6) m (n^2)-4 (b^2) (c^6) m (n^2)+(c^8) m (n^2)) (z^2))+x ((8 (a^6) (b^2) (l^2) m-8 (a^4) (b^4) (l^2) m-8 (a^2) (b^6) (l^2) m+8 (b^8) (l^2) m+2 (a^6) (c^2) (l^2) m+2 (a^4) (b^2) (c^2) (l^2) m+14 (a^2) (b^4) (c^2) (l^2) m-18 (b^6) (c^2) (l^2) m-6 (a^4) (c^4) (l^2) m-12 (a^2) (b^2) (c^4) (l^2) m+10 (b^4) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m+2 (b^2) (c^6) (l^2) m-2 (c^8) (l^2) m-8 (a^6) (b^2) l (m^2)+8 (a^4) (b^4) l (m^2)+8 (a^2) (b^6) l (m^2)-8 (b^8) l (m^2)+16 (a^4) (b^2) (c^2) l (m^2)-24 (a^2) (b^4) (c^2) l (m^2)+8 (b^6) (c^2) l (m^2)-8 (a^2) (b^2) (c^4) l (m^2)+(a^8) (l^2) n-2 (a^6) (b^2) (l^2) n-4 (a^4) (b^4) (l^2) n+10 (a^2) (b^6) (l^2) n-5 (b^8) (l^2) n-4 (a^6) (c^2) (l^2) n+2 (a^4) (b^2) (c^2) (l^2) n-8 (a^2) (b^4) (c^2) (l^2) n+10 (b^6) (c^2) (l^2) n+6 (a^4) (c^4) (l^2) n+2 (a^2) (b^2) (c^4) (l^2) n-4 (b^4) (c^4) (l^2) n-4 (a^2) (c^6) (l^2) n-2 (b^2) (c^6) (l^2) n+(c^8) (l^2) n-(a^8) l m n-4 (a^6) (b^2) l m n+10 (a^4) (b^4) l m n-4 (a^2) (b^6) l m n-(b^8) l m n-28 (a^4) (b^2) (c^2) l m n+8 (a^2) (b^4) (c^2) l m n+20 (b^6) (c^2) l m n+6 (a^4) (c^4) l m n+36 (a^2) (b^2) (c^4) l m n-18 (b^4) (c^4) l m n-8 (a^2) (c^6) l m n-4 (b^2) (c^6) l m n+3 (c^8) l m n+6 (a^6) (b^2) (m^2) n-6 (a^4) (b^4) (m^2) n-6 (a^2) (b^6) (m^2) n+6 (b^8) (m^2) n-10 (a^4) (b^2) (c^2) (m^2) n+20 (a^2) (b^4) (c^2) (m^2) n-10 (b^6) (c^2) (m^2) n+2 (a^2) (b^2) (c^4) (m^2) n+2 (b^4) (c^4) (m^2) n+2 (b^2) (c^6) (m^2) n-(a^8) l (n^2)+6 (a^4) (b^4) l (n^2)-8 (a^2) (b^6) l (n^2)+3 (b^8) l (n^2)+4 (a^6) (c^2) l (n^2)+4 (a^4) (b^2) (c^2) l (n^2)+4 (a^2) (b^4) (c^2) l (n^2)-12 (b^6) (c^2) l (n^2)-6 (a^4) (c^4) l (n^2)-8 (a^2) (b^2) (c^4) l (n^2)+6 (b^4) (c^4) l (n^2)+4 (a^2) (c^6) l (n^2)+4 (b^2) (c^6) l (n^2)-(c^8) l (n^2)+(a^8) m (n^2)-6 (a^4) (b^4) m (n^2)+8 (a^2) (b^6) m (n^2)-3 (b^8) m (n^2)-2 (a^6) (c^2) m (n^2)+14 (a^4) (b^2) (c^2) m (n^2)-14 (a^2) (b^4) (c^2) m (n^2)+2 (b^6) (c^2) m (n^2)-12 (a^2) (b^2) (c^4) m (n^2)+4 (b^4) (c^4) m (n^2)+2 (a^2) (c^6) m (n^2)-2 (b^2) (c^6) m (n^2)-(c^8) m (n^2)) (y^3)+(6 (a^8) (l^2) m-6 (a^6) (b^2) (l^2) m-18 (a^4) (b^4) (l^2) m+30 (a^2) (b^6) (l^2) m-12 (b^8) (l^2) m-10 (a^6) (c^2) (l^2) m+36 (a^4) (b^2) (c^2) (l^2) m-42 (a^2) (b^4) (c^2) (l^2) m+16 (b^6) (c^2) (l^2) m+10 (a^4) (c^4) (l^2) m+26 (a^2) (b^2) (c^4) (l^2) m+12 (b^4) (c^4) (l^2) m-14 (a^2) (c^6) (l^2) m-24 (b^2) (c^6) (l^2) m+8 (c^8) (l^2) m-6 (a^8) l (m^2)+6 (a^6) (b^2) l (m^2)+18 (a^4) (b^4) l (m^2)-30 (a^2) (b^6) l (m^2)+12 (b^8) l (m^2)+20 (a^6) (c^2) l (m^2)-42 (a^4) (b^2) (c^2) l (m^2)+24 (a^2) (b^4) (c^2) l (m^2)-2 (b^6) (c^2) l (m^2)-24 (a^4) (c^4) l (m^2)+34 (a^2) (b^2) (c^4) l (m^2)-10 (b^4) (c^4) l (m^2)+12 (a^2) (c^6) l (m^2)+2 (b^2) (c^6) l (m^2)-2 (c^8) l (m^2)-3 (a^8) (l^2) n-8 (a^6) (b^2) (l^2) n+30 (a^4) (b^4) (l^2) n-24 (a^2) (b^6) (l^2) n+5 (b^8) (l^2) n+12 (a^6) (c^2) (l^2) n-16 (a^4) (b^2) (c^2) (l^2) n+4 (a^2) (b^4) (c^2) (l^2) n-18 (a^4) (c^4) (l^2) n+8 (a^2) (b^2) (c^4) (l^2) n-18 (b^4) (c^4) (l^2) n+12 (a^2) (c^6) (l^2) n+16 (b^2) (c^6) (l^2) n-3 (c^8) (l^2) n-(a^8) l m n+20 (a^6) (b^2) l m n-30 (a^4) (b^4) l m n+4 (a^2) (b^6) l m n+7 (b^8) l m n-20 (a^6) (c^2) l m n-16 (a^4) (b^2) (c^2) l m n+76 (a^2) (b^4) (c^2) l m n-40 (b^6) (c^2) l m n+34 (a^4) (c^4) l m n-108 (a^2) (b^2) (c^4) l m n+2 (b^4) (c^4) l m n-4 (a^2) (c^6) l m n+40 (b^2) (c^6) l m n-9 (c^8) l m n+4 (a^8) (m^2) n-12 (a^6) (b^2) (m^2) n+20 (a^2) (b^6) (m^2) n-12 (b^8) (m^2) n-12 (a^6) (c^2) (m^2) n+44 (a^4) (b^2) (c^2) (m^2) n-44 (a^2) (b^4) (c^2) (m^2) n+12 (b^6) (c^2) (m^2) n+12 (a^4) (c^4) (m^2) n-20 (a^2) (b^2) (c^4) (m^2) n+12 (b^4) (c^4) (m^2) n-4 (a^2) (c^6) (m^2) n-12 (b^2) (c^6) (m^2) n+(a^8) l (n^2)+2 (a^6) (b^2) l (n^2)-12 (a^4) (b^4) l (n^2)+14 (a^2) (b^6) l (n^2)-5 (b^8) l (n^2)-4 (a^6) (c^2) l (n^2)+18 (a^4) (b^2) (c^2) l (n^2)-24 (a^2) (b^4) (c^2) l (n^2)+10 (b^6) (c^2) l (n^2)+6 (a^4) (c^4) l (n^2)+6 (a^2) (b^2) (c^4) l (n^2)+20 (b^4) (c^4) l (n^2)-4 (a^2) (c^6) l (n^2)-26 (b^2) (c^6) l (n^2)+(c^8) l (n^2)-(a^8) m (n^2)-2 (a^6) (b^2) m (n^2)+12 (a^4) (b^4) m (n^2)-14 (a^2) (b^6) m (n^2)+5 (b^8) m (n^2)+14 (a^6) (c^2) m (n^2)-24 (a^4) (b^2) (c^2) m (n^2)+6 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)-20 (a^4) (c^4) m (n^2)+54 (a^2) (b^2) (c^4) m (n^2)-18 (b^4) (c^4) m (n^2)+2 (a^2) (c^6) m (n^2)+4 (b^2) (c^6) m (n^2)+5 (c^8) m (n^2)) (y^2) z+(4 (a^8) (l^2) m-16 (a^6) (b^2) (l^2) m+24 (a^4) (b^4) (l^2) m-16 (a^2) (b^6) (l^2) m+4 (b^8) (l^2) m+10 (a^6) (c^2) (l^2) m-14 (a^4) (b^2) (c^2) (l^2) m-2 (a^2) (b^4) (c^2) (l^2) m+6 (b^6) (c^2) (l^2) m-14 (a^4) (c^4) (l^2) m+12 (a^2) (b^2) (c^4) (l^2) m-30 (b^4) (c^4) (l^2) m+6 (a^2) (c^6) (l^2) m+26 (b^2) (c^6) (l^2) m-6 (c^8) (l^2) m-4 (a^8) l (m^2)+16 (a^6) (b^2) l (m^2)-24 (a^4) (b^4) l (m^2)+16 (a^2) (b^6) l (m^2)-4 (b^8) l (m^2)-6 (a^6) (c^2) l (m^2)+2 (a^4) (b^2) (c^2) l (m^2)+14 (a^2) (b^4) (c^2) l (m^2)-10 (b^6) (c^2) l (m^2)+30 (a^4) (c^4) l (m^2)-12 (a^2) (b^2) (c^4) l (m^2)+14 (b^4) (c^4) l (m^2)-26 (a^2) (c^6) l (m^2)-6 (b^2) (c^6) l (m^2)+6 (c^8) l (m^2)-7 (a^8) (l^2) n+20 (a^6) (b^2) (l^2) n-18 (a^4) (b^4) (l^2) n+4 (a^2) (b^6) (l^2) n+(b^8) (l^2) n-2 (a^6) (c^2) (l^2) n-26 (a^4) (b^2) (c^2) (l^2) n+42 (a^2) (b^4) (c^2) (l^2) n-14 (b^6) (c^2) (l^2) n+24 (a^4) (c^4) (l^2) n-32 (a^2) (b^2) (c^4) (l^2) n+24 (b^4) (c^4) (l^2) n-14 (a^2) (c^6) (l^2) n-10 (b^2) (c^6) (l^2) n-(c^8) (l^2) n+8 (a^8) l m n-16 (a^6) (b^2) l m n+16 (a^2) (b^6) l m n-8 (b^8) l m n-20 (a^6) (c^2) l m n+92 (a^4) (b^2) (c^2) l m n-92 (a^2) (b^4) (c^2) l m n+20 (b^6) (c^2) l m n-32 (a^4) (c^4) l m n+32 (b^4) (c^4) l m n+44 (a^2) (c^6) l m n-44 (b^2) (c^6) l m n-(a^8) (m^2) n-4 (a^6) (b^2) (m^2) n+18 (a^4) (b^4) (m^2) n-20 (a^2) (b^6) (m^2) n+7 (b^8) (m^2) n+14 (a^6) (c^2) (m^2) n-42 (a^4) (b^2) (c^2) (m^2) n+26 (a^2) (b^4) (c^2) (m^2) n+2 (b^6) (c^2) (m^2) n-24 (a^4) (c^4) (m^2) n+32 (a^2) (b^2) (c^4) (m^2) n-24 (b^4) (c^4) (m^2) n+10 (a^2) (c^6) (m^2) n+14 (b^2) (c^6) (m^2) n+(c^8) (m^2) n+2 (a^8) l (n^2)-8 (a^6) (b^2) l (n^2)+12 (a^4) (b^4) l (n^2)-8 (a^2) (b^6) l (n^2)+2 (b^8) l (n^2)+10 (a^6) (c^2) l (n^2)-14 (a^4) (b^2) (c^2) l (n^2)-2 (a^2) (b^4) (c^2) l (n^2)+6 (b^6) (c^2) l (n^2)-18 (a^4) (c^4) l (n^2)+52 (a^2) (b^2) (c^4) l (n^2)-34 (b^4) (c^4) l (n^2)-2 (a^2) (c^6) l (n^2)+18 (b^2) (c^6) l (n^2)+8 (c^8) l (n^2)-2 (a^8) m (n^2)+8 (a^6) (b^2) m (n^2)-12 (a^4) (b^4) m (n^2)+8 (a^2) (b^6) m (n^2)-2 (b^8) m (n^2)-6 (a^6) (c^2) m (n^2)+2 (a^4) (b^2) (c^2) m (n^2)+14 (a^2) (b^4) (c^2) m (n^2)-10 (b^6) (c^2) m (n^2)+34 (a^4) (c^4) m (n^2)-52 (a^2) (b^2) (c^4) m (n^2)+18 (b^4) (c^4) m (n^2)-18 (a^2) (c^6) m (n^2)+2 (b^2) (c^6) m (n^2)-8 (c^8) m (n^2)) y (z^2)+(4 (a^6) (c^2) (l^2) m-12 (a^4) (b^2) (c^2) (l^2) m+12 (a^2) (b^4) (c^2) (l^2) m-4 (b^6) (c^2) (l^2) m-8 (a^2) (b^2) (c^4) (l^2) m+8 (b^4) (c^4) (l^2) m-4 (a^2) (c^6) (l^2) m-4 (b^2) (c^6) (l^2) m-4 (a^6) (c^2) l (m^2)+12 (a^4) (b^2) (c^2) l (m^2)-12 (a^2) (b^4) (c^2) l (m^2)+4 (b^6) (c^2) l (m^2)+4 (a^4) (c^4) l (m^2)-4 (b^4) (c^4) l (m^2)+4 (a^2) (c^6) l (m^2)+4 (b^2) (c^6) l (m^2)-4 (c^8) l (m^2)-(a^8) (l^2) n+4 (a^6) (b^2) (l^2) n-6 (a^4) (b^4) (l^2) n+4 (a^2) (b^6) (l^2) n-(b^8) (l^2) n-12 (a^6) (c^2) (l^2) n+28 (a^4) (b^2) (c^2) (l^2) n-20 (a^2) (b^4) (c^2) (l^2) n+4 (b^6) (c^2) (l^2) n-2 (a^4) (c^4) (l^2) n+4 (a^2) (b^2) (c^4) (l^2) n-2 (b^4) (c^4) (l^2) n+12 (a^2) (c^6) (l^2) n-4 (b^2) (c^6) (l^2) n+3 (c^8) (l^2) n+2 (a^8) l m n-8 (a^6) (b^2) l m n+12 (a^4) (b^4) l m n-8 (a^2) (b^6) l m n+2 (b^8) l m n+16 (a^6) (c^2) l m n-32 (a^4) (b^2) (c^2) l m n+16 (a^2) (b^4) (c^2) l m n-16 (a^4) (c^4) l m n+32 (a^2) (b^2) (c^4) l m n-16 (b^4) (c^4) l m n-8 (a^2) (c^6) l m n+8 (b^2) (c^6) l m n+6 (c^8) l m n-(a^8) (m^2) n+4 (a^6) (b^2) (m^2) n-6 (a^4) (b^4) (m^2) n+4 (a^2) (b^6) (m^2) n-(b^8) (m^2) n-4 (a^6) (c^2) (m^2) n+4 (a^4) (b^2) (c^2) (m^2) n+4 (a^2) (b^4) (c^2) (m^2) n-4 (b^6) (c^2) (m^2) n+10 (a^4) (c^4) (m^2) n-20 (a^2) (b^2) (c^4) (m^2) n+10 (b^4) (c^4) (m^2) n-4 (a^2) (c^6) (m^2) n-4 (b^2) (c^6) (m^2) n-(c^8) (m^2) n+4 (a^6) (c^2) l (n^2)-12 (a^4) (b^2) (c^2) l (n^2)+12 (a^2) (b^4) (c^2) l (n^2)-4 (b^6) (c^2) l (n^2)+16 (a^4) (c^4) l (n^2)-24 (a^2) (b^2) (c^4) l (n^2)+8 (b^4) (c^4) l (n^2)-12 (a^2) (c^6) l (n^2)+4 (b^2) (c^6) l (n^2)-8 (c^8) l (n^2)-4 (a^6) (c^2) m (n^2)+12 (a^4) (b^2) (c^2) m (n^2)-12 (a^2) (b^4) (c^2) m (n^2)+4 (b^6) (c^2) m (n^2)-12 (a^4) (c^4) m (n^2)+16 (a^2) (b^2) (c^4) m (n^2)-4 (b^4) (c^4) m (n^2)+12 (a^2) (c^6) m (n^2)-4 (b^2) (c^6) m (n^2)+4 (c^8) m (n^2)) (z^3))};(* QL-Tf5:QL-Orthopole *)
QLTf5[{x_,y_,z_}]:={2 (a^2) ((a^2)-(b^2)-(c^2)) l (m-n) (x^2)-2 (b^2) (-(a^2)+(b^2)+(c^2)) l (m-n) (y^2)+((a^4)-2 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)+6 (b^2) (c^2)+(c^4)) l (m-n) y z-2 (c^2) (-(a^2)+(b^2)+(c^2)) l (m-n) (z^2)+x ((-2 (a^4) l m+2 (b^4) l m+4 (a^2) (c^2) l m-2 (c^4) l m+(a^4) l n+2 (a^2) (b^2) l n-3 (b^4) l n-2 (a^2) (c^2) l n+2 (b^2) (c^2) l n+(c^4) l n+(a^4) m n-2 (a^2) (b^2) m n+(b^4) m n-2 (a^2) (c^2) m n-2 (b^2) (c^2) m n+(c^4) m n) y+(-(a^4) l m+2 (a^2) (b^2) l m-(b^4) l m-2 (a^2) (c^2) l m-2 (b^2) (c^2) l m+3 (c^4) l m+2 (a^4) l n-4 (a^2) (b^2) l n+2 (b^4) l n-2 (c^4) l n-(a^4) m n+2 (a^2) (b^2) m n-(b^4) m n+2 (a^2) (c^2) m n+2 (b^2) (c^2) m n-(c^4) m n) z),2 (a^2) ((a^2)-(b^2)+(c^2)) m (l-n) (x^2)-2 (b^2) (-(a^2)+(b^2)-(c^2)) m (l-n) (y^2)+((a^4) l m-2 (a^2) (b^2) l m+(b^4) l m+2 (a^2) (c^2) l m+2 (b^2) (c^2) l m-3 (c^4) l m+(a^4) l n-2 (a^2) (b^2) l n+(b^4) l n-2 (a^2) (c^2) l n-2 (b^2) (c^2) l n+(c^4) l n-2 (a^4) m n+4 (a^2) (b^2) m n-2 (b^4) m n+2 (c^4) m n) y z+2 (c^2) ((a^2)-(b^2)+(c^2)) m (l-n) (z^2)+x ((-2 (a^4) l m+2 (b^4) l m-4 (b^2) (c^2) l m+2 (c^4) l m-(a^4) l n+2 (a^2) (b^2) l n-(b^4) l n+2 (a^2) (c^2) l n+2 (b^2) (c^2) l n-(c^4) l n+3 (a^4) m n-2 (a^2) (b^2) m n-(b^4) m n-2 (a^2) (c^2) m n+2 (b^2) (c^2) m n-(c^4) m n) y-((a^4)-2 (a^2) (b^2)+(b^4)+6 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)) m (l-n) z),-2 (a^2) ((a^2)+(b^2)-(c^2)) (l-m) n (x^2)-2 (b^2) ((a^2)+(b^2)-(c^2)) (l-m) n (y^2)+(-(a^4) l m+2 (a^2) (b^2) l m-(b^4) l m+2 (a^2) (c^2) l m+2 (b^2) (c^2) l m-(c^4) l m-(a^4) l n-2 (a^2) (b^2) l n+3 (b^4) l n+2 (a^2) (c^2) l n-2 (b^2) (c^2) l n-(c^4) l n+2 (a^4) m n-2 (b^4) m n-4 (a^2) (c^2) m n+2 (c^4) m n) y z+2 (c^2) (-(a^2)-(b^2)+(c^2)) (l-m) n (z^2)+x (((a^4)+6 (a^2) (b^2)+(b^4)-2 (a^2) (c^2)-2 (b^2) (c^2)+(c^4)) (l-m) n y+((a^4) l m-2 (a^2) (b^2) l m+(b^4) l m-2 (a^2) (c^2) l m-2 (b^2) (c^2) l m+(c^4) l m+2 (a^4) l n-2 (b^4) l n+4 (b^2) (c^2) l n-2 (c^4) l n-3 (a^4) m n+2 (a^2) (b^2) m n+(b^4) m n+2 (a^2) (c^2) m n-2 (b^2) (c^2) m n+(c^4) m n) z)}   (* QL-Tf5:QL-Orthopolar Line *)
QLTf6[{x_,y_,z_}]:={y z (2 l x+m y+n z),x z (l x+2 m y+n z),x y (l x+m y+2 n z)}   (* QL-Tf6:QL-Trilinear Polar *)
QLTf7[{x_,y_,z_}]:={l y z (-n y+m z),m x z (n x-l z),n x y (-m x+l y)}   (* QL-Tf7: QL-5th Line point of tangency *)
QLTf8[{x_,y_,z_}]:={y z (2 (l^2) m x+2 (l^2) n x-2 l m n x+l (m^2) y+l m n y-3 (m^2) n y+l m n z+l (n^2) z-3 m (n^2) z),x z ((l^2) m x-3 (l^2) n x+l m n x+2 l (m^2) y-2 l m n y+2 (m^2) n y+l m n z-3 l (n^2) z+m (n^2) z),-x y (3 (l^2) m x-(l^2) n x-l m n x+3 l (m^2) y-l m n y-(m^2) n y+2 l m n z-2 l (n^2) z-2 m (n^2) z)}   (* QL-Tf8:QL-Involution Centerline *)
QLTf9[{x_,y_,z_}]:={m n x (-l (m^2) n (x^2)-l m (n^2) (x^2)+3 (m^2) (n^2) (x^2)+(l^2) m n x y+(l^2) (n^2) x y-3 l m (n^2) x y+(l^2) (m^2) x z+(l^2) m n x z-3 l (m^2) n x z-2 (l^3) m y z-2 (l^3) n y z+2 (l^2) m n y z),l n y (l (m^2) n x y-3 l m (n^2) x y+(m^2) (n^2) x y-(l^2) m n (y^2)+3 (l^2) (n^2) (y^2)-l m (n^2) (y^2)-2 l (m^3) x z+2 l (m^2) n x z-2 (m^3) n x z+(l^2) (m^2) y z-3 (l^2) m n y z+l (m^2) n y z),l m z (2 l m (n^2) x y-2 l (n^3) x y-2 m (n^3) x y-3 l (m^2) n x z+l m (n^2) x z+(m^2) (n^2) x z-3 (l^2) m n y z+(l^2) (n^2) y z+l m (n^2) y z+3 (l^2) (m^2) (z^2)-(l^2) m n (z^2)-l (m^2) n (z^2))}   (* QL-Tf9:QL-Involutary Centerline at the 5th Line point of tangency *)
QLTf10[{x_,y_,z_}]:={m n (3 m n x-l n y-l m z),l n (-m n x+3 l n y-l m z),l m (-m n x-l n y+3 l m z)}   (* QL-Tf10:QL-QuadriPole *)
QLTf11[{x_,y_,z_}]:={l (2 l x+m y+n z),m (l x+2 m y+n z),n (l x+m y+2 n z)}   (* QL-Tf11:QL-QuadriPolar *)

QL - Circles and Conics and Cubics and Quartics

QLCi1=-(l^2) (l m+l n-m n) ((b^2) (m^2)+(a^2) m n-(b^2) m n-(c^2) m n+(c^2) (n^2)) (x^2)-l m ((a^2) (l^2) (m^2)+(b^2) (l^2) (m^2)-(c^2) (l^2) (m^2)+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)+(c^2) (l^2) (n^2)-(a^2) (m^2) (n^2)+(b^2) (m^2) (n^2)+(c^2) (m^2) (n^2)) x y-(m^2) (l m-l n+m n) ((a^2) (l^2)-(a^2) l n+(b^2) l n-(c^2) l n+(c^2) (n^2)) (y^2)+l n (-(a^2) (l^2) (m^2)-(b^2) (l^2) (m^2)+(c^2) (l^2) (m^2)-(a^2) (l^2) (n^2)+(b^2) (l^2) (n^2)-(c^2) (l^2) (n^2)+(a^2) (m^2) (n^2)-(b^2) (m^2) (n^2)-(c^2) (m^2) (n^2)) x z-m n ((a^2) (l^2) (m^2)+(b^2) (l^2) (m^2)-(c^2) (l^2) (m^2)+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)+(c^2) (l^2) (n^2)-(a^2) (m^2) (n^2)+(b^2) (m^2) (n^2)+(c^2) (m^2) (n^2)) y z+((a^2) (l^2)-(a^2) l m-(b^2) l m+(c^2) l m+(b^2) (m^2)) (n^2) (l m-l n-m n) (z^2); (* Circumcircle QL-Diagonal Triangle *)
QLCi2=-(l^3) (m-n) (b m-c n) (b m+c n) (x^2)-l m ((a^2) (l^2) (m^2)+(b^2) (l^2) (m^2)-(c^2) (l^2) (m^2)-(b^2) (l^2) m n+(c^2) (l^2) m n-(a^2) l (m^2) n+(c^2) l (m^2) n-2 (c^2) l m (n^2)+(c^2) l (n^3)+(c^2) m (n^3)) x y-(m^3) (l-n) (a l-c n) (a l+c n) (y^2)-l n ((b^2) l (m^3)+(b^2) (l^2) m n-(c^2) (l^2) m n-2 (b^2) l (m^2) n+(b^2) (m^3) n+(a^2) (l^2) (n^2)-(b^2) (l^2) (n^2)+(c^2) (l^2) (n^2)-(a^2) l m (n^2)+(b^2) l m (n^2)) x z-m n ((a^2) (l^3) m+(a^2) (l^3) n-2 (a^2) (l^2) m n+(a^2) l (m^2) n-(c^2) l (m^2) n+(a^2) l m (n^2)-(b^2) l m (n^2)-(a^2) (m^2) (n^2)+(b^2) (m^2) (n^2)+(c^2) (m^2) (n^2)) y z-(l-m) (a l-b m) (a l+b m) (n^3) (z^2); (* Medial Circle QL-Diagonal Triangle *)
QLCi3=-(b^2) (c^2) l (m-n) (-2 (a^2) l+(a^2) m+(b^2) m-(c^2) m+(a^2) n-(b^2) n+(c^2) n) (x^2)+(c^2) (2 (a^4) (l^2) m+(a^2) (b^2) (l^2) m+(b^4) (l^2) m-3 (a^2) (c^2) (l^2) m-2 (b^2) (c^2) (l^2) m+(c^4) (l^2) m-(a^4) l (m^2)-(a^2) (b^2) l (m^2)-2 (b^4) l (m^2)+2 (a^2) (c^2) l (m^2)+3 (b^2) (c^2) l (m^2)-(c^4) l (m^2)-(a^4) (l^2) n-(b^4) (l^2) n+2 (a^2) (c^2) (l^2) n+2 (b^2) (c^2) (l^2) n-(c^4) (l^2) n-2 (a^4) l m n+2 (b^4) l m n+2 (a^2) (c^2) l m n-2 (b^2) (c^2) l m n+(a^4) (m^2) n+(b^4) (m^2) n-2 (a^2) (c^2) (m^2) n-2 (b^2) (c^2) (m^2) n+(c^4) (m^2) n+(a^4) l (n^2)-(a^2) (b^2) l (n^2)-2 (a^2) (c^2) l (n^2)-(b^2) (c^2) l (n^2)+(c^4) l (n^2)+(a^2) (b^2) m (n^2)-(b^4) m (n^2)+(a^2) (c^2) m (n^2)+2 (b^2) (c^2) m (n^2)-(c^4) m (n^2)) x y+(a^2) (c^2) m (l-n) ((a^2) l+(b^2) l-(c^2) l-2 (b^2) m-(a^2) n+(b^2) n+(c^2) n) (y^2)+(b^2) ((a^4) (l^2) m-2 (a^2) (b^2) (l^2) m+(b^4) (l^2) m-2 (b^2) (c^2) (l^2) m+(c^4) (l^2) m-(a^4) l (m^2)+2 (a^2) (b^2) l (m^2)-(b^4) l (m^2)+(a^2) (c^2) l (m^2)+(b^2) (c^2) l (m^2)-2 (a^4) (l^2) n+3 (a^2) (b^2) (l^2) n-(b^4) (l^2) n-(a^2) (c^2) (l^2) n+2 (b^2) (c^2) (l^2) n-(c^4) (l^2) n+2 (a^4) l m n-2 (a^2) (b^2) l m n+2 (b^2) (c^2) l m n-2 (c^4) l m n-(a^2) (b^2) (m^2) n+(b^4) (m^2) n-(a^2) (c^2) (m^2) n-2 (b^2) (c^2) (m^2) n+(c^4) (m^2) n+(a^4) l (n^2)-2 (a^2) (b^2) l (n^2)+(b^4) l (n^2)+(a^2) (c^2) l (n^2)-3 (b^2) (c^2) l (n^2)+2 (c^4) l (n^2)-(a^4) m (n^2)+2 (a^2) (b^2) m (n^2)-(b^4) m (n^2)+2 (b^2) (c^2) m (n^2)-(c^4) m (n^2)) x z+(a^2) ((a^4) (l^2) m-2 (a^2) (b^2) (l^2) m+(b^4) (l^2) m-(a^2) (c^2) (l^2) m-(b^2) (c^2) (l^2) m-(a^4) l (m^2)+2 (a^2) (b^2) l (m^2)-(b^4) l (m^2)+2 (a^2) (c^2) l (m^2)-(c^4) l (m^2)-(a^4) (l^2) n+(a^2) (b^2) (l^2) n+2 (a^2) (c^2) (l^2) n+(b^2) (c^2) (l^2) n-(c^4) (l^2) n+2 (a^2) (b^2) l m n-2 (b^4) l m n-2 (a^2) (c^2) l m n+2 (c^4) l m n+(a^4) (m^2) n-3 (a^2) (b^2) (m^2) n+2 (b^4) (m^2) n-2 (a^2) (c^2) (m^2) n+(b^2) (c^2) (m^2) n+(c^4) (m^2) n+(a^4) l (n^2)-2 (a^2) (b^2) l (n^2)+(b^4) l (n^2)-2 (a^2) (c^2) l (n^2)+(c^4) l (n^2)-(a^4) m (n^2)+2 (a^2) (b^2) m (n^2)-(b^4) m (n^2)+3 (a^2) (c^2) m (n^2)-(b^2) (c^2) m (n^2)-2 (c^4) m (n^2)) y z-(a^2) (b^2) (l-m) n ((a^2) l-(b^2) l+(c^2) l-(a^2) m+(b^2) m+(c^2) m-2 (c^2) n) (z^2);(* Miquel Circle *)
QLCi4=l (m-n) ((a^4) (b^2) l-2 (a^2) (b^4) l+(b^6) l+(a^4) (c^2) l+2 (a^2) (b^2) (c^2) l-(b^4) (c^2) l-2 (a^2) (c^4) l-(b^2) (c^4) l+(c^6) l-(a^4) (b^2) m+2 (a^2) (b^4) m-(b^6) m-(a^2) (b^2) (c^2) m-(b^4) (c^2) m+2 (b^2) (c^4) m-(a^4) (c^2) n-(a^2) (b^2) (c^2) n+2 (b^4) (c^2) n+2 (a^2) (c^4) n-(b^2) (c^4) n-(c^6) n) (x^2)+((a^6) (l^2) m-(a^4) (b^2) (l^2) m-(a^2) (b^4) (l^2) m+(b^6) (l^2) m+(a^4) (c^2) (l^2) m+5 (a^2) (b^2) (c^2) (l^2) m-2 (b^4) (c^2) (l^2) m-2 (a^2) (c^4) (l^2) m+(b^2) (c^4) (l^2) m-(a^6) l (m^2)+(a^4) (b^2) l (m^2)+(a^2) (b^4) l (m^2)-(b^6) l (m^2)+2 (a^4) (c^2) l (m^2)-5 (a^2) (b^2) (c^2) l (m^2)-(b^4) (c^2) l (m^2)-(a^2) (c^4) l (m^2)+2 (b^2) (c^4) l (m^2)-(a^4) (b^2) (l^2) n+2 (a^2) (b^4) (l^2) n-(b^6) (l^2) n-4 (a^2) (b^2) (c^2) (l^2) n+2 (b^4) (c^2) (l^2) n-(b^2) (c^4) (l^2) n-(a^6) l m n+3 (a^4) (b^2) l m n-3 (a^2) (b^4) l m n+(b^6) l m n-4 (a^4) (c^2) l m n+4 (b^4) (c^2) l m n+5 (a^2) (c^4) l m n-5 (b^2) (c^4) l m n+(a^6) (m^2) n-2 (a^4) (b^2) (m^2) n+(a^2) (b^4) (m^2) n-2 (a^4) (c^2) (m^2) n+4 (a^2) (b^2) (c^2) (m^2) n+(a^2) (c^4) (m^2) n+3 (a^2) (b^2) (c^2) l (n^2)-3 (b^4) (c^2) l (n^2)+3 (b^2) (c^4) l (n^2)+3 (a^4) (c^2) m (n^2)-3 (a^2) (b^2) (c^2) m (n^2)-3 (a^2) (c^4) m (n^2)) x y-m (l-n) (-(a^6) l+2 (a^4) (b^2) l-(a^2) (b^4) l-(a^4) (c^2) l-(a^2) (b^2) (c^2) l+2 (a^2) (c^4) l+(a^6) m-2 (a^4) (b^2) m+(a^2) (b^4) m-(a^4) (c^2) m+2 (a^2) (b^2) (c^2) m+(b^4) (c^2) m-(a^2) (c^4) m-2 (b^2) (c^4) m+(c^6) m+2 (a^4) (c^2) n-(a^2) (b^2) (c^2) n-(b^4) (c^2) n-(a^2) (c^4) n+2 (b^2) (c^4) n-(c^6) n) (y^2)+((a^4) (c^2) (l^2) m+4 (a^2) (b^2) (c^2) (l^2) m+(b^4) (c^2) (l^2) m-2 (a^2) (c^4) (l^2) m-2 (b^2) (c^4) (l^2) m+(c^6) (l^2) m-3 (a^2) (b^2) (c^2) l (m^2)-3 (b^4) (c^2) l (m^2)+3 (b^2) (c^4) l (m^2)-(a^6) (l^2) n-(a^4) (b^2) (l^2) n+2 (a^2) (b^4) (l^2) n+(a^4) (c^2) (l^2) n-5 (a^2) (b^2) (c^2) (l^2) n-(b^4) (c^2) (l^2) n+(a^2) (c^4) (l^2) n+2 (b^2) (c^4) (l^2) n-(c^6) (l^2) n+(a^6) l m n+4 (a^4) (b^2) l m n-5 (a^2) (b^4) l m n-3 (a^4) (c^2) l m n+5 (b^4) (c^2) l m n+3 (a^2) (c^4) l m n-4 (b^2) (c^4) l m n-(c^6) l m n-3 (a^4) (b^2) (m^2) n+3 (a^2) (b^4) (m^2) n+3 (a^2) (b^2) (c^2) (m^2) n+(a^6) l (n^2)-2 (a^4) (b^2) l (n^2)+(a^2) (b^4) l (n^2)-(a^4) (c^2) l (n^2)+5 (a^2) (b^2) (c^2) l (n^2)-2 (b^4) (c^2) l (n^2)-(a^2) (c^4) l (n^2)+(b^2) (c^4) l (n^2)+(c^6) l (n^2)-(a^6) m (n^2)+2 (a^4) (b^2) m (n^2)-(a^2) (b^4) m (n^2)+2 (a^4) (c^2) m (n^2)-4 (a^2) (b^2) (c^2) m (n^2)-(a^2) (c^4) m (n^2)) x z+(3 (a^4) (c^2) (l^2) m+3 (a^2) (b^2) (c^2) (l^2) m-3 (a^2) (c^4) (l^2) m-(a^4) (c^2) l (m^2)-4 (a^2) (b^2) (c^2) l (m^2)-(b^4) (c^2) l (m^2)+2 (a^2) (c^4) l (m^2)+2 (b^2) (c^4) l (m^2)-(c^6) l (m^2)-3 (a^4) (b^2) (l^2) n+3 (a^2) (b^4) (l^2) n-3 (a^2) (b^2) (c^2) (l^2) n+5 (a^4) (b^2) l m n-4 (a^2) (b^4) l m n-(b^6) l m n-5 (a^4) (c^2) l m n+3 (b^4) (c^2) l m n+4 (a^2) (c^4) l m n-3 (b^2) (c^4) l m n+(c^6) l m n-2 (a^4) (b^2) (m^2) n+(a^2) (b^4) (m^2) n+(b^6) (m^2) n+(a^4) (c^2) (m^2) n+5 (a^2) (b^2) (c^2) (m^2) n-(b^4) (c^2) (m^2) n-2 (a^2) (c^4) (m^2) n-(b^2) (c^4) (m^2) n+(c^6) (m^2) n+(a^4) (b^2) l (n^2)-2 (a^2) (b^4) l (n^2)+(b^6) l (n^2)+4 (a^2) (b^2) (c^2) l (n^2)-2 (b^4) (c^2) l (n^2)+(b^2) (c^4) l (n^2)-(a^4) (b^2) m (n^2)+2 (a^2) (b^4) m (n^2)-(b^6) m (n^2)+2 (a^4) (c^2) m (n^2)-5 (a^2) (b^2) (c^2) m (n^2)+(b^4) (c^2) m (n^2)-(a^2) (c^4) m (n^2)+(b^2) (c^4) m (n^2)-(c^6) m (n^2)) y z-(l-m) n ((a^6) l+(a^4) (b^2) l-2 (a^2) (b^4) l-2 (a^4) (c^2) l+(a^2) (b^2) (c^2) l+(a^2) (c^4) l-2 (a^4) (b^2) m+(a^2) (b^4) m+(b^6) m+(a^2) (b^2) (c^2) m-2 (b^4) (c^2) m+(b^2) (c^4) m-(a^6) n+(a^4) (b^2) n+(a^2) (b^4) n-(b^6) n+2 (a^4) (c^2) n-2 (a^2) (b^2) (c^2) n+2 (b^4) (c^2) n-(a^2) (c^4) n-(b^2) (c^4) n) (z^2); (* Hervey Circle *)
QLCi5=((a^2)-(b^2)-(c^2)) l (m-n) ((a^2) (b^2) l-(b^4) l+(a^2) (c^2) l+2 (b^2) (c^2) l-(c^4) l-(a^2) (b^2) m+(b^4) m-(b^2) (c^2) m-(a^2) (c^2) n-(b^2) (c^2) n+(c^4) n) (x^2)+((a^6) (l^2) m-(a^4) (b^2) (l^2) m-(a^2) (b^4) (l^2) m+(b^6) (l^2) m-(a^4) (c^2) (l^2) m+4 (a^2) (b^2) (c^2) (l^2) m-3 (b^4) (c^2) (l^2) m+(a^2) (c^4) (l^2) m+3 (b^2) (c^4) (l^2) m-(c^6) (l^2) m-(a^6) l (m^2)+(a^4) (b^2) l (m^2)+(a^2) (b^4) l (m^2)-(b^6) l (m^2)+3 (a^4) (c^2) l (m^2)-4 (a^2) (b^2) (c^2) l (m^2)+(b^4) (c^2) l (m^2)-3 (a^2) (c^4) l (m^2)-(b^2) (c^4) l (m^2)+(c^6) l (m^2)-(a^4) (b^2) (l^2) n+2 (a^2) (b^4) (l^2) n-(b^6) (l^2) n+(a^4) (c^2) (l^2) n-4 (a^2) (b^2) (c^2) (l^2) n+3 (b^4) (c^2) (l^2) n-2 (a^2) (c^4) (l^2) n-3 (b^2) (c^4) (l^2) n+(c^6) (l^2) n-(a^6) l m n+3 (a^4) (b^2) l m n-3 (a^2) (b^4) l m n+(b^6) l m n-2 (a^4) (c^2) l m n+2 (b^4) (c^2) l m n+3 (a^2) (c^4) l m n-3 (b^2) (c^4) l m n+(a^6) (m^2) n-2 (a^4) (b^2) (m^2) n+(a^2) (b^4) (m^2) n-3 (a^4) (c^2) (m^2) n+4 (a^2) (b^2) (c^2) (m^2) n-(b^4) (c^2) (m^2) n+3 (a^2) (c^4) (m^2) n+2 (b^2) (c^4) (m^2) n-(c^6) (m^2) n-(a^4) (c^2) l (n^2)+4 (a^2) (b^2) (c^2) l (n^2)-3 (b^4) (c^2) l (n^2)+2 (a^2) (c^4) l (n^2)+4 (b^2) (c^4) l (n^2)-(c^6) l (n^2)+3 (a^4) (c^2) m (n^2)-4 (a^2) (b^2) (c^2) m (n^2)+(b^4) (c^2) m (n^2)-4 (a^2) (c^4) m (n^2)-2 (b^2) (c^4) m (n^2)+(c^6) m (n^2)) x y-((a^2)-(b^2)+(c^2)) m (l-n) (-(a^4) l+(a^2) (b^2) l+(a^2) (c^2) l+(a^4) m-(a^2) (b^2) m-2 (a^2) (c^2) m-(b^2) (c^2) m+(c^4) m+(a^2) (c^2) n+(b^2) (c^2) n-(c^4) n) (y^2)+(-(a^4) (b^2) (l^2) m+2 (a^2) (b^4) (l^2) m-(b^6) (l^2) m+(a^4) (c^2) (l^2) m+4 (a^2) (b^2) (c^2) (l^2) m+3 (b^4) (c^2) (l^2) m-2 (a^2) (c^4) (l^2) m-3 (b^2) (c^4) (l^2) m+(c^6) (l^2) m+(a^4) (b^2) l (m^2)-2 (a^2) (b^4) l (m^2)+(b^6) l (m^2)-4 (a^2) (b^2) (c^2) l (m^2)-4 (b^4) (c^2) l (m^2)+3 (b^2) (c^4) l (m^2)-(a^6) (l^2) n+(a^4) (b^2) (l^2) n-(a^2) (b^4) (l^2) n+(b^6) (l^2) n+(a^4) (c^2) (l^2) n-4 (a^2) (b^2) (c^2) (l^2) n-3 (b^4) (c^2) (l^2) n+(a^2) (c^4) (l^2) n+3 (b^2) (c^4) (l^2) n-(c^6) (l^2) n+(a^6) l m n+2 (a^4) (b^2) l m n-3 (a^2) (b^4) l m n-3 (a^4) (c^2) l m n+3 (b^4) (c^2) l m n+3 (a^2) (c^4) l m n-2 (b^2) (c^4) l m n-(c^6) l m n-3 (a^4) (b^2) (m^2) n+4 (a^2) (b^4) (m^2) n-(b^6) (m^2) n+4 (a^2) (b^2) (c^2) (m^2) n+2 (b^4) (c^2) (m^2) n-(b^2) (c^4) (m^2) n+(a^6) l (n^2)-3 (a^4) (b^2) l (n^2)+3 (a^2) (b^4) l (n^2)-(b^6) l (n^2)-(a^4) (c^2) l (n^2)+4 (a^2) (b^2) (c^2) l (n^2)+(b^4) (c^2) l (n^2)-(a^2) (c^4) l (n^2)-(b^2) (c^4) l (n^2)+(c^6) l (n^2)-(a^6) m (n^2)+3 (a^4) (b^2) m (n^2)-3 (a^2) (b^4) m (n^2)+(b^6) m (n^2)+2 (a^4) (c^2) m (n^2)-4 (a^2) (b^2) (c^2) m (n^2)-2 (b^4) (c^2) m (n^2)-(a^2) (c^4) m (n^2)+(b^2) (c^4) m (n^2)) x z+(-(a^6) (l^2) m+2 (a^4) (b^2) (l^2) m-(a^2) (b^4) (l^2) m+4 (a^4) (c^2) (l^2) m+4 (a^2) (b^2) (c^2) (l^2) m-3 (a^2) (c^4) (l^2) m+(a^6) l (m^2)-2 (a^4) (b^2) l (m^2)+(a^2) (b^4) l (m^2)-3 (a^4) (c^2) l (m^2)-4 (a^2) (b^2) (c^2) l (m^2)-(b^4) (c^2) l (m^2)+3 (a^2) (c^4) l (m^2)+2 (b^2) (c^4) l (m^2)-(c^6) l (m^2)+(a^6) (l^2) n-4 (a^4) (b^2) (l^2) n+3 (a^2) (b^4) (l^2) n-2 (a^4) (c^2) (l^2) n-4 (a^2) (b^2) (c^2) (l^2) n+(a^2) (c^4) (l^2) n+3 (a^4) (b^2) l m n-2 (a^2) (b^4) l m n-(b^6) l m n-3 (a^4) (c^2) l m n+3 (b^4) (c^2) l m n+2 (a^2) (c^4) l m n-3 (b^2) (c^4) l m n+(c^6) l m n-(a^6) (m^2) n+(a^4) (b^2) (m^2) n-(a^2) (b^4) (m^2) n+(b^6) (m^2) n+3 (a^4) (c^2) (m^2) n+4 (a^2) (b^2) (c^2) (m^2) n-(b^4) (c^2) (m^2) n-3 (a^2) (c^4) (m^2) n-(b^2) (c^4) (m^2) n+(c^6) (m^2) n-(a^6) l (n^2)+3 (a^4) (b^2) l (n^2)-3 (a^2) (b^4) l (n^2)+(b^6) l (n^2)+2 (a^4) (c^2) l (n^2)+4 (a^2) (b^2) (c^2) l (n^2)-2 (b^4) (c^2) l (n^2)-(a^2) (c^4) l (n^2)+(b^2) (c^4) l (n^2)+(a^6) m (n^2)-3 (a^4) (b^2) m (n^2)+3 (a^2) (b^4) m (n^2)-(b^6) m (n^2)-(a^4) (c^2) m (n^2)-4 (a^2) (b^2) (c^2) m (n^2)+(b^4) (c^2) m (n^2)+(a^2) (c^4) m (n^2)+(b^2) (c^4) m (n^2)-(c^6) m (n^2)) y z-((a^2)+(b^2)-(c^2)) (l-m) n ((a^4) l-(a^2) (b^2) l-(a^2) (c^2) l-(a^2) (b^2) m+(b^4) m-(b^2) (c^2) m-(a^4) n+2 (a^2) (b^2) n-(b^4) n+(a^2) (c^2) n+(b^2) (c^2) n) (z^2);(* Pluecker Circle *)
QLCi6=l (m-n) ((b^2) l+(c^2) l-(b^2) m-(c^2) n) (x^2)+(l-m) ((a^2) l m+(b^2) l m-3 (c^2) l m-(b^2) l n+3 (c^2) l n-(a^2) m n+3 (c^2) m n-3 (c^2) (n^2)) x y-m (l-n) (-(a^2) l+(a^2) m+(c^2) m-(c^2) n) (y^2)-(l-n) (3 (b^2) l m-(c^2) l m-3 (b^2) (m^2)+(a^2) l n-3 (b^2) l n+(c^2) l n-(a^2) m n+3 (b^2) m n) x z-(m-n) (3 (a^2) (l^2)-3 (a^2) l m+(c^2) l m-3 (a^2) l n+(b^2) l n+3 (a^2) m n-(b^2) m n-(c^2) m n) y z-(l-m) n ((a^2) l+(b^2) m-(a^2) n-(b^2) n) (z^2);(* Dimidium Circle *)

QLCo1=((l^2) (m^2) (x^2)-2 (l^2) m n (x^2)+(l^2) (n^2) (x^2)+2 (l^2) (m^2) x y-2 (l^2) m n x y-2 l (m^2) n x y+2 l m (n^2) x y+(l^2) (m^2) (y^2)-2 l (m^2) n (y^2)+(m^2) (n^2) (y^2)-2 (l^2) m n x z+2 l (m^2) n x z+2 (l^2) (n^2) x z-2 l m (n^2) x z+2 (l^2) m n y z-2 l (m^2) n y z-2 l m (n^2) y z+2 (m^2) (n^2) y z+(l^2) (n^2) (z^2)-2 l m (n^2) (z^2)+(m^2) (n^2) (z^2));(* Inscribed Quadrilateral Parabola *)
QLCo2=((l^6) (m^6) (x^2)+2 (l^6) (m^5) n (x^2)-4 (l^5) (m^6) n (x^2)-(l^6) (m^4) (n^2) (x^2)-4 (l^5) (m^5) (n^2) (x^2)+6 (l^4) (m^6) (n^2) (x^2)-4 (l^6) (m^3) (n^3) (x^2)+8 (l^5) (m^4) (n^3) (x^2)-4 (l^3) (m^6) (n^3) (x^2)-(l^6) (m^2) (n^4) (x^2)+8 (l^5) (m^3) (n^4) (x^2)-12 (l^4) (m^4) (n^4) (x^2)+4 (l^3) (m^5) (n^4) (x^2)+(l^2) (m^6) (n^4) (x^2)+2 (l^6) m (n^5) (x^2)-4 (l^5) (m^2) (n^5) (x^2)+4 (l^3) (m^4) (n^5) (x^2)-2 (l^2) (m^5) (n^5) (x^2)+(l^6) (n^6) (x^2)-4 (l^5) m (n^6) (x^2)+6 (l^4) (m^2) (n^6) (x^2)-4 (l^3) (m^3) (n^6) (x^2)+(l^2) (m^4) (n^6) (x^2)+2 (l^6) (m^6) x y-2 (l^6) (m^5) n x y-2 (l^5) (m^6) n x y-4 (l^6) (m^4) (n^2) x y+10 (l^5) (m^5) (n^2) x y-4 (l^4) (m^6) (n^2) x y+4 (l^6) (m^3) (n^3) x y-4 (l^5) (m^4) (n^3) x y-4 (l^4) (m^5) (n^3) x y+4 (l^3) (m^6) (n^3) x y+2 (l^6) (m^2) (n^4) x y-12 (l^5) (m^3) (n^4) x y+20 (l^4) (m^4) (n^4) x y-12 (l^3) (m^5) (n^4) x y+2 (l^2) (m^6) (n^4) x y-2 (l^6) m (n^5) x y+6 (l^5) (m^2) (n^5) x y-4 (l^4) (m^3) (n^5) x y-4 (l^3) (m^4) (n^5) x y+6 (l^2) (m^5) (n^5) x y-2 l (m^6) (n^5) x y+2 (l^5) m (n^6) x y-8 (l^4) (m^2) (n^6) x y+12 (l^3) (m^3) (n^6) x y-8 (l^2) (m^4) (n^6) x y+2 l (m^5) (n^6) x y+(l^6) (m^6) (y^2)-4 (l^6) (m^5) n (y^2)+2 (l^5) (m^6) n (y^2)+6 (l^6) (m^4) (n^2) (y^2)-4 (l^5) (m^5) (n^2) (y^2)-(l^4) (m^6) (n^2) (y^2)-4 (l^6) (m^3) (n^3) (y^2)+8 (l^4) (m^5) (n^3) (y^2)-4 (l^3) (m^6) (n^3) (y^2)+(l^6) (m^2) (n^4) (y^2)+4 (l^5) (m^3) (n^4) (y^2)-12 (l^4) (m^4) (n^4) (y^2)+8 (l^3) (m^5) (n^4) (y^2)-(l^2) (m^6) (n^4) (y^2)-2 (l^5) (m^2) (n^5) (y^2)+4 (l^4) (m^3) (n^5) (y^2)-4 (l^2) (m^5) (n^5) (y^2)+2 l (m^6) (n^5) (y^2)+(l^4) (m^2) (n^6) (y^2)-4 (l^3) (m^3) (n^6) (y^2)+6 (l^2) (m^4) (n^6) (y^2)-4 l (m^5) (n^6) (y^2)+(m^6) (n^6) (y^2)-2 (l^6) (m^5) n x z+2 (l^5) (m^6) n x z+2 (l^6) (m^4) (n^2) x z+6 (l^5) (m^5) (n^2) x z-8 (l^4) (m^6) (n^2) x z+4 (l^6) (m^3) (n^3) x z-12 (l^5) (m^4) (n^3) x z-4 (l^4) (m^5) (n^3) x z+12 (l^3) (m^6) (n^3) x z-4 (l^6) (m^2) (n^4) x z-4 (l^5) (m^3) (n^4) x z+20 (l^4) (m^4) (n^4) x z-4 (l^3) (m^5) (n^4) x z-8 (l^2) (m^6) (n^4) x z-2 (l^6) m (n^5) x z+10 (l^5) (m^2) (n^5) x z-4 (l^4) (m^3) (n^5) x z-12 (l^3) (m^4) (n^5) x z+6 (l^2) (m^5) (n^5) x z+2 l (m^6) (n^5) x z+2 (l^6) (n^6) x z-2 (l^5) m (n^6) x z-4 (l^4) (m^2) (n^6) x z+4 (l^3) (m^3) (n^6) x z+2 (l^2) (m^4) (n^6) x z-2 l (m^5) (n^6) x z+2 (l^6) (m^5) n y z-2 (l^5) (m^6) n y z-8 (l^6) (m^4) (n^2) y z+6 (l^5) (m^5) (n^2) y z+2 (l^4) (m^6) (n^2) y z+12 (l^6) (m^3) (n^3) y z-4 (l^5) (m^4) (n^3) y z-12 (l^4) (m^5) (n^3) y z+4 (l^3) (m^6) (n^3) y z-8 (l^6) (m^2) (n^4) y z-4 (l^5) (m^3) (n^4) y z+20 (l^4) (m^4) (n^4) y z-4 (l^3) (m^5) (n^4) y z-4 (l^2) (m^6) (n^4) y z+2 (l^6) m (n^5) y z+6 (l^5) (m^2) (n^5) y z-12 (l^4) (m^3) (n^5) y z-4 (l^3) (m^4) (n^5) y z+10 (l^2) (m^5) (n^5) y z-2 l (m^6) (n^5) y z-2 (l^5) m (n^6) y z+2 (l^4) (m^2) (n^6) y z+4 (l^3) (m^3) (n^6) y z-4 (l^2) (m^4) (n^6) y z-2 l (m^5) (n^6) y z+2 (m^6) (n^6) y z+(l^6) (m^4) (n^2) (z^2)-2 (l^5) (m^5) (n^2) (z^2)+(l^4) (m^6) (n^2) (z^2)-4 (l^6) (m^3) (n^3) (z^2)+4 (l^5) (m^4) (n^3) (z^2)+4 (l^4) (m^5) (n^3) (z^2)-4 (l^3) (m^6) (n^3) (z^2)+6 (l^6) (m^2) (n^4) (z^2)-12 (l^4) (m^4) (n^4) (z^2)+6 (l^2) (m^6) (n^4) (z^2)-4 (l^6) m (n^5) (z^2)-4 (l^5) (m^2) (n^5) (z^2)+8 (l^4) (m^3) (n^5) (z^2)+8 (l^3) (m^4) (n^5) (z^2)-4 (l^2) (m^5) (n^5) (z^2)-4 l (m^6) (n^5) (z^2)+(l^6) (n^6) (z^2)+2 (l^5) m (n^6) (z^2)-(l^4) (m^2) (n^6) (z^2)-4 (l^3) (m^3) (n^6) (z^2)-(l^2) (m^4) (n^6) (z^2)+2 l (m^5) (n^6) (z^2)+(m^6) (n^6) (z^2)); (* Inscribed Midline Hyperbola *)
QLCo3=(l^2) (((m-n))^2) ((l^2) (m^2)-6 (l^2) m n+2 l (m^2) n+(l^2) (n^2)+2 l m (n^2)+(m^2) (n^2)) (x^2)+2 l m (l-n) (m-n) (((l m-l n-m n))^2) x y+(m^2) (((l-n))^2) ((l^2) (m^2)+2 (l^2) m n-6 l (m^2) n+(l^2) (n^2)+2 l m (n^2)+(m^2) (n^2)) (y^2)-2 l (l-m) (m-n) n (((l m-l n+m n))^2) x z+2 (l-m) m (l-n) n (((l m+l n-m n))^2) y z+(((l-m))^2) (n^2) ((l^2) (m^2)+2 (l^2) m n+2 l (m^2) n+(l^2) (n^2)-6 l m (n^2)+(m^2) (n^2)) (z^2);(* 2nd QL-Parabola *)
QL2Co1a=(((((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))-(-l m-l n+m n) W+(l m-l n+m n) W))^2) (x^2)+2 (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))-(-l m-l n+m n) W+(l m-l n+m n) W) (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)+2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))-(-l m-l n+m n) W+(l m-l n+m n) W) x y+(((((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)+2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))-(-l m-l n+m n) W+(l m-l n+m n) W))^2) (y^2)+2 (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))-(-l m-l n+m n) W+(l m-l n+m n) W) (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)+(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m-l n+m n) W+(l m-l n+m n) W) x z-2 (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)+2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))-(-l m-l n+m n) W+(l m-l n+m n) W) (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)+(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m-l n+m n) W+(l m-l n+m n) W) y z+(((((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)+(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m-l n+m n) W+(l m-l n+m n) W))^2) (z^2)/.W->√((a-b-c) (a+b-c) (a-b+c) (a+b+c) (m^2) (n^2)+(l^2) ((a-b-c) (a+b-c) (a-b+c) (a+b+c) (m^2)-2 (3 (a^4)-2 (a^2) (b^2)-(b^4)-2 (a^2) (c^2)+2 (b^2) (c^2)-(c^4)) m n+(a-b-c) (a+b-c) (a-b+c) (a+b+c) (n^2))+l (2 ((a^4)+2 (a^2) (b^2)-3 (b^4)-2 (a^2) (c^2)+2 (b^2) (c^2)+(c^4)) (m^2) n+2 ((a^4)-2 (a^2) (b^2)+(b^4)+2 (a^2) (c^2)+2 (b^2) (c^2)-3 (c^4)) m (n^2)));
QL2Co1b=(((((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W-(l m+l n-m n) W))^2) (x^2)+2 (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W-(l m+l n-m n) W) (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)+2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W-(l m+l n-m n) W) x y+(((((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)+2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W-(l m+l n-m n) W))^2) (y^2)+2 (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W-(l m+l n-m n) W) (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)+(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W+(l m+l n-m n) W) x z-2 (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)-(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)+2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W-(l m+l n-m n) W) (((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)+(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W+(l m+l n-m n) W) y z+(((((a^2)-(b^2)+(c^2)) (l m-l n-m n) (l m+l n-m n)+(-(a^2)+(b^2)+(c^2)) (l m-l n-m n) (l m-l n+m n)-2 ((c^2) (l^2) (m^2)+2 (a^2) (l^2) m n-2 (b^2) (l^2) m n-2 (a^2) l (m^2) n+2 (b^2) l (m^2) n+(c^2) (l^2) (n^2)-2 (c^2) l m (n^2)+(c^2) (m^2) (n^2))+(-l m+l n-m n) W+(l m+l n-m n) W))^2) (z^2)/.W->√((a-b-c) (a+b-c) (a-b+c) (a+b+c) (m^2) (n^2)+(l^2) ((a-b-c) (a+b-c) (a-b+c) (a+b+c) (m^2)-2 (3 (a^4)-2 (a^2) (b^2)-(b^4)-2 (a^2) (c^2)+2 (b^2) (c^2)-(c^4)) m n+(a-b-c) (a+b-c) (a-b+c) (a+b+c) (n^2))+l (2 ((a^4)+2 (a^2) (b^2)-3 (b^4)-2 (a^2) (c^2)+2 (b^2) (c^2)+(c^4)) (m^2) n+2 ((a^4)-2 (a^2) (b^2)+(b^4)+2 (a^2) (c^2)+2 (b^2) (c^2)-3 (c^4)) m (n^2))); (* Pair of Inscribed Orthogonal Hyperbolas *)

QLCo99=-(b^2) (c^2) (l^2) (((m-n))^2) ((b^2) l-(c^2) l-(b^2) m+(c^2) n) (x^2)-(a^2) (c^2) (m^2) (((l-n))^2) ((a^2) l-(a^2) m+(c^2) m-(c^2) n) (y^2)-2 (a^2) (b^2) (c^2) (l-m) m (l-n) (m-n) n y z+(a^2) (b^2) (((l-m))^2) (n^2) ((a^2) l-(b^2) m-(a^2) n+(b^2) n) (z^2)+x (-2 (a^2) (b^2) (c^2) l (l-m) m (l-n) (m-n) y-2 (a^2) (b^2) (c^2) l (l-m) (l-n) (m-n) n z); (* Steiner Axes  *)

QLCu1=(c^2) l n (x^2) y+(c^2) m n x (y^2)+(b^2) l m (x^2) z+((a^2) l m+(b^2) l m-(c^2) l m+(a^2) l n-(b^2) l n+(c^2) l n-(a^2) m n+(b^2) m n+(c^2) m n) x y z+(a^2) l m (y^2) z+(b^2) m n x (z^2)+(a^2) l n y (z^2); (* QL-Quasi Isogonal Cubic *)
QLCu2=(b^2) (c^2) l ((a^2) l m+(b^2) l m-(c^2) l m-(b^2) (m^2)+(a^2) l n-(b^2) l n+(c^2) l n-(a^2) m n+(b^2) m n+(c^2) m n-(c^2) (n^2)) (x^3)+3 (a^2) (b^2) (c^2) (l^2) m (x^2) y+3 (a^2) (b^2) (c^2) l (m^2) x (y^2)+(a^2) (c^2) m (-(a^2) (l^2)+(a^2) l m+(b^2) l m-(c^2) l m+(a^2) l n-(b^2) l n+(c^2) l n-(a^2) m n+(b^2) m n+(c^2) m n-(c^2) (n^2)) (y^3)+3 (a^2) (b^2) (c^2) (l^2) n (x^2) z+6 (a^2) (b^2) (c^2) l m n x y z+3 (a^2) (b^2) (c^2) (m^2) n (y^2) z+3 (a^2) (b^2) (c^2) l (n^2) x (z^2)+3 (a^2) (b^2) (c^2) m (n^2) y (z^2)+(a^2) (b^2) n (-(a^2) (l^2)+(a^2) l m+(b^2) l m-(c^2) l m-(b^2) (m^2)+(a^2) l n-(b^2) l n+(c^2) l n-(a^2) m n+(b^2) m n+(c^2) m n) (z^3);  (* Eckart's Cubic *)

QLQu1=(b^4) (c^4) (l^4) (m^2) (((m-n))^4) (n^2) (x^4)+(a^4) (c^4) (l^2) (m^4) (((l-n))^4) (n^2) (y^4)+2 (a^4) (c^2) (l^2) (m^3) (((l-n))^2) (n^2) ((a^2) (l^2) m+(b^2) (l^2) m-(a^2) l (m^2)-3 (b^2) l (m^2)+(c^2) l (m^2)+2 (b^2) (m^3)-(a^2) (l^2) n+(c^2) (l^2) n+2 (b^2) l m n-2 (c^2) l m n+(a^2) (m^2) n-2 (b^2) (m^2) n-(c^2) (m^2) n+(a^2) l (n^2)-(b^2) l (n^2)-(c^2) l (n^2)-(a^2) m (n^2)+(b^2) m (n^2)+2 (c^2) m (n^2)) (y^3) z+(a^4) (l^2) (m^2) (n^2) ((a^4) (l^4) (m^2)-2 (a^2) (b^2) (l^4) (m^2)+(b^4) (l^4) (m^2)-2 (a^4) (l^3) (m^3)+4 (a^2) (b^2) (l^3) (m^3)-2 (b^4) (l^3) (m^3)+2 (a^2) (c^2) (l^3) (m^3)-2 (b^2) (c^2) (l^3) (m^3)+(a^4) (l^2) (m^4)-2 (a^2) (b^2) (l^2) (m^4)+(b^4) (l^2) (m^4)-2 (a^2) (c^2) (l^2) (m^4)+2 (b^2) (c^2) (l^2) (m^4)+(c^4) (l^2) (m^4)-2 (a^4) (l^4) m n+2 (a^2) (b^2) (l^4) m n+2 (a^2) (c^2) (l^4) m n+4 (b^2) (c^2) (l^4) m n+2 (a^4) (l^3) (m^2) n+2 (a^2) (b^2) (l^3) (m^2) n-4 (b^4) (l^3) (m^2) n-8 (a^2) (c^2) (l^3) (m^2) n-6 (b^2) (c^2) (l^3) (m^2) n+2 (c^4) (l^3) (m^2) n+2 (a^4) (l^2) (m^3) n-10 (a^2) (b^2) (l^2) (m^3) n+8 (b^4) (l^2) (m^3) n+2 (a^2) (c^2) (l^2) (m^3) n+8 (b^2) (c^2) (l^2) (m^3) n-4 (c^4) (l^2) (m^3) n-2 (a^4) l (m^4) n+6 (a^2) (b^2) l (m^4) n-4 (b^4) l (m^4) n+4 (a^2) (c^2) l (m^4) n-6 (b^2) (c^2) l (m^4) n-2 (c^4) l (m^4) n+(a^4) (l^4) (n^2)-2 (a^2) (c^2) (l^4) (n^2)+(c^4) (l^4) (n^2)+2 (a^4) (l^3) m (n^2)-8 (a^2) (b^2) (l^3) m (n^2)+2 (b^4) (l^3) m (n^2)+2 (a^2) (c^2) (l^3) m (n^2)-6 (b^2) (c^2) (l^3) m (n^2)-4 (c^4) (l^3) m (n^2)-6 (a^4) (l^2) (m^2) (n^2)+12 (a^2) (b^2) (l^2) (m^2) (n^2)+12 (a^2) (c^2) (l^2) (m^2) (n^2)+4 (b^2) (c^2) (l^2) (m^2) (n^2)+2 (a^4) l (m^3) (n^2)-6 (b^4) l (m^3) (n^2)-10 (a^2) (c^2) l (m^3) (n^2)-2 (b^2) (c^2) l (m^3) (n^2)+8 (c^4) l (m^3) (n^2)+(a^4) (m^4) (n^2)-4 (a^2) (b^2) (m^4) (n^2)+4 (b^4) (m^4) (n^2)-2 (a^2) (c^2) (m^4) (n^2)+4 (b^2) (c^2) (m^4) (n^2)+(c^4) (m^4) (n^2)-2 (a^4) (l^3) (n^3)+2 (a^2) (b^2) (l^3) (n^3)+4 (a^2) (c^2) (l^3) (n^3)-2 (b^2) (c^2) (l^3) (n^3)-2 (c^4) (l^3) (n^3)+2 (a^4) (l^2) m (n^3)+2 (a^2) (b^2) (l^2) m (n^3)-4 (b^4) (l^2) m (n^3)-10 (a^2) (c^2) (l^2) m (n^3)+8 (b^2) (c^2) (l^2) m (n^3)+8 (c^4) (l^2) m (n^3)+2 (a^4) l (m^2) (n^3)-10 (a^2) (b^2) l (m^2) (n^3)+8 (b^4) l (m^2) (n^3)-2 (b^2) (c^2) l (m^2) (n^3)-6 (c^4) l (m^2) (n^3)-2 (a^4) (m^3) (n^3)+6 (a^2) (b^2) (m^3) (n^3)-4 (b^4) (m^3) (n^3)+6 (a^2) (c^2) (m^3) (n^3)-4 (b^2) (c^2) (m^3) (n^3)-4 (c^4) (m^3) (n^3)+(a^4) (l^2) (n^4)-2 (a^2) (b^2) (l^2) (n^4)+(b^4) (l^2) (n^4)-2 (a^2) (c^2) (l^2) (n^4)+2 (b^2) (c^2) (l^2) (n^4)+(c^4) (l^2) (n^4)-2 (a^4) l m (n^4)+4 (a^2) (b^2) l m (n^4)-2 (b^4) l m (n^4)+6 (a^2) (c^2) l m (n^4)-6 (b^2) (c^2) l m (n^4)-4 (c^4) l m (n^4)+(a^4) (m^2) (n^4)-2 (a^2) (b^2) (m^2) (n^4)+(b^4) (m^2) (n^4)-4 (a^2) (c^2) (m^2) (n^4)+4 (b^2) (c^2) (m^2) (n^4)+4 (c^4) (m^2) (n^4)) (y^2) (z^2)-2 (a^4) (b^2) (l^2) (((l-m))^2) (m^2) (n^3) ((a^2) (l^2) m-(b^2) (l^2) m-(a^2) l (m^2)+(b^2) l (m^2)+(c^2) l (m^2)-(a^2) (l^2) n-(c^2) (l^2) n+2 (b^2) l m n-2 (c^2) l m n+(a^2) (m^2) n-2 (b^2) (m^2) n-(c^2) (m^2) n+(a^2) l (n^2)-(b^2) l (n^2)+3 (c^2) l (n^2)-(a^2) m (n^2)+(b^2) m (n^2)+2 (c^2) m (n^2)-2 (c^2) (n^3)) y (z^3)+(a^4) (b^4) (l^2) (((l-m))^4) (m^2) (n^4) (z^4)+(x^3) (2 (b^2) (c^4) (l^3) (m^2) (((m-n))^2) (n^2) (2 (a^2) (l^3)-2 (a^2) (l^2) m-(b^2) (l^2) m+(c^2) (l^2) m+(a^2) l (m^2)+2 (b^2) l (m^2)-(c^2) l (m^2)-3 (a^2) (l^2) n+(b^2) (l^2) n-(c^2) (l^2) n+2 (a^2) l m n-2 (b^2) l m n-(a^2) (m^2) n-(b^2) (m^2) n+(c^2) (m^2) n+(a^2) l (n^2)+(c^2) l (n^2)+(b^2) m (n^2)-(c^2) m (n^2)) y+2 (b^4) (c^2) (l^3) (m^2) (((m-n))^2) (n^2) (2 (a^2) (l^3)-3 (a^2) (l^2) m-(b^2) (l^2) m+(c^2) (l^2) m+(a^2) l (m^2)+(b^2) l (m^2)-2 (a^2) (l^2) n+(b^2) (l^2) n-(c^2) (l^2) n+2 (a^2) l m n-2 (c^2) l m n-(b^2) (m^2) n+(c^2) (m^2) n+(a^2) l (n^2)-(b^2) l (n^2)+2 (c^2) l (n^2)-(a^2) m (n^2)+(b^2) m (n^2)-(c^2) m (n^2)) z)+(x^2) ((c^4) (l^2) (m^2) (n^2) (4 (a^4) (l^4) (m^2)+4 (a^2) (b^2) (l^4) (m^2)+(b^4) (l^4) (m^2)-4 (a^2) (c^2) (l^4) (m^2)-2 (b^2) (c^2) (l^4) (m^2)+(c^4) (l^4) (m^2)-4 (a^4) (l^3) (m^3)-4 (a^2) (b^2) (l^3) (m^3)-4 (b^4) (l^3) (m^3)+6 (a^2) (c^2) (l^3) (m^3)+6 (b^2) (c^2) (l^3) (m^3)-2 (c^4) (l^3) (m^3)+(a^4) (l^2) (m^4)+4 (a^2) (b^2) (l^2) (m^4)+4 (b^4) (l^2) (m^4)-2 (a^2) (c^2) (l^2) (m^4)-4 (b^2) (c^2) (l^2) (m^4)+(c^4) (l^2) (m^4)-4 (a^4) (l^4) m n-6 (a^2) (b^2) (l^4) m n-2 (b^4) (l^4) m n+6 (a^2) (c^2) (l^4) m n+4 (b^2) (c^2) (l^4) m n-2 (c^4) (l^4) m n-6 (a^4) (l^3) (m^2) n-2 (a^2) (b^2) (l^3) (m^2) n+8 (b^4) (l^3) (m^2) n-10 (b^2) (c^2) (l^3) (m^2) n+2 (c^4) (l^3) (m^2) n+8 (a^4) (l^2) (m^3) n-2 (a^2) (b^2) (l^2) (m^3) n-6 (b^4) (l^2) (m^3) n-10 (a^2) (c^2) (l^2) (m^3) n+2 (c^4) (l^2) (m^3) n-2 (a^4) l (m^4) n-6 (a^2) (b^2) l (m^4) n-4 (b^4) l (m^4) n+4 (a^2) (c^2) l (m^4) n+6 (b^2) (c^2) l (m^4) n-2 (c^4) l (m^4) n+(a^4) (l^4) (n^2)+2 (a^2) (b^2) (l^4) (n^2)+(b^4) (l^4) (n^2)-2 (a^2) (c^2) (l^4) (n^2)-2 (b^2) (c^2) (l^4) (n^2)+(c^4) (l^4) (n^2)+8 (a^4) (l^3) m (n^2)+8 (a^2) (b^2) (l^3) m (n^2)-4 (b^4) (l^3) m (n^2)-10 (a^2) (c^2) (l^3) m (n^2)+2 (b^2) (c^2) (l^3) m (n^2)+2 (c^4) (l^3) m (n^2)+4 (a^2) (b^2) (l^2) (m^2) (n^2)+12 (a^2) (c^2) (l^2) (m^2) (n^2)+12 (b^2) (c^2) (l^2) (m^2) (n^2)-6 (c^4) (l^2) (m^2) (n^2)-4 (a^4) l (m^3) (n^2)+8 (a^2) (b^2) l (m^3) (n^2)+8 (b^4) l (m^3) (n^2)+2 (a^2) (c^2) l (m^3) (n^2)-10 (b^2) (c^2) l (m^3) (n^2)+2 (c^4) l (m^3) (n^2)+(a^4) (m^4) (n^2)+2 (a^2) (b^2) (m^4) (n^2)+(b^4) (m^4) (n^2)-2 (a^2) (c^2) (m^4) (n^2)-2 (b^2) (c^2) (m^4) (n^2)+(c^4) (m^4) (n^2)-2 (a^4) (l^3) (n^3)-2 (a^2) (b^2) (l^3) (n^3)+4 (a^2) (c^2) (l^3) (n^3)+2 (b^2) (c^2) (l^3) (n^3)-2 (c^4) (l^3) (n^3)-4 (a^4) (l^2) m (n^3)-6 (a^2) (b^2) (l^2) m (n^3)+2 (b^4) (l^2) m (n^3)+2 (a^2) (c^2) (l^2) m (n^3)-8 (b^2) (c^2) (l^2) m (n^3)+2 (c^4) (l^2) m (n^3)+2 (a^4) l (m^2) (n^3)-6 (a^2) (b^2) l (m^2) (n^3)-4 (b^4) l (m^2) (n^3)-8 (a^2) (c^2) l (m^2) (n^3)+2 (b^2) (c^2) l (m^2) (n^3)+2 (c^4) l (m^2) (n^3)-2 (a^2) (b^2) (m^3) (n^3)-2 (b^4) (m^3) (n^3)+2 (a^2) (c^2) (m^3) (n^3)+4 (b^2) (c^2) (m^3) (n^3)-2 (c^4) (m^3) (n^3)+(a^4) (l^2) (n^4)-2 (a^2) (c^2) (l^2) (n^4)+(c^4) (l^2) (n^4)+4 (a^2) (b^2) l m (n^4)+2 (a^2) (c^2) l m (n^4)+2 (b^2) (c^2) l m (n^4)-2 (c^4) l m (n^4)+(b^4) (m^2) (n^4)-2 (b^2) (c^2) (m^2) (n^4)+(c^4) (m^2) (n^4)) (y^2)+2 (b^2) (c^2) (l^2) (m^2) (n^2) (4 (a^4) (l^4) (m^2)+(a^2) (b^2) (l^4) (m^2)+(b^4) (l^4) (m^2)-(a^2) (c^2) (l^4) (m^2)-2 (b^2) (c^2) (l^4) (m^2)+(c^4) (l^4) (m^2)-6 (a^4) (l^3) (m^3)-3 (a^2) (b^2) (l^3) (m^3)-3 (b^4) (l^3) (m^3)+5 (a^2) (c^2) (l^3) (m^3)+4 (b^2) (c^2) (l^3) (m^3)-(c^4) (l^3) (m^3)+2 (a^4) (l^2) (m^4)+2 (a^2) (b^2) (l^2) (m^4)+2 (b^4) (l^2) (m^4)-2 (a^2) (c^2) (l^2) (m^4)-(b^2) (c^2) (l^2) (m^4)-7 (a^4) (l^4) m n-2 (b^4) (l^4) m n+4 (b^2) (c^2) (l^4) m n-2 (c^4) (l^4) m n+4 (a^4) (l^3) (m^2) n+3 (a^2) (b^2) (l^3) (m^2) n+5 (b^4) (l^3) (m^2) n-5 (a^2) (c^2) (l^3) (m^2) n-4 (b^2) (c^2) (l^3) (m^2) n-(c^4) (l^3) (m^2) n+5 (a^4) (l^2) (m^3) n-2 (a^2) (b^2) (l^2) (m^3) n-6 (a^2) (c^2) (l^2) (m^3) n-8 (b^2) (c^2) (l^2) (m^3) n+4 (c^4) (l^2) (m^3) n-2 (a^4) l (m^4) n-(a^2) (b^2) l (m^4) n-3 (b^4) l (m^4) n+3 (a^2) (c^2) l (m^4) n+4 (b^2) (c^2) l (m^4) n-(c^4) l (m^4) n+4 (a^4) (l^4) (n^2)-(a^2) (b^2) (l^4) (n^2)+(b^4) (l^4) (n^2)+(a^2) (c^2) (l^4) (n^2)-2 (b^2) (c^2) (l^4) (n^2)+(c^4) (l^4) (n^2)+4 (a^4) (l^3) m (n^2)-5 (a^2) (b^2) (l^3) m (n^2)-(b^4) (l^3) m (n^2)+3 (a^2) (c^2) (l^3) m (n^2)-4 (b^2) (c^2) (l^3) m (n^2)+5 (c^4) (l^3) m (n^2)-8 (a^4) (l^2) (m^2) (n^2)+8 (a^2) (b^2) (l^2) (m^2) (n^2)-6 (b^4) (l^2) (m^2) (n^2)+8 (a^2) (c^2) (l^2) (m^2) (n^2)+18 (b^2) (c^2) (l^2) (m^2) (n^2)-6 (c^4) (l^2) (m^2) (n^2)-3 (a^2) (b^2) l (m^3) (n^2)+5 (b^4) l (m^3) (n^2)+(a^2) (c^2) l (m^3) (n^2)-4 (b^2) (c^2) l (m^3) (n^2)-(c^4) l (m^3) (n^2)+(a^2) (b^2) (m^4) (n^2)+(b^4) (m^4) (n^2)-(a^2) (c^2) (m^4) (n^2)-2 (b^2) (c^2) (m^4) (n^2)+(c^4) (m^4) (n^2)-6 (a^4) (l^3) (n^3)+5 (a^2) (b^2) (l^3) (n^3)-(b^4) (l^3) (n^3)-3 (a^2) (c^2) (l^3) (n^3)+4 (b^2) (c^2) (l^3) (n^3)-3 (c^4) (l^3) (n^3)+5 (a^4) (l^2) m (n^3)-6 (a^2) (b^2) (l^2) m (n^3)+4 (b^4) (l^2) m (n^3)-2 (a^2) (c^2) (l^2) m (n^3)-8 (b^2) (c^2) (l^2) m (n^3)+(a^2) (b^2) l (m^2) (n^3)-(b^4) l (m^2) (n^3)-3 (a^2) (c^2) l (m^2) (n^3)-4 (b^2) (c^2) l (m^2) (n^3)+5 (c^4) l (m^2) (n^3)+(a^4) (m^3) (n^3)-2 (b^4) (m^3) (n^3)+4 (b^2) (c^2) (m^3) (n^3)-2 (c^4) (m^3) (n^3)+2 (a^4) (l^2) (n^4)-2 (a^2) (b^2) (l^2) (n^4)+2 (a^2) (c^2) (l^2) (n^4)-(b^2) (c^2) (l^2) (n^4)+2 (c^4) (l^2) (n^4)-2 (a^4) l m (n^4)+3 (a^2) (b^2) l m (n^4)-(b^4) l m (n^4)-(a^2) (c^2) l m (n^4)+4 (b^2) (c^2) l m (n^4)-3 (c^4) l m (n^4)-(a^2) (b^2) (m^2) (n^4)+(b^4) (m^2) (n^4)+(a^2) (c^2) (m^2) (n^4)-2 (b^2) (c^2) (m^2) (n^4)+(c^4) (m^2) (n^4)) y z+(b^4) (l^2) (m^2) (n^2) ((a^4) (l^4) (m^2)-2 (a^2) (b^2) (l^4) (m^2)+(b^4) (l^4) (m^2)+2 (a^2) (c^2) (l^4) (m^2)-2 (b^2) (c^2) (l^4) (m^2)+(c^4) (l^4) (m^2)-2 (a^4) (l^3) (m^3)+4 (a^2) (b^2) (l^3) (m^3)-2 (b^4) (l^3) (m^3)-2 (a^2) (c^2) (l^3) (m^3)+2 (b^2) (c^2) (l^3) (m^3)+(a^4) (l^2) (m^4)-2 (a^2) (b^2) (l^2) (m^4)+(b^4) (l^2) (m^4)-4 (a^4) (l^4) m n+6 (a^2) (b^2) (l^4) m n-2 (b^4) (l^4) m n-6 (a^2) (c^2) (l^4) m n+4 (b^2) (c^2) (l^4) m n-2 (c^4) (l^4) m n+8 (a^4) (l^3) (m^2) n-10 (a^2) (b^2) (l^3) (m^2) n+2 (b^4) (l^3) (m^2) n+8 (a^2) (c^2) (l^3) (m^2) n+2 (b^2) (c^2) (l^3) (m^2) n-4 (c^4) (l^3) (m^2) n-4 (a^4) (l^2) (m^3) n+2 (a^2) (b^2) (l^2) (m^3) n+2 (b^4) (l^2) (m^3) n-6 (a^2) (c^2) (l^2) (m^3) n-8 (b^2) (c^2) (l^2) (m^3) n+2 (c^4) (l^2) (m^3) n+2 (a^2) (b^2) l (m^4) n-2 (b^4) l (m^4) n+4 (a^2) (c^2) l (m^4) n+2 (b^2) (c^2) l (m^4) n+4 (a^4) (l^4) (n^2)-4 (a^2) (b^2) (l^4) (n^2)+(b^4) (l^4) (n^2)+4 (a^2) (c^2) (l^4) (n^2)-2 (b^2) (c^2) (l^4) (n^2)+(c^4) (l^4) (n^2)-6 (a^4) (l^3) m (n^2)+2 (b^4) (l^3) m (n^2)-2 (a^2) (c^2) (l^3) m (n^2)-10 (b^2) (c^2) (l^3) m (n^2)+8 (c^4) (l^3) m (n^2)+12 (a^2) (b^2) (l^2) (m^2) (n^2)-6 (b^4) (l^2) (m^2) (n^2)+4 (a^2) (c^2) (l^2) (m^2) (n^2)+12 (b^2) (c^2) (l^2) (m^2) (n^2)+2 (a^4) l (m^3) (n^2)-8 (a^2) (b^2) l (m^3) (n^2)+2 (b^4) l (m^3) (n^2)-6 (a^2) (c^2) l (m^3) (n^2)+2 (b^2) (c^2) l (m^3) (n^2)-4 (c^4) l (m^3) (n^2)+(b^4) (m^4) (n^2)-2 (b^2) (c^2) (m^4) (n^2)+(c^4) (m^4) (n^2)-4 (a^4) (l^3) (n^3)+6 (a^2) (b^2) (l^3) (n^3)-2 (b^4) (l^3) (n^3)-4 (a^2) (c^2) (l^3) (n^3)+6 (b^2) (c^2) (l^3) (n^3)-4 (c^4) (l^3) (n^3)+8 (a^4) (l^2) m (n^3)-10 (a^2) (b^2) (l^2) m (n^3)+2 (b^4) (l^2) m (n^3)-2 (a^2) (c^2) (l^2) m (n^3)-6 (c^4) (l^2) m (n^3)-4 (a^4) l (m^2) (n^3)+2 (a^2) (b^2) l (m^2) (n^3)+2 (b^4) l (m^2) (n^3)+8 (a^2) (c^2) l (m^2) (n^3)-10 (b^2) (c^2) l (m^2) (n^3)+8 (c^4) l (m^2) (n^3)+2 (a^2) (b^2) (m^3) (n^3)-2 (b^4) (m^3) (n^3)-2 (a^2) (c^2) (m^3) (n^3)+4 (b^2) (c^2) (m^3) (n^3)-2 (c^4) (m^3) (n^3)+(a^4) (l^2) (n^4)-2 (a^2) (b^2) (l^2) (n^4)+(b^4) (l^2) (n^4)+4 (a^2) (c^2) (l^2) (n^4)-4 (b^2) (c^2) (l^2) (n^4)+4 (c^4) (l^2) (n^4)-2 (a^4) l m (n^4)+4 (a^2) (b^2) l m (n^4)-2 (b^4) l m (n^4)-6 (a^2) (c^2) l m (n^4)+6 (b^2) (c^2) l m (n^4)-4 (c^4) l m (n^4)+(a^4) (m^2) (n^4)-2 (a^2) (b^2) (m^2) (n^4)+(b^4) (m^2) (n^4)+2 (a^2) (c^2) (m^2) (n^4)-2 (b^2) (c^2) (m^2) (n^4)+(c^4) (m^2) (n^4)) (z^2))+x (2 (a^2) (c^4) (l^2) (m^3) (((l-n))^2) (n^2) (2 (a^2) (l^2) m+(b^2) (l^2) m-(c^2) (l^2) m-(a^2) l (m^2)-2 (b^2) l (m^2)+(c^2) l (m^2)+2 (b^2) (m^3)-(a^2) (l^2) n-(b^2) (l^2) n+(c^2) (l^2) n-2 (a^2) l m n+2 (b^2) l m n+(a^2) (m^2) n-3 (b^2) (m^2) n-(c^2) (m^2) n+(a^2) l (n^2)-(c^2) l (n^2)+(b^2) m (n^2)+(c^2) m (n^2)) (y^3)+2 (a^2) (c^2) (l^2) (m^2) (n^2) (2 (a^4) (l^4) (m^2)+2 (a^2) (b^2) (l^4) (m^2)+2 (b^4) (l^4) (m^2)-(a^2) (c^2) (l^4) (m^2)-2 (b^2) (c^2) (l^4) (m^2)-3 (a^4) (l^3) (m^3)-3 (a^2) (b^2) (l^3) (m^3)-6 (b^4) (l^3) (m^3)+4 (a^2) (c^2) (l^3) (m^3)+5 (b^2) (c^2) (l^3) (m^3)-(c^4) (l^3) (m^3)+(a^4) (l^2) (m^4)+(a^2) (b^2) (l^2) (m^4)+4 (b^4) (l^2) (m^4)-2 (a^2) (c^2) (l^2) (m^4)-(b^2) (c^2) (l^2) (m^4)+(c^4) (l^2) (m^4)-3 (a^4) (l^4) m n-(a^2) (b^2) (l^4) m n-2 (b^4) (l^4) m n+4 (a^2) (c^2) (l^4) m n+3 (b^2) (c^2) (l^4) m n-(c^4) (l^4) m n-2 (a^2) (b^2) (l^3) (m^2) n+5 (b^4) (l^3) (m^2) n-8 (a^2) (c^2) (l^3) (m^2) n-6 (b^2) (c^2) (l^3) (m^2) n+4 (c^4) (l^3) (m^2) n+5 (a^4) (l^2) (m^3) n+3 (a^2) (b^2) (l^2) (m^3) n+4 (b^4) (l^2) (m^3) n-4 (a^2) (c^2) (l^2) (m^3) n-5 (b^2) (c^2) (l^2) (m^3) n-(c^4) (l^2) (m^3) n-2 (a^4) l (m^4) n-7 (b^4) l (m^4) n+4 (a^2) (c^2) l (m^4) n-2 (c^4) l (m^4) n+(a^4) (l^4) (n^2)+(a^2) (b^2) (l^4) (n^2)-2 (a^2) (c^2) (l^4) (n^2)-(b^2) (c^2) (l^4) (n^2)+(c^4) (l^4) (n^2)+5 (a^4) (l^3) m (n^2)-3 (a^2) (b^2) (l^3) m (n^2)-4 (a^2) (c^2) (l^3) m (n^2)+(b^2) (c^2) (l^3) m (n^2)-(c^4) (l^3) m (n^2)-6 (a^4) (l^2) (m^2) (n^2)+8 (a^2) (b^2) (l^2) (m^2) (n^2)-8 (b^4) (l^2) (m^2) (n^2)+18 (a^2) (c^2) (l^2) (m^2) (n^2)+8 (b^2) (c^2) (l^2) (m^2) (n^2)-6 (c^4) (l^2) (m^2) (n^2)-(a^4) l (m^3) (n^2)-5 (a^2) (b^2) l (m^3) (n^2)+4 (b^4) l (m^3) (n^2)-4 (a^2) (c^2) l (m^3) (n^2)+3 (b^2) (c^2) l (m^3) (n^2)+5 (c^4) l (m^3) (n^2)+(a^4) (m^4) (n^2)-(a^2) (b^2) (m^4) (n^2)+4 (b^4) (m^4) (n^2)-2 (a^2) (c^2) (m^4) (n^2)+(b^2) (c^2) (m^4) (n^2)+(c^4) (m^4) (n^2)-2 (a^4) (l^3) (n^3)+(b^4) (l^3) (n^3)+4 (a^2) (c^2) (l^3) (n^3)-2 (c^4) (l^3) (n^3)-(a^4) (l^2) m (n^3)+(a^2) (b^2) (l^2) m (n^3)-4 (a^2) (c^2) (l^2) m (n^3)-3 (b^2) (c^2) (l^2) m (n^3)+5 (c^4) (l^2) m (n^3)+4 (a^4) l (m^2) (n^3)-6 (a^2) (b^2) l (m^2) (n^3)+5 (b^4) l (m^2) (n^3)-8 (a^2) (c^2) l (m^2) (n^3)-2 (b^2) (c^2) l (m^2) (n^3)-(a^4) (m^3) (n^3)+5 (a^2) (b^2) (m^3) (n^3)-6 (b^4) (m^3) (n^3)+4 (a^2) (c^2) (m^3) (n^3)-3 (b^2) (c^2) (m^3) (n^3)-3 (c^4) (m^3) (n^3)+(a^4) (l^2) (n^4)-(a^2) (b^2) (l^2) (n^4)-2 (a^2) (c^2) (l^2) (n^4)+(b^2) (c^2) (l^2) (n^4)+(c^4) (l^2) (n^4)-(a^4) l m (n^4)+3 (a^2) (b^2) l m (n^4)-2 (b^4) l m (n^4)+4 (a^2) (c^2) l m (n^4)-(b^2) (c^2) l m (n^4)-3 (c^4) l m (n^4)-2 (a^2) (b^2) (m^2) (n^4)+2 (b^4) (m^2) (n^4)-(a^2) (c^2) (m^2) (n^4)+2 (b^2) (c^2) (m^2) (n^4)+2 (c^4) (m^2) (n^4)) (y^2) z+2 (a^2) (b^2) (l^2) (m^2) (n^2) ((a^4) (l^4) (m^2)-2 (a^2) (b^2) (l^4) (m^2)+(b^4) (l^4) (m^2)+(a^2) (c^2) (l^4) (m^2)-(b^2) (c^2) (l^4) (m^2)-2 (a^4) (l^3) (m^3)+4 (a^2) (b^2) (l^3) (m^3)-2 (b^4) (l^3) (m^3)+(c^4) (l^3) (m^3)+(a^4) (l^2) (m^4)-2 (a^2) (b^2) (l^2) (m^4)+(b^4) (l^2) (m^4)-(a^2) (c^2) (l^2) (m^4)+(b^2) (c^2) (l^2) (m^4)-3 (a^4) (l^4) m n+4 (a^2) (b^2) (l^4) m n-(b^4) (l^4) m n-(a^2) (c^2) (l^4) m n+3 (b^2) (c^2) (l^4) m n-2 (c^4) (l^4) m n+5 (a^4) (l^3) (m^2) n-4 (a^2) (b^2) (l^3) (m^2) n-(b^4) (l^3) (m^2) n-3 (a^2) (c^2) (l^3) (m^2) n+(b^2) (c^2) (l^3) (m^2) n-(a^4) (l^2) (m^3) n-4 (a^2) (b^2) (l^2) (m^3) n+5 (b^4) (l^2) (m^3) n+(a^2) (c^2) (l^2) (m^3) n-3 (b^2) (c^2) (l^2) (m^3) n-(a^4) l (m^4) n+4 (a^2) (b^2) l (m^4) n-3 (b^4) l (m^4) n+3 (a^2) (c^2) l (m^4) n-(b^2) (c^2) l (m^4) n-2 (c^4) l (m^4) n+2 (a^4) (l^4) (n^2)-(a^2) (b^2) (l^4) (n^2)+2 (a^2) (c^2) (l^4) (n^2)-2 (b^2) (c^2) (l^4) (n^2)+2 (c^4) (l^4) (n^2)-8 (a^2) (b^2) (l^3) m (n^2)+4 (b^4) (l^3) m (n^2)-2 (a^2) (c^2) (l^3) m (n^2)-6 (b^2) (c^2) (l^3) m (n^2)+5 (c^4) (l^3) m (n^2)-6 (a^4) (l^2) (m^2) (n^2)+18 (a^2) (b^2) (l^2) (m^2) (n^2)-6 (b^4) (l^2) (m^2) (n^2)+8 (a^2) (c^2) (l^2) (m^2) (n^2)+8 (b^2) (c^2) (l^2) (m^2) (n^2)-8 (c^4) (l^2) (m^2) (n^2)+4 (a^4) l (m^3) (n^2)-8 (a^2) (b^2) l (m^3) (n^2)-6 (a^2) (c^2) l (m^3) (n^2)-2 (b^2) (c^2) l (m^3) (n^2)+5 (c^4) l (m^3) (n^2)-(a^2) (b^2) (m^4) (n^2)+2 (b^4) (m^4) (n^2)-2 (a^2) (c^2) (m^4) (n^2)+2 (b^2) (c^2) (m^4) (n^2)+2 (c^4) (m^4) (n^2)-3 (a^4) (l^3) (n^3)+4 (a^2) (b^2) (l^3) (n^3)-(b^4) (l^3) (n^3)-3 (a^2) (c^2) (l^3) (n^3)+5 (b^2) (c^2) (l^3) (n^3)-6 (c^4) (l^3) (n^3)+5 (a^4) (l^2) m (n^3)-4 (a^2) (b^2) (l^2) m (n^3)-(b^4) (l^2) m (n^3)+3 (a^2) (c^2) (l^2) m (n^3)-5 (b^2) (c^2) (l^2) m (n^3)+4 (c^4) (l^2) m (n^3)-(a^4) l (m^2) (n^3)-4 (a^2) (b^2) l (m^2) (n^3)+5 (b^4) l (m^2) (n^3)-5 (a^2) (c^2) l (m^2) (n^3)+3 (b^2) (c^2) l (m^2) (n^3)+4 (c^4) l (m^2) (n^3)-(a^4) (m^3) (n^3)+4 (a^2) (b^2) (m^3) (n^3)-3 (b^4) (m^3) (n^3)+5 (a^2) (c^2) (m^3) (n^3)-3 (b^2) (c^2) (m^3) (n^3)-6 (c^4) (m^3) (n^3)+(a^4) (l^2) (n^4)-2 (a^2) (b^2) (l^2) (n^4)+(b^4) (l^2) (n^4)+(a^2) (c^2) (l^2) (n^4)-(b^2) (c^2) (l^2) (n^4)+4 (c^4) (l^2) (n^4)-2 (a^4) l m (n^4)+4 (a^2) (b^2) l m (n^4)-2 (b^4) l m (n^4)-7 (c^4) l m (n^4)+(a^4) (m^2) (n^4)-2 (a^2) (b^2) (m^2) (n^4)+(b^4) (m^2) (n^4)-(a^2) (c^2) (m^2) (n^4)+(b^2) (c^2) (m^2) (n^4)+4 (c^4) (m^2) (n^4)) y (z^2)-2 (a^2) (b^4) (l^2) (((l-m))^2) (m^2) (n^3) ((a^2) (l^2) m-(b^2) (l^2) m+(c^2) (l^2) m-(a^2) l (m^2)+(b^2) l (m^2)-2 (a^2) (l^2) n+(b^2) (l^2) n-(c^2) (l^2) n+2 (a^2) l m n-2 (c^2) l m n-(b^2) (m^2) n-(c^2) (m^2) n+(a^2) l (n^2)-(b^2) l (n^2)+2 (c^2) l (n^2)-(a^2) m (n^2)+(b^2) m (n^2)+3 (c^2) m (n^2)-2 (c^2) (n^3)) (z^3));(* Cardiode *)
QLQu2=(c^8) (((l-n))^4) (((-m+n))^4) (((l x+m y+l z))^2) (((l x+m y+m z))^2)+(a^8) (((l-m))^4) (((l-n))^4) (((m x+m y+n z))^2) (((n x+m y+n z))^2)+(b^8) (((l-m))^4) (((m-n))^4) (((l x+l y+n z))^2) (((l x+n y+n z))^2)-2 (b^2) (c^6) (l-m) (((l-n))^3) (((m-n))^4) (l x+m y+m z) (2 (l^3) (x^3)+(l^3) (x^2) y+4 (l^2) m (x^2) y+(l^2) n (x^2) y+2 (l^2) m x (y^2)+2 l (m^2) x (y^2)+2 l m n x (y^2)+l (m^2) (y^3)+(m^2) n (y^3)+3 (l^3) (x^2) z+(l^2) m (x^2) z+2 (l^2) n (x^2) z-(l^3) x y z+6 (l^2) m x y z+l (m^2) x y z+4 (l^2) n x y z+2 l m n x y z-(l^2) m (y^2) z+3 l (m^2) (y^2) z+4 l m n (y^2) z+(l^3) x (z^2)+(l^2) m x (z^2)+3 (l^2) n x (z^2)+l m n x (z^2)-(l^2) m y (z^2)+2 l (m^2) y (z^2)+(l^2) n y (z^2)+5 l m n y (z^2)-(m^2) n y (z^2)+(l^2) n (z^3)+l m n (z^3))-2 (b^6) (c^2) (((l-m))^3) (l-n) (((m-n))^4) (l x+n y+n z) (2 (l^3) (x^3)+3 (l^3) (x^2) y+2 (l^2) m (x^2) y+(l^2) n (x^2) y+(l^3) x (y^2)+3 (l^2) m x (y^2)+(l^2) n x (y^2)+l m n x (y^2)+(l^2) m (y^3)+l m n (y^3)+(l^3) (x^2) z+(l^2) m (x^2) z+4 (l^2) n (x^2) z-(l^3) x y z+4 (l^2) m x y z+6 (l^2) n x y z+2 l m n x y z+l (n^2) x y z+(l^2) m (y^2) z-(l^2) n (y^2) z+5 l m n (y^2) z+2 l (n^2) (y^2) z-m (n^2) (y^2) z+2 (l^2) n x (z^2)+2 l m n x (z^2)+2 l (n^2) x (z^2)-(l^2) n y (z^2)+4 l m n y (z^2)+3 l (n^2) y (z^2)+l (n^2) (z^3)+m (n^2) (z^3))+(b^4) (c^4) (((l-m))^2) (((l-n))^2) (((m-n))^4) (6 (l^4) (x^4)+6 (l^4) (x^3) y+12 (l^3) m (x^3) y+6 (l^3) n (x^3) y+(l^4) (x^2) (y^2)+12 (l^3) m (x^2) (y^2)+6 (l^2) (m^2) (x^2) (y^2)+4 (l^3) n (x^2) (y^2)+12 (l^2) m n (x^2) (y^2)+(l^2) (n^2) (x^2) (y^2)+2 (l^3) m x (y^3)+6 (l^2) (m^2) x (y^3)+8 (l^2) m n x (y^3)+6 l (m^2) n x (y^3)+2 l m (n^2) x (y^3)+(l^2) (m^2) (y^4)+4 l (m^2) n (y^4)+(m^2) (n^2) (y^4)+6 (l^4) (x^3) z+6 (l^3) m (x^3) z+12 (l^3) n (x^3) z-4 (l^4) (x^2) y z+22 (l^3) m (x^2) y z+6 (l^2) (m^2) (x^2) y z+22 (l^3) n (x^2) y z+20 (l^2) m n (x^2) y z+6 (l^2) (n^2) (x^2) y z-2 (l^3) m x (y^2) z+16 (l^2) (m^2) x (y^2) z-4 (l^3) n x (y^2) z+40 (l^2) m n x (y^2) z+8 l (m^2) n x (y^2) z+10 (l^2) (n^2) x (y^2) z+4 l m (n^2) x (y^2) z+2 (l^2) (m^2) (y^3) z-4 (l^2) m n (y^3) z+18 l (m^2) n (y^3) z+10 l m (n^2) (y^3) z-2 (m^2) (n^2) (y^3) z+(l^4) (x^2) (z^2)+4 (l^3) m (x^2) (z^2)+(l^2) (m^2) (x^2) (z^2)+12 (l^3) n (x^2) (z^2)+12 (l^2) m n (x^2) (z^2)+6 (l^2) (n^2) (x^2) (z^2)-4 (l^3) m x y (z^2)+10 (l^2) (m^2) x y (z^2)-2 (l^3) n x y (z^2)+40 (l^2) m n x y (z^2)+4 l (m^2) n x y (z^2)+16 (l^2) (n^2) x y (z^2)+8 l m (n^2) x y (z^2)+(l^2) (m^2) (y^2) (z^2)-8 (l^2) m n (y^2) (z^2)+24 l (m^2) n (y^2) (z^2)+(l^2) (n^2) (y^2) (z^2)+24 l m (n^2) (y^2) (z^2)-6 (m^2) (n^2) (y^2) (z^2)+2 (l^3) n x (z^3)+8 (l^2) m n x (z^3)+2 l (m^2) n x (z^3)+6 (l^2) (n^2) x (z^3)+6 l m (n^2) x (z^3)-4 (l^2) m n y (z^3)+10 l (m^2) n y (z^3)+2 (l^2) (n^2) y (z^3)+18 l m (n^2) y (z^3)-2 (m^2) (n^2) y (z^3)+(l^2) (n^2) (z^4)+4 l m (n^2) (z^4)+(m^2) (n^2) (z^4))+(a^6) (2 (c^2) (((l-m))^3) (((l-n))^4) (m-n) (n x+m y+n z) (l (m^2) (x^3)+l m n (x^3)+3 l (m^2) (x^2) y+(m^3) (x^2) y+l m n (x^2) y+(m^2) n (x^2) y+2 l (m^2) x (y^2)+3 (m^3) x (y^2)+(m^2) n x (y^2)+2 (m^3) (y^3)+l (m^2) (x^2) z+5 l m n (x^2) z-(m^2) n (x^2) z-l (n^2) (x^2) z+2 m (n^2) (x^2) z+4 l (m^2) x y z-(m^3) x y z+2 l m n x y z+6 (m^2) n x y z+m (n^2) x y z+l (m^2) (y^2) z+(m^3) (y^2) z+4 (m^2) n (y^2) z+4 l m n x (z^2)-(m^2) n x (z^2)+3 m (n^2) x (z^2)+2 l m n y (z^2)+2 (m^2) n y (z^2)+2 m (n^2) y (z^2)+l (n^2) (z^3)+m (n^2) (z^3))+2 (b^2) (((l-m))^4) (((l-n))^3) (m-n) (m x+m y+n z) (-l m n (x^3)-l (n^2) (x^3)+l (m^2) (x^2) y-5 l m n (x^2) y-2 (m^2) n (x^2) y-l (n^2) (x^2) y+m (n^2) (x^2) y-4 l m n x (y^2)-3 (m^2) n x (y^2)+m (n^2) x (y^2)-l (m^2) (y^3)-(m^2) n (y^3)-l m n (x^2) z-3 l (n^2) (x^2) z-m (n^2) (x^2) z-(n^3) (x^2) z-2 l m n x y z-(m^2) n x y z-4 l (n^2) x y z-6 m (n^2) x y z+(n^3) x y z-2 l m n (y^2) z-2 (m^2) n (y^2) z-2 m (n^2) (y^2) z-2 l (n^2) x (z^2)-m (n^2) x (z^2)-3 (n^3) x (z^2)-l (n^2) y (z^2)-4 m (n^2) y (z^2)-(n^3) y (z^2)-2 (n^3) (z^3)))+(a^2) (2 (c^6) (l-m) (((l-n))^4) (((m-n))^3) (l x+m y+l z) ((l^2) m (x^3)+(l^2) n (x^3)+2 (l^2) m (x^2) y+2 l (m^2) (x^2) y+2 l m n (x^2) y+4 l (m^2) x (y^2)+(m^3) x (y^2)+(m^2) n x (y^2)+2 (m^3) (y^3)+3 (l^2) m (x^2) z-l (m^2) (x^2) z+4 l m n (x^2) z+(l^2) m x y z+6 l (m^2) x y z-(m^3) x y z+2 l m n x y z+4 (m^2) n x y z+l (m^2) (y^2) z+3 (m^3) (y^2) z+2 (m^2) n (y^2) z+2 (l^2) m x (z^2)-l (m^2) x (z^2)-(l^2) n x (z^2)+5 l m n x (z^2)+(m^2) n x (z^2)+l (m^2) y (z^2)+(m^3) y (z^2)+l m n y (z^2)+3 (m^2) n y (z^2)+l m n (z^3)+(m^2) n (z^3))-2 (b^6) (((l-m))^4) (l-n) (((m-n))^3) (l x+l y+n z) ((l^2) m (x^3)+(l^2) n (x^3)+3 (l^2) n (x^2) y+4 l m n (x^2) y-l (n^2) (x^2) y-(l^2) m x (y^2)+2 (l^2) n x (y^2)+5 l m n x (y^2)-l (n^2) x (y^2)+m (n^2) x (y^2)+l m n (y^3)+m (n^2) (y^3)+2 (l^2) n (x^2) z+2 l m n (x^2) z+2 l (n^2) (x^2) z+(l^2) n x y z+2 l m n x y z+6 l (n^2) x y z+4 m (n^2) x y z-(n^3) x y z+l m n (y^2) z+l (n^2) (y^2) z+3 m (n^2) (y^2) z+(n^3) (y^2) z+4 l (n^2) x (z^2)+m (n^2) x (z^2)+(n^3) x (z^2)+l (n^2) y (z^2)+2 m (n^2) y (z^2)+3 (n^3) y (z^2)+2 (n^3) (z^3))-2 (b^2) (c^4) (((l-m))^2) (((l-n))^3) (((m-n))^3) (3 (l^3) m (x^4)+3 (l^3) n (x^4)+5 (l^3) m (x^3) y+6 (l^2) (m^2) (x^3) y+4 (l^3) n (x^3) y+10 (l^2) m n (x^3) y-(l^2) (n^2) (x^3) y+3 (l^3) m (x^2) (y^2)+10 (l^2) (m^2) (x^2) (y^2)+3 l (m^3) (x^2) (y^2)+11 (l^2) m n (x^2) (y^2)+11 l (m^2) n (x^2) (y^2)-2 l m (n^2) (x^2) (y^2)+6 (l^2) (m^2) x (y^3)+5 l (m^3) x (y^3)+10 l (m^2) n x (y^3)+4 (m^3) n x (y^3)-(m^2) (n^2) x (y^3)+3 l (m^3) (y^4)+3 (m^3) n (y^4)+8 (l^3) m (x^3) z-2 (l^2) (m^2) (x^3) z+4 (l^3) n (x^3) z+11 (l^2) m n (x^3) z+3 (l^2) (n^2) (x^3) z+5 (l^3) m (x^2) y z+13 (l^2) (m^2) (x^2) y z-2 l (m^3) (x^2) y z+2 (l^3) n (x^2) y z+34 (l^2) m n (x^2) y z+13 l (m^2) n (x^2) y z+2 (l^2) (n^2) (x^2) y z+5 l m (n^2) (x^2) y z-2 (l^3) m x (y^2) z+13 (l^2) (m^2) x (y^2) z+5 l (m^3) x (y^2) z+13 (l^2) m n x (y^2) z+34 l (m^2) n x (y^2) z+2 (m^3) n x (y^2) z+5 l m (n^2) x (y^2) z+2 (m^2) (n^2) x (y^2) z-2 (l^2) (m^2) (y^3) z+8 l (m^3) (y^3) z+11 l (m^2) n (y^3) z+4 (m^3) n (y^3) z+3 (m^2) (n^2) (y^3) z+5 (l^3) m (x^2) (z^2)-2 (l^2) (m^2) (x^2) (z^2)+2 (l^3) n (x^2) (z^2)+20 (l^2) m n (x^2) (z^2)-l (m^2) n (x^2) (z^2)+4 (l^2) (n^2) (x^2) (z^2)+8 l m (n^2) (x^2) (z^2)-5 (l^3) m x y (z^2)+15 (l^2) (m^2) x y (z^2)-5 l (m^3) x y (z^2)+4 (l^3) n x y (z^2)+18 (l^2) m n x y (z^2)+18 l (m^2) n x y (z^2)+4 (m^3) n x y (z^2)-2 (l^2) (n^2) x y (z^2)+27 l m (n^2) x y (z^2)-2 (m^2) (n^2) x y (z^2)-2 (l^2) (m^2) (y^2) (z^2)+5 l (m^3) (y^2) (z^2)-(l^2) m n (y^2) (z^2)+20 l (m^2) n (y^2) (z^2)+2 (m^3) n (y^2) (z^2)+8 l m (n^2) (y^2) (z^2)+4 (m^2) (n^2) (y^2) (z^2)+(l^3) n x (z^3)+9 (l^2) m n x (z^3)-l (m^2) n x (z^3)+2 (l^2) (n^2) x (z^3)+12 l m (n^2) x (z^3)+(m^2) (n^2) x (z^3)-(l^2) m n y (z^3)+9 l (m^2) n y (z^3)+(m^3) n y (z^3)+(l^2) (n^2) y (z^3)+12 l m (n^2) y (z^3)+2 (m^2) (n^2) y (z^3)+(l^2) (n^2) (z^4)+4 l m (n^2) (z^4)+(m^2) (n^2) (z^4))+2 (b^4) (c^2) (((l-m))^3) (((l-n))^2) (((m-n))^3) (3 (l^3) m (x^4)+3 (l^3) n (x^4)+4 (l^3) m (x^3) y+3 (l^2) (m^2) (x^3) y+8 (l^3) n (x^3) y+11 (l^2) m n (x^3) y-2 (l^2) (n^2) (x^3) y+2 (l^3) m (x^2) (y^2)+4 (l^2) (m^2) (x^2) (y^2)+5 (l^3) n (x^2) (y^2)+20 (l^2) m n (x^2) (y^2)+8 l (m^2) n (x^2) (y^2)-2 (l^2) (n^2) (x^2) (y^2)-l m (n^2) (x^2) (y^2)+(l^3) m x (y^3)+2 (l^2) (m^2) x (y^3)+9 (l^2) m n x (y^3)+12 l (m^2) n x (y^3)-l m (n^2) x (y^3)+(m^2) (n^2) x (y^3)+(l^2) (m^2) (y^4)+4 l (m^2) n (y^4)+(m^2) (n^2) (y^4)+4 (l^3) m (x^3) z-(l^2) (m^2) (x^3) z+5 (l^3) n (x^3) z+10 (l^2) m n (x^3) z+6 (l^2) (n^2) (x^3) z+2 (l^3) m (x^2) y z+2 (l^2) (m^2) (x^2) y z+5 (l^3) n (x^2) y z+34 (l^2) m n (x^2) y z+5 l (m^2) n (x^2) y z+13 (l^2) (n^2) (x^2) y z+13 l m (n^2) (x^2) y z-2 l (n^3) (x^2) y z+4 (l^3) m x (y^2) z-2 (l^2) (m^2) x (y^2) z-5 (l^3) n x (y^2) z+18 (l^2) m n x (y^2) z+27 l (m^2) n x (y^2) z+15 (l^2) (n^2) x (y^2) z+18 l m (n^2) x (y^2) z-2 (m^2) (n^2) x (y^2) z-5 l (n^3) x (y^2) z+4 m (n^3) x (y^2) z+(l^2) (m^2) (y^3) z-(l^2) m n (y^3) z+12 l (m^2) n (y^3) z+9 l m (n^2) (y^3) z+2 (m^2) (n^2) (y^3) z+m (n^3) (y^3) z+3 (l^3) n (x^2) (z^2)+11 (l^2) m n (x^2) (z^2)-2 l (m^2) n (x^2) (z^2)+10 (l^2) (n^2) (x^2) (z^2)+11 l m (n^2) (x^2) (z^2)+3 l (n^3) (x^2) (z^2)-2 (l^3) n x y (z^2)+13 (l^2) m n x y (z^2)+5 l (m^2) n x y (z^2)+13 (l^2) (n^2) x y (z^2)+34 l m (n^2) x y (z^2)+2 (m^2) (n^2) x y (z^2)+5 l (n^3) x y (z^2)+2 m (n^3) x y (z^2)-(l^2) m n (y^2) (z^2)+8 l (m^2) n (y^2) (z^2)-2 (l^2) (n^2) (y^2) (z^2)+20 l m (n^2) (y^2) (z^2)+4 (m^2) (n^2) (y^2) (z^2)+5 l (n^3) (y^2) (z^2)+2 m (n^3) (y^2) (z^2)+6 (l^2) (n^2) x (z^3)+10 l m (n^2) x (z^3)-(m^2) (n^2) x (z^3)+5 l (n^3) x (z^3)+4 m (n^3) x (z^3)-2 (l^2) (n^2) y (z^3)+11 l m (n^2) y (z^3)+3 (m^2) (n^2) y (z^3)+8 l (n^3) y (z^3)+4 m (n^3) y (z^3)+3 l (n^3) (z^4)+3 m (n^3) (z^4)))+(a^4) ((c^4) (((l-m))^2) (((l-n))^4) (((m-n))^2) ((l^2) (m^2) (x^4)+4 (l^2) m n (x^4)+(l^2) (n^2) (x^4)+6 (l^2) (m^2) (x^3) y+2 l (m^3) (x^3) y+6 (l^2) m n (x^3) y+8 l (m^2) n (x^3) y+2 l m (n^2) (x^3) y+6 (l^2) (m^2) (x^2) (y^2)+12 l (m^3) (x^2) (y^2)+(m^4) (x^2) (y^2)+12 l (m^2) n (x^2) (y^2)+4 (m^3) n (x^2) (y^2)+(m^2) (n^2) (x^2) (y^2)+12 l (m^3) x (y^3)+6 (m^4) x (y^3)+6 (m^3) n x (y^3)+6 (m^4) (y^4)+2 (l^2) (m^2) (x^3) z+18 (l^2) m n (x^3) z-4 l (m^2) n (x^3) z-2 (l^2) (n^2) (x^3) z+10 l m (n^2) (x^3) z+16 (l^2) (m^2) (x^2) y z-2 l (m^3) (x^2) y z+8 (l^2) m n (x^2) y z+40 l (m^2) n (x^2) y z-4 (m^3) n (x^2) y z+4 l m (n^2) (x^2) y z+10 (m^2) (n^2) (x^2) y z+6 (l^2) (m^2) x (y^2) z+22 l (m^3) x (y^2) z-4 (m^4) x (y^2) z+20 l (m^2) n x (y^2) z+22 (m^3) n x (y^2) z+6 (m^2) (n^2) x (y^2) z+6 l (m^3) (y^3) z+6 (m^4) (y^3) z+12 (m^3) n (y^3) z+(l^2) (m^2) (x^2) (z^2)+24 (l^2) m n (x^2) (z^2)-8 l (m^2) n (x^2) (z^2)-6 (l^2) (n^2) (x^2) (z^2)+24 l m (n^2) (x^2) (z^2)+(m^2) (n^2) (x^2) (z^2)+10 (l^2) (m^2) x y (z^2)-4 l (m^3) x y (z^2)+4 (l^2) m n x y (z^2)+40 l (m^2) n x y (z^2)-2 (m^3) n x y (z^2)+8 l m (n^2) x y (z^2)+16 (m^2) (n^2) x y (z^2)+(l^2) (m^2) (y^2) (z^2)+4 l (m^3) (y^2) (z^2)+(m^4) (y^2) (z^2)+12 l (m^2) n (y^2) (z^2)+12 (m^3) n (y^2) (z^2)+6 (m^2) (n^2) (y^2) (z^2)+10 (l^2) m n x (z^3)-4 l (m^2) n x (z^3)-2 (l^2) (n^2) x (z^3)+18 l m (n^2) x (z^3)+2 (m^2) (n^2) x (z^3)+2 (l^2) m n y (z^3)+8 l (m^2) n y (z^3)+2 (m^3) n y (z^3)+6 l m (n^2) y (z^3)+6 (m^2) (n^2) y (z^3)+(l^2) (n^2) (z^4)+4 l m (n^2) (z^4)+(m^2) (n^2) (z^4))-2 (b^2) (c^2) (((l-m))^3) (((l-n))^3) (((m-n))^2) ((l^2) (m^2) (x^4)+4 (l^2) m n (x^4)+(l^2) (n^2) (x^4)+2 (l^2) (m^2) (x^3) y+l (m^3) (x^3) y+12 (l^2) m n (x^3) y+9 l (m^2) n (x^3) y+(l^2) (n^2) (x^3) y-l m (n^2) (x^3) y+4 (l^2) (m^2) (x^2) (y^2)+2 l (m^3) (x^2) (y^2)+8 (l^2) m n (x^2) (y^2)+20 l (m^2) n (x^2) (y^2)+5 (m^3) n (x^2) (y^2)-l m (n^2) (x^2) (y^2)-2 (m^2) (n^2) (x^2) (y^2)+3 (l^2) (m^2) x (y^3)+4 l (m^3) x (y^3)+11 l (m^2) n x (y^3)+8 (m^3) n x (y^3)-2 (m^2) (n^2) x (y^3)+3 l (m^3) (y^4)+3 (m^3) n (y^4)+(l^2) (m^2) (x^3) z+12 (l^2) m n (x^3) z-l (m^2) n (x^3) z+2 (l^2) (n^2) (x^3) z+9 l m (n^2) (x^3) z+l (n^3) (x^3) z-2 (l^2) (m^2) (x^2) y z+4 l (m^3) (x^2) y z+27 (l^2) m n (x^2) y z+18 l (m^2) n (x^2) y z-5 (m^3) n (x^2) y z-2 (l^2) (n^2) (x^2) y z+18 l m (n^2) (x^2) y z+15 (m^2) (n^2) (x^2) y z+4 l (n^3) (x^2) y z-5 m (n^3) (x^2) y z+2 (l^2) (m^2) x (y^2) z+2 l (m^3) x (y^2) z+5 (l^2) m n x (y^2) z+34 l (m^2) n x (y^2) z+5 (m^3) n x (y^2) z+13 l m (n^2) x (y^2) z+13 (m^2) (n^2) x (y^2) z-2 m (n^3) x (y^2) z-(l^2) (m^2) (y^3) z+4 l (m^3) (y^3) z+10 l (m^2) n (y^3) z+5 (m^3) n (y^3) z+6 (m^2) (n^2) (y^3) z+8 (l^2) m n (x^2) (z^2)-l (m^2) n (x^2) (z^2)+4 (l^2) (n^2) (x^2) (z^2)+20 l m (n^2) (x^2) (z^2)-2 (m^2) (n^2) (x^2) (z^2)+2 l (n^3) (x^2) (z^2)+5 m (n^3) (x^2) (z^2)+5 (l^2) m n x y (z^2)+13 l (m^2) n x y (z^2)-2 (m^3) n x y (z^2)+2 (l^2) (n^2) x y (z^2)+34 l m (n^2) x y (z^2)+13 (m^2) (n^2) x y (z^2)+2 l (n^3) x y (z^2)+5 m (n^3) x y (z^2)-2 (l^2) m n (y^2) (z^2)+11 l (m^2) n (y^2) (z^2)+3 (m^3) n (y^2) (z^2)+11 l m (n^2) (y^2) (z^2)+10 (m^2) (n^2) (y^2) (z^2)+3 m (n^3) (y^2) (z^2)+3 (l^2) (n^2) x (z^3)+11 l m (n^2) x (z^3)-2 (m^2) (n^2) x (z^3)+4 l (n^3) x (z^3)+8 m (n^3) x (z^3)-(l^2) (n^2) y (z^3)+10 l m (n^2) y (z^3)+6 (m^2) (n^2) y (z^3)+4 l (n^3) y (z^3)+5 m (n^3) y (z^3)+3 l (n^3) (z^4)+3 m (n^3) (z^4))+(b^4) (((l-m))^4) (((l-n))^2) (((m-n))^2) ((l^2) (m^2) (x^4)+4 (l^2) m n (x^4)+(l^2) (n^2) (x^4)-2 (l^2) (m^2) (x^3) y+18 (l^2) m n (x^3) y+10 l (m^2) n (x^3) y+2 (l^2) (n^2) (x^3) y-4 l m (n^2) (x^3) y-6 (l^2) (m^2) (x^2) (y^2)+24 (l^2) m n (x^2) (y^2)+24 l (m^2) n (x^2) (y^2)+(l^2) (n^2) (x^2) (y^2)-8 l m (n^2) (x^2) (y^2)+(m^2) (n^2) (x^2) (y^2)-2 (l^2) (m^2) x (y^3)+10 (l^2) m n x (y^3)+18 l (m^2) n x (y^3)-4 l m (n^2) x (y^3)+2 (m^2) (n^2) x (y^3)+(l^2) (m^2) (y^4)+4 l (m^2) n (y^4)+(m^2) (n^2) (y^4)+6 (l^2) m n (x^3) z+2 l (m^2) n (x^3) z+6 (l^2) (n^2) (x^3) z+8 l m (n^2) (x^3) z+2 l (n^3) (x^3) z+8 (l^2) m n (x^2) y z+4 l (m^2) n (x^2) y z+16 (l^2) (n^2) (x^2) y z+40 l m (n^2) (x^2) y z+10 (m^2) (n^2) (x^2) y z-2 l (n^3) (x^2) y z-4 m (n^3) (x^2) y z+4 (l^2) m n x (y^2) z+8 l (m^2) n x (y^2) z+10 (l^2) (n^2) x (y^2) z+40 l m (n^2) x (y^2) z+16 (m^2) (n^2) x (y^2) z-4 l (n^3) x (y^2) z-2 m (n^3) x (y^2) z+2 (l^2) m n (y^3) z+6 l (m^2) n (y^3) z+8 l m (n^2) (y^3) z+6 (m^2) (n^2) (y^3) z+2 m (n^3) (y^3) z+6 (l^2) (n^2) (x^2) (z^2)+12 l m (n^2) (x^2) (z^2)+(m^2) (n^2) (x^2) (z^2)+12 l (n^3) (x^2) (z^2)+4 m (n^3) (x^2) (z^2)+(n^4) (x^2) (z^2)+6 (l^2) (n^2) x y (z^2)+20 l m (n^2) x y (z^2)+6 (m^2) (n^2) x y (z^2)+22 l (n^3) x y (z^2)+22 m (n^3) x y (z^2)-4 (n^4) x y (z^2)+(l^2) (n^2) (y^2) (z^2)+12 l m (n^2) (y^2) (z^2)+6 (m^2) (n^2) (y^2) (z^2)+4 l (n^3) (y^2) (z^2)+12 m (n^3) (y^2) (z^2)+(n^4) (y^2) (z^2)+12 l (n^3) x (z^3)+6 m (n^3) x (z^3)+6 (n^4) x (z^3)+6 l (n^3) y (z^3)+12 m (n^3) y (z^3)+6 (n^4) y (z^3)+6 (n^4) (z^4)));   (* Kantor-Hervey Deltoid *)