QA - Vertices

P1={1,0,0};P2={0,1,0};P3={0,0,1};P4={p,q,r};

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)};
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)};

QA - Points

QAP1={2 p+q+r,p+2 q+r,p+q+2 r}; (* QA-Centroid*)
QAP2={-p (-(a^2) q+(b^2) q-(c^2) q+(a^2) r+(b^2) r-(c^2) r) (-(c^2) p q+(b^2) p r+(b^2) q r-(c^2) q r),-q (-(a^2) p+(b^2) p+(c^2) p-(a^2) r-(b^2) r+(c^2) r) ((c^2) p q-(a^2) p r+(c^2) p r-(a^2) q r),(-(a^2) p+(b^2) p+(c^2) p-(a^2) q+(b^2) q-(c^2) q) r ((a^2) p q-(b^2) p q-(b^2) p r+(a^2) q r)}; (* Euler-Poncelet Point *)
QAP3={((a^2) (p^2)-(b^2) (p^2)-(c^2) (p^2)+(a^2) p q-(b^2) p q+(a^2) p r-(c^2) p r+(a^2) q r) (-(c^2) p (q^2)+2 (a^2) p q r-(b^2) p q r-(c^2) p q r+(a^2) (q^2) r-(b^2) p (r^2)+(a^2) q (r^2)),((a^2) p q-(b^2) p q+(a^2) (q^2)-(b^2) (q^2)+(c^2) (q^2)-(b^2) p r-(b^2) q r+(c^2) q r) ((c^2) (p^2) q-(b^2) (p^2) r+(a^2) p q r-2 (b^2) p q r+(c^2) p q r-(b^2) p (r^2)+(a^2) q (r^2)),((c^2) (p^2) q+(c^2) p (q^2)-(b^2) (p^2) r-(a^2) p q r-(b^2) p q r+2 (c^2) p q r-(a^2) (q^2) r) ((c^2) p q-(a^2) p r+(c^2) p r-(b^2) q r+(c^2) q r-(a^2) (r^2)-(b^2) (r^2)+(c^2) (r^2))}; (*  Gergonne-Steiner Point *)
QAP4={(a^2) q r ((a^2) (p^2)-(b^2) (p^2)-(c^2) (p^2)+(a^2) p q-(b^2) p q+(a^2) p r-(c^2) p r+(a^2) q r),(b^2) p r (-(a^2) p q+(b^2) p q-(a^2) (q^2)+(b^2) (q^2)-(c^2) (q^2)+(b^2) p r+(b^2) q r-(c^2) q r),(c^2) p q ((c^2) p q-(a^2) p r+(c^2) p r-(b^2) q r+(c^2) q r-(a^2) (r^2)-(b^2) (r^2)+(c^2) (r^2))}; (* Isogonal Center *)
QAP5={q r (q+r) (2 p+q+r),p r (p+r) (p+2 q+r),p q (p+q) (p+q+2 r)}; (* Isotomic Center *)
QAP6={-2 (a^4) q (p+q) r (p+r)-((b^2)-(c^2)) p (q+r) ((b^2) (p+q) r-(c^2) q (p+r))-(a^2) p (-(b^2) (p+q) (3 q-r) r+(c^2) q (q-3 r) (p+r)),-(a^4) q (p+q) r (p+r)-p (q+r) ((b^2) (c^2) q (p-3 r)+2 (b^4) (p+q) r+(c^4) q (p+r))+(a^2) q ((b^2) (p+q) (3 p-r) r+(c^2) (p+r) (q r+p (q+2 r))),-2 (c^4) p q (p+r) (q+r)-((a^2)-(b^2)) (p+q) r ((a^2) q (p+r)-(b^2) p (q+r))-(c^2) r (-(a^2) (3 p-q) q (p+r)+(b^2) p (p-3 q) (q+r))}; (* Parabola Axes Crosspoint *)
QAP7={-(b^4) p q r (2 p+q+r)+2 (b^2) (c^2) p q r (2 p+q+r)-(c^4) p q r (2 p+q+r)+(a^4) q r (-(p^2)+q r)+(a^2) ((c^2) p q r (3 p+2 q+r)+(b^2) p q r (3 p+q+2 r)),-(a^4) p q r (p+2 q+r)-(c^4) p q r (p+2 q+r)+(b^2) (c^2) p q r (2 p+3 q+r)+(b^4) p r (-(q^2)+p r)+(a^2) (2 (c^2) p q r (p+2 q+r)+(b^2) p q r (p+3 q+2 r)),-(a^4) p q r (p+q+2 r)-(b^4) p q r (p+q+2 r)+(b^2) (c^2) p q r (2 p+q+3 r)+(c^4) p q (p q-(r^2))+(a^2) (2 (b^2) p q r (p+q+2 r)+(c^2) p q r (p+2 q+3 r))}; (* QA-Nine-point Homothetic Center *)
QAP8={(c^4) (p^2) q (q-r)-(b^2) (c^2) (p^2) (((q-r))^2)-(b^4) (p^2) (q-r) r-(a^4) q r (3 (p^2)+2 p q+2 p r+q r)+(a^2) ((b^2) p r (4 p q+2 (q^2)+p r+3 q r)+(c^2) p q (p q+4 p r+3 q r+2 (r^2))),(c^4) p (q^2) (p-r)-(a^4) (q^2) (p-r) r-(b^4) p r (2 p q+3 (q^2)+p r+2 q r)+(b^2) (c^2) p q (p q+3 p r+4 q r+2 (r^2))+(a^2) (-(c^2) (q^2) (((p-r))^2)+(b^2) q r (2 (p^2)+4 p q+3 p r+q r)),(b^4) p (p-q) (r^2)-(a^4) (p-q) q (r^2)+(b^2) (c^2) p r (3 p q+2 (q^2)+p r+4 q r)-(c^4) p q (p q+2 p r+2 q r+3 (r^2))+(a^2) (-(b^2) (((p-q))^2) (r^2)+(c^2) q r (2 (p^2)+3 p q+4 p r+q r))}; (* Midray Homothetic Center *)
QAP9={-(a^2) (-2 (a^6) (c^2) (p^4) (q^2)+6 (a^4) (b^2) (c^2) (p^4) (q^2)-6 (a^2) (b^4) (c^2) (p^4) (q^2)+2 (b^6) (c^2) (p^4) (q^2)+4 (a^4) (c^4) (p^4) (q^2)-6 (a^2) (b^2) (c^4) (p^4) (q^2)+2 (b^4) (c^4) (p^4) (q^2)-2 (a^2) (c^6) (p^4) (q^2)+4 (b^2) (c^6) (p^4) (q^2)-4 (a^6) (c^2) (p^3) (q^3)+12 (a^4) (b^2) (c^2) (p^3) (q^3)-12 (a^2) (b^4) (c^2) (p^3) (q^3)+4 (b^6) (c^2) (p^3) (q^3)+4 (a^4) (c^4) (p^3) (q^3)-4 (a^2) (b^2) (c^4) (p^3) (q^3)+2 (a^2) (c^6) (p^3) (q^3)+2 (b^2) (c^6) (p^3) (q^3)-2 (c^8) (p^3) (q^3)-2 (a^6) (c^2) (p^2) (q^4)+6 (a^4) (b^2) (c^2) (p^2) (q^4)-6 (a^2) (b^4) (c^2) (p^2) (q^4)+2 (b^6) (c^2) (p^2) (q^4)+2 (a^2) (b^2) (c^4) (p^2) (q^4)-2 (b^4) (c^4) (p^2) (q^4)+2 (a^2) (c^6) (p^2) (q^4)+(a^8) (p^4) q r-3 (a^6) (b^2) (p^4) q r+3 (a^4) (b^4) (p^4) q r-(a^2) (b^6) (p^4) q r-3 (a^6) (c^2) (p^4) q r+10 (a^4) (b^2) (c^2) (p^4) q r-13 (a^2) (b^4) (c^2) (p^4) q r+6 (b^6) (c^2) (p^4) q r+3 (a^4) (c^4) (p^4) q r-13 (a^2) (b^2) (c^4) (p^4) q r+4 (b^4) (c^4) (p^4) q r-(a^2) (c^6) (p^4) q r+6 (b^2) (c^6) (p^4) q r+2 (a^8) (p^3) (q^2) r-5 (a^6) (b^2) (p^3) (q^2) r+3 (a^4) (b^4) (p^3) (q^2) r+(a^2) (b^6) (p^3) (q^2) r-(b^8) (p^3) (q^2) r-8 (a^6) (c^2) (p^3) (q^2) r+22 (a^4) (b^2) (c^2) (p^3) (q^2) r-26 (a^2) (b^4) (c^2) (p^3) (q^2) r+12 (b^6) (c^2) (p^3) (q^2) r+7 (a^4) (c^4) (p^3) (q^2) r-15 (a^2) (b^2) (c^4) (p^3) (q^2) r-6 (b^4) (c^4) (p^3) (q^2) r+2 (a^2) (c^6) (p^3) (q^2) r+10 (b^2) (c^6) (p^3) (q^2) r-3 (c^8) (p^3) (q^2) r+(a^8) (p^2) (q^3) r-(a^6) (b^2) (p^2) (q^3) r-3 (a^4) (b^4) (p^2) (q^3) r+5 (a^2) (b^6) (p^2) (q^3) r-2 (b^8) (p^2) (q^3) r-9 (a^6) (c^2) (p^2) (q^3) r+20 (a^4) (b^2) (c^2) (p^2) (q^3) r-19 (a^2) (b^4) (c^2) (p^2) (q^3) r+8 (b^6) (c^2) (p^2) (q^3) r+5 (a^4) (c^4) (p^2) (q^3) r-5 (a^2) (b^2) (c^4) (p^2) (q^3) r-10 (b^4) (c^4) (p^2) (q^3) r+7 (a^2) (c^6) (p^2) (q^3) r+8 (b^2) (c^6) (p^2) (q^3) r-4 (c^8) (p^2) (q^3) r+(a^6) (b^2) p (q^4) r-3 (a^4) (b^4) p (q^4) r+3 (a^2) (b^6) p (q^4) r-(b^8) p (q^4) r-4 (a^6) (c^2) p (q^4) r+8 (a^4) (b^2) (c^2) p (q^4) r-6 (a^2) (b^4) (c^2) p (q^4) r+2 (b^6) (c^2) p (q^4) r-(a^2) (b^2) (c^4) p (q^4) r-(b^4) (c^4) p (q^4) r+4 (a^2) (c^6) p (q^4) r-2 (a^6) (b^2) (p^4) (r^2)+4 (a^4) (b^4) (p^4) (r^2)-2 (a^2) (b^6) (p^4) (r^2)+6 (a^4) (b^2) (c^2) (p^4) (r^2)-6 (a^2) (b^4) (c^2) (p^4) (r^2)+4 (b^6) (c^2) (p^4) (r^2)-6 (a^2) (b^2) (c^4) (p^4) (r^2)+2 (b^4) (c^4) (p^4) (r^2)+2 (b^2) (c^6) (p^4) (r^2)+2 (a^8) (p^3) q (r^2)-8 (a^6) (b^2) (p^3) q (r^2)+7 (a^4) (b^4) (p^3) q (r^2)+2 (a^2) (b^6) (p^3) q (r^2)-3 (b^8) (p^3) q (r^2)-5 (a^6) (c^2) (p^3) q (r^2)+22 (a^4) (b^2) (c^2) (p^3) q (r^2)-15 (a^2) (b^4) (c^2) (p^3) q (r^2)+10 (b^6) (c^2) (p^3) q (r^2)+3 (a^4) (c^4) (p^3) q (r^2)-26 (a^2) (b^2) (c^4) (p^3) q (r^2)-6 (b^4) (c^4) (p^3) q (r^2)+(a^2) (c^6) (p^3) q (r^2)+12 (b^2) (c^6) (p^3) q (r^2)-(c^8) (p^3) q (r^2)+4 (a^8) (p^2) (q^2) (r^2)-9 (a^6) (b^2) (p^2) (q^2) (r^2)+11 (a^2) (b^6) (p^2) (q^2) (r^2)-6 (b^8) (p^2) (q^2) (r^2)-9 (a^6) (c^2) (p^2) (q^2) (r^2)+28 (a^4) (b^2) (c^2) (p^2) (q^2) (r^2)-21 (a^2) (b^4) (c^2) (p^2) (q^2) (r^2)+14 (b^6) (c^2) (p^2) (q^2) (r^2)-21 (a^2) (b^2) (c^4) (p^2) (q^2) (r^2)-16 (b^4) (c^4) (p^2) (q^2) (r^2)+11 (a^2) (c^6) (p^2) (q^2) (r^2)+14 (b^2) (c^6) (p^2) (q^2) (r^2)-6 (c^8) (p^2) (q^2) (r^2)+2 (a^8) p (q^3) (r^2)-2 (a^6) (b^2) p (q^3) (r^2)-5 (a^4) (b^4) p (q^3) (r^2)+8 (a^2) (b^6) p (q^3) (r^2)-3 (b^8) p (q^3) (r^2)-6 (a^6) (c^2) p (q^3) (r^2)+14 (a^4) (b^2) (c^2) p (q^3) (r^2)-12 (a^2) (b^4) (c^2) p (q^3) (r^2)+8 (b^6) (c^2) p (q^3) (r^2)-2 (a^4) (c^4) p (q^3) (r^2)-4 (a^2) (b^2) (c^4) p (q^3) (r^2)-9 (b^4) (c^4) p (q^3) (r^2)+8 (a^2) (c^6) p (q^3) (r^2)+6 (b^2) (c^6) p (q^3) (r^2)-2 (c^8) p (q^3) (r^2)+(a^6) (b^2) (q^4) (r^2)-2 (a^4) (b^4) (q^4) (r^2)+(a^2) (b^6) (q^4) (r^2)-2 (a^6) (c^2) (q^4) (r^2)+2 (a^4) (b^2) (c^2) (q^4) (r^2)-3 (a^2) (b^2) (c^4) (q^4) (r^2)+2 (a^2) (c^6) (q^4) (r^2)-4 (a^6) (b^2) (p^3) (r^3)+4 (a^4) (b^4) (p^3) (r^3)+2 (a^2) (b^6) (p^3) (r^3)-2 (b^8) (p^3) (r^3)+12 (a^4) (b^2) (c^2) (p^3) (r^3)-4 (a^2) (b^4) (c^2) (p^3) (r^3)+2 (b^6) (c^2) (p^3) (r^3)-12 (a^2) (b^2) (c^4) (p^3) (r^3)+4 (b^2) (c^6) (p^3) (r^3)+(a^8) (p^2) q (r^3)-9 (a^6) (b^2) (p^2) q (r^3)+5 (a^4) (b^4) (p^2) q (r^3)+7 (a^2) (b^6) (p^2) q (r^3)-4 (b^8) (p^2) q (r^3)-(a^6) (c^2) (p^2) q (r^3)+20 (a^4) (b^2) (c^2) (p^2) q (r^3)-5 (a^2) (b^4) (c^2) (p^2) q (r^3)+8 (b^6) (c^2) (p^2) q (r^3)-3 (a^4) (c^4) (p^2) q (r^3)-19 (a^2) (b^2) (c^4) (p^2) q (r^3)-10 (b^4) (c^4) (p^2) q (r^3)+5 (a^2) (c^6) (p^2) q (r^3)+8 (b^2) (c^6) (p^2) q (r^3)-2 (c^8) (p^2) q (r^3)+2 (a^8) p (q^2) (r^3)-6 (a^6) (b^2) p (q^2) (r^3)-2 (a^4) (b^4) p (q^2) (r^3)+8 (a^2) (b^6) p (q^2) (r^3)-2 (b^8) p (q^2) (r^3)-2 (a^6) (c^2) p (q^2) (r^3)+14 (a^4) (b^2) (c^2) p (q^2) (r^3)-4 (a^2) (b^4) (c^2) p (q^2) (r^3)+6 (b^6) (c^2) p (q^2) (r^3)-5 (a^4) (c^4) p (q^2) (r^3)-12 (a^2) (b^2) (c^4) p (q^2) (r^3)-9 (b^4) (c^4) p (q^2) (r^3)+8 (a^2) (c^6) p (q^2) (r^3)+8 (b^2) (c^6) p (q^2) (r^3)-3 (c^8) p (q^2) (r^3)+(a^8) (q^3) (r^3)-(a^6) (b^2) (q^3) (r^3)-3 (a^4) (b^4) (q^3) (r^3)+3 (a^2) (b^6) (q^3) (r^3)-(a^6) (c^2) (q^3) (r^3)+6 (a^4) (b^2) (c^2) (q^3) (r^3)-3 (a^2) (b^4) (c^2) (q^3) (r^3)-3 (a^4) (c^4) (q^3) (r^3)-3 (a^2) (b^2) (c^4) (q^3) (r^3)+3 (a^2) (c^6) (q^3) (r^3)-2 (a^6) (b^2) (p^2) (r^4)+2 (a^2) (b^6) (p^2) (r^4)+6 (a^4) (b^2) (c^2) (p^2) (r^4)+2 (a^2) (b^4) (c^2) (p^2) (r^4)-6 (a^2) (b^2) (c^4) (p^2) (r^4)-2 (b^4) (c^4) (p^2) (r^4)+2 (b^2) (c^6) (p^2) (r^4)-4 (a^6) (b^2) p q (r^4)+4 (a^2) (b^6) p q (r^4)+(a^6) (c^2) p q (r^4)+8 (a^4) (b^2) (c^2) p q (r^4)-(a^2) (b^4) (c^2) p q (r^4)-3 (a^4) (c^4) p q (r^4)-6 (a^2) (b^2) (c^4) p q (r^4)-(b^4) (c^4) p q (r^4)+3 (a^2) (c^6) p q (r^4)+2 (b^2) (c^6) p q (r^4)-(c^8) p q (r^4)-2 (a^6) (b^2) (q^2) (r^4)+2 (a^2) (b^6) (q^2) (r^4)+(a^6) (c^2) (q^2) (r^4)+2 (a^4) (b^2) (c^2) (q^2) (r^4)-3 (a^2) (b^4) (c^2) (q^2) (r^4)-2 (a^4) (c^4) (q^2) (r^4)+(a^2) (c^6) (q^2) (r^4)),-(b^2) (2 (a^6) (c^2) (p^4) (q^2)-6 (a^4) (b^2) (c^2) (p^4) (q^2)+6 (a^2) (b^4) (c^2) (p^4) (q^2)-2 (b^6) (c^2) (p^4) (q^2)-2 (a^4) (c^4) (p^4) (q^2)+2 (a^2) (b^2) (c^4) (p^4) (q^2)+2 (b^2) (c^6) (p^4) (q^2)+4 (a^6) (c^2) (p^3) (q^3)-12 (a^4) (b^2) (c^2) (p^3) (q^3)+12 (a^2) (b^4) (c^2) (p^3) (q^3)-4 (b^6) (c^2) (p^3) (q^3)-4 (a^2) (b^2) (c^4) (p^3) (q^3)+4 (b^4) (c^4) (p^3) (q^3)+2 (a^2) (c^6) (p^3) (q^3)+2 (b^2) (c^6) (p^3) (q^3)-2 (c^8) (p^3) (q^3)+2 (a^6) (c^2) (p^2) (q^4)-6 (a^4) (b^2) (c^2) (p^2) (q^4)+6 (a^2) (b^4) (c^2) (p^2) (q^4)-2 (b^6) (c^2) (p^2) (q^4)+2 (a^4) (c^4) (p^2) (q^4)-6 (a^2) (b^2) (c^4) (p^2) (q^4)+4 (b^4) (c^4) (p^2) (q^4)+4 (a^2) (c^6) (p^2) (q^4)-2 (b^2) (c^6) (p^2) (q^4)-(a^8) (p^4) q r+3 (a^6) (b^2) (p^4) q r-3 (a^4) (b^4) (p^4) q r+(a^2) (b^6) (p^4) q r+2 (a^6) (c^2) (p^4) q r-6 (a^4) (b^2) (c^2) (p^4) q r+8 (a^2) (b^4) (c^2) (p^4) q r-4 (b^6) (c^2) (p^4) q r-(a^4) (c^4) (p^4) q r-(a^2) (b^2) (c^4) (p^4) q r+4 (b^2) (c^6) (p^4) q r-2 (a^8) (p^3) (q^2) r+5 (a^6) (b^2) (p^3) (q^2) r-3 (a^4) (b^4) (p^3) (q^2) r-(a^2) (b^6) (p^3) (q^2) r+(b^8) (p^3) (q^2) r+8 (a^6) (c^2) (p^3) (q^2) r-19 (a^4) (b^2) (c^2) (p^3) (q^2) r+20 (a^2) (b^4) (c^2) (p^3) (q^2) r-9 (b^6) (c^2) (p^3) (q^2) r-10 (a^4) (c^4) (p^3) (q^2) r-5 (a^2) (b^2) (c^4) (p^3) (q^2) r+5 (b^4) (c^4) (p^3) (q^2) r+8 (a^2) (c^6) (p^3) (q^2) r+7 (b^2) (c^6) (p^3) (q^2) r-4 (c^8) (p^3) (q^2) r-(a^8) (p^2) (q^3) r+(a^6) (b^2) (p^2) (q^3) r+3 (a^4) (b^4) (p^2) (q^3) r-5 (a^2) (b^6) (p^2) (q^3) r+2 (b^8) (p^2) (q^3) r+12 (a^6) (c^2) (p^2) (q^3) r-26 (a^4) (b^2) (c^2) (p^2) (q^3) r+22 (a^2) (b^4) (c^2) (p^2) (q^3) r-8 (b^6) (c^2) (p^2) (q^3) r-6 (a^4) (c^4) (p^2) (q^3) r-15 (a^2) (b^2) (c^4) (p^2) (q^3) r+7 (b^4) (c^4) (p^2) (q^3) r+10 (a^2) (c^6) (p^2) (q^3) r+2 (b^2) (c^6) (p^2) (q^3) r-3 (c^8) (p^2) (q^3) r-(a^6) (b^2) p (q^4) r+3 (a^4) (b^4) p (q^4) r-3 (a^2) (b^6) p (q^4) r+(b^8) p (q^4) r+6 (a^6) (c^2) p (q^4) r-13 (a^4) (b^2) (c^2) p (q^4) r+10 (a^2) (b^4) (c^2) p (q^4) r-3 (b^6) (c^2) p (q^4) r+4 (a^4) (c^4) p (q^4) r-13 (a^2) (b^2) (c^4) p (q^4) r+3 (b^4) (c^4) p (q^4) r+6 (a^2) (c^6) p (q^4) r-(b^2) (c^6) p (q^4) r+(a^6) (b^2) (p^4) (r^2)-2 (a^4) (b^4) (p^4) (r^2)+(a^2) (b^6) (p^4) (r^2)+2 (a^2) (b^4) (c^2) (p^4) (r^2)-2 (b^6) (c^2) (p^4) (r^2)-3 (a^2) (b^2) (c^4) (p^4) (r^2)+2 (b^2) (c^6) (p^4) (r^2)-3 (a^8) (p^3) q (r^2)+8 (a^6) (b^2) (p^3) q (r^2)-5 (a^4) (b^4) (p^3) q (r^2)-2 (a^2) (b^6) (p^3) q (r^2)+2 (b^8) (p^3) q (r^2)+8 (a^6) (c^2) (p^3) q (r^2)-12 (a^4) (b^2) (c^2) (p^3) q (r^2)+14 (a^2) (b^4) (c^2) (p^3) q (r^2)-6 (b^6) (c^2) (p^3) q (r^2)-9 (a^4) (c^4) (p^3) q (r^2)-4 (a^2) (b^2) (c^4) (p^3) q (r^2)-2 (b^4) (c^4) (p^3) q (r^2)+6 (a^2) (c^6) (p^3) q (r^2)+8 (b^2) (c^6) (p^3) q (r^2)-2 (c^8) (p^3) q (r^2)-6 (a^8) (p^2) (q^2) (r^2)+11 (a^6) (b^2) (p^2) (q^2) (r^2)-9 (a^2) (b^6) (p^2) (q^2) (r^2)+4 (b^8) (p^2) (q^2) (r^2)+14 (a^6) (c^2) (p^2) (q^2) (r^2)-21 (a^4) (b^2) (c^2) (p^2) (q^2) (r^2)+28 (a^2) (b^4) (c^2) (p^2) (q^2) (r^2)-9 (b^6) (c^2) (p^2) (q^2) (r^2)-16 (a^4) (c^4) (p^2) (q^2) (r^2)-21 (a^2) (b^2) (c^4) (p^2) (q^2) (r^2)+14 (a^2) (c^6) (p^2) (q^2) (r^2)+11 (b^2) (c^6) (p^2) (q^2) (r^2)-6 (c^8) (p^2) (q^2) (r^2)-3 (a^8) p (q^3) (r^2)+2 (a^6) (b^2) p (q^3) (r^2)+7 (a^4) (b^4) p (q^3) (r^2)-8 (a^2) (b^6) p (q^3) (r^2)+2 (b^8) p (q^3) (r^2)+10 (a^6) (c^2) p (q^3) (r^2)-15 (a^4) (b^2) (c^2) p (q^3) (r^2)+22 (a^2) (b^4) (c^2) p (q^3) (r^2)-5 (b^6) (c^2) p (q^3) (r^2)-6 (a^4) (c^4) p (q^3) (r^2)-26 (a^2) (b^2) (c^4) p (q^3) (r^2)+3 (b^4) (c^4) p (q^3) (r^2)+12 (a^2) (c^6) p (q^3) (r^2)+(b^2) (c^6) p (q^3) (r^2)-(c^8) p (q^3) (r^2)-2 (a^6) (b^2) (q^4) (r^2)+4 (a^4) (b^4) (q^4) (r^2)-2 (a^2) (b^6) (q^4) (r^2)+4 (a^6) (c^2) (q^4) (r^2)-6 (a^4) (b^2) (c^2) (q^4) (r^2)+6 (a^2) (b^4) (c^2) (q^4) (r^2)+2 (a^4) (c^4) (q^4) (r^2)-6 (a^2) (b^2) (c^4) (q^4) (r^2)+2 (a^2) (c^6) (q^4) (r^2)+3 (a^6) (b^2) (p^3) (r^3)-3 (a^4) (b^4) (p^3) (r^3)-(a^2) (b^6) (p^3) (r^3)+(b^8) (p^3) (r^3)-3 (a^4) (b^2) (c^2) (p^3) (r^3)+6 (a^2) (b^4) (c^2) (p^3) (r^3)-(b^6) (c^2) (p^3) (r^3)-3 (a^2) (b^2) (c^4) (p^3) (r^3)-3 (b^4) (c^4) (p^3) (r^3)+3 (b^2) (c^6) (p^3) (r^3)-2 (a^8) (p^2) q (r^3)+8 (a^6) (b^2) (p^2) q (r^3)-2 (a^4) (b^4) (p^2) q (r^3)-6 (a^2) (b^6) (p^2) q (r^3)+2 (b^8) (p^2) q (r^3)+6 (a^6) (c^2) (p^2) q (r^3)-4 (a^4) (b^2) (c^2) (p^2) q (r^3)+14 (a^2) (b^4) (c^2) (p^2) q (r^3)-2 (b^6) (c^2) (p^2) q (r^3)-9 (a^4) (c^4) (p^2) q (r^3)-12 (a^2) (b^2) (c^4) (p^2) q (r^3)-5 (b^4) (c^4) (p^2) q (r^3)+8 (a^2) (c^6) (p^2) q (r^3)+8 (b^2) (c^6) (p^2) q (r^3)-3 (c^8) (p^2) q (r^3)-4 (a^8) p (q^2) (r^3)+7 (a^6) (b^2) p (q^2) (r^3)+5 (a^4) (b^4) p (q^2) (r^3)-9 (a^2) (b^6) p (q^2) (r^3)+(b^8) p (q^2) (r^3)+8 (a^6) (c^2) p (q^2) (r^3)-5 (a^4) (b^2) (c^2) p (q^2) (r^3)+20 (a^2) (b^4) (c^2) p (q^2) (r^3)-(b^6) (c^2) p (q^2) (r^3)-10 (a^4) (c^4) p (q^2) (r^3)-19 (a^2) (b^2) (c^4) p (q^2) (r^3)-3 (b^4) (c^4) p (q^2) (r^3)+8 (a^2) (c^6) p (q^2) (r^3)+5 (b^2) (c^6) p (q^2) (r^3)-2 (c^8) p (q^2) (r^3)-2 (a^8) (q^3) (r^3)+2 (a^6) (b^2) (q^3) (r^3)+4 (a^4) (b^4) (q^3) (r^3)-4 (a^2) (b^6) (q^3) (r^3)+2 (a^6) (c^2) (q^3) (r^3)-4 (a^4) (b^2) (c^2) (q^3) (r^3)+12 (a^2) (b^4) (c^2) (q^3) (r^3)-12 (a^2) (b^2) (c^4) (q^3) (r^3)+4 (a^2) (c^6) (q^3) (r^3)+2 (a^6) (b^2) (p^2) (r^4)-2 (a^2) (b^6) (p^2) (r^4)-3 (a^4) (b^2) (c^2) (p^2) (r^4)+2 (a^2) (b^4) (c^2) (p^2) (r^4)+(b^6) (c^2) (p^2) (r^4)-2 (b^4) (c^4) (p^2) (r^4)+(b^2) (c^6) (p^2) (r^4)+4 (a^6) (b^2) p q (r^4)-4 (a^2) (b^6) p q (r^4)-(a^4) (b^2) (c^2) p q (r^4)+8 (a^2) (b^4) (c^2) p q (r^4)+(b^6) (c^2) p q (r^4)-(a^4) (c^4) p q (r^4)-6 (a^2) (b^2) (c^4) p q (r^4)-3 (b^4) (c^4) p q (r^4)+2 (a^2) (c^6) p q (r^4)+3 (b^2) (c^6) p q (r^4)-(c^8) p q (r^4)+2 (a^6) (b^2) (q^2) (r^4)-2 (a^2) (b^6) (q^2) (r^4)+2 (a^4) (b^2) (c^2) (q^2) (r^4)+6 (a^2) (b^4) (c^2) (q^2) (r^4)-2 (a^4) (c^4) (q^2) (r^4)-6 (a^2) (b^2) (c^4) (q^2) (r^4)+2 (a^2) (c^6) (q^2) (r^4)),-(c^2) ((a^6) (c^2) (p^4) (q^2)-3 (a^2) (b^4) (c^2) (p^4) (q^2)+2 (b^6) (c^2) (p^4) (q^2)-2 (a^4) (c^4) (p^4) (q^2)+2 (a^2) (b^2) (c^4) (p^4) (q^2)+(a^2) (c^6) (p^4) (q^2)-2 (b^2) (c^6) (p^4) (q^2)+3 (a^6) (c^2) (p^3) (q^3)-3 (a^4) (b^2) (c^2) (p^3) (q^3)-3 (a^2) (b^4) (c^2) (p^3) (q^3)+3 (b^6) (c^2) (p^3) (q^3)-3 (a^4) (c^4) (p^3) (q^3)+6 (a^2) (b^2) (c^4) (p^3) (q^3)-3 (b^4) (c^4) (p^3) (q^3)-(a^2) (c^6) (p^3) (q^3)-(b^2) (c^6) (p^3) (q^3)+(c^8) (p^3) (q^3)+2 (a^6) (c^2) (p^2) (q^4)-3 (a^4) (b^2) (c^2) (p^2) (q^4)+(b^6) (c^2) (p^2) (q^4)+2 (a^2) (b^2) (c^4) (p^2) (q^4)-2 (b^4) (c^4) (p^2) (q^4)-2 (a^2) (c^6) (p^2) (q^4)+(b^2) (c^6) (p^2) (q^4)-(a^8) (p^4) q r+2 (a^6) (b^2) (p^4) q r-(a^4) (b^4) (p^4) q r+3 (a^6) (c^2) (p^4) q r-6 (a^4) (b^2) (c^2) (p^4) q r-(a^2) (b^4) (c^2) (p^4) q r+4 (b^6) (c^2) (p^4) q r-3 (a^4) (c^4) (p^4) q r+8 (a^2) (b^2) (c^4) (p^4) q r+(a^2) (c^6) (p^4) q r-4 (b^2) (c^6) (p^4) q r-3 (a^8) (p^3) (q^2) r+8 (a^6) (b^2) (p^3) (q^2) r-9 (a^4) (b^4) (p^3) (q^2) r+6 (a^2) (b^6) (p^3) (q^2) r-2 (b^8) (p^3) (q^2) r+8 (a^6) (c^2) (p^3) (q^2) r-12 (a^4) (b^2) (c^2) (p^3) (q^2) r-4 (a^2) (b^4) (c^2) (p^3) (q^2) r+8 (b^6) (c^2) (p^3) (q^2) r-5 (a^4) (c^4) (p^3) (q^2) r+14 (a^2) (b^2) (c^4) (p^3) (q^2) r-2 (b^4) (c^4) (p^3) (q^2) r-2 (a^2) (c^6) (p^3) (q^2) r-6 (b^2) (c^6) (p^3) (q^2) r+2 (c^8) (p^3) (q^2) r-2 (a^8) (p^2) (q^3) r+6 (a^6) (b^2) (p^2) (q^3) r-9 (a^4) (b^4) (p^2) (q^3) r+8 (a^2) (b^6) (p^2) (q^3) r-3 (b^8) (p^2) (q^3) r+8 (a^6) (c^2) (p^2) (q^3) r-4 (a^4) (b^2) (c^2) (p^2) (q^3) r-12 (a^2) (b^4) (c^2) (p^2) (q^3) r+8 (b^6) (c^2) (p^2) (q^3) r-2 (a^4) (c^4) (p^2) (q^3) r+14 (a^2) (b^2) (c^4) (p^2) (q^3) r-5 (b^4) (c^4) (p^2) (q^3) r-6 (a^2) (c^6) (p^2) (q^3) r-2 (b^2) (c^6) (p^2) (q^3) r+2 (c^8) (p^2) (q^3) r-(a^4) (b^4) p (q^4) r+2 (a^2) (b^6) p (q^4) r-(b^8) p (q^4) r+4 (a^6) (c^2) p (q^4) r-(a^4) (b^2) (c^2) p (q^4) r-6 (a^2) (b^4) (c^2) p (q^4) r+3 (b^6) (c^2) p (q^4) r+8 (a^2) (b^2) (c^4) p (q^4) r-3 (b^4) (c^4) p (q^4) r-4 (a^2) (c^6) p (q^4) r+(b^2) (c^6) p (q^4) r+2 (a^6) (b^2) (p^4) (r^2)-2 (a^4) (b^4) (p^4) (r^2)-6 (a^4) (b^2) (c^2) (p^4) (r^2)+2 (a^2) (b^4) (c^2) (p^4) (r^2)+2 (b^6) (c^2) (p^4) (r^2)+6 (a^2) (b^2) (c^4) (p^4) (r^2)-2 (b^2) (c^6) (p^4) (r^2)-2 (a^8) (p^3) q (r^2)+8 (a^6) (b^2) (p^3) q (r^2)-10 (a^4) (b^4) (p^3) q (r^2)+8 (a^2) (b^6) (p^3) q (r^2)-4 (b^8) (p^3) q (r^2)+5 (a^6) (c^2) (p^3) q (r^2)-19 (a^4) (b^2) (c^2) (p^3) q (r^2)-5 (a^2) (b^4) (c^2) (p^3) q (r^2)+7 (b^6) (c^2) (p^3) q (r^2)-3 (a^4) (c^4) (p^3) q (r^2)+20 (a^2) (b^2) (c^4) (p^3) q (r^2)+5 (b^4) (c^4) (p^3) q (r^2)-(a^2) (c^6) (p^3) q (r^2)-9 (b^2) (c^6) (p^3) q (r^2)+(c^8) (p^3) q (r^2)-6 (a^8) (p^2) (q^2) (r^2)+14 (a^6) (b^2) (p^2) (q^2) (r^2)-16 (a^4) (b^4) (p^2) (q^2) (r^2)+14 (a^2) (b^6) (p^2) (q^2) (r^2)-6 (b^8) (p^2) (q^2) (r^2)+11 (a^6) (c^2) (p^2) (q^2) (r^2)-21 (a^4) (b^2) (c^2) (p^2) (q^2) (r^2)-21 (a^2) (b^4) (c^2) (p^2) (q^2) (r^2)+11 (b^6) (c^2) (p^2) (q^2) (r^2)+28 (a^2) (b^2) (c^4) (p^2) (q^2) (r^2)-9 (a^2) (c^6) (p^2) (q^2) (r^2)-9 (b^2) (c^6) (p^2) (q^2) (r^2)+4 (c^8) (p^2) (q^2) (r^2)-4 (a^8) p (q^3) (r^2)+8 (a^6) (b^2) p (q^3) (r^2)-10 (a^4) (b^4) p (q^3) (r^2)+8 (a^2) (b^6) p (q^3) (r^2)-2 (b^8) p (q^3) (r^2)+7 (a^6) (c^2) p (q^3) (r^2)-5 (a^4) (b^2) (c^2) p (q^3) (r^2)-19 (a^2) (b^4) (c^2) p (q^3) (r^2)+5 (b^6) (c^2) p (q^3) (r^2)+5 (a^4) (c^4) p (q^3) (r^2)+20 (a^2) (b^2) (c^4) p (q^3) (r^2)-3 (b^4) (c^4) p (q^3) (r^2)-9 (a^2) (c^6) p (q^3) (r^2)-(b^2) (c^6) p (q^3) (r^2)+(c^8) p (q^3) (r^2)-2 (a^4) (b^4) (q^4) (r^2)+2 (a^2) (b^6) (q^4) (r^2)+2 (a^6) (c^2) (q^4) (r^2)+2 (a^4) (b^2) (c^2) (q^4) (r^2)-6 (a^2) (b^4) (c^2) (q^4) (r^2)+6 (a^2) (b^2) (c^4) (q^4) (r^2)-2 (a^2) (c^6) (q^4) (r^2)+4 (a^6) (b^2) (p^3) (r^3)+2 (a^2) (b^6) (p^3) (r^3)-2 (b^8) (p^3) (r^3)-12 (a^4) (b^2) (c^2) (p^3) (r^3)-4 (a^2) (b^4) (c^2) (p^3) (r^3)+2 (b^6) (c^2) (p^3) (r^3)+12 (a^2) (b^2) (c^4) (p^3) (r^3)+4 (b^4) (c^4) (p^3) (r^3)-4 (b^2) (c^6) (p^3) (r^3)-(a^8) (p^2) q (r^3)+12 (a^6) (b^2) (p^2) q (r^3)-6 (a^4) (b^4) (p^2) q (r^3)+10 (a^2) (b^6) (p^2) q (r^3)-3 (b^8) (p^2) q (r^3)+(a^6) (c^2) (p^2) q (r^3)-26 (a^4) (b^2) (c^2) (p^2) q (r^3)-15 (a^2) (b^4) (c^2) (p^2) q (r^3)+2 (b^6) (c^2) (p^2) q (r^3)+3 (a^4) (c^4) (p^2) q (r^3)+22 (a^2) (b^2) (c^4) (p^2) q (r^3)+7 (b^4) (c^4) (p^2) q (r^3)-5 (a^2) (c^6) (p^2) q (r^3)-8 (b^2) (c^6) (p^2) q (r^3)+2 (c^8) (p^2) q (r^3)-3 (a^8) p (q^2) (r^3)+10 (a^6) (b^2) p (q^2) (r^3)-6 (a^4) (b^4) p (q^2) (r^3)+12 (a^2) (b^6) p (q^2) (r^3)-(b^8) p (q^2) (r^3)+2 (a^6) (c^2) p (q^2) (r^3)-15 (a^4) (b^2) (c^2) p (q^2) (r^3)-26 (a^2) (b^4) (c^2) p (q^2) (r^3)+(b^6) (c^2) p (q^2) (r^3)+7 (a^4) (c^4) p (q^2) (r^3)+22 (a^2) (b^2) (c^4) p (q^2) (r^3)+3 (b^4) (c^4) p (q^2) (r^3)-8 (a^2) (c^6) p (q^2) (r^3)-5 (b^2) (c^6) p (q^2) (r^3)+2 (c^8) p (q^2) (r^3)-2 (a^8) (q^3) (r^3)+2 (a^6) (b^2) (q^3) (r^3)+4 (a^2) (b^6) (q^3) (r^3)+2 (a^6) (c^2) (q^3) (r^3)-4 (a^4) (b^2) (c^2) (q^3) (r^3)-12 (a^2) (b^4) (c^2) (q^3) (r^3)+4 (a^4) (c^4) (q^3) (r^3)+12 (a^2) (b^2) (c^4) (q^3) (r^3)-4 (a^2) (c^6) (q^3) (r^3)+2 (a^6) (b^2) (p^2) (r^4)+2 (a^4) (b^4) (p^2) (r^4)+4 (a^2) (b^6) (p^2) (r^4)-6 (a^4) (b^2) (c^2) (p^2) (r^4)-6 (a^2) (b^4) (c^2) (p^2) (r^4)-2 (b^6) (c^2) (p^2) (r^4)+6 (a^2) (b^2) (c^4) (p^2) (r^4)+4 (b^4) (c^4) (p^2) (r^4)-2 (b^2) (c^6) (p^2) (r^4)+6 (a^6) (b^2) p q (r^4)+4 (a^4) (b^4) p q (r^4)+6 (a^2) (b^6) p q (r^4)-(a^6) (c^2) p q (r^4)-13 (a^4) (b^2) (c^2) p q (r^4)-13 (a^2) (b^4) (c^2) p q (r^4)-(b^6) (c^2) p q (r^4)+3 (a^4) (c^4) p q (r^4)+10 (a^2) (b^2) (c^4) p q (r^4)+3 (b^4) (c^4) p q (r^4)-3 (a^2) (c^6) p q (r^4)-3 (b^2) (c^6) p q (r^4)+(c^8) p q (r^4)+4 (a^6) (b^2) (q^2) (r^4)+2 (a^4) (b^4) (q^2) (r^4)+2 (a^2) (b^6) (q^2) (r^4)-2 (a^6) (c^2) (q^2) (r^4)-6 (a^4) (b^2) (c^2) (q^2) (r^4)-6 (a^2) (b^4) (c^2) (q^2) (r^4)+4 (a^4) (c^4) (q^2) (r^4)+6 (a^2) (b^2) (c^4) (q^2) (r^4)-2 (a^2) (c^6) (q^2) (r^4))}; (* QA-Miquel Center *)
QAP10={-p (q+r) (2 p+q+r),-q (p+r) (p+2 q+r),-(p+q) r (p+q+2 r)}; (* Centroid QA-Diagonal Triangle *)
QAP11={-(a^2) (c^2) (p^3) (q^3)+(b^2) (c^2) (p^3) (q^3)-(c^4) (p^3) (q^3)-(a^4) (p^3) (q^2) r+2 (a^2) (b^2) (p^3) (q^2) r-(b^4) (p^3) (q^2) r+3 (a^2) (c^2) (p^3) (q^2) r+3 (b^2) (c^2) (p^3) (q^2) r-2 (c^4) (p^3) (q^2) r-(a^4) (p^2) (q^3) r+2 (a^2) (b^2) (p^2) (q^3) r-(b^4) (p^2) (q^3) r+2 (b^2) (c^2) (p^2) (q^3) r-(c^4) (p^2) (q^3) r-(a^4) (p^3) q (r^2)+3 (a^2) (b^2) (p^3) q (r^2)-2 (b^4) (p^3) q (r^2)+2 (a^2) (c^2) (p^3) q (r^2)+3 (b^2) (c^2) (p^3) q (r^2)-(c^4) (p^3) q (r^2)+2 (a^2) (b^2) (p^2) (q^2) (r^2)-2 (b^4) (p^2) (q^2) (r^2)+2 (a^2) (c^2) (p^2) (q^2) (r^2)+4 (b^2) (c^2) (p^2) (q^2) (r^2)-2 (c^4) (p^2) (q^2) (r^2)+(a^4) p (q^3) (r^2)-(a^2) (b^2) p (q^3) (r^2)+(a^2) (c^2) p (q^3) (r^2)-(a^2) (b^2) (p^3) (r^3)-(b^4) (p^3) (r^3)+(b^2) (c^2) (p^3) (r^3)-(a^4) (p^2) q (r^3)-(b^4) (p^2) q (r^3)+2 (a^2) (c^2) (p^2) q (r^3)+2 (b^2) (c^2) (p^2) q (r^3)-(c^4) (p^2) q (r^3)+(a^4) p (q^2) (r^3)+(a^2) (b^2) p (q^2) (r^3)-(a^2) (c^2) p (q^2) (r^3)+2 (a^4) (q^3) (r^3),(a^2) (c^2) (p^3) (q^3)-(b^2) (c^2) (p^3) (q^3)-(c^4) (p^3) (q^3)-(a^4) (p^3) (q^2) r+2 (a^2) (b^2) (p^3) (q^2) r-(b^4) (p^3) (q^2) r+2 (a^2) (c^2) (p^3) (q^2) r-(c^4) (p^3) (q^2) r-(a^4) (p^2) (q^3) r+2 (a^2) (b^2) (p^2) (q^3) r-(b^4) (p^2) (q^3) r+3 (a^2) (c^2) (p^2) (q^3) r+3 (b^2) (c^2) (p^2) (q^3) r-2 (c^4) (p^2) (q^3) r-(a^2) (b^2) (p^3) q (r^2)+(b^4) (p^3) q (r^2)+(b^2) (c^2) (p^3) q (r^2)-2 (a^4) (p^2) (q^2) (r^2)+2 (a^2) (b^2) (p^2) (q^2) (r^2)+4 (a^2) (c^2) (p^2) (q^2) (r^2)+2 (b^2) (c^2) (p^2) (q^2) (r^2)-2 (c^4) (p^2) (q^2) (r^2)-2 (a^4) p (q^3) (r^2)+3 (a^2) (b^2) p (q^3) (r^2)-(b^4) p (q^3) (r^2)+3 (a^2) (c^2) p (q^3) (r^2)+2 (b^2) (c^2) p (q^3) (r^2)-(c^4) p (q^3) (r^2)+2 (b^4) (p^3) (r^3)+(a^2) (b^2) (p^2) q (r^3)+(b^4) (p^2) q (r^3)-(b^2) (c^2) (p^2) q (r^3)-(a^4) p (q^2) (r^3)-(b^4) p (q^2) (r^3)+2 (a^2) (c^2) p (q^2) (r^3)+2 (b^2) (c^2) p (q^2) (r^3)-(c^4) p (q^2) (r^3)-(a^4) (q^3) (r^3)-(a^2) (b^2) (q^3) (r^3)+(a^2) (c^2) (q^3) (r^3),2 (c^4) (p^3) (q^3)-(a^2) (c^2) (p^3) (q^2) r+(b^2) (c^2) (p^3) (q^2) r+(c^4) (p^3) (q^2) r+(a^2) (c^2) (p^2) (q^3) r-(b^2) (c^2) (p^2) (q^3) r+(c^4) (p^2) (q^3) r-(a^4) (p^3) q (r^2)+2 (a^2) (b^2) (p^3) q (r^2)-(b^4) (p^3) q (r^2)+2 (a^2) (c^2) (p^3) q (r^2)-(c^4) (p^3) q (r^2)-2 (a^4) (p^2) (q^2) (r^2)+4 (a^2) (b^2) (p^2) (q^2) (r^2)-2 (b^4) (p^2) (q^2) (r^2)+2 (a^2) (c^2) (p^2) (q^2) (r^2)+2 (b^2) (c^2) (p^2) (q^2) (r^2)-(a^4) p (q^3) (r^2)+2 (a^2) (b^2) p (q^3) (r^2)-(b^4) p (q^3) (r^2)+2 (b^2) (c^2) p (q^3) (r^2)-(c^4) p (q^3) (r^2)+(a^2) (b^2) (p^3) (r^3)-(b^4) (p^3) (r^3)-(b^2) (c^2) (p^3) (r^3)-(a^4) (p^2) q (r^3)+3 (a^2) (b^2) (p^2) q (r^3)-2 (b^4) (p^2) q (r^3)+2 (a^2) (c^2) (p^2) q (r^3)+3 (b^2) (c^2) (p^2) q (r^3)-(c^4) (p^2) q (r^3)-2 (a^4) p (q^2) (r^3)+3 (a^2) (b^2) p (q^2) (r^3)-(b^4) p (q^2) (r^3)+3 (a^2) (c^2) p (q^2) (r^3)+2 (b^2) (c^2) p (q^2) (r^3)-(c^4) p (q^2) (r^3)-(a^4) (q^3) (r^3)+(a^2) (b^2) (q^3) (r^3)-(a^2) (c^2) (q^3) (r^3)}; (* Circumcenter QA-Diagonal Triangle *)
QAP12={-(-(a^2) p q+(b^2) p q-(c^2) p q-(a^2) p r-(b^2) p r+(c^2) p r-2 (a^2) q r) ((c^2) (p^2) (q^2)-(a^2) (p^2) q r+(b^2) (p^2) q r+(c^2) (p^2) q r+(b^2) (p^2) (r^2)-(a^2) (q^2) (r^2)),(-(a^2) p q+(b^2) p q+(c^2) p q+2 (b^2) p r+(a^2) q r+(b^2) q r-(c^2) q r) ((c^2) (p^2) (q^2)+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2)),-(-2 (c^2) p q+(a^2) p r-(b^2) p r-(c^2) p r-(a^2) q r+(b^2) q r-(c^2) q r) (-(c^2) (p^2) (q^2)+(b^2) (p^2) (r^2)+(a^2) p q (r^2)+(b^2) p q (r^2)-(c^2) p q (r^2)+(a^2) (q^2) (r^2))}; (* Orthocenter QA-Diagonal Triangle *)
QAP13={-(a^2) (c^2) (p^3) (q^3)+(b^2) (c^2) (p^3) (q^3)-(c^4) (p^3) (q^3)+3 (a^4) (p^3) (q^2) r-6 (a^2) (b^2) (p^3) (q^2) r+3 (b^4) (p^3) (q^2) r-5 (a^2) (c^2) (p^3) (q^2) r-5 (b^2) (c^2) (p^3) (q^2) r+2 (c^4) (p^3) (q^2) r+(a^4) (p^2) (q^3) r-2 (a^2) (b^2) (p^2) (q^3) r+(b^4) (p^2) (q^3) r-4 (a^2) (c^2) (p^2) (q^3) r-2 (b^2) (c^2) (p^2) (q^3) r+(c^4) (p^2) (q^3) r+3 (a^4) (p^3) q (r^2)-5 (a^2) (b^2) (p^3) q (r^2)+2 (b^4) (p^3) q (r^2)-6 (a^2) (c^2) (p^3) q (r^2)-5 (b^2) (c^2) (p^3) q (r^2)+3 (c^4) (p^3) q (r^2)+4 (a^4) (p^2) (q^2) (r^2)-6 (a^2) (b^2) (p^2) (q^2) (r^2)+2 (b^4) (p^2) (q^2) (r^2)-6 (a^2) (c^2) (p^2) (q^2) (r^2)-4 (b^2) (c^2) (p^2) (q^2) (r^2)+2 (c^4) (p^2) (q^2) (r^2)+(a^4) p (q^3) (r^2)-(a^2) (b^2) p (q^3) (r^2)+(a^2) (c^2) p (q^3) (r^2)-(a^2) (b^2) (p^3) (r^3)-(b^4) (p^3) (r^3)+(b^2) (c^2) (p^3) (r^3)+(a^4) (p^2) q (r^3)-4 (a^2) (b^2) (p^2) q (r^3)+(b^4) (p^2) q (r^3)-2 (a^2) (c^2) (p^2) q (r^3)-2 (b^2) (c^2) (p^2) q (r^3)+(c^4) (p^2) q (r^3)+(a^4) p (q^2) (r^3)+(a^2) (b^2) p (q^2) (r^3)-(a^2) (c^2) p (q^2) (r^3)+2 (a^4) (q^3) (r^3),(a^2) (c^2) (p^3) (q^3)-(b^2) (c^2) (p^3) (q^3)-(c^4) (p^3) (q^3)+(a^4) (p^3) (q^2) r-2 (a^2) (b^2) (p^3) (q^2) r+(b^4) (p^3) (q^2) r-2 (a^2) (c^2) (p^3) (q^2) r-4 (b^2) (c^2) (p^3) (q^2) r+(c^4) (p^3) (q^2) r+3 (a^4) (p^2) (q^3) r-6 (a^2) (b^2) (p^2) (q^3) r+3 (b^4) (p^2) (q^3) r-5 (a^2) (c^2) (p^2) (q^3) r-5 (b^2) (c^2) (p^2) (q^3) r+2 (c^4) (p^2) (q^3) r-(a^2) (b^2) (p^3) q (r^2)+(b^4) (p^3) q (r^2)+(b^2) (c^2) (p^3) q (r^2)+2 (a^4) (p^2) (q^2) (r^2)-6 (a^2) (b^2) (p^2) (q^2) (r^2)+4 (b^4) (p^2) (q^2) (r^2)-4 (a^2) (c^2) (p^2) (q^2) (r^2)-6 (b^2) (c^2) (p^2) (q^2) (r^2)+2 (c^4) (p^2) (q^2) (r^2)+2 (a^4) p (q^3) (r^2)-5 (a^2) (b^2) p (q^3) (r^2)+3 (b^4) p (q^3) (r^2)-5 (a^2) (c^2) p (q^3) (r^2)-6 (b^2) (c^2) p (q^3) (r^2)+3 (c^4) p (q^3) (r^2)+2 (b^4) (p^3) (r^3)+(a^2) (b^2) (p^2) q (r^3)+(b^4) (p^2) q (r^3)-(b^2) (c^2) (p^2) q (r^3)+(a^4) p (q^2) (r^3)-4 (a^2) (b^2) p (q^2) (r^3)+(b^4) p (q^2) (r^3)-2 (a^2) (c^2) p (q^2) (r^3)-2 (b^2) (c^2) p (q^2) (r^3)+(c^4) p (q^2) (r^3)-(a^4) (q^3) (r^3)-(a^2) (b^2) (q^3) (r^3)+(a^2) (c^2) (q^3) (r^3),2 (c^4) (p^3) (q^3)-(a^2) (c^2) (p^3) (q^2) r+(b^2) (c^2) (p^3) (q^2) r+(c^4) (p^3) (q^2) r+(a^2) (c^2) (p^2) (q^3) r-(b^2) (c^2) (p^2) (q^3) r+(c^4) (p^2) (q^3) r+(a^4) (p^3) q (r^2)-2 (a^2) (b^2) (p^3) q (r^2)+(b^4) (p^3) q (r^2)-2 (a^2) (c^2) (p^3) q (r^2)-4 (b^2) (c^2) (p^3) q (r^2)+(c^4) (p^3) q (r^2)+2 (a^4) (p^2) (q^2) (r^2)-4 (a^2) (b^2) (p^2) (q^2) (r^2)+2 (b^4) (p^2) (q^2) (r^2)-6 (a^2) (c^2) (p^2) (q^2) (r^2)-6 (b^2) (c^2) (p^2) (q^2) (r^2)+4 (c^4) (p^2) (q^2) (r^2)+(a^4) p (q^3) (r^2)-2 (a^2) (b^2) p (q^3) (r^2)+(b^4) p (q^3) (r^2)-4 (a^2) (c^2) p (q^3) (r^2)-2 (b^2) (c^2) p (q^3) (r^2)+(c^4) p (q^3) (r^2)+(a^2) (b^2) (p^3) (r^3)-(b^4) (p^3) (r^3)-(b^2) (c^2) (p^3) (r^3)+3 (a^4) (p^2) q (r^3)-5 (a^2) (b^2) (p^2) q (r^3)+2 (b^4) (p^2) q (r^3)-6 (a^2) (c^2) (p^2) q (r^3)-5 (b^2) (c^2) (p^2) q (r^3)+3 (c^4) (p^2) q (r^3)+2 (a^4) p (q^2) (r^3)-5 (a^2) (b^2) p (q^2) (r^3)+3 (b^4) p (q^2) (r^3)-5 (a^2) (c^2) p (q^2) (r^3)-6 (b^2) (c^2) p (q^2) (r^3)+3 (c^4) p (q^2) (r^3)-(a^4) (q^3) (r^3)+(a^2) (b^2) (q^3) (r^3)-(a^2) (c^2) (q^3) (r^3)}; (* Nine-point Center QA-Diagonal Triangle *)

QAP14={(a^4) (3 p (((q+r))^3)+(p^2) (3 (q^2)+2 q r+3 (r^2))+q r (5 (q^2)+6 q r+5 (r^2)))+2 (a^2) ((b^2) (3 (p^2) (((q+r))^2)+(p^3) (3 q+r)+q r ((q^2)-(r^2))+p r (4 (q^2)+3 q r+(r^2)))+(c^2) (-(q^3) r+q (r^3)+3 (p^2) (((q+r))^2)+(p^3) (q+3 r)+p q ((q^2)+3 q r+4 (r^2))))-((b^2)-(c^2)) (q+r) (-(c^2) (6 (p^3)+9 (p^2) (q+r)+3 q r (q+r)+p (5 (q^2)+10 q r+3 (r^2)))+(b^2) (6 (p^3)+9 (p^2) (q+r)+3 q r (q+r)+p (3 (q^2)+10 q r+5 (r^2)))),(b^4) (3 q (r^2) (q+r)+(p^3) (3 q+5 r)+3 (p^2) ((q^2)+3 q r+2 (r^2))+p r (2 (q^2)+9 q r+5 (r^2)))+2 (b^2) (c^2) ((p^3) (q-r)+3 (p^2) q (q+r)+3 (q^2) r (q+r)+p ((q^3)+6 (q^2) r+4 q (r^2)+(r^3)))-(a^4) (3 (p^3) (q+r)+q r (6 (q^2)+9 q r+5 (r^2))+(p^2) (9 (q^2)+13 q r+6 (r^2))+3 p (2 (q^3)+6 (q^2) r+5 q (r^2)+(r^3)))-(c^4) ((p^3) (5 q+3 r)+3 q r (2 (q^2)+3 q r+(r^2))+3 (p^2) (3 (q^2)+5 q r+2 (r^2))+p (6 (q^3)+18 (q^2) r+13 q (r^2)+3 (r^3)))+2 (a^2) ((b^2) ((p^3) r+(p^2) q (3 q+4 r)+q r ((q^2)+3 q r+(r^2))+p (3 (q^3)+6 (q^2) r+3 q (r^2)-(r^3)))+(c^2) ((p^3) (4 q+3 r)+q r (6 (q^2)+9 q r+4 (r^2))+(p^2) (9 (q^2)+14 q r+6 (r^2))+p (6 (q^3)+18 (q^2) r+14 q (r^2)+3 (r^3)))),(c^4) (3 (q^2) r (q+r)+(p^3) (5 q+3 r)+3 (p^2) (2 (q^2)+3 q r+(r^2))+p q (5 (q^2)+9 q r+2 (r^2)))+2 (b^2) (c^2) ((p^3) (-q+r)+3 (p^2) r (q+r)+3 q (r^2) (q+r)+p ((q^3)+4 (q^2) r+6 q (r^2)+(r^3)))-(a^4) (3 (p^3) (q+r)+q r (5 (q^2)+9 q r+6 (r^2))+(p^2) (6 (q^2)+13 q r+9 (r^2))+3 p ((q^3)+5 (q^2) r+6 q (r^2)+2 (r^3)))-(b^4) ((p^3) (3 q+5 r)+3 q r ((q^2)+3 q r+2 (r^2))+3 (p^2) (2 (q^2)+5 q r+3 (r^2))+p (3 (q^3)+13 (q^2) r+18 q (r^2)+6 (r^3)))+2 (a^2) ((c^2) ((p^3) q+(p^2) r (4 q+3 r)+q r ((q^2)+3 q r+(r^2))+p (-(q^3)+3 (q^2) r+6 q (r^2)+3 (r^3)))+(b^2) ((p^3) (3 q+4 r)+q r (4 (q^2)+9 q r+6 (r^2))+(p^2) (6 (q^2)+14 q r+9 (r^2))+p (3 (q^3)+14 (q^2) r+18 q (r^2)+6 (r^3))))}; (* Centroid Morley Triangle *)
QAP15={(a^4) (p+q) (p+r) (p ((q^2)+(r^2))+(q+r) ((q^2)+q r+(r^2)))+(a^2) ((b^2) (p+q) (2 (p^3) q+q r (((q+r))^2)+p r (q+r) (2 q+r)+(p^2) (2 (q^2)+5 q r+(r^2)))+(c^2) (p+r) (2 (p^3) r+q r (((q+r))^2)+p q (q+r) (q+2 r)+(p^2) ((q^2)+5 q r+2 (r^2))))-(q+r) ((c^4) (p+r) (2 (p^3)+q (((q+r))^2)+p (q+r) (3 q+r)+(p^2) (5 q+3 r))+(b^4) (p+q) (2 (p^3)+r (((q+r))^2)+p (q+r) (q+3 r)+(p^2) (3 q+5 r))-(b^2) (c^2) (4 (p^4)+10 (p^3) (q+r)+2 q r (((q+r))^2)+p (q+r) (3 q+r) (q+3 r)+(p^2) (9 (q^2)+22 q r+9 (r^2)))),-(a^4) (p+q) (p+r) (q (p+q) (p+2 q)+((p^2)+4 p q+5 (q^2)) r+(2 p+3 q) (r^2)+(r^3))+(a^2) ((b^2) (p+q) (2 p (q^2) (p+q)+p ((p^2)+2 p q+5 (q^2)) r+(p+q) (2 p+q) (r^2)+(p+q) (r^3))+(c^2) (p+r) (q (p+q) (3 (p^2)+6 p q+4 (q^2))+(2 (p^3)+13 (p^2) q+22 p (q^2)+10 (q^3)) r+(p+q) (4 p+9 q) (r^2)+(2 p+3 q) (r^3)))+(q+r) ((b^4) (p+q) ((p^3)+2 p (r^2)+(r^2) (q+r)+(p^2) (q+2 r))+(b^2) (c^2) ((p^3) (q+r)+2 (q^2) r (q+r)+(p^2) (q+r) (q+2 r)+p r (5 (q^2)+2 q r+(r^2)))-(c^4) (p+r) ((p^3)+q (q+r) (2 q+r)+(p^2) (3 q+2 r)+p (5 (q^2)+4 q r+(r^2)))),-(a^4) (p+q) (p+r) (q (((p+q))^2)+(p+q) (p+3 q) r+(3 p+5 q) (r^2)+2 (r^3))+(a^2) ((c^2) (p+r) (p q (((p+q))^2)+q (p+q) (2 p+q) r+(2 (p^2)+5 p q+(q^2)) (r^2)+2 p (r^3))+(b^2) (p+q) (2 p q (((p+q))^2)+(p+q) (3 p+q) (p+3 q) r+(9 (p^2)+22 p q+9 (q^2)) (r^2)+10 (p+q) (r^3)+4 (r^4)))-(q+r) ((b^4) (p+q) (p (((p+q))^2)+(p+q) (3 p+q) r+(5 p+3 q) (r^2)+2 (r^3))-(b^2) (c^2) (p q (((p+q))^2)+p (p+q) (p+2 q) r+((p^2)+5 p q+2 (q^2)) (r^2)+2 q (r^3))-(c^4) (p+r) ((p^3)+2 p (q^2)+(q^2) (q+r)+(p^2) (2 q+r)))};(* Orthocenter Morley Triangle *)
QAP16={p (2 p+q+r),q (p+2 q+r),r (p+q+2 r)}; (* QA-Harmonic Center *)QAP17={q r (2 p+q+r) (-(p^2) (q^2)-p (q^3)-p (q^2) r+(q^3) r-(p^2) (r^2)-p q (r^2)+2 (q^2) (r^2)-p (r^3)+q (r^3)),p r (p+2 q+r) (-(p^3) q-(p^2) (q^2)+(p^3) r-(p^2) q r+2 (p^2) (r^2)-p q (r^2)-(q^2) (r^2)+p (r^3)-q (r^3)),p q (p+q+2 r) ((p^3) q+2 (p^2) (q^2)+p (q^3)-(p^3) r-(p^2) q r-p (q^2) r-(q^3) r-(p^2) (r^2)-(q^2) (r^2))};
QAP18={-p (2 p+q+r) ((p^2)+p q+p r-q r) ((q^2)+(r^2)),-q (p+2 q+r) (p q+(q^2)-p r+q r) ((p^2)+(r^2)),((p^2)+(q^2)) r (p+q+2 r) (p q-p r-q r-(r^2))};QAP19={p (2 p+q+r) ((q^3)+(q^2) r+q (r^2)+(r^3)),q (p+2 q+r) ((p^3)+(p^2) r+p (r^2)+(r^3)),((p^3)+(p^2) q+p (q^2)+(q^3)) r (p+q+2 r)};
QAP20={(q+r) (2 p+q+r) (-(p^2)-p q-p r+q r),(p+r) (p+2 q+r) (-p q-(q^2)+p r-q r),(p+q) (p+q+2 r) (p q-p r-q r-(r^2))};
QAP21={-(2 p+q+r) ((q^2)+q r+(r^2)),-(p+2 q+r) ((p^2)+p r+(r^2)),-((p^2)+p q+(q^2)) (p+q+2 r)};
QAP22={(q+r) (2 p+q+r) (-3 (p^2)-3 p q-3 p r+q r),-(p+r) (p+2 q+r) (3 p q+3 (q^2)-p r+3 q r),(p+q) (p+q+2 r) (p q-3 p r-3 q r-3 (r^2))};
QAP23={(a^2) p q-(b^2) p q+(c^2) p q+(a^2) p r+(b^2) p r-(c^2) p r+2 (a^2) q r,-(a^2) p q+(b^2) p q+(c^2) p q+2 (b^2) p r+(a^2) q r+(b^2) q r-(c^2) q r,2 (c^2) p q-(a^2) p r+(b^2) p r+(c^2) p r+(a^2) q r-(b^2) q r+(c^2) q r}; (* Inscribed Square Axes Crosspoint *)
QAP24={(a^4) (p^3) q+(a^2) (b^2) (p^3) q-2 (b^4) (p^3) q-(a^2) (c^2) (p^3) q+4 (b^2) (c^2) (p^3) q-2 (c^4) (p^3) q+3 (a^4) (p^2) (q^2)-3 (b^4) (p^2) (q^2)+6 (b^2) (c^2) (p^2) (q^2)-3 (c^4) (p^2) (q^2)+2 (a^4) p (q^3)-(a^2) (b^2) p (q^3)-(b^4) p (q^3)+3 (b^2) (c^2) p (q^3)-2 (c^4) p (q^3)+(a^4) (p^3) r-(a^2) (b^2) (p^3) r-2 (b^4) (p^3) r+(a^2) (c^2) (p^3) r+4 (b^2) (c^2) (p^3) r-2 (c^4) (p^3) r+4 (a^4) (p^2) q r-6 (b^4) (p^2) q r+12 (b^2) (c^2) (p^2) q r-6 (c^4) (p^2) q r+7 (a^4) p (q^2) r-(a^2) (b^2) p (q^2) r-4 (b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r+9 (b^2) (c^2) p (q^2) r-5 (c^4) p (q^2) r+3 (a^4) (q^3) r-(b^4) (q^3) r-2 (a^2) (c^2) (q^3) r+2 (b^2) (c^2) (q^3) r-(c^4) (q^3) r+3 (a^4) (p^2) (r^2)-3 (b^4) (p^2) (r^2)+6 (b^2) (c^2) (p^2) (r^2)-3 (c^4) (p^2) (r^2)+7 (a^4) p q (r^2)-2 (a^2) (b^2) p q (r^2)-5 (b^4) p q (r^2)-(a^2) (c^2) p q (r^2)+9 (b^2) (c^2) p q (r^2)-4 (c^4) p q (r^2)+4 (a^4) (q^2) (r^2)-2 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)-2 (a^2) (c^2) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)+2 (a^4) p (r^3)-2 (b^4) p (r^3)-(a^2) (c^2) p (r^3)+3 (b^2) (c^2) p (r^3)-(c^4) p (r^3)+3 (a^4) q (r^3)-2 (a^2) (b^2) q (r^3)-(b^4) q (r^3)+2 (b^2) (c^2) q (r^3)-(c^4) q (r^3),-(a^4) (p^3) q-(a^2) (b^2) (p^3) q+2 (b^4) (p^3) q+3 (a^2) (c^2) (p^3) q-2 (c^4) (p^3) q-3 (a^4) (p^2) (q^2)+3 (b^4) (p^2) (q^2)+6 (a^2) (c^2) (p^2) (q^2)-3 (c^4) (p^2) (q^2)-2 (a^4) p (q^3)+(a^2) (b^2) p (q^3)+(b^4) p (q^3)+4 (a^2) (c^2) p (q^3)-(b^2) (c^2) p (q^3)-2 (c^4) p (q^3)-(a^4) (p^3) r+3 (b^4) (p^3) r+2 (a^2) (c^2) (p^3) r-2 (b^2) (c^2) (p^3) r-(c^4) (p^3) r-4 (a^4) (p^2) q r-(a^2) (b^2) (p^2) q r+7 (b^4) (p^2) q r+9 (a^2) (c^2) (p^2) q r-2 (b^2) (c^2) (p^2) q r-5 (c^4) (p^2) q r-6 (a^4) p (q^2) r+4 (b^4) p (q^2) r+12 (a^2) (c^2) p (q^2) r-6 (c^4) p (q^2) r-2 (a^4) (q^3) r-(a^2) (b^2) (q^3) r+(b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+(b^2) (c^2) (q^3) r-2 (c^4) (q^3) r-2 (a^4) (p^2) (r^2)-2 (a^2) (b^2) (p^2) (r^2)+4 (b^4) (p^2) (r^2)+4 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)-2 (c^4) (p^2) (r^2)-5 (a^4) p q (r^2)-2 (a^2) (b^2) p q (r^2)+7 (b^4) p q (r^2)+9 (a^2) (c^2) p q (r^2)-(b^2) (c^2) p q (r^2)-4 (c^4) p q (r^2)-3 (a^4) (q^2) (r^2)+3 (b^4) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)-3 (c^4) (q^2) (r^2)-(a^4) p (r^3)-2 (a^2) (b^2) p (r^3)+3 (b^4) p (r^3)+2 (a^2) (c^2) p (r^3)-(c^4) p (r^3)-2 (a^4) q (r^3)+2 (b^4) q (r^3)+3 (a^2) (c^2) q (r^3)-(b^2) (c^2) q (r^3)-(c^4) q (r^3),-(a^4) (p^3) q+2 (a^2) (b^2) (p^3) q-(b^4) (p^3) q-2 (b^2) (c^2) (p^3) q+3 (c^4) (p^3) q-2 (a^4) (p^2) (q^2)+4 (a^2) (b^2) (p^2) (q^2)-2 (b^4) (p^2) (q^2)-2 (a^2) (c^2) (p^2) (q^2)-2 (b^2) (c^2) (p^2) (q^2)+4 (c^4) (p^2) (q^2)-(a^4) p (q^3)+2 (a^2) (b^2) p (q^3)-(b^4) p (q^3)-2 (a^2) (c^2) p (q^3)+3 (c^4) p (q^3)-(a^4) (p^3) r+3 (a^2) (b^2) (p^3) r-2 (b^4) (p^3) r-(a^2) (c^2) (p^3) r+2 (c^4) (p^3) r-4 (a^4) (p^2) q r+9 (a^2) (b^2) (p^2) q r-5 (b^4) (p^2) q r-(a^2) (c^2) (p^2) q r-2 (b^2) (c^2) (p^2) q r+7 (c^4) (p^2) q r-5 (a^4) p (q^2) r+9 (a^2) (b^2) p (q^2) r-4 (b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r-(b^2) (c^2) p (q^2) r+7 (c^4) p (q^2) r-2 (a^4) (q^3) r+3 (a^2) (b^2) (q^3) r-(b^4) (q^3) r-(b^2) (c^2) (q^3) r+2 (c^4) (q^3) r-3 (a^4) (p^2) (r^2)+6 (a^2) (b^2) (p^2) (r^2)-3 (b^4) (p^2) (r^2)+3 (c^4) (p^2) (r^2)-6 (a^4) p q (r^2)+12 (a^2) (b^2) p q (r^2)-6 (b^4) p q (r^2)+4 (c^4) p q (r^2)-3 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)-3 (b^4) (q^2) (r^2)+3 (c^4) (q^2) (r^2)-2 (a^4) p (r^3)+4 (a^2) (b^2) p (r^3)-2 (b^4) p (r^3)+(a^2) (c^2) p (r^3)-(b^2) (c^2) p (r^3)+(c^4) p (r^3)-2 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)-2 (b^4) q (r^3)-(a^2) (c^2) q (r^3)+(b^2) (c^2) q (r^3)+(c^4) q (r^3)};(* Perspector Morley Triangle and Quasi Circumcenter Triangle *)
QAP25={(q+r) (2 p+q+r) (2 (p^2)+2 p q+2 p r+3 q r),(p+r) (p+2 q+r) (2 p q+2 (q^2)+3 p r+2 q r),(p+q) (p+q+2 r) (3 p q+2 p r+2 q r+2 (r^2))}; (* 1st QA-Quasi Centroid *)
QAP26={(q+r) (2 p+q+r) (5 (p^2)+5 p q+5 p r+3 q r),(p+r) (p+2 q+r) (5 p q+5 (q^2)+3 p r+5 q r),(p+q) (p+q+2 r) (3 p q+5 p r+5 q r+5 (r^2))}; (* 2nd QA-Quasi Centroid *)
QAP27={-(q+r) (2 p+q+r) ((q^2)+q r+(r^2)) (-(p^4)-2 (p^3) q-2 (p^2) (q^2)-p (q^3)-2 (p^3) r+p (q^2) r+(q^3) r-2 (p^2) (r^2)+p q (r^2)+(q^2) (r^2)-p (r^3)+q (r^3)),-(p+r) (p+2 q+r) ((p^2)+p r+(r^2)) (-(p^3) q-2 (p^2) (q^2)-2 p (q^3)-(q^4)+(p^3) r+(p^2) q r-2 (q^3) r+(p^2) (r^2)+p q (r^2)-2 (q^2) (r^2)+p (r^3)-q (r^3)),-(p+q) ((p^2)+p q+(q^2)) (p+q+2 r) ((p^3) q+(p^2) (q^2)+p (q^3)-(p^3) r+(p^2) q r+p (q^2) r-(q^3) r-2 (p^2) (r^2)-2 (q^2) (r^2)-2 p (r^3)-2 q (r^3)-(r^4))}; (* M3D Center *)
QAP28={-(q+r) (-(a^2) q (p+q) r (p+r) ((a^2) (p+q) (p+r)-p ((b^2) (p+q)+(c^2) (p+r)))-p (2 p+q+r) ((c^4) p q (p+r) (q+r)-2 (c^2) p q r ((a^2) (p+r)+(b^2) (q+r))+(p+q) r (-2 (a^2) (b^2) p q+(a^4) q (p+r)+(b^4) p (q+r)))),-(p+r) (-(b^2) p (p+q) r (q+r) (-(a^2) q (p+q)+(-(c^2) q+(b^2) (p+q)) (q+r))-q (p+2 q+r) ((c^4) p q (p+r) (q+r)-2 (c^2) p q r ((a^2) (p+r)+(b^2) (q+r))+(p+q) r (-2 (a^2) (b^2) p q+(a^4) q (p+r)+(b^4) p (q+r)))),-(p+q) (-(c^4) p q (p+r) (q+r) (p q+2 (p+q) r+3 (r^2))+(c^2) p q r (p q+3 (p+q) r+5 (r^2)) ((a^2) (p+r)+(b^2) (q+r))-(p+q) (r^2) (p+q+2 r) (-2 (a^2) (b^2) p q+(a^4) q (p+r)+(b^4) p (q+r)))}; (* Midpoint of the foci of the QA-Parabolas *)
QAP29={-p (q+r) (-(a^2) (c^2) (p^3) (q^2)+(b^2) (c^2) (p^3) (q^2)+3 (c^4) (p^3) (q^2)-(a^2) (c^2) (p^2) (q^3)+(b^2) (c^2) (p^2) (q^3)+(c^4) (p^2) (q^3)+4 (a^4) (p^3) q r-7 (a^2) (b^2) (p^3) q r+3 (b^4) (p^3) q r-7 (a^2) (c^2) (p^3) q r+2 (b^2) (c^2) (p^3) q r+3 (c^4) (p^3) q r+6 (a^4) (p^2) (q^2) r-10 (a^2) (b^2) (p^2) (q^2) r+4 (b^4) (p^2) (q^2) r-5 (a^2) (c^2) (p^2) (q^2) r-3 (b^2) (c^2) (p^2) (q^2) r+5 (c^4) (p^2) (q^2) r+2 (a^4) p (q^3) r-3 (a^2) (b^2) p (q^3) r+(b^4) p (q^3) r-2 (a^2) (c^2) p (q^3) r-(b^2) (c^2) p (q^3) r-(a^2) (b^2) (p^3) (r^2)+3 (b^4) (p^3) (r^2)+(b^2) (c^2) (p^3) (r^2)+6 (a^4) (p^2) q (r^2)-5 (a^2) (b^2) (p^2) q (r^2)+5 (b^4) (p^2) q (r^2)-10 (a^2) (c^2) (p^2) q (r^2)-3 (b^2) (c^2) (p^2) q (r^2)+4 (c^4) (p^2) q (r^2)+8 (a^4) p (q^2) (r^2)-3 (a^2) (b^2) p (q^2) (r^2)+(b^4) p (q^2) (r^2)-3 (a^2) (c^2) p (q^2) (r^2)-2 (b^2) (c^2) p (q^2) (r^2)+(c^4) p (q^2) (r^2)+2 (a^4) (q^3) (r^2)+(a^2) (b^2) (q^3) (r^2)-(b^4) (q^3) (r^2)-(a^2) (c^2) (q^3) (r^2)+2 (b^2) (c^2) (q^3) (r^2)-(c^4) (q^3) (r^2)-(a^2) (b^2) (p^2) (r^3)+(b^4) (p^2) (r^3)+(b^2) (c^2) (p^2) (r^3)+2 (a^4) p q (r^3)-2 (a^2) (b^2) p q (r^3)-3 (a^2) (c^2) p q (r^3)-(b^2) (c^2) p q (r^3)+(c^4) p q (r^3)+2 (a^4) (q^2) (r^3)-(a^2) (b^2) (q^2) (r^3)-(b^4) (q^2) (r^3)+(a^2) (c^2) (q^2) (r^3)+2 (b^2) (c^2) (q^2) (r^3)-(c^4) (q^2) (r^3)),q (p+r) (-(a^2) (c^2) (p^3) (q^2)+(b^2) (c^2) (p^3) (q^2)-(c^4) (p^3) (q^2)-(a^2) (c^2) (p^2) (q^3)+(b^2) (c^2) (p^2) (q^3)-3 (c^4) (p^2) (q^3)-(a^4) (p^3) q r+3 (a^2) (b^2) (p^3) q r-2 (b^4) (p^3) q r+(a^2) (c^2) (p^3) q r+2 (b^2) (c^2) (p^3) q r-4 (a^4) (p^2) (q^2) r+10 (a^2) (b^2) (p^2) (q^2) r-6 (b^4) (p^2) (q^2) r+3 (a^2) (c^2) (p^2) (q^2) r+5 (b^2) (c^2) (p^2) (q^2) r-5 (c^4) (p^2) (q^2) r-3 (a^4) p (q^3) r+7 (a^2) (b^2) p (q^3) r-4 (b^4) p (q^3) r-2 (a^2) (c^2) p (q^3) r+7 (b^2) (c^2) p (q^3) r-3 (c^4) p (q^3) r+(a^4) (p^3) (r^2)-(a^2) (b^2) (p^3) (r^2)-2 (b^4) (p^3) (r^2)-2 (a^2) (c^2) (p^3) (r^2)+(b^2) (c^2) (p^3) (r^2)+(c^4) (p^3) (r^2)-(a^4) (p^2) q (r^2)+3 (a^2) (b^2) (p^2) q (r^2)-8 (b^4) (p^2) q (r^2)+2 (a^2) (c^2) (p^2) q (r^2)+3 (b^2) (c^2) (p^2) q (r^2)-(c^4) (p^2) q (r^2)-5 (a^4) p (q^2) (r^2)+5 (a^2) (b^2) p (q^2) (r^2)-6 (b^4) p (q^2) (r^2)+3 (a^2) (c^2) p (q^2) (r^2)+10 (b^2) (c^2) p (q^2) (r^2)-4 (c^4) p (q^2) (r^2)-3 (a^4) (q^3) (r^2)+(a^2) (b^2) (q^3) (r^2)-(a^2) (c^2) (q^3) (r^2)+(a^4) (p^2) (r^3)+(a^2) (b^2) (p^2) (r^3)-2 (b^4) (p^2) (r^3)-2 (a^2) (c^2) (p^2) (r^3)-(b^2) (c^2) (p^2) (r^3)+(c^4) (p^2) (r^3)+2 (a^2) (b^2) p q (r^3)-2 (b^4) p q (r^3)+(a^2) (c^2) p q (r^3)+3 (b^2) (c^2) p q (r^3)-(c^4) p q (r^3)-(a^4) (q^2) (r^3)+(a^2) (b^2) (q^2) (r^3)-(a^2) (c^2) (q^2) (r^3)),-(p+q) r (-(a^4) (p^3) (q^2)+2 (a^2) (b^2) (p^3) (q^2)-(b^4) (p^3) (q^2)+(a^2) (c^2) (p^3) (q^2)-(b^2) (c^2) (p^3) (q^2)+2 (c^4) (p^3) (q^2)-(a^4) (p^2) (q^3)+2 (a^2) (b^2) (p^2) (q^3)-(b^4) (p^2) (q^3)-(a^2) (c^2) (p^2) (q^3)+(b^2) (c^2) (p^2) (q^3)+2 (c^4) (p^2) (q^3)+(a^4) (p^3) q r-(a^2) (b^2) (p^3) q r-3 (a^2) (c^2) (p^3) q r-2 (b^2) (c^2) (p^3) q r+2 (c^4) (p^3) q r+(a^4) (p^2) (q^2) r-2 (a^2) (b^2) (p^2) (q^2) r+(b^4) (p^2) (q^2) r-3 (a^2) (c^2) (p^2) (q^2) r-3 (b^2) (c^2) (p^2) (q^2) r+8 (c^4) (p^2) (q^2) r-(a^2) (b^2) p (q^3) r+(b^4) p (q^3) r-2 (a^2) (c^2) p (q^3) r-3 (b^2) (c^2) p (q^3) r+2 (c^4) p (q^3) r+(a^2) (b^2) (p^3) (r^2)+(b^4) (p^3) (r^2)-(b^2) (c^2) (p^3) (r^2)+4 (a^4) (p^2) q (r^2)-3 (a^2) (b^2) (p^2) q (r^2)+5 (b^4) (p^2) q (r^2)-10 (a^2) (c^2) (p^2) q (r^2)-5 (b^2) (c^2) (p^2) q (r^2)+6 (c^4) (p^2) q (r^2)+5 (a^4) p (q^2) (r^2)-3 (a^2) (b^2) p (q^2) (r^2)+4 (b^4) p (q^2) (r^2)-5 (a^2) (c^2) p (q^2) (r^2)-10 (b^2) (c^2) p (q^2) (r^2)+6 (c^4) p (q^2) (r^2)+(a^4) (q^3) (r^2)+(a^2) (b^2) (q^3) (r^2)-(a^2) (c^2) (q^3) (r^2)+(a^2) (b^2) (p^2) (r^3)+3 (b^4) (p^2) (r^3)-(b^2) (c^2) (p^2) (r^3)+3 (a^4) p q (r^3)+2 (a^2) (b^2) p q (r^3)+3 (b^4) p q (r^3)-7 (a^2) (c^2) p q (r^3)-7 (b^2) (c^2) p q (r^3)+4 (c^4) p q (r^3)+3 (a^4) (q^2) (r^3)+(a^2) (b^2) (q^2) (r^3)-(a^2) (c^2) (q^2) (r^3))}; (* Complement of QA-P2 wrt the Diagonal Triangle *)
QAP30={((a^2) (c^2) (p^2) (q^2)-(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+2 (a^4) (p^2) q r-3 (a^2) (b^2) (p^2) q r+(b^4) (p^2) q r-3 (a^2) (c^2) (p^2) q r-2 (b^2) (c^2) (p^2) q r+(c^4) (p^2) q r+2 (a^4) p (q^2) r-3 (a^2) (b^2) p (q^2) r+(b^4) p (q^2) r+(a^2) (c^2) p (q^2) r-2 (b^2) (c^2) p (q^2) r+(c^4) p (q^2) r+(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)-(b^2) (c^2) (p^2) (r^2)+2 (a^4) p q (r^2)+(a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-3 (a^2) (c^2) p q (r^2)-2 (b^2) (c^2) p q (r^2)+(c^4) p q (r^2)+2 (a^4) (q^2) (r^2)) (2 (c^4) (p^3) (q^3)+(a^4) (p^3) (q^2) r-2 (a^2) (b^2) (p^3) (q^2) r+(b^4) (p^3) (q^2) r-4 (a^2) (c^2) (p^3) (q^2) r+2 (b^2) (c^2) (p^3) (q^2) r+3 (c^4) (p^3) (q^2) r+(a^4) (p^2) (q^3) r-2 (a^2) (b^2) (p^2) (q^3) r+(b^4) (p^2) (q^3) r-2 (b^2) (c^2) (p^2) (q^3) r+(c^4) (p^2) (q^3) r+(a^4) (p^3) q (r^2)-4 (a^2) (b^2) (p^3) q (r^2)+3 (b^4) (p^3) q (r^2)-2 (a^2) (c^2) (p^3) q (r^2)+2 (b^2) (c^2) (p^3) q (r^2)+(c^4) (p^3) q (r^2)-2 (a^2) (b^2) (p^2) (q^2) (r^2)+2 (b^4) (p^2) (q^2) (r^2)-2 (a^2) (c^2) (p^2) (q^2) (r^2)-4 (b^2) (c^2) (p^2) (q^2) (r^2)+2 (c^4) (p^2) (q^2) (r^2)-(a^4) p (q^3) (r^2)+2 (a^2) (b^2) p (q^3) (r^2)-(b^4) p (q^3) (r^2)+2 (b^2) (c^2) p (q^3) (r^2)-(c^4) p (q^3) (r^2)+2 (b^4) (p^3) (r^3)+(a^4) (p^2) q (r^3)+(b^4) (p^2) q (r^3)-2 (a^2) (c^2) (p^2) q (r^3)-2 (b^2) (c^2) (p^2) q (r^3)+(c^4) (p^2) q (r^3)-(a^4) p (q^2) (r^3)-(b^4) p (q^2) (r^3)+2 (a^2) (c^2) p (q^2) (r^3)+2 (b^2) (c^2) p (q^2) (r^3)-(c^4) p (q^2) (r^3)-2 (a^4) (q^3) (r^3)),(-(a^2) (c^2) (p^2) (q^2)+(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+(a^4) (p^2) q r-3 (a^2) (b^2) (p^2) q r+2 (b^4) (p^2) q r-2 (a^2) (c^2) (p^2) q r+(b^2) (c^2) (p^2) q r+(c^4) (p^2) q r+(a^4) p (q^2) r-3 (a^2) (b^2) p (q^2) r+2 (b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r-3 (b^2) (c^2) p (q^2) r+(c^4) p (q^2) r+2 (b^4) (p^2) (r^2)+(a^4) p q (r^2)+(a^2) (b^2) p q (r^2)+2 (b^4) p q (r^2)-2 (a^2) (c^2) p q (r^2)-3 (b^2) (c^2) p q (r^2)+(c^4) p q (r^2)+(a^4) (q^2) (r^2)+(a^2) (b^2) (q^2) (r^2)-(a^2) (c^2) (q^2) (r^2)) (2 (c^4) (p^3) (q^3)+(a^4) (p^3) (q^2) r-2 (a^2) (b^2) (p^3) (q^2) r+(b^4) (p^3) (q^2) r-2 (a^2) (c^2) (p^3) (q^2) r+(c^4) (p^3) (q^2) r+(a^4) (p^2) (q^3) r-2 (a^2) (b^2) (p^2) (q^3) r+(b^4) (p^2) (q^3) r+2 (a^2) (c^2) (p^2) (q^3) r-4 (b^2) (c^2) (p^2) (q^3) r+3 (c^4) (p^2) (q^3) r-(a^4) (p^3) q (r^2)+2 (a^2) (b^2) (p^3) q (r^2)-(b^4) (p^3) q (r^2)+2 (a^2) (c^2) (p^3) q (r^2)-(c^4) (p^3) q (r^2)+2 (a^4) (p^2) (q^2) (r^2)-2 (a^2) (b^2) (p^2) (q^2) (r^2)-4 (a^2) (c^2) (p^2) (q^2) (r^2)-2 (b^2) (c^2) (p^2) (q^2) (r^2)+2 (c^4) (p^2) (q^2) (r^2)+3 (a^4) p (q^3) (r^2)-4 (a^2) (b^2) p (q^3) (r^2)+(b^4) p (q^3) (r^2)+2 (a^2) (c^2) p (q^3) (r^2)-2 (b^2) (c^2) p (q^3) (r^2)+(c^4) p (q^3) (r^2)-2 (b^4) (p^3) (r^3)-(a^4) (p^2) q (r^3)-(b^4) (p^2) q (r^3)+2 (a^2) (c^2) (p^2) q (r^3)+2 (b^2) (c^2) (p^2) q (r^3)-(c^4) (p^2) q (r^3)+(a^4) p (q^2) (r^3)+(b^4) p (q^2) (r^3)-2 (a^2) (c^2) p (q^2) (r^3)-2 (b^2) (c^2) p (q^2) (r^3)+(c^4) p (q^2) (r^3)+2 (a^4) (q^3) (r^3)),-(2 (c^4) (p^2) (q^2)+(a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r+(b^4) (p^2) q r-3 (a^2) (c^2) (p^2) q r+(b^2) (c^2) (p^2) q r+2 (c^4) (p^2) q r+(a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+(b^4) p (q^2) r+(a^2) (c^2) p (q^2) r-3 (b^2) (c^2) p (q^2) r+2 (c^4) p (q^2) r-(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)+(b^2) (c^2) (p^2) (r^2)+(a^4) p q (r^2)-2 (a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-3 (a^2) (c^2) p q (r^2)-3 (b^2) (c^2) p q (r^2)+2 (c^4) p q (r^2)+(a^4) (q^2) (r^2)-(a^2) (b^2) (q^2) (r^2)+(a^2) (c^2) (q^2) (r^2)) (2 (c^4) (p^3) (q^3)+(a^4) (p^3) (q^2) r-2 (a^2) (b^2) (p^3) (q^2) r+(b^4) (p^3) (q^2) r-2 (a^2) (c^2) (p^3) (q^2) r+(c^4) (p^3) (q^2) r+(a^4) (p^2) (q^3) r-2 (a^2) (b^2) (p^2) (q^3) r+(b^4) (p^2) (q^3) r-2 (b^2) (c^2) (p^2) (q^3) r+(c^4) (p^2) (q^3) r-(a^4) (p^3) q (r^2)+2 (a^2) (b^2) (p^3) q (r^2)-(b^4) (p^3) q (r^2)+2 (a^2) (c^2) (p^3) q (r^2)-(c^4) (p^3) q (r^2)-2 (a^4) (p^2) (q^2) (r^2)+4 (a^2) (b^2) (p^2) (q^2) (r^2)-2 (b^4) (p^2) (q^2) (r^2)+2 (a^2) (c^2) (p^2) (q^2) (r^2)+2 (b^2) (c^2) (p^2) (q^2) (r^2)-(a^4) p (q^3) (r^2)+2 (a^2) (b^2) p (q^3) (r^2)-(b^4) p (q^3) (r^2)+2 (b^2) (c^2) p (q^3) (r^2)-(c^4) p (q^3) (r^2)-2 (b^4) (p^3) (r^3)-(a^4) (p^2) q (r^3)-2 (a^2) (b^2) (p^2) q (r^3)-3 (b^4) (p^2) q (r^3)+2 (a^2) (c^2) (p^2) q (r^3)+4 (b^2) (c^2) (p^2) q (r^3)-(c^4) (p^2) q (r^3)-3 (a^4) p (q^2) (r^3)-2 (a^2) (b^2) p (q^2) (r^3)-(b^4) p (q^2) (r^3)+4 (a^2) (c^2) p (q^2) (r^3)+2 (b^2) (c^2) p (q^2) (r^3)-(c^4) p (q^2) (r^3)-2 (a^4) (q^3) (r^3))}; (* Reflection of QA-P2 in QA-P11 *)
QAP31={p (q+r) (2 p+q+r) ((p^2)+p q+2 (q^2)+p r+q r+2 (r^2)),q (p+r) (p+2 q+r) (2 (p^2)+p q+(q^2)+p r+q r+2 (r^2)),(p+q) r (p+q+2 r) (2 (p^2)+p q+2 (q^2)+p r+q r+(r^2))};(* Complement of QA-p16 wrt QA-DT *)
QAP32={(a^2) (c^2) (p^2) (q^2)-(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)-4 (a^4) (p^2) q r+5 (a^2) (b^2) (p^2) q r-(b^4) (p^2) q r+5 (a^2) (c^2) (p^2) q r+2 (b^2) (c^2) (p^2) q r-(c^4) (p^2) q r-3 (a^4) p (q^2) r+3 (a^2) (b^2) p (q^2) r+3 (a^2) (c^2) p (q^2) r+(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)-(b^2) (c^2) (p^2) (r^2)-3 (a^4) p q (r^2)+3 (a^2) (b^2) p q (r^2)+3 (a^2) (c^2) p q (r^2)-2 (a^4) (q^2) (r^2),-(a^2) (c^2) (p^2) (q^2)+(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+3 (a^2) (b^2) (p^2) q r-3 (b^4) (p^2) q r+3 (b^2) (c^2) (p^2) q r-(a^4) p (q^2) r+5 (a^2) (b^2) p (q^2) r-4 (b^4) p (q^2) r+2 (a^2) (c^2) p (q^2) r+5 (b^2) (c^2) p (q^2) r-(c^4) p (q^2) r-2 (b^4) (p^2) (r^2)+3 (a^2) (b^2) p q (r^2)-3 (b^4) p q (r^2)+3 (b^2) (c^2) p q (r^2)+(a^4) (q^2) (r^2)+(a^2) (b^2) (q^2) (r^2)-(a^2) (c^2) (q^2) (r^2),-2 (c^4) (p^2) (q^2)+3 (a^2) (c^2) (p^2) q r+3 (b^2) (c^2) (p^2) q r-3 (c^4) (p^2) q r+3 (a^2) (c^2) p (q^2) r+3 (b^2) (c^2) p (q^2) r-3 (c^4) p (q^2) r-(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)+(b^2) (c^2) (p^2) (r^2)-(a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)-(b^4) p q (r^2)+5 (a^2) (c^2) p q (r^2)+5 (b^2) (c^2) p q (r^2)-4 (c^4) p q (r^2)+(a^4) (q^2) (r^2)-(a^2) (b^2) (q^2) (r^2)+(a^2) (c^2) (q^2) (r^2)}; (* Centroid Circumcenter Quadrangle *)
QAP33={-2 (a^2) (c^2) (p^2) (q^2)+2 (b^2) (c^2) (p^2) (q^2)-2 (c^4) (p^2) (q^2)+2 (a^4) (p^2) q r+2 (a^2) (b^2) (p^2) q r-4 (b^4) (p^2) q r+2 (a^2) (c^2) (p^2) q r+8 (b^2) (c^2) (p^2) q r-4 (c^4) (p^2) q r+3 (a^4) p (q^2) r-3 (b^4) p (q^2) r+6 (b^2) (c^2) p (q^2) r-3 (c^4) p (q^2) r-2 (a^2) (b^2) (p^2) (r^2)-2 (b^4) (p^2) (r^2)+2 (b^2) (c^2) (p^2) (r^2)+3 (a^4) p q (r^2)-3 (b^4) p q (r^2)+6 (b^2) (c^2) p q (r^2)-3 (c^4) p q (r^2)+4 (a^4) (q^2) (r^2),2 (a^2) (c^2) (p^2) (q^2)-2 (b^2) (c^2) (p^2) (q^2)-2 (c^4) (p^2) (q^2)-3 (a^4) (p^2) q r+3 (b^4) (p^2) q r+6 (a^2) (c^2) (p^2) q r-3 (c^4) (p^2) q r-4 (a^4) p (q^2) r+2 (a^2) (b^2) p (q^2) r+2 (b^4) p (q^2) r+8 (a^2) (c^2) p (q^2) r+2 (b^2) (c^2) p (q^2) r-4 (c^4) p (q^2) r+4 (b^4) (p^2) (r^2)-3 (a^4) p q (r^2)+3 (b^4) p q (r^2)+6 (a^2) (c^2) p q (r^2)-3 (c^4) p q (r^2)-2 (a^4) (q^2) (r^2)-2 (a^2) (b^2) (q^2) (r^2)+2 (a^2) (c^2) (q^2) (r^2),4 (c^4) (p^2) (q^2)-3 (a^4) (p^2) q r+6 (a^2) (b^2) (p^2) q r-3 (b^4) (p^2) q r+3 (c^4) (p^2) q r-3 (a^4) p (q^2) r+6 (a^2) (b^2) p (q^2) r-3 (b^4) p (q^2) r+3 (c^4) p (q^2) r+2 (a^2) (b^2) (p^2) (r^2)-2 (b^4) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)-4 (a^4) p q (r^2)+8 (a^2) (b^2) p q (r^2)-4 (b^4) p q (r^2)+2 (a^2) (c^2) p q (r^2)+2 (b^2) (c^2) p q (r^2)+2 (c^4) p q (r^2)-2 (a^4) (q^2) (r^2)+2 (a^2) (b^2) (q^2) (r^2)-2 (a^2) (c^2) (q^2) (r^2)}; (* Centroid Orthocenter Quadrangle *)  
QAP34={-2 (a^4) q (p+q) r (p+r) (2 p+q+r)-p (q+r) ((b^4) (p+q) r (3 p+q+r)+(c^4) q (p+r) (3 p+q+r)+(b^2) (c^2) ((p^2) (q+r)-2 q r (q+r)+p ((q^2)-4 q r+(r^2))))+(a^2) p ((b^2) r ((p^2) (7 q+r)+q (3 (q^2)+4 q r+(r^2))+p (10 (q^2)+5 q r+(r^2)))+(c^2) q ((p^2) (q+7 r)+r ((q^2)+4 q r+3 (r^2))+p ((q^2)+5 q r+10 (r^2)))),-(a^4) q (p+q) r (p+r) (p+3 q+r)-p (q+r) (2 (b^4) (p+q) r (p+2 q+r)+(c^4) q (p+r) (p+3 q+r)-(b^2) (c^2) q ((p^2)+r (7 q+3 r)+p (q+4 r)))-(a^2) q ((c^2) (p+r) ((p^2) (q-2 r)+q r (q+r)+p ((q^2)-4 q r-2 (r^2)))-(b^2) r (3 (p^3)+q r (q+r)+2 (p^2) (5 q+2 r)+p (7 (q^2)+5 q r+(r^2)))),-2 (c^4) p q (p+r) (q+r) (p+q+2 r)+(c^2) r ((b^2) p (q+r) ((p^2)+p (4 q+r)+q (3 q+7 r))+(a^2) q (p+r) (3 (p^2)+q (q+r)+p (4 q+7 r)))-(p+q) r ((a^4) q (p+r) (p+q+3 r)+(b^4) p (q+r) (p+q+3 r)+(a^2) (b^2) ((p^2) (-2 q+r)+q r (q+r)+p (-2 (q^2)-4 q r+(r^2))))}; (* Euler-Poncelet Point of the Centroid Quadrangle *)
QAP35={-p (q+r) (4 (a^4) q (p+q) r (p+r) (2 p+q+r)-(a^2) ((b^2) (p+q) r (q r (-q+r)+p (q+r) (7 q+r)+(p^2) (15 q+r))+(c^2) q (p+r) (q (q-r) r+p (q+r) (q+7 r)+(p^2) (q+15 r)))+(q+r) ((b^4) (p+q) r (7 (p^2)-q r+3 p (q+r))+(c^4) q (p+r) (7 (p^2)-q r+3 p (q+r))+(b^2) (c^2) (2 (q^2) (r^2)+(p^3) (q+r)-5 p q r (q+r)+(p^2) ((q^2)-12 q r+(r^2))))),-q (p+r) ((a^4) (p+q) r (p+r) (3 p q+7 (q^2)-p r+3 q r)+p (q+r) (4 (b^4) (p+q) r (p+2 q+r)+(c^4) (p+r) (3 p q+7 (q^2)-p r+3 q r)-(b^2) (c^2) (p q (p+q)+(p+3 q) (p+5 q) r-(p-7 q) (r^2)))+(a^2) (-(b^2) (p+q) r ((p^2) (7 q-r)+q r (q+r)+p (3 q+r) (5 q+r))+(c^2) (p+r) ((q^2) r (q+r)+p q ((q^2)-12 q r-5 (r^2))+(p^2) ((q^2)-5 q r+2 (r^2))))),(p+q) r ((a^4) q (p+q) (p+r) (p q-3 (p+q) r-7 (r^2))+p (q+r) (-4 (c^4) q (p+r) (p+q+2 r)+(b^4) (p+q) (p q-3 (p+q) r-7 (r^2))+(b^2) (c^2) (p (p-q) q+(p+q) (p+7 q) r+(p+15 q) (r^2)))+(a^2) ((c^2) q (p+r) (p q (-p+q)+(p+q) (7 p+q) r+(15 p+q) (r^2))+(b^2) (p+q) (-2 (p^2) (q^2)+5 p q (p+q) r-((p^2)-12 p q+(q^2)) (r^2)-(p+q) (r^3))))}; (* PentaPoint *)
QAP36={(a-b-c) (a+b-c) (a-b+c) (a+b+c) (p^2) q (p+q) r (p+r) (q+r) ((b^2) (p+q) r-(c^2) q (p+r)) ((a^2) (-q+r)+(b-c) (b+c) (q+r))+2 (-(b-c) (b+c) p (q-r)+(a^2) (2 q r+p (q+r))) ((c^4) p q (p+r) (q+r)-2 (c^2) p q r ((a^2) (p+r)+(b^2) (q+r))+(p+q) r (-2 (a^2) (b^2) p q+(a^4) q (p+r)+(b^4) p (q+r))) (-(c^2) (p^2) q (q+r)+r (-(b^2) (p^2) (q+r)+(a^2) q ((p^2)+q r))),(a-b-c) (a+b-c) (a-b+c) (a+b+c) p (q^2) (p+q) r (p+r) (q+r) ((b^2) (p-r)-(a^2) (p+r)+(c^2) (p+r)) (-(a^2) (p+q) r+(c^2) p (q+r))+2 ((a^2) q (p-r)+(c^2) q (-p+r)-(b^2) (p q+2 p r+q r)) ((c^4) p q (p+r) (q+r)-2 (c^2) p q r ((a^2) (p+r)+(b^2) (q+r))+(p+q) r (-2 (a^2) (b^2) p q+(a^4) q (p+r)+(b^4) p (q+r))) ((c^2) p (q^2) (p+r)+r ((a^2) (q^2) (p+r)-(b^2) p ((q^2)+p r))),-(a-b-c) (a+b-c) (a-b+c) (a+b+c) p q (p+q) ((c^2) (p-q)-(a^2) (p+q)+(b^2) (p+q)) (r^2) (p+r) (q+r) ((a^2) q (p+r)-(b^2) p (q+r))+2 (-(a-b) (a+b) (p-q) r+(c^2) (2 p q+(p+q) r)) (-(p+q) ((b^2) p+(a^2) q) (r^2)+(c^2) p q (p q+(r^2))) ((c^4) p q (p+r) (q+r)-2 (c^2) p q r ((a^2) (p+r)+(b^2) (q+r))+(p+q) r (-2 (a^2) (b^2) p q+(a^4) q (p+r)+(b^4) p (q+r)))};(* Complement of QA-P30 wrt QA-DT *)
QAP37={(a^4) q r (-(p^3) (((q-r))^2)-(p^2) (((q-r))^2) (q+r)+4 (q^2) (r^2) (q+r)+p q r ((q^2)+6 q r+(r^2)))-((b^2)-(c^2)) p (q+r) (-(c^2) q (2 (p^3) q+q (r^2) (q+r)+(p^2) (2 (q^2)+3 q r+(r^2))+p r ((q^2)+4 q r+(r^2)))+(b^2) r (2 (p^3) r+(q^2) r (q+r)+p q ((q^2)+4 q r+(r^2))+(p^2) ((q^2)+3 q r+2 (r^2))))-2 (a^2) p ((b^2) r ((p^3) r (-q+r)-2 (q^2) (r^2) (q+r)-(p^2) (q-r) (((q+r))^2)-p q ((q^3)+2 (q^2) r+2 q (r^2)-(r^3)))+(c^2) q ((p^3) q (q-r)-2 (q^2) (r^2) (q+r)+(p^2) (q-r) (((q+r))^2)-p r (-(q^3)+2 (q^2) r+2 q (r^2)+(r^3)))),-(a^4) q r (p+r) ((p^3) (q+r)+2 (q^2) r (q+r)+p q r (3 q+r)+(p^2) ((q^2)+4 q r+(r^2)))+2 (a^2) q ((b^2) r ((p^4) q-(q^2) (r^2) (q+r)+p q r ((q^2)-q r-(r^2))+(p^3) ((q^2)+2 q r+2 (r^2))+(p^2) r ((q^2)+2 q r+2 (r^2)))+(c^2) (p+r) ((q^2) (r^2) (q+r)+p q (r^2) (2 q+r)+(p^3) ((q^2)+q r+(r^2))+(p^2) ((q^3)+2 (q^2) r+4 q (r^2)+(r^3))))-p (2 (b^2) (c^2) q (-q (r^3) (q+r)+(p^3) ((q^2)+q r-2 (r^2))-p q r ((q^2)+q r+2 (r^2))+(p^2) ((q^3)+(q^2) r-2 q (r^2)-2 (r^3)))+(c^4) q (p+r) (q (r^2) (q+r)+(p^2) (2 (q^2)+q r+(r^2))+p (2 (q^3)+3 (q^2) r+4 q (r^2)+(r^3)))-(b^4) r (-(q^2) (r^2) (q+r)+p q r (2 (q^2)+q r+(r^2))+(p^3) (-(q^2)+q r+4 (r^2))+(p^2) (-(q^3)+(q^2) r+6 q (r^2)+4 (r^3)))),(c^4) p q (-(q^2) (r^2) (q+r)+(p^3) (4 (q^2)+q r-(r^2))+p q r ((q^2)+q r+2 (r^2))+(p^2) (4 (q^3)+6 (q^2) r+q (r^2)-(r^3)))+2 (c^2) r ((a^2) q ((p^4) r-(q^2) (r^2) (q+r)-p q r ((q^2)+q r-(r^2))+(p^3) (2 (q^2)+2 q r+(r^2))+(p^2) q (2 (q^2)+2 q r+(r^2)))+(b^2) p ((q^3) r (q+r)+(p^3) (2 (q^2)-q r-(r^2))+p q r (2 (q^2)+q r+(r^2))+(p^2) (2 (q^3)+2 (q^2) r-q (r^2)-(r^3))))-((a^2)-(b^2)) (p+q) r ((a^2) q ((p^3) (q+r)+2 q (r^2) (q+r)+p q r (q+3 r)+(p^2) ((q^2)+4 q r+(r^2)))-(b^2) p ((q^2) r (q+r)+(p^2) ((q^2)+q r+2 (r^2))+p ((q^3)+4 (q^2) r+3 q (r^2)+2 (r^3))))};(*Reflection of QA-P12 in QA-P1*)
QAP38={((c^2) p q (p+r) (q+r)+(p+q) r ((a^2) q (p+r)-(b^2) p (q+r))) ((c^2) p q (p+r) (q+r)-(p+q) r ((a^2) q (p+r)+(b^2) p (q+r))) ((c^2) p q (2 p+q-r) (p+r) (q+r)-(p+q) r (-(b^2) p (2 p-q+r) (q+r)-(a^2) q (p+r) (-2 p+q+r))),((c^2) p q (p+r) (q+r)-(p+q) r ((a^2) q (p+r)-(b^2) p (q+r))) ((c^2) p q (p+r) (q+r)-(p+q) r ((a^2) q (p+r)+(b^2) p (q+r))) ((c^2) p q (p+2 q-r) (p+r) (q+r)-(p+q) r ((a^2) q (p-2 q-r) (p+r)-(b^2) p (p-2 q+r) (q+r))),-((c^2) p q (p+r) (q+r)-(p+q) r ((a^2) q (p+r)-(b^2) p (q+r))) ((c^2) p q (p+r) (q+r)+(p+q) r ((a^2) q (p+r)-(b^2) p (q+r))) ((c^2) p q (p+q-2 r) (p+r) (q+r)-(p+q) r ((a^2) q (p-q-2 r) (p+r)-(b^2) p (q+r) (p-q+2 r)))}; (* Montesdeoca-Hutson Point *)
QAP39={-((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) p q r (q+r) (2 p+q+r) (-(p^2)+q r-p (q+r))+2 (p+q+r) (-((b^2)-(c^2)) p (q-r)+(a^2) (2 q r+p (q+r))) (-(c^2) (p^2) q (q+r)+r (-(b^2) (p^2) (q+r)+(a^2) q ((p^2)+q r))),-((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) p q r (p+r) (p+2 q+r) (p (-q+r)-q (q+r))+2 (p+q+r) ((a^2) q (p-r)+(c^2) q (-p+r)-(b^2) (p q+2 p r+q r)) ((c^2) p (q^2) (p+r)+r ((a^2) (q^2) (p+r)-(b^2) p ((q^2)+p r))),-((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) p q (p+q) r (p+q+2 r) (p (q-r)-r (q+r))+2 (p+q+r) (-(p+q) ((b^2) p+(a^2) q) (r^2)+(c^2) p q (p q+(r^2))) (-((a^2)-(b^2)) (p-q) r+(c^2) (q r+p (2 q+r)))};  (* Midpoint of QA-P12 and QA-P20 *)
QAP40={-5 (a^4) (p^3) q+7 (a^2) (b^2) (p^3) q-2 (b^4) (p^3) q+9 (a^2) (c^2) (p^3) q+4 (b^2) (c^2) (p^3) q-2 (c^4) (p^3) q-9 (a^4) (p^2) (q^2)+12 (a^2) (b^2) (p^2) (q^2)-3 (b^4) (p^2) (q^2)+12 (a^2) (c^2) (p^2) (q^2)+6 (b^2) (c^2) (p^2) (q^2)-3 (c^4) (p^2) (q^2)-4 (a^4) p (q^3)+5 (a^2) (b^2) p (q^3)-(b^4) p (q^3)+4 (a^2) (c^2) p (q^3)+(b^2) (c^2) p (q^3)-5 (a^4) (p^3) r+9 (a^2) (b^2) (p^3) r-2 (b^4) (p^3) r+7 (a^2) (c^2) (p^3) r+4 (b^2) (c^2) (p^3) r-2 (c^4) (p^3) r-16 (a^4) (p^2) q r+24 (a^2) (b^2) (p^2) q r-6 (b^4) (p^2) q r+24 (a^2) (c^2) (p^2) q r+12 (b^2) (c^2) (p^2) q r-6 (c^4) (p^2) q r-15 (a^4) p (q^2) r+17 (a^2) (b^2) p (q^2) r-4 (b^4) p (q^2) r+18 (a^2) (c^2) p (q^2) r+7 (b^2) (c^2) p (q^2) r-3 (c^4) p (q^2) r-4 (a^4) (q^3) r+2 (a^2) (b^2) (q^3) r+4 (a^2) (c^2) (q^3) r-9 (a^4) (p^2) (r^2)+12 (a^2) (b^2) (p^2) (r^2)-3 (b^4) (p^2) (r^2)+12 (a^2) (c^2) (p^2) (r^2)+6 (b^2) (c^2) (p^2) (r^2)-3 (c^4) (p^2) (r^2)-15 (a^4) p q (r^2)+18 (a^2) (b^2) p q (r^2)-3 (b^4) p q (r^2)+17 (a^2) (c^2) p q (r^2)+7 (b^2) (c^2) p q (r^2)-4 (c^4) p q (r^2)-6 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)-4 (a^4) p (r^3)+4 (a^2) (b^2) p (r^3)+5 (a^2) (c^2) p (r^3)+(b^2) (c^2) p (r^3)-(c^4) p (r^3)-4 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)+2 (a^2) (c^2) q (r^3),-(a^4) (p^3) q+5 (a^2) (b^2) (p^3) q-4 (b^4) (p^3) q+(a^2) (c^2) (p^3) q+4 (b^2) (c^2) (p^3) q-3 (a^4) (p^2) (q^2)+12 (a^2) (b^2) (p^2) (q^2)-9 (b^4) (p^2) (q^2)+6 (a^2) (c^2) (p^2) (q^2)+12 (b^2) (c^2) (p^2) (q^2)-3 (c^4) (p^2) (q^2)-2 (a^4) p (q^3)+7 (a^2) (b^2) p (q^3)-5 (b^4) p (q^3)+4 (a^2) (c^2) p (q^3)+9 (b^2) (c^2) p (q^3)-2 (c^4) p (q^3)+2 (a^2) (b^2) (p^3) r-4 (b^4) (p^3) r+4 (b^2) (c^2) (p^3) r-4 (a^4) (p^2) q r+17 (a^2) (b^2) (p^2) q r-15 (b^4) (p^2) q r+7 (a^2) (c^2) (p^2) q r+18 (b^2) (c^2) (p^2) q r-3 (c^4) (p^2) q r-6 (a^4) p (q^2) r+24 (a^2) (b^2) p (q^2) r-16 (b^4) p (q^2) r+12 (a^2) (c^2) p (q^2) r+24 (b^2) (c^2) p (q^2) r-6 (c^4) p (q^2) r-2 (a^4) (q^3) r+9 (a^2) (b^2) (q^3) r-5 (b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+7 (b^2) (c^2) (q^3) r-2 (c^4) (q^3) r+6 (a^2) (b^2) (p^2) (r^2)-6 (b^4) (p^2) (r^2)+6 (b^2) (c^2) (p^2) (r^2)-3 (a^4) p q (r^2)+18 (a^2) (b^2) p q (r^2)-15 (b^4) p q (r^2)+7 (a^2) (c^2) p q (r^2)+17 (b^2) (c^2) p q (r^2)-4 (c^4) p q (r^2)-3 (a^4) (q^2) (r^2)+12 (a^2) (b^2) (q^2) (r^2)-9 (b^4) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)+12 (b^2) (c^2) (q^2) (r^2)-3 (c^4) (q^2) (r^2)+4 (a^2) (b^2) p (r^3)-4 (b^4) p (r^3)+2 (b^2) (c^2) p (r^3)+4 (a^2) (b^2) q (r^3)-4 (b^4) q (r^3)+(a^2) (c^2) q (r^3)+5 (b^2) (c^2) q (r^3)-(c^4) q (r^3),2 (a^2) (c^2) (p^3) q+4 (b^2) (c^2) (p^3) q-4 (c^4) (p^3) q+6 (a^2) (c^2) (p^2) (q^2)+6 (b^2) (c^2) (p^2) (q^2)-6 (c^4) (p^2) (q^2)+4 (a^2) (c^2) p (q^3)+2 (b^2) (c^2) p (q^3)-4 (c^4) p (q^3)-(a^4) (p^3) r+(a^2) (b^2) (p^3) r+5 (a^2) (c^2) (p^3) r+4 (b^2) (c^2) (p^3) r-4 (c^4) (p^3) r-4 (a^4) (p^2) q r+7 (a^2) (b^2) (p^2) q r-3 (b^4) (p^2) q r+17 (a^2) (c^2) (p^2) q r+18 (b^2) (c^2) (p^2) q r-15 (c^4) (p^2) q r-3 (a^4) p (q^2) r+7 (a^2) (b^2) p (q^2) r-4 (b^4) p (q^2) r+18 (a^2) (c^2) p (q^2) r+17 (b^2) (c^2) p (q^2) r-15 (c^4) p (q^2) r+(a^2) (b^2) (q^3) r-(b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+5 (b^2) (c^2) (q^3) r-4 (c^4) (q^3) r-3 (a^4) (p^2) (r^2)+6 (a^2) (b^2) (p^2) (r^2)-3 (b^4) (p^2) (r^2)+12 (a^2) (c^2) (p^2) (r^2)+12 (b^2) (c^2) (p^2) (r^2)-9 (c^4) (p^2) (r^2)-6 (a^4) p q (r^2)+12 (a^2) (b^2) p q (r^2)-6 (b^4) p q (r^2)+24 (a^2) (c^2) p q (r^2)+24 (b^2) (c^2) p q (r^2)-16 (c^4) p q (r^2)-3 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)-3 (b^4) (q^2) (r^2)+12 (a^2) (c^2) (q^2) (r^2)+12 (b^2) (c^2) (q^2) (r^2)-9 (c^4) (q^2) (r^2)-2 (a^4) p (r^3)+4 (a^2) (b^2) p (r^3)-2 (b^4) p (r^3)+7 (a^2) (c^2) p (r^3)+9 (b^2) (c^2) p (r^3)-5 (c^4) p (r^3)-2 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)-2 (b^4) q (r^3)+9 (a^2) (c^2) q (r^3)+7 (b^2) (c^2) q (r^3)-5 (c^4) q (r^3)};  (* QA-Circumcenter QL-P17-Triple Triangle & QA-Centroid QL-P6-Triple Triangle*)
QAP41={(a^2) q r ((a^2) (p^2)-(b^2) (p^2)-(c^2) (p^2)+(a^2) p q-(b^2) p q+(a^2) p r-(c^2) p r+(a^2) q r) (-(c^4) (p^3) (q^3)+(a^2) (c^2) (p^3) (q^2) r-(c^4) (p^3) (q^2) r+(b^2) (c^2) (p^2) (q^3) r-(c^4) (p^2) (q^3) r+(a^2) (b^2) (p^3) q (r^2)-(b^4) (p^3) q (r^2)+(a^4) (p^2) (q^2) (r^2)-(b^4) (p^2) (q^2) (r^2)+2 (b^2) (c^2) (p^2) (q^2) (r^2)-(c^4) (p^2) (q^2) (r^2)+(a^4) p (q^3) (r^2)-(a^2) (b^2) p (q^3) (r^2)-(b^4) (p^3) (r^3)-(b^4) (p^2) q (r^3)+(b^2) (c^2) (p^2) q (r^3)+(a^4) p (q^2) (r^3)-(a^2) (c^2) p (q^2) (r^3)+(a^4) (q^3) (r^3)),(b^2) p r (-(a^2) p q+(b^2) p q-(a^2) (q^2)+(b^2) (q^2)-(c^2) (q^2)+(b^2) p r+(b^2) q r-(c^2) q r) (-(c^4) (p^3) (q^3)+(a^2) (c^2) (p^3) (q^2) r-(c^4) (p^3) (q^2) r+(b^2) (c^2) (p^2) (q^3) r-(c^4) (p^2) (q^3) r-(a^2) (b^2) (p^3) q (r^2)+(b^4) (p^3) q (r^2)-(a^4) (p^2) (q^2) (r^2)+(b^4) (p^2) (q^2) (r^2)+2 (a^2) (c^2) (p^2) (q^2) (r^2)-(c^4) (p^2) (q^2) (r^2)-(a^4) p (q^3) (r^2)+(a^2) (b^2) p (q^3) (r^2)+(b^4) (p^3) (r^3)+(b^4) (p^2) q (r^3)-(b^2) (c^2) (p^2) q (r^3)-(a^4) p (q^2) (r^3)+(a^2) (c^2) p (q^2) (r^3)-(a^4) (q^3) (r^3)),(c^2) p q ((c^2) p q-(a^2) p r+(c^2) p r-(b^2) q r+(c^2) q r-(a^2) (r^2)-(b^2) (r^2)+(c^2) (r^2)) ((c^4) (p^3) (q^3)-(a^2) (c^2) (p^3) (q^2) r+(c^4) (p^3) (q^2) r-(b^2) (c^2) (p^2) (q^3) r+(c^4) (p^2) (q^3) r+(a^2) (b^2) (p^3) q (r^2)-(b^4) (p^3) q (r^2)-(a^4) (p^2) (q^2) (r^2)+2 (a^2) (b^2) (p^2) (q^2) (r^2)-(b^4) (p^2) (q^2) (r^2)+(c^4) (p^2) (q^2) (r^2)-(a^4) p (q^3) (r^2)+(a^2) (b^2) p (q^3) (r^2)-(b^4) (p^3) (r^3)-(b^4) (p^2) q (r^3)+(b^2) (c^2) (p^2) q (r^3)-(a^4) p (q^2) (r^3)+(a^2) (c^2) p (q^2) (r^3)-(a^4) (q^3) (r^3))};  (* Involutary Conjugate of QA-P4 *)
QAP42={((b^2)-(c^2)) (p^2) (q-r) ((c^2) q+(b^2) r)+(a^4) q r ((p^2)-q r)-(a^2) p ((b^2) r (3 q r+p (2 q+r))+(c^2) q (3 q r+p (q+2 r))),(a^4) (q^2) (p-r) r+(a^2) q ((c^2) q (((p-r))^2)-(b^2) r (2 p q+3 p r+q r))-p ((c^4) (q^2) (p-r)+(b^4) r (-(q^2)+p r)+(b^2) (c^2) q (p q+3 p r+2 q r)),((a^2)-(b^2)) (p-q) ((b^2) p+(a^2) q) (r^2)-(c^4) p q (p q-(r^2))-(c^2) r ((a^2) q (3 p q+2 p r+q r)+(b^2) p (2 q r+p (3 q+r)))} ; (* QA-Orthopole Center was QA-P9035 *)
QAP43={(q+r) (2 p+q+r) (2 (p^2)+2 p q+2 p r+q r),(p+r) (p+2 q+r) (2 p q+2 (q^2)+p r+2 q r),(p+q) (p+q+2 r) (p q+2 p r+2 q r+2 (r^2))};   (* LSD-point QA & QA-DT, used to be QA-P9048*)
QAP44={(a^6) (q^2) (p+q) (r^2) (p+r)+(c^6) (p^2) (q^2) (p+r) (3 q+2 r)+(b^6) (p^2) (p+q) (r^2) (2 q+3 r)+(a^4) (c^2) (q^2) r (p+r) (2 (p^2)-2 (q^2)-2 p r-q r)+(a^4) (b^2) q (p+q) (r^2) (2 (p^2)-2 p q-q r-2 (r^2))-(a^2) (c^4) p (q^2) (p+r) (3 p q+3 (q^2)+4 p r-(r^2))-(a^2) (b^4) p (p+q) (r^2) (4 p q-(q^2)+3 p r+3 (r^2))-(b^4) (c^2) (p^2) r (4 (p^2) q-4 (q^3)+6 (p^2) r+9 p q r+2 (q^2) r+6 p (r^2)+7 q (r^2))-(b^2) (c^4) (p^2) q (6 (p^2) q+6 p (q^2)+4 (p^2) r+9 p q r+7 (q^2) r+2 q (r^2)-4 (r^3))+2 (a^2) (b^2) (c^2) p q r (2 (p^3)-(p^2) q-2 p (q^2)+(q^3)-(p^2) r-4 p q r-3 (q^2) r-2 p (r^2)-3 q (r^2)+(r^3)),(b^6) (p^2) (p+q) (r^2) (q+r)+(c^6) (p^2) (q^2) (q+r) (3 p+2 r)+(a^6) (q^2) (p+q) (r^2) (2 p+3 r)+(b^4) (c^2) (p^2) r (q+r) (-2 (p^2)+2 (q^2)-p r-2 q r)+(a^2) (b^4) p (p+q) (r^2) (-2 p q+2 (q^2)-p r-2 (r^2))-(b^2) (c^4) (p^2) q (q+r) (3 (p^2)+3 p q+4 q r-(r^2))-(a^4) (b^2) q (p+q) (r^2) (-(p^2)+4 p q+3 q r+3 (r^2))-(a^4) (c^2) (q^2) r (-4 (p^3)+4 p (q^2)+2 (p^2) r+9 p q r+6 (q^2) r+7 p (r^2)+6 q (r^2))-(a^2) (c^4) p (q^2) (6 (p^2) q+6 p (q^2)+7 (p^2) r+9 p q r+4 (q^2) r+2 p (r^2)-4 (r^3))+2 (a^2) (b^2) (c^2) p q r ((p^3)-2 (p^2) q-p (q^2)+2 (q^3)-3 (p^2) r-4 p q r-(q^2) r-3 p (r^2)-2 q (r^2)+(r^3)),(a^6) (q^2) (2 p+3 q) (r^2) (p+r)+(b^6) (p^2) (3 p+2 q) (r^2) (q+r)+(c^6) (p^2) (q^2) (p+r) (q+r)-(a^4) (c^2) (q^2) r (p+r) (-(p^2)+3 (q^2)+4 p r+3 q r)-(b^4) (c^2) (p^2) r (q+r) (3 (p^2)-(q^2)+3 p r+4 q r)+(a^2) (c^4) p (q^2) (p+r) (-p q-2 (q^2)-2 p r+2 (r^2))+(b^2) (c^4) (p^2) q (q+r) (-2 (p^2)-p q-2 q r+2 (r^2))-(a^2) (b^4) p (r^2) (7 (p^2) q+2 p (q^2)-4 (q^3)+6 (p^2) r+9 p q r+6 p (r^2)+4 q (r^2))-(a^4) (b^2) q (r^2) (-4 (p^3)+2 (p^2) q+7 p (q^2)+9 p q r+6 (q^2) r+4 p (r^2)+6 q (r^2))+2 (a^2) (b^2) (c^2) p q r ((p^3)-3 (p^2) q-3 p (q^2)+(q^3)-2 (p^2) r-4 p q r-2 (q^2) r-p (r^2)-q (r^2)+2 (r^3))}; (* LSD-point QA-sidelines*)

Foci QA-Parabola

F1={-(p^2) q r (q+r) (p+q+r) ((a^2) q r ((p^3) ((q^4)+2 (q^3) r-30 (q^2) (r^2)+2 q (r^3)+(r^4))-q r (((q+r))^2) ((q^2) r+3 r (Sqrt[-p q r (p+q+r)])+q ((r^2)-3 (Sqrt[-p q r (p+q+r)])))+p (q+r) (2 (q^4) r+2 q (r^4)-17 q (r^2) (Sqrt[-p q r (p+q+r)])-(r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (-12 (r^2)+(Sqrt[-p q r (p+q+r)]))+(q^2) (-12 (r^3)+17 r (Sqrt[-p q r (p+q+r)])))+(p^2) ((q^5)+6 (q^4) r+6 q (r^4)+(r^5)-19 q (r^2) (Sqrt[-p q r (p+q+r)])-3 (r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (-35 (r^2)+3 (Sqrt[-p q r (p+q+r)]))+(q^2) (-35 (r^3)+19 r (Sqrt[-p q r (p+q+r)]))))-p (((q+r))^3) ((b^2) r ((p^2) q (q-3 r)+q (q+r) (Sqrt[-p q r (p+q+r)])+p ((q^3)-(q^2) r-2 q (r^2)+3 q (Sqrt[-p q r (p+q+r)])-r (Sqrt[-p q r (p+q+r)])))-(c^2) q ((p^2) (3 q-r) r+r (q+r) (Sqrt[-p q r (p+q+r)])-p (-2 (q^2) r+(r^3)-3 r (Sqrt[-p q r (p+q+r)])+q (-(r^2)+(Sqrt[-p q r (p+q+r)])))))),p (q^2) r (p+q+r) ((a^2) q r (q (r^2) (((q+r))^3) (Sqrt[-p q r (p+q+r)])+(p^4) q ((q^3)-21 (q^2) r+35 q (r^2)-7 (r^3))-p r (((q+r))^2) (-5 (q^3) r+2 q (r^3)-13 q r (Sqrt[-p q r (p+q+r)])+(r^2) (Sqrt[-p q r (p+q+r)])+(q^2) (-3 (r^2)+10 (Sqrt[-p q r (p+q+r)])))+(p^3) ((q^5)-29 (q^4) r-16 q (r^4)+21 q (r^2) (Sqrt[-p q r (p+q+r)])-(r^3) (Sqrt[-p q r (p+q+r)])+7 (q^3) (5 (r^2)+(Sqrt[-p q r (p+q+r)]))-7 (q^2) (-7 (r^3)+5 r (Sqrt[-p q r (p+q+r)])))+(p^2) (q+r) (-10 (q^4) r-2 (r^3) (Sqrt[-p q r (p+q+r)])-11 q (r^2) ((r^2)-3 (Sqrt[-p q r (p+q+r)]))+5 (q^3) (5 (r^2)+(Sqrt[-p q r (p+q+r)]))-8 (q^2) (-3 (r^3)+5 r (Sqrt[-p q r (p+q+r)]))))-p (q+r) (-(c^2) q (2 (p^3) q r (3 (q^2)-10 q r+3 (r^2))+(r^2) (((q+r))^2) ((q^2) r+r (Sqrt[-p q r (p+q+r)])+q ((r^2)-5 (Sqrt[-p q r (p+q+r)])))-(p^2) (-5 (q^4) r-13 q (r^4)+15 q (r^2) (Sqrt[-p q r (p+q+r)])-(r^3) (Sqrt[-p q r (p+q+r)])+(q^2) r (17 (r^2)-15 (Sqrt[-p q r (p+q+r)]))+(q^3) (25 (r^2)+(Sqrt[-p q r (p+q+r)])))+2 p r (q+r) (-5 (q^3) r+4 q (r^3)-10 q r (Sqrt[-p q r (p+q+r)])+(r^2) (Sqrt[-p q r (p+q+r)])+(q^2) (-(r^2)+5 (Sqrt[-p q r (p+q+r)]))))+(b^2) r ((p^3) ((q^4)-20 (q^3) r+20 (q^2) (r^2)+8 q (r^3)-(r^4))+q r (((q+r))^2) ((q^2) r+r (Sqrt[-p q r (p+q+r)])+q ((r^2)-5 (Sqrt[-p q r (p+q+r)])))+p (q+r) (-8 (q^4) r+2 q (r^4)+3 q (r^2) (Sqrt[-p q r (p+q+r)])+3 (r^3) (Sqrt[-p q r (p+q+r)])+(q^2) r (14 (r^2)-27 (Sqrt[-p q r (p+q+r)]))+(q^3) (4 (r^2)+5 (Sqrt[-p q r (p+q+r)])))+(p^2) ((q^5)-26 (q^4) r-(r^5)+5 (r^3) (Sqrt[-p q r (p+q+r)])+(q^2) r (39 (r^2)-29 (Sqrt[-p q r (p+q+r)]))+q (r^2) (8 (r^2)+(Sqrt[-p q r (p+q+r)]))+(q^3) (3 (r^2)+7 (Sqrt[-p q r (p+q+r)])))))),p q (r^2) (p+q+r) (-(c^2) p q (q+r) ((p^3) (-(q^4)+8 (q^3) r+20 (q^2) (r^2)-20 q (r^3)+(r^4))+p (q+r) (2 (q^4) r-8 q (r^4)+27 q (r^2) (Sqrt[-p q r (p+q+r)])-5 (r^3) (Sqrt[-p q r (p+q+r)])+(q^2) r (4 (r^2)-3 (Sqrt[-p q r (p+q+r)]))+(q^3) (14 (r^2)-3 (Sqrt[-p q r (p+q+r)])))+q r (((q+r))^2) ((q^2) r+5 r (Sqrt[-p q r (p+q+r)])+q ((r^2)-(Sqrt[-p q r (p+q+r)])))-(p^2) ((q^5)-8 (q^4) r+26 q (r^4)-(r^5)-29 q (r^2) (Sqrt[-p q r (p+q+r)])+7 (r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (-39 (r^2)+5 (Sqrt[-p q r (p+q+r)]))+(q^2) (-3 (r^3)+r (Sqrt[-p q r (p+q+r)]))))+r ((a^2) q (-(q^2) r (((q+r))^3) (Sqrt[-p q r (p+q+r)])+(p^4) r (-7 (q^3)+35 (q^2) r-21 q (r^2)+(r^3))+p q (((q+r))^2) (-2 (q^3) r+5 q (r^3)-13 q r (Sqrt[-p q r (p+q+r)])+10 (r^2) (Sqrt[-p q r (p+q+r)])+(q^2) (3 (r^2)+(Sqrt[-p q r (p+q+r)])))+(p^2) (q+r) (-11 (q^4) r-5 (r^3) (Sqrt[-p q r (p+q+r)])+(q^2) r (25 (r^2)-33 (Sqrt[-p q r (p+q+r)]))-10 q (r^2) ((r^2)-4 (Sqrt[-p q r (p+q+r)]))+2 (q^3) (12 (r^2)+(Sqrt[-p q r (p+q+r)])))+(p^3) (-16 (q^4) r-29 q (r^4)+(r^5)+35 q (r^2) (Sqrt[-p q r (p+q+r)])-7 (r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (49 (r^2)+(Sqrt[-p q r (p+q+r)]))-7 (q^2) (-5 (r^3)+3 r (Sqrt[-p q r (p+q+r)]))))+(b^2) p (q+r) (2 (p^3) q r (3 (q^2)-10 q r+3 (r^2))+(q^2) (((q+r))^2) ((q^2) r+5 r (Sqrt[-p q r (p+q+r)])+q ((r^2)-(Sqrt[-p q r (p+q+r)])))-2 p q (q+r) (-4 (q^3) r+5 (r^2) (Sqrt[-p q r (p+q+r)])+5 q r ((r^2)-2 (Sqrt[-p q r (p+q+r)]))+(q^2) ((r^2)+(Sqrt[-p q r (p+q+r)])))-(p^2) (-13 (q^4) r-(r^3) (Sqrt[-p q r (p+q+r)])-5 q (r^2) ((r^2)-3 (Sqrt[-p q r (p+q+r)]))+(q^3) (17 (r^2)+(Sqrt[-p q r (p+q+r)]))-5 (q^2) (-5 (r^3)+3 r (Sqrt[-p q r (p+q+r)]))))))}; (* 1st Focus QA-parabola *)
F2={(p^2) q r (q+r) (p+q+r) (-(a^2) q r (-(p^3) ((q^4)+2 (q^3) r-30 (q^2) (r^2)+2 q (r^3)+(r^4))+q r (((q+r))^2) ((q^2) r-3 r (Sqrt[-p q r (p+q+r)])+q ((r^2)+3 (Sqrt[-p q r (p+q+r)])))+p (q+r) (-2 (q^4) r-2 q (r^4)-17 q (r^2) (Sqrt[-p q r (p+q+r)])-(r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (12 (r^2)+(Sqrt[-p q r (p+q+r)]))+(q^2) (12 (r^3)+17 r (Sqrt[-p q r (p+q+r)])))-(p^2) ((q^5)+6 (q^4) r+6 q (r^4)+(r^5)+19 q (r^2) (Sqrt[-p q r (p+q+r)])+3 (r^3) (Sqrt[-p q r (p+q+r)])-(q^3) (35 (r^2)+3 (Sqrt[-p q r (p+q+r)]))-(q^2) (35 (r^3)+19 r (Sqrt[-p q r (p+q+r)]))))+p (((q+r))^3) ((b^2) r (-(p^2) q (q-3 r)+q (q+r) (Sqrt[-p q r (p+q+r)])+p (-(q^3)+(q^2) r+2 q (r^2)+3 q (Sqrt[-p q r (p+q+r)])-r (Sqrt[-p q r (p+q+r)])))+(c^2) q ((p^2) (3 q-r) r-r (q+r) (Sqrt[-p q r (p+q+r)])+p (2 (q^2) r+q ((r^2)+(Sqrt[-p q r (p+q+r)]))-r ((r^2)+3 (Sqrt[-p q r (p+q+r)])))))),-p (q^2) r (p+q+r) ((a^2) q r (-q (r^2) (((q+r))^3) (Sqrt[-p q r (p+q+r)])+(p^4) q ((q^3)-21 (q^2) r+35 q (r^2)-7 (r^3))+p r (((q+r))^2) (5 (q^3) r-2 q (r^3)-13 q r (Sqrt[-p q r (p+q+r)])+(r^2) (Sqrt[-p q r (p+q+r)])+(q^2) (3 (r^2)+10 (Sqrt[-p q r (p+q+r)])))+(p^3) ((q^5)-29 (q^4) r-16 q (r^4)-21 q (r^2) (Sqrt[-p q r (p+q+r)])+(r^3) (Sqrt[-p q r (p+q+r)])-7 (q^3) (-5 (r^2)+(Sqrt[-p q r (p+q+r)]))+7 (q^2) (7 (r^3)+5 r (Sqrt[-p q r (p+q+r)])))-(p^2) (q+r) (10 (q^4) r-2 (r^3) (Sqrt[-p q r (p+q+r)])+5 (q^3) (-5 (r^2)+(Sqrt[-p q r (p+q+r)]))-8 (q^2) (3 (r^3)+5 r (Sqrt[-p q r (p+q+r)]))+11 q ((r^4)+3 (r^2) (Sqrt[-p q r (p+q+r)]))))-p (q+r) (-(c^2) q (2 (p^3) q r (3 (q^2)-10 q r+3 (r^2))+(r^2) (((q+r))^2) ((q^2) r-r (Sqrt[-p q r (p+q+r)])+q ((r^2)+5 (Sqrt[-p q r (p+q+r)])))-2 p r (q+r) (5 (q^3) r+(r^2) (Sqrt[-p q r (p+q+r)])+(q^2) ((r^2)+5 (Sqrt[-p q r (p+q+r)]))-2 q (2 (r^3)+5 r (Sqrt[-p q r (p+q+r)])))+(p^2) (5 (q^4) r+13 q (r^4)+15 q (r^2) (Sqrt[-p q r (p+q+r)])-(r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (-25 (r^2)+(Sqrt[-p q r (p+q+r)]))-(q^2) (17 (r^3)+15 r (Sqrt[-p q r (p+q+r)]))))-(b^2) r ((p^3) (-(q^4)+20 (q^3) r-20 (q^2) (r^2)-8 q (r^3)+(r^4))-q r (((q+r))^2) ((q^2) r-r (Sqrt[-p q r (p+q+r)])+q ((r^2)+5 (Sqrt[-p q r (p+q+r)])))+p (q+r) (8 (q^4) r-2 q (r^4)+3 q (r^2) (Sqrt[-p q r (p+q+r)])+3 (r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (-4 (r^2)+5 (Sqrt[-p q r (p+q+r)]))-(q^2) (14 (r^3)+27 r (Sqrt[-p q r (p+q+r)])))+(p^2) (-(q^5)+26 (q^4) r+(r^5)+5 (r^3) (Sqrt[-p q r (p+q+r)])+q (r^2) (-8 (r^2)+(Sqrt[-p q r (p+q+r)]))+(q^3) (-3 (r^2)+7 (Sqrt[-p q r (p+q+r)]))-(q^2) (39 (r^3)+29 r (Sqrt[-p q r (p+q+r)])))))),-p q (r^2) (p+q+r) (-(c^2) p q (q+r) ((p^3) (-(q^4)+8 (q^3) r+20 (q^2) (r^2)-20 q (r^3)+(r^4))+q r (((q+r))^2) ((q^2) r-5 r (Sqrt[-p q r (p+q+r)])+q ((r^2)+(Sqrt[-p q r (p+q+r)])))+(p^2) (-(q^5)+8 (q^4) r-26 q (r^4)+(r^5)-29 q (r^2) (Sqrt[-p q r (p+q+r)])+7 (r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (39 (r^2)+5 (Sqrt[-p q r (p+q+r)]))+(q^2) (3 (r^3)+r (Sqrt[-p q r (p+q+r)])))+p (q+r) (2 (q^4) r-8 q (r^4)-27 q (r^2) (Sqrt[-p q r (p+q+r)])+5 (r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (14 (r^2)+3 (Sqrt[-p q r (p+q+r)]))+(q^2) (4 (r^3)+3 r (Sqrt[-p q r (p+q+r)]))))+r ((b^2) p (q+r) (2 (p^3) q r (3 (q^2)-10 q r+3 (r^2))+(q^2) (((q+r))^2) ((q^2) r-5 r (Sqrt[-p q r (p+q+r)])+q ((r^2)+(Sqrt[-p q r (p+q+r)])))+2 p q (q+r) (4 (q^3) r+5 (r^2) (Sqrt[-p q r (p+q+r)])+(q^2) (-(r^2)+(Sqrt[-p q r (p+q+r)]))-5 q ((r^3)+2 r (Sqrt[-p q r (p+q+r)])))+(p^2) (13 (q^4) r-(r^3) (Sqrt[-p q r (p+q+r)])+(q^3) (-17 (r^2)+(Sqrt[-p q r (p+q+r)]))-5 (q^2) (5 (r^3)+3 r (Sqrt[-p q r (p+q+r)]))+5 q ((r^4)+3 (r^2) (Sqrt[-p q r (p+q+r)]))))-(a^2) q (-(q^2) r (((q+r))^3) (Sqrt[-p q r (p+q+r)])-(p^4) r (-7 (q^3)+35 (q^2) r-21 q (r^2)+(r^3))+p q (((q+r))^2) (2 (q^3) r-5 q (r^3)-13 q r (Sqrt[-p q r (p+q+r)])+10 (r^2) (Sqrt[-p q r (p+q+r)])+(q^2) (-3 (r^2)+(Sqrt[-p q r (p+q+r)])))+(p^3) (16 (q^4) r+29 q (r^4)+35 q (r^2) (Sqrt[-p q r (p+q+r)])+(q^3) (-49 (r^2)+(Sqrt[-p q r (p+q+r)]))-(r^3) ((r^2)+7 (Sqrt[-p q r (p+q+r)]))-7 (q^2) (5 (r^3)+3 r (Sqrt[-p q r (p+q+r)])))+(p^2) (q+r) (11 (q^4) r-5 (r^3) (Sqrt[-p q r (p+q+r)])+2 (q^3) (-12 (r^2)+(Sqrt[-p q r (p+q+r)]))-(q^2) (25 (r^3)+33 r (Sqrt[-p q r (p+q+r)]))+10 q ((r^4)+4 (r^2) (Sqrt[-p q r (p+q+r)]))))))}; (* 2nd Focus QA-Parabolas *)

QG - Points in a QA-Quadrigon

QGP1={p,0,r};  (* Diagonal Crosspoint *)
QGP2={-p (q+r),-q (p+2 q+r),(-p-q) r};  (* Midpoint of the 3rd QA-Diagonal *)
QGP3={-p (p+q),q (-p+r),r (q+r)};  (* Midpoint of the 3rd QL-Diagonal *)
QGP4={-3 (p^3)-3 (p^2) q-9 (p^2) r-9 p q r-3 (q^2) r-9 p (r^2)-6 q (r^2)-3 (r^3),-3 (p^3)-9 (p^2) q-6 p (q^2)-9 (p^2) r-18 p q r-6 (q^2) r-9 p (r^2)-9 q (r^2)-3 (r^3),-3 (p^3)-6 (p^2) q-3 p (q^2)-9 (p^2) r-9 p q r-9 p (r^2)-3 q (r^2)-3 (r^3)}; (* 1st Quasi Centroid *)
QGP5={-((b^2)-(c^2)) p ((c^2) q+(b^2) r)-(a^4) ((p^2)+r (2 q+r)+p (q+2 r))+(a^2) ((b^2) ((p^2)+(r^2)+p (q+r))+(c^2) ((p^2)+2 p r+r (2 q+r))),(b^2) (-(b^2) ((p^2)+p q+r (q+r))+(a^2) ((p^2)+r (3 q+r)+p (q+2 r))+(c^2) ((p^2)+r (q+r)+p (3 q+2 r))),-(b^4) p r+(a^4) q r+(b^2) (c^2) ((p^2)+p r+r (q+r))-(c^4) ((p^2)+2 p (q+r)+r (q+r))+(a^2) ((b^2) (p-q) r+(c^2) ((p^2)+(r^2)+2 p (q+r)))};  (* 1st Quasi Circumcenter *)
QGP6={-(a^4) ((p^2)+2 p (q+r)+r (3 q+r))+2 (a^2) ((c^2) q r+(b^2) (p q-p r-q r))+((b^2)-(c^2)) ((b^2) ((p^2)+r (q+r))-(c^2) ((p^2)+2 p (q+r)+r (q+r))),((b^2) (-p+r)+(a^2) (p+r)-(c^2) (p+r)) ((b^2) (p-r)+(a^2) (p+2 q+r)-(c^2) (p+2 q+r)),(b^4) ((p^2)+p q+(r^2))-(c^4) ((p^2)+3 p q+2 p r+2 q r+(r^2))-2 (b^2) (c^2) (-q r+p (q+r))+(a^4) ((p^2)+r (2 q+r)+p (q+2 r))-2 (a^2) (-(c^2) p q+(b^2) ((p^2)+p (q+r)+r (q+r)))};  (* 1st Quasi Orthocenter *)
QGP7={-(a^4) q (p+r)-(a^2) ((c^2) (((p+r))^2)+(b^2) ((p^2)-p q+3 p r+2 q r+(r^2)))+((b^2)-(c^2)) (-(c^2) (p+r) (p+q+r)+(b^2) ((p^2)+p r+r (q+r))),(a^4) (p+r) (p+2 q+r)+(c^4) (p+r) (p+2 q+r)+(b^4) (q r+p (q+2 r))-(b^2) (c^2) ((p^2)+r (3 q+r)+p (q+2 r))-(a^2) (2 (c^2) (p+r) (p+2 q+r)+(b^2) ((p^2)+r (q+r)+p (3 q+2 r))),-(c^4) q (p+r)+(a^4) (p+r) (p+q+r)-(b^2) (c^2) ((p^2)+2 p q+3 p r-q r+(r^2))+(b^4) ((p^2)+(r^2)+p (q+r))-(a^2) ((c^2) (((p+r))^2)+(b^2) (2 (p^2)+r (q+2 r)+p (2 q+3 r)))};  (* 1st Quasi Nine-point Center *)
QGP8={-12 (p^6)-9 (p^5) q-63 (p^5) r-39 (p^4) q r-135 (p^4) (r^2)-66 (p^3) q (r^2)-150 (p^3) (r^3)-54 (p^2) q (r^3)-90 (p^2) (r^4)-21 p q (r^4)-27 p (r^5)-3 q (r^5)-3 (r^6),-3 (p^6)-6 (p^5) q-18 (p^5) r-30 (p^4) q r-45 (p^4) (r^2)-60 (p^3) q (r^2)-60 (p^3) (r^3)-60 (p^2) q (r^3)-45 (p^2) (r^4)-30 p q (r^4)-18 p (r^5)-6 q (r^5)-3 (r^6),-3 (p^6)-3 (p^5) q-27 (p^5) r-21 (p^4) q r-90 (p^4) (r^2)-54 (p^3) q (r^2)-150 (p^3) (r^3)-66 (p^2) q (r^3)-135 (p^2) (r^4)-39 p q (r^4)-63 p (r^5)-9 q (r^5)-12 (r^6)};  (* 2nd Quasi Centroid *)
QGP9={-(a^4) (p+r) (2 p+2 q+r)-((b^2)-(c^2)) p (-(c^2) (p+r)+(b^2) (p+q+2 r))+(a^2) ((c^2) (p+r) (3 p+2 q+r)+(b^2) (3 (p^2)+(r^2)+3 p (q+r))),(b^2) (-(b^2) ((p^2)+p q+r (q+r))+(a^2) ((p^2)+r (3 q+r)+p (q+2 r))+(c^2) ((p^2)+r (q+r)+p (3 q+2 r))),-(a^4) r (p+r)-(b^4) r (2 p+q+r)-(c^4) (p+r) (p+2 (q+r))+(b^2) (c^2) ((p^2)+3 p r+3 r (q+r))+(a^2) ((b^2) r (3 p+q+2 r)+(c^2) (p+r) (p+2 q+3 r))};  (* 2nd Quasi Circumcenter *)
QGP10={(a^4) (p (q+r)+r (3 q+r))+2 (a^2) ((b^2) ((p^2)+2 p r+q r)+(c^2) ((p^2)-q r+p (q+r)))-((b^2)-(c^2)) ((b^2) (2 (p^2)+p (q+r)+r (q+r))-(c^2) (2 (p^2)+3 p (q+r)+r (q+r))),(-(b^2) (-p+r)-(a^2) (p+r)+(c^2) (p+r)) ((b^2) (p-r)+(a^2) (p+2 q+r)-(c^2) (p+2 q+r)),(c^4) ((p^2)+q r+p (3 q+r))+2 (b^2) (c^2) ((r^2)+p (q+2 r))-(b^4) ((p^2)+p (q+r)+r (q+2 r))-(a^4) ((p^2)+r (3 q+2 r)+p (q+3 r))+2 (a^2) ((c^2) (p (-q+r)+r (q+r))+(b^2) ((p^2)+2 r (q+r)+p (q+2 r)))};  (* 2nd Quasi Orthocenter *)
QGP11={(a^4) (2 (p^2)-q r+p (q+2 r))-(a^2) ((c^2) (5 (p^2)+4 p q+6 p r+(r^2))+(b^2) (5 (p^2)+3 p q+7 p r+2 q r+(r^2)))+((b^2)-(c^2)) (-(c^2) (3 p+r) (p+q+r)+(b^2) (3 (p^2)+r (q+r)+p (2 q+3 r))),(a^4) (p+r) (p+2 q+r)+(c^4) (p+r) (p+2 q+r)+(b^4) (q r+p (q+2 r))-(b^2) (c^2) ((p^2)+r (3 q+r)+p (q+2 r))-(a^2) (2 (c^2) (p+r) (p+2 q+r)+(b^2) ((p^2)+r (q+r)+p (3 q+2 r))),(a^4) (p+q+r) (p+3 r)+(c^4) (-p q+2 p r+q r+2 (r^2))+(b^4) ((p^2)+p q+3 p r+2 q r+3 (r^2))-(b^2) (c^2) ((p^2)+2 p q+7 p r+3 q r+5 (r^2))-(a^2) ((c^2) ((p^2)+6 p r+4 q r+5 (r^2))+(b^2) (2 (p^2)+2 p q+7 p r+5 q r+6 (r^2)))};  (* 2nd Quasi Nine-point Center *)
QGP12={p (-q+r),-q (p+2 q+r),(p-q) r};  (* Inscribed Harmonic Conic Center *)
QGP13={-p (p+2 q-r),-2 q (p+2 q+r),(p-2 q-r) r};  (* Circumscribed Harmonic Conic Center *)
QGP14={p (q+r) (p q-p r-3 q r-(r^2)),-q (((p-r))^2) (p+2 q+r),(-p-q) r ((p^2)+3 p q+p r-q r)};  (* Center of the M3D Hyperbola *)
QGP15={p (q-r)-r (q+r),-(p+r) (p+2 q+r),-(p^2)+q r-p (q+r)};  (* Kirikami Center *)
QGP16={(a^2) (p+q+r) (-(c^2) (p^2) q-(c^2) p (q^2)+(b^2) (p^2) r+(a^2) p q r+(b^2) p q r-2 (c^2) p q r+(a^2) (q^2) r),-((c^2) p q+(b^2) p r+(a^2) q r) ((a^2) p q-(b^2) p q+(a^2) (q^2)-(b^2) (q^2)+(c^2) (q^2)-(b^2) p r-(b^2) q r+(c^2) q r),(c^2) (p+q+r) ((c^2) p (q^2)-2 (a^2) p q r+(b^2) p q r+(c^2) p q r-(a^2) (q^2) r+(b^2) p (r^2)-(a^2) q (r^2))};  (* Schmidt Point *)
QGP17={-p ((c^2) (p^2) q (q+r)+r ((b^2) (p^2) (q+r)-(a^2) q ((p^2)+q r))),p q r ((a^2) q (p-r)+(c^2) q (-p+r)-(b^2) (p q+2 p r+q r)),(-p-q) ((b^2) p+(a^2) q) (r^3)+(c^2) p q r (p q+(r^2))};  (* Perpendicular projection QG-P1 on QG-L1 = CSC(QGP18) *)QGP18={-(a^2) q r ((p+q) ((b^2) p+(a^2) q) (r^2)-(c^2) p q (p q+(r^2))),-p r ((b^4) p (p+q) r (q+r)-((a^2)-(c^2)) (q^2) ((a^2) (p+q) r-(c^2) p (q+r))+(b^2) q (-(a^2) (p+q) (p-q-r) r+(c^2) p (p+q-r) (q+r))),-(c^2) p q ((c^2) (p^2) q (q+r)+r ((b^2) (p^2) (q+r)-(a^2) q ((p^2)+q r)))};  (* 1st Quasi Isogonal Conjugate QG-L1 *)QGP19={(a^2) q r ((p+q) ((b^2) p+(a^2) q) (r^2)+(c^2) p q (p q-(r^2))),-p r ((b^4) p (p+q) r (q+r)-((a^2)-(c^2)) (q^2) ((a^2) (p+q) r-(c^2) p (q+r))+(b^2) q (-(a^2) (p+q) (p-q-r) r+(c^2) p (p+q-r) (q+r))),(c^2) p q ((c^2) (p^2) q (q+r)+r ((b^2) (p^2) (q+r)+(a^2) q (-(p^2)+q r)))};  (* 2nd Quasi Isogonal Crosspoint *)
QGP98={(p+r) ((b^2) p-(c^2) p-(a^2) r),b q (b p+(Sqrt[(c^2) p (p+r)+r (-(b^2) p+(a^2) (p+r))])),(p+r) ((c^2) p+(a^2) r+b (Sqrt[(c^2) p (p+r)+r (-(b^2) p+(a^2) (p+r))]))};  (* Center Inscribed QG-Rhombus *)

QG2P1a={(a^4) (p^2) (q^2)-2 (a^2) (b^2) (p^2) (q^2)+(b^4) (p^2) (q^2)-2 (b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+2 (a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r-2 (a^2) (c^2) (p^2) q r+2 (a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+2 (a^2) (c^2) p (q^2) r+(a^4) (p^2) (r^2)+(b^4) (p^2) (r^2)-2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)+(c^4) (p^2) (r^2)+2 (a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)-2 (a^2) (c^2) p q (r^2)+2 (a^4) (q^2) (r^2),-(a^2) (c^2) (p^2) (q^2)-(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+(a^4) p (q^3)-2 (a^2) (b^2) p (q^3)+(b^4) p (q^3)-2 (a^2) (c^2) p (q^3)-2 (b^2) (c^2) p (q^3)+(c^4) p (q^3)+(a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+(b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r-2 (b^2) (c^2) p (q^2) r+(c^4) p (q^2) r+(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)-(b^2) (c^2) (p^2) (r^2)+(a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-2 (a^2) (c^2) p q (r^2)-2 (b^2) (c^2) p q (r^2)+(c^4) p q (r^2)+(a^4) (q^2) (r^2)+(a^2) (b^2) (q^2) (r^2)-(a^2) (c^2) (q^2) (r^2)+(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2) (p^2) (q^2)-(b^2) (p^2) (q^2)+(a^2) p (q^3)-(b^2) p (q^3)+(c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+2 (a^2) p (q^2) r+2 (a^2) (q^3) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2)),-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((c^2) (p^2) (q^2)-(a^2) (p^2) q r+(b^2) (p^2) q r+(c^2) (p^2) q r-(a^2) (p^2) (r^2)+(c^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))+((a^2)-(b^2)+(c^2)) ((c^2) (p^2) (q^2)+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2))}; (* 1st Inscribed Square Center *)
QG2P1b={(a^4) (p^2) (q^2)-2 (a^2) (b^2) (p^2) (q^2)+(b^4) (p^2) (q^2)-2 (b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+2 (a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r-2 (a^2) (c^2) (p^2) q r+2 (a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+2 (a^2) (c^2) p (q^2) r+(a^4) (p^2) (r^2)+(b^4) (p^2) (r^2)-2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)+(c^4) (p^2) (r^2)+2 (a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)-2 (a^2) (c^2) p q (r^2)+2 (a^4) (q^2) (r^2),-(a^2) (c^2) (p^2) (q^2)-(b^2) (c^2) (p^2) (q^2)+(c^4) (p^2) (q^2)+(a^4) p (q^3)-2 (a^2) (b^2) p (q^3)+(b^4) p (q^3)-2 (a^2) (c^2) p (q^3)-2 (b^2) (c^2) p (q^3)+(c^4) p (q^3)+(a^4) p (q^2) r-2 (a^2) (b^2) p (q^2) r+(b^4) p (q^2) r-2 (a^2) (c^2) p (q^2) r-2 (b^2) (c^2) p (q^2) r+(c^4) p (q^2) r+(a^2) (b^2) (p^2) (r^2)+(b^4) (p^2) (r^2)-(b^2) (c^2) (p^2) (r^2)+(a^4) p q (r^2)+2 (a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-2 (a^2) (c^2) p q (r^2)-2 (b^2) (c^2) p q (r^2)+(c^4) p q (r^2)+(a^4) (q^2) (r^2)+(a^2) (b^2) (q^2) (r^2)-(a^2) (c^2) (q^2) (r^2)-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2) (p^2) (q^2)-(b^2) (p^2) (q^2)+(a^2) p (q^3)-(b^2) p (q^3)+(c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+2 (a^2) p (q^2) r+2 (a^2) (q^3) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2)),(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((c^2) (p^2) (q^2)-(a^2) (p^2) q r+(b^2) (p^2) q r+(c^2) (p^2) q r-(a^2) (p^2) (r^2)+(c^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))+((a^2)-(b^2)+(c^2)) ((c^2) (p^2) (q^2)+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)+(a^2) (q^2) (r^2))}; (* 2nd Inscribed Square Center *)
QG2P2a={p,q,0};  (* 1st Endpoint QA-Diagonal *)
QG2P2b={0,q,r}; (* 2nd Endpoint QA-Diagonal *)
QG2P3a={p,0,-r};  (* 1st Endpoint QA-Diagonal *)
QG2P3b={p,2 q,r}; (* 2nd Endpoint QA-Diagonal *)
QG2P4a= {-2 ((a^2)-(b^2)+(c^2)) (-(c^2) (p^2) (q^2)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))+(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (2 (c^2) (p^3) q+2 (c^2) (p^2) (q^2)-(a^2) (p^3) r+(b^2) (p^3) r+(c^2) (p^3) r-2 (a^2) (p^2) q r+2 (b^2) (p^2) q r-2 (b^2) p q (r^2)+2 (c^2) p q (r^2)-2 (a^2) (q^2) (r^2)-(a^2) p (r^3)-(b^2) p (r^3)+(c^2) p (r^3)-2 (a^2) q (r^3)),-2 (a^2) (c^2) (p^2) (q^2)+2 (b^2) (c^2) (p^2) (q^2)+2 (c^4) (p^2) (q^2)+(a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r+(b^4) (p^2) q r-2 (a^2) (c^2) (p^2) q r+6 (b^2) (c^2) (p^2) q r+(c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r+4 (b^2) (c^2) p (q^2) r-4 (c^4) p (q^2) r-2 (a^4) (q^3) r+4 (a^2) (b^2) (q^3) r-2 (b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+4 (b^2) (c^2) (q^3) r-2 (c^4) (q^3) r-2 (a^2) (b^2) (p^2) (r^2)+2 (b^4) (p^2) (r^2)+2 (b^2) (c^2) (p^2) (r^2)-2 (a^4) p q (r^2)+2 (b^4) p q (r^2)+4 (a^2) (c^2) p q (r^2)-2 (c^4) p q (r^2)-4 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-(a^4) q (r^3)+2 (a^2) (b^2) q (r^3)-(b^4) q (r^3)+2 (a^2) (c^2) q (r^3)+2 (b^2) (c^2) q (r^3)-(c^4) q (r^3)-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-2 (c^2) (p^2) (q^2)-4 (c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+4 (a^2) p (q^2) r-4 (b^2) p (q^2) r-4 (c^2) p (q^2) r+2 (a^2) (q^3) r-2 (b^2) (q^3) r+2 (c^2) (q^3) r+2 (a^2) p q (r^2)-4 (b^2) p q (r^2)-2 (c^2) p q (r^2)-2 (b^2) (q^2) (r^2)+2 (c^2) (q^2) (r^2)-2 (b^2) p (r^3)-(a^2) q (r^3)-(b^2) q (r^3)+(c^2) q (r^3)),-4 (c^4) (p^2) (q^2)+4 (a^2) (c^2) (p^2) q r-4 (b^2) (c^2) (p^2) q r-4 (c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r-4 (b^2) (c^2) p (q^2) r+4 (c^4) p (q^2) r-(a^4) (p^2) (r^2)+2 (a^2) (b^2) (p^2) (r^2)-(b^4) (p^2) (r^2)+2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)-(c^4) (p^2) (r^2)-2 (a^4) p q (r^2)+4 (a^2) (b^2) p q (r^2)-2 (b^4) p q (r^2)+2 (c^4) p q (r^2)-2 (a^4) (q^2) (r^2)+4 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-2 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)-2 (b^4) q (r^3)+4 (a^2) (c^2) q (r^3)+4 (b^2) (c^2) q (r^3)-2 (c^4) q (r^3)-(a^4) (r^4)+2 (a^2) (b^2) (r^4)-(b^4) (r^4)+2 (a^2) (c^2) (r^4)+2 (b^2) (c^2) (r^4)-(c^4) (r^4)}; (* 1st Intersectionpoint QA-DT-ThalesCircle & QL-DT-ThalesCircle *)
QG2P4b={-2 ((a^2)-(b^2)+(c^2)) (-(c^2) (p^2) (q^2)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+(a^2) p (q^2) r-(b^2) p (q^2) r+(c^2) p (q^2) r-(b^2) (p^2) (r^2)-(a^2) p q (r^2)-(b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2))-(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (2 (c^2) (p^3) q+2 (c^2) (p^2) (q^2)-(a^2) (p^3) r+(b^2) (p^3) r+(c^2) (p^3) r-2 (a^2) (p^2) q r+2 (b^2) (p^2) q r-2 (b^2) p q (r^2)+2 (c^2) p q (r^2)-2 (a^2) (q^2) (r^2)-(a^2) p (r^3)-(b^2) p (r^3)+(c^2) p (r^3)-2 (a^2) q (r^3)),-2 (a^2) (c^2) (p^2) (q^2)+2 (b^2) (c^2) (p^2) (q^2)+2 (c^4) (p^2) (q^2)+(a^4) (p^2) q r-2 (a^2) (b^2) (p^2) q r+(b^4) (p^2) q r-2 (a^2) (c^2) (p^2) q r+6 (b^2) (c^2) (p^2) q r+(c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r+4 (b^2) (c^2) p (q^2) r-4 (c^4) p (q^2) r-2 (a^4) (q^3) r+4 (a^2) (b^2) (q^3) r-2 (b^4) (q^3) r+4 (a^2) (c^2) (q^3) r+4 (b^2) (c^2) (q^3) r-2 (c^4) (q^3) r-2 (a^2) (b^2) (p^2) (r^2)+2 (b^4) (p^2) (r^2)+2 (b^2) (c^2) (p^2) (r^2)-2 (a^4) p q (r^2)+2 (b^4) p q (r^2)+4 (a^2) (c^2) p q (r^2)-2 (c^4) p q (r^2)-4 (a^4) (q^2) (r^2)+6 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+6 (a^2) (c^2) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-(a^4) q (r^3)+2 (a^2) (b^2) q (r^3)-(b^4) q (r^3)+2 (a^2) (c^2) q (r^3)+2 (b^2) (c^2) q (r^3)-(c^4) q (r^3)+(Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-2 (c^2) (p^2) (q^2)-4 (c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+4 (a^2) p (q^2) r-4 (b^2) p (q^2) r-4 (c^2) p (q^2) r+2 (a^2) (q^3) r-2 (b^2) (q^3) r+2 (c^2) (q^3) r+2 (a^2) p q (r^2)-4 (b^2) p q (r^2)-2 (c^2) p q (r^2)-2 (b^2) (q^2) (r^2)+2 (c^2) (q^2) (r^2)-2 (b^2) p (r^3)-(a^2) q (r^3)-(b^2) q (r^3)+(c^2) q (r^3)),-4 (c^4) (p^2) (q^2)+4 (a^2) (c^2) (p^2) q r-4 (b^2) (c^2) (p^2) q r-4 (c^4) (p^2) q r+4 (a^2) (c^2) p (q^2) r-4 (b^2) (c^2) p (q^2) r+4 (c^4) p (q^2) r-(a^4) (p^2) (r^2)+2 (a^2) (b^2) (p^2) (r^2)-(b^4) (p^2) (r^2)+2 (a^2) (c^2) (p^2) (r^2)-2 (b^2) (c^2) (p^2) (r^2)-(c^4) (p^2) (r^2)-2 (a^4) p q (r^2)+4 (a^2) (b^2) p q (r^2)-2 (b^4) p q (r^2)+2 (c^4) p q (r^2)-2 (a^4) (q^2) (r^2)+4 (a^2) (b^2) (q^2) (r^2)-2 (b^4) (q^2) (r^2)+4 (b^2) (c^2) (q^2) (r^2)-2 (c^4) (q^2) (r^2)-2 (a^4) q (r^3)+4 (a^2) (b^2) q (r^3)-2 (b^4) q (r^3)+4 (a^2) (c^2) q (r^3)+4 (b^2) (c^2) q (r^3)-2 (c^4) q (r^3)-(a^4) (r^4)+2 (a^2) (b^2) (r^4)-(b^4) (r^4)+2 (a^2) (c^2) (r^4)+2 (b^2) (c^2) (r^4)-(c^4) (r^4)}; (* 2nd Intersectionpoint QA-DT-ThalesCircle & QL-DT-ThalesCircle *)
QG2P5a={(-(a^2)+(c^2)) q-(b^2) (p+q),0,(a^2) q-(c^2) q-(b^2) (q+r)};  (* intersection point QG-Ci2 ^ 1st QG-diagonal *)
QG2P5b={-(c^2) (p^3)+(a^2) p (r^2),p r ((b^2) (p-r)-(a^2) (p+r)+(c^2) (p+r)),-(c^2) (p^2) r+(a^2) (r^3)};  (* intersection point QG-Ci2 ^ 2nd QG-diagonal *)

QL - Points in a QA-Quadrigon

QLP1g={(a^2) (p+q) (p+q+r),(a^2) q (p+q)-(-(c^2) q+(b^2) (p+q)) (q+r),(c^2) (q+r) (p+q+r)};
QLP2g={-(a^4) (p ((q^2)+(r^2))+q ((q^2)+q r+2 (r^2)))+((b^2)-(c^2)) (q+r) ((b^2) (2 p+q) (p+q+r)-(c^2) (2 (p^2)+q (q+r)+p (2 q+r)))-(a^2) ((c^2) (2 (p^2) r+q r (q+r)+p q (q+3 r))+(b^2) (2 (p^2) q-q r (q+r)+p (2 (q^2)+q r+(r^2)))),(c^4) ((p^2) (2 q+r)+q (2 (q^2)+3 q r+(r^2))+p (3 (q^2)+3 q r+(r^2)))-(b^2) (c^2) ((p^2) (q-r)+2 (q^2) (q+r)+p (4 (q^2)+3 q r+(r^2)))+(a^4) ((p^2) (q+r)+p (3 (q^2)+3 q r+(r^2))+q (2 (q^2)+3 q r+2 (r^2)))-(b^4) (q r (q+r)+(p^2) (q+2 r)+p ((q^2)+4 q r+2 (r^2)))-(a^2) ((b^2) ((p^2) r+p (2 (q^2)+3 q r-(r^2))+q (2 (q^2)+4 q r+(r^2)))+(c^2) ((p^2) (3 q+2 r)+2 p (3 (q^2)+3 q r+(r^2))+q (4 (q^2)+6 q r+3 (r^2)))),(b^4) (p+q) (p+q+r) (q+2 r)+(b^2) (c^2) ((p^2) (q-r)+p q (q-r)-2 q r (q+r))-(c^4) (p (q^2)+(q^2) (q+r)+(p^2) (2 q+r))+(a^4) ((p^2) (q+r)+q ((q^2)+2 q r+2 (r^2))+p (2 (q^2)+3 q r+2 (r^2)))-(a^2) ((c^2) ((p^2) q+(q^2) r+p ((q^2)+3 q r+2 (r^2)))+(b^2) (4 p (((q+r))^2)+(p^2) (2 q+3 r)+q (2 (q^2)+5 q r+4 (r^2))))};
QLP3g={(a^4) (q^2) (p+q)-((b^2)-(c^2)) p (q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))+(a^2) (-(b^2) q (p+q) (-p+q+r)+(c^2) ((p^2) r+p ((q^2)+3 q r+(r^2))+q (2 (q^2)+3 q r+(r^2)))),-(a^4) q ((p^2)+3 p q+2 (q^2))-(-(c^2) q+(b^2) (p+q)) (q+r) ((b^2) q-(c^2) (2 q+r))+(a^2) ((c^2) q ((p^2)-2 (q^2)+(r^2))+(b^2) (p+q) (p (q+r)+q (3 q+2 r))),-(a^4) (p+q) r (p+2 q+r)-(-(c^2) q+(b^2) (p+q)) (q+r) ((c^2) q+(b^2) r)+(a^2) ((b^2) (p+q) r (p+3 q+2 r)+(c^2) ((p^2) (q+r)+(q^2) (2 q+r)+p (3 (q^2)+3 q r+(r^2))))};
QLP4g={(a^2) ((c^2) p (2 (q^2)+2 q r+(r^2)+p (2 q+r))+(b^2) (p+q) ((((q+r))^2)+p (q+2 r))-(a^2) ((p^2) (q+r)+q ((q^2)+q r+(r^2))+p (2 (q^2)+2 q r+(r^2)))),-(a^4) q (p+q) r-(-(c^2) q+(b^2) (p+q)) (q+r) (-(c^2) p+(b^2) (p+q+r))+(a^2) (p+q) (2 (c^2) q (q+r)+(b^2) (p q+(((q+r))^2))),(c^2) (-(c^2) (q+r) ((p^2)+p (q+r)+q (q+r))+(b^2) (q+r) ((p^2)+2 p (q+r)+q (q+r))+(a^2) r ((p^2)+2 q (q+r)+p (2 q+r)))};
QLP5g={(q+r) ((a^4) (p+q) (p+r)+((b^2)-(c^2)) p ((b^2) (p+q)-(c^2) (p+2 q+r))-(a^2) ((b^2) (p+q) (2 p+r)+(c^2) (2 (p^2)+q (2 q+r)+p (3 q+2 r)))),(p+2 q+r) ((a^4) q (p+q)+((b^2)-(c^2)) (-(c^2) q+(b^2) (p+q)) (q+r)-(a^2) ((c^2) q (p+r)+(b^2) (p+q) (2 q+r))),(p+q) ((a^4) r (p+2 q+r)+((b^2)-(c^2)) (q+r) ((b^2) r-(c^2) (p+r))-(a^2) ((b^2) r (p+3 q+2 r)+(c^2) (2 (q^2)+3 q r+2 (r^2)+p (q+2 r))))};
QLP6g={-((b^2)-(c^2)) p (q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))-(a^4) (3 (p^2) (q+r)+q (2 (q^2)+3 q r+3 (r^2))+p (5 (q^2)+6 q r+3 (r^2)))+(a^2) ((b^2) (p+q) (2 p+q+r) (2 q+3 r)+(c^2) ((p^2) (6 q+4 r)+q (2 (q^2)+3 q r+(r^2))+p (7 (q^2)+9 q r+4 (r^2)))),-(a^4) q (p+q) (p+2 q+3 r)-(-(c^2) q+(b^2) (p+q)) (q+r) (-(c^2) (3 p+2 q+r)+(b^2) (3 p+4 q+3 r))+(a^2) ((c^2) q ((p^2)+4 (q^2)+6 q r+(r^2)+6 p (q+r))+(b^2) ((p^2) (4 q+r)+q (6 (q^2)+8 q r+3 (r^2))+p (10 (q^2)+9 q r+3 (r^2)))),-(a^4) (p+q) r (p+2 q+r)-(q+r) ((b^4) (p+q) r-(b^2) (c^2) (3 p+2 q) (p+q+2 r)+(c^4) (3 (p^2)+3 p (q+r)+q (2 q+3 r)))+(a^2) ((b^2) (p+q) r (p+3 q+2 r)+(c^2) ((p^2) (q+4 r)+p (3 (q^2)+9 q r+4 (r^2))+q (2 (q^2)+7 q r+6 (r^2))))};
QLP7g={-((b^2)-(c^2)) (q+r) (3 p+2 q+r)+(a^2) (2 (p^2)+2 (q^2)+q r+(r^2)+p (5 q+r)),(p+2 q+r) ((a^2) (p+2 q-r)+(b^2) (p+r)+(c^2) (-p+2 q+r)),(a^2) (p+q) (p+2 q+3 r)-(b^2) (p+q) (p+2 q+3 r)+(c^2) ((p^2)+2 (q^2)+5 q r+2 (r^2)+p (q+r))};
QLP8g={p (3 (p^2)-(r^2)+2 p (2 q+r)),2 q ((p^2)-(r^2)),r ((p^2)-2 p r-r (4 q+3 r))};
QLP9g={-(a^4) (p+2 q) ((p^2)-(r^2))-((b^2)-(c^2)) p ((c^2) (-(p^2)+(r^2))+(b^2) ((p^2)-(r^2)+2 p (q+r)))+2 (a^2) ((c^2) (p+q) ((p^2)-(r^2))+(b^2) ((p^3)+p (r^2)+q (r^2)+(p^2) (2 q+r))),-2 (b^2) (-(c^2) p ((r^2)+p (2 q+r))+r ((b^2) p (-p+r)+(a^2) ((p^2)+p r+2 q r))),(a^4) r (-(p^2)+(r^2))+(c^4) (2 q+r) (-(p^2)+(r^2))+(b^4) r (-(p^2)+2 p r+r (2 q+r))-2 (b^2) (c^2) (p (r^2)+(p^2) (q+r)+(r^2) (2 q+r))-2 (a^2) ((c^2) (q+r) (-(p^2)+(r^2))+(b^2) r (-(p^2)+p r+r (q+r)))};
QLP10g={-(a^4) ((p^3)+2 (p^2) r+p (r^2)+4 q (r^2))-((b^2)-(c^2)) p ((b^2) (((p-r))^2)-(c^2) ((p^2)+4 p q+2 p r+(r^2)))+2 (a^2) ((b^2) ((p^3)-3 p (r^2)-2 q (r^2))+(c^2) ((p^3)+p (r^2)+2 q (r^2)+2 (p^2) (q+r))),-2 ((b^2) (-p+r)+(a^2) (p+r)-(c^2) (p+r)) ((a^2) q (p-r)+(c^2) q (-p+r)-(b^2) (p q+2 p r+q r)),(b^4) (((p-r))^2) r+(c^4) (2 p (r^2)+(r^3)+(p^2) (4 q+r))+(a^4) r ((p^2)+2 p r+r (4 q+r))+2 (b^2) (c^2) (-(r^3)+(p^2) (2 q+3 r))-2 (a^2) ((b^2) r ((p^2)+r (2 q+r))+(c^2) (2 p (r^2)+(p^2) (2 q+r)+(r^2) (2 q+r)))};
QLP11g={(a^4) ((p^3)+q (r^2)+(p^2) (q+r))+((b^2)-(c^2)) (p^2) ((b^2) (p+q)-(c^2) (p+2 q+r))-(a^2) ((b^2) (2 (p^3)-2 p (r^2)-q (r^2)+(p^2) (2 q+r))+(c^2) (2 (p^3)+q (r^2)+(p^2) (3 q+2 r))),(b^2) (c^2) r ((p^2)+p r+2 q r)+(a^4) q ((p^2)-(r^2))+(c^4) q ((p^2)-(r^2))+(b^4) (p-r) (q r+p (q+r))-(a^2) (2 (c^2) q ((p^2)-(r^2))+(b^2) p (2 p q+p r+(r^2))),-(b^4) (r^2) (q+r)-(a^4) (r^2) (p+2 q+r)-(c^4) ((p^2) q+p (r^2)+(r^2) (q+r))-(b^2) (c^2) (-p (r^2)-2 (r^2) (q+r)+(p^2) (q+2 r))+(a^2) ((b^2) (r^2) (p+3 q+2 r)+(c^2) ((p^2) q+2 p (r^2)+3 q (r^2)+2 (r^3)))};
QLP12g={(q+r) (3 (p^2)+4 p q+(q^2)+2 p r+q r),(p+2 q+r) (2 p q+2 (q^2)+p r+2 q r),(p+q) (p q+(q^2)+2 p r+4 q r+3 (r^2))};
QLP13g={-p (3 p+2 q+r),-2 q (p+2 q+r),-r (p+2 q+3 r)};
QLP14g={3 (p^5) (q+r)-2 q (r^2) (((q+r))^2) (2 q+r)+5 (p^4) (2 (q^2)+3 q r+(r^2))-9 (p^2) (r^2) (2 (q^2)+3 q r+(r^2))+(p^3) (7 (q^3)+14 (q^2) r+4 q (r^2)-3 (r^3))-p (r^2) (17 (q^3)+34 (q^2) r+21 q (r^2)+4 (r^3)),2 ((p^2)-(r^2)) ((p^3) (2 q+r)+(p^2) (9 (q^2)+9 q r+2 (r^2))+p (14 (q^3)+21 (q^2) r+9 q (r^2)+(r^3))+q (7 (q^3)+14 (q^2) r+9 q (r^2)+2 (r^3))),2 (p^5) (q+2 r)-q (r^3) (7 (q^2)+10 q r+3 (r^2))-p (r^3) (14 (q^2)+15 q r+3 (r^2))+(p^4) (8 (q^2)+21 q r+9 (r^2))+(p^3) (10 (q^3)+34 (q^2) r+27 q (r^2)+3 (r^3))+(p^2) (4 (q^4)+17 (q^3) r+18 (q^2) (r^2)-4 q (r^3)-5 (r^4))};
QLP15g={6 (p^5) (q+r)+20 (p^3) q (((q+r))^2)-q (r^2) (((q+r))^2) (2 q+r)+10 (p^4) (2 (q^2)+3 q r+(r^2))-2 p (r^2) (5 (q^3)+10 (q^2) r+6 q (r^2)+(r^3))+3 (p^2) (2 (q^4)+5 (q^3) r-5 q (r^3)-2 (r^4)),((p^2)-(r^2)) ((p^3) (2 q+r)+2 (p^2) (6 (q^2)+6 q r+(r^2))+2 q (5 (q^3)+10 (q^2) r+6 q (r^2)+(r^3))+p (20 (q^3)+30 (q^2) r+12 q (r^2)+(r^3))),(p^5) (q+2 r)+5 (p^3) q ((q^2)+4 q r+3 (r^2))+2 (p^4) (2 (q^2)+6 q r+3 (r^2))-2 q (r^2) (3 (q^3)+10 (q^2) r+10 q (r^2)+3 (r^3))-p (r^2) (15 (q^3)+40 (q^2) r+30 q (r^2)+6 (r^3))+2 (p^2) ((q^4)+5 (q^3) r-10 q (r^3)-5 (r^4))};
QLP16g={-2 (a^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (p+q) (p+q+r) (p+2 q+r) ((p^2)-(r^2))-((a^2) (p+q) (p+2 q+r)-(q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))) (-(a^4) ((p^3)+2 (p^2) r+p (r^2)+4 q (r^2))-((b^2)-(c^2)) p ((b^2) (((p-r))^2)-(c^2) ((p^2)+4 p q+2 p r+(r^2)))+2 (a^2) ((b^2) ((p^3)-3 p (r^2)-2 q (r^2))+(c^2) ((p^3)+p (r^2)+2 q (r^2)+2 (p^2) (q+r)))),-2 ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (p+2 q+r) ((p^2)-(r^2)) ((a^2) q (p+q)-(-(c^2) q+(b^2) (p+q)) (q+r))+2 ((b^2) (-p+r)+(a^2) (p+r)-(c^2) (p+r)) ((a^2) q (p-r)+(c^2) q (-p+r)-(b^2) (p q+2 p r+q r)) ((a^2) (p+q) (p+2 q+r)-(q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))),-2 (c^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (q+r) (p+q+r) (p+2 q+r) ((p^2)-(r^2))-((a^2) (p+q) (p+2 q+r)-(q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))) ((b^4) (((p-r))^2) r+(c^4) (2 p (r^2)+(r^3)+(p^2) (4 q+r))+(a^4) r ((p^2)+2 p r+r (4 q+r))+2 (b^2) (c^2) (-(r^3)+(p^2) (2 q+3 r))-2 (a^2) ((b^2) r ((p^2)+r (2 q+r))+(c^2) (2 p (r^2)+(p^2) (2 q+r)+(r^2) (2 q+r))))};
QLP17g={-(a^2) (p+q) ((p^2)-(r^2)) (p+2 (q+r))-p (q+r) ((b^2) (p+q) (p+2 q+3 r)+(c^2) (-(p^2)+(r^2))),-2 (b^2) (p+q) (q+r) ((p^2)+3 p q+2 (q^2)+2 p r+3 q r+(r^2)),(c^2) (q+r) (2 p+2 q+r) ((p^2)-(r^2))-(p+q) r ((b^2) (q+r) (3 p+2 q+r)+(a^2) ((p^2)-(r^2)))};
QLP18g={-(q+r) (2 p (r^2) (((2 q+r))^2)+2 (p^3) ((q^2)+q r+(r^2))+q (r^2) (2 (q^2)+3 q r+(r^2))+(p^2) (2 (q^3)+3 (q^2) r+9 q (r^2)+4 (r^3))),((p^2)-(r^2)) ((p^3) (2 q+r)+2 (p^2) (((2 q+r))^2)+2 q (3 (q^3)+6 (q^2) r+4 q (r^2)+(r^3))+p (12 (q^3)+18 (q^2) r+8 q (r^2)+(r^3))),(p+q) (2 (q^2) (r^2) (q+r)+(p^4) (q+2 r)+p q (r^2) (3 q+2 r)+(p^3) (3 (q^2)+8 q r+4 (r^2))+(p^2) (2 (q^3)+8 (q^2) r+9 q (r^2)+2 (r^3)))};
QLP19g={(3 p+2 q+r) (-((b^2)-(c^2)) (q+r)+(a^2) (2 p+3 q+r)),(a^2) ((p^2)+8 p q+8 (q^2)-(r^2))+(c^2) (-(p^2)+8 (q^2)+8 q r+(r^2))+(b^2) ((p^2)-4 (q^2)-2 q r+(r^2)-2 p (q+r)),(p+2 q+3 r) ((a^2) (p+q)-(b^2) (p+q)+(c^2) (p+3 q+2 r))};
QLP20g={-(q+r) ((a^4) ((p^2)+2 p q+q (q-r))+((b^2)-(c^2)) (-(c^2) ((p^2)+q (q+r))+(b^2) ((p^2)+2 p (q+r)+q (q+r)))-2 (a^2) ((c^2) ((p^2)+p q-(q^2))+(b^2) ((p^2)+(q^2)+p (2 q+r)))),(((b^2)-(c^2)) p+(a^2) (p+2 q)) (p+2 q+r) ((-(a^2)+(b^2)) r+(c^2) (2 q+r)),-(p+q) ((a^4) (p q+(q^2)+(r^2))-2 (a^2) ((c^2) (-(q^2)+q r+(r^2))+(b^2) ((q^2)+q r+(r^2)+p (q+r)))+((b^2)-(c^2)) ((c^2) (p q-(((q+r))^2))+(b^2) ((((q+r))^2)+p (q+2 r))))};QLP21g={(q+r) ((a^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (((p+q))^2) (((p+q+r))^2)-((a^2) (p+q) (p+2 q+r)-(q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))) ((a^4) ((p^2)+2 p q+q (q-r))+((b^2)-(c^2)) (-(c^2) ((p^2)+q (q+r))+(b^2) ((p^2)+2 p (q+r)+q (q+r)))-2 (a^2) ((c^2) ((p^2)+p q-(q^2))+(b^2) ((p^2)+(q^2)+p (2 q+r))))),(1/2) (2 ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (p+q) (q+r) (p+q+r) ((a^2) q (p+q)-(-(c^2) q+(b^2) (p+q)) (q+r))+2 (((b^2)-(c^2)) p+(a^2) (p+2 q)) (p+2 q+r) ((-(a^2)+(b^2)) r+(c^2) (2 q+r)) ((a^2) (p+q) (p+2 q+r)-(q+r) ((b^2) (p+q)-(c^2) (p+2 q+r)))),(p+q) ((c^2) ((a^4)+((((b^2)-(c^2)))^2)-2 (a^2) ((b^2)+(c^2))) (((q+r))^2) (((p+q+r))^2)-((a^2) (p+q) (p+2 q+r)-(q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))) ((a^4) (p q+(q^2)+(r^2))-2 (a^2) ((c^2) (-(q^2)+q r+(r^2))+(b^2) ((q^2)+q r+(r^2)+p (q+r)))+((b^2)-(c^2)) ((c^2) (p q-(((q+r))^2))+(b^2) ((((q+r))^2)+p (q+2 r)))))};
QLP22g={-(q+r) ((a^4) (2 (p^2)+(q^2)+p (3 q+r))+((b^2)-(c^2)) ((b^2) (2 p+q) (p+q+r)-(c^2) (2 (p^2)+q (q+r)+p (2 q+r)))-(a^2) ((c^2) (4 (p^2)+5 p q+2 p r+q r)+(b^2) (4 (p^2)+3 p (2 q+r)+q (2 q+r)))),-(a^4) ((p^2) (q+r)+p (3 (q^2)+5 q r+(r^2))+q (2 (q^2)+5 q r+2 (r^2)))-((b^2)-(c^2)) (p+2 q+r) ((b^2) q (p+q+r)-(c^2) (q (q+r)+p (2 q+r)))+(a^2) (p+2 q+r) ((c^2) (3 p q+4 (q^2)+2 p r+3 q r)+(b^2) (p (2 q+r)+q (2 q+3 r))),-(a^4) ((p^2) (q+r)+q ((q^2)+2 q r+2 (r^2))+p (2 (q^2)+3 q r+2 (r^2)))-((b^2)-(c^2)) (p+q) ((b^2) (p+q+r) (q+2 r)-(c^2) ((q^2)+3 q r+r (p+2 r)))+(a^2) (p+q) ((b^2) (2 p q+2 (q^2)+3 p r+5 q r+4 (r^2))+(c^2) (p (q+2 r)+r (5 q+4 r)))};
QLP23g={-(q+r) (3 (p^2)-(r^2)+2 p (2 q+r)),-(((p+2 q+r))^3),(p^3)+(p^2) (q-2 r)-3 p r (2 q+r)-q r (4 q+3 r)};
QLP24g={(a^4) q (p+q) r ((p^2)-(r^2)) ((p^3)+2 (p^2) (q-r)-4 q r (q+r)-3 p r (2 q+r))+(p^2) (q+r) (3 (p^2)-(r^2)+2 p (2 q+r)) ((b^4) (p+q) (p-r) r+(c^4) q ((p^2)-(r^2))+2 (b^2) (c^2) (q (r^2)+(p^2) (q+r)+p ((q^2)+q r+(r^2))))-2 (a^2) p (p+q) ((c^2) q ((p^2)-(r^2)) (-2 (r^2) (q+r)+(p^2) (q+2 r)+p q (2 q+3 r))-(b^2) r (2 q (r^3) (q+r)-(p^4) (2 q+r)+(p^3) (-3 (q^2)+q r+(r^2))+(p^2) r (8 (q^2)+10 q r+5 (r^2))+p r (4 (q^3)+9 (q^2) r+9 q (r^2)+3 (r^3)))),2 (p+2 q+r) ((c^4) (p^2) (q^2) (q+r) ((p^2)-(r^2))+(p+q) (r^2) (-2 (b^4) (p^2) (q+r) (p+2 q+r)+(a^4) (q^2) (-(p^2)+(r^2))+(a^2) (b^2) p q ((p^2)+(r^2)+2 p (2 q+r)))+(c^2) p q r (-(a^2) q (((p-r))^2) (p+r)+(b^2) p (q+r) ((p^2)+2 p r+r (4 q+r)))),(r^2) ((p^3)+(p^2) (q-2 r)-3 p r (2 q+r)-q r (4 q+3 r)) ((b^4) p (p-r) (q+r)-2 (a^2) (b^2) (q+r) ((p^2)+p r+q r)+(a^4) q ((p^2)-(r^2)))+(c^4) p q (q+r) ((p^2)-(r^2)) (-(r^2) (2 q+r)+(p^2) (4 q+3 r)+2 p (2 (q^2)+3 q r+(r^2)))-2 (c^2) r (q+r) ((a^2) q ((p^2)-(r^2)) (2 (p^3)+2 (p^2) q-q r (2 q+r)-p r (3 q+2 r))-(b^2) p (-q (r^3) (3 q+2 r)+(p^4) (2 q+3 r)+(p^2) r (9 (q^2)+10 q r+(r^2))+(p^3) (2 (q^2)+9 q r+5 (r^2))+p r (4 (q^3)+8 (q^2) r+q (r^2)-(r^3))))};
QLP25g={-(p+q) (p+q+r) ((a^2) ((p^2)-(r^2)) ((p^3)-p (r^2)+(r^2) (2 q+r)+(p^2) (2 q+3 r))+4 (p^2) (q+r) ((b^2) (p+q) (p+2 q+3 r)+(c^2) (-(p^2)+(r^2)))),((p^2)-(r^2)) (-(a^2) q (p+q) (p+2 q+3 r) ((p^2)-(r^2))+(q+r) ((c^2) q (3 p+2 q+r) ((p^2)-(r^2))+(b^2) ((p^4)+3 (p^3) (q+r)+q (r^2) (2 q+r)+p (r^2) (5 q+r)+(p^2) (2 (q^2)+3 q r+3 (r^2))))),(q+r) (p+q+r) (-(c^2) ((p^2)-(r^2)) ((p^3)+(p^2) (2 q-r)+3 p (r^2)+(r^2) (2 q+r))+4 (p+q) (r^2) ((b^2) (q+r) (3 p+2 q+r)+(a^2) ((p^2)-(r^2))))};
QLP26g={-(a^2) (-2 (c^2) (p^2) (q^2)-2 (c^2) p (q^3)+(a^2) (p^2) q r-(b^2) (p^2) q r-(c^2) (p^2) q r+(a^2) p (q^2) r-(b^2) p (q^2) r-2 (c^2) p (q^2) r-2 (b^2) (p^2) (r^2)-(a^2) p q (r^2)-2 (b^2) p q (r^2)+(c^2) p q (r^2)-(a^2) (q^2) (r^2)),2 (b^2) (c^2) (p^2) (q^2)+4 (a^2) (c^2) p (q^3)+2 (b^2) (c^2) p (q^3)-2 (c^4) p (q^3)+4 (a^2) (c^2) (q^4)-(a^2) (b^2) (p^2) q r+(b^4) (p^2) q r+2 (b^2) (c^2) (p^2) q r-2 (a^4) p (q^2) r+(a^2) (b^2) p (q^2) r+(b^4) p (q^2) r+4 (a^2) (c^2) p (q^2) r+(b^2) (c^2) p (q^2) r-2 (c^4) p (q^2) r-2 (a^4) (q^3) r+2 (a^2) (b^2) (q^3) r+4 (a^2) (c^2) (q^3) r+(b^4) (p^2) (r^2)+2 (a^2) (b^2) p q (r^2)+(b^4) p q (r^2)-(b^2) (c^2) p q (r^2)+2 (a^2) (b^2) (q^2) (r^2),(c^2) ((c^2) (p^2) (q^2)-(a^2) (p^2) q r+2 (b^2) (p^2) q r+(c^2) (p^2) q r+2 (a^2) p (q^2) r+(b^2) p (q^2) r-(c^2) p (q^2) r+2 (a^2) (q^3) r+2 (b^2) (p^2) (r^2)+(a^2) p q (r^2)+(b^2) p q (r^2)-(c^2) p q (r^2)+2 (a^2) (q^2) (r^2))};
QLP27g={-((b^2)-(c^2)) p (q+r) ((b^2) (p+q)-(c^2) (p+2 q+r))-(a^4) (2 (p^2) (q+r)+q ((q^2)+2 q r+2 (r^2))+p (3 (q^2)+4 q r+2 (r^2)))+(a^2) ((b^2) ((p^2) (3 q+4 r)+q ((q^2)+3 q r+2 (r^2))+p (4 (q^2)+7 q r+2 (r^2)))+(c^2) ((p^2) (4 q+3 r)+q (2 (q^2)+3 q r+(r^2))+p (5 (q^2)+7 q r+3 (r^2)))),-(a^4) q (p+q) (p+2 (q+r))-(-(c^2) q+(b^2) (p+q)) (q+r) (-(c^2) (2 p+2 q+r)+(b^2) (2 p+3 q+2 r))+(a^2) ((c^2) q ((p^2)+2 (q^2)+4 q r+(r^2)+4 p (q+r))+(b^2) ((p^2) (3 q+r)+q (5 (q^2)+6 q r+2 (r^2))+p (8 (q^2)+7 q r+2 (r^2)))),-(a^4) (p+q) r (p+2 q+r)-(q+r) ((b^4) (p+q) r-(b^2) (c^2) (2 (p^2)+3 p q+(q^2)+4 p r+3 q r)+(c^4) (2 (p^2)+2 p (q+r)+q (q+2 r)))+(a^2) ((b^2) (p+q) r (p+3 q+2 r)+(c^2) ((p^2) (q+3 r)+p (3 (q^2)+7 q r+3 (r^2))+q (2 (q^2)+5 q r+4 (r^2))))};
QLP28g={(a^2) ((b^2) (c^4) (-3 (p^2) (q^2) r+(q^2) (((q+r))^3)+(p^3) ((q^2)-3 q r-(r^2)))+(b^4) (c^2) (-3 (p^2) q (r^2)-3 p q (((q+r))^3)-2 (q^2) (((q+r))^3)+(p^3) ((q^2)+3 q r-(r^2)))-(c^6) (p^2) (2 (q^3)+3 (q^2) r+3 q (r^2)+(r^3)+p (3 (q^2)+3 q r+(r^2)))+(a^6) ((p^3) (-(q^2)+(r^2))+3 p q (-(q^3)+q (r^2)+(r^3))+(p^2) (-3 (q^3)+3 q (r^2)+(r^3))+(q^2) (-(q^3)+q (r^2)+2 (r^3)))+(b^6) (3 p q (((q+r))^3)+(q^2) (((q+r))^3)+(p^3) ((q^2)+3 q r+3 (r^2))+(p^2) (3 (q^3)+9 (q^2) r+9 q (r^2)+2 (r^3)))+(a^2) (3 (c^4) p ((p^2) (((q+r))^2)+q (2 (q^3)+3 (q^2) r+3 q (r^2)+(r^3))+p (3 (q^3)+4 (q^2) r+3 q (r^2)+(r^3)))+(b^2) (c^2) (3 (p^2) q r (3 q+r)+(q^2) (((q+r))^2) (4 q+r)-2 (p^3) ((q^2)-(r^2))+3 p q (2 (q^3)+6 (q^2) r+3 q (r^2)+(r^3)))-3 (b^4) ((p^3) (((q+r))^2)+(q^3) (((q+r))^2)+(p^2) (3 (q^3)+6 (q^2) r+3 q (r^2)+(r^3))+p q (3 (q^3)+6 (q^2) r+3 q (r^2)+(r^3))))+(a^4) ((b^2) ((p^3) (3 (q^2)+3 q r-(r^2))+3 (p^2) q (3 (q^2)+3 q r-(r^2))+(q^2) (3 (q^3)+3 (q^2) r-q (r^2)-3 (r^3))+3 p q (3 (q^3)+3 (q^2) r-q (r^2)-(r^3)))+(c^2) ((p^3) ((q^2)-3 q r-3 (r^2))-3 (p^2) r (3 (q^2)+3 q r+(r^2))-3 p q ((q^3)+3 (q^2) r+4 q (r^2)+2 (r^3))-(q^2) (2 (q^3)+3 (q^2) r+5 q (r^2)+2 (r^3))))),(a^8) q ((p^2)+3 p q+2 (q^2)) (r^2)-((b^2)-(c^2)) (-(c^2) q+(b^2) (p+q)) (q+r) (-(c^4) (p^2) (2 q+r)+(b^2) (c^2) ((p^2) (q-r)-q (((q+r))^2))+(b^4) (2 p (((q+r))^2)+q (((q+r))^2)+(p^2) (q+2 r)))+(a^6) (p+q) (-(c^2) q r (3 p q+6 (q^2)+4 p r+5 q r)+(b^2) ((p^2) (q^2)+q ((q^3)-5 q (r^2)-2 (r^3))+p (2 (q^3)-q (r^2)-(r^3))))+(a^2) (-(c^6) p q (q+r) (3 q (2 q+r)+p (5 q+4 r))+(b^2) (c^4) (9 p (q^3) (q+r)+3 (q^3) (((q+r))^2)+(p^3) r (3 q+2 r)+(p^2) (6 (q^3)+9 (q^2) r+q (r^2)-(r^3)))+(b^6) (p+q) (3 (q^2) (((q+r))^2)+(p^2) (3 (q^2)+6 q r+2 (r^2))+3 p (2 (q^3)+4 (q^2) r+3 q (r^2)+(r^3)))-(b^4) (c^2) (6 (q^3) (((q+r))^2)+(p^3) r (3 q+r)+(p^2) (6 (q^3)+9 (q^2) r+2 q (r^2)+(r^3))+3 p q (4 (q^3)+6 (q^2) r+3 q (r^2)+(r^3))))+(a^4) (3 (c^4) q (p+q) (q+r) (q (2 q+r)+p (q+2 r))-3 (b^4) q ((p^3) (q+r)+q (q-r) (((q+r))^2)+(p^2) (3 (q^2)+3 q r+(r^2))+p (3 (q^3)+3 (q^2) r-(r^3)))+(b^2) (c^2) (-(p^3) (r^2)+3 (q^3) ((q^2)+3 q r+2 (r^2))+3 p q (2 (q^3)+3 (q^2) r+3 q (r^2)+(r^3))+(p^2) (3 (q^3)+q (r^2)+2 (r^3)))),(c^2) (-(a^6) (r^2) ((p^3)+3 p q (q+r)+(p^2) (3 q+r)+(q^2) (2 q+3 r))+((b^2)-(c^2)) (q+r) ((b^2) (c^2) ((p^3) (q-r)-3 p q (((q+r))^2)-2 (q^2) (((q+r))^2))-(c^4) ((p^2) (((q+r))^2)-(q^2) (((q+r))^2)+(p^3) (2 q+r))+(b^4) (3 (p^2) (((q+r))^2)+3 p q (((q+r))^2)+(q^2) (((q+r))^2)+(p^3) (q+2 r)))+(a^4) (3 (c^2) r ((p^3) (q+r)+(q^2) (2 (q^2)+3 q r+(r^2))+(p^2) (3 (q^2)+3 q r+(r^2))+p q (3 (q^2)+4 q r+2 (r^2)))+(b^2) ((p^3) (q^2)+(p^2) (3 (q^3)-(r^3))+3 p q ((q^3)-q (r^2)-(r^3))+(q^2) ((q^3)+(r^3))))-(a^2) ((b^4) (3 p q (2 q-r) (((q+r))^2)+(q^2) (2 q-r) (((q+r))^2)+(p^3) q (2 q+3 r)+(p^2) (6 (q^3)+9 (q^2) r+3 q (r^2)+(r^3)))-(b^2) (c^2) (9 p (q^2) (((q+r))^2)+2 (q^2) (2 q-r) (((q+r))^2)+(p^3) q (q+3 r)+(p^2) (6 (q^3)+9 (q^2) r+3 q (r^2)+2 (r^3)))+(c^4) ((q^2) (2 q-r) (((q+r))^2)+3 p q (((q+r))^3)+(p^3) (2 (q^2)+6 q r+3 (r^2))+(p^2) (5 (q^3)+12 (q^2) r+9 q (r^2)+3 (r^3)))))};
QLP29g={(a^4) r ((q^2)+p r+2 q r)-((b^2)-(c^2)) (q+r) (-(c^2) ((p^2)+q (q+r))+(b^2) ((p^2)+2 p (q+r)+q (q+r)))+(a^2) (-(c^2) (2 (q^3)+2 (q^2) r+p r (-p+r))+(b^2) ((p^2) q+(q^3)-q (r^2)+p (2 (q^2)+2 q r+(r^2)))),(b^2) (c^2) (2 p (q^2)+(p^2) (q-r)-q (((q+r))^2))-(c^4) p (3 (q^2)+3 q r+(r^2)+p (2 q+r))-(a^4) r ((p^2)+p (3 q+r)+q (3 q+2 r))+(b^4) (q (((q+r))^2)+(p^2) (q+2 r)+p (2 (q^2)+5 q r+2 (r^2)))+(a^2) (-(b^2) ((p^2) q+q ((q^2)-2 q r-(r^2))+p (2 (q^2)+(r^2)))+2 (c^2) ((p^2) (q+r)+p (3 (q^2)+3 q r+(r^2))+q (3 (q^2)+3 q r+(r^2)))),-(a^4) ((p^2) q+2 p (q^2)+(q^3)+p (r^2)+q (r^2))-(b^2) (c^2) ((p^2) (q-r)-2 p q r-q (((q+r))^2))+(c^4) p ((q^2)+p (2 q+r))-(b^4) (p+q) ((((q+r))^2)+p (q+2 r))+(a^2) (-(c^2) (2 p (q^2)+2 (q^3)+(p^2) r-p (r^2))+2 (b^2) ((p^2) (q+r)+q ((q^2)+q r+(r^2))+p (2 (q^2)+2 q r+(r^2))))};
QLP30g={-(a^4) (-q (r^2)+(p^2) (q+r)+p q (q+2 r))-((b^2)-(c^2)) (q+r) ((b^2) (2 p+q) (p+q+r)-(c^2) (2 (p^2)+q (q+r)+p (2 q+r)))+(a^2) ((c^2) (q r (q+r)+(p^2) (2 q+3 r)+p (3 (q^2)+5 q r+(r^2)))+(b^2) ((q^2) (q+r)+(p^2) (3 q+2 r)+p (4 (q^2)+5 q r+2 (r^2)))),-(a^4) (p+2 q) (q+r) (p+q+r)-(c^4) (p+q) (p+q+r) (2 q+r)+(b^4) ((p^2) r-(q^2) (q+r)+p (-(q^2)+q r+(r^2)))+(b^2) (c^2) (2 (p^2) q+q (3 (q^2)+4 q r+(r^2))+p (6 (q^2)+5 q r+(r^2)))+(a^2) ((b^2) ((p^2) (q+r)+p q (4 q+5 r)+q (3 (q^2)+6 q r+2 (r^2)))+(c^2) (2 p (((2 q+r))^2)+(p^2) (3 q+2 r)+q (6 (q^2)+8 q r+3 (r^2)))),-(b^4) (p+q) (p+q+r) (q+2 r)-(c^4) (-(p^2) q+q r (q+r)+p r (2 q+r))-(a^4) ((p^2) (q+r)+q ((q^2)+2 q r+2 (r^2))+p (2 (q^2)+3 q r+2 (r^2)))+(b^2) (c^2) (2 (p^2) r+p ((q^2)+5 q r+2 (r^2))+q ((q^2)+4 q r+3 (r^2)))+(a^2) ((c^2) ((p^2) (q+r)+q r (3 q+2 r)+p ((q^2)+5 q r+3 (r^2)))+(b^2) (4 p (((q+r))^2)+(p^2) (2 q+3 r)+q (2 (q^2)+5 q r+4 (r^2))))};

QA - Lines

QAL1={-(a^4) q (p+q) (q-r) r (p+r)-p (q+r) (-(b^2) (c^2) (p+q) (q-r) (p+r)+(b^4) (p+q) r (p+2 q+r)-(c^4) q (p+r) (p+q+2 r))-(a^2) (p+q) (p+r) (q+r) (-(b^2) (p+3 q) r+(c^2) q (p+3 r)),(a^4) q (p+q) r (p+r) (2 p+q+r)-(a^2) (p+q) (p+r) (q+r) ((c^2) q (p-r)+(b^2) (3 p+q) r)+p (q+r) ((b^4) (p+q) (p-r) r-(c^4) q (p+r) (p+q+2 r)+(b^2) (c^2) (p+q) (p+r) (q+3 r)),-(a^4) q (p+q) r (p+r) (2 p+q+r)+(a^2) (p+q) (p+r) (q+r) ((b^2) (p-q) r+(c^2) q (3 p+r))+p (q+r) (-(c^4) (p-q) q (p+r)+(b^4) (p+q) r (p+2 q+r)-(b^2) (c^2) (p+q) (p+r) (3 q+r))};
QAL2={p (-(a^6) (q^2) (p+q) (r^2) (p+r) ((b^2) (p+q)-(c^2) (p+r))+(a^4) q r (-(b^2) (c^2) q (p+q) (q-r) r (p+r)-(c^4) q (((p+r))^2) (2 p q+(q^2)+3 p r+2 q r)+(b^4) (((p+q))^2) r (3 p q+2 p r+2 q r+(r^2)))+p (((q+r))^2) ((b^4) (c^4) p q (q-r) r+(b^8) (((p+q))^2) (r^2)+(b^6) (c^2) ((p^2)-p q-2 (q^2)) (r^2)-(c^8) (q^2) (((p+r))^2)+(b^2) (c^6) (q^2) (-(p^2)+p r+2 (r^2)))+(a^2) (q+r) ((b^2) (c^4) (q^2) r (p+r) (2 (p^2)-3 p r-3 q r)+(b^4) (c^2) q (p+q) (r^2) (-2 (p^2)+3 p q+3 q r)-(b^6) (((p+q))^2) (r^2) (q r+p (3 q+r))+(c^6) (q^2) (((p+r))^2) (q r+p (q+3 r)))),q (-(a^8) q (((p+q))^2) (r^2) (((p+r))^2)-(c^2) ((b^2)-(c^2)) (p^2) (((q+r))^2) (-(b^2) r+(c^2) (p+r)) (-(b^2) (p+q) r+(c^2) q (p+r))-(a^4) p r ((c^4) (q^2) (p-r) (((p+r))^2)+(b^4) (((p+q))^2) r (3 p q+2 p r+2 q r+(r^2))+(b^2) (c^2) (p+q) r (p+r) (-2 (q^2)+3 p (q+r)))+(a^6) (p+q) (r^2) (p+r) ((c^2) (2 p-q) q (p+r)+(b^2) (p+q) (q r+p (3 q+r)))+(a^2) (p^2) (q+r) ((b^6) (((p+q))^2) (r^2)+(b^4) (c^2) (p+q) (p-r) (r^2)+(c^6) q (q-2 r) (((p+r))^2)+(b^2) (c^4) r (3 (p^2) r+q r (-2 q+3 r)+p (-2 (q^2)+3 q r+3 (r^2))))),r ((a^8) (q^2) (((p+q))^2) r (((p+r))^2)-(b^2) ((b^2)-(c^2)) (p^2) (-(c^2) q+(b^2) (p+q)) (((q+r))^2) ((b^2) (p+q) r-(c^2) q (p+r))-(a^6) (q^2) (p+q) (p+r) ((b^2) (p+q) (2 p-r) r+(c^2) (p+r) (q r+p (q+3 r)))+(a^2) (p^2) (q+r) ((b^6) (((p+q))^2) (2 q-r) r-(b^2) (c^4) (p-q) (q^2) (p+r)-(c^6) (q^2) (((p+r))^2)-(b^4) (c^2) q (3 (p^2) q+q (3 q-2 r) r+p (3 (q^2)+3 q r-2 (r^2))))+(a^4) p q ((b^4) (p-q) (((p+q))^2) (r^2)+(c^4) q (((p+r))^2) (2 p q+(q^2)+3 p r+2 q r)+(b^2) (c^2) q (p+r) (-2 q (r^2)+3 (p^2) (q+r)+p (3 (q^2)+3 q r-2 (r^2)))))};
QAL3={p (q-r) ((p^2)+2 (q^2)+5 q r+2 (r^2)+3 p (q+r)),-q (p-r) (2 (p^2)+3 p q+(q^2)+5 p r+3 q r+2 (r^2)),(p-q) r (2 (p^2)+5 p q+2 (q^2)+3 p r+3 q r+(r^2))};
QAL4={-(a^2) (p+q) (q-r) (p+r)+(q+r) (-(c^2) (p+3 q) (p+r)+(b^2) (p+q) (p+3 r)),-(a^2) (p+q) (p+r) (q+3 r)+(q+r) ((b^2) (p+q) (p-r)+(c^2) (3 p+q) (p+r)),(a^2) (p+q) (p+r) (3 q+r)-(q+r) ((c^2) (p-q) (p+r)+(b^2) (p+q) (3 p+r))};
QAL5={-(c^4) p (q^2) (((p+r))^2) (q+r) (2 (p^2) q+q r (-q+r)+p (4 (q^2)+q r+(r^2)))+(c^2) q r (-(b^2) p ((q^2)-(r^2)) (2 (p^4)-(p^2) (((q-r))^2)+2 (q^2) (r^2)+3 (p^3) (q+r)-p q r (q+r))+(a^2) q (((p+r))^2) (2 (p^3) q+3 (q^2) r (q+r)+(p^2) (3 (q^2)+q r+2 (r^2))-p ((q^3)-3 q (r^2))))+(((p+q))^2) (r^2) ((a^4) (q^2) (q-r) (((p+r))^2)+(b^4) p (q+r) (2 (p^2) r+q (q-r) r+p ((q^2)+q r+4 (r^2)))-(a^2) (b^2) q (2 (p^3) r+3 q (r^2) (q+r)+(p^2) (2 (q^2)+q r+3 (r^2))+p (3 (q^2) r-(r^3)))),(c^4) (p^2) q (p+r) (((q+r))^2) ((p^2) (4 q-r)+q (r^2)+p (2 (q^2)+q r+(r^2)))-(((p+q))^2) (r^2) ((b^4) (p^2) (p-r) (((q+r))^2)+(a^4) q (p+r) (p (q-r) r+(p^2) (q+r)+2 q r (q+2 r))-(a^2) (b^2) p (q r (2 (q^2)+3 q r-(r^2))+p r ((q^2)+3 (r^2))+(p^2) (2 (q^2)+3 q r+3 (r^2))))-(c^2) p r ((b^2) p (((q+r))^2) (-(p^3) (q-3 r)+2 (q^2) (r^2)+3 (p^2) ((q^2)+(r^2))+p q (2 (q^2)+q r+3 (r^2)))+(a^2) q ((p^4) ((q^2)+q r-2 (r^2))+p q (r^2) (3 (q^2)+2 q r-(r^2))+(q^2) (r^2) (2 (q^2)+3 q r-(r^2))+(p^3) q (-3 (q^2)-2 q r+(r^2))-(p^2) (2 (q^4)+3 (q^3) r+q (r^3)-2 (r^4)))),(a^4) (q^2) (p+q) r (((p+r))^2) (p q (-q+r)+(p^2) (q+r)+2 q r (2 q+r))+(p^2) (((q+r))^2) ((c^4) (p-q) (q^2) (((p+r))^2)+(b^4) (p+q) r ((p^2) (q-4 r)-(q^2) r-p ((q^2)+q r+2 (r^2)))+(b^2) (c^2) q ((p^3) (3 q-r)+2 (q^2) (r^2)+3 (p^2) ((q^2)+(r^2))+p r (3 (q^2)+q r+2 (r^2))))-(a^2) p q ((c^2) q (((p+r))^2) (p q (3 (q^2)+(r^2))+q r (-(q^2)+3 q r+2 (r^2))+(p^2) (3 (q^2)+3 q r+2 (r^2)))+(b^2) r (p (q^2) r ((q^2)-2 q r-3 (r^2))+(q^2) (r^2) ((q^2)-3 q r-2 (r^2))+(p^4) (2 (q^2)-q r-(r^2))+(p^3) r (-(q^2)+2 q r+3 (r^2))+(p^2) (-2 (q^4)+(q^3) r+3 q (r^3)+2 (r^4))))};
QAL6={(a^4) q (p+q) (q-r) r (p+r)-(q+r) (-(b^2) (c^2) (q-r) ((p^2) (q+r)-q r (q+r)+p ((q^2)+(r^2)))-(c^4) (p+r) ((p^3)+(p^2) (3 q+2 r)+q (2 (q^2)+3 q r+(r^2))+p (4 (q^2)+3 q r+(r^2)))+(b^4) ((p^4)+3 (p^3) (q+r)+q r ((q^2)+3 q r+2 (r^2))+(p^2) (3 (q^2)+6 q r+4 (r^2))+p ((q^3)+4 (q^2) r+7 q (r^2)+2 (r^3))))+(a^2) (-(c^2) ((p^4) (q+r)+(p^3) (3 (q^2)+8 q r+3 (r^2))+q r (2 (q^3)+6 (q^2) r+7 q (r^2)+3 (r^3))+(p^2) (4 (q^3)+15 (q^2) r+14 q (r^2)+3 (r^3))+p (2 (q^4)+10 (q^3) r+19 (q^2) (r^2)+10 q (r^3)+(r^4)))+(b^2) ((p^4) (q+r)+(p^3) (3 (q^2)+8 q r+3 (r^2))+q r (3 (q^3)+7 (q^2) r+6 q (r^2)+2 (r^3))+(p^2) (3 (q^3)+14 (q^2) r+15 q (r^2)+4 (r^3))+p ((q^4)+10 (q^3) r+19 (q^2) (r^2)+10 q (r^3)+2 (r^4)))),(a^4) ((p^4) (q+r)+(p^3) (3 (q^2)+5 q r+4 (r^2))+q r ((q^3)+3 (q^2) r+4 q (r^2)+2 (r^3))+(p^2) (3 (q^3)+9 (q^2) r+11 q (r^2)+5 (r^3))+p ((q^4)+6 (q^3) r+10 (q^2) (r^2)+9 q (r^3)+2 (r^4)))+(q+r) (-(b^4) p (p+q) (p-r) r-(c^4) (p+r) (2 (p^3)+q (((q+r))^2)+(p^2) (4 q+3 r)+p (3 (q^2)+3 q r+(r^2)))+(b^2) (c^2) (2 (p^4)+q r (((q+r))^2)+(p^3) (4 q+6 r)+(p^2) (3 (q^2)+12 q r+7 (r^2))+p ((q^3)+7 (q^2) r+7 q (r^2)+3 (r^3))))-(a^2) ((c^2) ((p^2)-(r^2)) ((p^2) (q-r)+q r (q+r)+p ((q^2)-(r^2)))+(b^2) ((p^4) (q+3 r)+p (((q+r))^2) ((q^2)+6 q r+2 (r^2))+(p^3) (3 (q^2)+10 q r+7 (r^2))+q r ((q^3)+3 (q^2) r+4 q (r^2)+2 (r^3))+(p^2) (3 (q^3)+14 (q^2) r+19 q (r^2)+6 (r^3)))),-(a^4) ((p^4) (q+r)+(p^3) (4 (q^2)+5 q r+3 (r^2))+q r (2 (q^3)+4 (q^2) r+3 q (r^2)+(r^3))+(p^2) (5 (q^3)+11 (q^2) r+9 q (r^2)+3 (r^3))+p (2 (q^4)+9 (q^3) r+10 (q^2) (r^2)+6 q (r^3)+(r^4)))+(q+r) ((c^4) p (p-q) q (p+r)+(b^4) (2 (p^4)+q r (((q+r))^2)+(p^3) (5 q+4 r)+(p^2) (4 (q^2)+7 q r+3 (r^2))+p ((q^3)+4 (q^2) r+5 q (r^2)+(r^3)))-(b^2) (c^2) (2 (p^4)+q r (((q+r))^2)+(p^3) (6 q+4 r)+(p^2) (7 (q^2)+12 q r+3 (r^2))+p (3 (q^3)+7 (q^2) r+7 q (r^2)+(r^3))))+(a^2) (-(b^2) ((p^2)-(q^2)) ((p^2) (q-r)-q r (q+r)+p ((q^2)-(r^2)))+(c^2) ((p^4) (3 q+r)+p (((q+r))^2) (2 (q^2)+6 q r+(r^2))+(p^3) (7 (q^2)+10 q r+3 (r^2))+q r (2 (q^3)+4 (q^2) r+3 q (r^2)+(r^3))+(p^2) (6 (q^3)+19 (q^2) r+14 q (r^2)+3 (r^3))))};
QAL7=
{-2 (q^2) (r^2) (((q+r))^2)+(p^4) ((q^2)+(r^2))+p q r ((q^3)-2 (q^2) r-2 q (r^2)+(r^3))+(p^3) (2 (q^3)+3 (q^2) r+3 q (r^2)+2 (r^3))+(p^2) ((q^4)+4 (q^3) r+4 (q^2) (r^2)+4 q (r^3)+(r^4)),(q^2) (r^2) (((q+r))^2)+(p^4) ((q^2)+q r-2 (r^2))+p q (r^2) (3 (q^2)+4 q r+(r^2))+2 (p^3) ((q^3)+2 (q^2) r-q (r^2)-2 (r^3))+(p^2) ((q^4)+3 (q^3) r+4 (q^2) (r^2)-2 q (r^3)-2 (r^4)),(q^2) (r^2) (((q+r))^2)+(p^4) (-2 (q^2)+q r+(r^2))+p (q^2) r ((q^2)+4 q r+3 (r^2))+(p^3) (-4 (q^3)-2 (q^2) r+4 q (r^2)+2 (r^3))+(p^2) (-2 (q^4)-2 (q^3) r+4 (q^2) (r^2)+3 q (r^3)+(r^4))};
QAL8={2 p (q+r) ((c^4) (p^2) q (q-r) (p+r) (q+r)+(c^2) q r ((a^2) (p+r) (p q (-p+q)+(2 (p^2)+p q+(q^2)) r)+2 (b^2) (p^2) (-(q^2)+(r^2)))+(p+q) r ((a^4) p q (q-r) (p+r)+(b^4) (p^2) (q-r) (q+r)-(a^2) (b^2) q (2 (p^2) q+p (-p+q) r+(p+q) (r^2)))),-2 q (p+r) ((c^4) p (q^2) (p-r) (p+r) (q+r)+(p+q) r ((a^4) (q^2) (p-r) (p+r)+(b^4) p q (p-r) (q+r)-(a^2) (b^2) p (2 p (q^2)+(p-q) q r+(p+q) (r^2)))+(c^2) p r (2 (a^2) (q^2) (-(p^2)+(r^2))+(b^2) (q+r) (2 (q^2) r+p q (-q+r)+(p^2) (q+r)))),2 (p+q) r ((a^4) (p-q) q (p+q) (r^2) (p+r)-(a^2) p q (2 (b^2) (p-q) (p+q) (r^2)+(c^2) (p+r) (p (q^2)+q (p+q) r+(2 p-q) (r^2)))+p (q+r) ((b^4) (p-q) (p+q) (r^2)+(c^4) (p-q) q r (p+r)+(b^2) (c^2) q (p (q-r) r+2 q (r^2)+(p^2) (q+r))))};
QAL9={(c^2) p q (p+r) (q+r)-(p+q) r ((a^2) q (p+r)-(b^2) p (q+r)),(c^2) p q (p+r) (q+r)+(p+q) r ((a^2) q (p+r)-(b^2) p (q+r)),-(c^2) p q (p+r) (q+r)+(p+q) r ((a^2) q (p+r)+(b^2) p (q+r))};
QAL11={-q r (-(p^2)+p q+(q^2)+p r+q r+(r^2)),-p r ((p^2)+p q-(q^2)+p r+q r+(r^2)),-p q ((p^2)+p q+(q^2)+p r+q r-(r^2))};

QA - Triangle

QATr1[P1_,P2_,P3_,P4_]:=Module[{DT1,DT2,DT3},DT1=Punto[Recta[P1,P2],Recta[P3,P4]];DT2=Punto[Recta[P1,P3],Recta[P2,P4]];DT3=Punto[Recta[P1,P4],Recta[P2,P3]];{DT1,DT2,DT3}]

QA - Transformations

QA-Tf1:  QA-Line Involution Center

QATf1[{l_,m_,n_}]:={m n p (m q+n r-l (q+r)),l n q (l p+n r-m (p+r)),l m (l p+m q-n (p+q)) r};

QA-Tf1b:  QA-Line Involution Double Points

QATf1b[{l_,m_,n_}]:={{m n p (m q+n r),-l m n p q-n(Sqrt[-l m n p q r (l p+m q+n r)]),-l m n p r+m(Sqrt[-l m n p q r (l p+m q+n r)])},{m n p (m q+n r),-l m n p q+n(Sqrt[-l m n p q r (l p+m q+n r)]),-l m n p r-m(Sqrt[-l m n p q r (l p+m q+n r)])}};

QA-Tf2:  Involutary Conjugate

QATf2[{u_,v_,w_}]:=Factor[Simplificar[{u (q r u-p r v-p q w),v (-q r u+p r v-p q w),w (-q r u-p r v+p q w)}]];

QA-Tf3:  QA-Orthopole Transformation

QATf3[{u_,v_,w_}]:=Simplificar[{(b^2) p (r (u+v)-q w)+(c^2) p (-r v+q (u+w))+(a^2) (q r (v+w)+p (r v+q w)),(b^2) (q r u+p (q w+r (u+w)))+q ((a^2) (r (u+v)-p w)+(c^2) (-r u+p (v+w))),(c^2) (q r u+p (r v+q (u+v)))+r ((a^2) (-p v+q (u+w))+(b^2) (-q u+p (v+w)))}];

QA-Tf4:  Moebius Conjugates

QATf4[{x_,y_,z_}]:=Simplificar[{(a^2) (-(b^2) (c^2) p (-(a^2) (p^2)+(b^2) (p^2)+(c^2) (p^2)-(a^2) p q+(b^2) p q-(c^2) p q-(a^2) p r-(b^2) p r+(c^2) p r-2 (a^2) q r) ((c^2) (q^2)-(a^2) q r+(b^2) q r+(c^2) q r+(b^2) (r^2)) (x^2)+(c^2) ((a^4) (c^2) (p^3) (q^2)-(b^4) (c^2) (p^3) (q^2)-2 (a^2) (c^4) (p^3) (q^2)-2 (b^2) (c^4) (p^3) (q^2)+(c^6) (p^3) (q^2)+(a^4) (c^2) (p^2) (q^3)-(b^4) (c^2) (p^2) (q^3)-(a^2) (c^4) (p^2) (q^3)+(b^2) (c^4) (p^2) (q^3)-(a^6) (p^3) q r+2 (a^4) (b^2) (p^3) q r-(a^2) (b^4) (p^3) q r+3 (a^4) (c^2) (p^3) q r-(a^2) (b^2) (c^2) (p^3) q r-4 (b^4) (c^2) (p^3) q r-3 (a^2) (c^4) (p^3) q r-(b^2) (c^4) (p^3) q r+(c^6) (p^3) q r-(a^6) (p^2) (q^2) r+3 (a^4) (b^2) (p^2) (q^2) r-3 (a^2) (b^4) (p^2) (q^2) r+(b^6) (p^2) (q^2) r+4 (a^4) (c^2) (p^2) (q^2) r-3 (a^2) (b^2) (c^2) (p^2) (q^2) r-(b^4) (c^2) (p^2) (q^2) r-5 (a^2) (c^4) (p^2) (q^2) r-2 (b^2) (c^4) (p^2) (q^2) r+2 (c^6) (p^2) (q^2) r+(a^4) (b^2) p (q^3) r-2 (a^2) (b^4) p (q^3) r+(b^6) p (q^3) r+2 (a^4) (c^2) p (q^3) r+2 (a^2) (b^2) (c^2) p (q^3) r-2 (b^4) (c^2) p (q^3) r-2 (a^2) (c^4) p (q^3) r+(b^2) (c^4) p (q^3) r+(a^2) (b^4) (p^3) (r^2)-(b^6) (p^3) (r^2)-(b^4) (c^2) (p^3) (r^2)-2 (a^6) (p^2) q (r^2)+3 (a^4) (b^2) (p^2) q (r^2)-3 (a^2) (b^4) (p^2) q (r^2)+2 (b^6) (p^2) q (r^2)+6 (a^4) (c^2) (p^2) q (r^2)-(b^4) (c^2) (p^2) q (r^2)-6 (a^2) (c^4) (p^2) q (r^2)-3 (b^2) (c^4) (p^2) q (r^2)+2 (c^6) (p^2) q (r^2)-2 (a^6) p (q^2) (r^2)+2 (a^4) (b^2) p (q^2) (r^2)-(a^2) (b^4) p (q^2) (r^2)+(b^6) p (q^2) (r^2)+5 (a^4) (c^2) p (q^2) (r^2)+(a^2) (b^2) (c^2) p (q^2) (r^2)-(b^4) (c^2) p (q^2) (r^2)-4 (a^2) (c^4) p (q^2) (r^2)-(b^2) (c^4) p (q^2) (r^2)+(c^6) p (q^2) (r^2)+(a^4) (b^2) (q^3) (r^2)-(a^2) (b^4) (q^3) (r^2)+(a^4) (c^2) (q^3) (r^2)+2 (a^2) (b^2) (c^2) (q^3) (r^2)-(a^2) (c^4) (q^3) (r^2)+(a^2) (b^4) (p^2) (r^3)+(b^6) (p^2) (r^3)-(b^4) (c^2) (p^2) (r^3)-(a^6) p q (r^3)+(a^4) (b^2) p q (r^3)+3 (a^4) (c^2) p q (r^3)+(a^2) (b^2) (c^2) p q (r^3)+(b^4) (c^2) p q (r^3)-3 (a^2) (c^4) p q (r^3)-2 (b^2) (c^4) p q (r^3)+(c^6) p q (r^3)-(a^6) (q^2) (r^3)-(a^2) (b^4) (q^2) (r^3)+2 (a^4) (c^2) (q^2) (r^3)+2 (a^2) (b^2) (c^2) (q^2) (r^3)-(a^2) (c^4) (q^2) (r^3)) x y+(c^2) q ((a^4) p q-(a^2) (b^2) p q-2 (a^2) (c^2) p q-(b^2) (c^2) p q+(c^4) p q+(a^4) (q^2)-(a^2) (b^2) (q^2)-(a^2) (c^2) (q^2)-(a^2) (b^2) p r-(b^4) p r+(b^2) (c^2) p r-2 (a^2) (b^2) q r) ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) (y^2)+(b^2) ((a^2) (c^4) (p^3) (q^2)-(b^2) (c^4) (p^3) (q^2)-(c^6) (p^3) (q^2)+(a^2) (c^4) (p^2) (q^3)-(b^2) (c^4) (p^2) (q^3)+(c^6) (p^2) (q^3)-(a^6) (p^3) q r+3 (a^4) (b^2) (p^3) q r-3 (a^2) (b^4) (p^3) q r+(b^6) (p^3) q r+2 (a^4) (c^2) (p^3) q r-(a^2) (b^2) (c^2) (p^3) q r-(b^4) (c^2) (p^3) q r-(a^2) (c^4) (p^3) q r-4 (b^2) (c^4) (p^3) q r-2 (a^6) (p^2) (q^2) r+6 (a^4) (b^2) (p^2) (q^2) r-6 (a^2) (b^4) (p^2) (q^2) r+2 (b^6) (p^2) (q^2) r+3 (a^4) (c^2) (p^2) (q^2) r-3 (b^4) (c^2) (p^2) (q^2) r-3 (a^2) (c^4) (p^2) (q^2) r-(b^2) (c^4) (p^2) (q^2) r+2 (c^6) (p^2) (q^2) r-(a^6) p (q^3) r+3 (a^4) (b^2) p (q^3) r-3 (a^2) (b^4) p (q^3) r+(b^6) p (q^3) r+(a^4) (c^2) p (q^3) r+(a^2) (b^2) (c^2) p (q^3) r-2 (b^4) (c^2) p (q^3) r+(b^2) (c^4) p (q^3) r+(a^4) (b^2) (p^3) (r^2)-2 (a^2) (b^4) (p^3) (r^2)+(b^6) (p^3) (r^2)-2 (b^4) (c^2) (p^3) (r^2)-(b^2) (c^4) (p^3) (r^2)-(a^6) (p^2) q (r^2)+4 (a^4) (b^2) (p^2) q (r^2)-5 (a^2) (b^4) (p^2) q (r^2)+2 (b^6) (p^2) q (r^2)+3 (a^4) (c^2) (p^2) q (r^2)-3 (a^2) (b^2) (c^2) (p^2) q (r^2)-2 (b^4) (c^2) (p^2) q (r^2)-3 (a^2) (c^4) (p^2) q (r^2)-(b^2) (c^4) (p^2) q (r^2)+(c^6) (p^2) q (r^2)-2 (a^6) p (q^2) (r^2)+5 (a^4) (b^2) p (q^2) (r^2)-4 (a^2) (b^4) p (q^2) (r^2)+(b^6) p (q^2) (r^2)+2 (a^4) (c^2) p (q^2) (r^2)+(a^2) (b^2) (c^2) p (q^2) (r^2)-(b^4) (c^2) p (q^2) (r^2)-(a^2) (c^4) p (q^2) (r^2)-(b^2) (c^4) p (q^2) (r^2)+(c^6) p (q^2) (r^2)-(a^6) (q^3) (r^2)+2 (a^4) (b^2) (q^3) (r^2)-(a^2) (b^4) (q^3) (r^2)+2 (a^2) (b^2) (c^2) (q^3) (r^2)-(a^2) (c^4) (q^3) (r^2)+(a^4) (b^2) (p^2) (r^3)-(a^2) (b^4) (p^2) (r^3)+(b^4) (c^2) (p^2) (r^3)-(b^2) (c^4) (p^2) (r^3)+2 (a^4) (b^2) p q (r^3)-2 (a^2) (b^4) p q (r^3)+(a^4) (c^2) p q (r^3)+2 (a^2) (b^2) (c^2) p q (r^3)+(b^4) (c^2) p q (r^3)-2 (a^2) (c^4) p q (r^3)-2 (b^2) (c^4) p q (r^3)+(c^6) p q (r^3)+(a^4) (b^2) (q^2) (r^3)-(a^2) (b^4) (q^2) (r^3)+(a^4) (c^2) (q^2) (r^3)+2 (a^2) (b^2) (c^2) (q^2) (r^3)-(a^2) (c^4) (q^2) (r^3)) x z+((a^4) (c^4) (p^3) (q^2)-(a^2) (b^2) (c^4) (p^3) (q^2)-2 (a^2) (c^6) (p^3) (q^2)-(b^2) (c^6) (p^3) (q^2)+(c^8) (p^3) (q^2)+(a^4) (c^4) (p^2) (q^3)-(a^2) (b^2) (c^4) (p^2) (q^3)-(a^2) (c^6) (p^2) (q^3)-(a^8) (p^3) q r+3 (a^6) (b^2) (p^3) q r-3 (a^4) (b^4) (p^3) q r+(a^2) (b^6) (p^3) q r+3 (a^6) (c^2) (p^3) q r-2 (a^4) (b^2) (c^2) (p^3) q r-2 (a^2) (b^4) (c^2) (p^3) q r+(b^6) (c^2) (p^3) q r-3 (a^4) (c^4) (p^3) q r-2 (a^2) (b^2) (c^4) (p^3) q r-2 (b^4) (c^4) (p^3) q r+(a^2) (c^6) (p^3) q r+(b^2) (c^6) (p^3) q r-2 (a^8) (p^2) (q^2) r+6 (a^6) (b^2) (p^2) (q^2) r-6 (a^4) (b^4) (p^2) (q^2) r+2 (a^2) (b^6) (p^2) (q^2) r+6 (a^6) (c^2) (p^2) (q^2) r-5 (a^4) (b^2) (c^2) (p^2) (q^2) r-2 (a^2) (b^4) (c^2) (p^2) (q^2) r+(b^6) (c^2) (p^2) (q^2) r-5 (a^4) (c^4) (p^2) (q^2) r-2 (a^2) (b^2) (c^4) (p^2) (q^2) r-(b^4) (c^4) (p^2) (q^2) r-(b^2) (c^6) (p^2) (q^2) r+(c^8) (p^2) (q^2) r-(a^8) p (q^3) r+3 (a^6) (b^2) p (q^3) r-3 (a^4) (b^4) p (q^3) r+(a^2) (b^6) p (q^3) r+3 (a^6) (c^2) p (q^3) r-3 (a^4) (b^2) (c^2) p (q^3) r-(a^4) (c^4) p (q^3) r-(a^2) (c^6) p (q^3) r+(a^4) (b^4) (p^3) (r^2)-2 (a^2) (b^6) (p^3) (r^2)+(b^8) (p^3) (r^2)-(a^2) (b^4) (c^2) (p^3) (r^2)-(b^6) (c^2) (p^3) (r^2)-2 (a^8) (p^2) q (r^2)+6 (a^6) (b^2) (p^2) q (r^2)-5 (a^4) (b^4) (p^2) q (r^2)+(b^8) (p^2) q (r^2)+6 (a^6) (c^2) (p^2) q (r^2)-5 (a^4) (b^2) (c^2) (p^2) q (r^2)-2 (a^2) (b^4) (c^2) (p^2) q (r^2)-(b^6) (c^2) (p^2) q (r^2)-6 (a^4) (c^4) (p^2) q (r^2)-2 (a^2) (b^2) (c^4) (p^2) q (r^2)-(b^4) (c^4) (p^2) q (r^2)+2 (a^2) (c^6) (p^2) q (r^2)+(b^2) (c^6) (p^2) q (r^2)-3 (a^8) p (q^2) (r^2)+8 (a^6) (b^2) p (q^2) (r^2)-7 (a^4) (b^4) p (q^2) (r^2)+2 (a^2) (b^6) p (q^2) (r^2)+8 (a^6) (c^2) p (q^2) (r^2)-4 (a^4) (b^2) (c^2) p (q^2) (r^2)-2 (a^2) (b^4) (c^2) p (q^2) (r^2)-7 (a^4) (c^4) p (q^2) (r^2)-2 (a^2) (b^2) (c^4) p (q^2) (r^2)+2 (a^2) (c^6) p (q^2) (r^2)-(a^8) (q^3) (r^2)+2 (a^6) (b^2) (q^3) (r^2)-(a^4) (b^4) (q^3) (r^2)+3 (a^6) (c^2) (q^3) (r^2)-(a^4) (b^2) (c^2) (q^3) (r^2)-2 (a^4) (c^4) (q^3) (r^2)+(a^4) (b^4) (p^2) (r^3)-(a^2) (b^6) (p^2) (r^3)-(a^2) (b^4) (c^2) (p^2) (r^3)-(a^8) p q (r^3)+3 (a^6) (b^2) p q (r^3)-(a^4) (b^4) p q (r^3)-(a^2) (b^6) p q (r^3)+3 (a^6) (c^2) p q (r^3)-3 (a^4) (b^2) (c^2) p q (r^3)-3 (a^4) (c^4) p q (r^3)+(a^2) (c^6) p q (r^3)-(a^8) (q^2) (r^3)+3 (a^6) (b^2) (q^2) (r^3)-2 (a^4) (b^4) (q^2) (r^3)+2 (a^6) (c^2) (q^2) (r^3)-(a^4) (b^2) (c^2) (q^2) (r^3)-(a^4) (c^4) (q^2) (r^3)) y z+(b^2) ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) r (-(a^2) (c^2) p q+(b^2) (c^2) p q-(c^4) p q+(a^4) p r-2 (a^2) (b^2) p r+(b^4) p r-(a^2) (c^2) p r-(b^2) (c^2) p r-2 (a^2) (c^2) q r+(a^4) (r^2)-(a^2) (b^2) (r^2)-(a^2) (c^2) (r^2)) (z^2)),(b^2) ((c^2) p (-(a^2) (b^2) (p^2)+(b^4) (p^2)-(b^2) (c^2) (p^2)-(a^2) (b^2) p q+(b^4) p q-(a^2) (c^2) p q-2 (b^2) (c^2) p q+(c^4) p q-2 (a^2) (b^2) p r-(a^4) q r-(a^2) (b^2) q r+(a^2) (c^2) q r) ((c^2) (q^2)-(a^2) q r+(b^2) q r+(c^2) q r+(b^2) (r^2)) (x^2)+(c^2) (-(a^4) (c^2) (p^3) (q^2)+(b^4) (c^2) (p^3) (q^2)+(a^2) (c^4) (p^3) (q^2)-(b^2) (c^4) (p^3) (q^2)-(a^4) (c^2) (p^2) (q^3)+(b^4) (c^2) (p^2) (q^3)-2 (a^2) (c^4) (p^2) (q^3)-2 (b^2) (c^4) (p^2) (q^3)+(c^6) (p^2) (q^3)+(a^6) (p^3) q r-2 (a^4) (b^2) (p^3) q r+(a^2) (b^4) (p^3) q r-2 (a^4) (c^2) (p^3) q r+2 (a^2) (b^2) (c^2) (p^3) q r+2 (b^4) (c^2) (p^3) q r+(a^2) (c^4) (p^3) q r-2 (b^2) (c^4) (p^3) q r+(a^6) (p^2) (q^2) r-3 (a^4) (b^2) (p^2) (q^2) r+3 (a^2) (b^4) (p^2) (q^2) r-(b^6) (p^2) (q^2) r-(a^4) (c^2) (p^2) (q^2) r-3 (a^2) (b^2) (c^2) (p^2) (q^2) r+4 (b^4) (c^2) (p^2) (q^2) r-2 (a^2) (c^4) (p^2) (q^2) r-5 (b^2) (c^4) (p^2) (q^2) r+2 (c^6) (p^2) (q^2) r-(a^4) (b^2) p (q^3) r+2 (a^2) (b^4) p (q^3) r-(b^6) p (q^3) r-4 (a^4) (c^2) p (q^3) r-(a^2) (b^2) (c^2) p (q^3) r+3 (b^4) (c^2) p (q^3) r-(a^2) (c^4) p (q^3) r-3 (b^2) (c^4) p (q^3) r+(c^6) p (q^3) r-(a^4) (b^2) (p^3) (r^2)+(a^2) (b^4) (p^3) (r^2)+2 (a^2) (b^2) (c^2) (p^3) (r^2)+(b^4) (c^2) (p^3) (r^2)-(b^2) (c^4) (p^3) (r^2)+(a^6) (p^2) q (r^2)-(a^4) (b^2) (p^2) q (r^2)+2 (a^2) (b^4) (p^2) q (r^2)-2 (b^6) (p^2) q (r^2)-(a^4) (c^2) (p^2) q (r^2)+(a^2) (b^2) (c^2) (p^2) q (r^2)+5 (b^4) (c^2) (p^2) q (r^2)-(a^2) (c^4) (p^2) q (r^2)-4 (b^2) (c^4) (p^2) q (r^2)+(c^6) (p^2) q (r^2)+2 (a^6) p (q^2) (r^2)-3 (a^4) (b^2) p (q^2) (r^2)+3 (a^2) (b^4) p (q^2) (r^2)-2 (b^6) p (q^2) (r^2)-(a^4) (c^2) p (q^2) (r^2)+6 (b^4) (c^2) p (q^2) (r^2)-3 (a^2) (c^4) p (q^2) (r^2)-6 (b^2) (c^4) p (q^2) (r^2)+2 (c^6) p (q^2) (r^2)-(a^6) (q^3) (r^2)+(a^4) (b^2) (q^3) (r^2)-(a^4) (c^2) (q^3) (r^2)-(a^4) (b^2) (p^2) (r^3)-(b^6) (p^2) (r^3)+2 (a^2) (b^2) (c^2) (p^2) (r^3)+2 (b^4) (c^2) (p^2) (r^3)-(b^2) (c^4) (p^2) (r^3)+(a^2) (b^4) p q (r^3)-(b^6) p q (r^3)+(a^4) (c^2) p q (r^3)+(a^2) (b^2) (c^2) p q (r^3)+3 (b^4) (c^2) p q (r^3)-2 (a^2) (c^4) p q (r^3)-3 (b^2) (c^4) p q (r^3)+(c^6) p q (r^3)+(a^6) (q^2) (r^3)+(a^4) (b^2) (q^2) (r^3)-(a^4) (c^2) (q^2) (r^3)) x y-(a^2) (c^2) q ((a^2) p q-(b^2) p q-(c^2) p q+(a^2) (q^2)-(b^2) (q^2)+(c^2) (q^2)-2 (b^2) p r-(a^2) q r-(b^2) q r+(c^2) q r) ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) (y^2)+(-(a^2) (b^2) (c^4) (p^3) (q^2)+(b^4) (c^4) (p^3) (q^2)-(b^2) (c^6) (p^3) (q^2)-(a^2) (b^2) (c^4) (p^2) (q^3)+(b^4) (c^4) (p^2) (q^3)-(a^2) (c^6) (p^2) (q^3)-2 (b^2) (c^6) (p^2) (q^3)+(c^8) (p^2) (q^3)+(a^6) (b^2) (p^3) q r-3 (a^4) (b^4) (p^3) q r+3 (a^2) (b^6) (p^3) q r-(b^8) (p^3) q r-3 (a^2) (b^4) (c^2) (p^3) q r+3 (b^6) (c^2) (p^3) q r-(b^4) (c^4) (p^3) q r-(b^2) (c^6) (p^3) q r+2 (a^6) (b^2) (p^2) (q^2) r-6 (a^4) (b^4) (p^2) (q^2) r+6 (a^2) (b^6) (p^2) (q^2) r-2 (b^8) (p^2) (q^2) r+(a^6) (c^2) (p^2) (q^2) r-2 (a^4) (b^2) (c^2) (p^2) (q^2) r-5 (a^2) (b^4) (c^2) (p^2) (q^2) r+6 (b^6) (c^2) (p^2) (q^2) r-(a^4) (c^4) (p^2) (q^2) r-2 (a^2) (b^2) (c^4) (p^2) (q^2) r-5 (b^4) (c^4) (p^2) (q^2) r-(a^2) (c^6) (p^2) (q^2) r+(c^8) (p^2) (q^2) r+(a^6) (b^2) p (q^3) r-3 (a^4) (b^4) p (q^3) r+3 (a^2) (b^6) p (q^3) r-(b^8) p (q^3) r+(a^6) (c^2) p (q^3) r-2 (a^4) (b^2) (c^2) p (q^3) r-2 (a^2) (b^4) (c^2) p (q^3) r+3 (b^6) (c^2) p (q^3) r-2 (a^4) (c^4) p (q^3) r-2 (a^2) (b^2) (c^4) p (q^3) r-3 (b^4) (c^4) p (q^3) r+(a^2) (c^6) p (q^3) r+(b^2) (c^6) p (q^3) r-(a^4) (b^4) (p^3) (r^2)+2 (a^2) (b^6) (p^3) (r^2)-(b^8) (p^3) (r^2)-(a^2) (b^4) (c^2) (p^3) (r^2)+3 (b^6) (c^2) (p^3) (r^2)-2 (b^4) (c^4) (p^3) (r^2)+2 (a^6) (b^2) (p^2) q (r^2)-7 (a^4) (b^4) (p^2) q (r^2)+8 (a^2) (b^6) (p^2) q (r^2)-3 (b^8) (p^2) q (r^2)-2 (a^4) (b^2) (c^2) (p^2) q (r^2)-4 (a^2) (b^4) (c^2) (p^2) q (r^2)+8 (b^6) (c^2) (p^2) q (r^2)-2 (a^2) (b^2) (c^4) (p^2) q (r^2)-7 (b^4) (c^4) (p^2) q (r^2)+2 (b^2) (c^6) (p^2) q (r^2)+(a^8) p (q^2) (r^2)-5 (a^4) (b^4) p (q^2) (r^2)+6 (a^2) (b^6) p (q^2) (r^2)-2 (b^8) p (q^2) (r^2)-(a^6) (c^2) p (q^2) (r^2)-2 (a^4) (b^2) (c^2) p (q^2) (r^2)-5 (a^2) (b^4) (c^2) p (q^2) (r^2)+6 (b^6) (c^2) p (q^2) (r^2)-(a^4) (c^4) p (q^2) (r^2)-2 (a^2) (b^2) (c^4) p (q^2) (r^2)-6 (b^4) (c^4) p (q^2) (r^2)+(a^2) (c^6) p (q^2) (r^2)+2 (b^2) (c^6) p (q^2) (r^2)+(a^8) (q^3) (r^2)-2 (a^6) (b^2) (q^3) (r^2)+(a^4) (b^4) (q^3) (r^2)-(a^6) (c^2) (q^3) (r^2)-(a^4) (b^2) (c^2) (q^3) (r^2)-2 (a^4) (b^4) (p^2) (r^3)+3 (a^2) (b^6) (p^2) (r^3)-(b^8) (p^2) (r^3)-(a^2) (b^4) (c^2) (p^2) (r^3)+2 (b^6) (c^2) (p^2) (r^3)-(b^4) (c^4) (p^2) (r^3)-(a^6) (b^2) p q (r^3)-(a^4) (b^4) p q (r^3)+3 (a^2) (b^6) p q (r^3)-(b^8) p q (r^3)-3 (a^2) (b^4) (c^2) p q (r^3)+3 (b^6) (c^2) p q (r^3)-3 (b^4) (c^4) p q (r^3)+(b^2) (c^6) p q (r^3)-(a^6) (b^2) (q^2) (r^3)+(a^4) (b^4) (q^2) (r^3)-(a^4) (b^2) (c^2) (q^2) (r^3)) x z+(a^2) (-(a^2) (c^4) (p^3) (q^2)+(b^2) (c^4) (p^3) (q^2)+(c^6) (p^3) (q^2)-(a^2) (c^4) (p^2) (q^3)+(b^2) (c^4) (p^2) (q^3)-(c^6) (p^2) (q^3)+(a^6) (p^3) q r-3 (a^4) (b^2) (p^3) q r+3 (a^2) (b^4) (p^3) q r-(b^6) (p^3) q r-2 (a^4) (c^2) (p^3) q r+(a^2) (b^2) (c^2) (p^3) q r+(b^4) (c^2) (p^3) q r+(a^2) (c^4) (p^3) q r+2 (a^6) (p^2) (q^2) r-6 (a^4) (b^2) (p^2) (q^2) r+6 (a^2) (b^4) (p^2) (q^2) r-2 (b^6) (p^2) (q^2) r-3 (a^4) (c^2) (p^2) (q^2) r+3 (b^4) (c^2) (p^2) (q^2) r-(a^2) (c^4) (p^2) (q^2) r-3 (b^2) (c^4) (p^2) (q^2) r+2 (c^6) (p^2) (q^2) r+(a^6) p (q^3) r-3 (a^4) (b^2) p (q^3) r+3 (a^2) (b^4) p (q^3) r-(b^6) p (q^3) r-(a^4) (c^2) p (q^3) r-(a^2) (b^2) (c^2) p (q^3) r+2 (b^4) (c^2) p (q^3) r-4 (a^2) (c^4) p (q^3) r-(b^2) (c^4) p (q^3) r-(a^4) (b^2) (p^3) (r^2)+2 (a^2) (b^4) (p^3) (r^2)-(b^6) (p^3) (r^2)+2 (a^2) (b^2) (c^2) (p^3) (r^2)-(b^2) (c^4) (p^3) (r^2)+(a^6) (p^2) q (r^2)-4 (a^4) (b^2) (p^2) q (r^2)+5 (a^2) (b^4) (p^2) q (r^2)-2 (b^6) (p^2) q (r^2)-(a^4) (c^2) (p^2) q (r^2)+(a^2) (b^2) (c^2) (p^2) q (r^2)+2 (b^4) (c^2) (p^2) q (r^2)-(a^2) (c^4) (p^2) q (r^2)-(b^2) (c^4) (p^2) q (r^2)+(c^6) (p^2) q (r^2)+2 (a^6) p (q^2) (r^2)-5 (a^4) (b^2) p (q^2) (r^2)+4 (a^2) (b^4) p (q^2) (r^2)-(b^6) p (q^2) (r^2)-2 (a^4) (c^2) p (q^2) (r^2)-3 (a^2) (b^2) (c^2) p (q^2) (r^2)+3 (b^4) (c^2) p (q^2) (r^2)-(a^2) (c^4) p (q^2) (r^2)-3 (b^2) (c^4) p (q^2) (r^2)+(c^6) p (q^2) (r^2)+(a^6) (q^3) (r^2)-2 (a^4) (b^2) (q^3) (r^2)+(a^2) (b^4) (q^3) (r^2)-2 (a^4) (c^2) (q^3) (r^2)-(a^2) (c^4) (q^3) (r^2)-(a^4) (b^2) (p^2) (r^3)+(a^2) (b^4) (p^2) (r^3)+2 (a^2) (b^2) (c^2) (p^2) (r^3)+(b^4) (c^2) (p^2) (r^3)-(b^2) (c^4) (p^2) (r^3)-2 (a^4) (b^2) p q (r^3)+2 (a^2) (b^4) p q (r^3)+(a^4) (c^2) p q (r^3)+2 (a^2) (b^2) (c^2) p q (r^3)+(b^4) (c^2) p q (r^3)-2 (a^2) (c^4) p q (r^3)-2 (b^2) (c^4) p q (r^3)+(c^6) p q (r^3)-(a^4) (b^2) (q^2) (r^3)+(a^2) (b^4) (q^2) (r^3)+(a^4) (c^2) (q^2) (r^3)-(a^2) (c^4) (q^2) (r^3)) y z+(a^2) ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) r ((a^2) (c^2) p q-(b^2) (c^2) p q-(c^4) p q-2 (b^2) (c^2) p r+(a^4) q r-2 (a^2) (b^2) q r+(b^4) q r-(a^2) (c^2) q r-(b^2) (c^2) q r-(a^2) (b^2) (r^2)+(b^4) (r^2)-(b^2) (c^2) (r^2)) (z^2)),(c^2) ((b^2) p (-(a^2) (c^2) (p^2)-(b^2) (c^2) (p^2)+(c^4) (p^2)-2 (a^2) (c^2) p q-(a^2) (b^2) p r+(b^4) p r-(a^2) (c^2) p r-2 (b^2) (c^2) p r+(c^4) p r-(a^4) q r+(a^2) (b^2) q r-(a^2) (c^2) q r) ((c^2) (q^2)-(a^2) q r+(b^2) q r+(c^2) q r+(b^2) (r^2)) (x^2)+(-(a^4) (c^4) (p^3) (q^2)-(a^2) (b^2) (c^4) (p^3) (q^2)-2 (b^4) (c^4) (p^3) (q^2)+2 (a^2) (c^6) (p^3) (q^2)+3 (b^2) (c^6) (p^3) (q^2)-(c^8) (p^3) (q^2)-2 (a^4) (c^4) (p^2) (q^3)-(a^2) (b^2) (c^4) (p^2) (q^3)-(b^4) (c^4) (p^2) (q^3)+3 (a^2) (c^6) (p^2) (q^3)+2 (b^2) (c^6) (p^2) (q^3)-(c^8) (p^2) (q^3)+(a^6) (c^2) (p^3) q r-(b^6) (c^2) (p^3) q r-3 (a^4) (c^4) (p^3) q r-3 (a^2) (b^2) (c^4) (p^3) q r-(b^4) (c^4) (p^3) q r+3 (a^2) (c^6) (p^3) q r+3 (b^2) (c^6) (p^3) q r-(c^8) (p^3) q r+2 (a^6) (c^2) (p^2) (q^2) r-2 (a^4) (b^2) (c^2) (p^2) (q^2) r-2 (a^2) (b^4) (c^2) (p^2) (q^2) r+2 (b^6) (c^2) (p^2) (q^2) r-7 (a^4) (c^4) (p^2) (q^2) r-4 (a^2) (b^2) (c^4) (p^2) (q^2) r-7 (b^4) (c^4) (p^2) (q^2) r+8 (a^2) (c^6) (p^2) (q^2) r+8 (b^2) (c^6) (p^2) (q^2) r-3 (c^8) (p^2) (q^2) r-(a^6) (c^2) p (q^3) r+(b^6) (c^2) p (q^3) r-(a^4) (c^4) p (q^3) r-3 (a^2) (b^2) (c^4) p (q^3) r-3 (b^4) (c^4) p (q^3) r+3 (a^2) (c^6) p (q^3) r+3 (b^2) (c^6) p (q^3) r-(c^8) p (q^3) r-(a^2) (b^4) (c^2) (p^3) (r^2)-(b^6) (c^2) (p^3) (r^2)+(b^4) (c^4) (p^3) (r^2)+(a^6) (b^2) (p^2) q (r^2)-(a^4) (b^4) (p^2) q (r^2)-(a^2) (b^6) (p^2) q (r^2)+(b^8) (p^2) q (r^2)+2 (a^6) (c^2) (p^2) q (r^2)-2 (a^4) (b^2) (c^2) (p^2) q (r^2)-2 (a^2) (b^4) (c^2) (p^2) q (r^2)-6 (a^4) (c^4) (p^2) q (r^2)-5 (a^2) (b^2) (c^4) (p^2) q (r^2)-5 (b^4) (c^4) (p^2) q (r^2)+6 (a^2) (c^6) (p^2) q (r^2)+6 (b^2) (c^6) (p^2) q (r^2)-2 (c^8) (p^2) q (r^2)+(a^8) p (q^2) (r^2)-(a^6) (b^2) p (q^2) (r^2)-(a^4) (b^4) p (q^2) (r^2)+(a^2) (b^6) p (q^2) (r^2)-2 (a^4) (b^2) (c^2) p (q^2) (r^2)-2 (a^2) (b^4) (c^2) p (q^2) (r^2)+2 (b^6) (c^2) p (q^2) (r^2)-5 (a^4) (c^4) p (q^2) (r^2)-5 (a^2) (b^2) (c^4) p (q^2) (r^2)-6 (b^4) (c^4) p (q^2) (r^2)+6 (a^2) (c^6) p (q^2) (r^2)+6 (b^2) (c^6) p (q^2) (r^2)-2 (c^8) p (q^2) (r^2)-(a^6) (c^2) (q^3) (r^2)-(a^4) (b^2) (c^2) (q^3) (r^2)+(a^4) (c^4) (q^3) (r^2)-(a^2) (b^6) (p^2) (r^3)+(b^8) (p^2) (r^3)-(a^2) (b^4) (c^2) (p^2) (r^3)-2 (b^6) (c^2) (p^2) (r^3)+(b^4) (c^4) (p^2) (r^3)+(a^6) (b^2) p q (r^3)-2 (a^4) (b^4) p q (r^3)+(a^2) (b^6) p q (r^3)+(a^6) (c^2) p q (r^3)-2 (a^4) (b^2) (c^2) p q (r^3)-2 (a^2) (b^4) (c^2) p q (r^3)+(b^6) (c^2) p q (r^3)-3 (a^4) (c^4) p q (r^3)-2 (a^2) (b^2) (c^4) p q (r^3)-3 (b^4) (c^4) p q (r^3)+3 (a^2) (c^6) p q (r^3)+3 (b^2) (c^6) p q (r^3)-(c^8) p q (r^3)+(a^8) (q^2) (r^3)-(a^6) (b^2) (q^2) (r^3)-2 (a^6) (c^2) (q^2) (r^3)-(a^4) (b^2) (c^2) (q^2) (r^3)+(a^4) (c^4) (q^2) (r^3)) x y+(a^2) q (-2 (b^2) (c^2) p q-(a^2) (c^2) (q^2)-(b^2) (c^2) (q^2)+(c^4) (q^2)+(a^2) (b^2) p r-(b^4) p r-(b^2) (c^2) p r+(a^4) q r-(a^2) (b^2) q r-2 (a^2) (c^2) q r-(b^2) (c^2) q r+(c^4) q r) ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) (y^2)+(b^2) (-(a^4) (c^2) (p^3) (q^2)+2 (a^2) (b^2) (c^2) (p^3) (q^2)-(b^4) (c^2) (p^3) (q^2)+(a^2) (c^4) (p^3) (q^2)+(b^2) (c^4) (p^3) (q^2)-(a^4) (c^2) (p^2) (q^3)+2 (a^2) (b^2) (c^2) (p^2) (q^3)-(b^4) (c^2) (p^2) (q^3)+2 (b^2) (c^4) (p^2) (q^3)-(c^6) (p^2) (q^3)+(a^6) (p^3) q r-2 (a^4) (b^2) (p^3) q r+(a^2) (b^4) (p^3) q r-2 (a^4) (c^2) (p^3) q r+2 (a^2) (b^2) (c^2) (p^3) q r-2 (b^4) (c^2) (p^3) q r+(a^2) (c^4) (p^3) q r+2 (b^2) (c^4) (p^3) q r+(a^6) (p^2) (q^2) r-(a^4) (b^2) (p^2) (q^2) r-(a^2) (b^4) (p^2) (q^2) r+(b^6) (p^2) (q^2) r-(a^4) (c^2) (p^2) (q^2) r+(a^2) (b^2) (c^2) (p^2) (q^2) r-4 (b^4) (c^2) (p^2) (q^2) r+2 (a^2) (c^4) (p^2) (q^2) r+5 (b^2) (c^4) (p^2) (q^2) r-2 (c^6) (p^2) (q^2) r+(a^4) (b^2) p (q^3) r-2 (a^2) (b^4) p (q^3) r+(b^6) p (q^3) r+(a^2) (b^2) (c^2) p (q^3) r-3 (b^4) (c^2) p (q^3) r+(a^2) (c^4) p (q^3) r+3 (b^2) (c^4) p (q^3) r-(c^6) p (q^3) r-(a^4) (b^2) (p^3) (r^2)+(a^2) (b^4) (p^3) (r^2)-(b^4) (c^2) (p^3) (r^2)+(b^2) (c^4) (p^3) (r^2)+(a^6) (p^2) q (r^2)-(a^4) (b^2) (p^2) q (r^2)-2 (a^2) (b^4) (p^2) q (r^2)+2 (b^6) (p^2) q (r^2)-3 (a^4) (c^2) (p^2) q (r^2)-3 (a^2) (b^2) (c^2) (p^2) q (r^2)-5 (b^4) (c^2) (p^2) q (r^2)+3 (a^2) (c^4) (p^2) q (r^2)+4 (b^2) (c^4) (p^2) q (r^2)-(c^6) (p^2) q (r^2)+2 (a^6) p (q^2) (r^2)-(a^4) (b^2) p (q^2) (r^2)-3 (a^2) (b^4) p (q^2) (r^2)+2 (b^6) p (q^2) (r^2)-3 (a^4) (c^2) p (q^2) (r^2)-6 (b^4) (c^2) p (q^2) (r^2)+3 (a^2) (c^4) p (q^2) (r^2)+6 (b^2) (c^4) p (q^2) (r^2)-2 (c^6) p (q^2) (r^2)+(a^6) (q^3) (r^2)-(a^4) (b^2) (q^3) (r^2)+(a^4) (c^2) (q^3) (r^2)-(a^4) (b^2) (p^2) (r^3)-2 (a^2) (b^4) (p^2) (r^3)+(b^6) (p^2) (r^3)-2 (b^4) (c^2) (p^2) (r^3)+(b^2) (c^4) (p^2) (r^3)-4 (a^4) (b^2) p q (r^3)-(a^2) (b^4) p q (r^3)+(b^6) p q (r^3)-(a^4) (c^2) p q (r^3)-(a^2) (b^2) (c^2) p q (r^3)-3 (b^4) (c^2) p q (r^3)+2 (a^2) (c^4) p q (r^3)+3 (b^2) (c^4) p q (r^3)-(c^6) p q (r^3)-(a^6) (q^2) (r^3)-(a^4) (b^2) (q^2) (r^3)+(a^4) (c^2) (q^2) (r^3)) x z+(a^2) (-(a^4) (c^2) (p^3) (q^2)+2 (a^2) (b^2) (c^2) (p^3) (q^2)-(b^4) (c^2) (p^3) (q^2)+2 (a^2) (c^4) (p^3) (q^2)-(c^6) (p^3) (q^2)-(a^4) (c^2) (p^2) (q^3)+2 (a^2) (b^2) (c^2) (p^2) (q^3)-(b^4) (c^2) (p^2) (q^3)+(a^2) (c^4) (p^2) (q^3)+(b^2) (c^4) (p^2) (q^3)+(a^6) (p^3) q r-2 (a^4) (b^2) (p^3) q r+(a^2) (b^4) (p^3) q r-3 (a^4) (c^2) (p^3) q r+(a^2) (b^2) (c^2) (p^3) q r+3 (a^2) (c^4) (p^3) q r+(b^2) (c^4) (p^3) q r-(c^6) (p^3) q r+(a^6) (p^2) (q^2) r-(a^4) (b^2) (p^2) (q^2) r-(a^2) (b^4) (p^2) (q^2) r+(b^6) (p^2) (q^2) r-4 (a^4) (c^2) (p^2) (q^2) r+(a^2) (b^2) (c^2) (p^2) (q^2) r-(b^4) (c^2) (p^2) (q^2) r+5 (a^2) (c^4) (p^2) (q^2) r+2 (b^2) (c^4) (p^2) (q^2) r-2 (c^6) (p^2) (q^2) r+(a^4) (b^2) p (q^3) r-2 (a^2) (b^4) p (q^3) r+(b^6) p (q^3) r-2 (a^4) (c^2) p (q^3) r+2 (a^2) (b^2) (c^2) p (q^3) r-2 (b^4) (c^2) p (q^3) r+2 (a^2) (c^4) p (q^3) r+(b^2) (c^4) p (q^3) r-(a^2) (b^4) (p^3) (r^2)+(b^6) (p^3) (r^2)+(b^4) (c^2) (p^3) (r^2)+2 (a^6) (p^2) q (r^2)-3 (a^4) (b^2) (p^2) q (r^2)-(a^2) (b^4) (p^2) q (r^2)+2 (b^6) (p^2) q (r^2)-6 (a^4) (c^2) (p^2) q (r^2)-3 (b^4) (c^2) (p^2) q (r^2)+6 (a^2) (c^4) (p^2) q (r^2)+3 (b^2) (c^4) (p^2) q (r^2)-2 (c^6) (p^2) q (r^2)+2 (a^6) p (q^2) (r^2)-2 (a^4) (b^2) p (q^2) (r^2)-(a^2) (b^4) p (q^2) (r^2)+(b^6) p (q^2) (r^2)-5 (a^4) (c^2) p (q^2) (r^2)-3 (a^2) (b^2) (c^2) p (q^2) (r^2)-3 (b^4) (c^2) p (q^2) (r^2)+4 (a^2) (c^4) p (q^2) (r^2)+3 (b^2) (c^4) p (q^2) (r^2)-(c^6) p (q^2) (r^2)+(a^4) (b^2) (q^3) (r^2)-(a^2) (b^4) (q^3) (r^2)-(a^4) (c^2) (q^3) (r^2)+(a^2) (c^4) (q^3) (r^2)-(a^2) (b^4) (p^2) (r^3)-(b^6) (p^2) (r^3)+(b^4) (c^2) (p^2) (r^3)+(a^6) p q (r^3)-(a^4) (b^2) p q (r^3)-4 (a^2) (b^4) p q (r^3)-3 (a^4) (c^2) p q (r^3)-(a^2) (b^2) (c^2) p q (r^3)-(b^4) (c^2) p q (r^3)+3 (a^2) (c^4) p q (r^3)+2 (b^2) (c^4) p q (r^3)-(c^6) p q (r^3)+(a^6) (q^2) (r^3)-2 (a^4) (b^2) (q^2) (r^3)-(a^2) (b^4) (q^2) (r^3)-2 (a^4) (c^2) (q^2) (r^3)+(a^2) (c^4) (q^2) (r^3)) y z-(a^2) (b^2) ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) r (-2 (c^2) p q+(a^2) p r-(b^2) p r-(c^2) p r-(a^2) q r+(b^2) q r-(c^2) q r+(a^2) (r^2)+(b^2) (r^2)-(c^2) (r^2)) (z^2))}]

QA-Tf5:  QA-5th point Tangent Involution Center

QATf5[{x_,y_,z_}]:={x (q r (x^2)-p r x y-p q x z-p q y z-p r y z),y (-q r x y+p r (y^2)-p q x z-q r x z-p q y z),z (-p r x y-q r x y-q r x z-p r y z+p q (z^2))};

QA-Tf6:  Quang Duong's Transformation

QATf6[{x_,y_,z_}]:={-(a^4) (p^2) (x^2)+(b^4) (p^2) (x^2)-2 (b^2) (c^2) (p^2) (x^2)+(c^4) (p^2) (x^2)+(a^4) (p^2) x y+(a^2) (b^2) (p^2) x y-2 (b^4) (p^2) x y-2 (a^2) (c^2) (p^2) x y+(b^2) (c^2) (p^2) x y+(c^4) (p^2) x y+(a^4) (q^2) x y-(a^2) (b^2) (q^2) x y+(a^2) (c^2) (q^2) x y-(a^2) (b^2) (p^2) (y^2)+(b^4) (p^2) (y^2)+(b^2) (c^2) (p^2) (y^2)-(a^4) (q^2) (y^2)+(a^2) (b^2) (q^2) (y^2)+(a^2) (c^2) (q^2) (y^2)+(a^4) (p^2) x z-2 (a^2) (b^2) (p^2) x z+(b^4) (p^2) x z+(a^2) (c^2) (p^2) x z+(b^2) (c^2) (p^2) x z-2 (c^4) (p^2) x z+(a^4) (r^2) x z+(a^2) (b^2) (r^2) x z-(a^2) (c^2) (r^2) x z-(a^4) (p^2) y z+2 (a^2) (b^2) (p^2) y z-(b^4) (p^2) y z+2 (a^2) (c^2) (p^2) y z-2 (b^2) (c^2) (p^2) y z-(c^4) (p^2) y z-2 (a^2) (c^2) (q^2) y z-2 (a^2) (b^2) (r^2) y z-(a^2) (c^2) (p^2) (z^2)+(b^2) (c^2) (p^2) (z^2)+(c^4) (p^2) (z^2)-(a^4) (r^2) (z^2)+(a^2) (b^2) (r^2) (z^2)+(a^2) (c^2) (r^2) (z^2),(a^2) (b^2) (p^2) (x^2)-(b^4) (p^2) (x^2)+(b^2) (c^2) (p^2) (x^2)+(a^4) (q^2) (x^2)-(a^2) (b^2) (q^2) (x^2)+(a^2) (c^2) (q^2) (x^2)-(a^2) (b^2) (p^2) x y+(b^4) (p^2) x y+(b^2) (c^2) (p^2) x y-2 (a^4) (q^2) x y+(a^2) (b^2) (q^2) x y+(b^4) (q^2) x y+(a^2) (c^2) (q^2) x y-2 (b^2) (c^2) (q^2) x y+(c^4) (q^2) x y+(a^4) (q^2) (y^2)-(b^4) (q^2) (y^2)-2 (a^2) (c^2) (q^2) (y^2)+(c^4) (q^2) (y^2)-2 (b^2) (c^2) (p^2) x z-(a^4) (q^2) x z+2 (a^2) (b^2) (q^2) x z-(b^4) (q^2) x z-2 (a^2) (c^2) (q^2) x z+2 (b^2) (c^2) (q^2) x z-(c^4) (q^2) x z-2 (a^2) (b^2) (r^2) x z+(a^4) (q^2) y z-2 (a^2) (b^2) (q^2) y z+(b^4) (q^2) y z+(a^2) (c^2) (q^2) y z+(b^2) (c^2) (q^2) y z-2 (c^4) (q^2) y z+(a^2) (b^2) (r^2) y z+(b^4) (r^2) y z-(b^2) (c^2) (r^2) y z+(a^2) (c^2) (q^2) (z^2)-(b^2) (c^2) (q^2) (z^2)+(c^4) (q^2) (z^2)+(a^2) (b^2) (r^2) (z^2)-(b^4) (r^2) (z^2)+(b^2) (c^2) (r^2) (z^2),(a^2) (c^2) (p^2) (x^2)+(b^2) (c^2) (p^2) (x^2)-(c^4) (p^2) (x^2)+(a^4) (r^2) (x^2)+(a^2) (b^2) (r^2) (x^2)-(a^2) (c^2) (r^2) (x^2)-2 (b^2) (c^2) (p^2) x y-2 (a^2) (c^2) (q^2) x y-(a^4) (r^2) x y-2 (a^2) (b^2) (r^2) x y-(b^4) (r^2) x y+2 (a^2) (c^2) (r^2) x y+2 (b^2) (c^2) (r^2) x y-(c^4) (r^2) x y+(a^2) (c^2) (q^2) (y^2)+(b^2) (c^2) (q^2) (y^2)-(c^4) (q^2) (y^2)+(a^2) (b^2) (r^2) (y^2)+(b^4) (r^2) (y^2)-(b^2) (c^2) (r^2) (y^2)-(a^2) (c^2) (p^2) x z+(b^2) (c^2) (p^2) x z+(c^4) (p^2) x z-2 (a^4) (r^2) x z+(a^2) (b^2) (r^2) x z+(b^4) (r^2) x z+(a^2) (c^2) (r^2) x z-2 (b^2) (c^2) (r^2) x z+(c^4) (r^2) x z+(a^2) (c^2) (q^2) y z-(b^2) (c^2) (q^2) y z+(c^4) (q^2) y z+(a^4) (r^2) y z+(a^2) (b^2) (r^2) y z-2 (b^4) (r^2) y z-2 (a^2) (c^2) (r^2) y z+(b^2) (c^2) (r^2) y z+(c^4) (r^2) y z+(a^4) (r^2) (z^2)-2 (a^2) (b^2) (r^2) (z^2)+(b^4) (r^2) (z^2)-(c^4) (r^2) (z^2)}

QA-Tf7:  QA-Trilinear Pole

QATf7[{x_,y_,z_}]:={-y z (2 p x+q y+r z),-x z (p x+2 q y+r z),-x y (p x+q y+2 r z)}

QA-Tf8:  QA-Orthopolar Line

QATf8[{x_,y_,z_}]:={2 (a^6) p q (x^3)-4 (a^4) (b^2) p q (x^3)+2 (a^2) (b^4) p q (x^3)-2 (a^2) (c^4) p q (x^3)-2 (a^6) p r (x^3)+2 (a^2) (b^4) p r (x^3)+4 (a^4) (c^2) p r (x^3)-2 (a^2) (c^4) p r (x^3)-4 (a^6) p q (x^2) y+6 (a^4) (b^2) p q (x^2) y-2 (b^6) p q (x^2) y+6 (a^4) (c^2) p q (x^2) y-8 (a^2) (b^2) (c^2) p q (x^2) y+2 (b^4) (c^2) p q (x^2) y+2 (b^2) (c^4) p q (x^2) y-2 (c^6) p q (x^2) y+(a^6) p r (x^2) y+7 (a^4) (b^2) p r (x^2) y-5 (a^2) (b^4) p r (x^2) y-3 (b^6) p r (x^2) y-3 (a^4) (c^2) p r (x^2) y-6 (a^2) (b^2) (c^2) p r (x^2) y+5 (b^4) (c^2) p r (x^2) y+3 (a^2) (c^4) p r (x^2) y-(b^2) (c^4) p r (x^2) y-(c^6) p r (x^2) y-2 (a^6) q r (x^2) y+4 (a^4) (b^2) q r (x^2) y-2 (a^2) (b^4) q r (x^2) y+4 (a^4) (c^2) q r (x^2) y+4 (a^2) (b^2) (c^2) q r (x^2) y-2 (a^2) (c^4) q r (x^2) y+2 (a^6) p q x (y^2)-6 (a^2) (b^4) p q x (y^2)+4 (b^6) p q x (y^2)-6 (a^4) (c^2) p q x (y^2)+4 (a^2) (b^2) (c^2) p q x (y^2)+2 (b^4) (c^2) p q x (y^2)+6 (a^2) (c^4) p q x (y^2)-4 (b^2) (c^4) p q x (y^2)-2 (c^6) p q x (y^2)-4 (a^4) (b^2) p r x (y^2)-4 (a^2) (b^4) p r x (y^2)+8 (b^6) p r x (y^2)+8 (a^2) (b^2) (c^2) p r x (y^2)-4 (b^4) (c^2) p r x (y^2)-4 (b^2) (c^4) p r x (y^2)+(a^6) q r x (y^2)-(a^4) (b^2) q r x (y^2)-(a^2) (b^4) q r x (y^2)+(b^6) q r x (y^2)-3 (a^4) (c^2) q r x (y^2)-2 (a^2) (b^2) (c^2) q r x (y^2)-3 (b^4) (c^2) q r x (y^2)+3 (a^2) (c^4) q r x (y^2)+3 (b^2) (c^4) q r x (y^2)-(c^6) q r x (y^2)-2 (a^4) (b^2) p q (y^3)+4 (a^2) (b^4) p q (y^3)-2 (b^6) p q (y^3)+4 (a^2) (b^2) (c^2) p q (y^3)-4 (b^4) (c^2) p q (y^3)-2 (b^2) (c^4) p q (y^3)+4 (a^2) (b^4) p r (y^3)-4 (b^6) p r (y^3)-4 (b^4) (c^2) p r (y^3)-(a^6) p q (x^2) z+3 (a^4) (b^2) p q (x^2) z-3 (a^2) (b^4) p q (x^2) z+(b^6) p q (x^2) z-7 (a^4) (c^2) p q (x^2) z+6 (a^2) (b^2) (c^2) p q (x^2) z+(b^4) (c^2) p q (x^2) z+5 (a^2) (c^4) p q (x^2) z-5 (b^2) (c^4) p q (x^2) z+3 (c^6) p q (x^2) z+4 (a^6) p r (x^2) z-6 (a^4) (b^2) p r (x^2) z+2 (b^6) p r (x^2) z-6 (a^4) (c^2) p r (x^2) z+8 (a^2) (b^2) (c^2) p r (x^2) z-2 (b^4) (c^2) p r (x^2) z-2 (b^2) (c^4) p r (x^2) z+2 (c^6) p r (x^2) z+2 (a^6) q r (x^2) z-4 (a^4) (b^2) q r (x^2) z+2 (a^2) (b^4) q r (x^2) z-4 (a^4) (c^2) q r (x^2) z-4 (a^2) (b^2) (c^2) q r (x^2) z+2 (a^2) (c^4) q r (x^2) z+2 (a^6) p q x y z-6 (a^4) (b^2) p q x y z+6 (a^2) (b^4) p q x y z-2 (b^6) p q x y z+4 (a^4) (c^2) p q x y z+8 (a^2) (b^2) (c^2) p q x y z-12 (b^4) (c^2) p q x y z-14 (a^2) (c^4) p q x y z+6 (b^2) (c^4) p q x y z+8 (c^6) p q x y z-2 (a^6) p r x y z-4 (a^4) (b^2) p r x y z+14 (a^2) (b^4) p r x y z-8 (b^6) p r x y z+6 (a^4) (c^2) p r x y z-8 (a^2) (b^2) (c^2) p r x y z-6 (b^4) (c^2) p r x y z-6 (a^2) (c^4) p r x y z+12 (b^2) (c^4) p r x y z+2 (c^6) p r x y z-2 (a^4) (b^2) q r x y z+4 (a^2) (b^4) q r x y z-2 (b^6) q r x y z+2 (a^4) (c^2) q r x y z+6 (b^4) (c^2) q r x y z-4 (a^2) (c^4) q r x y z-6 (b^2) (c^4) q r x y z+2 (c^6) q r x y z-(a^6) p q (y^2) z+3 (a^4) (b^2) p q (y^2) z-3 (a^2) (b^4) p q (y^2) z+(b^6) p q (y^2) z+3 (a^4) (c^2) p q (y^2) z-14 (a^2) (b^2) (c^2) p q (y^2) z+11 (b^4) (c^2) p q (y^2) z-3 (a^2) (c^4) p q (y^2) z+11 (b^2) (c^4) p q (y^2) z+(c^6) p q (y^2) z+4 (a^4) (b^2) p r (y^2) z-8 (a^2) (b^4) p r (y^2) z+4 (b^6) p r (y^2) z-8 (a^2) (b^2) (c^2) p r (y^2) z+16 (b^4) (c^2) p r (y^2) z+4 (b^2) (c^4) p r (y^2) z+4 (a^4) (c^2) p q x (z^2)-8 (a^2) (b^2) (c^2) p q x (z^2)+4 (b^4) (c^2) p q x (z^2)+4 (a^2) (c^4) p q x (z^2)+4 (b^2) (c^4) p q x (z^2)-8 (c^6) p q x (z^2)-2 (a^6) p r x (z^2)+6 (a^4) (b^2) p r x (z^2)-6 (a^2) (b^4) p r x (z^2)+2 (b^6) p r x (z^2)-4 (a^2) (b^2) (c^2) p r x (z^2)+4 (b^4) (c^2) p r x (z^2)+6 (a^2) (c^4) p r x (z^2)-2 (b^2) (c^4) p r x (z^2)-4 (c^6) p r x (z^2)-(a^6) q r x (z^2)+3 (a^4) (b^2) q r x (z^2)-3 (a^2) (b^4) q r x (z^2)+(b^6) q r x (z^2)+(a^4) (c^2) q r x (z^2)+2 (a^2) (b^2) (c^2) q r x (z^2)-3 (b^4) (c^2) q r x (z^2)+(a^2) (c^4) q r x (z^2)+3 (b^2) (c^4) q r x (z^2)-(c^6) q r x (z^2)-4 (a^4) (c^2) p q y (z^2)+8 (a^2) (b^2) (c^2) p q y (z^2)-4 (b^4) (c^2) p q y (z^2)+8 (a^2) (c^4) p q y (z^2)-16 (b^2) (c^4) p q y (z^2)-4 (c^6) p q y (z^2)+(a^6) p r y (z^2)-3 (a^4) (b^2) p r y (z^2)+3 (a^2) (b^4) p r y (z^2)-(b^6) p r y (z^2)-3 (a^4) (c^2) p r y (z^2)+14 (a^2) (b^2) (c^2) p r y (z^2)-11 (b^4) (c^2) p r y (z^2)+3 (a^2) (c^4) p r y (z^2)-11 (b^2) (c^4) p r y (z^2)-(c^6) p r y (z^2)-4 (a^2) (c^4) p q (z^3)+4 (b^2) (c^4) p q (z^3)+4 (c^6) p q (z^3)+2 (a^4) (c^2) p r (z^3)-4 (a^2) (b^2) (c^2) p r (z^3)+2 (b^4) (c^2) p r (z^3)-4 (a^2) (c^4) p r (z^3)+4 (b^2) (c^4) p r (z^3)+2 (c^6) p r (z^3),2 (a^6) p q (x^3)-4 (a^4) (b^2) p q (x^3)+2 (a^2) (b^4) p q (x^3)+4 (a^4) (c^2) p q (x^3)-4 (a^2) (b^2) (c^2) p q (x^3)+2 (a^2) (c^4) p q (x^3)+4 (a^6) q r (x^3)-4 (a^4) (b^2) q r (x^3)+4 (a^4) (c^2) q r (x^3)-4 (a^6) p q (x^2) y+6 (a^4) (b^2) p q (x^2) y-2 (b^6) p q (x^2) y-2 (a^4) (c^2) p q (x^2) y-4 (a^2) (b^2) (c^2) p q (x^2) y+6 (b^4) (c^2) p q (x^2) y+4 (a^2) (c^4) p q (x^2) y-6 (b^2) (c^4) p q (x^2) y+2 (c^6) p q (x^2) y-(a^6) p r (x^2) y+(a^4) (b^2) p r (x^2) y+(a^2) (b^4) p r (x^2) y-(b^6) p r (x^2) y+3 (a^4) (c^2) p r (x^2) y+2 (a^2) (b^2) (c^2) p r (x^2) y+3 (b^4) (c^2) p r (x^2) y-3 (a^2) (c^4) p r (x^2) y-3 (b^2) (c^4) p r (x^2) y+(c^6) p r (x^2) y-8 (a^6) q r (x^2) y+4 (a^4) (b^2) q r (x^2) y+4 (a^2) (b^4) q r (x^2) y+4 (a^4) (c^2) q r (x^2) y-8 (a^2) (b^2) (c^2) q r (x^2) y+4 (a^2) (c^4) q r (x^2) y+2 (a^6) p q x (y^2)-6 (a^2) (b^4) p q x (y^2)+4 (b^6) p q x (y^2)-2 (a^4) (c^2) p q x (y^2)+8 (a^2) (b^2) (c^2) p q x (y^2)-6 (b^4) (c^2) p q x (y^2)-2 (a^2) (c^4) p q x (y^2)+2 (c^6) p q x (y^2)+2 (a^4) (b^2) p r x (y^2)-4 (a^2) (b^4) p r x (y^2)+2 (b^6) p r x (y^2)-4 (a^2) (b^2) (c^2) p r x (y^2)-4 (b^4) (c^2) p r x (y^2)+2 (b^2) (c^4) p r x (y^2)+3 (a^6) q r x (y^2)+5 (a^4) (b^2) q r x (y^2)-7 (a^2) (b^4) q r x (y^2)-(b^6) q r x (y^2)-5 (a^4) (c^2) q r x (y^2)+6 (a^2) (b^2) (c^2) q r x (y^2)+3 (b^4) (c^2) q r x (y^2)+(a^2) (c^4) q r x (y^2)-3 (b^2) (c^4) q r x (y^2)+(c^6) q r x (y^2)-2 (a^4) (b^2) p q (y^3)+4 (a^2) (b^4) p q (y^3)-2 (b^6) p q (y^3)+2 (b^2) (c^4) p q (y^3)-2 (a^4) (b^2) q r (y^3)+2 (b^6) q r (y^3)-4 (b^4) (c^2) q r (y^3)+2 (b^2) (c^4) q r (y^3)-(a^6) p q (x^2) z+3 (a^4) (b^2) p q (x^2) z-3 (a^2) (b^4) p q (x^2) z+(b^6) p q (x^2) z-11 (a^4) (c^2) p q (x^2) z+14 (a^2) (b^2) (c^2) p q (x^2) z-3 (b^4) (c^2) p q (x^2) z-11 (a^2) (c^4) p q (x^2) z+3 (b^2) (c^4) p q (x^2) z-(c^6) p q (x^2) z-4 (a^6) q r (x^2) z+8 (a^4) (b^2) q r (x^2) z-4 (a^2) (b^4) q r (x^2) z-16 (a^4) (c^2) q r (x^2) z+8 (a^2) (b^2) (c^2) q r (x^2) z-4 (a^2) (c^4) q r (x^2) z+2 (a^6) p q x y z-6 (a^4) (b^2) p q x y z+6 (a^2) (b^4) p q x y z-2 (b^6) p q x y z+12 (a^4) (c^2) p q x y z-8 (a^2) (b^2) (c^2) p q x y z-4 (b^4) (c^2) p q x y z-6 (a^2) (c^4) p q x y z+14 (b^2) (c^4) p q x y z-8 (c^6) p q x y z+2 (a^6) p r x y z-4 (a^4) (b^2) p r x y z+2 (a^2) (b^4) p r x y z-6 (a^4) (c^2) p r x y z-2 (b^4) (c^2) p r x y z+6 (a^2) (c^4) p r x y z+4 (b^2) (c^4) p r x y z-2 (c^6) p r x y z+8 (a^6) q r x y z-14 (a^4) (b^2) q r x y z+4 (a^2) (b^4) q r x y z+2 (b^6) q r x y z+6 (a^4) (c^2) q r x y z+8 (a^2) (b^2) (c^2) q r x y z-6 (b^4) (c^2) q r x y z-12 (a^2) (c^4) q r x y z+6 (b^2) (c^4) q r x y z-2 (c^6) q r x y z-(a^6) p q (y^2) z+3 (a^4) (b^2) p q (y^2) z-3 (a^2) (b^4) p q (y^2) z+(b^6) p q (y^2) z-(a^4) (c^2) p q (y^2) z-6 (a^2) (b^2) (c^2) p q (y^2) z+7 (b^4) (c^2) p q (y^2) z+5 (a^2) (c^4) p q (y^2) z-5 (b^2) (c^4) p q (y^2) z-3 (c^6) p q (y^2) z-2 (a^4) (b^2) p r (y^2) z+4 (a^2) (b^4) p r (y^2) z-2 (b^6) p r (y^2) z+4 (a^2) (b^2) (c^2) p r (y^2) z+4 (b^4) (c^2) p r (y^2) z-2 (b^2) (c^4) p r (y^2) z-2 (a^6) q r (y^2) z+6 (a^2) (b^4) q r (y^2) z-4 (b^6) q r (y^2) z+2 (a^4) (c^2) q r (y^2) z-8 (a^2) (b^2) (c^2) q r (y^2) z+6 (b^4) (c^2) q r (y^2) z+2 (a^2) (c^4) q r (y^2) z-2 (c^6) q r (y^2) z+4 (a^4) (c^2) p q x (z^2)-8 (a^2) (b^2) (c^2) p q x (z^2)+4 (b^4) (c^2) p q x (z^2)+16 (a^2) (c^4) p q x (z^2)-8 (b^2) (c^4) p q x (z^2)+4 (c^6) p q x (z^2)+(a^6) q r x (z^2)-3 (a^4) (b^2) q r x (z^2)+3 (a^2) (b^4) q r x (z^2)-(b^6) q r x (z^2)+11 (a^4) (c^2) q r x (z^2)-14 (a^2) (b^2) (c^2) q r x (z^2)+3 (b^4) (c^2) q r x (z^2)+11 (a^2) (c^4) q r x (z^2)-3 (b^2) (c^4) q r x (z^2)+(c^6) q r x (z^2)-4 (a^4) (c^2) p q y (z^2)+8 (a^2) (b^2) (c^2) p q y (z^2)-4 (b^4) (c^2) p q y (z^2)-4 (a^2) (c^4) p q y (z^2)-4 (b^2) (c^4) p q y (z^2)+8 (c^6) p q y (z^2)-(a^6) p r y (z^2)+3 (a^4) (b^2) p r y (z^2)-3 (a^2) (b^4) p r y (z^2)+(b^6) p r y (z^2)+3 (a^4) (c^2) p r y (z^2)-2 (a^2) (b^2) (c^2) p r y (z^2)-(b^4) (c^2) p r y (z^2)-3 (a^2) (c^4) p r y (z^2)-(b^2) (c^4) p r y (z^2)+(c^6) p r y (z^2)-2 (a^6) q r y (z^2)+6 (a^4) (b^2) q r y (z^2)-6 (a^2) (b^4) q r y (z^2)+2 (b^6) q r y (z^2)-4 (a^4) (c^2) q r y (z^2)+4 (a^2) (b^2) (c^2) q r y (z^2)+2 (a^2) (c^4) q r y (z^2)-6 (b^2) (c^4) q r y (z^2)+4 (c^6) q r y (z^2)-4 (a^2) (c^4) p q (z^3)+4 (b^2) (c^4) p q (z^3)-4 (c^6) p q (z^3)-2 (a^4) (c^2) q r (z^3)+4 (a^2) (b^2) (c^2) q r (z^3)-2 (b^4) (c^2) q r (z^3)-4 (a^2) (c^4) q r (z^3)+4 (b^2) (c^4) q r (z^3)-2 (c^6) q r (z^3),-2 (a^6) p r (x^3)-4 (a^4) (b^2) p r (x^3)-2 (a^2) (b^4) p r (x^3)+4 (a^4) (c^2) p r (x^3)+4 (a^2) (b^2) (c^2) p r (x^3)-2 (a^2) (c^4) p r (x^3)-4 (a^6) q r (x^3)-4 (a^4) (b^2) q r (x^3)+4 (a^4) (c^2) q r (x^3)+(a^6) p r (x^2) y+11 (a^4) (b^2) p r (x^2) y+11 (a^2) (b^4) p r (x^2) y+(b^6) p r (x^2) y-3 (a^4) (c^2) p r (x^2) y-14 (a^2) (b^2) (c^2) p r (x^2) y-3 (b^4) (c^2) p r (x^2) y+3 (a^2) (c^4) p r (x^2) y+3 (b^2) (c^4) p r (x^2) y-(c^6) p r (x^2) y+4 (a^6) q r (x^2) y+16 (a^4) (b^2) q r (x^2) y+4 (a^2) (b^4) q r (x^2) y-8 (a^4) (c^2) q r (x^2) y-8 (a^2) (b^2) (c^2) q r (x^2) y+4 (a^2) (c^4) q r (x^2) y-4 (a^4) (b^2) p r x (y^2)-16 (a^2) (b^4) p r x (y^2)-4 (b^6) p r x (y^2)+8 (a^2) (b^2) (c^2) p r x (y^2)+8 (b^4) (c^2) p r x (y^2)-4 (b^2) (c^4) p r x (y^2)-(a^6) q r x (y^2)-11 (a^4) (b^2) q r x (y^2)-11 (a^2) (b^4) q r x (y^2)-(b^6) q r x (y^2)+3 (a^4) (c^2) q r x (y^2)+14 (a^2) (b^2) (c^2) q r x (y^2)+3 (b^4) (c^2) q r x (y^2)-3 (a^2) (c^4) q r x (y^2)-3 (b^2) (c^4) q r x (y^2)+(c^6) q r x (y^2)+4 (a^2) (b^4) p r (y^3)+4 (b^6) p r (y^3)-4 (b^4) (c^2) p r (y^3)+2 (a^4) (b^2) q r (y^3)+4 (a^2) (b^4) q r (y^3)+2 (b^6) q r (y^3)-4 (a^2) (b^2) (c^2) q r (y^3)-4 (b^4) (c^2) q r (y^3)+2 (b^2) (c^4) q r (y^3)+(a^6) p q (x^2) z-3 (a^4) (b^2) p q (x^2) z+3 (a^2) (b^4) p q (x^2) z-(b^6) p q (x^2) z-(a^4) (c^2) p q (x^2) z-2 (a^2) (b^2) (c^2) p q (x^2) z+3 (b^4) (c^2) p q (x^2) z-(a^2) (c^4) p q (x^2) z-3 (b^2) (c^4) p q (x^2) z+(c^6) p q (x^2) z+4 (a^6) p r (x^2) z+2 (a^4) (b^2) p r (x^2) z-4 (a^2) (b^4) p r (x^2) z-2 (b^6) p r (x^2) z-6 (a^4) (c^2) p r (x^2) z+4 (a^2) (b^2) (c^2) p r (x^2) z+6 (b^4) (c^2) p r (x^2) z-6 (b^2) (c^4) p r (x^2) z+2 (c^6) p r (x^2) z+8 (a^6) q r (x^2) z-4 (a^4) (b^2) q r (x^2) z-4 (a^2) (b^4) q r (x^2) z-4 (a^4) (c^2) q r (x^2) z+8 (a^2) (b^2) (c^2) q r (x^2) z-4 (a^2) (c^4) q r (x^2) z-2 (a^6) p q x y z+6 (a^4) (b^2) p q x y z-6 (a^2) (b^4) p q x y z+2 (b^6) p q x y z+4 (a^4) (c^2) p q x y z-4 (b^4) (c^2) p q x y z-2 (a^2) (c^4) p q x y z+2 (b^2) (c^4) p q x y z-2 (a^6) p r x y z-12 (a^4) (b^2) p r x y z+6 (a^2) (b^4) p r x y z+8 (b^6) p r x y z+6 (a^4) (c^2) p r x y z+8 (a^2) (b^2) (c^2) p r x y z-14 (b^4) (c^2) p r x y z-6 (a^2) (c^4) p r x y z+4 (b^2) (c^4) p r x y z+2 (c^6) p r x y z-8 (a^6) q r x y z-6 (a^4) (b^2) q r x y z+12 (a^2) (b^4) q r x y z+2 (b^6) q r x y z+14 (a^4) (c^2) q r x y z-8 (a^2) (b^2) (c^2) q r x y z-6 (b^4) (c^2) q r x y z-4 (a^2) (c^4) q r x y z+6 (b^2) (c^4) q r x y z-2 (c^6) q r x y z+(a^6) p q (y^2) z-3 (a^4) (b^2) p q (y^2) z+3 (a^2) (b^4) p q (y^2) z-(b^6) p q (y^2) z-3 (a^4) (c^2) p q (y^2) z+2 (a^2) (b^2) (c^2) p q (y^2) z+(b^4) (c^2) p q (y^2) z+3 (a^2) (c^4) p q (y^2) z+(b^2) (c^4) p q (y^2) z-(c^6) p q (y^2) z+4 (a^4) (b^2) p r (y^2) z+4 (a^2) (b^4) p r (y^2) z-8 (b^6) p r (y^2) z-8 (a^2) (b^2) (c^2) p r (y^2) z+4 (b^4) (c^2) p r (y^2) z+4 (b^2) (c^4) p r (y^2) z+2 (a^6) q r (y^2) z+4 (a^4) (b^2) q r (y^2) z-2 (a^2) (b^4) q r (y^2) z-4 (b^6) q r (y^2) z-6 (a^4) (c^2) q r (y^2) z-4 (a^2) (b^2) (c^2) q r (y^2) z+6 (b^4) (c^2) q r (y^2) z+6 (a^2) (c^4) q r (y^2) z-2 (c^6) q r (y^2) z-2 (a^4) (c^2) p q x (z^2)+4 (a^2) (b^2) (c^2) p q x (z^2)-2 (b^4) (c^2) p q x (z^2)+4 (a^2) (c^4) p q x (z^2)+4 (b^2) (c^4) p q x (z^2)-2 (c^6) p q x (z^2)-2 (a^6) p r x (z^2)+2 (a^4) (b^2) p r x (z^2)+2 (a^2) (b^4) p r x (z^2)-2 (b^6) p r x (z^2)-8 (a^2) (b^2) (c^2) p r x (z^2)+6 (a^2) (c^4) p r x (z^2)+6 (b^2) (c^4) p r x (z^2)-4 (c^6) p r x (z^2)-3 (a^6) q r x (z^2)+5 (a^4) (b^2) q r x (z^2)-(a^2) (b^4) q r x (z^2)-(b^6) q r x (z^2)-5 (a^4) (c^2) q r x (z^2)-6 (a^2) (b^2) (c^2) q r x (z^2)+3 (b^4) (c^2) q r x (z^2)+7 (a^2) (c^4) q r x (z^2)-3 (b^2) (c^4) q r x (z^2)+(c^6) q r x (z^2)+2 (a^4) (c^2) p q y (z^2)-4 (a^2) (b^2) (c^2) p q y (z^2)+2 (b^4) (c^2) p q y (z^2)-4 (a^2) (c^4) p q y (z^2)-4 (b^2) (c^4) p q y (z^2)+2 (c^6) p q y (z^2)+(a^6) p r y (z^2)+(a^4) (b^2) p r y (z^2)-5 (a^2) (b^4) p r y (z^2)+3 (b^6) p r y (z^2)-3 (a^4) (c^2) p r y (z^2)+6 (a^2) (b^2) (c^2) p r y (z^2)+5 (b^4) (c^2) p r y (z^2)+3 (a^2) (c^4) p r y (z^2)-7 (b^2) (c^4) p r y (z^2)-(c^6) p r y (z^2)+2 (a^6) q r y (z^2)-2 (a^4) (b^2) q r y (z^2)-2 (a^2) (b^4) q r y (z^2)+2 (b^6) q r y (z^2)+8 (a^2) (b^2) (c^2) q r y (z^2)-6 (a^2) (c^4) q r y (z^2)-6 (b^2) (c^4) q r y (z^2)+4 (c^6) q r y (z^2)+2 (a^4) (c^2) p r (z^3)-2 (b^4) (c^2) p r (z^3)-4 (a^2) (c^4) p r (z^3)+2 (c^6) p r (z^3)+2 (a^4) (c^2) q r (z^3)-2 (b^4) (c^2) q r (z^3)+4 (b^2) (c^4) q r (z^3)-2 (c^6) q r (z^3)}

QA-Tf9:  5th Point Tangent

QATf9[{x_,y_,z_}]:={p y z (r y-q z),q x z (-r x+p z),r x y (q x-p y)}

QA-Tf10:  QA-QuadriPole

QATf10[{x_,y_,z_}]:={p (2 p x+q y+r z),q (p x+2 q y+r z),r (p x+q y+2 r z)}

QA-Tf11:  QA-QuadriPolar

QATf11[{x_,y_,z_}]:={q r (-3 q r x+p r y+p q z),p r (q r x-3 p r y+p q z),p q (q r x+p r y-3 p q z)}

QA-Tf12:  QA-Pedal Point

QATf12[{x_,y_,z_}]:={p (r y-q z) (2 (b^2) (c^2) p r (x^3) y+(a^2) (c^2) q r (x^3) y+(b^2) (c^2) q r (x^3) y-(c^4) q r (x^3) y+(a^2) (c^2) p r (x^2) (y^2)+(b^2) (c^2) p r (x^2) (y^2)-(c^4) p r (x^2) (y^2)+2 (a^2) (c^2) q r (x^2) (y^2)-2 (b^2) (c^2) p q (x^3) z-(a^2) (b^2) q r (x^3) z+(b^4) q r (x^3) z-(b^2) (c^2) q r (x^3) z-2 (a^2) (c^2) p q (x^2) y z-2 (b^2) (c^2) p q (x^2) y z+2 (c^4) p q (x^2) y z+2 (a^2) (b^2) p r (x^2) y z-2 (b^4) p r (x^2) y z+2 (b^2) (c^2) p r (x^2) y z-2 (a^2) (c^2) p q x (y^2) z+(a^4) p r x (y^2) z-(b^4) p r x (y^2) z+2 (b^2) (c^2) p r x (y^2) z-(c^4) p r x (y^2) z+(a^4) q r x (y^2) z-(a^2) (b^2) q r x (y^2) z+(a^2) (c^2) q r x (y^2) z-(a^2) (b^2) p q (x^2) (z^2)+(b^4) p q (x^2) (z^2)-(b^2) (c^2) p q (x^2) (z^2)-2 (a^2) (b^2) q r (x^2) (z^2)-(a^4) p q x y (z^2)+(b^4) p q x y (z^2)-2 (b^2) (c^2) p q x y (z^2)+(c^4) p q x y (z^2)+2 (a^2) (b^2) p r x y (z^2)-(a^4) q r x y (z^2)-(a^2) (b^2) q r x y (z^2)+(a^2) (c^2) q r x y (z^2)-(a^4) p q (y^2) (z^2)+(a^2) (b^2) p q (y^2) (z^2)-(a^2) (c^2) p q (y^2) (z^2)+(a^4) p r (y^2) (z^2)+(a^2) (b^2) p r (y^2) (z^2)-(a^2) (c^2) p r (y^2) (z^2)),q (r x-p z) (2 (b^2) (c^2) p r (x^2) (y^2)+(a^2) (c^2) q r (x^2) (y^2)+(b^2) (c^2) q r (x^2) (y^2)-(c^4) q r (x^2) (y^2)+(a^2) (c^2) p r x (y^3)+(b^2) (c^2) p r x (y^3)-(c^4) p r x (y^3)+2 (a^2) (c^2) q r x (y^3)-2 (b^2) (c^2) p q (x^2) y z-(a^2) (b^2) p r (x^2) y z+(b^4) p r (x^2) y z+(b^2) (c^2) p r (x^2) y z-(a^4) q r (x^2) y z+(b^4) q r (x^2) y z+2 (a^2) (c^2) q r (x^2) y z-(c^4) q r (x^2) y z-2 (a^2) (c^2) p q x (y^2) z-2 (b^2) (c^2) p q x (y^2) z+2 (c^4) p q x (y^2) z-2 (a^4) q r x (y^2) z+2 (a^2) (b^2) q r x (y^2) z+2 (a^2) (c^2) q r x (y^2) z-2 (a^2) (c^2) p q (y^3) z+(a^4) p r (y^3) z-(a^2) (b^2) p r (y^3) z-(a^2) (c^2) p r (y^3) z+(a^2) (b^2) p q (x^2) (z^2)-(b^4) p q (x^2) (z^2)-(b^2) (c^2) p q (x^2) (z^2)+(a^2) (b^2) q r (x^2) (z^2)+(b^4) q r (x^2) (z^2)-(b^2) (c^2) q r (x^2) (z^2)+(a^4) p q x y (z^2)-(b^4) p q x y (z^2)-2 (a^2) (c^2) p q x y (z^2)+(c^4) p q x y (z^2)-(a^2) (b^2) p r x y (z^2)-(b^4) p r x y (z^2)+(b^2) (c^2) p r x y (z^2)+2 (a^2) (b^2) q r x y (z^2)+(a^4) p q (y^2) (z^2)-(a^2) (b^2) p q (y^2) (z^2)-(a^2) (c^2) p q (y^2) (z^2)-2 (a^2) (b^2) p r (y^2) (z^2)),r (q x-p y) ((a^2) (c^2) p r (x^2) (y^2)-(b^2) (c^2) p r (x^2) (y^2)-(c^4) p r (x^2) (y^2)+(a^2) (c^2) q r (x^2) (y^2)-(b^2) (c^2) q r (x^2) (y^2)+(c^4) q r (x^2) (y^2)-(a^2) (c^2) p q (x^2) y z+(b^2) (c^2) p q (x^2) y z+(c^4) p q (x^2) y z-2 (b^2) (c^2) p r (x^2) y z-(a^4) q r (x^2) y z+2 (a^2) (b^2) q r (x^2) y z-(b^4) q r (x^2) y z+(c^4) q r (x^2) y z-(a^2) (c^2) p q x (y^2) z+(b^2) (c^2) p q x (y^2) z-(c^4) p q x (y^2) z+(a^4) p r x (y^2) z-2 (a^2) (b^2) p r x (y^2) z+(b^4) p r x (y^2) z-(c^4) p r x (y^2) z+2 (a^2) (c^2) q r x (y^2) z+2 (b^2) (c^2) p q (x^2) (z^2)+(a^2) (b^2) q r (x^2) (z^2)-(b^4) q r (x^2) (z^2)+(b^2) (c^2) q r (x^2) (z^2)-2 (a^2) (b^2) p r x y (z^2)+2 (b^4) p r x y (z^2)-2 (b^2) (c^2) p r x y (z^2)-2 (a^4) q r x y (z^2)+2 (a^2) (b^2) q r x y (z^2)+2 (a^2) (c^2) q r x y (z^2)-2 (a^2) (c^2) p q (y^2) (z^2)+(a^4) p r (y^2) (z^2)-(a^2) (b^2) p r (y^2) (z^2)-(a^2) (c^2) p r (y^2) (z^2)+(a^2) (b^2) p q x (z^3)-(b^4) p q x (z^3)+(b^2) (c^2) p q x (z^3)+2 (a^2) (b^2) q r x (z^3)+(a^4) p q y (z^3)-(a^2) (b^2) p q y (z^3)-(a^2) (c^2) p q y (z^3)-2 (a^2) (b^2) p r y (z^3))}

QA-Tf13:  QA-AntiPedal Point

Too long coordinates See:

QA-Tf14:  QA-Orthotransversal Point

QATf14[{x_,y_,z_}]:={-2 (a^2) p r (y^2) z+2 (a^2) p q y (z^2)+(x^2) (-p ((a^2) r-(b^2) r-(c^2) r) y-p (-(a^2) q+(b^2) q+(c^2) q) z)+x (-p ((a^2) r-(b^2) r+(c^2) r) (y^2)-p (-(a^2) q+(b^2) q-(c^2) q+(a^2) r+(b^2) r-(c^2) r) y z-p (-(a^2) q-(b^2) q+(c^2) q) (z^2)),((a^2) p-(b^2) p+(c^2) p) q (y^2) z+(-(a^2) p-(b^2) p+(c^2) p) q y (z^2)+(x^2) (q (-(a^2) r+(b^2) r+(c^2) r) y+2 (b^2) q r z)+x (q (-(a^2) r+(b^2) r-(c^2) r) (y^2)+q ((a^2) p-(b^2) p-(c^2) p+(a^2) r+(b^2) r-(c^2) r) y z-2 (b^2) p q (z^2)),-(-(a^2) p+(b^2) p-(c^2) p) r (y^2) z-((a^2) p+(b^2) p-(c^2) p) r y (z^2)+(x^2) (-2 (c^2) q r y-(-(a^2) q+(b^2) q+(c^2) q) r z)+x (2 (c^2) p r (y^2)-((a^2) p-(b^2) p-(c^2) p+(a^2) q-(b^2) q+(c^2) q) r y z-(-(a^2) q-(b^2) q+(c^2) q) r (z^2))};

QA-Tf15:  P-Circumscribed Conic Center

QATf15[{x_,y_,z_}]:={p (q-r)^2 (q+r) (2 p+q+r) (p^2+p q+q^2+p r+3 q r+r^2),q (p-r)^2 (p+r) (p+2 q+r) (p^2+p q+q^2+3 p r+q r+r^2),r (p-q)^2 (p+q) (p+q+2 r) (p^2+3 p q+q^2+p r+q r+r^2)};

QA-Tf16:  QA-Keizer-Schmidt Conjugate

QATf16[{x_,y_,z_}]:={(a^2) (-(c^2) (q^2) x y+(b^2) p r x y+(a^2) q r x y-(c^2) q r x y+(c^2) p q (y^2)+(b^2) p r (y^2)+(a^2) q r (y^2)-(b^2) p q x z-(b^2) (q^2) x z-(b^2) q r x z-(a^2) p q y z+(c^2) p q y z-(a^2) (q^2) y z+(b^2) p r y z) (-(b^2) (c^2) (p^2) (x^2)-(b^2) (c^2) p q (x^2)-(b^2) (c^2) p r (x^2)-(a^2) (c^2) (p^2) x y+(c^4) (p^2) x y-(a^2) (c^2) p q x y-(a^2) (c^2) p r x y-(b^2) (c^2) p r x y+(c^4) p r x y-(a^2) (c^2) q r x y-(a^2) (b^2) (p^2) x z+(b^4) (p^2) x z-(a^2) (b^2) p q x z+(b^4) p q x z-(b^2) (c^2) p q x z-(a^2) (b^2) p r x z-(a^2) (b^2) q r x z-(a^4) (p^2) y z+(a^2) (b^2) (p^2) y z+(a^2) (c^2) (p^2) y z-(a^4) p q y z+(a^2) (b^2) p q y z-(a^4) p r y z+(a^2) (c^2) p r y z-(a^4) q r y z) (-(c^2) p r x y-(c^2) q r x y-(c^2) (r^2) x y+(c^2) p q x z+(a^2) q r x z-(b^2) q r x z-(b^2) (r^2) x z+(c^2) p q y z-(a^2) p r y z+(b^2) p r y z-(a^2) (r^2) y z+(c^2) p q (z^2)+(b^2) p r (z^2)+(a^2) q r (z^2)),(b^2) (-(c^2) p q (x^2)-(b^2) p r (x^2)-(a^2) q r (x^2)+(c^2) (p^2) x y-(b^2) p r x y+(c^2) p r x y-(a^2) q r x y+(b^2) (p^2) x z+(b^2) p q x z-(c^2) p q x z-(a^2) q r x z+(a^2) (p^2) y z+(a^2) p q y z+(a^2) p r y z) ((b^2) (c^2) p q x y+(b^2) (c^2) (q^2) x y-(c^4) (q^2) x y+(b^2) (c^2) p r x y+(a^2) (c^2) q r x y+(b^2) (c^2) q r x y-(c^4) q r x y+(a^2) (c^2) p q (y^2)+(a^2) (c^2) (q^2) (y^2)+(a^2) (c^2) q r (y^2)-(a^2) (b^2) p q x z+(b^4) p q x z-(a^2) (b^2) (q^2) x z+(b^4) (q^2) x z-(b^2) (c^2) (q^2) x z+(b^4) p r x z+(b^4) q r x z-(b^2) (c^2) q r x z-(a^4) p q y z+(a^2) (b^2) p q y z+(a^2) (c^2) p q y z-(a^4) (q^2) y z+(a^2) (b^2) (q^2) y z+(a^2) (b^2) p r y z+(a^2) (b^2) q r y z) (-(c^2) p r x y-(c^2) q r x y-(c^2) (r^2) x y+(c^2) p q x z+(a^2) q r x z-(b^2) q r x z-(b^2) (r^2) x z+(c^2) p q y z-(a^2) p r y z+(b^2) p r y z-(a^2) (r^2) y z+(c^2) p q (z^2)+(b^2) p r (z^2)+(a^2) q r (z^2)),(c^2) (-(c^2) p q (x^2)-(b^2) p r (x^2)-(a^2) q r (x^2)+(c^2) (p^2) x y-(b^2) p r x y+(c^2) p r x y-(a^2) q r x y+(b^2) (p^2) x z+(b^2) p q x z-(c^2) p q x z-(a^2) q r x z+(a^2) (p^2) y z+(a^2) p q y z+(a^2) p r y z) (-(c^2) (q^2) x y+(b^2) p r x y+(a^2) q r x y-(c^2) q r x y+(c^2) p q (y^2)+(b^2) p r (y^2)+(a^2) q r (y^2)-(b^2) p q x z-(b^2) (q^2) x z-(b^2) q r x z-(a^2) p q y z+(c^2) p q y z-(a^2) (q^2) y z+(b^2) p r y z) ((c^4) p q x y-(a^2) (c^2) p r x y+(c^4) p r x y-(b^2) (c^2) q r x y+(c^4) q r x y-(a^2) (c^2) (r^2) x y-(b^2) (c^2) (r^2) x y+(c^4) (r^2) x y+(b^2) (c^2) p q x z+(b^2) (c^2) p r x z+(a^2) (b^2) q r x z-(b^4) q r x z+(b^2) (c^2) q r x z-(b^4) (r^2) x z+(b^2) (c^2) (r^2) x z+(a^2) (c^2) p q y z-(a^4) p r y z+(a^2) (b^2) p r y z+(a^2) (c^2) p r y z+(a^2) (c^2) q r y z-(a^4) (r^2) y z+(a^2) (c^2) (r^2) y z+(a^2) (b^2) p r (z^2)+(a^2) (b^2) q r (z^2)+(a^2) (b^2) (r^2) (z^2))}

QA - Circles and Conics

QACi1=-(c^2) (p^2) (q^3) r (x^2)+(a^2) (p^2) (q^2) (r^2) (x^2)-(b^2) (p^2) (q^2) (r^2) (x^2)-(c^2) (p^2) (q^2) (r^2) (x^2)+(a^2) p (q^3) (r^2) (x^2)-(b^2) p (q^3) (r^2) (x^2)-(c^2) p (q^3) (r^2) (x^2)-(b^2) (p^2) q (r^3) (x^2)+(a^2) p (q^2) (r^3) (x^2)-(b^2) p (q^2) (r^3) (x^2)-(c^2) p (q^2) (r^3) (x^2)+(a^2) (q^3) (r^3) (x^2)+(c^2) (p^3) (q^2) r x y+(c^2) (p^2) (q^3) r x y-(a^2) (p^3) q (r^2) x y+(b^2) (p^3) q (r^2) x y+(c^2) (p^3) q (r^2) x y+2 (c^2) (p^2) (q^2) (r^2) x y+(a^2) p (q^3) (r^2) x y-(b^2) p (q^3) (r^2) x y+(c^2) p (q^3) (r^2) x y+(b^2) (p^3) (r^3) x y-(a^2) (p^2) q (r^3) x y+(c^2) (p^2) q (r^3) x y-(b^2) p (q^2) (r^3) x y+(c^2) p (q^2) (r^3) x y+(a^2) (q^3) (r^3) x y-(c^2) (p^3) (q^2) r (y^2)-(a^2) (p^3) q (r^2) (y^2)+(b^2) (p^3) q (r^2) (y^2)-(c^2) (p^3) q (r^2) (y^2)-(a^2) (p^2) (q^2) (r^2) (y^2)+(b^2) (p^2) (q^2) (r^2) (y^2)-(c^2) (p^2) (q^2) (r^2) (y^2)+(b^2) (p^3) (r^3) (y^2)-(a^2) (p^2) q (r^3) (y^2)+(b^2) (p^2) q (r^3) (y^2)-(c^2) (p^2) q (r^3) (y^2)-(a^2) p (q^2) (r^3) (y^2)+(c^2) (p^3) (q^3) x z-(a^2) (p^3) (q^2) r x z+(b^2) (p^3) (q^2) r x z+(c^2) (p^3) (q^2) r x z-(a^2) (p^2) (q^3) r x z+(b^2) (p^2) (q^3) r x z+(b^2) (p^3) q (r^2) x z+2 (b^2) (p^2) (q^2) (r^2) x z+(b^2) p (q^3) (r^2) x z-(c^2) p (q^3) (r^2) x z+(b^2) (p^2) q (r^3) x z+(a^2) p (q^2) (r^3) x z+(b^2) p (q^2) (r^3) x z-(c^2) p (q^2) (r^3) x z+(a^2) (q^3) (r^3) x z+(c^2) (p^3) (q^3) y z+(a^2) (p^3) (q^2) r y z-(b^2) (p^3) (q^2) r y z+(a^2) (p^2) (q^3) r y z-(b^2) (p^2) (q^3) r y z+(c^2) (p^2) (q^3) r y z+(a^2) (p^3) q (r^2) y z-(c^2) (p^3) q (r^2) y z+2 (a^2) (p^2) (q^2) (r^2) y z+(a^2) p (q^3) (r^2) y z+(b^2) (p^3) (r^3) y z+(a^2) (p^2) q (r^3) y z+(b^2) (p^2) q (r^3) y z-(c^2) (p^2) q (r^3) y z+(a^2) p (q^2) (r^3) y z+(c^2) (p^3) (q^3) (z^2)-(a^2) (p^3) (q^2) r (z^2)-(b^2) (p^3) (q^2) r (z^2)+(c^2) (p^3) (q^2) r (z^2)-(a^2) (p^2) (q^3) r (z^2)-(b^2) (p^2) (q^3) r (z^2)+(c^2) (p^2) (q^3) r (z^2)-(b^2) (p^3) q (r^2) (z^2)-(a^2) (p^2) (q^2) (r^2) (z^2)-(b^2) (p^2) (q^2) (r^2) (z^2)+(c^2) (p^2) (q^2) (r^2) (z^2)-(a^2) p (q^3) (r^2) (z^2);(* QA-Circumcircle Diagonal Triangle*)
QACi2=-(c^2) (p^2) (q^3) r (x^2)+(a^2) (p^2) (q^2) (r^2) (x^2)-(b^2) (p^2) (q^2) (r^2) (x^2)-(c^2) (p^2) (q^2) (r^2) (x^2)+(a^2) p (q^3) (r^2) (x^2)-(b^2) p (q^3) (r^2) (x^2)-3 (c^2) p (q^3) (r^2) (x^2)-(b^2) (p^2) q (r^3) (x^2)+(a^2) p (q^2) (r^3) (x^2)-3 (b^2) p (q^2) (r^3) (x^2)-(c^2) p (q^2) (r^3) (x^2)-(a^2) (q^3) (r^3) (x^2)+3 (c^2) (p^3) (q^2) r x y+3 (c^2) (p^2) (q^3) r x y-(a^2) (p^3) q (r^2) x y+(b^2) (p^3) q (r^2) x y+(c^2) (p^3) q (r^2) x y+6 (c^2) (p^2) (q^2) (r^2) x y+(a^2) p (q^3) (r^2) x y-(b^2) p (q^3) (r^2) x y+(c^2) p (q^3) (r^2) x y-(b^2) (p^3) (r^3) x y-3 (a^2) (p^2) q (r^3) x y+3 (c^2) (p^2) q (r^3) x y-3 (b^2) p (q^2) (r^3) x y+3 (c^2) p (q^2) (r^3) x y-(a^2) (q^3) (r^3) x y-(c^2) (p^3) (q^2) r (y^2)-(a^2) (p^3) q (r^2) (y^2)+(b^2) (p^3) q (r^2) (y^2)-3 (c^2) (p^3) q (r^2) (y^2)-(a^2) (p^2) (q^2) (r^2) (y^2)+(b^2) (p^2) (q^2) (r^2) (y^2)-(c^2) (p^2) (q^2) (r^2) (y^2)-(b^2) (p^3) (r^3) (y^2)-3 (a^2) (p^2) q (r^3) (y^2)+(b^2) (p^2) q (r^3) (y^2)-(c^2) (p^2) q (r^3) (y^2)-(a^2) p (q^2) (r^3) (y^2)-(c^2) (p^3) (q^3) x z-(a^2) (p^3) (q^2) r x z+(b^2) (p^3) (q^2) r x z+(c^2) (p^3) (q^2) r x z-3 (a^2) (p^2) (q^3) r x z+3 (b^2) (p^2) (q^3) r x z+3 (b^2) (p^3) q (r^2) x z+6 (b^2) (p^2) (q^2) (r^2) x z+3 (b^2) p (q^3) (r^2) x z-3 (c^2) p (q^3) (r^2) x z+3 (b^2) (p^2) q (r^3) x z+(a^2) p (q^2) (r^3) x z+(b^2) p (q^2) (r^3) x z-(c^2) p (q^2) (r^3) x z-(a^2) (q^3) (r^3) x z-(c^2) (p^3) (q^3) y z+3 (a^2) (p^3) (q^2) r y z-3 (b^2) (p^3) (q^2) r y z+(a^2) (p^2) (q^3) r y z-(b^2) (p^2) (q^3) r y z+(c^2) (p^2) (q^3) r y z+3 (a^2) (p^3) q (r^2) y z-3 (c^2) (p^3) q (r^2) y z+6 (a^2) (p^2) (q^2) (r^2) y z+3 (a^2) p (q^3) (r^2) y z-(b^2) (p^3) (r^3) y z+(a^2) (p^2) q (r^3) y z+(b^2) (p^2) q (r^3) y z-(c^2) (p^2) q (r^3) y z+3 (a^2) p (q^2) (r^3) y z-(c^2) (p^3) (q^3) (z^2)-(a^2) (p^3) (q^2) r (z^2)-3 (b^2) (p^3) (q^2) r (z^2)+(c^2) (p^3) (q^2) r (z^2)-3 (a^2) (p^2) (q^3) r (z^2)-(b^2) (p^2) (q^3) r (z^2)+(c^2) (p^2) (q^3) r (z^2)-(b^2) (p^3) q (r^2) (z^2)-(a^2) (p^2) (q^2) (r^2) (z^2)-(b^2) (p^2) (q^2) (r^2) (z^2)+(c^2) (p^2) (q^2) (r^2) (z^2)-(a^2) p (q^3) (r^2) (z^2);(* QA-Medial Circle Diagonal Triangle *)
QACi99=p ((b^2) (p^5) (q^2)+4 (b^2) (p^4) (q^3)+6 (b^2) (p^3) (q^4)+4 (b^2) (p^2) (q^5)+(b^2) p (q^6)+(a^2) (p^5) q r+(b^2) (p^5) q r+(c^2) (p^5) q r+4 (a^2) (p^4) (q^2) r+8 (b^2) (p^4) (q^2) r+4 (c^2) (p^4) (q^2) r+5 (a^2) (p^3) (q^3) r+21 (b^2) (p^3) (q^3) r+7 (c^2) (p^3) (q^3) r+2 (a^2) (p^2) (q^4) r+24 (b^2) (p^2) (q^4) r+4 (c^2) (p^2) (q^4) r+12 (b^2) p (q^5) r+2 (b^2) (q^6) r+(c^2) (p^5) (r^2)+4 (a^2) (p^4) q (r^2)+4 (b^2) (p^4) q (r^2)+8 (c^2) (p^4) q (r^2)+12 (a^2) (p^3) (q^2) (r^2)+22 (b^2) (p^3) (q^2) (r^2)+22 (c^2) (p^3) (q^2) (r^2)+12 (a^2) (p^2) (q^3) (r^2)+40 (b^2) (p^2) (q^3) (r^2)+24 (c^2) (p^2) (q^3) (r^2)+4 (a^2) p (q^4) (r^2)+30 (b^2) p (q^4) (r^2)+8 (c^2) p (q^4) (r^2)+8 (b^2) (q^5) (r^2)+4 (c^2) (p^4) (r^3)+5 (a^2) (p^3) q (r^3)+7 (b^2) (p^3) q (r^3)+21 (c^2) (p^3) q (r^3)+12 (a^2) (p^2) (q^2) (r^3)+24 (b^2) (p^2) (q^2) (r^3)+40 (c^2) (p^2) (q^2) (r^3)+9 (a^2) p (q^3) (r^3)+27 (b^2) p (q^3) (r^3)+27 (c^2) p (q^3) (r^3)+2 (a^2) (q^4) (r^3)+10 (b^2) (q^4) (r^3)+4 (c^2) (q^4) (r^3)+6 (c^2) (p^3) (r^4)+2 (a^2) (p^2) q (r^4)+4 (b^2) (p^2) q (r^4)+24 (c^2) (p^2) q (r^4)+4 (a^2) p (q^2) (r^4)+8 (b^2) p (q^2) (r^4)+30 (c^2) p (q^2) (r^4)+2 (a^2) (q^3) (r^4)+4 (b^2) (q^3) (r^4)+10 (c^2) (q^3) (r^4)+4 (c^2) (p^2) (r^5)+12 (c^2) p q (r^5)+8 (c^2) (q^2) (r^5)+(c^2) p (r^6)+2 (c^2) q (r^6)) (x^2)+p q ((a^2) (p^5) q+(b^2) (p^5) q-(c^2) (p^5) q+4 (a^2) (p^4) (q^2)+4 (b^2) (p^4) (q^2)-4 (c^2) (p^4) (q^2)+6 (a^2) (p^3) (q^3)+6 (b^2) (p^3) (q^3)-6 (c^2) (p^3) (q^3)+4 (a^2) (p^2) (q^4)+4 (b^2) (p^2) (q^4)-4 (c^2) (p^2) (q^4)+(a^2) p (q^5)+(b^2) p (q^5)-(c^2) p (q^5)+3 (a^2) (p^5) r+(b^2) (p^5) r-(c^2) (p^5) r+16 (a^2) (p^4) q r+8 (b^2) (p^4) q r-8 (c^2) (p^4) q r+29 (a^2) (p^3) (q^2) r+23 (b^2) (p^3) (q^2) r-15 (c^2) (p^3) (q^2) r+23 (a^2) (p^2) (q^3) r+29 (b^2) (p^2) (q^3) r-15 (c^2) (p^2) (q^3) r+8 (a^2) p (q^4) r+16 (b^2) p (q^4) r-8 (c^2) p (q^4) r+(a^2) (q^5) r+3 (b^2) (q^5) r-(c^2) (q^5) r+12 (a^2) (p^4) (r^2)+4 (b^2) (p^4) (r^2)-4 (c^2) (p^4) (r^2)+42 (a^2) (p^3) q (r^2)+26 (b^2) (p^3) q (r^2)-10 (c^2) (p^3) q (r^2)+52 (a^2) (p^2) (q^2) (r^2)+52 (b^2) (p^2) (q^2) (r^2)-10 (c^2) (p^2) (q^2) (r^2)+26 (a^2) p (q^3) (r^2)+42 (b^2) p (q^3) (r^2)-10 (c^2) p (q^3) (r^2)+4 (a^2) (q^4) (r^2)+12 (b^2) (q^4) (r^2)-4 (c^2) (q^4) (r^2)+15 (a^2) (p^3) (r^3)+9 (b^2) (p^3) (r^3)-(c^2) (p^3) (r^3)+39 (a^2) (p^2) q (r^3)+33 (b^2) (p^2) q (r^3)+9 (c^2) (p^2) q (r^3)+33 (a^2) p (q^2) (r^3)+39 (b^2) p (q^2) (r^3)+9 (c^2) p (q^2) (r^3)+9 (a^2) (q^3) (r^3)+15 (b^2) (q^3) (r^3)-(c^2) (q^3) (r^3)+6 (a^2) (p^2) (r^4)+6 (b^2) (p^2) (r^4)+8 (c^2) (p^2) (r^4)+12 (a^2) p q (r^4)+12 (b^2) p q (r^4)+20 (c^2) p q (r^4)+6 (a^2) (q^2) (r^4)+6 (b^2) (q^2) (r^4)+8 (c^2) (q^2) (r^4)+8 (c^2) p (r^5)+8 (c^2) q (r^5)+2 (c^2) (r^6)) x y+q ((a^2) (p^6) q+4 (a^2) (p^5) (q^2)+6 (a^2) (p^4) (q^3)+4 (a^2) (p^3) (q^4)+(a^2) (p^2) (q^5)+2 (a^2) (p^6) r+12 (a^2) (p^5) q r+24 (a^2) (p^4) (q^2) r+2 (b^2) (p^4) (q^2) r+4 (c^2) (p^4) (q^2) r+21 (a^2) (p^3) (q^3) r+5 (b^2) (p^3) (q^3) r+7 (c^2) (p^3) (q^3) r+8 (a^2) (p^2) (q^4) r+4 (b^2) (p^2) (q^4) r+4 (c^2) (p^2) (q^4) r+(a^2) p (q^5) r+(b^2) p (q^5) r+(c^2) p (q^5) r+8 (a^2) (p^5) (r^2)+30 (a^2) (p^4) q (r^2)+4 (b^2) (p^4) q (r^2)+8 (c^2) (p^4) q (r^2)+40 (a^2) (p^3) (q^2) (r^2)+12 (b^2) (p^3) (q^2) (r^2)+24 (c^2) (p^3) (q^2) (r^2)+22 (a^2) (p^2) (q^3) (r^2)+12 (b^2) (p^2) (q^3) (r^2)+22 (c^2) (p^2) (q^3) (r^2)+4 (a^2) p (q^4) (r^2)+4 (b^2) p (q^4) (r^2)+8 (c^2) p (q^4) (r^2)+(c^2) (q^5) (r^2)+10 (a^2) (p^4) (r^3)+2 (b^2) (p^4) (r^3)+4 (c^2) (p^4) (r^3)+27 (a^2) (p^3) q (r^3)+9 (b^2) (p^3) q (r^3)+27 (c^2) (p^3) q (r^3)+24 (a^2) (p^2) (q^2) (r^3)+12 (b^2) (p^2) (q^2) (r^3)+40 (c^2) (p^2) (q^2) (r^3)+7 (a^2) p (q^3) (r^3)+5 (b^2) p (q^3) (r^3)+21 (c^2) p (q^3) (r^3)+4 (c^2) (q^4) (r^3)+4 (a^2) (p^3) (r^4)+2 (b^2) (p^3) (r^4)+10 (c^2) (p^3) (r^4)+8 (a^2) (p^2) q (r^4)+4 (b^2) (p^2) q (r^4)+30 (c^2) (p^2) q (r^4)+4 (a^2) p (q^2) (r^4)+2 (b^2) p (q^2) (r^4)+24 (c^2) p (q^2) (r^4)+6 (c^2) (q^3) (r^4)+8 (c^2) (p^2) (r^5)+12 (c^2) p q (r^5)+4 (c^2) (q^2) (r^5)+2 (c^2) p (r^6)+(c^2) q (r^6)) (y^2)+p r (3 (a^2) (p^5) q-(b^2) (p^5) q+(c^2) (p^5) q+12 (a^2) (p^4) (q^2)-4 (b^2) (p^4) (q^2)+4 (c^2) (p^4) (q^2)+15 (a^2) (p^3) (q^3)-(b^2) (p^3) (q^3)+9 (c^2) (p^3) (q^3)+6 (a^2) (p^2) (q^4)+8 (b^2) (p^2) (q^4)+6 (c^2) (p^2) (q^4)+8 (b^2) p (q^5)+2 (b^2) (q^6)+(a^2) (p^5) r-(b^2) (p^5) r+(c^2) (p^5) r+16 (a^2) (p^4) q r-8 (b^2) (p^4) q r+8 (c^2) (p^4) q r+42 (a^2) (p^3) (q^2) r-10 (b^2) (p^3) (q^2) r+26 (c^2) (p^3) (q^2) r+39 (a^2) (p^2) (q^3) r+9 (b^2) (p^2) (q^3) r+33 (c^2) (p^2) (q^3) r+12 (a^2) p (q^4) r+20 (b^2) p (q^4) r+12 (c^2) p (q^4) r+8 (b^2) (q^5) r+4 (a^2) (p^4) (r^2)-4 (b^2) (p^4) (r^2)+4 (c^2) (p^4) (r^2)+29 (a^2) (p^3) q (r^2)-15 (b^2) (p^3) q (r^2)+23 (c^2) (p^3) q (r^2)+52 (a^2) (p^2) (q^2) (r^2)-10 (b^2) (p^2) (q^2) (r^2)+52 (c^2) (p^2) (q^2) (r^2)+33 (a^2) p (q^3) (r^2)+9 (b^2) p (q^3) (r^2)+39 (c^2) p (q^3) (r^2)+6 (a^2) (q^4) (r^2)+8 (b^2) (q^4) (r^2)+6 (c^2) (q^4) (r^2)+6 (a^2) (p^3) (r^3)-6 (b^2) (p^3) (r^3)+6 (c^2) (p^3) (r^3)+23 (a^2) (p^2) q (r^3)-15 (b^2) (p^2) q (r^3)+29 (c^2) (p^2) q (r^3)+26 (a^2) p (q^2) (r^3)-10 (b^2) p (q^2) (r^3)+42 (c^2) p (q^2) (r^3)+9 (a^2) (q^3) (r^3)-(b^2) (q^3) (r^3)+15 (c^2) (q^3) (r^3)+4 (a^2) (p^2) (r^4)-4 (b^2) (p^2) (r^4)+4 (c^2) (p^2) (r^4)+8 (a^2) p q (r^4)-8 (b^2) p q (r^4)+16 (c^2) p q (r^4)+4 (a^2) (q^2) (r^4)-4 (b^2) (q^2) (r^4)+12 (c^2) (q^2) (r^4)+(a^2) p (r^5)-(b^2) p (r^5)+(c^2) p (r^5)+(a^2) q (r^5)-(b^2) q (r^5)+3 (c^2) q (r^5)) x z+q r (2 (a^2) (p^6)+8 (a^2) (p^5) q+8 (a^2) (p^4) (q^2)+6 (b^2) (p^4) (q^2)+6 (c^2) (p^4) (q^2)-(a^2) (p^3) (q^3)+15 (b^2) (p^3) (q^3)+9 (c^2) (p^3) (q^3)-4 (a^2) (p^2) (q^4)+12 (b^2) (p^2) (q^4)+4 (c^2) (p^2) (q^4)-(a^2) p (q^5)+3 (b^2) p (q^5)+(c^2) p (q^5)+8 (a^2) (p^5) r+20 (a^2) (p^4) q r+12 (b^2) (p^4) q r+12 (c^2) (p^4) q r+9 (a^2) (p^3) (q^2) r+39 (b^2) (p^3) (q^2) r+33 (c^2) (p^3) (q^2) r-10 (a^2) (p^2) (q^3) r+42 (b^2) (p^2) (q^3) r+26 (c^2) (p^2) (q^3) r-8 (a^2) p (q^4) r+16 (b^2) p (q^4) r+8 (c^2) p (q^4) r-(a^2) (q^5) r+(b^2) (q^5) r+(c^2) (q^5) r+8 (a^2) (p^4) (r^2)+6 (b^2) (p^4) (r^2)+6 (c^2) (p^4) (r^2)+9 (a^2) (p^3) q (r^2)+33 (b^2) (p^3) q (r^2)+39 (c^2) (p^3) q (r^2)-10 (a^2) (p^2) (q^2) (r^2)+52 (b^2) (p^2) (q^2) (r^2)+52 (c^2) (p^2) (q^2) (r^2)-15 (a^2) p (q^3) (r^2)+29 (b^2) p (q^3) (r^2)+23 (c^2) p (q^3) (r^2)-4 (a^2) (q^4) (r^2)+4 (b^2) (q^4) (r^2)+4 (c^2) (q^4) (r^2)-(a^2) (p^3) (r^3)+9 (b^2) (p^3) (r^3)+15 (c^2) (p^3) (r^3)-10 (a^2) (p^2) q (r^3)+26 (b^2) (p^2) q (r^3)+42 (c^2) (p^2) q (r^3)-15 (a^2) p (q^2) (r^3)+23 (b^2) p (q^2) (r^3)+29 (c^2) p (q^2) (r^3)-6 (a^2) (q^3) (r^3)+6 (b^2) (q^3) (r^3)+6 (c^2) (q^3) (r^3)-4 (a^2) (p^2) (r^4)+4 (b^2) (p^2) (r^4)+12 (c^2) (p^2) (r^4)-8 (a^2) p q (r^4)+8 (b^2) p q (r^4)+16 (c^2) p q (r^4)-4 (a^2) (q^2) (r^4)+4 (b^2) (q^2) (r^4)+4 (c^2) (q^2) (r^4)-(a^2) p (r^5)+(b^2) p (r^5)+3 (c^2) p (r^5)-(a^2) q (r^5)+(b^2) q (r^5)+(c^2) q (r^5)) y z+r (2 (a^2) (p^6) q+8 (a^2) (p^5) (q^2)+10 (a^2) (p^4) (q^3)+4 (b^2) (p^4) (q^3)+2 (c^2) (p^4) (q^3)+4 (a^2) (p^3) (q^4)+10 (b^2) (p^3) (q^4)+2 (c^2) (p^3) (q^4)+8 (b^2) (p^2) (q^5)+2 (b^2) p (q^6)+(a^2) (p^6) r+12 (a^2) (p^5) q r+30 (a^2) (p^4) (q^2) r+8 (b^2) (p^4) (q^2) r+4 (c^2) (p^4) (q^2) r+27 (a^2) (p^3) (q^3) r+27 (b^2) (p^3) (q^3) r+9 (c^2) (p^3) (q^3) r+8 (a^2) (p^2) (q^4) r+30 (b^2) (p^2) (q^4) r+4 (c^2) (p^2) (q^4) r+12 (b^2) p (q^5) r+(b^2) (q^6) r+4 (a^2) (p^5) (r^2)+24 (a^2) (p^4) q (r^2)+4 (b^2) (p^4) q (r^2)+2 (c^2) (p^4) q (r^2)+40 (a^2) (p^3) (q^2) (r^2)+24 (b^2) (p^3) (q^2) (r^2)+12 (c^2) (p^3) (q^2) (r^2)+24 (a^2) (p^2) (q^3) (r^2)+40 (b^2) (p^2) (q^3) (r^2)+12 (c^2) (p^2) (q^3) (r^2)+4 (a^2) p (q^4) (r^2)+24 (b^2) p (q^4) (r^2)+2 (c^2) p (q^4) (r^2)+4 (b^2) (q^5) (r^2)+6 (a^2) (p^4) (r^3)+21 (a^2) (p^3) q (r^3)+7 (b^2) (p^3) q (r^3)+5 (c^2) (p^3) q (r^3)+22 (a^2) (p^2) (q^2) (r^3)+22 (b^2) (p^2) (q^2) (r^3)+12 (c^2) (p^2) (q^2) (r^3)+7 (a^2) p (q^3) (r^3)+21 (b^2) p (q^3) (r^3)+5 (c^2) p (q^3) (r^3)+6 (b^2) (q^4) (r^3)+4 (a^2) (p^3) (r^4)+8 (a^2) (p^2) q (r^4)+4 (b^2) (p^2) q (r^4)+4 (c^2) (p^2) q (r^4)+4 (a^2) p (q^2) (r^4)+8 (b^2) p (q^2) (r^4)+4 (c^2) p (q^2) (r^4)+4 (b^2) (q^3) (r^4)+(a^2) (p^2) (r^5)+(a^2) p q (r^5)+(b^2) p q (r^5)+(c^2) p q (r^5)+(b^2) (q^2) (r^5)) (z^2);  (* Equal sum of Squares QA- and DT-distances Circle *)
QACo1=-q r (x^2)+p r x y+q r x y-p r (y^2)+p q x z+q r x z+p q y z+p r y z-p q (z^2); (* Nine Point Conic *)
QACo2=(a^2) p r x y-(b^2) p r x y-(c^2) p r x y+(a^2) q r x y-(b^2) q r x y+(c^2) q r x y-(a^2) p q x z+(b^2) p q x z+(c^2) p q x z-(a^2) q r x z-(b^2) q r x z+(c^2) q r x z-(a^2) p q y z+(b^2) p q y z-(c^2) p q y z+(a^2) p r y z+(b^2) p r y z-(c^2) p r y z; (* Circumscribed QA-Orthogonal Hyperbola *)
QACo3=(-(c^2) (p^2) q r x y-(c^2) p (q^2) r x y+(b^2) (p^2) (r^2) x y+(a^2) p q (r^2) x y+(b^2) p q (r^2) x y-2 (c^2) p q (r^2) x y+(a^2) (q^2) (r^2) x y+(c^2) (p^2) (q^2) x z-(b^2) (p^2) q r x z+(a^2) p (q^2) r x z-2 (b^2) p (q^2) r x z+(c^2) p (q^2) r x z-(b^2) p q (r^2) x z+(a^2) (q^2) (r^2) x z+(c^2) (p^2) (q^2) y z-2 (a^2) (p^2) q r y z+(b^2) (p^2) q r y z+(c^2) (p^2) q r y z-(a^2) p (q^2) r y z+(b^2) (p^2) (r^2) y z-(a^2) p q (r^2) y z);(* QA-Gergonne-Steiner Conic *)
QACo4=((a^2) (p^2) (q^2) r (x^2)-(b^2) (p^2) (q^2) r (x^2)+(c^2) (p^2) (q^2) r (x^2)+(a^2) p (q^3) r (x^2)-(b^2) p (q^3) r (x^2)+3 (c^2) p (q^3) r (x^2)-(a^2) (p^2) q (r^2) (x^2)-(b^2) (p^2) q (r^2) (x^2)+(c^2) (p^2) q (r^2) (x^2)-4 (b^2) p (q^2) (r^2) (x^2)+4 (c^2) p (q^2) (r^2) (x^2)+(a^2) (q^3) (r^2) (x^2)-3 (b^2) (q^3) (r^2) (x^2)+3 (c^2) (q^3) (r^2) (x^2)-(a^2) p q (r^3) (x^2)-3 (b^2) p q (r^3) (x^2)+(c^2) p q (r^3) (x^2)-(a^2) (q^2) (r^3) (x^2)-3 (b^2) (q^2) (r^3) (x^2)+3 (c^2) (q^2) (r^3) (x^2)-(a^2) (p^3) q r x y+(b^2) (p^3) q r x y-(c^2) (p^3) q r x y-2 (a^2) (p^2) (q^2) r x y+2 (b^2) (p^2) (q^2) r x y-(a^2) p (q^3) r x y+(b^2) p (q^3) r x y+(c^2) p (q^3) r x y+(a^2) (p^3) (r^2) x y+(b^2) (p^3) (r^2) x y-(c^2) (p^3) (r^2) x y-3 (a^2) (p^2) q (r^2) x y+5 (b^2) (p^2) q (r^2) x y-(c^2) (p^2) q (r^2) x y-5 (a^2) p (q^2) (r^2) x y+3 (b^2) p (q^2) (r^2) x y+(c^2) p (q^2) (r^2) x y-(a^2) (q^3) (r^2) x y-(b^2) (q^3) (r^2) x y+(c^2) (q^3) (r^2) x y+(a^2) (p^2) (r^3) x y+3 (b^2) (p^2) (r^3) x y-(c^2) (p^2) (r^3) x y-2 (a^2) p q (r^3) x y+2 (b^2) p q (r^3) x y-3 (a^2) (q^2) (r^3) x y-(b^2) (q^2) (r^3) x y+(c^2) (q^2) (r^3) x y+(a^2) (p^3) q r (y^2)-(b^2) (p^3) q r (y^2)-3 (c^2) (p^3) q r (y^2)+(a^2) (p^2) (q^2) r (y^2)-(b^2) (p^2) (q^2) r (y^2)-(c^2) (p^2) (q^2) r (y^2)+3 (a^2) (p^3) (r^2) (y^2)-(b^2) (p^3) (r^2) (y^2)-3 (c^2) (p^3) (r^2) (y^2)+4 (a^2) (p^2) q (r^2) (y^2)-4 (c^2) (p^2) q (r^2) (y^2)+(a^2) p (q^2) (r^2) (y^2)+(b^2) p (q^2) (r^2) (y^2)-(c^2) p (q^2) (r^2) (y^2)+3 (a^2) (p^2) (r^3) (y^2)+(b^2) (p^2) (r^3) (y^2)-3 (c^2) (p^2) (r^3) (y^2)+3 (a^2) p q (r^3) (y^2)+(b^2) p q (r^3) (y^2)-(c^2) p q (r^3) (y^2)-(a^2) (p^3) (q^2) x z+(b^2) (p^3) (q^2) x z-(c^2) (p^3) (q^2) x z-(a^2) (p^2) (q^3) x z+(b^2) (p^2) (q^3) x z-3 (c^2) (p^2) (q^3) x z+(a^2) (p^3) q r x z+(b^2) (p^3) q r x z-(c^2) (p^3) q r x z+3 (a^2) (p^2) (q^2) r x z+(b^2) (p^2) (q^2) r x z-5 (c^2) (p^2) (q^2) r x z+2 (a^2) p (q^3) r x z-2 (c^2) p (q^3) r x z+2 (a^2) (p^2) q (r^2) x z-2 (c^2) (p^2) q (r^2) x z+5 (a^2) p (q^2) (r^2) x z-(b^2) p (q^2) (r^2) x z-3 (c^2) p (q^2) (r^2) x z+3 (a^2) (q^3) (r^2) x z-(b^2) (q^3) (r^2) x z+(c^2) (q^3) (r^2) x z+(a^2) p q (r^3) x z-(b^2) p q (r^3) x z-(c^2) p q (r^3) x z+(a^2) (q^2) (r^3) x z-(b^2) (q^2) (r^3) x z+(c^2) (q^2) (r^3) x z-(a^2) (p^3) (q^2) y z+(b^2) (p^3) (q^2) y z+3 (c^2) (p^3) (q^2) y z-(a^2) (p^2) (q^3) y z+(b^2) (p^2) (q^3) y z+(c^2) (p^2) (q^3) y z-2 (b^2) (p^3) q r y z+2 (c^2) (p^3) q r y z-(a^2) (p^2) (q^2) r y z-3 (b^2) (p^2) (q^2) r y z+5 (c^2) (p^2) (q^2) r y z-(a^2) p (q^3) r y z-(b^2) p (q^3) r y z+(c^2) p (q^3) r y z+(a^2) (p^3) (r^2) y z-3 (b^2) (p^3) (r^2) y z-(c^2) (p^3) (r^2) y z+(a^2) (p^2) q (r^2) y z-5 (b^2) (p^2) q (r^2) y z+3 (c^2) (p^2) q (r^2) y z-2 (b^2) p (q^2) (r^2) y z+2 (c^2) p (q^2) (r^2) y z+(a^2) (p^2) (r^3) y z-(b^2) (p^2) (r^3) y z-(c^2) (p^2) (r^3) y z+(a^2) p q (r^3) y z-(b^2) p q (r^3) y z+(c^2) p q (r^3) y z-3 (a^2) (p^3) (q^2) (z^2)+3 (b^2) (p^3) (q^2) (z^2)+(c^2) (p^3) (q^2) (z^2)-3 (a^2) (p^2) (q^3) (z^2)+3 (b^2) (p^2) (q^3) (z^2)-(c^2) (p^2) (q^3) (z^2)-(a^2) (p^3) q r (z^2)+3 (b^2) (p^3) q r (z^2)+(c^2) (p^3) q r (z^2)-4 (a^2) (p^2) (q^2) r (z^2)+4 (b^2) (p^2) (q^2) r (z^2)-3 (a^2) p (q^3) r (z^2)+(b^2) p (q^3) r (z^2)-(c^2) p (q^3) r (z^2)-(a^2) (p^2) q (r^2) (z^2)+(b^2) (p^2) q (r^2) (z^2)+(c^2) (p^2) q (r^2) (z^2)-(a^2) p (q^2) (r^2) (z^2)+(b^2) p (q^2) (r^2) (z^2)-(c^2) p (q^2) (r^2) (z^2));(* QA-DT-P3-P12 Orthogonal Hyperbola *)
QACo5=(-(p^3) (q^2) r (x^2)-3 (p^2) (q^3) r (x^2)-2 p (q^4) r (x^2)+(p^3) q (r^2) (x^2)-3 p (q^3) (r^2) (x^2)+3 (p^2) q (r^3) (x^2)+3 p (q^2) (r^3) (x^2)+2 p q (r^4) (x^2)+(p^4) q r x y+(p^3) (q^2) r x y-(p^2) (q^3) r x y-p (q^4) r x y-(p^4) (r^2) x y+(q^4) (r^2) x y-3 (p^3) (r^3) x y-3 (p^2) q (r^3) x y+3 p (q^2) (r^3) x y+3 (q^3) (r^3) x y-2 (p^2) (r^4) x y+2 (q^2) (r^4) x y+2 (p^4) q r (y^2)+3 (p^3) (q^2) r (y^2)+(p^2) (q^3) r (y^2)+3 (p^3) q (r^2) (y^2)-p (q^3) (r^2) (y^2)-3 (p^2) q (r^3) (y^2)-3 p (q^2) (r^3) (y^2)-2 p q (r^4) (y^2)+(p^4) (q^2) x z+3 (p^3) (q^3) x z+2 (p^2) (q^4) x z-(p^4) q r x z+3 (p^2) (q^3) r x z-(p^3) q (r^2) x z-3 p (q^3) (r^2) x z-2 (q^4) (r^2) x z+(p^2) q (r^3) x z-3 (q^3) (r^3) x z+p q (r^4) x z-(q^2) (r^4) x z-2 (p^4) (q^2) y z-3 (p^3) (q^3) y z-(p^2) (q^4) y z-3 (p^3) (q^2) r y z+p (q^4) r y z+2 (p^4) (r^2) y z+3 (p^3) q (r^2) y z+p (q^3) (r^2) y z+3 (p^3) (r^3) y z-p (q^2) (r^3) y z+(p^2) (r^4) y z-p q (r^4) y z-2 (p^4) q r (z^2)-3 (p^3) (q^2) r (z^2)+3 (p^2) (q^3) r (z^2)+2 p (q^4) r (z^2)-3 (p^3) q (r^2) (z^2)+3 p (q^3) (r^2) (z^2)-(p^2) q (r^3) (z^2)+p (q^2) (r^3) (z^2));(* QA-DT-P1-P16 Conic *)
QACo99=(p^2) (-(a^2) (c^2) p q+(b^2) (c^2) p q+(c^4) p q-(a^2) (b^2) p r+(b^4) p r+(b^2) (c^2) p r-(a^2) (b^2) q r+(b^4) q r-(a^2) (c^2) q r-2 (b^2) (c^2) q r+(c^4) q r) (-(a^2) (c^2) p (q^2)+(b^2) (c^2) p (q^2)+(c^4) p (q^2)+(a^4) p q r-3 (a^2) (b^2) p q r+2 (b^4) p q r-2 (a^2) (c^2) p q r+(b^2) (c^2) p q r+(c^4) p q r-(a^2) (b^2) (q^2) r+(b^4) (q^2) r-(a^2) (c^2) (q^2) r-2 (b^2) (c^2) (q^2) r+(c^4) (q^2) r+2 (b^4) p (r^2)+(a^4) q (r^2)+(b^4) q (r^2)-2 (a^2) (c^2) q (r^2)-2 (b^2) (c^2) q (r^2)+(c^4) q (r^2)) (2 (c^4) p (q^2)+(a^4) p q r-2 (a^2) (b^2) p q r+(b^4) p q r-3 (a^2) (c^2) p q r+(b^2) (c^2) p q r+2 (c^4) p q r+(a^4) (q^2) r-2 (a^2) (b^2) (q^2) r+(b^4) (q^2) r-2 (b^2) (c^2) (q^2) r+(c^4) (q^2) r-(a^2) (b^2) p (r^2)+(b^4) p (r^2)+(b^2) (c^2) p (r^2)-(a^2) (b^2) q (r^2)+(b^4) q (r^2)-(a^2) (c^2) q (r^2)-2 (b^2) (c^2) q (r^2)+(c^4) q (r^2)) (x^2)+p q (4 (a^4) (c^8) (p^4) (q^4)-8 (a^2) (b^2) (c^8) (p^4) (q^4)+4 (b^4) (c^8) (p^4) (q^4)-4 (c^12) (p^4) (q^4)+2 (a^8) (c^4) (p^4) (q^3) r-8 (a^6) (b^2) (c^4) (p^4) (q^3) r+12 (a^4) (b^4) (c^4) (p^4) (q^3) r-8 (a^2) (b^6) (c^4) (p^4) (q^3) r+2 (b^8) (c^4) (p^4) (q^3) r-3 (a^6) (c^6) (p^4) (q^3) r+13 (a^4) (b^2) (c^6) (p^4) (q^3) r-17 (a^2) (b^4) (c^6) (p^4) (q^3) r+7 (b^6) (c^6) (p^4) (q^3) r-9 (a^4) (c^8) (p^4) (q^3) r+6 (a^2) (b^2) (c^8) (p^4) (q^3) r+3 (b^4) (c^8) (p^4) (q^3) r+19 (a^2) (c^10) (p^4) (q^3) r-3 (b^2) (c^10) (p^4) (q^3) r-9 (c^12) (p^4) (q^3) r+2 (a^8) (c^4) (p^3) (q^4) r-8 (a^6) (b^2) (c^4) (p^3) (q^4) r+12 (a^4) (b^4) (c^4) (p^3) (q^4) r-8 (a^2) (b^6) (c^4) (p^3) (q^4) r+2 (b^8) (c^4) (p^3) (q^4) r+7 (a^6) (c^6) (p^3) (q^4) r-17 (a^4) (b^2) (c^6) (p^3) (q^4) r+13 (a^2) (b^4) (c^6) (p^3) (q^4) r-3 (b^6) (c^6) (p^3) (q^4) r+3 (a^4) (c^8) (p^3) (q^4) r+6 (a^2) (b^2) (c^8) (p^3) (q^4) r-9 (b^4) (c^8) (p^3) (q^4) r-3 (a^2) (c^10) (p^3) (q^4) r+19 (b^2) (c^10) (p^3) (q^4) r-9 (c^12) (p^3) (q^4) r+(a^10) (c^2) (p^4) (q^2) (r^2)-(a^8) (b^2) (c^2) (p^4) (q^2) (r^2)-6 (a^6) (b^4) (c^2) (p^4) (q^2) (r^2)+14 (a^4) (b^6) (c^2) (p^4) (q^2) (r^2)-11 (a^2) (b^8) (c^2) (p^4) (q^2) (r^2)+3 (b^10) (c^2) (p^4) (q^2) (r^2)-10 (a^8) (c^4) (p^4) (q^2) (r^2)+23 (a^6) (b^2) (c^4) (p^4) (q^2) (r^2)-13 (a^4) (b^4) (c^4) (p^4) (q^2) (r^2)-3 (a^2) (b^6) (c^4) (p^4) (q^2) (r^2)+3 (b^8) (c^4) (p^4) (q^2) (r^2)+30 (a^6) (c^6) (p^4) (q^2) (r^2)-49 (a^4) (b^2) (c^6) (p^4) (q^2) (r^2)+4 (a^2) (b^4) (c^6) (p^4) (q^2) (r^2)+15 (b^6) (c^6) (p^4) (q^2) (r^2)-40 (a^4) (c^8) (p^4) (q^2) (r^2)+33 (a^2) (b^2) (c^8) (p^4) (q^2) (r^2)-9 (b^4) (c^8) (p^4) (q^2) (r^2)+25 (a^2) (c^10) (p^4) (q^2) (r^2)-6 (b^2) (c^10) (p^4) (q^2) (r^2)-6 (c^12) (p^4) (q^2) (r^2)+4 (a^10) (c^2) (p^3) (q^3) (r^2)-12 (a^8) (b^2) (c^2) (p^3) (q^3) (r^2)+8 (a^6) (b^4) (c^2) (p^3) (q^3) (r^2)+8 (a^4) (b^6) (c^2) (p^3) (q^3) (r^2)-12 (a^2) (b^8) (c^2) (p^3) (q^3) (r^2)+4 (b^10) (c^2) (p^3) (q^3) (r^2)-13 (a^8) (c^4) (p^3) (q^3) (r^2)+44 (a^6) (b^2) (c^4) (p^3) (q^3) (r^2)-62 (a^4) (b^4) (c^4) (p^3) (q^3) (r^2)+44 (a^2) (b^6) (c^4) (p^3) (q^3) (r^2)-13 (b^8) (c^4) (p^3) (q^3) (r^2)+11 (a^6) (c^6) (p^3) (q^3) (r^2)-11 (a^4) (b^2) (c^6) (p^3) (q^3) (r^2)-11 (a^2) (b^4) (c^6) (p^3) (q^3) (r^2)+11 (b^6) (c^6) (p^3) (q^3) (r^2)-19 (a^4) (c^8) (p^3) (q^3) (r^2)-26 (a^2) (b^2) (c^8) (p^3) (q^3) (r^2)-19 (b^4) (c^8) (p^3) (q^3) (r^2)+37 (a^2) (c^10) (p^3) (q^3) (r^2)+37 (b^2) (c^10) (p^3) (q^3) (r^2)-20 (c^12) (p^3) (q^3) (r^2)+3 (a^10) (c^2) (p^2) (q^4) (r^2)-11 (a^8) (b^2) (c^2) (p^2) (q^4) (r^2)+14 (a^6) (b^4) (c^2) (p^2) (q^4) (r^2)-6 (a^4) (b^6) (c^2) (p^2) (q^4) (r^2)-(a^2) (b^8) (c^2) (p^2) (q^4) (r^2)+(b^10) (c^2) (p^2) (q^4) (r^2)+3 (a^8) (c^4) (p^2) (q^4) (r^2)-3 (a^6) (b^2) (c^4) (p^2) (q^4) (r^2)-13 (a^4) (b^4) (c^4) (p^2) (q^4) (r^2)+23 (a^2) (b^6) (c^4) (p^2) (q^4) (r^2)-10 (b^8) (c^4) (p^2) (q^4) (r^2)+15 (a^6) (c^6) (p^2) (q^4) (r^2)+4 (a^4) (b^2) (c^6) (p^2) (q^4) (r^2)-49 (a^2) (b^4) (c^6) (p^2) (q^4) (r^2)+30 (b^6) (c^6) (p^2) (q^4) (r^2)-9 (a^4) (c^8) (p^2) (q^4) (r^2)+33 (a^2) (b^2) (c^8) (p^2) (q^4) (r^2)-40 (b^4) (c^8) (p^2) (q^4) (r^2)-6 (a^2) (c^10) (p^2) (q^4) (r^2)+25 (b^2) (c^10) (p^2) (q^4) (r^2)-6 (c^12) (p^2) (q^4) (r^2)-(a^12) (p^4) q (r^3)+7 (a^10) (b^2) (p^4) q (r^3)-18 (a^8) (b^4) (p^4) q (r^3)+22 (a^6) (b^6) (p^4) q (r^3)-13 (a^4) (b^8) (p^4) q (r^3)+3 (a^2) (b^10) (p^4) q (r^3)+6 (a^10) (c^2) (p^4) q (r^3)-31 (a^8) (b^2) (c^2) (p^4) q (r^3)+47 (a^6) (b^4) (c^2) (p^4) q (r^3)-19 (a^4) (b^6) (c^2) (p^4) q (r^3)-9 (a^2) (b^8) (c^2) (p^4) q (r^3)+6 (b^10) (c^2) (p^4) q (r^3)-15 (a^8) (c^4) (p^4) q (r^3)+54 (a^6) (b^2) (c^4) (p^4) q (r^3)-51 (a^4) (b^4) (c^4) (p^4) q (r^3)+12 (a^2) (b^6) (c^4) (p^4) q (r^3)+20 (a^6) (c^6) (p^4) q (r^3)-46 (a^4) (b^2) (c^6) (p^4) q (r^3)+33 (a^2) (b^4) (c^6) (p^4) q (r^3)+9 (b^6) (c^6) (p^4) q (r^3)-15 (a^4) (c^8) (p^4) q (r^3)+19 (a^2) (b^2) (c^8) (p^4) q (r^3)-11 (b^4) (c^8) (p^4) q (r^3)+6 (a^2) (c^10) (p^4) q (r^3)-3 (b^2) (c^10) (p^4) q (r^3)-(c^12) (p^4) q (r^3)-2 (a^12) (p^3) (q^2) (r^3)+17 (a^10) (b^2) (p^3) (q^2) (r^3)-49 (a^8) (b^4) (p^3) (q^2) (r^3)+66 (a^6) (b^6) (p^3) (q^2) (r^3)-44 (a^4) (b^8) (p^3) (q^2) (r^3)+13 (a^2) (b^10) (p^3) (q^2) (r^3)-(b^12) (p^3) (q^2) (r^3)+8 (a^10) (c^2) (p^3) (q^2) (r^3)-41 (a^8) (b^2) (c^2) (p^3) (q^2) (r^3)+55 (a^6) (b^4) (c^2) (p^3) (q^2) (r^3)-11 (a^4) (b^6) (c^2) (p^3) (q^2) (r^3)-19 (a^2) (b^8) (c^2) (p^3) (q^2) (r^3)+8 (b^10) (c^2) (p^3) (q^2) (r^3)-25 (a^8) (c^4) (p^3) (q^2) (r^3)+46 (a^6) (b^2) (c^4) (p^3) (q^2) (r^3)-37 (a^4) (b^4) (c^4) (p^3) (q^2) (r^3)+48 (a^2) (b^6) (c^4) (p^3) (q^2) (r^3)-32 (b^8) (c^4) (p^3) (q^2) (r^3)+60 (a^6) (c^6) (p^3) (q^2) (r^3)-20 (a^4) (b^2) (c^6) (p^3) (q^2) (r^3)-27 (a^2) (b^4) (c^6) (p^3) (q^2) (r^3)+35 (b^6) (c^6) (p^3) (q^2) (r^3)-80 (a^4) (c^8) (p^3) (q^2) (r^3)-19 (a^2) (b^2) (c^8) (p^3) (q^2) (r^3)-14 (b^4) (c^8) (p^3) (q^2) (r^3)+52 (a^2) (c^10) (p^3) (q^2) (r^3)+17 (b^2) (c^10) (p^3) (q^2) (r^3)-13 (c^12) (p^3) (q^2) (r^3)-(a^12) (p^2) (q^3) (r^3)+13 (a^10) (b^2) (p^2) (q^3) (r^3)-44 (a^8) (b^4) (p^2) (q^3) (r^3)+66 (a^6) (b^6) (p^2) (q^3) (r^3)-49 (a^4) (b^8) (p^2) (q^3) (r^3)+17 (a^2) (b^10) (p^2) (q^3) (r^3)-2 (b^12) (p^2) (q^3) (r^3)+8 (a^10) (c^2) (p^2) (q^3) (r^3)-19 (a^8) (b^2) (c^2) (p^2) (q^3) (r^3)-11 (a^6) (b^4) (c^2) (p^2) (q^3) (r^3)+55 (a^4) (b^6) (c^2) (p^2) (q^3) (r^3)-41 (a^2) (b^8) (c^2) (p^2) (q^3) (r^3)+8 (b^10) (c^2) (p^2) (q^3) (r^3)-32 (a^8) (c^4) (p^2) (q^3) (r^3)+48 (a^6) (b^2) (c^4) (p^2) (q^3) (r^3)-37 (a^4) (b^4) (c^4) (p^2) (q^3) (r^3)+46 (a^2) (b^6) (c^4) (p^2) (q^3) (r^3)-25 (b^8) (c^4) (p^2) (q^3) (r^3)+35 (a^6) (c^6) (p^2) (q^3) (r^3)-27 (a^4) (b^2) (c^6) (p^2) (q^3) (r^3)-20 (a^2) (b^4) (c^6) (p^2) (q^3) (r^3)+60 (b^6) (c^6) (p^2) (q^3) (r^3)-14 (a^4) (c^8) (p^2) (q^3) (r^3)-19 (a^2) (b^2) (c^8) (p^2) (q^3) (r^3)-80 (b^4) (c^8) (p^2) (q^3) (r^3)+17 (a^2) (c^10) (p^2) (q^3) (r^3)+52 (b^2) (c^10) (p^2) (q^3) (r^3)-13 (c^12) (p^2) (q^3) (r^3)+3 (a^10) (b^2) p (q^4) (r^3)-13 (a^8) (b^4) p (q^4) (r^3)+22 (a^6) (b^6) p (q^4) (r^3)-18 (a^4) (b^8) p (q^4) (r^3)+7 (a^2) (b^10) p (q^4) (r^3)-(b^12) p (q^4) (r^3)+6 (a^10) (c^2) p (q^4) (r^3)-9 (a^8) (b^2) (c^2) p (q^4) (r^3)-19 (a^6) (b^4) (c^2) p (q^4) (r^3)+47 (a^4) (b^6) (c^2) p (q^4) (r^3)-31 (a^2) (b^8) (c^2) p (q^4) (r^3)+6 (b^10) (c^2) p (q^4) (r^3)+12 (a^6) (b^2) (c^4) p (q^4) (r^3)-51 (a^4) (b^4) (c^4) p (q^4) (r^3)+54 (a^2) (b^6) (c^4) p (q^4) (r^3)-15 (b^8) (c^4) p (q^4) (r^3)+9 (a^6) (c^6) p (q^4) (r^3)+33 (a^4) (b^2) (c^6) p (q^4) (r^3)-46 (a^2) (b^4) (c^6) p (q^4) (r^3)+20 (b^6) (c^6) p (q^4) (r^3)-11 (a^4) (c^8) p (q^4) (r^3)+19 (a^2) (b^2) (c^8) p (q^4) (r^3)-15 (b^4) (c^8) p (q^4) (r^3)-3 (a^2) (c^10) p (q^4) (r^3)+6 (b^2) (c^10) p (q^4) (r^3)-(c^12) p (q^4) (r^3)-3 (a^8) (b^4) (p^4) (r^4)+9 (a^6) (b^6) (p^4) (r^4)-9 (a^4) (b^8) (p^4) (r^4)+3 (a^2) (b^10) (p^4) (r^4)+12 (a^6) (b^4) (c^2) (p^4) (r^4)-17 (a^4) (b^6) (c^2) (p^4) (r^4)+2 (a^2) (b^8) (c^2) (p^4) (r^4)+3 (b^10) (c^2) (p^4) (r^4)-18 (a^4) (b^4) (c^4) (p^4) (r^4)+7 (a^2) (b^6) (c^4) (p^4) (r^4)-(b^8) (c^4) (p^4) (r^4)+12 (a^2) (b^4) (c^6) (p^4) (r^4)+(b^6) (c^6) (p^4) (r^4)-3 (b^4) (c^8) (p^4) (r^4)-2 (a^12) (p^3) q (r^4)+9 (a^10) (b^2) (p^3) q (r^4)-24 (a^8) (b^4) (p^3) q (r^4)+40 (a^6) (b^6) (p^3) q (r^4)-36 (a^4) (b^8) (p^3) q (r^4)+15 (a^2) (b^10) (p^3) q (r^4)-2 (b^12) (p^3) q (r^4)+12 (a^10) (c^2) (p^3) q (r^4)-37 (a^8) (b^2) (c^2) (p^3) q (r^4)+43 (a^6) (b^4) (c^2) (p^3) q (r^4)-11 (a^4) (b^6) (c^2) (p^3) q (r^4)-11 (a^2) (b^8) (c^2) (p^3) q (r^4)+4 (b^10) (c^2) (p^3) q (r^4)-30 (a^8) (c^4) (p^3) q (r^4)+58 (a^6) (b^2) (c^4) (p^3) q (r^4)-21 (a^4) (b^4) (c^4) (p^3) q (r^4)-6 (a^2) (b^6) (c^4) (p^3) q (r^4)-17 (b^8) (c^4) (p^3) q (r^4)+40 (a^6) (c^6) (p^3) q (r^4)-42 (a^4) (b^2) (c^6) (p^3) q (r^4)+9 (a^2) (b^4) (c^6) (p^3) q (r^4)+25 (b^6) (c^6) (p^3) q (r^4)-30 (a^4) (c^8) (p^3) q (r^4)+13 (a^2) (b^2) (c^8) (p^3) q (r^4)-7 (b^4) (c^8) (p^3) q (r^4)+12 (a^2) (c^10) (p^3) q (r^4)-(b^2) (c^10) (p^3) q (r^4)-2 (c^12) (p^3) q (r^4)-4 (a^12) (p^2) (q^2) (r^4)+21 (a^10) (b^2) (p^2) (q^2) (r^4)-48 (a^8) (b^4) (p^2) (q^2) (r^4)+62 (a^6) (b^6) (p^2) (q^2) (r^4)-48 (a^4) (b^8) (p^2) (q^2) (r^4)+21 (a^2) (b^10) (p^2) (q^2) (r^4)-4 (b^12) (p^2) (q^2) (r^4)+13 (a^10) (c^2) (p^2) (q^2) (r^4)-50 (a^8) (b^2) (c^2) (p^2) (q^2) (r^4)+37 (a^6) (b^4) (c^2) (p^2) (q^2) (r^4)+37 (a^4) (b^6) (c^2) (p^2) (q^2) (r^4)-50 (a^2) (b^8) (c^2) (p^2) (q^2) (r^4)+13 (b^10) (c^2) (p^2) (q^2) (r^4)-20 (a^8) (c^4) (p^2) (q^2) (r^4)+37 (a^6) (b^2) (c^4) (p^2) (q^2) (r^4)-42 (a^4) (b^4) (c^4) (p^2) (q^2) (r^4)+37 (a^2) (b^6) (c^4) (p^2) (q^2) (r^4)-20 (b^8) (c^4) (p^2) (q^2) (r^4)+30 (a^6) (c^6) (p^2) (q^2) (r^4)+21 (a^4) (b^2) (c^6) (p^2) (q^2) (r^4)+21 (a^2) (b^4) (c^6) (p^2) (q^2) (r^4)+30 (b^6) (c^6) (p^2) (q^2) (r^4)-40 (a^4) (c^8) (p^2) (q^2) (r^4)-58 (a^2) (b^2) (c^8) (p^2) (q^2) (r^4)-40 (b^4) (c^8) (p^2) (q^2) (r^4)+29 (a^2) (c^10) (p^2) (q^2) (r^4)+29 (b^2) (c^10) (p^2) (q^2) (r^4)-8 (c^12) (p^2) (q^2) (r^4)-2 (a^12) p (q^3) (r^4)+15 (a^10) (b^2) p (q^3) (r^4)-36 (a^8) (b^4) p (q^3) (r^4)+40 (a^6) (b^6) p (q^3) (r^4)-24 (a^4) (b^8) p (q^3) (r^4)+9 (a^2) (b^10) p (q^3) (r^4)-2 (b^12) p (q^3) (r^4)+4 (a^10) (c^2) p (q^3) (r^4)-11 (a^8) (b^2) (c^2) p (q^3) (r^4)-11 (a^6) (b^4) (c^2) p (q^3) (r^4)+43 (a^4) (b^6) (c^2) p (q^3) (r^4)-37 (a^2) (b^8) (c^2) p (q^3) (r^4)+12 (b^10) (c^2) p (q^3) (r^4)-17 (a^8) (c^4) p (q^3) (r^4)-6 (a^6) (b^2) (c^4) p (q^3) (r^4)-21 (a^4) (b^4) (c^4) p (q^3) (r^4)+58 (a^2) (b^6) (c^4) p (q^3) (r^4)-30 (b^8) (c^4) p (q^3) (r^4)+25 (a^6) (c^6) p (q^3) (r^4)+9 (a^4) (b^2) (c^6) p (q^3) (r^4)-42 (a^2) (b^4) (c^6) p (q^3) (r^4)+40 (b^6) (c^6) p (q^3) (r^4)-7 (a^4) (c^8) p (q^3) (r^4)+13 (a^2) (b^2) (c^8) p (q^3) (r^4)-30 (b^4) (c^8) p (q^3) (r^4)-(a^2) (c^10) p (q^3) (r^4)+12 (b^2) (c^10) p (q^3) (r^4)-2 (c^12) p (q^3) (r^4)+3 (a^10) (b^2) (q^4) (r^4)-9 (a^8) (b^4) (q^4) (r^4)+9 (a^6) (b^6) (q^4) (r^4)-3 (a^4) (b^8) (q^4) (r^4)+3 (a^10) (c^2) (q^4) (r^4)+2 (a^8) (b^2) (c^2) (q^4) (r^4)-17 (a^6) (b^4) (c^2) (q^4) (r^4)+12 (a^4) (b^6) (c^2) (q^4) (r^4)-(a^8) (c^4) (q^4) (r^4)+7 (a^6) (b^2) (c^4) (q^4) (r^4)-18 (a^4) (b^4) (c^4) (q^4) (r^4)+(a^6) (c^6) (q^4) (r^4)+12 (a^4) (b^2) (c^6) (q^4) (r^4)-3 (a^4) (c^8) (q^4) (r^4)-3 (a^8) (b^4) (p^3) (r^5)+6 (a^6) (b^6) (p^3) (r^5)-4 (a^4) (b^8) (p^3) (r^5)+2 (a^2) (b^10) (p^3) (r^5)-(b^12) (p^3) (r^5)+12 (a^6) (b^4) (c^2) (p^3) (r^5)-8 (a^4) (b^6) (c^2) (p^3) (r^5)-4 (a^2) (b^8) (c^2) (p^3) (r^5)-18 (a^4) (b^4) (c^4) (p^3) (r^5)-2 (a^2) (b^6) (c^4) (p^3) (r^5)+12 (a^2) (b^4) (c^6) (p^3) (r^5)+4 (b^6) (c^6) (p^3) (r^5)-3 (b^4) (c^8) (p^3) (r^5)-(a^12) (p^2) q (r^5)+2 (a^10) (b^2) (p^2) q (r^5)-10 (a^8) (b^4) (p^2) q (r^5)+18 (a^6) (b^6) (p^2) q (r^5)-11 (a^4) (b^8) (p^2) q (r^5)+4 (a^2) (b^10) (p^2) q (r^5)-2 (b^12) (p^2) q (r^5)+6 (a^10) (c^2) (p^2) q (r^5)-6 (a^8) (b^2) (c^2) (p^2) q (r^5)+12 (a^6) (b^4) (c^2) (p^2) q (r^5)-8 (a^4) (b^6) (c^2) (p^2) q (r^5)-10 (a^2) (b^8) (c^2) (p^2) q (r^5)+6 (b^10) (c^2) (p^2) q (r^5)-15 (a^8) (c^4) (p^2) q (r^5)+4 (a^6) (b^2) (c^4) (p^2) q (r^5)+6 (a^4) (b^4) (c^4) (p^2) q (r^5)+14 (a^2) (b^6) (c^4) (p^2) q (r^5)-5 (b^8) (c^4) (p^2) q (r^5)+20 (a^6) (c^6) (p^2) q (r^5)+4 (a^4) (b^2) (c^6) (p^2) q (r^5)-8 (a^2) (b^4) (c^6) (p^2) q (r^5)-15 (a^4) (c^8) (p^2) q (r^5)-6 (a^2) (b^2) (c^8) (p^2) q (r^5)+6 (a^2) (c^10) (p^2) q (r^5)+2 (b^2) (c^10) (p^2) q (r^5)-(c^12) (p^2) q (r^5)-2 (a^12) p (q^2) (r^5)+4 (a^10) (b^2) p (q^2) (r^5)-11 (a^8) (b^4) p (q^2) (r^5)+18 (a^6) (b^6) p (q^2) (r^5)-10 (a^4) (b^8) p (q^2) (r^5)+2 (a^2) (b^10) p (q^2) (r^5)-(b^12) p (q^2) (r^5)+6 (a^10) (c^2) p (q^2) (r^5)-10 (a^8) (b^2) (c^2) p (q^2) (r^5)-8 (a^6) (b^4) (c^2) p (q^2) (r^5)+12 (a^4) (b^6) (c^2) p (q^2) (r^5)-6 (a^2) (b^8) (c^2) p (q^2) (r^5)+6 (b^10) (c^2) p (q^2) (r^5)-5 (a^8) (c^4) p (q^2) (r^5)+14 (a^6) (b^2) (c^4) p (q^2) (r^5)+6 (a^4) (b^4) (c^4) p (q^2) (r^5)+4 (a^2) (b^6) (c^4) p (q^2) (r^5)-15 (b^8) (c^4) p (q^2) (r^5)-8 (a^4) (b^2) (c^6) p (q^2) (r^5)+4 (a^2) (b^4) (c^6) p (q^2) (r^5)+20 (b^6) (c^6) p (q^2) (r^5)-6 (a^2) (b^2) (c^8) p (q^2) (r^5)-15 (b^4) (c^8) p (q^2) (r^5)+2 (a^2) (c^10) p (q^2) (r^5)+6 (b^2) (c^10) p (q^2) (r^5)-(c^12) p (q^2) (r^5)-(a^12) (q^3) (r^5)+2 (a^10) (b^2) (q^3) (r^5)-4 (a^8) (b^4) (q^3) (r^5)+6 (a^6) (b^6) (q^3) (r^5)-3 (a^4) (b^8) (q^3) (r^5)-4 (a^8) (b^2) (c^2) (q^3) (r^5)-8 (a^6) (b^4) (c^2) (q^3) (r^5)+12 (a^4) (b^6) (c^2) (q^3) (r^5)-2 (a^6) (b^2) (c^4) (q^3) (r^5)-18 (a^4) (b^4) (c^4) (q^3) (r^5)+4 (a^6) (c^6) (q^3) (r^5)+12 (a^4) (b^2) (c^6) (q^3) (r^5)-3 (a^4) (c^8) (q^3) (r^5)) x y+(q^2) ((a^2) (c^2) p q-(b^2) (c^2) p q+(c^4) p q+(a^4) p r-(a^2) (b^2) p r-2 (a^2) (c^2) p r-(b^2) (c^2) p r+(c^4) p r+(a^4) q r-(a^2) (b^2) q r+(a^2) (c^2) q r) ((a^2) (c^2) (p^2) q-(b^2) (c^2) (p^2) q+(c^4) (p^2) q+(a^4) (p^2) r-(a^2) (b^2) (p^2) r-2 (a^2) (c^2) (p^2) r-(b^2) (c^2) (p^2) r+(c^4) (p^2) r+2 (a^4) p q r-3 (a^2) (b^2) p q r+(b^4) p q r+(a^2) (c^2) p q r-2 (b^2) (c^2) p q r+(c^4) p q r+(a^4) p (r^2)+(b^4) p (r^2)-2 (a^2) (c^2) p (r^2)-2 (b^2) (c^2) p (r^2)+(c^4) p (r^2)+2 (a^4) q (r^2)) (2 (c^4) (p^2) q+(a^4) (p^2) r-2 (a^2) (b^2) (p^2) r+(b^4) (p^2) r-2 (a^2) (c^2) (p^2) r+(c^4) (p^2) r+(a^4) p q r-2 (a^2) (b^2) p q r+(b^4) p q r+(a^2) (c^2) p q r-3 (b^2) (c^2) p q r+2 (c^4) p q r+(a^4) p (r^2)-(a^2) (b^2) p (r^2)-2 (a^2) (c^2) p (r^2)-(b^2) (c^2) p (r^2)+(c^4) p (r^2)+(a^4) q (r^2)-(a^2) (b^2) q (r^2)+(a^2) (c^2) q (r^2)) (y^2)-p r (3 (a^8) (c^4) (p^4) (q^4)-12 (a^6) (b^2) (c^4) (p^4) (q^4)+18 (a^4) (b^4) (c^4) (p^4) (q^4)-12 (a^2) (b^6) (c^4) (p^4) (q^4)+3 (b^8) (c^4) (p^4) (q^4)-9 (a^6) (c^6) (p^4) (q^4)+17 (a^4) (b^2) (c^6) (p^4) (q^4)-7 (a^2) (b^4) (c^6) (p^4) (q^4)-(b^6) (c^6) (p^4) (q^4)+9 (a^4) (c^8) (p^4) (q^4)-2 (a^2) (b^2) (c^8) (p^4) (q^4)+(b^4) (c^8) (p^4) (q^4)-3 (a^2) (c^10) (p^4) (q^4)-3 (b^2) (c^10) (p^4) (q^4)+3 (a^8) (c^4) (p^3) (q^5)-12 (a^6) (b^2) (c^4) (p^3) (q^5)+18 (a^4) (b^4) (c^4) (p^3) (q^5)-12 (a^2) (b^6) (c^4) (p^3) (q^5)+3 (b^8) (c^4) (p^3) (q^5)-6 (a^6) (c^6) (p^3) (q^5)+8 (a^4) (b^2) (c^6) (p^3) (q^5)+2 (a^2) (b^4) (c^6) (p^3) (q^5)-4 (b^6) (c^6) (p^3) (q^5)+4 (a^4) (c^8) (p^3) (q^5)+4 (a^2) (b^2) (c^8) (p^3) (q^5)-2 (a^2) (c^10) (p^3) (q^5)+(c^12) (p^3) (q^5)+(a^12) (p^4) (q^3) r-6 (a^10) (b^2) (p^4) (q^3) r+15 (a^8) (b^4) (p^4) (q^3) r-20 (a^6) (b^6) (p^4) (q^3) r+15 (a^4) (b^8) (p^4) (q^3) r-6 (a^2) (b^10) (p^4) (q^3) r+(b^12) (p^4) (q^3) r-7 (a^10) (c^2) (p^4) (q^3) r+31 (a^8) (b^2) (c^2) (p^4) (q^3) r-54 (a^6) (b^4) (c^2) (p^4) (q^3) r+46 (a^4) (b^6) (c^2) (p^4) (q^3) r-19 (a^2) (b^8) (c^2) (p^4) (q^3) r+3 (b^10) (c^2) (p^4) (q^3) r+18 (a^8) (c^4) (p^4) (q^3) r-47 (a^6) (b^2) (c^4) (p^4) (q^3) r+51 (a^4) (b^4) (c^4) (p^4) (q^3) r-33 (a^2) (b^6) (c^4) (p^4) (q^3) r+11 (b^8) (c^4) (p^4) (q^3) r-22 (a^6) (c^6) (p^4) (q^3) r+19 (a^4) (b^2) (c^6) (p^4) (q^3) r-12 (a^2) (b^4) (c^6) (p^4) (q^3) r-9 (b^6) (c^6) (p^4) (q^3) r+13 (a^4) (c^8) (p^4) (q^3) r+9 (a^2) (b^2) (c^8) (p^4) (q^3) r-3 (a^2) (c^10) (p^4) (q^3) r-6 (b^2) (c^10) (p^4) (q^3) r+2 (a^12) (p^3) (q^4) r-12 (a^10) (b^2) (p^3) (q^4) r+30 (a^8) (b^4) (p^3) (q^4) r-40 (a^6) (b^6) (p^3) (q^4) r+30 (a^4) (b^8) (p^3) (q^4) r-12 (a^2) (b^10) (p^3) (q^4) r+2 (b^12) (p^3) (q^4) r-9 (a^10) (c^2) (p^3) (q^4) r+37 (a^8) (b^2) (c^2) (p^3) (q^4) r-58 (a^6) (b^4) (c^2) (p^3) (q^4) r+42 (a^4) (b^6) (c^2) (p^3) (q^4) r-13 (a^2) (b^8) (c^2) (p^3) (q^4) r+(b^10) (c^2) (p^3) (q^4) r+24 (a^8) (c^4) (p^3) (q^4) r-43 (a^6) (b^2) (c^4) (p^3) (q^4) r+21 (a^4) (b^4) (c^4) (p^3) (q^4) r-9 (a^2) (b^6) (c^4) (p^3) (q^4) r+7 (b^8) (c^4) (p^3) (q^4) r-40 (a^6) (c^6) (p^3) (q^4) r+11 (a^4) (b^2) (c^6) (p^3) (q^4) r+6 (a^2) (b^4) (c^6) (p^3) (q^4) r-25 (b^6) (c^6) (p^3) (q^4) r+36 (a^4) (c^8) (p^3) (q^4) r+11 (a^2) (b^2) (c^8) (p^3) (q^4) r+17 (b^4) (c^8) (p^3) (q^4) r-15 (a^2) (c^10) (p^3) (q^4) r-4 (b^2) (c^10) (p^3) (q^4) r+2 (c^12) (p^3) (q^4) r+(a^12) (p^2) (q^5) r-6 (a^10) (b^2) (p^2) (q^5) r+15 (a^8) (b^4) (p^2) (q^5) r-20 (a^6) (b^6) (p^2) (q^5) r+15 (a^4) (b^8) (p^2) (q^5) r-6 (a^2) (b^10) (p^2) (q^5) r+(b^12) (p^2) (q^5) r-2 (a^10) (c^2) (p^2) (q^5) r+6 (a^8) (b^2) (c^2) (p^2) (q^5) r-4 (a^6) (b^4) (c^2) (p^2) (q^5) r-4 (a^4) (b^6) (c^2) (p^2) (q^5) r+6 (a^2) (b^8) (c^2) (p^2) (q^5) r-2 (b^10) (c^2) (p^2) (q^5) r+10 (a^8) (c^4) (p^2) (q^5) r-12 (a^6) (b^2) (c^4) (p^2) (q^5) r-6 (a^4) (b^4) (c^4) (p^2) (q^5) r+8 (a^2) (b^6) (c^4) (p^2) (q^5) r-18 (a^6) (c^6) (p^2) (q^5) r+8 (a^4) (b^2) (c^6) (p^2) (q^5) r-14 (a^2) (b^4) (c^6) (p^2) (q^5) r+11 (a^4) (c^8) (p^2) (q^5) r+10 (a^2) (b^2) (c^8) (p^2) (q^5) r+5 (b^4) (c^8) (p^2) (q^5) r-4 (a^2) (c^10) (p^2) (q^5) r-6 (b^2) (c^10) (p^2) (q^5) r+2 (c^12) (p^2) (q^5) r-(a^10) (b^2) (p^4) (q^2) (r^2)+10 (a^8) (b^4) (p^4) (q^2) (r^2)-30 (a^6) (b^6) (p^4) (q^2) (r^2)+40 (a^4) (b^8) (p^4) (q^2) (r^2)-25 (a^2) (b^10) (p^4) (q^2) (r^2)+6 (b^12) (p^4) (q^2) (r^2)+(a^8) (b^2) (c^2) (p^4) (q^2) (r^2)-23 (a^6) (b^4) (c^2) (p^4) (q^2) (r^2)+49 (a^4) (b^6) (c^2) (p^4) (q^2) (r^2)-33 (a^2) (b^8) (c^2) (p^4) (q^2) (r^2)+6 (b^10) (c^2) (p^4) (q^2) (r^2)+6 (a^6) (b^2) (c^4) (p^4) (q^2) (r^2)+13 (a^4) (b^4) (c^4) (p^4) (q^2) (r^2)-4 (a^2) (b^6) (c^4) (p^4) (q^2) (r^2)+9 (b^8) (c^4) (p^4) (q^2) (r^2)-14 (a^4) (b^2) (c^6) (p^4) (q^2) (r^2)+3 (a^2) (b^4) (c^6) (p^4) (q^2) (r^2)-15 (b^6) (c^6) (p^4) (q^2) (r^2)+11 (a^2) (b^2) (c^8) (p^4) (q^2) (r^2)-3 (b^4) (c^8) (p^4) (q^2) (r^2)-3 (b^2) (c^10) (p^4) (q^2) (r^2)+2 (a^12) (p^3) (q^3) (r^2)-8 (a^10) (b^2) (p^3) (q^3) (r^2)+25 (a^8) (b^4) (p^3) (q^3) (r^2)-60 (a^6) (b^6) (p^3) (q^3) (r^2)+80 (a^4) (b^8) (p^3) (q^3) (r^2)-52 (a^2) (b^10) (p^3) (q^3) (r^2)+13 (b^12) (p^3) (q^3) (r^2)-17 (a^10) (c^2) (p^3) (q^3) (r^2)+41 (a^8) (b^2) (c^2) (p^3) (q^3) (r^2)-46 (a^6) (b^4) (c^2) (p^3) (q^3) (r^2)+20 (a^4) (b^6) (c^2) (p^3) (q^3) (r^2)+19 (a^2) (b^8) (c^2) (p^3) (q^3) (r^2)-17 (b^10) (c^2) (p^3) (q^3) (r^2)+49 (a^8) (c^4) (p^3) (q^3) (r^2)-55 (a^6) (b^2) (c^4) (p^3) (q^3) (r^2)+37 (a^4) (b^4) (c^4) (p^3) (q^3) (r^2)+27 (a^2) (b^6) (c^4) (p^3) (q^3) (r^2)+14 (b^8) (c^4) (p^3) (q^3) (r^2)-66 (a^6) (c^6) (p^3) (q^3) (r^2)+11 (a^4) (b^2) (c^6) (p^3) (q^3) (r^2)-48 (a^2) (b^4) (c^6) (p^3) (q^3) (r^2)-35 (b^6) (c^6) (p^3) (q^3) (r^2)+44 (a^4) (c^8) (p^3) (q^3) (r^2)+19 (a^2) (b^2) (c^8) (p^3) (q^3) (r^2)+32 (b^4) (c^8) (p^3) (q^3) (r^2)-13 (a^2) (c^10) (p^3) (q^3) (r^2)-8 (b^2) (c^10) (p^3) (q^3) (r^2)+(c^12) (p^3) (q^3) (r^2)+4 (a^12) (p^2) (q^4) (r^2)-13 (a^10) (b^2) (p^2) (q^4) (r^2)+20 (a^8) (b^4) (p^2) (q^4) (r^2)-30 (a^6) (b^6) (p^2) (q^4) (r^2)+40 (a^4) (b^8) (p^2) (q^4) (r^2)-29 (a^2) (b^10) (p^2) (q^4) (r^2)+8 (b^12) (p^2) (q^4) (r^2)-21 (a^10) (c^2) (p^2) (q^4) (r^2)+50 (a^8) (b^2) (c^2) (p^2) (q^4) (r^2)-37 (a^6) (b^4) (c^2) (p^2) (q^4) (r^2)-21 (a^4) (b^6) (c^2) (p^2) (q^4) (r^2)+58 (a^2) (b^8) (c^2) (p^2) (q^4) (r^2)-29 (b^10) (c^2) (p^2) (q^4) (r^2)+48 (a^8) (c^4) (p^2) (q^4) (r^2)-37 (a^6) (b^2) (c^4) (p^2) (q^4) (r^2)+42 (a^4) (b^4) (c^4) (p^2) (q^4) (r^2)-21 (a^2) (b^6) (c^4) (p^2) (q^4) (r^2)+40 (b^8) (c^4) (p^2) (q^4) (r^2)-62 (a^6) (c^6) (p^2) (q^4) (r^2)-37 (a^4) (b^2) (c^6) (p^2) (q^4) (r^2)-37 (a^2) (b^4) (c^6) (p^2) (q^4) (r^2)-30 (b^6) (c^6) (p^2) (q^4) (r^2)+48 (a^4) (c^8) (p^2) (q^4) (r^2)+50 (a^2) (b^2) (c^8) (p^2) (q^4) (r^2)+20 (b^4) (c^8) (p^2) (q^4) (r^2)-21 (a^2) (c^10) (p^2) (q^4) (r^2)-13 (b^2) (c^10) (p^2) (q^4) (r^2)+4 (c^12) (p^2) (q^4) (r^2)+2 (a^12) p (q^5) (r^2)-6 (a^10) (b^2) p (q^5) (r^2)+5 (a^8) (b^4) p (q^5) (r^2)-2 (a^2) (b^10) p (q^5) (r^2)+(b^12) p (q^5) (r^2)-4 (a^10) (c^2) p (q^5) (r^2)+10 (a^8) (b^2) (c^2) p (q^5) (r^2)-14 (a^6) (b^4) (c^2) p (q^5) (r^2)+8 (a^4) (b^6) (c^2) p (q^5) (r^2)+6 (a^2) (b^8) (c^2) p (q^5) (r^2)-6 (b^10) (c^2) p (q^5) (r^2)+11 (a^8) (c^4) p (q^5) (r^2)+8 (a^6) (b^2) (c^4) p (q^5) (r^2)-6 (a^4) (b^4) (c^4) p (q^5) (r^2)-4 (a^2) (b^6) (c^4) p (q^5) (r^2)+15 (b^8) (c^4) p (q^5) (r^2)-18 (a^6) (c^6) p (q^5) (r^2)-12 (a^4) (b^2) (c^6) p (q^5) (r^2)-4 (a^2) (b^4) (c^6) p (q^5) (r^2)-20 (b^6) (c^6) p (q^5) (r^2)+10 (a^4) (c^8) p (q^5) (r^2)+6 (a^2) (b^2) (c^8) p (q^5) (r^2)+15 (b^4) (c^8) p (q^5) (r^2)-2 (a^2) (c^10) p (q^5) (r^2)-6 (b^2) (c^10) p (q^5) (r^2)+(c^12) p (q^5) (r^2)-2 (a^8) (b^4) (p^4) q (r^3)+3 (a^6) (b^6) (p^4) q (r^3)+9 (a^4) (b^8) (p^4) q (r^3)-19 (a^2) (b^10) (p^4) q (r^3)+9 (b^12) (p^4) q (r^3)+8 (a^6) (b^4) (c^2) (p^4) q (r^3)-13 (a^4) (b^6) (c^2) (p^4) q (r^3)-6 (a^2) (b^8) (c^2) (p^4) q (r^3)+3 (b^10) (c^2) (p^4) q (r^3)-12 (a^4) (b^4) (c^4) (p^4) q (r^3)+17 (a^2) (b^6) (c^4) (p^4) q (r^3)-3 (b^8) (c^4) (p^4) q (r^3)+8 (a^2) (b^4) (c^6) (p^4) q (r^3)-7 (b^6) (c^6) (p^4) q (r^3)-2 (b^4) (c^8) (p^4) q (r^3)-4 (a^10) (b^2) (p^3) (q^2) (r^3)+13 (a^8) (b^4) (p^3) (q^2) (r^3)-11 (a^6) (b^6) (p^3) (q^2) (r^3)+19 (a^4) (b^8) (p^3) (q^2) (r^3)-37 (a^2) (b^10) (p^3) (q^2) (r^3)+20 (b^12) (p^3) (q^2) (r^3)+12 (a^8) (b^2) (c^2) (p^3) (q^2) (r^3)-44 (a^6) (b^4) (c^2) (p^3) (q^2) (r^3)+11 (a^4) (b^6) (c^2) (p^3) (q^2) (r^3)+26 (a^2) (b^8) (c^2) (p^3) (q^2) (r^3)-37 (b^10) (c^2) (p^3) (q^2) (r^3)-8 (a^6) (b^2) (c^4) (p^3) (q^2) (r^3)+62 (a^4) (b^4) (c^4) (p^3) (q^2) (r^3)+11 (a^2) (b^6) (c^4) (p^3) (q^2) (r^3)+19 (b^8) (c^4) (p^3) (q^2) (r^3)-8 (a^4) (b^2) (c^6) (p^3) (q^2) (r^3)-44 (a^2) (b^4) (c^6) (p^3) (q^2) (r^3)-11 (b^6) (c^6) (p^3) (q^2) (r^3)+12 (a^2) (b^2) (c^8) (p^3) (q^2) (r^3)+13 (b^4) (c^8) (p^3) (q^2) (r^3)-4 (b^2) (c^10) (p^3) (q^2) (r^3)+(a^12) (p^2) (q^3) (r^3)-8 (a^10) (b^2) (p^2) (q^3) (r^3)+32 (a^8) (b^4) (p^2) (q^3) (r^3)-35 (a^6) (b^6) (p^2) (q^3) (r^3)+14 (a^4) (b^8) (p^2) (q^3) (r^3)-17 (a^2) (b^10) (p^2) (q^3) (r^3)+13 (b^12) (p^2) (q^3) (r^3)-13 (a^10) (c^2) (p^2) (q^3) (r^3)+19 (a^8) (b^2) (c^2) (p^2) (q^3) (r^3)-48 (a^6) (b^4) (c^2) (p^2) (q^3) (r^3)+27 (a^4) (b^6) (c^2) (p^2) (q^3) (r^3)+19 (a^2) (b^8) (c^2) (p^2) (q^3) (r^3)-52 (b^10) (c^2) (p^2) (q^3) (r^3)+44 (a^8) (c^4) (p^2) (q^3) (r^3)+11 (a^6) (b^2) (c^4) (p^2) (q^3) (r^3)+37 (a^4) (b^4) (c^4) (p^2) (q^3) (r^3)+20 (a^2) (b^6) (c^4) (p^2) (q^3) (r^3)+80 (b^8) (c^4) (p^2) (q^3) (r^3)-66 (a^6) (c^6) (p^2) (q^3) (r^3)-55 (a^4) (b^2) (c^6) (p^2) (q^3) (r^3)-46 (a^2) (b^4) (c^6) (p^2) (q^3) (r^3)-60 (b^6) (c^6) (p^2) (q^3) (r^3)+49 (a^4) (c^8) (p^2) (q^3) (r^3)+41 (a^2) (b^2) (c^8) (p^2) (q^3) (r^3)+25 (b^4) (c^8) (p^2) (q^3) (r^3)-17 (a^2) (c^10) (p^2) (q^3) (r^3)-8 (b^2) (c^10) (p^2) (q^3) (r^3)+2 (c^12) (p^2) (q^3) (r^3)+2 (a^12) p (q^4) (r^3)-4 (a^10) (b^2) p (q^4) (r^3)+17 (a^8) (b^4) p (q^4) (r^3)-25 (a^6) (b^6) p (q^4) (r^3)+7 (a^4) (b^8) p (q^4) (r^3)+(a^2) (b^10) p (q^4) (r^3)+2 (b^12) p (q^4) (r^3)-15 (a^10) (c^2) p (q^4) (r^3)+11 (a^8) (b^2) (c^2) p (q^4) (r^3)+6 (a^6) (b^4) (c^2) p (q^4) (r^3)-9 (a^4) (b^6) (c^2) p (q^4) (r^3)-13 (a^2) (b^8) (c^2) p (q^4) (r^3)-12 (b^10) (c^2) p (q^4) (r^3)+36 (a^8) (c^4) p (q^4) (r^3)+11 (a^6) (b^2) (c^4) p (q^4) (r^3)+21 (a^4) (b^4) (c^4) p (q^4) (r^3)+42 (a^2) (b^6) (c^4) p (q^4) (r^3)+30 (b^8) (c^4) p (q^4) (r^3)-40 (a^6) (c^6) p (q^4) (r^3)-43 (a^4) (b^2) (c^6) p (q^4) (r^3)-58 (a^2) (b^4) (c^6) p (q^4) (r^3)-40 (b^6) (c^6) p (q^4) (r^3)+24 (a^4) (c^8) p (q^4) (r^3)+37 (a^2) (b^2) (c^8) p (q^4) (r^3)+30 (b^4) (c^8) p (q^4) (r^3)-9 (a^2) (c^10) p (q^4) (r^3)-12 (b^2) (c^10) p (q^4) (r^3)+2 (c^12) p (q^4) (r^3)+(a^12) (q^5) (r^3)-4 (a^6) (b^6) (q^5) (r^3)+3 (a^4) (b^8) (q^5) (r^3)-2 (a^10) (c^2) (q^5) (r^3)+4 (a^8) (b^2) (c^2) (q^5) (r^3)+2 (a^6) (b^4) (c^2) (q^5) (r^3)-12 (a^4) (b^6) (c^2) (q^5) (r^3)+4 (a^8) (c^4) (q^5) (r^3)+8 (a^6) (b^2) (c^4) (q^5) (r^3)+18 (a^4) (b^4) (c^4) (q^5) (r^3)-6 (a^6) (c^6) (q^5) (r^3)-12 (a^4) (b^2) (c^6) (q^5) (r^3)+3 (a^4) (c^8) (q^5) (r^3)-4 (a^4) (b^8) (p^4) (r^4)+4 (b^12) (p^4) (r^4)+8 (a^2) (b^8) (c^2) (p^4) (r^4)-4 (b^8) (c^4) (p^4) (r^4)-2 (a^8) (b^4) (p^3) q (r^4)-7 (a^6) (b^6) (p^3) q (r^4)-3 (a^4) (b^8) (p^3) q (r^4)+3 (a^2) (b^10) (p^3) q (r^4)+9 (b^12) (p^3) q (r^4)+8 (a^6) (b^4) (c^2) (p^3) q (r^4)+17 (a^4) (b^6) (c^2) (p^3) q (r^4)-6 (a^2) (b^8) (c^2) (p^3) q (r^4)-19 (b^10) (c^2) (p^3) q (r^4)-12 (a^4) (b^4) (c^4) (p^3) q (r^4)-13 (a^2) (b^6) (c^4) (p^3) q (r^4)+9 (b^8) (c^4) (p^3) q (r^4)+8 (a^2) (b^4) (c^6) (p^3) q (r^4)+3 (b^6) (c^6) (p^3) q (r^4)-2 (b^4) (c^8) (p^3) q (r^4)-3 (a^10) (b^2) (p^2) (q^2) (r^4)-3 (a^8) (b^4) (p^2) (q^2) (r^4)-15 (a^6) (b^6) (p^2) (q^2) (r^4)+9 (a^4) (b^8) (p^2) (q^2) (r^4)+6 (a^2) (b^10) (p^2) (q^2) (r^4)+6 (b^12) (p^2) (q^2) (r^4)+11 (a^8) (b^2) (c^2) (p^2) (q^2) (r^4)+3 (a^6) (b^4) (c^2) (p^2) (q^2) (r^4)-4 (a^4) (b^6) (c^2) (p^2) (q^2) (r^4)-33 (a^2) (b^8) (c^2) (p^2) (q^2) (r^4)-25 (b^10) (c^2) (p^2) (q^2) (r^4)-14 (a^6) (b^2) (c^4) (p^2) (q^2) (r^4)+13 (a^4) (b^4) (c^4) (p^2) (q^2) (r^4)+49 (a^2) (b^6) (c^4) (p^2) (q^2) (r^4)+40 (b^8) (c^4) (p^2) (q^2) (r^4)+6 (a^4) (b^2) (c^6) (p^2) (q^2) (r^4)-23 (a^2) (b^4) (c^6) (p^2) (q^2) (r^4)-30 (b^6) (c^6) (p^2) (q^2) (r^4)+(a^2) (b^2) (c^8) (p^2) (q^2) (r^4)+10 (b^4) (c^8) (p^2) (q^2) (r^4)-(b^2) (c^10) (p^2) (q^2) (r^4)-6 (a^10) (b^2) p (q^3) (r^4)-9 (a^6) (b^6) p (q^3) (r^4)+11 (a^4) (b^8) p (q^3) (r^4)+3 (a^2) (b^10) p (q^3) (r^4)+(b^12) p (q^3) (r^4)-3 (a^10) (c^2) p (q^3) (r^4)+9 (a^8) (b^2) (c^2) p (q^3) (r^4)-12 (a^6) (b^4) (c^2) p (q^3) (r^4)-33 (a^4) (b^6) (c^2) p (q^3) (r^4)-19 (a^2) (b^8) (c^2) p (q^3) (r^4)-6 (b^10) (c^2) p (q^3) (r^4)+13 (a^8) (c^4) p (q^3) (r^4)+19 (a^6) (b^2) (c^4) p (q^3) (r^4)+51 (a^4) (b^4) (c^4) p (q^3) (r^4)+46 (a^2) (b^6) (c^4) p (q^3) (r^4)+15 (b^8) (c^4) p (q^3) (r^4)-22 (a^6) (c^6) p (q^3) (r^4)-47 (a^4) (b^2) (c^6) p (q^3) (r^4)-54 (a^2) (b^4) (c^6) p (q^3) (r^4)-20 (b^6) (c^6) p (q^3) (r^4)+18 (a^4) (c^8) p (q^3) (r^4)+31 (a^2) (b^2) (c^8) p (q^3) (r^4)+15 (b^4) (c^8) p (q^3) (r^4)-7 (a^2) (c^10) p (q^3) (r^4)-6 (b^2) (c^10) p (q^3) (r^4)+(c^12) p (q^3) (r^4)-3 (a^10) (b^2) (q^4) (r^4)+(a^8) (b^4) (q^4) (r^4)-(a^6) (b^6) (q^4) (r^4)+3 (a^4) (b^8) (q^4) (r^4)-3 (a^10) (c^2) (q^4) (r^4)-2 (a^8) (b^2) (c^2) (q^4) (r^4)-7 (a^6) (b^4) (c^2) (q^4) (r^4)-12 (a^4) (b^6) (c^2) (q^4) (r^4)+9 (a^8) (c^4) (q^4) (r^4)+17 (a^6) (b^2) (c^4) (q^4) (r^4)+18 (a^4) (b^4) (c^4) (q^4) (r^4)-9 (a^6) (c^6) (q^4) (r^4)-12 (a^4) (b^2) (c^6) (q^4) (r^4)+3 (a^4) (c^8) (q^4) (r^4)) x z-q r (3 (a^8) (c^4) (p^5) (q^3)-12 (a^6) (b^2) (c^4) (p^5) (q^3)+18 (a^4) (b^4) (c^4) (p^5) (q^3)-12 (a^2) (b^6) (c^4) (p^5) (q^3)+3 (b^8) (c^4) (p^5) (q^3)-4 (a^6) (c^6) (p^5) (q^3)+2 (a^4) (b^2) (c^6) (p^5) (q^3)+8 (a^2) (b^4) (c^6) (p^5) (q^3)-6 (b^6) (c^6) (p^5) (q^3)+4 (a^2) (b^2) (c^8) (p^5) (q^3)+4 (b^4) (c^8) (p^5) (q^3)-2 (b^2) (c^10) (p^5) (q^3)+(c^12) (p^5) (q^3)+3 (a^8) (c^4) (p^4) (q^4)-12 (a^6) (b^2) (c^4) (p^4) (q^4)+18 (a^4) (b^4) (c^4) (p^4) (q^4)-12 (a^2) (b^6) (c^4) (p^4) (q^4)+3 (b^8) (c^4) (p^4) (q^4)-(a^6) (c^6) (p^4) (q^4)-7 (a^4) (b^2) (c^6) (p^4) (q^4)+17 (a^2) (b^4) (c^6) (p^4) (q^4)-9 (b^6) (c^6) (p^4) (q^4)+(a^4) (c^8) (p^4) (q^4)-2 (a^2) (b^2) (c^8) (p^4) (q^4)+9 (b^4) (c^8) (p^4) (q^4)-3 (a^2) (c^10) (p^4) (q^4)-3 (b^2) (c^10) (p^4) (q^4)+(a^12) (p^5) (q^2) r-6 (a^10) (b^2) (p^5) (q^2) r+15 (a^8) (b^4) (p^5) (q^2) r-20 (a^6) (b^6) (p^5) (q^2) r+15 (a^4) (b^8) (p^5) (q^2) r-6 (a^2) (b^10) (p^5) (q^2) r+(b^12) (p^5) (q^2) r-2 (a^10) (c^2) (p^5) (q^2) r+6 (a^8) (b^2) (c^2) (p^5) (q^2) r-4 (a^6) (b^4) (c^2) (p^5) (q^2) r-4 (a^4) (b^6) (c^2) (p^5) (q^2) r+6 (a^2) (b^8) (c^2) (p^5) (q^2) r-2 (b^10) (c^2) (p^5) (q^2) r+8 (a^6) (b^2) (c^4) (p^5) (q^2) r-6 (a^4) (b^4) (c^4) (p^5) (q^2) r-12 (a^2) (b^6) (c^4) (p^5) (q^2) r+10 (b^8) (c^4) (p^5) (q^2) r-14 (a^4) (b^2) (c^6) (p^5) (q^2) r+8 (a^2) (b^4) (c^6) (p^5) (q^2) r-18 (b^6) (c^6) (p^5) (q^2) r+5 (a^4) (c^8) (p^5) (q^2) r+10 (a^2) (b^2) (c^8) (p^5) (q^2) r+11 (b^4) (c^8) (p^5) (q^2) r-6 (a^2) (c^10) (p^5) (q^2) r-4 (b^2) (c^10) (p^5) (q^2) r+2 (c^12) (p^5) (q^2) r+2 (a^12) (p^4) (q^3) r-12 (a^10) (b^2) (p^4) (q^3) r+30 (a^8) (b^4) (p^4) (q^3) r-40 (a^6) (b^6) (p^4) (q^3) r+30 (a^4) (b^8) (p^4) (q^3) r-12 (a^2) (b^10) (p^4) (q^3) r+2 (b^12) (p^4) (q^3) r+(a^10) (c^2) (p^4) (q^3) r-13 (a^8) (b^2) (c^2) (p^4) (q^3) r+42 (a^6) (b^4) (c^2) (p^4) (q^3) r-58 (a^4) (b^6) (c^2) (p^4) (q^3) r+37 (a^2) (b^8) (c^2) (p^4) (q^3) r-9 (b^10) (c^2) (p^4) (q^3) r+7 (a^8) (c^4) (p^4) (q^3) r-9 (a^6) (b^2) (c^4) (p^4) (q^3) r+21 (a^4) (b^4) (c^4) (p^4) (q^3) r-43 (a^2) (b^6) (c^4) (p^4) (q^3) r+24 (b^8) (c^4) (p^4) (q^3) r-25 (a^6) (c^6) (p^4) (q^3) r+6 (a^4) (b^2) (c^6) (p^4) (q^3) r+11 (a^2) (b^4) (c^6) (p^4) (q^3) r-40 (b^6) (c^6) (p^4) (q^3) r+17 (a^4) (c^8) (p^4) (q^3) r+11 (a^2) (b^2) (c^8) (p^4) (q^3) r+36 (b^4) (c^8) (p^4) (q^3) r-4 (a^2) (c^10) (p^4) (q^3) r-15 (b^2) (c^10) (p^4) (q^3) r+2 (c^12) (p^4) (q^3) r+(a^12) (p^3) (q^4) r-6 (a^10) (b^2) (p^3) (q^4) r+15 (a^8) (b^4) (p^3) (q^4) r-20 (a^6) (b^6) (p^3) (q^4) r+15 (a^4) (b^8) (p^3) (q^4) r-6 (a^2) (b^10) (p^3) (q^4) r+(b^12) (p^3) (q^4) r+3 (a^10) (c^2) (p^3) (q^4) r-19 (a^8) (b^2) (c^2) (p^3) (q^4) r+46 (a^6) (b^4) (c^2) (p^3) (q^4) r-54 (a^4) (b^6) (c^2) (p^3) (q^4) r+31 (a^2) (b^8) (c^2) (p^3) (q^4) r-7 (b^10) (c^2) (p^3) (q^4) r+11 (a^8) (c^4) (p^3) (q^4) r-33 (a^6) (b^2) (c^4) (p^3) (q^4) r+51 (a^4) (b^4) (c^4) (p^3) (q^4) r-47 (a^2) (b^6) (c^4) (p^3) (q^4) r+18 (b^8) (c^4) (p^3) (q^4) r-9 (a^6) (c^6) (p^3) (q^4) r-12 (a^4) (b^2) (c^6) (p^3) (q^4) r+19 (a^2) (b^4) (c^6) (p^3) (q^4) r-22 (b^6) (c^6) (p^3) (q^4) r+9 (a^2) (b^2) (c^8) (p^3) (q^4) r+13 (b^4) (c^8) (p^3) (q^4) r-6 (a^2) (c^10) (p^3) (q^4) r-3 (b^2) (c^10) (p^3) (q^4) r+(a^12) (p^5) q (r^2)-2 (a^10) (b^2) (p^5) q (r^2)+5 (a^4) (b^8) (p^5) q (r^2)-6 (a^2) (b^10) (p^5) q (r^2)+2 (b^12) (p^5) q (r^2)-6 (a^10) (c^2) (p^5) q (r^2)+6 (a^8) (b^2) (c^2) (p^5) q (r^2)+8 (a^6) (b^4) (c^2) (p^5) q (r^2)-14 (a^4) (b^6) (c^2) (p^5) q (r^2)+10 (a^2) (b^8) (c^2) (p^5) q (r^2)-4 (b^10) (c^2) (p^5) q (r^2)+15 (a^8) (c^4) (p^5) q (r^2)-4 (a^6) (b^2) (c^4) (p^5) q (r^2)-6 (a^4) (b^4) (c^4) (p^5) q (r^2)+8 (a^2) (b^6) (c^4) (p^5) q (r^2)+11 (b^8) (c^4) (p^5) q (r^2)-20 (a^6) (c^6) (p^5) q (r^2)-4 (a^4) (b^2) (c^6) (p^5) q (r^2)-12 (a^2) (b^4) (c^6) (p^5) q (r^2)-18 (b^6) (c^6) (p^5) q (r^2)+15 (a^4) (c^8) (p^5) q (r^2)+6 (a^2) (b^2) (c^8) (p^5) q (r^2)+10 (b^4) (c^8) (p^5) q (r^2)-6 (a^2) (c^10) (p^5) q (r^2)-2 (b^2) (c^10) (p^5) q (r^2)+(c^12) (p^5) q (r^2)+8 (a^12) (p^4) (q^2) (r^2)-29 (a^10) (b^2) (p^4) (q^2) (r^2)+40 (a^8) (b^4) (p^4) (q^2) (r^2)-30 (a^6) (b^6) (p^4) (q^2) (r^2)+20 (a^4) (b^8) (p^4) (q^2) (r^2)-13 (a^2) (b^10) (p^4) (q^2) (r^2)+4 (b^12) (p^4) (q^2) (r^2)-29 (a^10) (c^2) (p^4) (q^2) (r^2)+58 (a^8) (b^2) (c^2) (p^4) (q^2) (r^2)-21 (a^6) (b^4) (c^2) (p^4) (q^2) (r^2)-37 (a^4) (b^6) (c^2) (p^4) (q^2) (r^2)+50 (a^2) (b^8) (c^2) (p^4) (q^2) (r^2)-21 (b^10) (c^2) (p^4) (q^2) (r^2)+40 (a^8) (c^4) (p^4) (q^2) (r^2)-21 (a^6) (b^2) (c^4) (p^4) (q^2) (r^2)+42 (a^4) (b^4) (c^4) (p^4) (q^2) (r^2)-37 (a^2) (b^6) (c^4) (p^4) (q^2) (r^2)+48 (b^8) (c^4) (p^4) (q^2) (r^2)-30 (a^6) (c^6) (p^4) (q^2) (r^2)-37 (a^4) (b^2) (c^6) (p^4) (q^2) (r^2)-37 (a^2) (b^4) (c^6) (p^4) (q^2) (r^2)-62 (b^6) (c^6) (p^4) (q^2) (r^2)+20 (a^4) (c^8) (p^4) (q^2) (r^2)+50 (a^2) (b^2) (c^8) (p^4) (q^2) (r^2)+48 (b^4) (c^8) (p^4) (q^2) (r^2)-13 (a^2) (c^10) (p^4) (q^2) (r^2)-21 (b^2) (c^10) (p^4) (q^2) (r^2)+4 (c^12) (p^4) (q^2) (r^2)+13 (a^12) (p^3) (q^3) (r^2)-52 (a^10) (b^2) (p^3) (q^3) (r^2)+80 (a^8) (b^4) (p^3) (q^3) (r^2)-60 (a^6) (b^6) (p^3) (q^3) (r^2)+25 (a^4) (b^8) (p^3) (q^3) (r^2)-8 (a^2) (b^10) (p^3) (q^3) (r^2)+2 (b^12) (p^3) (q^3) (r^2)-17 (a^10) (c^2) (p^3) (q^3) (r^2)+19 (a^8) (b^2) (c^2) (p^3) (q^3) (r^2)+20 (a^6) (b^4) (c^2) (p^3) (q^3) (r^2)-46 (a^4) (b^6) (c^2) (p^3) (q^3) (r^2)+41 (a^2) (b^8) (c^2) (p^3) (q^3) (r^2)-17 (b^10) (c^2) (p^3) (q^3) (r^2)+14 (a^8) (c^4) (p^3) (q^3) (r^2)+27 (a^6) (b^2) (c^4) (p^3) (q^3) (r^2)+37 (a^4) (b^4) (c^4) (p^3) (q^3) (r^2)-55 (a^2) (b^6) (c^4) (p^3) (q^3) (r^2)+49 (b^8) (c^4) (p^3) (q^3) (r^2)-35 (a^6) (c^6) (p^3) (q^3) (r^2)-48 (a^4) (b^2) (c^6) (p^3) (q^3) (r^2)+11 (a^2) (b^4) (c^6) (p^3) (q^3) (r^2)-66 (b^6) (c^6) (p^3) (q^3) (r^2)+32 (a^4) (c^8) (p^3) (q^3) (r^2)+19 (a^2) (b^2) (c^8) (p^3) (q^3) (r^2)+44 (b^4) (c^8) (p^3) (q^3) (r^2)-8 (a^2) (c^10) (p^3) (q^3) (r^2)-13 (b^2) (c^10) (p^3) (q^3) (r^2)+(c^12) (p^3) (q^3) (r^2)+6 (a^12) (p^2) (q^4) (r^2)-25 (a^10) (b^2) (p^2) (q^4) (r^2)+40 (a^8) (b^4) (p^2) (q^4) (r^2)-30 (a^6) (b^6) (p^2) (q^4) (r^2)+10 (a^4) (b^8) (p^2) (q^4) (r^2)-(a^2) (b^10) (p^2) (q^4) (r^2)+6 (a^10) (c^2) (p^2) (q^4) (r^2)-33 (a^8) (b^2) (c^2) (p^2) (q^4) (r^2)+49 (a^6) (b^4) (c^2) (p^2) (q^4) (r^2)-23 (a^4) (b^6) (c^2) (p^2) (q^4) (r^2)+(a^2) (b^8) (c^2) (p^2) (q^4) (r^2)+9 (a^8) (c^4) (p^2) (q^4) (r^2)-4 (a^6) (b^2) (c^4) (p^2) (q^4) (r^2)+13 (a^4) (b^4) (c^4) (p^2) (q^4) (r^2)+6 (a^2) (b^6) (c^4) (p^2) (q^4) (r^2)-15 (a^6) (c^6) (p^2) (q^4) (r^2)+3 (a^4) (b^2) (c^6) (p^2) (q^4) (r^2)-14 (a^2) (b^4) (c^6) (p^2) (q^4) (r^2)-3 (a^4) (c^8) (p^2) (q^4) (r^2)+11 (a^2) (b^2) (c^8) (p^2) (q^4) (r^2)-3 (a^2) (c^10) (p^2) (q^4) (r^2)+3 (a^8) (b^4) (p^5) (r^3)-4 (a^6) (b^6) (p^5) (r^3)+(b^12) (p^5) (r^3)-12 (a^6) (b^4) (c^2) (p^5) (r^3)+2 (a^4) (b^6) (c^2) (p^5) (r^3)+4 (a^2) (b^8) (c^2) (p^5) (r^3)-2 (b^10) (c^2) (p^5) (r^3)+18 (a^4) (b^4) (c^4) (p^5) (r^3)+8 (a^2) (b^6) (c^4) (p^5) (r^3)+4 (b^8) (c^4) (p^5) (r^3)-12 (a^2) (b^4) (c^6) (p^5) (r^3)-6 (b^6) (c^6) (p^5) (r^3)+3 (b^4) (c^8) (p^5) (r^3)+2 (a^12) (p^4) q (r^3)+(a^10) (b^2) (p^4) q (r^3)+7 (a^8) (b^4) (p^4) q (r^3)-25 (a^6) (b^6) (p^4) q (r^3)+17 (a^4) (b^8) (p^4) q (r^3)-4 (a^2) (b^10) (p^4) q (r^3)+2 (b^12) (p^4) q (r^3)-12 (a^10) (c^2) (p^4) q (r^3)-13 (a^8) (b^2) (c^2) (p^4) q (r^3)-9 (a^6) (b^4) (c^2) (p^4) q (r^3)+6 (a^4) (b^6) (c^2) (p^4) q (r^3)+11 (a^2) (b^8) (c^2) (p^4) q (r^3)-15 (b^10) (c^2) (p^4) q (r^3)+30 (a^8) (c^4) (p^4) q (r^3)+42 (a^6) (b^2) (c^4) (p^4) q (r^3)+21 (a^4) (b^4) (c^4) (p^4) q (r^3)+11 (a^2) (b^6) (c^4) (p^4) q (r^3)+36 (b^8) (c^4) (p^4) q (r^3)-40 (a^6) (c^6) (p^4) q (r^3)-58 (a^4) (b^2) (c^6) (p^4) q (r^3)-43 (a^2) (b^4) (c^6) (p^4) q (r^3)-40 (b^6) (c^6) (p^4) q (r^3)+30 (a^4) (c^8) (p^4) q (r^3)+37 (a^2) (b^2) (c^8) (p^4) q (r^3)+24 (b^4) (c^8) (p^4) q (r^3)-12 (a^2) (c^10) (p^4) q (r^3)-9 (b^2) (c^10) (p^4) q (r^3)+2 (c^12) (p^4) q (r^3)+13 (a^12) (p^3) (q^2) (r^3)-17 (a^10) (b^2) (p^3) (q^2) (r^3)+14 (a^8) (b^4) (p^3) (q^2) (r^3)-35 (a^6) (b^6) (p^3) (q^2) (r^3)+32 (a^4) (b^8) (p^3) (q^2) (r^3)-8 (a^2) (b^10) (p^3) (q^2) (r^3)+(b^12) (p^3) (q^2) (r^3)-52 (a^10) (c^2) (p^3) (q^2) (r^3)+19 (a^8) (b^2) (c^2) (p^3) (q^2) (r^3)+27 (a^6) (b^4) (c^2) (p^3) (q^2) (r^3)-48 (a^4) (b^6) (c^2) (p^3) (q^2) (r^3)+19 (a^2) (b^8) (c^2) (p^3) (q^2) (r^3)-13 (b^10) (c^2) (p^3) (q^2) (r^3)+80 (a^8) (c^4) (p^3) (q^2) (r^3)+20 (a^6) (b^2) (c^4) (p^3) (q^2) (r^3)+37 (a^4) (b^4) (c^4) (p^3) (q^2) (r^3)+11 (a^2) (b^6) (c^4) (p^3) (q^2) (r^3)+44 (b^8) (c^4) (p^3) (q^2) (r^3)-60 (a^6) (c^6) (p^3) (q^2) (r^3)-46 (a^4) (b^2) (c^6) (p^3) (q^2) (r^3)-55 (a^2) (b^4) (c^6) (p^3) (q^2) (r^3)-66 (b^6) (c^6) (p^3) (q^2) (r^3)+25 (a^4) (c^8) (p^3) (q^2) (r^3)+41 (a^2) (b^2) (c^8) (p^3) (q^2) (r^3)+49 (b^4) (c^8) (p^3) (q^2) (r^3)-8 (a^2) (c^10) (p^3) (q^2) (r^3)-17 (b^2) (c^10) (p^3) (q^2) (r^3)+2 (c^12) (p^3) (q^2) (r^3)+20 (a^12) (p^2) (q^3) (r^3)-37 (a^10) (b^2) (p^2) (q^3) (r^3)+19 (a^8) (b^4) (p^2) (q^3) (r^3)-11 (a^6) (b^6) (p^2) (q^3) (r^3)+13 (a^4) (b^8) (p^2) (q^3) (r^3)-4 (a^2) (b^10) (p^2) (q^3) (r^3)-37 (a^10) (c^2) (p^2) (q^3) (r^3)+26 (a^8) (b^2) (c^2) (p^2) (q^3) (r^3)+11 (a^6) (b^4) (c^2) (p^2) (q^3) (r^3)-44 (a^4) (b^6) (c^2) (p^2) (q^3) (r^3)+12 (a^2) (b^8) (c^2) (p^2) (q^3) (r^3)+19 (a^8) (c^4) (p^2) (q^3) (r^3)+11 (a^6) (b^2) (c^4) (p^2) (q^3) (r^3)+62 (a^4) (b^4) (c^4) (p^2) (q^3) (r^3)-8 (a^2) (b^6) (c^4) (p^2) (q^3) (r^3)-11 (a^6) (c^6) (p^2) (q^3) (r^3)-44 (a^4) (b^2) (c^6) (p^2) (q^3) (r^3)-8 (a^2) (b^4) (c^6) (p^2) (q^3) (r^3)+13 (a^4) (c^8) (p^2) (q^3) (r^3)+12 (a^2) (b^2) (c^8) (p^2) (q^3) (r^3)-4 (a^2) (c^10) (p^2) (q^3) (r^3)+9 (a^12) p (q^4) (r^3)-19 (a^10) (b^2) p (q^4) (r^3)+9 (a^8) (b^4) p (q^4) (r^3)+3 (a^6) (b^6) p (q^4) (r^3)-2 (a^4) (b^8) p (q^4) (r^3)+3 (a^10) (c^2) p (q^4) (r^3)-6 (a^8) (b^2) (c^2) p (q^4) (r^3)-13 (a^6) (b^4) (c^2) p (q^4) (r^3)+8 (a^4) (b^6) (c^2) p (q^4) (r^3)-3 (a^8) (c^4) p (q^4) (r^3)+17 (a^6) (b^2) (c^4) p (q^4) (r^3)-12 (a^4) (b^4) (c^4) p (q^4) (r^3)-7 (a^6) (c^6) p (q^4) (r^3)+8 (a^4) (b^2) (c^6) p (q^4) (r^3)-2 (a^4) (c^8) p (q^4) (r^3)+3 (a^8) (b^4) (p^4) (r^4)-(a^6) (b^6) (p^4) (r^4)+(a^4) (b^8) (p^4) (r^4)-3 (a^2) (b^10) (p^4) (r^4)-12 (a^6) (b^4) (c^2) (p^4) (r^4)-7 (a^4) (b^6) (c^2) (p^4) (r^4)-2 (a^2) (b^8) (c^2) (p^4) (r^4)-3 (b^10) (c^2) (p^4) (r^4)+18 (a^4) (b^4) (c^4) (p^4) (r^4)+17 (a^2) (b^6) (c^4) (p^4) (r^4)+9 (b^8) (c^4) (p^4) (r^4)-12 (a^2) (b^4) (c^6) (p^4) (r^4)-9 (b^6) (c^6) (p^4) (r^4)+3 (b^4) (c^8) (p^4) (r^4)+(a^12) (p^3) q (r^4)+3 (a^10) (b^2) (p^3) q (r^4)+11 (a^8) (b^4) (p^3) q (r^4)-9 (a^6) (b^6) (p^3) q (r^4)-6 (a^2) (b^10) (p^3) q (r^4)-6 (a^10) (c^2) (p^3) q (r^4)-19 (a^8) (b^2) (c^2) (p^3) q (r^4)-33 (a^6) (b^4) (c^2) (p^3) q (r^4)-12 (a^4) (b^6) (c^2) (p^3) q (r^4)+9 (a^2) (b^8) (c^2) (p^3) q (r^4)-3 (b^10) (c^2) (p^3) q (r^4)+15 (a^8) (c^4) (p^3) q (r^4)+46 (a^6) (b^2) (c^4) (p^3) q (r^4)+51 (a^4) (b^4) (c^4) (p^3) q (r^4)+19 (a^2) (b^6) (c^4) (p^3) q (r^4)+13 (b^8) (c^4) (p^3) q (r^4)-20 (a^6) (c^6) (p^3) q (r^4)-54 (a^4) (b^2) (c^6) (p^3) q (r^4)-47 (a^2) (b^4) (c^6) (p^3) q (r^4)-22 (b^6) (c^6) (p^3) q (r^4)+15 (a^4) (c^8) (p^3) q (r^4)+31 (a^2) (b^2) (c^8) (p^3) q (r^4)+18 (b^4) (c^8) (p^3) q (r^4)-6 (a^2) (c^10) (p^3) q (r^4)-7 (b^2) (c^10) (p^3) q (r^4)+(c^12) (p^3) q (r^4)+6 (a^12) (p^2) (q^2) (r^4)+6 (a^10) (b^2) (p^2) (q^2) (r^4)+9 (a^8) (b^4) (p^2) (q^2) (r^4)-15 (a^6) (b^6) (p^2) (q^2) (r^4)-3 (a^4) (b^8) (p^2) (q^2) (r^4)-3 (a^2) (b^10) (p^2) (q^2) (r^4)-25 (a^10) (c^2) (p^2) (q^2) (r^4)-33 (a^8) (b^2) (c^2) (p^2) (q^2) (r^4)-4 (a^6) (b^4) (c^2) (p^2) (q^2) (r^4)+3 (a^4) (b^6) (c^2) (p^2) (q^2) (r^4)+11 (a^2) (b^8) (c^2) (p^2) (q^2) (r^4)+40 (a^8) (c^4) (p^2) (q^2) (r^4)+49 (a^6) (b^2) (c^4) (p^2) (q^2) (r^4)+13 (a^4) (b^4) (c^4) (p^2) (q^2) (r^4)-14 (a^2) (b^6) (c^4) (p^2) (q^2) (r^4)-30 (a^6) (c^6) (p^2) (q^2) (r^4)-23 (a^4) (b^2) (c^6) (p^2) (q^2) (r^4)+6 (a^2) (b^4) (c^6) (p^2) (q^2) (r^4)+10 (a^4) (c^8) (p^2) (q^2) (r^4)+(a^2) (b^2) (c^8) (p^2) (q^2) (r^4)-(a^2) (c^10) (p^2) (q^2) (r^4)+9 (a^12) p (q^3) (r^4)+3 (a^10) (b^2) p (q^3) (r^4)-3 (a^8) (b^4) p (q^3) (r^4)-7 (a^6) (b^6) p (q^3) (r^4)-2 (a^4) (b^8) p (q^3) (r^4)-19 (a^10) (c^2) p (q^3) (r^4)-6 (a^8) (b^2) (c^2) p (q^3) (r^4)+17 (a^6) (b^4) (c^2) p (q^3) (r^4)+8 (a^4) (b^6) (c^2) p (q^3) (r^4)+9 (a^8) (c^4) p (q^3) (r^4)-13 (a^6) (b^2) (c^4) p (q^3) (r^4)-12 (a^4) (b^4) (c^4) p (q^3) (r^4)+3 (a^6) (c^6) p (q^3) (r^4)+8 (a^4) (b^2) (c^6) p (q^3) (r^4)-2 (a^4) (c^8) p (q^3) (r^4)+4 (a^12) (q^4) (r^4)-4 (a^8) (b^4) (q^4) (r^4)+8 (a^8) (b^2) (c^2) (q^4) (r^4)-4 (a^8) (c^4) (q^4) (r^4)) y z+(r^2) ((a^4) p q-2 (a^2) (b^2) p q+(b^4) p q-(a^2) (c^2) p q-(b^2) (c^2) p q+(a^2) (b^2) p r+(b^4) p r-(b^2) (c^2) p r+(a^4) q r+(a^2) (b^2) q r-(a^2) (c^2) q r) ((a^4) (p^2) q-2 (a^2) (b^2) (p^2) q+(b^4) (p^2) q-(a^2) (c^2) (p^2) q-(b^2) (c^2) (p^2) q+(a^4) p (q^2)-2 (a^2) (b^2) p (q^2)+(b^4) p (q^2)-2 (b^2) (c^2) p (q^2)+(c^4) p (q^2)+(a^2) (b^2) (p^2) r+(b^4) (p^2) r-(b^2) (c^2) (p^2) r+2 (a^4) p q r+(a^2) (b^2) p q r+(b^4) p q r-3 (a^2) (c^2) p q r-2 (b^2) (c^2) p q r+(c^4) p q r+2 (a^4) (q^2) r) ((a^4) (p^2) q-2 (a^2) (b^2) (p^2) q+(b^4) (p^2) q-2 (a^2) (c^2) (p^2) q+(c^4) (p^2) q+(a^4) p (q^2)-2 (a^2) (b^2) p (q^2)+(b^4) p (q^2)-(a^2) (c^2) p (q^2)-(b^2) (c^2) p (q^2)+2 (b^4) (p^2) r+(a^4) p q r+(a^2) (b^2) p q r+2 (b^4) p q r-2 (a^2) (c^2) p q r-3 (b^2) (c^2) p q r+(c^4) p q r+(a^4) (q^2) r+(a^2) (b^2) (q^2) r-(a^2) (c^2) (q^2) r) (z^2); (* QA-P4 Pedal-Conic; see QA-Co99-QAP4-Pedal-Conic-01.nb *)
QA2Co1a=p q r x y+(q^2) r x y-p (r^2) x y+q (r^2) x y-p (q^2) x z+p q r x z+(q^2) r x z+q (r^2) x z-p (q^2) y z-2 p q r y z-p (r^2) y z+2 (Sqrt[-p q r (p+q+r)]) x (r y-q z);(* 1st Circumscribed QA-Parabola *)
QA2Co1b=p q r x y+(q^2) r x y-p (r^2) x y+q (r^2) x y-p (q^2) x z+p q r x z+(q^2) r x z+q (r^2) x z-p (q^2) y z-2 p q r y z-p (r^2) y z-2 (Sqrt[-p q r (p+q+r)]) x (r y-q z); (* 2nd Circumscribed QA-Parabola *)

QGCi1=-q (2 (c^2) q-(a^2) r+(b^2) r+(c^2) r) (x^2)+(2 (c^2) p q-(a^2) p r+(b^2) p r+(c^2) p r+(a^2) q r-(b^2) q r+(c^2) q r) x y-((a^2)-(b^2)+(c^2)) p r (y^2)+(-(a^2) p q+(b^2) p q+(c^2) p q-2 (a^2) (q^2)+2 (b^2) (q^2)-2 (c^2) (q^2)+2 (b^2) p r+(a^2) q r+(b^2) q r-(c^2) q r) x z+((a^2) p q-(b^2) p q+(c^2) p q+(a^2) p r+(b^2) p r-(c^2) p r+2 (a^2) q r) y z-q ((a^2) p+(b^2) p-(c^2) p+2 (a^2) q) (z^2);  (* QA-DT Thales Circle*)
QGCi2=r (-(a^2) q+(b^2) q+(c^2) q+(b^2) r) (x^2)+(2 (c^2) p q-(a^2) q r+(b^2) q r-(c^2) q r+(a^2) (r^2)+(b^2) (r^2)-(c^2) (r^2)) x y-(c p-a r) (c p+a r) (y^2)+q (-(a^2) p+(b^2) p+(c^2) p-(a^2) r-(b^2) r+(c^2) r) x z+((a^2) (p^2)-(b^2) (p^2)-(c^2) (p^2)+(a^2) p q-(b^2) p q+(c^2) p q-2 (a^2) q r) y z-p ((b^2) p+(a^2) q+(b^2) q-(c^2) q) (z^2);  (* QL-DT Thales Circle*)
QGCo1=(q^2) (r^2) (x^2)+2 p q (r^2) x y+(p^2) (r^2) (y^2)-6 p (q^2) r x z+2 (p^2) q r y z+(p^2) (q^2) (z^2);  (* Inscribed Harmonic Conic *)
QGCo2=r x y-2 q x z+p y z;  (* Circumscribed Harmonic Conic *)
QGCo3=-(((p+q))^2) r x y+q (p-r) (p+2 q+r) x z+p (((q+r))^2) y z;  (* M3D Hyperbola *)
QGCu1=((a^4) q ((p^2) q+(q^3)+2 (q^2) r+2 q (r^2)+(r^3)+p (2 (q^2)+2 q r+(r^2)))+(c^4) q ((p^2) q+(q^3)+2 (q^2) r+2 q (r^2)+(r^3)+p (2 (q^2)+2 q r+(r^2)))+(b^4) (q+r) ((q^3)+3 (q^2) r+4 q (r^2)+(r^3)+(p^2) (q+r)+p (2 (q^2)+4 q r+3 (r^2)))+(b^2) (c^2) ((p^2) (2 (q^2)+2 q r-(r^2))+2 (q^2) ((q^2)+3 q r+2 (r^2))+p (4 (q^3)+8 (q^2) r+2 q (r^2)-(r^3)))-(a^2) (2 (c^2) q ((p^2) q+(q^3)+2 (q^2) r+2 q (r^2)+(r^3)+p (2 (q^2)+2 q r+(r^2)))+(b^2) (2 (q^4)+6 (q^3) r+8 (q^2) (r^2)+4 q (r^3)+(r^4)+2 (p^2) q (q+r)+p (4 (q^3)+8 (q^2) r+6 q (r^2)+(r^3))))) (x^3)+(-(c^4) ((p^2) (3 (q^2)-(r^2))+p (4 (q^3)+6 (q^2) r+2 q (r^2)-(r^3))+q ((q^3)+4 (q^2) r+4 q (r^2)+2 (r^3)))-(b^4) ((q^4)+4 (q^3) r+7 (q^2) (r^2)+6 q (r^3)+(r^4)+2 (p^3) (q+r)+(p^2) (5 (q^2)+10 q r+6 (r^2))+2 p (2 (q^3)+6 (q^2) r+7 q (r^2)+3 (r^3)))-(a^4) (2 (p^3) q+(q^4)+4 (q^3) r+6 (q^2) (r^2)+4 q (r^3)+2 (r^4)+(p^2) (5 (q^2)+6 q r+(r^2))+p (4 (q^3)+10 (q^2) r+8 q (r^2)+3 (r^3)))-(b^2) (c^2) (2 (p^3) (q+r)+(p^2) (8 (q^2)+14 q r+3 (r^2))+p (8 (q^3)+22 (q^2) r+18 q (r^2)+5 (r^3))+2 ((q^4)+4 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)))+(a^2) (2 (c^2) ((p^3) q+(q^4)+4 (q^3) r+5 (q^2) (r^2)+3 q (r^3)+(r^4)+p (q+r) (((2 q+r))^2)+(p^2) q (4 q+3 r))+(b^2) (2 (q^4)+8 (q^3) r+14 (q^2) (r^2)+12 q (r^3)+3 (r^4)+2 (p^3) (2 q+r)+2 (p^2) (5 (q^2)+8 q r+4 (r^2))+p (8 (q^3)+22 (q^2) r+24 q (r^2)+11 (r^3))))) (x^2) y+((b^4) (p-r) (((p+q+r))^2) (p+q+2 r)+(c^4) (q r (((q+r))^2)+(p^3) (q+2 r)+(p^2) (3 (q^2)+5 q r+(r^2))+p q ((q^2)+6 q r+5 (r^2)))+(a^4) ((p^4)+(p^3) (3 q+4 r)+(p^2) (3 (q^2)+9 q r+5 (r^2))+r ((q^3)+2 (q^2) r+q (r^2)-(r^3))+p ((q^3)+6 (q^2) r+7 q (r^2)+2 (r^3)))+(b^2) (c^2) (-(p^4)+2 (r^2) (((q+r))^2)+(p^3) (2 q+r)+(p^2) (5 (q^2)+8 q r+5 (r^2))+p (2 (q^3)+5 (q^2) r+10 q (r^2)+7 (r^3)))-(a^2) ((b^2) (2 (p^4)+(p^3) (6 q+7 r)-(r^2) ((q^2)+2 q r+3 (r^2))+(p^2) (6 (q^2)+14 q r+7 (r^2))+p (2 (q^3)+7 (q^2) r+6 q (r^2)+(r^3)))+2 (c^2) ((p^3) (2 q+r)+(p^2) (3 (q^2)+7 q r+2 (r^2))+r ((q^3)+2 (q^2) r+q (r^2)+(r^3))+p ((q^3)+6 (q^2) r+6 q (r^2)+3 (r^3))))) x (y^2)+(-(b^2) (p-r) (((p+q+r))^2) ((c^2) p-(a^2) r)-(a^4) r ((p^3)-(r^3)+2 (p^2) (q+r)+p (((q+r))^2))-(c^4) p (-(p^3)+(p^2) r+2 p r (q+r)+r (((q+r))^2))+2 (a^2) (c^2) p r ((p^2)+(((q+r))^2)+p (2 q+r))) (y^3)+((a^4) (2 (p^3) q+3 (q^4)+6 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^2) (5 (q^2)+4 q r+(r^2))+p (6 (q^3)+8 (q^2) r+5 q (r^2)+2 (r^3)))+(c^4) (2 (p^3) q+3 (q^4)+6 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^2) (5 (q^2)+4 q r+(r^2))+p (6 (q^3)+8 (q^2) r+5 q (r^2)+2 (r^3)))-(b^4) ((p^2) (3 (q^2)+6 q r+2 (r^2))+q ((q^3)+2 (q^2) r+q (r^2)+(r^3))+p (4 (q^3)+10 (q^2) r+7 q (r^2)+3 (r^3)))+(b^2) (c^2) (2 (p^3) (q+2 r)+(p^2) (2 (q^2)+14 q r+9 (r^2))+2 q ((q^3)+4 (q^2) r+4 q (r^2)+2 (r^3))+p (2 (q^3)+16 (q^2) r+16 q (r^2)+5 (r^3)))-(a^2) (2 (c^2) (2 (p^3) q+3 (q^4)+6 (q^3) r+6 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^2) (5 (q^2)+4 q r+(r^2))+p (6 (q^3)+8 (q^2) r+5 q (r^2)+2 (r^3)))+(b^2) (2 (q^4)+8 (q^3) r+12 (q^2) (r^2)+8 q (r^3)+(r^4)+2 (p^3) (q+r)+2 (p^2) ((q^2)+3 q r+3 (r^2))+p (2 (q^3)+8 (q^2) r+12 q (r^2)+5 (r^3))))) (x^2) z-2 ((b^2) (c^2) (3 (p^3) r+2 p q r (q+2 r)+(r^2) ((q^2)-(r^2))+(p^2) (-(q^2)+4 q r+4 (r^2)))+(a^4) ((p^4)+3 (p^3) (q+r)+(p^2) (5 (q^2)+7 q r+3 (r^2))+p (4 (q^3)+9 (q^2) r+7 q (r^2)+(r^3))+q ((q^3)+4 (q^2) r+5 q (r^2)+3 (r^3)))+(c^4) ((q^4)+4 (q^3) r+5 (q^2) (r^2)+3 q (r^3)+(r^4)+(p^3) (3 q+r)+(p^2) (5 (q^2)+7 q r+3 (r^2))+p (4 (q^3)+9 (q^2) r+7 q (r^2)+3 (r^3)))-(b^4) ((p^3) (3 q+4 r)+(p^2) (6 (q^2)+13 q r+7 (r^2))+q ((q^3)+4 (q^2) r+6 q (r^2)+3 (r^3))+p (4 (q^3)+12 (q^2) r+13 q (r^2)+4 (r^3)))-(a^2) ((b^2) ((p^4)+(q^2) (r^2)-(p^2) (((q+2 r))^2)-p r (2 (q^2)+4 q r+3 (r^2)))+(c^2) ((p^4)+2 (q^4)+8 (q^3) r+10 (q^2) (r^2)+6 q (r^3)+(r^4)+(p^3) (6 q+4 r)+2 (p^2) (5 (q^2)+7 q r+3 (r^2))+2 p (4 (q^3)+9 (q^2) r+7 q (r^2)+2 (r^3))))) x y z+(-(b^4) (p-r) (((p+q+r))^2) (2 p+q+r)+(b^2) (c^2) (3 (p^4)+(p^3) (2 q-r)-7 p r (((q+r))^2)-2 r (((q+r))^3)+(p^2) ((q^2)-6 q r-7 (r^2)))+(c^4) (-(p^4)+r (((q+r))^3)+(p^3) (q+2 r)+p (((q+r))^2) (q+4 r)+(p^2) (2 (q^2)+7 q r+5 (r^2)))+(a^4) ((p^3) q+q r ((q^2)+3 q r+(r^2))+(p^2) (2 (q^2)+5 q r+(r^2))+p ((q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(a^2) ((b^2) (2 (p^4)+(p^3) (4 q+7 r)+p r (5 (q^2)+8 q r+(r^2))+(p^2) (2 (q^2)+10 q r+5 (r^2))+r (2 (q^3)+5 (q^2) r+2 q (r^2)-(r^3)))-2 (c^2) ((p^4)+(p^3) (q+3 r)+2 (p^2) ((q^2)+3 q r+(r^2))+q r ((q^2)+3 q r+2 (r^2))+p ((q^3)+6 (q^2) r+7 q (r^2)+(r^3))))) (y^2) z+(-(b^4) ((p^3) (q+3 r)+(p^2) ((q^2)+7 q r+2 (r^2))+(q^2) ((q^2)+4 q r+3 (r^2))+2 p q ((q^2)+5 q r+3 (r^2)))-(b^2) (c^2) ((p^4)+(p^3) (8 q+5 r)+6 (p^2) (2 (q^2)+2 q r+(r^2))+2 q ((q^3)+(q^2) r+q (r^2)+(r^3))+2 p (4 (q^3)+4 (q^2) r+3 q (r^2)+(r^3)))+(a^4) ((p^4)+(p^3) (3 q+2 r)+(p^2) (6 (q^2)+5 q r+(r^2))+2 p q (3 (q^2)+4 q r+2 (r^2))+q (3 (q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(c^4) ((p^4)+(p^3) (3 q+2 r)+(p^2) (6 (q^2)+5 q r+(r^2))+2 p q (3 (q^2)+4 q r+2 (r^2))+q (3 (q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(a^2) (-2 (c^2) ((p^4)+(p^3) (3 q+2 r)+(p^2) (6 (q^2)+5 q r+(r^2))+2 p q (3 (q^2)+4 q r+2 (r^2))+q (3 (q^3)+6 (q^2) r+5 q (r^2)+2 (r^3)))+(b^2) ((p^3) (4 q+5 r)+(p^2) (8 (q^2)+16 q r+9 (r^2))+2 q ((q^3)+(q^2) r+q (r^2)+(r^3))+2 p (4 (q^3)+8 (q^2) r+7 q (r^2)+2 (r^3))))) x (z^2)+(-(a^4) ((p^3) (2 q-r)+2 p (q^2) (2 q+3 r)+(p^2) (4 (q^2)+2 q r-(r^2))+(q^2) ((q^2)+4 q r+3 (r^2)))-(c^4) (2 (p^4)+q (((q+r))^2) (q+2 r)+(p^3) (4 q+3 r)+(p^2) (6 (q^2)+8 q r+(r^2))+2 p q (2 (q^2)+5 q r+3 (r^2)))-(b^4) ((p^4)+6 (p^3) (q+r)+q (((q+r))^2) (q+2 r)+(p^2) (7 (q^2)+14 q r+6 (r^2))+2 p (2 (q^3)+6 (q^2) r+5 q (r^2)+(r^3)))+(b^2) (c^2) (3 (p^4)+2 q (((q+r))^2) (q+2 r)+(p^3) (12 q+11 r)+2 (p^2) (7 (q^2)+12 q r+4 (r^2))+2 p (4 (q^3)+11 (q^2) r+8 q (r^2)+(r^3)))-(a^2) (-2 (c^2) ((p^4)+5 (p^2) q (q+r)+(p^3) (3 q+r)+p q (4 (q^2)+8 q r+3 (r^2))+q ((q^3)+4 (q^2) r+4 q (r^2)+(r^3)))+(b^2) (2 (p^4)+(p^3) (6 q+5 r)+3 (p^2) (4 (q^2)+6 q r+(r^2))+2 q ((q^3)+4 (q^2) r+4 q (r^2)+(r^3))+2 p (4 (q^3)+11 (q^2) r+7 q (r^2)+(r^3))))) y (z^2)+(((((a^2)-(c^2)))^2) q ((p^3)+2 p q (q+r)+q (((q+r))^2)+(p^2) (2 q+r))+(b^4) (p+q) ((p^3)+q (((q+r))^2)+(p^2) (4 q+3 r)+p (3 (q^2)+4 q r+(r^2)))-(b^2) ((a^2) ((p^3) r-2 (q^2) (((q+r))^2)+(p^2) (-4 (q^2)-2 q r+(r^2))-2 p q (3 (q^2)+4 q r+(r^2)))+(c^2) ((p^4)+2 (q^2) (((q+r))^2)+(p^3) (4 q+r)+2 (p^2) q (4 q+3 r)+2 p q (3 (q^2)+4 q r+(r^2))))) (z^3);
(* Van Aubel Cubic *)

QG2Cu1a=(-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q-(1/4) (((-(a^2)+(b^2)+(c^2)))^2) q-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) (x^2) y+((1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) p+(1/4) (((-(a^2)+(b^2)+(c^2)))^2) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) x (y^2)-((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((-(a^2)+(b^2)+(c^2)) q+(1/2) ((a^2)+(b^2)-(c^2)) r+(1/2) (-(a^2)+(b^2)+(c^2)) r) (x^2) z+2 ((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) p+(1/2) (-(a^2)+(b^2)+(c^2)) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) r-(1/2) ((a^2)+(b^2)-(c^2)) r) x y z+((1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) r-(1/4) ((((a^2)+(b^2)-(c^2)))^2) r) (y^2) z+((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((1/2) ((a^2)+(b^2)-(c^2)) p+(1/2) (-(a^2)+(b^2)+(c^2)) p+((a^2)+(b^2)-(c^2)) q) x (z^2)+((1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p+(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q+(1/4) ((((a^2)+(b^2)-(c^2)))^2) q) y (z^2);  (* 1st Perspective Square Cubic *)
QG2Cu1b=(-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q-(1/4) (((-(a^2)+(b^2)+(c^2)))^2) q+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) (x^2) y+((1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) p+(1/4) (((-(a^2)+(b^2)+(c^2)))^2) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) r+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) r) x (y^2)-((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((-(a^2)+(b^2)+(c^2)) q+(1/2) ((a^2)+(b^2)-(c^2)) r+(1/2) (-(a^2)+(b^2)+(c^2)) r) (x^2) z+2 ((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) (-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) p+(1/2) (-(a^2)+(b^2)+(c^2)) p+(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) r-(1/2) ((a^2)+(b^2)-(c^2)) r) x y z+(-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p-(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) r-(1/4) ((((a^2)+(b^2)-(c^2)))^2) r) (y^2) z+((1/2) ((a^2)+(b^2)-(c^2))+(1/2) (-(a^2)+(b^2)+(c^2))) ((1/2) ((a^2)+(b^2)-(c^2)) p+(1/2) (-(a^2)+(b^2)+(c^2)) p+((a^2)+(b^2)-(c^2)) q) x (z^2)+(-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) ((a^2)+(b^2)-(c^2)) p-(1/4) (Sqrt[(a+b-c) (a-b+c) (-a+b+c) (a+b+c)]) (-(a^2)+(b^2)+(c^2)) p+(1/4) (a+b-c) (a-b+c) (-a+b+c) (a+b+c) q+(1/4) ((((a^2)+(b^2)-(c^2)))^2) q) y (z^2);  (* 2nd Perspective Square Cubic *)

QL - Conics and QL-Cubics described in a QA-Quadrigon

QLCi1g=(b^2) (r^2) (p+2 q+r) (x^2)+(2 (c^2) (p^2) q-(a^2) (p^2) r+(b^2) (p^2) r+(c^2) (p^2) r+2 (b^2) q (r^2)-2 (c^2) q (r^2)+(a^2) (r^3)+(b^2) (r^3)-(c^2) (r^3)) x y-(p-r) ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) (y^2)+((a^2) (p^3)-(b^2) (p^3)-(c^2) (p^3)+2 (a^2) (p^2) q-2 (b^2) (p^2) q-(a^2) p (r^2)-(b^2) p (r^2)+(c^2) p (r^2)-2 (a^2) q (r^2)) y z-(b^2) (p^2) (p+2 q+r) (z^2);  (* QL-Circumcircle Diagonal Triangle *)
QLCi2g=-(r^2) ((a^2) q-(b^2) q-(c^2) q-(b^2) r) (x^2)+((c^2) (p^2) q+(a^2) p (r^2)-(c^2) p (r^2)+(b^2) q (r^2)-(c^2) q (r^2)+(a^2) (r^3)+(b^2) (r^3)-(c^2) (r^3)) x y-(p+q+r) (c p-a r) (c p+a r) (y^2)+(-(a^2) (p^2) q+(b^2) (p^2) q+(c^2) (p^2) q+(b^2) (p^2) r-(b^2) p (r^2)-(a^2) q (r^2)-(b^2) q (r^2)+(c^2) q (r^2)) x z+((a^2) (p^3)-(b^2) (p^3)-(c^2) (p^3)+(a^2) (p^2) q-(b^2) (p^2) q+(a^2) (p^2) r-(c^2) (p^2) r-(a^2) q (r^2)) y z-(p^2) ((b^2) p+(a^2) q+(b^2) q-(c^2) q) (z^2);  (* QL-Medial Circle Diagonal Triangle *)
QLCi3g=-(c^2) ((a^2) p+(b^2) p-(c^2) p+2 (a^2) q) (-(c^2) (q^2)+(a^2) q r-(b^2) q r-(c^2) q r-(b^2) (r^2)) (x^2)+(c^2) (-(a^2) (b^2) (p^2) q+(b^4) (p^2) q-(a^2) (c^2) (p^2) q-2 (b^2) (c^2) (p^2) q+(c^4) (p^2) q-2 (a^2) (b^2) p (q^2)+2 (b^4) p (q^2)-3 (a^2) (c^2) p (q^2)-3 (b^2) (c^2) p (q^2)+(c^4) p (q^2)-(a^2) (b^2) (q^3)+(b^4) (q^3)-(a^2) (c^2) (q^3)-2 (b^2) (c^2) (q^3)+(c^4) (q^3)+(a^4) (p^2) r+(b^4) (p^2) r-2 (a^2) (c^2) (p^2) r-2 (b^2) (c^2) (p^2) r+(c^4) (p^2) r+2 (a^4) p q r-2 (a^2) (b^2) p q r+4 (b^4) p q r-4 (a^2) (c^2) p q r-6 (b^2) (c^2) p q r+2 (c^4) p q r+2 (b^4) (q^2) r-4 (a^2) (c^2) (q^2) r-4 (b^2) (c^2) (q^2) r+2 (c^4) (q^2) r+(a^4) p (r^2)+(a^2) (b^2) p (r^2)+2 (b^4) p (r^2)-2 (a^2) (c^2) p (r^2)-3 (b^2) (c^2) p (r^2)+(c^4) p (r^2)+2 (a^4) q (r^2)+(a^2) (b^2) q (r^2)+(b^4) q (r^2)-3 (a^2) (c^2) q (r^2)-2 (b^2) (c^2) q (r^2)+(c^4) q (r^2)) x y-(a^2) (c^2) (p+q+r) ((a^2) p q-(b^2) p q-(c^2) p q+(a^2) (q^2)-(b^2) (q^2)+(c^2) (q^2)-2 (b^2) p r-(a^2) q r-(b^2) q r+(c^2) q r) (y^2)+((a^4) (b^2) (p^2) q-2 (a^2) (b^4) (p^2) q+(b^6) (p^2) q-2 (b^4) (c^2) (p^2) q+(b^2) (c^4) (p^2) q+2 (a^4) (b^2) p (q^2)-4 (a^2) (b^4) p (q^2)+2 (b^6) p (q^2)+2 (a^4) (c^2) p (q^2)-2 (a^2) (b^2) (c^2) p (q^2)-4 (b^4) (c^2) p (q^2)-(a^2) (c^4) p (q^2)+3 (b^2) (c^4) p (q^2)-(c^6) p (q^2)+(a^4) (b^2) (q^3)-2 (a^2) (b^4) (q^3)+(b^6) (q^3)+2 (a^4) (c^2) (q^3)-2 (a^2) (b^2) (c^2) (q^3)-2 (b^4) (c^2) (q^3)+2 (a^2) (c^4) (q^3)+(b^2) (c^4) (q^3)-(a^2) (b^4) (p^2) r+(b^6) (p^2) r-(a^2) (b^2) (c^2) (p^2) r-2 (b^4) (c^2) (p^2) r+(b^2) (c^4) (p^2) r-(a^6) p q r+3 (a^4) (b^2) p q r-5 (a^2) (b^4) p q r+3 (b^6) p q r+(a^4) (c^2) p q r-6 (a^2) (b^2) (c^2) p q r-5 (b^4) (c^2) p q r+(a^2) (c^4) p q r+3 (b^2) (c^4) p q r-(c^6) p q r-(a^6) (q^2) r+3 (a^4) (b^2) (q^2) r-4 (a^2) (b^4) (q^2) r+2 (b^6) (q^2) r-(a^4) (c^2) (q^2) r-2 (a^2) (b^2) (c^2) (q^2) r-4 (b^4) (c^2) (q^2) r+2 (a^2) (c^4) (q^2) r+2 (b^2) (c^4) (q^2) r+(a^4) (b^2) p (r^2)-2 (a^2) (b^4) p (r^2)+(b^6) p (r^2)-(a^2) (b^2) (c^2) p (r^2)-(b^4) (c^2) p (r^2)+(a^4) (b^2) q (r^2)-2 (a^2) (b^4) q (r^2)+(b^6) q (r^2)-2 (b^4) (c^2) q (r^2)+(b^2) (c^4) q (r^2)) x z+(a^2) ((a^4) (p^2) q-2 (a^2) (b^2) (p^2) q+(b^4) (p^2) q-3 (a^2) (c^2) (p^2) q+(b^2) (c^2) (p^2) q+2 (c^4) (p^2) q+2 (a^4) p (q^2)-4 (a^2) (b^2) p (q^2)+2 (b^4) p (q^2)-4 (a^2) (c^2) p (q^2)+(a^4) (q^3)-2 (a^2) (b^2) (q^3)+(b^4) (q^3)-(a^2) (c^2) (q^3)-(b^2) (c^2) (q^3)+(a^4) (p^2) r-3 (a^2) (b^2) (p^2) r+2 (b^4) (p^2) r-2 (a^2) (c^2) (p^2) r+(b^2) (c^2) (p^2) r+(c^4) (p^2) r+2 (a^4) p q r-6 (a^2) (b^2) p q r+4 (b^4) p q r-4 (a^2) (c^2) p q r-2 (b^2) (c^2) p q r+2 (c^4) p q r+(a^4) (q^2) r-3 (a^2) (b^2) (q^2) r+2 (b^4) (q^2) r-3 (a^2) (c^2) (q^2) r-2 (b^2) (c^2) (q^2) r+(a^4) p (r^2)-2 (a^2) (b^2) p (r^2)+(b^4) p (r^2)-2 (a^2) (c^2) p (r^2)+(c^4) p (r^2)+(a^4) q (r^2)-2 (a^2) (b^2) q (r^2)+(b^4) q (r^2)-(a^2) (c^2) q (r^2)-(b^2) (c^2) q (r^2)) y z-(a^2) ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) (-2 (c^2) q+(a^2) r-(b^2) r-(c^2) r) (z^2); 
QLCi4g=(-2 (a^4) (c^2) p (q^2)+4 (a^2) (b^2) (c^2) p (q^2)-2 (b^4) (c^2) p (q^2)+(a^2) (c^4) p (q^2)+(b^2) (c^4) p (q^2)+(c^6) p (q^2)-2 (a^4) (c^2) (q^3)+4 (a^2) (b^2) (c^2) (q^3)-2 (b^4) (c^2) (q^3)-2 (a^2) (c^4) (q^3)+4 (b^2) (c^4) (q^3)-2 (c^6) (q^3)+(a^6) p q r-3 (a^4) (b^2) p q r+3 (a^2) (b^4) p q r-(b^6) p q r-(a^4) (c^2) p q r+4 (a^2) (b^2) (c^2) p q r-3 (b^4) (c^2) p q r-(a^2) (c^4) p q r+3 (b^2) (c^4) p q r+(c^6) p q r+(a^6) (q^2) r-3 (a^4) (b^2) (q^2) r+3 (a^2) (b^4) (q^2) r-(b^6) (q^2) r+(a^4) (c^2) (q^2) r-(b^4) (c^2) (q^2) r+(a^2) (c^4) (q^2) r+5 (b^2) (c^4) (q^2) r-3 (c^6) (q^2) r-(a^4) (b^2) p (r^2)+2 (a^2) (b^4) p (r^2)-(b^6) p (r^2)-(a^2) (b^2) (c^2) p (r^2)-(b^4) (c^2) p (r^2)+2 (b^2) (c^4) p (r^2)-(a^4) (b^2) q (r^2)+2 (a^2) (b^4) q (r^2)-(b^6) q (r^2)-(a^4) (c^2) q (r^2)-2 (a^2) (b^2) (c^2) q (r^2)+(b^4) (c^2) q (r^2)+2 (a^2) (c^4) q (r^2)+(b^2) (c^4) q (r^2)-(c^6) q (r^2)) (x^2)+(3 (a^4) (c^2) (p^2) q-3 (a^2) (b^2) (c^2) (p^2) q-3 (a^2) (c^4) (p^2) q+5 (a^4) (c^2) p (q^2)-4 (a^2) (b^2) (c^2) p (q^2)-(b^4) (c^2) p (q^2)-(a^2) (c^4) p (q^2)-(b^2) (c^4) p (q^2)+2 (c^6) p (q^2)+2 (a^4) (c^2) (q^3)-(a^2) (b^2) (c^2) (q^3)-(b^4) (c^2) (q^3)-(a^2) (c^4) (q^3)+2 (b^2) (c^4) (q^3)-(c^6) (q^3)-(a^6) (p^2) r+2 (a^4) (b^2) (p^2) r-(a^2) (b^4) (p^2) r+2 (a^4) (c^2) (p^2) r-4 (a^2) (b^2) (c^2) (p^2) r-(a^2) (c^4) (p^2) r-(a^6) p q r+(a^4) (b^2) p q r+(a^2) (b^4) p q r-(b^6) p q r+4 (a^4) (c^2) p q r-6 (a^2) (b^2) (c^2) p q r-2 (b^4) (c^2) p q r-5 (a^2) (c^4) p q r+(b^2) (c^4) p q r+2 (c^6) p q r-(a^4) (b^2) (q^2) r+2 (a^2) (b^4) (q^2) r-(b^6) (q^2) r+5 (a^4) (c^2) (q^2) r-8 (a^2) (b^2) (c^2) (q^2) r+(b^4) (c^2) (q^2) r+2 (a^2) (c^4) (q^2) r+(b^2) (c^4) (q^2) r-(c^6) (q^2) r-(a^6) p (r^2)+(a^4) (b^2) p (r^2)+(a^2) (b^4) p (r^2)-(b^6) p (r^2)+2 (a^4) (c^2) p (r^2)-5 (a^2) (b^2) (c^2) p (r^2)-(b^4) (c^2) p (r^2)-(a^2) (c^4) p (r^2)+2 (b^2) (c^4) p (r^2)-(a^6) q (r^2)+(a^4) (b^2) q (r^2)+(a^2) (b^4) q (r^2)-(b^6) q (r^2)-(a^4) (c^2) q (r^2)-5 (a^2) (b^2) (c^2) q (r^2)+2 (b^4) (c^2) q (r^2)+2 (a^2) (c^4) q (r^2)-(b^2) (c^4) q (r^2)) x y-(p+q+r) (-2 (a^4) (c^2) p q+(a^2) (b^2) (c^2) p q+(b^4) (c^2) p q+(a^2) (c^4) p q-2 (b^2) (c^4) p q+(c^6) p q-3 (a^4) (c^2) (q^2)+3 (a^2) (b^2) (c^2) (q^2)-3 (a^2) (c^4) (q^2)+(a^6) p r-2 (a^4) (b^2) p r+(a^2) (b^4) p r-(a^4) (c^2) p r+2 (a^2) (b^2) (c^2) p r+(b^4) (c^2) p r-(a^2) (c^4) p r-2 (b^2) (c^4) p r+(c^6) p r+(a^6) q r-2 (a^4) (b^2) q r+(a^2) (b^4) q r+(a^4) (c^2) q r+(a^2) (b^2) (c^2) q r-2 (a^2) (c^4) q r) (y^2)+(-(a^6) (p^2) q+2 (a^4) (b^2) (p^2) q-(a^2) (b^4) (p^2) q+2 (a^4) (c^2) (p^2) q-4 (a^2) (b^2) (c^2) (p^2) q-(a^2) (c^4) (p^2) q-3 (a^6) p (q^2)+7 (a^4) (b^2) p (q^2)-5 (a^2) (b^4) p (q^2)+(b^6) p (q^2)-(a^4) (c^2) p (q^2)-3 (b^4) (c^2) p (q^2)+2 (a^2) (c^4) p (q^2)+2 (c^6) p (q^2)-2 (a^6) (q^3)+5 (a^4) (b^2) (q^3)-4 (a^2) (b^4) (q^3)+(b^6) (q^3)-4 (a^4) (c^2) (q^3)+6 (a^2) (b^2) (c^2) (q^3)-4 (b^4) (c^2) (q^3)-4 (a^2) (c^4) (q^3)+5 (b^2) (c^4) (q^3)-2 (c^6) (q^3)+3 (a^4) (b^2) (p^2) r-3 (a^2) (b^4) (p^2) r-3 (a^2) (b^2) (c^2) (p^2) r+2 (a^6) p q r+3 (a^4) (b^2) p q r-6 (a^2) (b^4) p q r+(b^6) p q r-2 (a^4) (c^2) p q r+2 (a^2) (b^2) (c^2) p q r-6 (b^4) (c^2) p q r-2 (a^2) (c^4) p q r+3 (b^2) (c^4) p q r+2 (c^6) p q r+2 (a^6) (q^2) r-3 (a^2) (b^4) (q^2) r+(b^6) (q^2) r+2 (a^4) (c^2) (q^2) r-5 (b^4) (c^2) (q^2) r-(a^2) (c^4) (q^2) r+7 (b^2) (c^4) (q^2) r-3 (c^6) (q^2) r-3 (a^2) (b^2) (c^2) p (r^2)-3 (b^4) (c^2) p (r^2)+3 (b^2) (c^4) p (r^2)-(a^4) (c^2) q (r^2)-4 (a^2) (b^2) (c^2) q (r^2)-(b^4) (c^2) q (r^2)+2 (a^2) (c^4) q (r^2)+2 (b^2) (c^4) q (r^2)-(c^6) q (r^2)) x z+(-(a^4) (b^2) (p^2) q+2 (a^2) (b^4) (p^2) q-(b^6) (p^2) q+2 (a^4) (c^2) (p^2) q-5 (a^2) (b^2) (c^2) (p^2) q+(b^4) (c^2) (p^2) q-(a^2) (c^4) (p^2) q+(b^2) (c^4) (p^2) q-(c^6) (p^2) q-(a^6) p (q^2)+(a^4) (b^2) p (q^2)+(a^2) (b^4) p (q^2)-(b^6) p (q^2)+2 (a^4) (c^2) p (q^2)-8 (a^2) (b^2) (c^2) p (q^2)+2 (b^4) (c^2) p (q^2)+5 (a^2) (c^4) p (q^2)-(b^2) (c^4) p (q^2)-(a^6) (q^3)+2 (a^4) (b^2) (q^3)-(a^2) (b^4) (q^3)-(a^4) (c^2) (q^3)-(a^2) (b^2) (c^2) (q^3)+2 (a^2) (c^4) (q^3)+2 (a^4) (b^2) (p^2) r-(a^2) (b^4) (p^2) r-(b^6) (p^2) r-(a^4) (c^2) (p^2) r-5 (a^2) (b^2) (c^2) (p^2) r+(b^4) (c^2) (p^2) r+2 (a^2) (c^4) (p^2) r+(b^2) (c^4) (p^2) r-(c^6) (p^2) r+2 (a^6) p q r+(a^4) (b^2) p q r-2 (a^2) (b^4) p q r-(b^6) p q r-5 (a^4) (c^2) p q r-6 (a^2) (b^2) (c^2) p q r+(b^4) (c^2) p q r+4 (a^2) (c^4) p q r+(b^2) (c^4) p q r-(c^6) p q r+2 (a^6) (q^2) r-(a^4) (b^2) (q^2) r-(a^2) (b^4) (q^2) r-(a^4) (c^2) (q^2) r-4 (a^2) (b^2) (c^2) (q^2) r+5 (a^2) (c^4) (q^2) r-(a^4) (c^2) p (r^2)-4 (a^2) (b^2) (c^2) p (r^2)-(b^4) (c^2) p (r^2)+2 (a^2) (c^4) p (r^2)+2 (b^2) (c^4) p (r^2)-(c^6) p (r^2)-3 (a^4) (c^2) q (r^2)-3 (a^2) (b^2) (c^2) q (r^2)+3 (a^2) (c^4) q (r^2)) y z+(-(a^6) (p^2) q+(a^4) (b^2) (p^2) q+(a^2) (b^4) (p^2) q-(b^6) (p^2) q+2 (a^4) (c^2) (p^2) q-2 (a^2) (b^2) (c^2) (p^2) q+2 (b^4) (c^2) (p^2) q-(a^2) (c^4) (p^2) q-(b^2) (c^4) (p^2) q-3 (a^6) p (q^2)+5 (a^4) (b^2) p (q^2)-(a^2) (b^4) p (q^2)-(b^6) p (q^2)+(a^4) (c^2) p (q^2)+3 (b^4) (c^2) p (q^2)+(a^2) (c^4) p (q^2)-3 (b^2) (c^4) p (q^2)+(c^6) p (q^2)-2 (a^6) (q^3)+4 (a^4) (b^2) (q^3)-2 (a^2) (b^4) (q^3)-2 (a^4) (c^2) (q^3)+4 (a^2) (b^2) (c^2) (q^3)-2 (a^2) (c^4) (q^3)+2 (a^4) (b^2) (p^2) r-(a^2) (b^4) (p^2) r-(b^6) (p^2) r-(a^2) (b^2) (c^2) (p^2) r+2 (b^4) (c^2) (p^2) r-(b^2) (c^4) (p^2) r+(a^6) p q r+3 (a^4) (b^2) p q r-3 (a^2) (b^4) p q r-(b^6) p q r-(a^4) (c^2) p q r+4 (a^2) (b^2) (c^2) p q r+3 (b^4) (c^2) p q r-(a^2) (c^4) p q r-3 (b^2) (c^4) p q r+(c^6) p q r+(a^6) (q^2) r+(a^4) (b^2) (q^2) r-2 (a^2) (b^4) (q^2) r+(a^4) (c^2) (q^2) r+4 (a^2) (b^2) (c^2) (q^2) r-2 (a^2) (c^4) (q^2) r) (z^2);  (* Hervey Circle *)
QLCi5g=(-2 (c^2) q+(a^2) r-(b^2) r-(c^2) r) ((a^4) p q-2 (a^2) (b^2) p q+(b^4) p q-(a^2) (c^2) p q-(b^2) (c^2) p q+(a^4) (q^2)-2 (a^2) (b^2) (q^2)+(b^4) (q^2)-2 (b^2) (c^2) (q^2)+(c^4) (q^2)-(a^2) (b^2) p r+(b^4) p r-(b^2) (c^2) p r-(a^2) (b^2) q r+(b^4) q r-(a^2) (c^2) q r-2 (b^2) (c^2) q r+(c^4) q r) (x^2)+(3 (a^4) (c^2) (p^2) q-4 (a^2) (b^2) (c^2) (p^2) q+(b^4) (c^2) (p^2) q-4 (a^2) (c^4) (p^2) q-2 (b^2) (c^4) (p^2) q+(c^6) (p^2) q+5 (a^4) (c^2) p (q^2)-6 (a^2) (b^2) (c^2) p (q^2)+(b^4) (c^2) p (q^2)-4 (a^2) (c^4) p (q^2)-4 (b^2) (c^4) p (q^2)+3 (c^6) p (q^2)+2 (a^4) (c^2) (q^3)-2 (a^2) (b^2) (c^2) (q^3)-2 (a^2) (c^4) (q^3)-(a^6) (p^2) r+2 (a^4) (b^2) (p^2) r-(a^2) (b^4) (p^2) r+3 (a^4) (c^2) (p^2) r-4 (a^2) (b^2) (c^2) (p^2) r+(b^4) (c^2) (p^2) r-3 (a^2) (c^4) (p^2) r-2 (b^2) (c^4) (p^2) r+(c^6) (p^2) r-(a^6) p q r+(a^4) (b^2) p q r+(a^2) (b^4) p q r-(b^6) p q r+6 (a^4) (c^2) p q r-8 (a^2) (b^2) (c^2) p q r+2 (b^4) (c^2) p q r-9 (a^2) (c^4) p q r-5 (b^2) (c^4) p q r+4 (c^6) p q r-(a^4) (b^2) (q^2) r+2 (a^2) (b^4) (q^2) r-(b^6) (q^2) r+5 (a^4) (c^2) (q^2) r-8 (a^2) (b^2) (c^2) (q^2) r+3 (b^4) (c^2) (q^2) r-2 (a^2) (c^4) (q^2) r-3 (b^2) (c^4) (q^2) r+(c^6) (q^2) r-(a^6) p (r^2)+(a^4) (b^2) p (r^2)+(a^2) (b^4) p (r^2)-(b^6) p (r^2)+3 (a^4) (c^2) p (r^2)-4 (a^2) (b^2) (c^2) p (r^2)+(b^4) (c^2) p (r^2)-3 (a^2) (c^4) p (r^2)-(b^2) (c^4) p (r^2)+(c^6) p (r^2)-(a^6) q (r^2)+(a^4) (b^2) q (r^2)+(a^2) (b^4) q (r^2)-(b^6) q (r^2)+(a^4) (c^2) q (r^2)-4 (a^2) (b^2) (c^2) q (r^2)+3 (b^4) (c^2) q (r^2)-(a^2) (c^4) q (r^2)-3 (b^2) (c^4) q (r^2)+(c^6) q (r^2)) x y-((a^2)-(b^2)+(c^2)) (p+q+r) (-(a^2) (c^2) p q-(b^2) (c^2) p q+(c^4) p q-2 (a^2) (c^2) (q^2)+(a^4) p r-(a^2) (b^2) p r-2 (a^2) (c^2) p r-(b^2) (c^2) p r+(c^4) p r+(a^4) q r-(a^2) (b^2) q r-(a^2) (c^2) q r) (y^2)+(-(a^6) (p^2) q+3 (a^4) (b^2) (p^2) q-3 (a^2) (b^4) (p^2) q+(b^6) (p^2) q+2 (a^4) (c^2) (p^2) q-4 (a^2) (b^2) (c^2) (p^2) q-2 (b^4) (c^2) (p^2) q-(a^2) (c^4) (p^2) q+(b^2) (c^4) (p^2) q-3 (a^6) p (q^2)+9 (a^4) (b^2) p (q^2)-9 (a^2) (b^4) p (q^2)+3 (b^6) p (q^2)+(a^4) (c^2) p (q^2)-2 (a^2) (b^2) (c^2) p (q^2)-7 (b^4) (c^2) p (q^2)+(a^2) (c^4) p (q^2)+3 (b^2) (c^4) p (q^2)+(c^6) p (q^2)-2 (a^6) (q^3)+6 (a^4) (b^2) (q^3)-6 (a^2) (b^4) (q^3)+2 (b^6) (q^3)-2 (a^4) (c^2) (q^3)+4 (a^2) (b^2) (c^2) (q^3)-6 (b^4) (c^2) (q^3)-2 (a^2) (c^4) (q^3)+6 (b^2) (c^4) (q^3)-2 (c^6) (q^3)+3 (a^4) (b^2) (p^2) r-4 (a^2) (b^4) (p^2) r+(b^6) (p^2) r-4 (a^2) (b^2) (c^2) (p^2) r-2 (b^4) (c^2) (p^2) r+(b^2) (c^4) (p^2) r+(a^6) p q r+6 (a^4) (b^2) p q r-11 (a^2) (b^4) p q r+4 (b^6) p q r-(a^4) (c^2) p q r-4 (a^2) (b^2) (c^2) p q r-11 (b^4) (c^2) p q r-(a^2) (c^4) p q r+6 (b^2) (c^4) p q r+(c^6) p q r+(a^6) (q^2) r+3 (a^4) (b^2) (q^2) r-7 (a^2) (b^4) (q^2) r+3 (b^6) (q^2) r+(a^4) (c^2) (q^2) r-2 (a^2) (b^2) (c^2) (q^2) r-9 (b^4) (c^2) (q^2) r+(a^2) (c^4) (q^2) r+9 (b^2) (c^4) (q^2) r-3 (c^6) (q^2) r+(a^4) (b^2) p (r^2)-2 (a^2) (b^4) p (r^2)+(b^6) p (r^2)-4 (a^2) (b^2) (c^2) p (r^2)-4 (b^4) (c^2) p (r^2)+3 (b^2) (c^4) p (r^2)+(a^4) (b^2) q (r^2)-2 (a^2) (b^4) q (r^2)+(b^6) q (r^2)-(a^4) (c^2) q (r^2)-4 (a^2) (b^2) (c^2) q (r^2)-3 (b^4) (c^2) q (r^2)+2 (a^2) (c^4) q (r^2)+3 (b^2) (c^4) q (r^2)-(c^6) q (r^2)) x z+((a^6) (p^2) q-3 (a^4) (b^2) (p^2) q+3 (a^2) (b^4) (p^2) q-(b^6) (p^2) q-(a^4) (c^2) (p^2) q-4 (a^2) (b^2) (c^2) (p^2) q+(b^4) (c^2) (p^2) q+(a^2) (c^4) (p^2) q+(b^2) (c^4) (p^2) q-(c^6) (p^2) q+(a^6) p (q^2)-3 (a^4) (b^2) p (q^2)+3 (a^2) (b^4) p (q^2)-(b^6) p (q^2)-2 (a^4) (c^2) p (q^2)-8 (a^2) (b^2) (c^2) p (q^2)+2 (b^4) (c^2) p (q^2)+5 (a^2) (c^4) p (q^2)-(b^2) (c^4) p (q^2)-2 (a^4) (c^2) (q^3)-2 (a^2) (b^2) (c^2) (q^3)+2 (a^2) (c^4) (q^3)+(a^6) (p^2) r-(a^4) (b^2) (p^2) r+(a^2) (b^4) (p^2) r-(b^6) (p^2) r-3 (a^4) (c^2) (p^2) r-4 (a^2) (b^2) (c^2) (p^2) r+(b^4) (c^2) (p^2) r+3 (a^2) (c^4) (p^2) r+(b^2) (c^4) (p^2) r-(c^6) (p^2) r+4 (a^6) p q r-5 (a^4) (b^2) p q r+2 (a^2) (b^4) p q r-(b^6) p q r-9 (a^4) (c^2) p q r-8 (a^2) (b^2) (c^2) p q r+(b^4) (c^2) p q r+6 (a^2) (c^4) p q r+(b^2) (c^4) p q r-(c^6) p q r+3 (a^6) (q^2) r-4 (a^4) (b^2) (q^2) r+(a^2) (b^4) (q^2) r-4 (a^4) (c^2) (q^2) r-6 (a^2) (b^2) (c^2) (q^2) r+5 (a^2) (c^4) (q^2) r+(a^6) p (r^2)-2 (a^4) (b^2) p (r^2)+(a^2) (b^4) p (r^2)-3 (a^4) (c^2) p (r^2)-4 (a^2) (b^2) (c^2) p (r^2)-(b^4) (c^2) p (r^2)+3 (a^2) (c^4) p (r^2)+2 (b^2) (c^4) p (r^2)-(c^6) p (r^2)+(a^6) q (r^2)-2 (a^4) (b^2) q (r^2)+(a^2) (b^4) q (r^2)-4 (a^4) (c^2) q (r^2)-4 (a^2) (b^2) (c^2) q (r^2)+3 (a^2) (c^4) q (r^2)) y z-((a^2) p+(b^2) p-(c^2) p+2 (a^2) q) ((a^4) p q-2 (a^2) (b^2) p q+(b^4) p q-(a^2) (c^2) p q-(b^2) (c^2) p q+(a^4) (q^2)-2 (a^2) (b^2) (q^2)+(b^4) (q^2)-2 (b^2) (c^2) (q^2)+(c^4) (q^2)-(a^2) (b^2) p r+(b^4) p r-(b^2) (c^2) p r-(a^2) (b^2) q r+(b^4) q r-(a^2) (c^2) q r-2 (b^2) (c^2) q r+(c^4) q r) (z^2);  (* Pluecker Circle *)
QLCi6g=(-2 (c^2) p (q^2)-2 (c^2) (q^3)+(a^2) p q r-(b^2) p q r-2 (c^2) p q r+(a^2) (q^2) r-(b^2) (q^2) r-3 (c^2) (q^2) r-(b^2) p (r^2)-(b^2) q (r^2)-(c^2) q (r^2)) (x^2)+(p+q) (3 (c^2) p q+2 (c^2) (q^2)-(a^2) p r+3 (c^2) p r-(b^2) q r+5 (c^2) q r-(a^2) (r^2)-(b^2) (r^2)+3 (c^2) (r^2)) x y-(p+q+r) ((c^2) p q+(a^2) p r+(c^2) p r+(a^2) q r) (y^2)+(-(a^2) (p^2) q+3 (b^2) (p^2) q-3 (a^2) p (q^2)+7 (b^2) p (q^2)-(c^2) p (q^2)-2 (a^2) (q^3)+4 (b^2) (q^3)-2 (c^2) (q^3)+3 (b^2) (p^2) r-(a^2) p q r+10 (b^2) p q r-(c^2) p q r-(a^2) (q^2) r+7 (b^2) (q^2) r-3 (c^2) (q^2) r+3 (b^2) p (r^2)+3 (b^2) q (r^2)-(c^2) q (r^2)) x z+(q+r) (3 (a^2) (p^2)-(b^2) (p^2)-(c^2) (p^2)+5 (a^2) p q-(b^2) p q+2 (a^2) (q^2)+3 (a^2) p r-(c^2) p r+3 (a^2) q r) y z+(-(a^2) (p^2) q-(b^2) (p^2) q-3 (a^2) p (q^2)-(b^2) p (q^2)+(c^2) p (q^2)-2 (a^2) (q^3)-(b^2) (p^2) r-2 (a^2) p q r-(b^2) p q r+(c^2) p q r-2 (a^2) (q^2) r) (z^2);  (* Dimidium Circle *)
QLCo1g=(r^2) (x^2)+2 p r x y+2 q r x y+2 (r^2) x y+(p^2) (y^2)+2 p q (y^2)+(q^2) (y^2)+2 p r (y^2)+2 q r (y^2)+(r^2) (y^2)-4 p q x z-4 (q^2) x z-2 p r x z-4 q r x z+2 (p^2) y z+2 p q y z+2 p r y z+(p^2) (z^2) ; (* Inscribed QL-Parabola *)
QLCo2g=(r^2) (((p+2 q+r))^4) (x^2)+2 (((p-r))^2) r (p+q+r) (((p+2 q+r))^2) x y+(((p-r))^4) (((p+q+r))^2) (y^2)-2 (((p+2 q+r))^2) (2 (p^3) q+2 (p^2) (q^2)+(p^3) r+2 (p^2) q r+2 (p^2) (r^2)+2 p q (r^2)+2 (q^2) (r^2)+p (r^3)+2 q (r^3)) x z+2 p (((p-r))^2) (p+q+r) (((p+2 q+r))^2) y z+(p^2) (((p+2 q+r))^4) (z^2); (* Inscribed Midline Conic *)
QLCo3g=(r^2) ((p^2)-4 p q-4 (q^2)-2 p r-4 q r+(r^2)) (x^2)+2 r (((p+r))^2) (p+q+r) x y+(((p+q+r))^2) ((p^2)+4 p q+4 (q^2)+6 p r+4 q r+(r^2)) (y^2)-2 (2 (p^3) q+2 (p^2) (q^2)+(p^3) r+2 (p^2) q r-2 (p^2) (r^2)+2 p q (r^2)+2 (q^2) (r^2)+p (r^3)+2 q (r^3)) x z+2 p (((p+r))^2) (p+q+r) y z+(p^2) ((p^2)-4 p q-4 (q^2)-2 p r-4 q r+(r^2)) (z^2);  (* 2nd QL-Parabola *)
QLCu1g=-(c^2) q (x^2) y+(c^2) p x (y^2)+((a^2) q-(b^2) q-(c^2) q-(b^2) r) (x^2) z+(-(a^2) p+(b^2) p+(c^2) p-(a^2) r-(b^2) r+(c^2) r) x y z-(a^2) r (y^2) z+((b^2) p+(a^2) q+(b^2) q-(c^2) q) x (z^2)+(a^2) q y (z^2);  (* QL-Quasi Isogonal Cubic *)

QA - Cubics

QACu1=(c^4) p (q^2) (x^2) y-(a^2) (c^2) p q r (x^2) y+(c^4) p q r (x^2) y-(b^2) (c^2) (q^2) r (x^2) y+(c^4) (q^2) r (x^2) y-(a^2) (c^2) q (r^2) (x^2) y-(b^2) (c^2) q (r^2) (x^2) y+(c^4) q (r^2) (x^2) y-(c^4) (p^2) q x (y^2)+(a^2) (c^2) (p^2) r x (y^2)-(c^4) (p^2) r x (y^2)+(b^2) (c^2) p q r x (y^2)-(c^4) p q r x (y^2)+(a^2) (c^2) p (r^2) x (y^2)+(b^2) (c^2) p (r^2) x (y^2)-(c^4) p (r^2) x (y^2)+(a^2) (b^2) p q r (x^2) z-(b^4) p q r (x^2) z+(a^2) (b^2) (q^2) r (x^2) z-(b^4) (q^2) r (x^2) z+(b^2) (c^2) (q^2) r (x^2) z-(b^4) p (r^2) (x^2) z-(b^4) q (r^2) (x^2) z+(b^2) (c^2) q (r^2) (x^2) z+(a^4) (p^2) r (y^2) z-(a^2) (b^2) (p^2) r (y^2) z-(a^2) (c^2) (p^2) r (y^2) z+(a^4) p q r (y^2) z-(a^2) (b^2) p q r (y^2) z+(a^4) p (r^2) (y^2) z-(a^2) (c^2) p (r^2) (y^2) z+(a^4) q (r^2) (y^2) z-(a^2) (b^2) (p^2) q x (z^2)+(b^4) (p^2) q x (z^2)-(a^2) (b^2) p (q^2) x (z^2)+(b^4) p (q^2) x (z^2)-(b^2) (c^2) p (q^2) x (z^2)+(b^4) (p^2) r x (z^2)+(b^4) p q r x (z^2)-(b^2) (c^2) p q r x (z^2)-(a^4) (p^2) q y (z^2)+(a^2) (b^2) (p^2) q y (z^2)+(a^2) (c^2) (p^2) q y (z^2)-(a^4) p (q^2) y (z^2)+(a^2) (b^2) p (q^2) y (z^2)-(a^4) p q r y (z^2)+(a^2) (c^2) p q r y (z^2)-(a^4) (q^2) r y (z^2);(* QA-DT-P3-P4 Cubic *)
QACu2=(-(p^2) q (x^2) y-2 p (q^2) (x^2) y-(q^3) (x^2) y-2 p q r (x^2) y-2 (q^2) r (x^2) y+(p^3) x (y^2)+2 (p^2) q x (y^2)+p (q^2) x (y^2)+2 (p^2) r x (y^2)+2 p q r x (y^2)+(p^2) r (x^2) z+2 p q r (x^2) z+2 p (r^2) (x^2) z+2 q (r^2) (x^2) z+(r^3) (x^2) z-2 p q r (y^2) z-(q^2) r (y^2) z-2 p (r^2) (y^2) z-2 q (r^2) (y^2) z-(r^3) (y^2) z-(p^3) x (z^2)-2 (p^2) q x (z^2)-2 (p^2) r x (z^2)-2 p q r x (z^2)-p (r^2) x (z^2)+2 p (q^2) y (z^2)+(q^3) y (z^2)+2 p q r y (z^2)+2 (q^2) r y (z^2)+q (r^2) y (z^2));(* QA-DT-P1-P5 Cubic *)
QACu3=((p^2) q (r^2) (x^2) y+2 p (q^2) (r^2) (x^2) y+(q^3) (r^2) (x^2) y+2 p q (r^3) (x^2) y+2 (q^2) (r^3) (x^2) y-(p^3) (r^2) x (y^2)-2 (p^2) q (r^2) x (y^2)-p (q^2) (r^2) x (y^2)-2 (p^2) (r^3) x (y^2)-2 p q (r^3) x (y^2)-(p^2) (q^2) r (x^2) z-2 p (q^3) r (x^2) z-2 p (q^2) (r^2) (x^2) z-2 (q^3) (r^2) (x^2) z-(q^2) (r^3) (x^2) z+2 (p^3) q r (y^2) z+(p^2) (q^2) r (y^2) z+2 (p^3) (r^2) (y^2) z+2 (p^2) q (r^2) (y^2) z+(p^2) (r^3) (y^2) z+(p^3) (q^2) x (z^2)+2 (p^2) (q^3) x (z^2)+2 (p^2) (q^2) r x (z^2)+2 p (q^3) r x (z^2)+p (q^2) (r^2) x (z^2)-2 (p^3) (q^2) y (z^2)-(p^2) (q^3) y (z^2)-2 (p^3) q r y (z^2)-2 (p^2) (q^2) r y (z^2)-(p^2) q (r^2) y (z^2));(* QA-DT-P1-P10 Cubic *)
QACu4=((p^4) q (r^2) (x^2) y+2 (p^3) (q^2) (r^2) (x^2) y+2 (p^2) (q^3) (r^2) (x^2) y+2 p (q^4) (r^2) (x^2) y+(q^5) (r^2) (x^2) y+2 (p^3) q (r^3) (x^2) y+2 (p^2) (q^2) (r^3) (x^2) y+2 p (q^3) (r^3) (x^2) y+2 (q^4) (r^3) (x^2) y-(p^5) (r^2) x (y^2)-2 (p^4) q (r^2) x (y^2)-2 (p^3) (q^2) (r^2) x (y^2)-2 (p^2) (q^3) (r^2) x (y^2)-p (q^4) (r^2) x (y^2)-2 (p^4) (r^3) x (y^2)-2 (p^3) q (r^3) x (y^2)-2 (p^2) (q^2) (r^3) x (y^2)-2 p (q^3) (r^3) x (y^2)-(p^4) (q^2) r (x^2) z-2 (p^3) (q^3) r (x^2) z-2 (p^3) (q^2) (r^2) (x^2) z-2 (p^2) (q^3) (r^2) (x^2) z-2 (p^2) (q^2) (r^3) (x^2) z-2 p (q^3) (r^3) (x^2) z-2 p (q^2) (r^4) (x^2) z-2 (q^3) (r^4) (x^2) z-(q^2) (r^5) (x^2) z+2 (p^3) (q^3) r (y^2) z+(p^2) (q^4) r (y^2) z+2 (p^3) (q^2) (r^2) (y^2) z+2 (p^2) (q^3) (r^2) (y^2) z+2 (p^3) q (r^3) (y^2) z+2 (p^2) (q^2) (r^3) (y^2) z+2 (p^3) (r^4) (y^2) z+2 (p^2) q (r^4) (y^2) z+(p^2) (r^5) (y^2) z+(p^5) (q^2) x (z^2)+2 (p^4) (q^3) x (z^2)+2 (p^4) (q^2) r x (z^2)+2 (p^3) (q^3) r x (z^2)+2 (p^3) (q^2) (r^2) x (z^2)+2 (p^2) (q^3) (r^2) x (z^2)+2 (p^2) (q^2) (r^3) x (z^2)+2 p (q^3) (r^3) x (z^2)+p (q^2) (r^4) x (z^2)-2 (p^3) (q^4) y (z^2)-(p^2) (q^5) y (z^2)-2 (p^3) (q^3) r y (z^2)-2 (p^2) (q^4) r y (z^2)-2 (p^3) (q^2) (r^2) y (z^2)-2 (p^2) (q^3) (r^2) y (z^2)-2 (p^3) q (r^3) y (z^2)-2 (p^2) (q^2) (r^3) y (z^2)-(p^2) q (r^4) y (z^2));(* QA-DT-P5-P10 Cubic *)
QACu5=-q r (p+q+2 r) (x^2) y+p r (p+q+2 r) x (y^2)+q r (p+2 q+r) (x^2) z-p r (2 p+q+r) (y^2) z-p q (p+2 q+r) x (z^2)+p q (2 p+q+r) y (z^2);(* QA-DT-P1-P20 Cubic *)
QACu6=-(p^2) r (x^2) y-4 p q r (x^2) y-3 (q^2) r (x^2) y-2 p (r^2) (x^2) y-6 q (r^2) (x^2) y+3 (p^2) r x (y^2)+4 p q r x (y^2)+(q^2) r x (y^2)+6 p (r^2) x (y^2)+2 q (r^2) x (y^2)+(p^2) q (x^2) z+2 p (q^2) (x^2) z+4 p q r (x^2) z+6 (q^2) r (x^2) z+3 q (r^2) (x^2) z-(p^2) q x y z+p (q^2) x y z+(p^2) r x y z-(q^2) r x y z-p (r^2) x y z+q (r^2) x y z-2 (p^2) q (y^2) z-p (q^2) (y^2) z-6 (p^2) r (y^2) z-4 p q r (y^2) z-3 p (r^2) (y^2) z-3 (p^2) q x (z^2)-6 p (q^2) x (z^2)-4 p q r x (z^2)-2 (q^2) r x (z^2)-q (r^2) x (z^2)+6 (p^2) q y (z^2)+3 p (q^2) y (z^2)+2 (p^2) r y (z^2)+4 p q r y (z^2)+p (r^2) y (z^2);(* QA-InvolutionCenter Cubic *)
QACu7=(b^2) (c^2) (p^2) q r ((c^2) (q^2)-(a^2) q r+(b^2) q r+(c^2) q r+(b^2) (r^2)) (x^3)+(b^2) (c^2) (p^3) r (-(c^2) (q^2)+(a^2) q r-(b^2) q r-(c^2) q r-(b^2) (r^2)) (x^2) y-(a^2) (c^2) (q^3) r ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) x (y^2)+(a^2) (c^2) p (q^2) r ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) (y^3)+(b^2) (c^2) (p^3) q (-(c^2) (q^2)+(a^2) q r-(b^2) q r-(c^2) q r-(b^2) (r^2)) (x^2) z+(-(a^2) (c^4) (p^3) (q^3)-(b^2) (c^4) (p^3) (q^3)+(c^6) (p^3) (q^3)+(a^4) (c^2) (p^3) (q^2) r-(a^2) (b^2) (c^2) (p^3) (q^2) r-2 (a^2) (c^4) (p^3) (q^2) r-(b^2) (c^4) (p^3) (q^2) r+(c^6) (p^3) (q^2) r-(a^2) (b^2) (c^2) (p^2) (q^3) r+(b^4) (c^2) (p^2) (q^3) r-(a^2) (c^4) (p^2) (q^3) r-2 (b^2) (c^4) (p^2) (q^3) r+(c^6) (p^2) (q^3) r+(a^4) (b^2) (p^3) q (r^2)-2 (a^2) (b^4) (p^3) q (r^2)+(b^6) (p^3) q (r^2)-(a^2) (b^2) (c^2) (p^3) q (r^2)-(b^4) (c^2) (p^3) q (r^2)+(a^6) (p^2) (q^2) (r^2)-(a^4) (b^2) (p^2) (q^2) (r^2)-(a^2) (b^4) (p^2) (q^2) (r^2)+(b^6) (p^2) (q^2) (r^2)-(a^4) (c^2) (p^2) (q^2) (r^2)-(b^4) (c^2) (p^2) (q^2) (r^2)-(a^2) (c^4) (p^2) (q^2) (r^2)-(b^2) (c^4) (p^2) (q^2) (r^2)+(c^6) (p^2) (q^2) (r^2)+(a^6) p (q^3) (r^2)-2 (a^4) (b^2) p (q^3) (r^2)+(a^2) (b^4) p (q^3) (r^2)-(a^4) (c^2) p (q^3) (r^2)-(a^2) (b^2) (c^2) p (q^3) (r^2)-(a^2) (b^4) (p^3) (r^3)+(b^6) (p^3) (r^3)-(b^4) (c^2) (p^3) (r^3)-(a^2) (b^4) (p^2) q (r^3)+(b^6) (p^2) q (r^3)-(a^2) (b^2) (c^2) (p^2) q (r^3)-2 (b^4) (c^2) (p^2) q (r^3)+(b^2) (c^4) (p^2) q (r^3)+(a^6) p (q^2) (r^3)-(a^4) (b^2) p (q^2) (r^3)-2 (a^4) (c^2) p (q^2) (r^3)-(a^2) (b^2) (c^2) p (q^2) (r^3)+(a^2) (c^4) p (q^2) (r^3)+(a^6) (q^3) (r^3)-(a^4) (b^2) (q^3) (r^3)-(a^4) (c^2) (q^3) (r^3)) x y z-(a^2) (c^2) p (q^3) ((c^2) (p^2)+(a^2) p r-(b^2) p r+(c^2) p r+(a^2) (r^2)) (y^2) z-(a^2) (b^2) q ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) (r^3) x (z^2)-(a^2) (b^2) p ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) (r^3) y (z^2)+(a^2) (b^2) p q ((b^2) (p^2)+(a^2) p q+(b^2) p q-(c^2) p q+(a^2) (q^2)) (r^2) (z^3);(* QA-Quasi Isogonal Cubic *)