(* ::Package:: *)

(* ::Input:: *)
\[CapitalDelta]R=Discriminant[R,u];
         
   \[CapitalDelta]R1=Simplify[ %/(8192 (8+2 p-q)^2 (-1+z)^2 z^2 )];

   \[CapitalDelta]R1=q^7 (1+z)^7-16 p^6 (-1+z) z^2 (1+z)^2 (2+(-2+q) z)-512 (-1+z)^5 (-100-34 z+45 z^2+25 z^3)+2 q^6 (1+z)^4 (4-44 z-33 z^2+12 z^3+z^4)+128 q (-1+z)^4 (-50-721 z-218 z^2+351 z^3+190 z^4)+q^5 (1+z)^2 (159-1167 z+934 z^2+2078 z^3+23 z^4-527 z^5+36 z^6)-8 q^2 (-1+z)^2 (-6240-3612 z+10855 z^2-2148 z^3-6534 z^4+1384 z^5+2199 z^6)-8 p^5 (64+8 (-4+5 q) z+(-208+20 q+3 q^2) z^2+(120-114 q+5 q^2) z^3-2 (-80+22 q+3 q^2) z^4-2 (32-36 q+7 q^2) z^5+(-48+32 q-5 q^2) z^6+(8-6 q+q^2) z^7)+q^4 (1272+2994 z+21694 z^2+9658 z^3-22234 z^4-11658 z^5+5274 z^6+2078 z^7-886 z^8)+8 q^3 (780+6801 z-3805 z^2-11479 z^3+5355 z^4+5003 z^5-2559 z^6-837 z^7+741 z^8)+4 p^4 (q^3 z (1+z)^3 (3-3 z-19 z^2+7 z^3)+8 (-1+z)^2 (-256-128 z+278 z^2+178 z^3-37 z^4-20 z^5+z^6)+2 q^2 (-8-18 z-164 z^2-161 z^3+197 z^4+208 z^5-10 z^6-29 z^7+z^8)-4 q (16+408 z-168 z^2-729 z^3+125 z^4+401 z^5-11 z^6-44 z^7+2 z^8))-2 p^3 (q^4 (1+z)^4 (1-3 z-25 z^2+19 z^3)-32 (-1+z)^3 (752+536 z-226 z^2-237 z^3+2 z^4+5 z^5)+8 q (-1+z)^2 (192+3224 z+2444 z^2-923 z^3-1100 z^4-23 z^5+26 z^6)+2 q^3 (8-111 z-196 z^2+431 z^3+782 z^4+71 z^5-280 z^6-71 z^7+6 z^8)-4 q^2 (-24-50 z-1971 z^2+23 z^3+2444 z^4+448 z^5-791 z^6-101 z^7+22 z^8))+p^2 (q^5 (1+z)^5 (-1-16 z+25 z^2)+32 (-1+z)^3 (3904+32 z-2753 z^2-629 z^3+461 z^4+9 z^5)+2 q^4 (1+z)^2 (26+87 z+601 z^2+90 z^3-416 z^4-49 z^5+13 z^6)-32 q (-1+z)^2 (368+4960 z+4 z^2-3753 z^3-933 z^4+613 z^5+21 z^6)-4 q^3 (-8-1575 z-1340 z^2+4463 z^3+2658 z^4-2569 z^5-1488 z^6+321 z^7+50 z^8)+8 q^2 (584-434 z-9429 z^2+7675 z^3+8564 z^4-4652 z^5-3405 z^6+1027 z^7+70 z^8))-2 p (q^6 (1+z)^6 (-1+4 z)+128 (-1+z)^4 (530+111 z-288 z^2-117 z^3+20 z^4)+q^5 (1+z)^3 (-15+132 z-74 z^2-170 z^3+25 z^4+6 z^5)-16 q (-1+z)^3 (480+6522 z+1187 z^2-3805 z^3-1559 z^4+247 z^5)+8 q^2 (-1+z)^2 (-1884-1821 z+7139 z^2+2280 z^3-4404 z^4-2083 z^5+261 z^6)-q^4 (279+693 z+4585 z^2+4921 z^3-2317 z^4-3473 z^5+515 z^6+931 z^7+10 z^8)-2 q^3 (552+7773 z+612 z^2-16545 z^3+1822 z^4+9995 z^5-1384 z^6-3015 z^7+190 z^8));


(* ::InheritFromParent:: *)
(**)
