\\ --------------- DATA ---------------------------- \\ \\ Time-stamp: \\ \\ Description: Covariants of general cubic \\ \\ Produced with: syzygy.gp \\ \\ File: /home/villegas/gp/syzygy.data \\ \\ Original Author: Fernando Rodriguez Villegas \\ villegas@math.utexas.edu \\ Created: Tue Apr 17 2001 \\ \\------------------------------------------------------- \r jac_cubic {getall(f,p, h,xx,yy,v,x1,y1,z1,A1,A5,A8,A3, A4,A10,A9,A7,A6,A2)= v=getcoeffh(f); A1=v[1];A5=v[2];A8=v[3]; A3=v[4];A4=v[5];A10=v[6]; A9=v[7];A7=v[8];A6=v[9];A2=v[10]; if(p,x1=p[1];y1=p[2];z1=p[3]; f=subst(subst(subst(f,x,x1),y,y1),z,z1) ,x1=x;y1=y;z1=z); h=((A9*A4+(A6*A5+(4*A8*A7-A10^2)))*A1+(-A8*A4^2+ A10*A5*A4-A7*A5^2))*x1^3+(((3*A9*A7+(-3*A6*A10+ 9*A2*A8))*A1+(3*A6*A5*A4-3*A2*A5^2))*y1+((9*A3*A7+ (-3*A9*A10+3*A6*A8))*A1+(-3*A3*A4^2+3*A9*A5*A4))*z1)*x1^2 +(((9*A9*A2-3*A6^2)*A1+(3*A2*A8*A4+(3*A6*A7- 3*A2*A10)*A5))*y1^2+((27*A3*A2-3*A9*A6)*A1+((-3*A3*A7+ 3*A6*A8)*A4+(3*A9*A7-3*A2*A8)*A5))*z1*y1+((9*A3*A6- 3*A9^2)*A1+((-3*A3*A10+3*A9*A8)*A4+3*A3*A7*A5))*z1^2)*x1+ (((4*A9*A2-A6^2)*A4+(A6*A2*A5+(-A9*A7^2+(A6*A10+ A2*A8)*A7-A2*A10^2)))*y1^3+(9*A3*A2*A4+(3*A9*A2*A5+ (-3*A3*A7^2+3*A6*A8*A7-3*A2*A8*A10)))*z1*y1^2+(3*A3*A6*A4 +(9*A3*A2*A5+((-3*A3*A10+3*A9*A8)*A7-3*A2*A8^2)))*z1^2*y1 +(A3*A9*A4+((4*A3*A6-A9^2)*A5+(A3*A8*A7+(-A3*A10^2+ A9*A8*A10-A6*A8^2))))*z1^3); xx=((-27*A3^2*A7^3+(27*A3*A9*A10+(-18*A3*A6- 3*A9^2)*A8)*A7^2+((-9*A3*A6-6*A9^2)*A10^2+(27*A3*A2+ 15*A9*A6)*A8*A10+(-18*A9*A2-3*A6^2)*A8^2)*A7+ (3*A9*A6*A10^3+(-9*A9*A2-6*A6^2)*A8*A10^2+ 27*A6*A2*A8^2*A10-27*A2^2*A8^3))*A1^3+(A9^3*A4^3+ (3*A9^2*A6*A5+(27*A3^2*A7^2+(-18*A3*A9*A10+(12*A3*A6+ 10*A9^2)*A8)*A7+(3*A3*A6*A10^2+(-9*A3*A2-5*A9*A6)*A8*A10 +(6*A9*A2+A6^2)*A8^2)))*A4^2+(3*A9*A6^2*A5^2+ (-18*A3*A9*A7^2+((12*A3*A6+8*A9^2)*A10+(-18*A3*A2+ 6*A9*A6)*A8)*A7+(-10*A9*A6*A10^2+(12*A9*A2+ 8*A6^2)*A8*A10-18*A6*A2*A8^2))*A5+((-12*A3*A8*A10+ 24*A9*A8^2)*A7^2+(3*A3*A10^3-6*A9*A8*A10^2- 12*A6*A8^2*A10+24*A2*A8^3)*A7+(3*A6*A8*A10^3- 6*A2*A8^2*A10^2)))*A4+(A6^3*A5^3+((6*A3*A6+A9^2)*A7^2+ ((-9*A3*A2-5*A9*A6)*A10+(12*A9*A2+10*A6^2)*A8)*A7+ (3*A9*A2*A10^2-18*A6*A2*A8*A10+27*A2^2*A8^2))*A5^2+ (24*A3*A8*A7^3+(-6*A3*A10^2-12*A9*A8*A10+ 24*A6*A8^2)*A7^2+(3*A9*A10^3-6*A6*A8*A10^2- 12*A2*A8^2*A10)*A7+3*A2*A8*A10^3)*A5))*A1^2+((-9*A3^2*A7+ (3*A3*A9*A10+(-2*A3*A6-2*A9^2)*A8))*A4^4+((12*A3*A9*A7+ ((-4*A3*A6-A9^2)*A10+6*A3*A2*A8))*A5+((7*A3*A8*A10- 10*A9*A8^2)*A7+(-A3*A10^3+A9*A8*A10^2+3*A6*A8^2*A10- 6*A2*A8^3)))*A4^3+(((-8*A3*A6-5*A9^2)*A7+((3*A3*A2+ 9*A9*A6)*A10+(-8*A9*A2-5*A6^2)*A8))*A5^2+(-14*A3*A8*A7^2 +(-A3*A10^2+9*A9*A8*A10-2*A6*A8^2)*A7+(-4*A6*A8*A10^2+ 9*A2*A8^2*A10))*A5)*A4^2+((6*A3*A2*A7+((-4*A9*A2- A6^2)*A10+12*A6*A2*A8))*A5^3+((9*A3*A10-2*A9*A8)*A7^2+ (-4*A9*A10^2+9*A6*A8*A10-14*A2*A8^2)*A7- A2*A8*A10^2)*A5^2)*A4+(((-2*A9*A2-2*A6^2)*A7+ (3*A6*A2*A10-9*A2^2*A8))*A5^4+(-6*A3*A7^3+(3*A9*A10- 10*A6*A8)*A7^2+(A6*A10^2+7*A2*A8*A10)*A7- A2*A10^3)*A5^3))*A1+(A3^2*A4^6+(-2*A3*A9*A5+(-A3*A8*A10 +A9*A8^2))*A4^5+((2*A3*A6+A9^2)*A5^2+(2*A3*A8*A7+ (A3*A10^2-A9*A8*A10-A6*A8^2))*A5)*A4^4+((-2*A3*A2- 2*A9*A6)*A5^3+(-3*A3*A10*A7+(A6*A8*A10+ 2*A2*A8^2))*A5^2)*A4^3+((2*A9*A2+A6^2)*A5^4+(2*A3*A7^2+ A9*A10*A7-3*A2*A8*A10)*A5^3)*A4^2+(-2*A6*A2*A5^5+ (-A9*A7^2+(-A6*A10+2*A2*A8)*A7+A2*A10^2)*A5^4)*A4+ (A2^2*A5^6+(A6*A7^2-A2*A10*A7)*A5^5)))*x1^6+ ((((-243*A3^2*A2+(36*A3*A9*A6-3*A9^3))*A7^2+ ((189*A3*A9*A2+(-36*A3*A6^2-9*A9^2*A6))*A10+((-54*A3*A6 -54*A9^2)*A2+24*A9*A6^2)*A8)*A7+(((-27*A3*A6- 27*A9^2)*A2+12*A9*A6^2)*A10^2+(81*A3*A2^2+63*A9*A6*A2- 24*A6^3)*A8*A10+(-135*A9*A2^2+45*A6^2*A2)*A8^2))*A1^3+ (((162*A3^2*A2+(-24*A3*A9*A6+7*A9^3))*A7+((-63*A3*A9*A2 +(12*A3*A6^2-2*A9^2*A6))*A10+((18*A3*A6+33*A9^2)*A2- 8*A9*A6^2)*A8))*A4^2+(((-126*A3*A9*A2+(24*A3*A6^2+ 16*A9^2*A6))*A7+(((36*A3*A6+36*A9^2)*A2-26*A9*A6^2)*A10 +(-54*A3*A2^2-12*A9*A6*A2+16*A6^3)*A8))*A5+ (27*A3^2*A7^3+(-21*A3*A9*A10+(-30*A3*A6+ 31*A9^2)*A8)*A7^2+((15*A3*A6-4*A9^2)*A10^2+(-45*A3*A2- 17*A9*A6)*A8*A10+(138*A9*A2-29*A6^2)*A8^2)*A7+((9*A3*A2 +2*A9*A6)*A10^3+(-33*A9*A2+8*A6^2)*A8*A10^2+ 3*A6*A2*A8^2*A10-9*A2^2*A8^3)))*A4+((((18*A3*A6+ 18*A9^2)*A2-3*A9*A6^2)*A7+((-27*A3*A2^2-21*A9*A6*A2+ 3*A6^3)*A10+(90*A9*A2^2-15*A6^2*A2)*A8))*A5^2+ (-12*A3*A9*A7^3+((12*A3*A6+6*A9^2)*A10+(180*A3*A2- 12*A9*A6)*A8)*A7^2+((-54*A3*A2-6*A9*A6)*A10^2+(-48*A9*A2 +12*A6^2)*A8*A10+36*A6*A2*A8^2)*A7+(18*A9*A2*A10^3- 24*A6*A2*A8*A10^2+18*A2^2*A8^2*A10))*A5))*A1^2+ ((-27*A3^2*A2+4*A3*A9*A6)*A4^4+((42*A3*A9*A2+(-8*A3*A6^2 +4*A9^2*A6))*A5+(-18*A3^2*A7^2+(7*A3*A9*A10+(22*A3*A6- 6*A9^2)*A8)*A7+(-4*A3*A6*A10^2+9*A3*A2*A8*A10+(-26*A9*A2 +8*A6^2)*A8^2)))*A4^3+(((-18*A3*A6-23*A9^2)*A2+ 19*A9*A6^2)*A5^2+(22*A3*A9*A7^2+((-20*A3*A6-A9^2)*A10+ (-84*A3*A2+36*A9*A6)*A8)*A7+((3*A3*A2-6*A9*A6)*A10^2+ (43*A9*A2-10*A6^2)*A8*A10-14*A6*A2*A8^2))*A5+ ((4*A3*A8*A10+4*A9*A8^2)*A7^2+(-A3*A10^3-A9*A8*A10^2- 8*A6*A8^2*A10+28*A2*A8^3)*A7+(2*A6*A8*A10^3- 7*A2*A8^2*A10^2)))*A4^2+((18*A3*A2^2+4*A9*A6*A2)*A5^3+ ((-2*A3*A6-10*A9^2)*A7^2+((66*A3*A2+9*A9*A6)*A10+ (-38*A9*A2+18*A6^2)*A8)*A7+((-19*A9*A2-3*A6^2)*A10^2+ 13*A6*A2*A8*A10+12*A2^2*A8^2))*A5^2+(-8*A3*A8*A7^3+ (2*A3*A10^2-8*A9*A8*A10+40*A6*A8^2)*A7^2+(2*A9*A10^3- 10*A6*A8*A10^2-32*A2*A8^2*A10)*A7+8*A2*A8*A10^3)*A5)*A4+ (-15*A9*A2^2*A5^4+((-42*A3*A2+6*A9*A6)*A7^2+((9*A9*A2- 6*A6^2)*A10-12*A6*A2*A8)*A7+(9*A6*A2*A10^2- 15*A2^2*A8*A10))*A5^3+(12*A9*A8*A7^3+(-3*A9*A10^2- 12*A6*A8*A10-12*A2*A8^2)*A7^2+(3*A6*A10^3+ 15*A2*A8*A10^2)*A7-3*A2*A10^4)*A5^2))*A1+((3*A3^2*A7- 4*A3*A6*A8)*A4^5+((-6*A3*A9*A7+(4*A3*A6*A10+(12*A3*A2- 4*A9*A6)*A8))*A5+((-A3*A8*A10-A9*A8^2)*A7+(2*A6*A8^2*A10 -7*A2*A8^3)))*A4^4+(((2*A3*A6+3*A9^2)*A7+((-12*A3*A2+ 4*A9*A6)*A10+(-4*A9*A2-3*A6^2)*A8))*A5^2+(2*A3*A8*A7^2+ (A3*A10^2+3*A9*A8*A10-10*A6*A8^2)*A7+(-2*A6*A8*A10^2+ 15*A2*A8^2*A10))*A5)*A4^3+(((6*A3*A2-10*A9*A6)*A7+ ((4*A9*A2+3*A6^2)*A10+6*A6*A2*A8))*A5^3+((-3*A3*A10- 4*A9*A8)*A7^2+(-2*A9*A10^2+15*A6*A8*A10-4*A2*A8^2)*A7- 11*A2*A8*A10^2)*A5^2)*A4^2+((2*A9*A2*A7+(-6*A6*A2*A10- 3*A2^2*A8))*A5^4+(2*A3*A7^3+(5*A9*A10-10*A6*A8)*A7^2+ (-3*A6*A10^2+5*A2*A8*A10)*A7+3*A2*A10^3)*A5^3)*A4+ (3*A2^2*A10*A5^5+(-3*A9*A7^3+(3*A6*A10+3*A2*A8)*A7^2- 3*A2*A10^2*A7)*A5^4)))*y1+(((-135*A3^2*A6+45*A3*A9^2)*A7^2 +((81*A3^2*A2+(63*A3*A9*A6-24*A9^3))*A10+(-54*A3*A9*A2 +(-54*A3*A6^2+24*A9^2*A6))*A8)*A7+((-27*A3*A9*A2+ (-27*A3*A6^2+12*A9^2*A6))*A10^2+((189*A3*A6-36*A9^2)*A2 -9*A9*A6^2)*A8*A10+(-243*A3*A2^2+36*A9*A6*A2- 3*A6^3)*A8^2))*A1^3+(((90*A3^2*A6-15*A3*A9^2)*A7+ ((-27*A3^2*A2+(-21*A3*A9*A6+3*A9^3))*A10+(18*A3*A9*A2+ (18*A3*A6^2-3*A9^2*A6))*A8))*A4^2+(((-54*A3^2*A2+ (-12*A3*A9*A6+16*A9^3))*A7+((36*A3*A9*A2+(36*A3*A6^2- 26*A9^2*A6))*A10+((-126*A3*A6+24*A9^2)*A2+ 16*A9*A6^2)*A8))*A5+((18*A3^2*A10+36*A3*A9*A8)*A7^2+ (-24*A3*A9*A10^2+(-48*A3*A6+12*A9^2)*A8*A10+(180*A3*A2- 12*A9*A6)*A8^2)*A7+(18*A3*A6*A10^3+(-54*A3*A2- 6*A9*A6)*A8*A10^2+(12*A9*A2+6*A6^2)*A8^2*A10- 12*A6*A2*A8^3)))*A4+(((18*A3*A9*A2+(33*A3*A6^2- 8*A9^2*A6))*A7+(((-63*A3*A6+12*A9^2)*A2-2*A9*A6^2)*A10+ (162*A3*A2^2-24*A9*A6*A2+7*A6^3)*A8))*A5^2+(-9*A3^2*A7^3 +(3*A3*A9*A10+(138*A3*A6-29*A9^2)*A8)*A7^2+((-33*A3*A6 +8*A9^2)*A10^2+(-45*A3*A2-17*A9*A6)*A8*A10+(-30*A9*A2+ 31*A6^2)*A8^2)*A7+((9*A3*A2+2*A9*A6)*A10^3+(15*A9*A2- 4*A6^2)*A8*A10^2-21*A6*A2*A8^2*A10+ 27*A2^2*A8^3))*A5))*A1^2+(-15*A3^2*A6*A4^4+((18*A3^2*A2+ 4*A3*A9*A6)*A5+((-15*A3^2*A10-12*A3*A9*A8)*A7+ (9*A3*A9*A10^2+(9*A3*A6-6*A9^2)*A8*A10+(-42*A3*A2+ 6*A9*A6)*A8^2)))*A4^3+((-18*A3*A9*A2+(-23*A3*A6^2+ 19*A9^2*A6))*A5^2+(12*A3^2*A7^2+(13*A3*A9*A10+(-38*A3*A6 +18*A9^2)*A8)*A7+((-19*A3*A6-3*A9^2)*A10^2+(66*A3*A2+ 9*A9*A6)*A8*A10+(-2*A9*A2-10*A6^2)*A8^2))*A5+ (-12*A3*A8^2*A7^2+(15*A3*A8*A10^2-12*A9*A8^2*A10+ 12*A6*A8^3)*A7+(-3*A3*A10^4+3*A9*A8*A10^3- 3*A6*A8^2*A10^2)))*A4^2+(((42*A3*A6-8*A9^2)*A2+ 4*A9*A6^2)*A5^3+(-14*A3*A9*A7^2+((43*A3*A6-10*A9^2)*A10 +(-84*A3*A2+36*A9*A6)*A8)*A7+((3*A3*A2-6*A9*A6)*A10^2+ (-20*A9*A2-A6^2)*A8*A10+22*A6*A2*A8^2))*A5^2+ ((-32*A3*A8*A10+40*A9*A8^2)*A7^2+(8*A3*A10^3- 10*A9*A8*A10^2-8*A6*A8^2*A10-8*A2*A8^3)*A7+ (2*A6*A8*A10^3+2*A2*A8^2*A10^2))*A5)*A4+((-27*A3*A2^2+ 4*A9*A6*A2)*A5^4+((-26*A3*A6+8*A9^2)*A7^2+(9*A3*A2*A10+ (22*A9*A2-6*A6^2)*A8)*A7+(-4*A9*A2*A10^2+7*A6*A2*A8*A10 -18*A2^2*A8^2))*A5^3+(28*A3*A8*A7^3+(-7*A3*A10^2- 8*A9*A8*A10+4*A6*A8^2)*A7^2+(2*A9*A10^3-A6*A8*A10^2+ 4*A2*A8^2*A10)*A7-A2*A8*A10^3)*A5^2))*A1+(3*A3^2*A10*A4^5 +((-3*A3^2*A7+(-6*A3*A9*A10+2*A3*A6*A8))*A5+ (3*A3*A8^2*A7+(-3*A3*A8*A10^2+3*A9*A8^2*A10- 3*A6*A8^3)))*A4^4+((6*A3*A9*A7+((4*A3*A6+3*A9^2)*A10+ (6*A3*A2-10*A9*A6)*A8))*A5^2+((5*A3*A8*A10- 10*A9*A8^2)*A7+(3*A3*A10^3-3*A9*A8*A10^2+5*A6*A8^2*A10+ 2*A2*A8^3))*A5)*A4^3+(((-4*A3*A6-3*A9^2)*A7+((-12*A3*A2 +4*A9*A6)*A10+(2*A9*A2+3*A6^2)*A8))*A5^3+(-4*A3*A8*A7^2 +(-11*A3*A10^2+15*A9*A8*A10-4*A6*A8^2)*A7+ (-2*A6*A8*A10^2-3*A2*A8^2*A10))*A5^2)*A4^2+(((12*A3*A2- 4*A9*A6)*A7+(4*A9*A2*A10-6*A6*A2*A8))*A5^4+((15*A3*A10- 10*A9*A8)*A7^2+(-2*A9*A10^2+3*A6*A8*A10+2*A2*A8^2)*A7+ A2*A8*A10^2)*A5^3)*A4+((-4*A9*A2*A7+3*A2^2*A8)*A5^5+ (-7*A3*A7^3+(2*A9*A10-A6*A8)*A7^2- A2*A8*A10*A7)*A5^4)))*z1)*x1^5+((((-729*A3^2*A2^2+ (270*A3*A9*A6-36*A9^3)*A2+(-36*A3*A6^3+3*A9^2*A6^2))*A7 +((324*A3*A9*A2^2+(-108*A3*A6^2-36*A9^2*A6)*A2+ 12*A9*A6^3)*A10+(-216*A9^2*A2^2+144*A9*A6^2*A2- 24*A6^4)*A8))*A1^3+((243*A3^2*A2^2+(-90*A3*A9*A6+ 27*A9^3)*A2+(12*A3*A6^3-6*A9^2*A6^2))*A4^2+ ((-216*A3*A9*A2^2+(72*A3*A6^2+54*A9^2*A6)*A2- 18*A9*A6^3)*A5+((81*A3^2*A2+(-30*A3*A9*A6+10*A9^3))*A7^2 +((9*A3*A9*A2+(12*A3*A6^2-11*A9^2*A6))*A10+((-180*A3*A6 +156*A9^2)*A2-26*A9*A6^2)*A8)*A7+(((27*A3*A6- 45*A9^2)*A2+15*A9*A6^2)*A10^2+(27*A3*A2^2+15*A9*A6*A2- 12*A6^3)*A8*A10+(-54*A9*A2^2+27*A6^2*A2)*A8^2)))*A4+ ((72*A9^2*A2^2-33*A9*A6^2*A2+3*A6^4)*A5^2+((-90*A3*A9*A2 +(36*A3*A6^2+A9^2*A6))*A7^2+(((-18*A3*A6+48*A9^2)*A2- 20*A9*A6^2)*A10+(486*A3*A2^2-120*A9*A6*A2+ 28*A6^3)*A8)*A7+((-108*A3*A2^2+12*A9*A6*A2+3*A6^3)*A10^2 +(36*A9*A2^2-30*A6^2*A2)*A8*A10+27*A6*A2^2*A8^2))*A5+ 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4*A3*A9^2)*A8*A10^2+(-18*A3^2*A2+(9*A3*A9*A6+ A9^3))*A8^2*A10+(12*A3*A9*A2-10*A3*A6^2)*A8^3)*A7+ (3*A3^2*A2*A8*A10^3-A3*A9*A2*A8^2*A10^2+(7*A3*A6- 3*A9^2)*A2*A8^3*A10+(-9*A3*A2^2+2*A9*A6*A2)*A8^4))*A5+ (A3^2*A8^3*A7^3+(-A3*A9*A8^3*A10+(-2*A3*A6+ A9^2)*A8^4)*A7^2+(A3*A6*A8^3*A10^2+(3*A3*A2- A9*A6)*A8^4*A10+(-2*A9*A2+A6^2)*A8^5)*A7+ (-A3*A2*A8^3*A10^3+A9*A2*A8^4*A10^2-A6*A2*A8^5*A10+ A2^2*A8^6)))))*z1^6); yy=(((486*A3^3*A2+(-135*A3^2*A9*A6+27*A3*A9^3))*A7^3+ ((-486*A3^2*A9*A2+(117*A3^2*A6^2+57*A3*A9^2*A6- 14*A9^4))*A10+((81*A3^2*A6+135*A3*A9^2)*A2+ (-90*A3*A9*A6^2+12*A9^3*A6))*A8)*A7^2+(((54*A3^2*A6+ 144*A3*A9^2)*A2+(-87*A3*A9*A6^2+11*A9^3*A6))*A10^2+ (-243*A3^2*A2^2+(-36*A3*A9*A6-78*A9^3)*A2+(84*A3*A6^3+ 5*A9^2*A6^2))*A8*A10+(81*A3*A9*A2^2+(-108*A3*A6^2+ 72*A9^2*A6)*A2-15*A9*A6^3)*A8^2)*A7+((54*A3^2*A2^2+ (-27*A3*A9*A6-13*A9^3)*A2+(14*A3*A6^3+ 2*A9^2*A6^2))*A10^3+(54*A3*A9*A2^2+(-99*A3*A6^2+ 75*A9^2*A6)*A2-16*A9*A6^3)*A8*A10^2+((243*A3*A6- 126*A9^2)*A2^2-24*A9*A6^2*A2+13*A6^4)*A8^2*A10+ 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(189*A3^2*A9*A10+(18*A3^2*A6-69*A3*A9^2)*A8)*A7^3+ ((-87*A3^2*A6-70*A3*A9^2)*A10^2+(216*A3^2*A2+ (51*A3*A9*A6+41*A9^3))*A8*A10+(-414*A3*A9*A2+(57*A3*A6^2 -6*A9^2*A6))*A8^2)*A7^2+((-27*A3^2*A2+(63*A3*A9*A6+ 3*A9^3))*A10^3+(30*A3*A9*A2+(-22*A3*A6^2- 65*A9^2*A6))*A8*A10^2+((-51*A3*A6+146*A9^2)*A2+ 26*A9*A6^2)*A8^2*A10+(243*A3*A2^2-132*A9*A6*A2+ 12*A6^3)*A8^3)*A7+((-12*A3*A9*A2-14*A3*A6^2)*A10^4+ ((57*A3*A6-10*A9^2)*A2+21*A9*A6^2)*A8*A10^3+(-99*A3*A2^2 -49*A9*A6*A2-16*A6^3)*A8^2*A10^2+(57*A9*A2^2+ 53*A6^2*A2)*A8^3*A10-54*A6*A2^2*A8^4)))*A4+((-9*A3*A6^3*A2 +A9*A6^4)*A5^3+(((-27*A3^2*A6-45*A3*A9^2)*A2+ (30*A3*A9*A6^2-4*A9^3*A6))*A7^2+((81*A3^2*A2^2+ (12*A3*A9*A6+26*A9^3)*A2+(-27*A3*A6^3-2*A9^2*A6^2))*A10 +(-54*A3*A9*A2^2+(-18*A3*A6^2-48*A9^2*A6)*A2+ 20*A9*A6^3)*A8)*A7+((-18*A3*A9*A2^2+(54*A3*A6^2- 25*A9^2*A6)*A2+3*A9*A6^3)*A10^2+((-162*A3*A6+ 84*A9^2)*A2^2+17*A9*A6^2*A2-9*A6^4)*A8*A10+(243*A3*A2^3 -108*A9*A6*A2^2+27*A6^3*A2)*A8^2))*A5^2+(27*A3^2*A9*A7^4 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13*A2^2*A8^3*A10^3))))*A1^4+(((162*A3^3*A2+(-45*A3^2*A9*A6 +10*A3*A9^3))*A7+((-54*A3^2*A9*A2+(13*A3^2*A6^2+ 6*A3*A9^2*A6-2*A9^4))*A10+((9*A3^2*A6+36*A3*A9^2)*A2- 10*A3*A9*A6^2)*A8))*A4^4+(((-216*A3^2*A9*A2+(54*A3^2*A6^2 +27*A3*A9^2*A6-5*A9^4))*A7+(((21*A3^2*A6+45*A3*A9^2)*A2 +(-39*A3*A9*A6^2+5*A9^3*A6))*A10+(-27*A3^2*A2^2+ (30*A3*A9*A6-17*A9^3)*A2+18*A3*A6^3)*A8))*A5+ (162*A3^3*A7^3+(-171*A3^2*A9*A10+(-21*A3^2*A6+ 74*A3*A9^2)*A8)*A7^2+((56*A3^2*A6+39*A3*A9^2)*A10^2+ (-126*A3^2*A2+(-32*A3*A9*A6-31*A9^3))*A8*A10+ (210*A3*A9*A2+(-34*A3*A6^2+18*A9^2*A6))*A8^2)*A7+ ((5*A3^2*A2+(-20*A3*A9*A6+A9^3))*A10^3+(11*A3*A6^2+ 15*A9^2*A6)*A8*A10^2+((-A3*A6-39*A9^2)*A2- 8*A9*A6^2)*A8^2*A10+(-54*A3*A2^2+36*A9*A6*A2- 3*A6^3)*A8^3)))*A4^3+((((36*A3^2*A6+117*A3*A9^2)*A2+ (-55*A3*A9*A6^2+8*A9^3*A6))*A7+((-18*A3^2*A2^2+ (-64*A3*A9*A6-27*A9^3)*A2+(27*A3*A6^3+4*A9^2*A6^2))*A10 +(36*A3*A9*A2^2+(-45*A3*A6^2+53*A9^2*A6)*A2- 10*A9*A6^3)*A8))*A5^2+(-144*A3^2*A9*A7^3+((113*A3^2*A6+ 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