// Optimized equations for X_1(N), as described in "Constructing elliptic curves over finite fields with // prescribed torsion", Math. Comp. 81 (2012), 1131-1147. Please cite this paper if you use these equations. // // For 6<=N<=50 the value XN:=f(x,y) defines a plane curve f(x,y)=0 birationally equivalent to X_1(N). // The rational functions rN(x,y) and sN(x,y) define a birational map from points (x,y) on X_N to pairs // (r,s) which may be used to define an elliptic curve containing with the point (0,0) of order N by setting // c=s(r-1) and b=rc and defining the curve E(b,c): y^2+(1-c)xy-by=x^3-bx^2. R:=PolynomialRing(Rationals(),2); X6:=y; r6:=x; s6:=1; X7:=y; r7:=x; s7:=x; X8:=y; r8:=1/(2-x); s8:=x; X9:=y; r9:=x^2-x+1; s9:=x; X10:=y; r10:= -x^2/(x^2-3*x+1); s10:= x; X11:= y^2 + (x^2 + 1)*y + x; r11:=x*y+1; s11:=-x+1; X11s:=y^2-x^3+432*x-8208; r11s:=(y+108)/216; s11s:=1+(y-108)/(6*x+72); X12:=y; r12:=(2*x^2-2*x+1) / x; s12:=(3*x^2-3*x+1) / x^2; X13:=y^2 + (x^3 + x^2 + 1)*y - x^2 - x; r13:=-x*y + 1; s13:=1-x*y/(y + 1); X14:=y^2 + (x^2 + x)*y + x; r14:= 1-(x+y)/((y+1)*(x+y+1)); s14:=(1-x)/(y+1); X14s:=y^2-x^3+675*x-13662; r14s:= 1+(108*x - 36*y + 3564)/(3*x^2-x*y-342*x+75*y+999); s14s:=(6*x-234) / (9*x-y-135); X15:=y^2 + (x^2 + x + 1)*y + x^2; r15:=1+(x*y+y^2) / (x^2*(x+y+1)); s15:=1+y/(x*(x+1)); X15s:=y^2-x^3+27*x-8694; r15s:=1 - (6*x-90)*(18*x+6*y-918)/(x^2*y - 189*x^2 + 42*x*y - 4050*x - 3*y^2 + 441*y - 1701); s15s:=1 -(6*x-90)*(18*x+6*y-918)/(x^2*y - 81*x^2 + 6*x*y - 3402*x - 3*y^2 + 981*y - 35721); X16:=y^2 + (x^3 + x^2 - x + 1)*y + x^2; r16:=(x^2 - x*y + y^2 + y)/(x^2 + x - y - 1); s16:=(x - y)/(x + 1); X17:=y^4 + (x^3 + x^2 - x + 2)*y^3 + (x^3 - 3*x + 1)*y^2 - (x^4 + 2*x)*y + x^3 + x^2; r17:=(x^2 + x - y)/(x^2 + x*y + x - y^2 - y); s17:=(x + 1)/(x + y + 1); X18:=y^2 + (x^3 - 2*x^2 + 3*x + 1)*y + 2*x; r18:=(x^2 - x*y - 3*x + 1)/((x-1)^2*(x*y+1)); s18:=(x^2 - 2*x - y)/(x^2 - x*y - 3*x - y^2 - 2*y); X19:=y^5 - (x^2 + 2)*y^4 - (2*x^3 + 2*x^2 + 2*x - 1)*y^3 + (x^5 + 3*x^4 + 7*x^3 + 6*x^2 + 2*x)*y^2 - (x^5 + 2*x^4 + 4*x^3 + 3*x^2)*y + x^3 + x^2; r19:=1+x*(x+y)*(y-1)/((x+1)*(x^2-x*y+2*x-y^2+y)); s19:=1+x*(y-1)/((x+1)*(x-y+1)); X20:=y^3 + (x^2 + 3)*y^2 + (x^3 + 4)*y + 2; r20:=1+(x^3+x*y+x)/((x-1)^2*(x^2-x+y+1)); s20:=1+(x^2+y+1)/((x-1)*(x^2-x+y+2)); X21:=y^4 + (3*x^2 + 1)*y^3 + (x^5 + x^4 + 2*x^2 + 2*x)*y^2 + (2*x^4 + x^3 + x)*y + x^3; r21:=1+(y^2+y)*(x*y+y+1)/((x*y+1)*(x*y-y^2+1)); s21:=1+(y^2+y)/(x*y+1); X22:=y^4 + (x^3 + 2*x^2 + x + 2)*y^3 + (x^5 + x^4 + 2*x^3 + 2*x^2 + 1)*y^2 + (x^5 - x^4 - 2*x^3 - x^2 - x)*y - x^4 - x^3; r22:=(x^2*y + x^2 + x*y + y)/(x^3 + 2*x^2 + y); s22:=(x*y + y)/(x^2 + y); X23:=y^7 + (x^5 - x^4 + x^3 + 4*x^2 + 3)*y^6 + (x^7 + 3*x^5 + x^4 + 5*x^3 + 7*x^2 - 4*x + 3)*y^5 + (2*x^7 + 3*x^5 - x^4 - 2*x^3 - x^2 - 8*x + 1)*y^4 + (x^7 - 4*x^6 - 5*x^5 - 6*x^4 - 6*x^3 - 2*x^2 - 3*x)*y^3 - (3*x^6 - 5*x^4 - 3*x^3 - 3*x^2 - 2*x)*y^2 + (3*x^5 + 4*x^4 + x)*y - x^2*(x+1)^2; r23:=(x^2 + x + y + 1)/(x^2 - x*y); s23:=(x + y + 1)/x; // Original curve published in Table 6 of "Constructing elliptic curves with prescribed torsion over finite fields". X24:=y^5 + (x^4 + 4*x^3 + 3*x^2 - x - 2)*y^4 - (2*x^4 + 8*x^3 + 7*x^2 - 1)*y^3 - (2*x^5 + 4*x^4 - 3*x^3 - 5*x^2 - x)*y^2 + (2*x^5 + 5*x^4 + 2*x^3)*y + x^6 + x^5; r24:=(x^2 + x - y + 1)/(x^2 + x*y - y^2 + y); s24:=(x + 1)/(x + y); // Improved curve obtained by optimizing the curve given in the paper "Infinite families of elliptic curves over Dihedral quartic number fields" // by Daeyeol Jeon, Chang Heon Kim, and Yoonjin Lee, Journal of Number Thoery 131 (2013), 115-122. // Note that, as explained in the paper, the point (0,0) will only have order 12 on the curve E(b,c), but it will be twice a rational point of order 24. X24:=16*y^4 + (64*x^4 - 64*x^3)*y^3 + (64*x^8 - 256*x^7 + 352*x^6 - 352*x^5 + 256*x^4 - 64*x^3 - 32*x^2 + 32*x - 8)*y^2 + (-64*x^10 + 256*x^9 - 384*x^8 + 384*x^7 - 320*x^6 + 192*x^5 - 80*x^4 + 16*x^3)*y + 16*x^12 - 32*x^11 - 112*x^10 + 512*x^9 - 960*x^8 + 1120*x^7 - 872*x^6 + 440*x^5 - 112*x^4 - 16*x^3 + 24*x^2 - 8*x + 1; r24:=(2*x^2-2*x+1)/(2*x^2-x); s24:=(x^2-x+1)/x^2; X25:=y^8 + (4*x^2 + 7*x - 4)*y^7 - (x^5 - x^4 - 14*x^3 - 4*x^2 + 24*x - 6)*y^6 - (x^7 + 4*x^6 - 3*x^5 - 18*x^4 + 15*x^3 + 33*x^2 - 30*x + 4)*y^5 - (x^8 + 2*x^7 - 8*x^6 - 14*x^5 + 24*x^4 + 17*x^3 - 41*x^2 + 16*x - 1)*y^4 + (x^8 + 6*x^7 + 3*x^6 - 20*x^5 - 3*x^4 + 28*x^3 - 19*x^2 + 3*x)*y^3 - (3*x^7 + 9*x^6 - 3*x^5 - 13*x^4 + 11*x^3 - 3*x^2)*y^2 + (3*x^6 + 4*x^5 - 4*x^4 + x^3)*y - x^5; r25:=(x^2 + x*y + y^2 - y)/(x^2 + x + y - 1); s25:=(x + y)/(x + 1); X26:=y^6 + (3*x^2 + 4*x - 2)*y^5 + (3*x^4 + 10*x^3 - 9*x + 1)*y^4 + (x^6 + 7*x^5 + 8*x^4 - 14*x^3 - 11*x^2 + 6*x)*y^3 + (x^7 + 4*x^6 - x^5 - 13*x^4 + 2*x^3 + 10*x^2 - x)*y^2 - (x^6 - 7*x^4 - 4*x^3 + 2*x^2)*y - x^4 - x^3; r26:=(x^3*y + 3*x^2*y - x^2 + x*y^2) /((x+1)*(x^2*y+x^2+3*x*y+y^2)); s26:=(x*y - x)/(x*y + y); X27:=y^8 + (3*x^2 + 6*x - 3)*y^7 - (3*x^5 - 18*x^3 - 9*x^2 + 18*x - 3)*y^6 - (x^8 + 8*x^7 + 13*x^6 - 21*x^5 - 48*x^4 + 20*x^3 + 42*x^2 - 18*x + 1)*y^5 - (x^10 + 6*x^9 + 12*x^8 - 14*x^7 - 72*x^6 - 27*x^5 + 93*x^4 + 33*x^3 - 45*x^2 + 6*x)*y^4 + (x^10 + 11*x^9 + 40*x^8 + 36*x^7 - 69*x^6 - 105*x^5 + 33*x^4 + 54*x^3 - 15*x^2)*y^3 - (4*x^9 + 30*x^8 + 63*x^7 + 10*x^6 - 69*x^5 - 24*x^4 + 19*x^3)*y^2 + (6*x^8 + 27*x^7 + 27*x^6 - 6*x^5 - 12*x^4)*y - 3*x^7 - 6*x^6 - 3*x^5; r27:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s27:=(-x^2 - x - y)/(x*y - x - y); X28:=y^7 + 3*x*y^6 + (x^5 + 3*x^4 + 5*x^3 + 9*x^2 + 2*x)*y^5 - (2*x^5 - 6*x^3 + 2*x^2 + 2*x)*y^4 + (3*x^6 + 16*x^5 + 18*x^4 - 2*x^2)*y^3 + (x^7 - 2*x^6 - 20*x^5 - 28*x^4 - 12*x^3 - 2*x^2)*y^2 - (2*x^7 + 3*x^6 - 5*x^5 - 10*x^4 - 5*x^3 - x^2)*y + x^7 + 2*x^6 + x^5; r28:=1+(x*y+y) / ((y-1)*(x*y-x+2*y-1)); s28:=1-(x*y+y) / ((y-1)*(x-y+1)); X29:=y^11 + (2*x^3 + 5*x^2 + 5*x - 3)*y^10 + (x^6 + 8*x^5 + 18*x^4 + 11*x^3 - 5*x^2 - 12*x + 3)*y^9 + (3*x^8 + 15*x^7 + 29*x^6 + 6*x^5 - 39*x^4 - 19*x^3 + 5*x^2 + 5*x - 1)*y^8 + (3*x^10 + 14*x^9 + 18*x^8 - 26*x^7 - 99*x^6 - 45*x^5 + 95*x^4 + 25*x^3 - 37*x^2 + 7*x)*y^7 + (x^12 + 5*x^11 - 44*x^9 - 106*x^8 - 40*x^7 + 197*x^6 + 190*x^5 - 140*x^4 - 93*x^3 + 59*x^2 - 6*x)*y^6 - (2*x^12 + 16*x^11 + 37*x^10 - 9*x^9 - 184*x^8 - 256*x^7 + 99*x^6 + 346*x^5 - 20*x^4 - 130*x^3 + 32*x^2 - x)*y^5 + (x^12 + 15*x^11 + 65*x^10 + 99*x^9 - 55*x^8 - 320*x^7 - 165*x^6 + 223*x^5 + 100*x^4 - 66*x^3 + 5*x^2)*y^4 - (4*x^11 + 36*x^10 + 108*x^9 + 98*x^8 - 110*x^7 - 191*x^6 + 15*x^5 + 64*x^4 - 10*x^3)*y^3 + (6*x^10 + 38*x^9 + 76*x^8 + 25*x^7 - 55*x^6 - 26*x^5 + 10*x^4)*y^2 - (4*x^9 + 17*x^8 + 18*x^7 - 5*x^5)*y + x^8 + 2*x^7 + x^6; r29:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s29:=1-(x^2 + x*y)/(x*y - x - y); X30:=y^8 - (2*x^3 + 4*x^2 + x + 5)*y^7 + (x^6 + 4*x^5 + 6*x^4 + 9*x^3 + 14*x^2 + 10)*y^6 - (x^7 + 4*x^6 + 9*x^5 + 10*x^4 + 4*x^3 + 15*x^2 - 10*x + 10)*y^5 + (x^8 + 4*x^7 + 4*x^6 - 5*x^4 - 20*x^3 + 5*x^2 - 20*x + 5)*y^4 + (3*x^7 + 11*x^6 + 15*x^5 + 9*x^4 + 18*x^3 - 9*x^2 + 14*x - 1)*y^3 + (3*x^6 + 9*x^5 + 14*x^4 + 2*x^3 + 13*x^2 - 3*x)*y^2 + (x^5 + x^4 + 4*x^3 - 3*x^2)*y - x^3; r30:=(x^2*y + x + y)/(x^2*y - x*y + x); s30:=(x^2*y + x*y + x + y)/(x^2*y + x); X31:=y^13 + (x^3 + 7*x^2 + 10*x - 6)*y^12 + (6*x^5 + 30*x^4 + 51*x^3 + 3*x^2 - 54*x + 15)*y^11 + (15*x^7 + 73*x^6 + 132*x^5 + 42*x^4 - 175*x^3 - 119*x^2 + 124*x - 20)*y^10 + (15*x^9 + 95*x^8 + 193*x^7 + 66*x^6 - 334*x^5 - 439*x^4 + 143*x^3 + 335*x^2 - 155*x + 15)*y^9 - (x^12 - 2*x^11 - 54*x^10 - 156*x^9 - 39*x^8 + 453*x^7 + 693*x^6 - 9*x^5 - 828*x^4 - 201*x^3 + 447*x^2 - 111*x + 6)*y^8 - (x^14 + 4*x^13 - 9*x^12 - 66*x^11 - 21*x^10 + 368*x^9 + 649*x^8 - 8*x^7 - 1061*x^6 - 812*x^5 + 619*x^4 + 529*x^3 - 329*x^2 + 43*x - 1)*y^7 + (3*x^14 + 19*x^13 + 16*x^12 - 142*x^11 - 344*x^10 + 51*x^9 + 951*x^8 + 935*x^7 - 429*x^6 - 1157*x^5 + 5*x^4 + 480*x^3 - 129*x^2 + 7*x)*y^6 - (3*x^14 + 30*x^13 + 83*x^12 - 31*x^11 - 471*x^10 - 582*x^9 + 291*x^8 + 1122*x^7 + 477*x^6 - 642*x^5 - 303*x^4 + 207*x^3 - 21*x^2)*y^5 + (x^14 + 19*x^13 + 96*x^12 + 146*x^11 - 142*x^10 - 611*x^9 - 435*x^8 + 390*x^7 + 584*x^6 - 50*x^5 - 185*x^4 + 35*x^3)*y^4 - (4*x^13 + 42*x^12 + 136*x^11 + 125*x^10 - 157*x^9 - 377*x^8 - 119*x^7 + 189*x^6 + 81*x^5 - 35*x^4)*y^3 + (6*x^12 + 42*x^11 + 93*x^10 + 54*x^9 - 75*x^8 - 96*x^7 - 3*x^6 + 21*x^5)*y^2 - (4*x^11 + 19*x^10 + 29*x^9 + 10*x^8 - 11*x^7 - 7*x^6)*y + x^7*(x+1)^3; r31:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s31:=(-x^2 - x - y)/(x*y - x - y); X32:=y^10 + (x^3 + 5*x^2 + 5*x - 5)*y^9 + (4*x^5 + 15*x^4 + 15*x^3 - 16*x^2 - 25*x + 10)*y^8 + (6*x^7 + 26*x^6 + 23*x^5 - 45*x^4 - 88*x^3 + 50*x - 10)*y^7 + (4*x^9 + 23*x^8 + 26*x^7 - 70*x^6 - 165*x^5 - 33*x^4 + 150*x^3 + 55*x^2 - 50*x + 5)*y^6 + (x^11 + 9*x^10 + 15*x^9 - 47*x^8 - 161*x^7 - 65*x^6 + 226*x^5 + 202*x^4 - 83*x^3 - 81*x^2 + 25*x - 1)*y^5 - (x^11 + 17*x^10 + 63*x^9 + 40*x^8 - 165*x^7 - 253*x^6 + 36*x^5 + 205*x^4 + 23*x^3 - 47*x^2 + 5*x)*y^4 + (8*x^10 + 56*x^9 + 108*x^8 - 2*x^7 - 182*x^6 - 104*x^5 + 64*x^4 + 38*x^3 - 10*x^2)*y^3 - (x^10 + 18*x^9 + 63*x^8 + 60*x^7 - 29*x^6 - 60*x^5 - 7*x^4 + 10*x^3)*y^2 + (2*x^9 + 14*x^8 + 25*x^7 + 11*x^6 - 7*x^5 - 5*x^4)*y - x^5*(x+1)^3; r32:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s32:=1+(-x^2 - x*y)/(x*y - x - y); X33:=y^12 + (3*x^3 - 8*x^2 - 7*x - 7)*y^11 + (3*x^6 - 15*x^5 + 7*x^4 + 23*x^3 + 75*x^2 + 43*x + 21)*y^10 + (x^9 - 10*x^8 + 14*x^7 + 14*x^6 + 38*x^5 - 152*x^4 - 228*x^3 - 268*x^2 - 111*x - 35)*y^9 - (2*x^11 - 8*x^10 - 6*x^9 - 12*x^8 + 110*x^7 + 2*x^6 - 189*x^5 - 696*x^4 - 677*x^3 - 496*x^2 - 155*x - 35)*y^8 + (x^13 - x^12 - 5*x^11 - 33*x^10 + 18*x^9 + 81*x^8 + 202*x^7 - 359*x^6 - 915*x^5 - 1428*x^4 - 1000*x^3 - 525*x^2 - 125*x - 21)*y^7 + (4*x^12 + 21*x^11 + 24*x^10 - 134*x^9 - 174*x^8 + 39*x^7 + 1063*x^6 + 1550*x^5 + 1565*x^4 + 817*x^3 + 323*x^2 + 57*x + 7)*y^6 - (26*x^11 - 38*x^10 - 215*x^9 - 36*x^8 + 484*x^7 + 1335*x^6 + 1323*x^5 + 957*x^4 + 368*x^3 + 110*x^2 + 13*x + 1)*y^5 + (21*x^11 - 74*x^10 - 133*x^9 + 180*x^8 + 570*x^7 + 866*x^6 + 600*x^5 + 317*x^4 + 83*x^3 + 18*x^2 + x)*y^4 - (7*x^11 - 52*x^10 - 15*x^9 + 191*x^8 + 297*x^7 + 296*x^6 + 136*x^5 + 51*x^4 + 7*x^3 + x^2)*y^3 + (x^11 - 16*x^10 + 19*x^9 + 80*x^8 + 73*x^7 + 49*x^6 + 12*x^5 + 3*x^4)*y^2 + (2*x^10 - 8*x^9 - 15*x^8 - 7*x^7 - 3*x^6)*y + x^9 + x^8; r33:=1+x*(y-1)*(x*y-y+1) / ((x-y+1)*(x^2*y-x*y+2*x-y+1)); s33:=1+(x*y - x)/(x^2 - x*y + 2*x - y + 1); X34:=y^11 + (x^3 + 8*x^2 + 6*x - 5)*y^10 + (8*x^5 + 28*x^4 + 34*x^3 - 20*x^2 - 30*x + 10)*y^9 + (x^8 + 19*x^7 + 61*x^6 + 63*x^5 - 39*x^4 - 140*x^3 - 15*x^2 + 60*x - 10)*y^8 + (2*x^10 + 20*x^9 + 66*x^8 + 54*x^7 - 104*x^6 - 256*x^5 - 130*x^4 + 180*x^3 + 100*x^2 - 60*x + 5)*y^7 + (x^12 + 8*x^11 + 26*x^10 + 6*x^9 - 143*x^8 - 279*x^7 - 127*x^6 + 235*x^5 + 339*x^4 - 35*x^3 - 130*x^2 + 30*x - 1)*y^6 - (x^12 + 14*x^11 + 71*x^10 + 129*x^9 + x^8 - 271*x^7 - 358*x^6 - 88*x^5 + 253*x^4 + 106*x^3 - 72*x^2 + 6*x)*y^5 + (5*x^11 + 50*x^10 + 149*x^9 + 162*x^8 + 11*x^7 - 193*x^6 - 226*x^5 + 21*x^4 + 86*x^3 - 15*x^2)*y^4 - (10*x^10 + 52*x^9 + 96*x^8 + 109*x^7 + 36*x^6 - 88*x^5 - 49*x^4 + 20*x^3)*y^3 + (2*x^9 + 4*x^8 + 29*x^7 + 48*x^6 + 6*x^5 - 15*x^4)*y^2 + (x^9 + 7*x^8 + 6*x^7 - 6*x^6 - 6*x^5)*y - x^8 - 2*x^7 - x^6; r34:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s34:=1+(-x^2 - x*y)/(x*y - x - y); X35:=5*y^15 + (15*x^2 + 10*x + 40)*y^14 + (20*x^4 + 35*x^3 + 90*x^2 + 105*x + 145)*y^13 + (15*x^6 + 55*x^5 + 90*x^4 + 280*x^3 + 275*x^2 + 460*x + 315)*y^12 + (6*x^8 + 58*x^7 + 27*x^6 + 359*x^5 + 290*x^4 + 880*x^3 + 686*x^2 + 1144*x + 456)*y^11 + (x^10 + 39*x^9 - 17*x^8 + 303*x^7 + 85*x^6 + 914*x^5 + 913*x^4 + 1506*x^3 + 1517*x^2 + 1824*x + 461)*y^10 + (14*x^11 + 4*x^10 + 78*x^9 + 147*x^8 + 411*x^7 + 534*x^6 + 1401*x^5 + 1876*x^4 + 1764*x^3 + 2576*x^2 + 1975*x + 330)*y^9 + (2*x^13 + 18*x^12 - 66*x^11 + 334*x^10 - 515*x^9 + 1270*x^8 - 397*x^7 + 1469*x^6 + 1781*x^5 + 2191*x^4 + 1893*x^3 + 3075*x^2 + 1485*x + 165)*y^8 + (8*x^14 - 44*x^13 + 198*x^12 - 522*x^11 + 1308*x^10 - 2007*x^9 + 3233*x^8 - 2017*x^7 + 2464*x^6 + 1865*x^5 + 1489*x^4 + 2065*x^3 + 2520*x^2 + 770*x + 55)*y^7 + (x^16 - 7*x^15 + 35*x^14 - 117*x^13 + 362*x^12 - 841*x^11 + 1839*x^10 - 2789*x^9 + 4119*x^8 - 3050*x^7 + 2983*x^6 + 1186*x^5 + 745*x^4 + 1860*x^3 + 1396*x^2 + 264*x + 11)*y^6 + (6*x^14 - 36*x^13 + 162*x^12 - 446*x^11 + 1102*x^10 - 1817*x^9 + 2879*x^8 - 2444*x^7 + 2486*x^6 + 254*x^5 + 503*x^4 + 1161*x^3 + 502*x^2 + 54*x + 1)*y^5 + (15*x^12 - 67*x^11 + 263*x^10 - 528*x^9 + 1056*x^8 - 1030*x^7 + 1269*x^6 - 114*x^5 + 386*x^4 + 459*x^3 + 106*x^2 + 5*x)*y^4 + (x^11 + 16*x^10 - 43*x^9 + 169*x^8 - 182*x^7 + 349*x^6 - 54*x^5 + 191*x^4 + 103*x^3 + 10*x^2)*y^3 + (3*x^9 + 6*x^8 + 3*x^7 + 39*x^6 + 10*x^5 + 49*x^4 + 10*x^3)*y^2 + (3*x^7 + 8*x^5 + 5*x^4)*y + x^5; r35:=1+x*(y+1)*(x+y)/((x-1)*(x^2-x*y-2*x-y^2-y)); s35:=1+(x*y + x)/(x^2 - x*y - 2*x + y + 1); X36:=y^11 + (3*x^3 + 5*x^2 + 7*x - 4)*y^10 + (3*x^6 + 12*x^5 + 22*x^4 + 18*x^3 + 7*x^2 - 28*x + 6)*y^9 + (x^9 + 9*x^8 + 25*x^7 + 30*x^6 + 26*x^5 + 16*x^4 - 32*x^3 - 73*x^2 + 42*x - 4)*y^8 + (2*x^11 + 10*x^10 + 18*x^9 + 2*x^8 - 20*x^7 + 27*x^6 + 22*x^5 - 129*x^4 - 82*x^3 + 127*x^2 - 28*x + 1)*y^7 + (x^13 + 3*x^12 - 2*x^11 - 30*x^10 - 61*x^9 + 17*x^8 + 153*x^7 - 30*x^6 - 277*x^5 + 36*x^4 + 213*x^3 - 88*x^2 + 7*x)*y^6 - (2*x^13 + 13*x^12 + 26*x^11 - 23*x^10 - 172*x^9 - 136*x^8 + 278*x^7 + 286*x^6 - 278*x^5 - 186*x^4 + 160*x^3 - 22*x^2)*y^5 + (x^13 + 14*x^12 + 60*x^11 + 79*x^10 - 119*x^9 - 345*x^8 + 5*x^7 + 395*x^6 + 16*x^5 - 176*x^4 + 40*x^3)*y^4 - (4*x^12 + 38*x^11 + 115*x^10 + 68*x^9 - 206*x^8 - 210*x^7 + 127*x^6 + 108*x^5 - 45*x^4)*y^3 + (7*x^11 + 48*x^10 + 90*x^9 - 2*x^8 - 105*x^7 - 24*x^6 + 31*x^5)*y^2 - (6*x^10 + 26*x^9 + 24*x^8 - 8*x^7 - 12*x^6)*y + 2*x^9 + 4*x^8 + 2*x^7; r36:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s36:=(-x^2 - x - y)/(x*y - x - y); X37:=y^18 - (x^3 + 7*x^2 + 12*x - 6)*y^17 + (26*x^4 + 77*x^3 + 30*x^2 - 72*x + 15)*y^16 + (10*x^8 + 35*x^7 - 15*x^6 - 265*x^5 - 325*x^4 + 201*x^3 + 321*x^2 - 180*x + 20)*y^15 - (5*x^11 + 60*x^10 + 210*x^9 + 180*x^8 - 555*x^7 - 1350*x^6 - 185*x^5 + 1655*x^4 + 400*x^3 - 910*x^2 + 240*x - 15)*y^14 + (x^14 + 22*x^13 + 166*x^12 + 564*x^11 + 678*x^10 - 891*x^9 - 3469*x^8 - 2293*x^7 + 3656*x^6 + 4495*x^5 - 2053*x^4 - 2249*x^3 + 1275*x^2 - 180*x + 6)*y^13 - (3*x^16 + 39*x^15 + 243*x^14 + 807*x^13 + 1079*x^12 - 1278*x^11 - 6267*x^10 - 6155*x^9 + 4834*x^8 + 13100*x^7 + 1905*x^6 - 9941*x^5 - 1372*x^4 + 3726*x^3 - 978*x^2 + 72*x - 1)*y^12 + (3*x^18 + 32*x^17 + 180*x^16 + 595*x^15 + 789*x^14 - 1585*x^13 - 7639*x^12 - 9008*x^11 + 5183*x^10 + 22272*x^9 + 12561*x^8 - 16256*x^7 - 16253*x^6 + 7183*x^5 + 5741*x^4 - 3053*x^3 + 395*x^2 - 12*x)*y^11 - (x^20 + 10*x^19 + 52*x^18 + 172*x^17 + 162*x^16 - 1311*x^15 - 5622*x^14 - 7317*x^13 + 5435*x^12 + 25859*x^11 + 20839*x^10 - 16281*x^9 - 34475*x^8 - 2999*x^7 + 20366*x^6 + 2065*x^5 - 5725*x^4 + 1264*x^3 - 66*x^2)*y^10 - (x^20 + 5*x^19 + 52*x^18 + 501*x^17 + 2023*x^16 + 2681*x^15 - 4715*x^14 - 19581*x^13 - 18001*x^12 + 14660*x^11 + 40593*x^10 + 16842*x^9 - 25005*x^8 - 20440*x^7 + 8210*x^6 + 5975*x^5 - 2525*x^4 + 210*x^3)*y^9 + (26*x^19 + 184*x^18 + 129*x^17 - 2320*x^16 - 8129*x^15 - 7355*x^14 + 12096*x^13 + 31592*x^12 + 16424*x^11 - 20987*x^10 - 29776*x^9 - 1252*x^8 + 14573*x^7 + 1991*x^6 - 3145*x^5 + 412*x^4 + x^3)*y^8 + (35*x^19 + 363*x^18 + 1210*x^17 + 414*x^16 - 6515*x^15 - 14529*x^14 - 6010*x^13 + 16913*x^12 + 23552*x^11 + 4413*x^10 - 13117*x^9 - 8675*x^8 + 2488*x^7 + 2270*x^6 - 494*x^5 - 8*x^4)*y^7 + (21*x^19 + 294*x^18 + 1420*x^17 + 2579*x^16 - 870*x^15 - 9749*x^14 - 11481*x^13 + 664*x^12 + 10483*x^11 + 6962*x^10 - 527*x^9 - 2730*x^8 - 733*x^7 + 322*x^6 + 28*x^5)*y^6 + (7*x^19 + 137*x^18 + 885*x^17 + 2414*x^16 + 2085*x^15 - 2931*x^14 - 6951*x^13 - 2982*x^12 + 2372*x^11 + 2034*x^10 + 306*x^9 + 38*x^8 - 50*x^7 - 56*x^6)*y^5 + (x^19 + 36*x^18 + 334*x^17 + 1256*x^16 + 1944*x^15 + 227*x^14 - 2560*x^13 - 1975*x^12 + 530*x^11 + 635*x^10 - 205*x^9 - 65*x^8 + 70*x^7)*y^4 + (4*x^18 + 70*x^17 + 390*x^16 + 899*x^15 + 697*x^14 - 460*x^13 - 878*x^12 - 71*x^11 + 299*x^10 + 18*x^9 - 56*x^8)*y^3 + (6*x^17 + 64*x^16 + 227*x^15 + 318*x^14 + 86*x^13 - 186*x^12 - 123*x^11 + 28*x^10 + 28*x^9)*y^2 + (4*x^16 + 27*x^15 + 61*x^14 + 53*x^13 + 3*x^12 - 20*x^11 - 8*x^10)*y + x^11*(x+1)^4; r37:=(x^3 + x^2 + x - y)/(x^2*y + x*y + x - y); s37:=(x^2 + x - y)/(x*y + x - y); X38:=y^14 - (x^3 + 8*x^2 + 11*x - 5)*y^13 + (7*x^5 + 38*x^4 + 76*x^3 + 15*x^2 - 56*x + 10)*y^12 - (21*x^7 + 119*x^6 + 259*x^5 + 171*x^4 - 228*x^3 - 197*x^2 + 115*x - 10)*y^11 + (35*x^9 + 223*x^8 + 546*x^7 + 488*x^6 - 413*x^5 - 1038*x^4 - 11*x^3 + 485*x^2 - 120*x + 5)*y^10 - (29*x^11 + 232*x^10 + 680*x^9 + 739*x^8 - 544*x^7 - 2215*x^6 - 1204*x^5 + 1485*x^4 + 790*x^3 - 550*x^2 + 65*x - 1)*y^9 - (x^14 - 5*x^13 - 109*x^12 - 449*x^11 - 614*x^10 + 537*x^9 + 2748*x^8 + 2627*x^7 - 1556*x^6 - 3430*x^5 + 265*x^4 + 1206*x^3 - 317*x^2 + 16*x)*y^8 + (x^16 + 5*x^15 - 11*x^14 - 132*x^13 - 259*x^12 + 322*x^11 + 1978*x^10 + 2565*x^9 - 815*x^8 - 4935*x^7 - 2274*x^6 + 2762*x^5 + 1133*x^4 - 784*x^3 + 85*x^2 - x)*y^7 + (2*x^16 + 20*x^15 + 53*x^14 - 91*x^13 - 718*x^12 - 1195*x^11 + 362*x^10 + 3679*x^9 + 3572*x^8 - 1863*x^7 - 3729*x^6 + 271*x^5 + 1054*x^4 - 227*x^3 + 7*x^2)*y^6 + (x^16 + 19*x^15 + 108*x^14 + 206*x^13 - 200*x^12 - 1469*x^11 - 2026*x^10 + 518*x^9 + 3524*x^8 + 1571*x^7 - 1617*x^6 - 688*x^5 + 347*x^4 - 21*x^3)*y^5 + (5*x^15 + 60*x^14 + 250*x^13 + 390*x^12 - 215*x^11 - 1540*x^10 - 1463*x^9 + 690*x^8 + 1389*x^7 + 20*x^6 - 311*x^5 + 35*x^4)*y^4 + (10*x^14 + 90*x^13 + 295*x^12 + 360*x^11 - 184*x^10 - 786*x^9 - 375*x^8 + 268*x^7 + 151*x^6 - 35*x^5)*y^3 + (10*x^13 + 70*x^12 + 175*x^11 + 141*x^10 - 79*x^9 - 151*x^8 - 25*x^7 + 21*x^6)*y^2 + (5*x^12 + 26*x^11 + 43*x^10 + 21*x^9 - 8*x^8 - 7*x^7)*y + x^8*(x+1)^3; r38:=(x^3 + x^2 + x - y)/(x^2*y + x*y + x - y); s38:=(x^2 + x - y)/(x*y + x - y); X39:=y^17 - (2*x^3 - 7*x^2 - 9*x - 12)*y^16 + (x^6 - 13*x^5 + 8*x^4 + 41*x^3 + 112*x^2 + 93*x + 66)*y^15 + (6*x^8 - 31*x^7 - 31*x^6 + 24*x^5 + 308*x^4 + 551*x^3 + 700*x^2 + 439*x + 220)*y^14 + (15*x^10 - 31*x^9 - 87*x^8 - 143*x^7 + 256*x^6 + 1103*x^5 + 2266*x^4 + 2721*x^3 + 2450*x^2 + 1250*x + 495)*y^13 + (20*x^12 - 5*x^11 - 65*x^10 - 305*x^9 - 173*x^8 + 803*x^7 + 3080*x^6 + 5955*x^5 + 8076*x^4 + 7631*x^3 + 5527*x^2 + 2386*x + 792)*y^12 + (15*x^14 + 13*x^13 + 22*x^12 - 248*x^11 - 424*x^10 - 110*x^9 + 1818*x^8 + 5903*x^7 + 11226*x^6 + 16047*x^5 + 17523*x^4 + 13977*x^3 + 8608*x^2 + 3206*x + 924)*y^11 + (6*x^16 + 7*x^15 + 55*x^14 - 81*x^13 - 238*x^12 - 572*x^11 + 257*x^10 + 2916*x^9 + 7554*x^8 + 14786*x^7 + 22136*x^6 + 27053*x^5 + 25700*x^4 + 17843*x^3 + 9576*x^2 + 3094*x + 792)*y^10 + (x^18 + 22*x^16 - 5*x^15 + 8*x^14 - 393*x^13 - 304*x^12 + 488*x^11 + 3017*x^10 + 7076*x^9 + 12121*x^8 + 20627*x^7 + 28542*x^6 + 31756*x^5 + 26943*x^4 + 16357*x^3 + 7700*x^2 + 2144*x + 495)*y^9 + (x^18 - 3*x^17 + 34*x^16 - 80*x^15 - 117*x^14 - 403*x^13 + 632*x^12 + 2334*x^11 + 4035*x^10 + 6421*x^9 + 10631*x^8 + 19848*x^7 + 27178*x^6 + 27542*x^5 + 20686*x^4 + 10821*x^3 + 4445*x^2 + 1045*x + 220)*y^8 - (2*x^17 - 32*x^16 + 157*x^15 + 68*x^14 - 131*x^13 - 1423*x^12 - 1918*x^11 - 1003*x^10 - 2230*x^9 - 7144*x^8 - 15846*x^7 - 20396*x^6 - 17920*x^5 - 11571*x^4 - 5066*x^3 - 1792*x^2 - 341*x - 66)*y^7 + (x^17 + 15*x^16 - 145*x^15 + 129*x^14 + 471*x^13 + 846*x^12 - 180*x^11 - 1633*x^10 + 572*x^9 + 5639*x^8 + 10992*x^7 + 11829*x^6 + 8477*x^5 + 4548*x^4 + 1594*x^3 + 476*x^2 + 67*x + 12)*y^6 + (2*x^16 - 72*x^15 + 195*x^14 + 277*x^13 - 105*x^12 - 1068*x^11 - 1247*x^10 + 1285*x^9 + 4310*x^8 + 5843*x^7 + 4888*x^6 + 2711*x^5 + 1167*x^4 + 302*x^3 + 74*x^2 + 6*x + 1)*y^5 + (x^16 - 20*x^15 + 114*x^14 + 19*x^13 - 354*x^12 - 570*x^11 - 57*x^10 + 1363*x^9 + 2220*x^8 + 2058*x^7 + 1294*x^6 + 517*x^5 + 170*x^4 + 26*x^3 + 5*x^2)*y^4 - (4*x^15 - 36*x^14 + 46*x^13 + 172*x^12 + 60*x^11 - 278*x^10 - 656*x^9 - 667*x^8 - 416*x^7 - 187*x^6 - 44*x^5 - 10*x^4)*y^3 + (6*x^14 - 23*x^13 - 31*x^12 + 51*x^11 + 132*x^10 + 154*x^9 + 101*x^8 + 36*x^7 + 10*x^6)*y^2 - (4*x^13 - 2*x^12 - 20*x^11 - 23*x^10 - 14*x^9 - 5*x^8)*y + x^12 + 2*x^11 + x^10; r39:=1-x*(y+1)*(x*y-y-1) / ((x+y+1)*(x^2*y-x*y-2*x-y-1)); s39:=1-(x*y + x)/(x^2 + x*y + 2*x + y + 1); X40:=2*y^15 - (4*x^3 + 16*x^2 - 14*x + 18)*y^14 + (3*x^6 + 26*x^5 + 31*x^4 - 64*x^3 + 177*x^2 - 110*x + 73)*y^13 - (x^9 + 15*x^8 + 55*x^7 - 3*x^6 - 23*x^5 + 507*x^4 - 653*x^3 + 793*x^2 - 384*x + 176)*y^12 + (4*x^11 + 26*x^10 + 44*x^9 - 32*x^8 + 222*x^7 + 494*x^6 - 1174*x^5 + 2543*x^4 - 2384*x^3 + 1972*x^2 - 784*x + 280)*y^11 - (6*x^13 + 18*x^12 + 8*x^11 + 28*x^10 + 332*x^9 + 36*x^8 - 538*x^7 + 3234*x^6 - 4843*x^5 + 6381*x^4 - 4760*x^3 + 3080*x^2 - 1036*x + 308)*y^10 + (4*x^15 + 3*x^14 - 2*x^13 + 66*x^12 + 140*x^11 - 126*x^10 + 402*x^9 + 1602*x^8 - 3816*x^7 + 8299*x^6 - 9448*x^5 + 9505*x^4 - 5936*x^3 + 3206*x^2 - 924*x + 238)*y^9 - (x^17 - x^16 + x^15 + 27*x^14 - 13*x^13 + x^12 + 392*x^11 + 152*x^10 - 882*x^9 + 4618*x^8 - 7427*x^7 + 11443*x^6 - 10867*x^5 + 9171*x^4 - 4914*x^3 + 2282*x^2 - 560*x + 128)*y^8 - (18*x^15 - 22*x^14 - 66*x^13 + 117*x^12 - 200*x^11 - 1099*x^10 + 2206*x^9 - 5589*x^8 + 7398*x^7 - 9816*x^6 + 8214*x^5 - 6047*x^4 + 2768*x^3 - 1108*x^2 + 224*x - 46)*y^7 + (4*x^16 + 28*x^15 + 48*x^14 - 117*x^13 - 37*x^12 + 285*x^11 - 1239*x^10 + 1543*x^9 - 3661*x^8 + 4730*x^7 - 5938*x^6 + 4389*x^5 - 2783*x^4 + 1044*x^3 - 352*x^2 + 54*x - 10)*y^6 - (x^16 + 24*x^15 + 87*x^14 - 238*x^12 + 228*x^11 - 347*x^10 + 346*x^9 - 1797*x^8 + 2448*x^7 - 2740*x^6 + 1662*x^5 - 856*x^4 + 240*x^3 - 65*x^2 + 6*x - 1)*y^5 + (5*x^15 + 55*x^14 + 95*x^13 - 135*x^12 - 119*x^11 + 135*x^10 + 120*x^9 - 940*x^8 + 1050*x^7 - 890*x^6 + 390*x^5 - 150*x^4 + 25*x^3 - 5*x^2)*y^4 - (10*x^14 + 60*x^13 + 20*x^12 - 146*x^11 + 25*x^10 + 180*x^9 - 390*x^8 + 280*x^7 - 160*x^6 + 40*x^5 - 10*x^4)*y^3 + (10*x^13 + 30*x^12 - 29*x^11 - 45*x^10 + 80*x^9 - 80*x^8 + 30*x^7 - 10*x^6)*y^2 - (5*x^12 + 4*x^11 - 15*x^10 + 10*x^9 - 5*x^8)*y + x^11 - x^10; r40:=1-x*(y-1)*(x*y+y-1)/((x+y-1)*(x^2*y+x*y-2*x-y+1)); s40:=1-(x*y - x)/(x^2 + x*y - 2*x - y + 1); X41:=y^22 + (2*x^3 + 12*x^2 + 16*x - 10)*y^21 + (x^6 + 22*x^5 + 96*x^4 + 150*x^3 - 150*x + 45)*y^20 + (10*x^8 + 124*x^7 + 488*x^6 + 804*x^5 + 210*x^4 - 950*x^3 - 530*x^2 + 640*x - 120)*y^19 + (45*x^10 + 425*x^9 + 1631*x^8 + 2812*x^7 + 1021*x^6 - 3720*x^5 - 4295*x^4 + 1830*x^3 + 2920*x^2 - 1635*x + 210)*y^18 + (99*x^12 + 927*x^11 + 3630*x^10 + 6660*x^9 + 2586*x^8 - 10875*x^7 - 16359*x^6 + 987*x^5 + 16116*x^4 + 1551*x^3 - 8172*x^2 + 2766*x - 252)*y^17 - (7*x^15 - 84*x^14 - 1215*x^13 - 5412*x^12 - 10776*x^11 - 4023*x^10 + 23813*x^9 + 41226*x^8 + 5223*x^7 - 46888*x^6 - 28687*x^5 + 28229*x^4 + 14814*x^3 - 14434*x^2 + 3233*x - 210)*y^16 - (x^18 + 31*x^17 + 82*x^16 - 782*x^15 - 5335*x^14 - 12279*x^13 - 4043*x^12 + 37823*x^11 + 73256*x^10 + 16626*x^9 - 99095*x^8 - 97411*x^7 + 44017*x^6 + 89492*x^5 - 19014*x^4 - 35035*x^3 + 17276*x^2 - 2640*x + 120)*y^15 - (3*x^20 + 54*x^19 + 259*x^18 + 7*x^17 - 3549*x^16 - 10596*x^15 - 3558*x^14 + 43020*x^13 + 92542*x^12 + 26698*x^11 - 158031*x^10 - 202419*x^9 + 39903*x^8 + 227934*x^7 + 55728*x^6 - 133101*x^5 - 20700*x^4 + 48030*x^3 - 14310*x^2 + 1485*x - 45)*y^14 - (3*x^22 + 43*x^21 + 223*x^20 + 253*x^19 - 1942*x^18 - 7586*x^17 - 3686*x^16 + 35143*x^15 + 84660*x^14 + 26688*x^13 - 185952*x^12 - 289666*x^11 + 10886*x^10 + 391202*x^9 + 235651*x^8 - 223418*x^7 - 211159*x^6 + 100160*x^5 + 63920*x^4 - 42975*x^3 + 8120*x^2 - 550*x + 10)*y^13 - (x^24 + 13*x^23 + 64*x^22 + 23*x^21 - 1078*x^20 - 4151*x^19 - 2370*x^18 + 21726*x^17 + 57157*x^16 + 17031*x^15 - 160804*x^14 - 286393*x^13 - 21475*x^12 + 477386*x^11 + 447968*x^10 - 227293*x^9 - 510031*x^8 - 2971*x^7 + 272539*x^6 - 8266*x^5 - 74154*x^4 + 25576*x^3 - 3022*x^2 + 121*x - 1)*y^12 + (3*x^24 + 51*x^23 + 360*x^22 + 1085*x^21 - 202*x^20 - 10725*x^19 - 26835*x^18 - 3939*x^17 + 102792*x^16 + 193280*x^15 + 20612*x^14 - 411561*x^13 - 519547*x^12 + 127154*x^11 + 723513*x^10 + 281625*x^9 - 434313*x^8 - 251415*x^7 + 174533*x^6 + 59048*x^5 - 50196*x^4 + 9807*x^3 - 666*x^2 + 12*x)*y^11 - (3*x^24 + 72*x^23 + 690*x^22 + 3153*x^21 + 5988*x^20 - 5004*x^19 - 47393*x^18 - 83070*x^17 + 5802*x^16 + 252964*x^15 + 373102*x^14 - 30350*x^13 - 658274*x^12 - 513572*x^11 + 369889*x^10 + 583854*x^9 - 71505*x^8 - 279852*x^7 + 31189*x^6 + 60155*x^5 - 20695*x^4 + 2200*x^3 - 66*x^2)*y^10 + (x^24 + 43*x^23 + 604*x^22 + 3845*x^21 + 12222*x^20 + 15542*x^19 - 19781*x^18 - 107985*x^17 - 155889*x^16 + 18353*x^15 + 391719*x^14 + 453492*x^13 - 158819*x^12 - 657562*x^11 - 197946*x^10 + 386126*x^9 + 172843*x^8 - 134685*x^7 - 34040*x^6 + 29245*x^5 - 4840*x^4 + 220*x^3)*y^9 - (9*x^23 + 243*x^22 + 2262*x^21 + 10281*x^20 + 24999*x^19 + 26370*x^18 - 29103*x^17 - 152994*x^16 - 208894*x^15 + 36272*x^14 + 422826*x^13 + 315292*x^12 - 247574*x^11 - 351141*x^10 + 50658*x^9 + 150360*x^8 - 15210*x^7 - 26910*x^6 + 7425*x^5 - 495*x^4)*y^8 + (36*x^22 + 591*x^21 + 3873*x^20 + 14148*x^19 + 32524*x^18 + 40087*x^17 - 19925*x^16 - 161672*x^15 - 189911*x^14 + 73831*x^13 + 291673*x^12 + 87011*x^11 - 160393*x^10 - 71953*x^9 + 46608*x^8 + 13614*x^7 - 8052*x^6 + 792*x^5)*y^7 - (29*x^21 + 326*x^20 + 2108*x^19 + 10672*x^18 + 33831*x^17 + 48123*x^16 - 15118*x^15 - 125934*x^14 - 95657*x^13 + 72454*x^12 + 105878*x^11 - 8129*x^10 - 40173*x^9 + 381*x^8 + 6072*x^7 - 924*x^6)*y^6 - (11*x^21 + 191*x^20 + 1167*x^19 + 2080*x^18 - 5897*x^17 - 29025*x^16 - 33898*x^15 + 16583*x^14 + 59655*x^13 + 20511*x^12 - 29256*x^11 - 16200*x^10 + 6120*x^9 + 2970*x^8 - 792*x^7)*y^5 + (x^21 + 53*x^20 + 581*x^19 + 2433*x^18 + 3430*x^17 - 3914*x^16 - 16427*x^15 - 11994*x^14 + 9228*x^13 + 14395*x^12 + 820*x^11 - 4550*x^10 - 715*x^9 + 495*x^8)*y^4 - (4*x^20 + 98*x^19 + 690*x^18 + 1945*x^17 + 1740*x^16 - 2071*x^15 - 5032*x^14 - 2005*x^13 + 2020*x^12 + 1565*x^11 - 110*x^10 - 220*x^9)*y^3 + (6*x^19 + 86*x^18 + 395*x^17 + 741*x^16 + 404*x^15 - 502*x^14 - 741*x^13 - 183*x^12 + 144*x^11 + 66*x^10)*y^2 - (4*x^18 + 35*x^17 + 104*x^16 + 134*x^15 + 56*x^14 - 37*x^13 - 44*x^12 - 12*x^11)*y + x^12*(x+1)^5; r41:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s41:=(-x^2 - x - y)/(x*y - x - y); X42:=y^15 + (3*x^3 + 6*x^2 + 7*x - 6)*y^14 + (3*x^6 + 15*x^5 + 34*x^4 + 21*x^3 - 16*x^2 - 45*x + 15)*y^13 + (x^9 + 12*x^8 + 48*x^7 + 91*x^6 + 57*x^5 - 105*x^4 - 184*x^3 - 57*x^2 + 119*x - 20)*y^12 + (3*x^11 + 25*x^10 + 93*x^9 + 163*x^8 + 71*x^7 - 293*x^6 - 608*x^5 - 265*x^4 + 346*x^3 + 304*x^2 - 166*x + 15)*y^11 + (4*x^13 + 33*x^12 + 116*x^11 + 196*x^10 + 34*x^9 - 533*x^8 - 1145*x^7 - 797*x^6 + 738*x^5 + 1278*x^4 + 11*x^3 - 536*x^2 + 129*x - 6)*y^10 + (3*x^15 + 26*x^14 + 89*x^13 + 133*x^12 - 49*x^11 - 628*x^10 - 1313*x^9 - 1180*x^8 + 746*x^7 + 2790*x^6 + 1242*x^5 - 1466*x^4 - 731*x^3 + 468*x^2 - 53*x + 1)*y^9 + (x^17 + 9*x^16 + 29*x^15 + 20*x^14 - 124*x^13 - 455*x^12 - 831*x^11 - 832*x^10 + 422*x^9 + 3034*x^8 + 3201*x^7 - 1307*x^6 - 3110*x^5 + 115*x^4 + 902*x^3 - 205*x^2 + 9*x)*y^8 - (2*x^17 + 20*x^16 + 78*x^15 + 146*x^14 + 143*x^13 + 98*x^12 - 192*x^11 - 1600*x^10 - 3152*x^9 - 531*x^8 + 4298*x^7 + 2517*x^6 - 1869*x^5 - 899*x^4 + 452*x^3 - 36*x^2)*y^7 + (2*x^17 + 23*x^16 + 92*x^15 + 136*x^14 + 15*x^13 + 167*x^12 + 1232*x^11 + 1279*x^10 - 2216*x^9 - 4169*x^8 + 239*x^7 + 2807*x^6 + 189*x^5 - 616*x^4 + 84*x^3)*y^6 - (x^17 + 18*x^16 + 98*x^15 + 182*x^14 - 104*x^13 - 645*x^12 + 175*x^11 + 2329*x^10 + 1510*x^9 - 2103*x^8 - 1919*x^7 + 623*x^6 + 518*x^5 - 126*x^4)*y^5 + (5*x^16 + 55*x^15 + 195*x^14 + 165*x^13 - 490*x^12 - 950*x^11 + 350*x^10 + 1653*x^9 + 430*x^8 - 797*x^7 - 238*x^6 + 126*x^5)*y^4 - (10*x^15 + 80*x^14 + 200*x^13 + 56*x^12 - 466*x^11 - 495*x^10 + 231*x^9 + 438*x^8 + 20*x^7 - 84*x^6)*y^3 + (10*x^14 + 60*x^13 + 107*x^12 - 165*x^10 - 106*x^9 + 38*x^8 + 36*x^7)*y^2 - (5*x^13 + 22*x^12 + 28*x^11 + x^10 - 19*x^9 - 9*x^8)*y + x^9*(x+1)^3; r42:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s42:=(-x^2 - x - y)/(x*y - x - y); X43:=y^24 + (5*x^3 + 15*x^2 + 14*x - 10)*y^23 + (10*x^6 + 60*x^5 + 160*x^4 + 155*x^3 - 49*x^2 - 140*x + 45)*y^22 + (10*x^9 + 100*x^8 + 425*x^7 + 975*x^6 + 1070*x^5 - 170*x^4 - 1311*x^3 - 325*x^2 + 630*x - 120)*y^21 + (5*x^12 + 85*x^11 + 530*x^10 + 1860*x^9 + 3960*x^8 + 4485*x^7 - 160*x^6 - 7080*x^5 - 4879*x^4 + 3650*x^3 + 2655*x^2 - 1680*x + 210)*y^20 + (x^15 + 36*x^14 + 352*x^13 + 1746*x^12 + 5374*x^11 + 10842*x^10 + 12424*x^9 - 114*x^8 - 24248*x^7 - 27229*x^6 + 7874*x^5 + 24412*x^4 - 1884*x^3 - 8610*x^2 + 2940*x - 252)*y^19 + (6*x^17 + 117*x^16 + 884*x^15 + 3758*x^14 + 10396*x^13 + 19746*x^12 + 22496*x^11 - 1739*x^10 - 58318*x^9 - 85928*x^8 - 4903*x^7 + 95864*x^6 + 41729*x^5 - 50964*x^4 - 14111*x^3 + 16590*x^2 - 3528*x + 210)*y^18 + (15*x^19 + 220*x^18 + 1422*x^17 + 5323*x^16 + 13022*x^15 + 22348*x^14 + 24211*x^13 - 7315*x^12 - 98143*x^11 - 176658*x^10 - 60591*x^9 + 215685*x^8 + 228682*x^7 - 95699*x^6 - 165552*x^5 + 43842*x^4 + 44010*x^3 - 21042*x^2 + 2940*x - 120)*y^17 + (20*x^21 + 255*x^20 + 1466*x^19 + 4767*x^18 + 9343*x^17 + 11734*x^16 + 9728*x^15 - 12474*x^14 - 105659*x^13 - 242510*x^12 - 155357*x^11 + 313479*x^10 + 583597*x^9 + 28834*x^8 - 540958*x^7 - 146688*x^6 + 264207*x^5 + 24795*x^4 - 67323*x^3 + 18150*x^2 - 1680*x + 45)*y^16 + (15*x^23 + 180*x^22 + 925*x^21 + 2359*x^20 + 1880*x^19 - 4402*x^18 - 9043*x^17 - 4171*x^16 - 49593*x^15 - 212124*x^14 - 243430*x^13 + 282627*x^12 + 925825*x^11 + 428110*x^10 - 902737*x^9 - 872357*x^8 + 432234*x^7 + 525874*x^6 - 193290*x^5 - 110052*x^4 + 64015*x^3 - 10605*x^2 + 630*x - 10)*y^15 + (6*x^25 + 71*x^24 + 312*x^23 + 326*x^22 - 2431*x^21 - 10512*x^20 - 11958*x^19 + 18190*x^18 + 34797*x^17 - 104333*x^16 - 284022*x^15 + 84230*x^14 + 989537*x^13 + 914112*x^12 - 874986*x^11 - 1861411*x^10 - 58083*x^9 + 1473699*x^8 + 273514*x^7 - 640871*x^6 - 13491*x^5 + 136923*x^4 - 39596*x^3 + 4035*x^2 - 140*x + 1)*y^14 + (x^27 + 12*x^26 + 34*x^25 - 199*x^24 - 1837*x^23 - 5453*x^22 - 1996*x^21 + 30228*x^20 + 67892*x^19 - 26941*x^18 - 272468*x^17 - 153552*x^16 + 727712*x^15 + 1170816*x^14 - 418242*x^13 - 2369114*x^12 - 1136425*x^11 + 1935162*x^10 + 1715545*x^9 - 871715*x^8 - 895117*x^7 + 348503*x^6 + 160656*x^5 - 95836*x^4 + 15601*x^3 - 905*x^2 + 14*x)*y^13 - (4*x^27 + 61*x^26 + 347*x^25 + 619*x^24 - 2795*x^23 - 18606*x^22 - 36596*x^21 + 20660*x^20 + 206509*x^19 + 225820*x^18 - 394632*x^17 - 1064236*x^16 - 110362*x^15 + 2066349*x^14 + 1943924*x^13 - 1409510*x^12 - 3016516*x^11 - 93601*x^10 + 2077189*x^9 + 351675*x^8 - 801916*x^7 - 17389*x^6 + 152723*x^5 - 40388*x^4 + 3575*x^3 - 91*x^2)*y^12 + (6*x^27 + 120*x^26 + 954*x^25 + 3670*x^24 + 4131*x^23 - 22364*x^22 - 99791*x^21 - 115926*x^20 + 204111*x^19 + 701625*x^18 + 308728*x^17 - 1326336*x^16 - 1921232*x^15 + 516868*x^14 + 3072933*x^13 + 1424819*x^12 - 2142028*x^11 - 1854941*x^10 + 826123*x^9 + 871053*x^8 - 286142*x^7 - 147697*x^6 + 73128*x^5 - 9620*x^4 + 364*x^3)*y^11 - (4*x^27 + 114*x^26 + 1240*x^25 + 6905*x^24 + 19364*x^23 + 9886*x^22 - 104634*x^21 - 300123*x^20 - 158787*x^19 + 677996*x^18 + 1260208*x^17 - 4694*x^16 - 2156958*x^15 - 1832390*x^14 + 1225757*x^13 + 2546023*x^12 + 181231*x^11 - 1547225*x^10 - 341625*x^9 + 527648*x^8 + 45569*x^7 - 93181*x^6 + 18590*x^5 - 1001*x^4)*y^10 + (x^27 + 52*x^26 + 836*x^25 + 6521*x^24 + 27424*x^23 + 55476*x^22 - 5148*x^21 - 278357*x^20 - 514801*x^19 - 21322*x^18 + 1120012*x^17 + 1283277*x^16 - 442474*x^15 - 1984810*x^14 - 937279*x^13 + 1188033*x^12 + 1126527*x^11 - 343797*x^10 - 482466*x^9 + 96150*x^8 + 80134*x^7 - 26455*x^6 + 2002*x^5)*y^9 - (9*x^26 + 279*x^25 + 3294*x^24 + 19769*x^23 + 63486*x^22 + 89383*x^21 - 61787*x^20 - 424147*x^19 - 520351*x^18 + 166957*x^17 + 1046996*x^16 + 806593*x^15 - 512778*x^14 - 1112813*x^13 - 188738*x^12 + 592070*x^11 + 206343*x^10 - 170908*x^9 - 38403*x^8 + 27885*x^7 - 3003*x^6)*y^8 + (36*x^25 + 840*x^24 + 7706*x^23 + 35974*x^22 + 88106*x^21 + 83693*x^20 - 105979*x^19 - 381647*x^18 - 337411*x^17 + 179122*x^16 + 613394*x^15 + 332651*x^14 - 306047*x^13 - 370406*x^12 + 38627*x^11 + 139817*x^10 - 3270*x^9 - 21450*x^8 + 3432*x^7)*y^7 - (84*x^24 + 1518*x^23 + 10844*x^22 + 39453*x^21 + 74899*x^20 + 50789*x^19 - 80155*x^18 - 215887*x^17 - 162101*x^16 + 90998*x^15 + 240554*x^14 + 81353*x^13 - 104691*x^12 - 61930*x^11 + 21303*x^10 + 11440*x^9 - 3003*x^8)*y^6 + (113*x^23 + 1575*x^22 + 8776*x^21 + 25533*x^20 + 40832*x^19 + 26692*x^18 - 29806*x^17 - 84604*x^16 - 59180*x^15 + 30593*x^14 + 59172*x^13 + 8256*x^12 - 17439*x^11 - 3575*x^10 + 2002*x^9)*y^5 + (x^23 - 64*x^22 - 747*x^21 - 3472*x^20 - 9337*x^19 - 15860*x^18 - 13347*x^17 + 5828*x^16 + 23332*x^15 + 13591*x^14 - 6339*x^13 - 7526*x^12 - 65*x^11 + 1001*x^10)*y^4 - (4*x^22 + 30*x^21 + 86*x^20 - 154*x^19 - 1818*x^18 - 4690*x^17 - 4449*x^16 + 604*x^15 + 3771*x^14 + 1648*x^13 - 520*x^12 - 364*x^11)*y^3 + (6*x^21 + 64*x^20 + 246*x^19 + 338*x^18 - 149*x^17 - 872*x^16 - 765*x^15 - 33*x^14 + 250*x^13 + 91*x^12)*y^2 - (4*x^20 + 32*x^19 + 89*x^18 + 102*x^17 + 18*x^16 - 64*x^15 - 55*x^14 - 14*x^13)*y + x^14*(x+1)^5; r43:= - (x^3 + x^2 + x + y)/(x^2*y + x*y - x - y); s43:= - (x^2 + x + y)/(x*y - x - y); X44:=y^19 - (2*x^2 - 6*x + 10)*y^18 + (x^4 - 20*x^3 + 29*x^2 - 58*x + 45)*y^17 + (20*x^5 - 70*x^4 + 148*x^3 - 202*x^2 + 256*x - 120)*y^16 - (6*x^7 - 110*x^6 + 76*x^5 - 614*x^4 + 547*x^3 - 818*x^2 + 679*x - 210)*y^15 - (72*x^8 - 34*x^7 + 682*x^6 - 356*x^5 + 2381*x^4 - 1479*x^3 + 2115*x^2 - 1197*x + 252)*y^14 + (15*x^10 - 68*x^9 + 114*x^8 - 876*x^7 + 1214*x^6 - 2220*x^5 + 5406*x^4 - 3281*x^3 + 3697*x^2 - 1463*x + 210)*y^13 + (10*x^11 + 66*x^10 + 752*x^9 + 922*x^8 + 4684*x^7 + 454*x^6 + 7808*x^5 - 8421*x^4 + 5711*x^3 - 4507*x^2 + 1253*x - 120)*y^12 + (25*x^13 + 10*x^12 - 25*x^11 - 226*x^10 - 1713*x^9 - 2283*x^8 - 10272*x^7 - 4061*x^6 - 16179*x^5 + 10193*x^4 - 7308*x^3 + 3867*x^2 - 741*x + 45)*y^11 - (10*x^15 - 35*x^14 - 105*x^13 - 427*x^12 - 329*x^11 + 339*x^10 + 449*x^9 + 1602*x^8 - 9874*x^7 - 4485*x^6 - 22291*x^5 + 10262*x^4 - 6622*x^3 + 2303*x^2 - 289*x + 10)*y^10 + (x^17 - 39*x^16 - 206*x^15 - 880*x^14 - 2026*x^13 - 3764*x^12 - 3551*x^11 - 361*x^10 + 5315*x^9 + 11486*x^8 - 43*x^7 + 1021*x^6 - 22297*x^5 + 8381*x^4 - 4129*x^3 + 910*x^2 - 67*x + 1)*y^9 + (11*x^18 + 75*x^17 + 388*x^16 + 1272*x^15 + 3516*x^14 + 7000*x^13 + 11487*x^12 + 12329*x^11 + 7437*x^10 - 4281*x^9 - 16719*x^8 - 10417*x^7 - 7985*x^6 + 16957*x^5 - 5111*x^4 + 1691*x^3 - 215*x^2 + 7*x)*y^8 - (x^20 + 8*x^19 + 49*x^18 + 201*x^17 + 742*x^16 + 2117*x^15 + 5324*x^14 + 10372*x^13 + 17102*x^12 + 20334*x^11 + 17283*x^10 + 4571*x^9 - 10756*x^8 - 12279*x^7 - 10677*x^6 + 9759*x^5 - 2115*x^4 + 411*x^3 - 23*x^2)*y^7 + (11*x^18 + 75*x^17 + 383*x^16 + 1275*x^15 + 3600*x^14 + 7646*x^13 + 13782*x^12 + 18352*x^11 + 18961*x^10 + 10983*x^9 - 1101*x^8 - 7041*x^7 - 8297*x^6 + 4049*x^5 - 523*x^4 + 45*x^3)*y^6 - (x^18 + 6*x^17 + 65*x^16 + 295*x^15 + 1125*x^14 + 2866*x^13 + 6151*x^12 + 9475*x^11 + 11726*x^10 + 9201*x^9 + 3324*x^8 - 1753*x^7 - 4184*x^6 + 1120*x^5 - 58*x^4)*y^5 + (5*x^16 + 25*x^15 + 160*x^14 + 520*x^13 + 1485*x^12 + 2765*x^11 + 4245*x^10 + 4165*x^9 + 2595*x^8 + 279*x^7 - 1366*x^6 + 186*x^5)*y^4 - (10*x^14 + 40*x^13 + 185*x^12 + 430*x^11 + 885*x^10 + 1075*x^9 + 941*x^8 + 335*x^7 - 277*x^6 + 17*x^5)*y^3 + (10*x^12 + 30*x^11 + 101*x^10 + 153*x^9 + 189*x^8 + 101*x^7 - 33*x^6 + x^5)*y^2 - (5*x^10 + 10*x^9 + 21*x^8 + 15*x^7 - 2*x^6)*y + x^8 + x^7; r44:=1+x*(y-1)*(x+y)/((x+1)*(x^2-x*y+2*x-y^2+y)); s44:=1+(x*y-x)/((x+1)*(x-y+1)); X45:=y^23 - (3*x^3 + 12*x^2 + 15*x - 9)*y^22 + (3*x^6 + 33*x^5 + 108*x^4 + 141*x^3 + 6*x^2 - 135*x + 36)*y^21 - (x^9 + 30*x^8 + 204*x^7 + 622*x^6 + 861*x^5 + 219*x^4 - 823*x^3 - 585*x^2 + 540*x - 84)*y^20 + (9*x^11 + 147*x^10 + 846*x^9 + 2466*x^8 + 3618*x^7 + 1323*x^6 - 3522*x^5 - 4512*x^4 + 693*x^3 + 3024*x^2 - 1260*x + 126)*y^19 - (36*x^13 + 459*x^12 + 2469*x^11 + 7062*x^10 + 10713*x^9 + 4611*x^8 - 11544*x^7 - 19122*x^6 - 4386*x^5 + 13923*x^4 + 6174*x^3 - 7812*x^2 + 1890*x - 126)*y^18 + (84*x^15 + 990*x^14 + 5155*x^13 + 14733*x^12 + 22603*x^11 + 9552*x^10 - 29486*x^9 - 55701*x^8 - 25291*x^7 + 35166*x^6 + 45164*x^5 - 10836*x^4 - 24486*x^3 + 12348*x^2 - 1890*x + 84)*y^17 - (126*x^17 + 1476*x^16 + 7652*x^15 + 21940*x^14 + 33300*x^13 + 9752*x^12 - 60434*x^11 - 114960*x^10 - 66770*x^9 + 63884*x^8 + 134172*x^7 + 39361*x^6 - 90538*x^5 - 30870*x^4 + 45234*x^3 - 12726*x^2 + 1260*x - 36)*y^16 + (117*x^19 + 1449*x^18 + 7747*x^17 + 22347*x^16 + 31981*x^15 - 2973*x^14 - 97819*x^13 - 168382*x^12 - 96261*x^11 + 99318*x^10 + 247982*x^9 + 169254*x^8 - 120125*x^7 - 216707*x^6 + 48953*x^5 + 96516*x^4 - 50382*x^3 + 8640*x^2 - 540*x + 9)*y^15 + (x^22 - 52*x^21 - 830*x^20 - 4911*x^19 - 14402*x^18 - 16978*x^17 + 23244*x^16 + 116843*x^15 + 168209*x^14 + 54760*x^13 - 160556*x^12 - 300880*x^11 - 275070*x^10 + 27511*x^9 + 421861*x^8 + 218973*x^7 - 285620*x^6 - 94659*x^5 + 127998*x^4 - 35727*x^3 + 3744*x^2 - 135*x + 1)*y^14 - (2*x^24 + 4*x^23 - 201*x^22 - 1678*x^21 - 5153*x^20 - 2286*x^19 + 30394*x^18 + 93862*x^17 + 99858*x^16 - 52635*x^15 - 239341*x^14 - 232119*x^13 - 154760*x^12 - 88524*x^11 + 336924*x^10 + 631265*x^9 - 102868*x^8 - 579252*x^7 + 86958*x^6 + 208449*x^5 - 98712*x^4 + 15879*x^3 - 942*x^2 + 15*x)*y^13 + (x^26 + 9*x^25 + x^24 - 273*x^23 - 940*x^22 + 1676*x^21 + 18198*x^20 + 44652*x^19 + 19055*x^18 - 124943*x^17 - 249753*x^16 - 80190*x^15 + 175637*x^14 - 7483*x^13 - 90069*x^12 + 591217*x^11 + 552084*x^10 - 710075*x^9 - 623758*x^8 + 476949*x^7 + 181956*x^6 - 189531*x^5 + 45909*x^4 - 4053*x^3 + 105*x^2)*y^12 + (5*x^26 + 58*x^25 + 184*x^24 - 528*x^23 - 5033*x^22 - 10385*x^21 + 12863*x^20 + 97397*x^19 + 150857*x^18 - 52978*x^17 - 395659*x^16 - 187897*x^15 + 463920*x^14 + 83293*x^13 - 936271*x^12 - 94587*x^11 + 1270679*x^10 + 166028*x^9 - 853999*x^8 + 46963*x^7 + 250236*x^6 - 95225*x^5 + 12012*x^4 - 455*x^3)*y^11 + (10*x^26 + 150*x^25 + 793*x^24 + 942*x^23 - 7446*x^22 - 34067*x^21 - 41123*x^20 + 84576*x^19 + 316849*x^18 + 201524*x^17 - 504495*x^16 - 664928*x^15 + 600313*x^14 + 1055784*x^13 - 774136*x^12 - 1295686*x^11 + 657630*x^10 + 858393*x^9 - 407601*x^8 - 202581*x^7 + 144490*x^6 - 25921*x^5 + 1365*x^4)*y^10 + (10*x^26 + 200*x^25 + 1496*x^24 + 4751*x^23 + 752*x^22 - 41284*x^21 - 119305*x^20 - 63506*x^19 + 326511*x^18 + 607012*x^17 - 147317*x^16 - 1181988*x^15 - 251734*x^14 + 1479407*x^13 + 506625*x^12 - 1264086*x^11 - 362216*x^10 + 649820*x^9 + 34895*x^8 - 158755*x^7 + 41897*x^6 - 3002*x^5)*y^9 + (5*x^26 + 145*x^25 + 1513*x^24 + 7461*x^23 + 16026*x^22 - 8857*x^21 - 128248*x^20 - 243279*x^19 + 35506*x^18 + 697628*x^17 + 572017*x^16 - 797261*x^15 - 1132174*x^14 + 557900*x^13 + 1104704*x^12 - 292672*x^11 - 569317*x^10 + 152948*x^9 + 118564*x^8 - 51237*x^7 + 4995*x^6)*y^8 + (x^26 + 54*x^25 + 846*x^24 + 6052*x^23 + 22050*x^22 + 32795*x^21 - 42397*x^20 - 246663*x^19 - 277980*x^18 + 274192*x^17 + 793266*x^16 + 101911*x^15 - 902408*x^14 - 364638*x^13 + 587503*x^12 + 244454*x^11 - 231828*x^10 - 45794*x^9 + 47073*x^8 - 6390*x^7)*y^7 + (8*x^25 + 244*x^24 + 2692*x^23 + 14661*x^22 + 40925*x^21 + 38173*x^20 - 94188*x^19 - 287673*x^18 - 141458*x^17 + 383327*x^16 + 442700*x^15 - 195190*x^14 - 405842*x^13 + 41016*x^12 + 174379*x^11 - 13136*x^10 - 31497*x^9 + 6315*x^8)*y^6 + (28*x^24 + 616*x^23 + 5264*x^22 + 22568*x^21 + 47327*x^20 + 19249*x^19 - 112876*x^18 - 189768*x^17 + 6148*x^16 + 230841*x^15 + 100971*x^14 - 118207*x^13 - 68734*x^12 + 31735*x^11 + 14112*x^10 - 4795*x^9)*y^5 + (56*x^23 + 966*x^22 + 6573*x^21 + 21930*x^20 + 32604*x^19 - 3032*x^18 - 71985*x^17 - 64836*x^16 + 30764*x^15 + 62762*x^14 + 4137*x^13 - 21479*x^12 - 3087*x^11 + 2751*x^10)*y^4 + (70*x^22 + 965*x^21 + 5150*x^20 + 12875*x^19 + 12530*x^18 - 6735*x^17 - 23230*x^16 - 10635*x^15 + 8800*x^14 + 7375*x^13 - 630*x^12 - 1155*x^11)*y^3 + (55*x^21 + 590*x^20 + 2365*x^19 + 4240*x^18 + 2570*x^17 - 2075*x^16 - 3535*x^15 - 930*x^14 + 705*x^13 + 335*x^12)*y^2 + (25*x^20 + 195*x^19 + 555*x^18 + 710*x^17 + 315*x^16 - 165*x^15 - 215*x^14 - 60*x^13)*y + 5*x^14*(x+1)^5; r45:=(x^3 + x^2 + x - y)/(x^2*y + x*y + x - y); s45:=(x^2 + x - y)/(x*y + x - y); X46:=y^21 - (7*x^2 - x + 10)*y^20 + (21*x^4 + 4*x^3 + 75*x^2 - 16*x + 45)*y^19 - (35*x^6 + 7*x^5 + 154*x^4 - 49*x^3 + 366*x^2 - 99*x + 120)*y^18 + (35*x^8 - 28*x^7 + 45*x^6 - 369*x^5 + 227*x^4 - 716*x^3 + 1094*x^2 - 336*x + 210)*y^17 - (21*x^10 - 91*x^9 - 252*x^8 - 1055*x^7 - 1320*x^6 - 3155*x^5 - 1032*x^4 - 3619*x^3 + 2265*x^2 - 714*x + 252)*y^16 + (7*x^12 - 112*x^11 - 392*x^10 - 1324*x^9 - 2491*x^8 - 4946*x^7 - 5562*x^6 - 10094*x^5 - 4656*x^4 - 10513*x^3 + 3451*x^2 - 1008*x + 210)*y^15 - (x^14 - 71*x^13 - 213*x^12 - 608*x^11 - 990*x^10 - 1626*x^9 - 2298*x^8 - 4846*x^7 - 4903*x^6 - 14459*x^5 - 6802*x^4 - 20378*x^3 + 3955*x^2 - 966*x + 120)*y^14 - (23*x^15 - 9*x^14 - 266*x^13 - 1571*x^12 - 4729*x^11 - 9718*x^10 - 15567*x^9 - 18698*x^8 - 17363*x^7 - 16269*x^6 + 2449*x^5 - 592*x^4 + 28304*x^3 - 3381*x^2 + 624*x - 45)*y^13 + (3*x^17 - 60*x^16 - 406*x^15 - 1981*x^14 - 6344*x^13 - 15567*x^12 - 30350*x^11 - 46045*x^10 - 58768*x^9 - 59791*x^8 - 54666*x^7 - 50103*x^6 - 24919*x^5 - 18867*x^4 + 29301*x^3 - 2084*x^2 + 261*x - 10)*y^12 + (24*x^18 + 140*x^17 + 750*x^16 + 2695*x^15 + 8054*x^14 + 19286*x^13 + 37983*x^12 + 62673*x^11 + 81919*x^10 + 89590*x^9 + 75542*x^8 + 61196*x^7 + 57878*x^6 + 43594*x^5 + 36732*x^4 - 23115*x^3 + 870*x^2 - 64*x + 1)*y^11 - (3*x^20 + x^18 - 41*x^17 + 119*x^16 + 929*x^15 + 4418*x^14 + 13740*x^13 + 31953*x^12 + 58336*x^11 + 77080*x^10 + 77169*x^9 + 46490*x^8 + 21740*x^7 + 23363*x^6 + 35531*x^5 + 41510*x^4 - 14065*x^3 + 219*x^2 - 7*x)*y^10 - (8*x^21 + 58*x^20 + 307*x^19 + 1117*x^18 + 3393*x^17 + 8217*x^16 + 16525*x^15 + 25986*x^14 + 29853*x^13 + 18356*x^12 - 12506*x^11 - 44350*x^10 - 53717*x^9 - 19910*x^8 + 15924*x^7 + 19361*x^6 - 11449*x^5 - 32393*x^4 + 6643*x^3 - 25*x^2)*y^9 + (x^23 + 9*x^22 + 59*x^21 + 269*x^20 + 1032*x^19 + 3254*x^18 + 8875*x^17 + 20432*x^16 + 39987*x^15 + 64553*x^14 + 83389*x^13 + 79390*x^12 + 42494*x^11 - 10409*x^10 - 43755*x^9 - 25009*x^8 + 15564*x^7 + 34070*x^6 + 6609*x^5 - 18437*x^4 + 2435*x^3)*y^8 - (x^23 + 9*x^22 + 58*x^21 + 269*x^20 + 1051*x^19 + 3401*x^18 + 9457*x^17 + 22274*x^16 + 44670*x^15 + 74777*x^14 + 102266*x^13 + 108276*x^12 + 78158*x^11 + 20626*x^10 - 29310*x^9 - 34102*x^8 - 3797*x^7 + 22982*x^6 + 10573*x^5 - 7765*x^4 + 680*x^3)*y^7 + (7*x^21 + 62*x^20 + 353*x^19 + 1434*x^18 + 4672*x^17 + 12403*x^16 + 27417*x^15 + 50118*x^14 + 74919*x^13 + 88319*x^12 + 76126*x^11 + 37279*x^10 - 6529*x^9 - 25233*x^8 - 13004*x^7 + 8024*x^6 + 6741*x^5 - 2384*x^4 + 136*x^3)*y^6 - (x^20 + 28*x^19 + 208*x^18 + 991*x^17 + 3410*x^16 + 9151*x^15 + 19578*x^14 + 33603*x^13 + 45441*x^12 + 46310*x^11 + 31075*x^10 + 7123*x^9 - 9589*x^8 - 9343*x^7 + 734*x^6 + 2625*x^5 - 506*x^4 + 17*x^3)*y^5 + (5*x^18 + 65*x^17 + 385*x^16 + 1480*x^15 + 4140*x^14 + 8790*x^13 + 14330*x^12 + 17608*x^11 + 15073*x^10 + 7172*x^9 - 1008*x^8 - 3492*x^7 - 606*x^6 + 647*x^5 - 66*x^4 + x^3)*y^4 - (10*x^16 + 85*x^15 + 395*x^14 + 1186*x^13 + 2549*x^12 + 3974*x^11 + 4334*x^10 + 2997*x^9 + 653*x^8 - 684*x^7 - 287*x^6 + 93*x^5 - 4*x^4)*y^3 + (10*x^14 + 61*x^13 + 214*x^12 + 473*x^11 + 694*x^10 + 661*x^9 + 295*x^8 - 42*x^7 - 54*x^6 + 6*x^5)*y^2 - (5*x^12 + 22*x^11 + 52*x^10 + 73*x^9 + 49*x^8 + 7*x^7 - 4*x^6)*y + x^7*(x+1)^3; r46:=1+x*(y-1)*(x+y)/((x+1)*(x^2-x*y+2*x-y^2+y)); s46:=1+(x*y-x)/(x^2-x*y+2*x-y+1); X47:=y^29 + (x^20 + 2*x^19 - 16*x^18 - 31*x^17 + 109*x^16 + 201*x^15 - 413*x^14 - 706*x^13 + 954*x^12 + 1454*x^11 - 1382*x^10 - 1774*x^9 + 1238*x^8 + 1234*x^7 - 642*x^6 - 443*x^5 + 170*x^4 + 75*x^3 - 5*x^2 + 20*x - 9)*y^28 - (34*x^20 + 120*x^19 - 373*x^18 - 1609*x^17 + 1490*x^16 + 8904*x^15 - 2345*x^14 - 26433*x^13 - 139*x^12 + 45680*x^11 + 4642*x^10 - 46600*x^9 - 4798*x^8 + 26936*x^7 + 1242*x^6 - 8105*x^5 + 30*x^4 + 800*x^3 - 230*x^2 + 175*x - 36)*y^27 + (561*x^20 + 2890*x^19 - 1700*x^18 - 29304*x^17 - 18029*x^16 + 120731*x^15 + 122955*x^14 - 263150*x^13 - 311809*x^12 + 337506*x^11 + 398508*x^10 - 269280*x^9 - 262800*x^8 + 137614*x^7 + 84114*x^6 - 38076*x^5 - 8420*x^4 + 4855*x^3 - 1755*x^2 + 680*x - 84)*y^26 + (x^33 + 8*x^32 + 7*x^31 - 100*x^30 - 229*x^29 + 544*x^28 + 1964*x^27 - 1436*x^26 - 9277*x^25 + 996*x^24 + 28840*x^23 + 6272*x^22 - 62079*x^21 - 29016*x^20 + 58023*x^19 - 2907*x^18 + 124065*x^17 + 493374*x^16 - 381735*x^15 - 1853396*x^14 + 181025*x^13 + 3252303*x^12 + 368534*x^11 - 3144155*x^10 - 384284*x^9 + 1740017*x^8 + 56758*x^7 - 494540*x^6 + 49262*x^5 + 53080*x^4 - 19345*x^3 + 6370*x^2 - 1540*x + 126)*y^25 - (18*x^33 + 170*x^32 + 332*x^31 - 1605*x^30 - 6583*x^29 + 3598*x^28 + 46016*x^27 + 21943*x^26 - 179017*x^25 - 177383*x^24 + 453661*x^23 + 623426*x^22 - 759740*x^21 - 1314048*x^20 + 638666*x^19 + 962987*x^18 - 535332*x^17 + 2738206*x^16 + 3653557*x^15 - 8266652*x^14 - 10399141*x^13 + 10062859*x^12 + 13020995*x^11 - 7584814*x^10 - 8176098*x^9 + 3933917*x^8 + 2348216*x^7 - 1225686*x^6 - 167506*x^5 + 174380*x^4 - 51390*x^3 + 13720*x^2 - 2240*x + 126)*y^24 + (153*x^33 + 1692*x^32 + 5149*x^31 - 8729*x^30 - 74877*x^29 - 57432*x^28 + 395204*x^27 + 699909*x^26 - 1051488*x^25 - 3091671*x^24 + 1381869*x^23 + 8197380*x^22 + 429766*x^21 - 13354710*x^20 - 3894409*x^19 + 10558469*x^18 - 2797626*x^17 - 1492772*x^16 + 30164832*x^15 + 3697269*x^14 - 55621203*x^13 - 12887494*x^12 + 52185735*x^11 + 10085449*x^10 - 28170253*x^9 - 1293642*x^8 + 8035564*x^7 - 1120798*x^6 - 866652*x^5 + 370960*x^4 - 92530*x^3 + 19110*x^2 - 2170*x + 84)*y^23 - (816*x^33 + 10506*x^32 + 43890*x^31 + 7239*x^30 - 447710*x^29 - 945343*x^28 + 1310474*x^27 + 6175108*x^26 + 514616*x^25 - 20200575*x^24 - 14002295*x^23 + 39876566*x^22 + 44644250*x^21 - 45467715*x^20 - 63509880*x^19 + 34106967*x^18 + 20084148*x^17 - 61077675*x^16 + 52960253*x^15 + 130601715*x^14 - 78667302*x^13 - 148906442*x^12 + 61492825*x^11 + 88409726*x^10 - 35497420*x^9 - 24306988*x^8 + 12519868*x^7 + 1467064*x^6 - 1902984*x^5 + 547680*x^4 - 114530*x^3 + 17780*x^2 - 1400*x + 36)*y^22 + (3060*x^33 + 45696*x^32 + 246126*x^31 + 391761*x^30 - 1354130*x^29 - 5991510*x^28 - 2027059*x^27 + 25844164*x^26 + 34783802*x^25 - 53928620*x^24 - 130828430*x^23 + 43356206*x^22 + 256147579*x^21 + 30634017*x^20 - 274386255*x^19 - 25397910*x^18 + 184576623*x^17 - 169576023*x^16 - 160436352*x^15 + 352102965*x^14 + 178791715*x^13 - 330211127*x^12 - 110045780*x^11 + 180073297*x^10 + 18622800*x^9 - 53160580*x^8 + 7103914*x^7 + 5944862*x^6 - 2607006*x^5 + 574185*x^4 - 97680*x^3 + 11030*x^2 - 580*x + 9)*y^21 + (x^39 + 18*x^38 + 141*x^37 + 627*x^36 + 1773*x^35 + 3798*x^34 + 767*x^33 - 117783*x^32 - 900198*x^31 - 2597365*x^30 + 398403*x^29 + 20131814*x^28 + 34433528*x^27 - 43792905*x^26 - 179580828*x^25 - 30900999*x^24 + 433466382*x^23 + 332274768*x^22 - 563960206*x^21 - 635766129*x^20 + 470228301*x^19 + 500571610*x^18 - 518159943*x^17 - 93808152*x^16 + 769825414*x^15 - 124360380*x^14 - 771985981*x^13 + 155730802*x^12 + 438073899*x^11 - 124451984*x^10 - 120911361*x^9 + 53349258*x^8 + 8137647*x^7 - 8963941*x^6 + 2434257*x^5 - 426855*x^4 + 56495*x^3 - 4395*x^2 + 140*x - 1)*y^20 - (7*x^39 + 140*x^38 + 1216*x^37 + 5976*x^36 + 18388*x^35 + 40241*x^34 + 74534*x^33 - 53712*x^32 - 1911351*x^31 - 9023077*x^30 - 13167284*x^29 + 31183505*x^28 + 134631973*x^27 + 66902668*x^26 - 405667591*x^25 - 599593803*x^24 + 492735542*x^23 + 1474821901*x^22 - 65053131*x^21 - 1858033572*x^20 - 209395938*x^19 + 1539667341*x^18 - 317829949*x^17 - 1240581905*x^16 + 931818254*x^15 + 1017980250*x^14 - 931472283*x^13 - 551750250*x^12 + 535143913*x^11 + 117017120*x^10 - 168781392*x^9 + 14789203*x^8 + 20647124*x^7 - 8188054*x^6 + 1585920*x^5 - 220080*x^4 + 21190*x^3 - 1020*x^2 + 15*x)*y^19 + (21*x^39 + 476*x^38 + 4658*x^37 + 25656*x^36 + 87259*x^35 + 199005*x^34 + 391022*x^33 + 714786*x^32 - 1232050*x^31 - 17351161*x^30 - 53360378*x^29 - 21391099*x^28 + 247840612*x^27 + 494113891*x^26 - 221275964*x^25 - 1607756760*x^24 - 812956762*x^23 - 1882836028*x^22 - 1994839974*x^21 + 2123478925*x^20 + 1812974871*x^19 + 1957401131*x^18 + 1459413542*x^17 + 2066436539*x^16 - 566587990*x^15 + 1998173022*x^14 + 67661984*x^13 - 1103537017*x^12 + 153721723*x^11 + 315400030*x^10 - 104182338*x^9 - 27000371*x^8 + 20750397*x^7 - 4937905*x^6 + 713496*x^5 - 74830*x^4 + 4655*x^3 - 105*x^2)*y^18 - (35*x^39 + 924*x^38 + 10402*x^37 + 65348*x^36 + 250329*x^35 + 611830*x^34 + 1136878*x^33 + 2576958*x^32 + 4708001*x^31 - 12146783*x^30 - 99532365*x^29 - 198113574*x^28 + 107973568*x^27 + 1008478704*x^26 + 977935658*x^25 - 1647939865*x^24 + 868219870*x^23 + 710427569*x^22 + 768504331*x^21 + 571720143*x^20 - 394510599*x^19 - 189015969*x^18 - 596759227*x^17 - 882051495*x^16 + 1631742366*x^15 + 1165547490*x^14 + 1355818394*x^13 - 769620181*x^12 - 332429094*x^11 + 272180771*x^10 - 748635*x^9 - 38141379*x^8 + 12401191*x^7 - 1982946*x^6 + 212058*x^5 - 15085*x^4 + 455*x^3)*y^17 + (35*x^39 + 1120*x^38 + 14924*x^37 + 109382*x^36 + 482779*x^35 + 1311035*x^34 + 2308840*x^33 + 4430482*x^32 + 14081246*x^31 + 21972271*x^30 - 71219325*x^29 - 377495790*x^28 - 454267996*x^27 + 755591593*x^26 - 1844086535*x^25 + 654990465*x^24 - 132717839*x^23 + 566298163*x^22 - 10945631*x^21 + 829410577*x^20 + 885424301*x^19 + 336837526*x^18 - 1107208122*x^17 - 2099321819*x^16 + 1657867228*x^15 - 822304645*x^14 + 1451458885*x^13 + 48832938*x^12 - 438496607*x^11 + 89078906*x^10 + 47470330*x^9 - 24422080*x^8 + 4662187*x^7 - 510811*x^6 + 37548*x^5 - 1365*x^4)*y^16 - (21*x^39 + 868*x^38 + 14266*x^37 + 125748*x^36 + 657643*x^35 + 2071486*x^34 + 3744987*x^33 + 4553548*x^32 + 15133178*x^31 + 59829034*x^30 + 65820156*x^29 - 275443028*x^28 - 962883752*x^27 - 550225967*x^26 - 2077445872*x^25 - 672263594*x^24 - 1419379596*x^23 + 2129131758*x^22 - 800472539*x^21 - 2048836710*x^20 + 1321105989*x^19 - 818045383*x^18 - 315419954*x^17 - 860915369*x^16 - 424834121*x^15 - 1694710297*x^14 + 488745341*x^13 + 457332234*x^12 - 219327590*x^11 - 30030477*x^10 + 36980030*x^9 - 9046405*x^8 + 1068270*x^7 - 76286*x^6 + 3003*x^5)*y^15 + (7*x^39 + 420*x^38 + 9086*x^37 + 100576*x^36 + 645939*x^35 + 2476082*x^34 + 5261472*x^33 + 4424391*x^32 + 2939364*x^31 + 48825182*x^30 + 179330832*x^29 + 109618462*x^28 - 727046824*x^27 - 1646317176*x^26 + 4064254*x^25 - 457395732*x^24 - 1341121597*x^23 + 246777953*x^22 - 845373846*x^21 - 1425255316*x^20 + 330340987*x^19 + 2101296078*x^18 + 1432675720*x^17 + 1710222012*x^16 + 1236231490*x^15 - 970656339*x^14 - 258106814*x^13 + 317421918*x^12 - 19131423*x^11 - 41925479*x^10 + 14215970*x^9 - 1924545*x^8 + 132725*x^7 - 5005*x^6)*y^14 - (x^39 + 115*x^38 + 3686*x^37 + 54770*x^36 + 452201*x^35 + 2206063*x^34 + 6115888*x^33 + 6976542*x^32 - 6333558*x^31 - 4639098*x^30 + 130401448*x^29 + 365565935*x^28 + 48499426*x^27 - 1318245146*x^26 - 1825078774*x^25 + 1155042483*x^24 - 173698121*x^23 + 606711958*x^22 - 261880976*x^21 - 1597387097*x^20 - 772725068*x^19 + 1105070761*x^18 + 2054479708*x^17 - 329999100*x^16 + 1083076351*x^15 - 56751026*x^14 - 312234307*x^13 + 77744324*x^12 + 33300075*x^11 - 17870499*x^10 + 2930975*x^9 - 203490*x^8 + 6435*x^7)*y^13 + (13*x^38 + 839*x^37 + 18961*x^36 + 215315*x^35 + 1395900*x^34 + 5262016*x^33 + 9958470*x^32 - 194150*x^31 - 34922822*x^30 - 4749515*x^29 + 256689323*x^28 + 499272886*x^27 - 183931781*x^26 - 1629685712*x^25 - 1174752330*x^24 + 1936470134*x^23 - 1653063280*x^22 - 1191992315*x^21 + 1626424478*x^20 + 640551290*x^19 + 1741052851*x^18 - 460245180*x^17 - 789331499*x^16 + 293986960*x^15 + 205669315*x^14 - 111131258*x^13 - 14128023*x^12 + 17761653*x^11 - 3710408*x^10 + 276055*x^9 - 6435*x^8)*y^12 - (78*x^37 + 3646*x^36 + 64404*x^35 + 589355*x^34 + 3084680*x^33 + 8994015*x^32 + 9967768*x^31 - 19577636*x^30 - 66966465*x^29 + 21425205*x^28 + 355938897*x^27 + 442714740*x^26 - 438130528*x^25 - 1343062555*x^24 - 236022540*x^23 + 1641013601*x^22 + 829834207*x^21 - 1235670813*x^20 - 722149875*x^19 + 728700745*x^18 + 333136464*x^17 - 341121194*x^16 - 70036780*x^15 + 102906735*x^14 - 4995865*x^13 - 13687401*x^12 + 3859128*x^11 - 326690*x^10 + 5005*x^9)*y^11 + (286*x^36 + 10615*x^35 + 153857*x^34 + 1166706*x^33 + 4996942*x^32 + 11104730*x^31 + 3890846*x^30 - 40732784*x^29 - 74848309*x^28 + 62847140*x^27 + 341348759*x^26 + 230676850*x^25 - 479840644*x^24 - 701471796*x^23 + 244294614*x^22 + 787361776*x^21 - 28175396*x^20 - 524961448*x^19 + 1107149*x^18 + 238399996*x^17 - 21003901*x^16 - 66755858*x^15 + 14924690*x^14 + 7820260*x^13 - 3269175*x^12 + 330603*x^11 - 3003*x^10)*y^10 - (715*x^35 + 21989*x^34 + 268015*x^33 + 1707517*x^32 + 6003152*x^31 + 9807943*x^30 - 4612178*x^29 - 47158326*x^28 - 51692809*x^27 + 81268412*x^26 + 221726687*x^25 + 42243192*x^24 - 307303272*x^23 - 204844499*x^22 + 218887303*x^21 + 201906841*x^20 - 109782311*x^19 - 103843896*x^18 + 46781842*x^17 + 29103568*x^16 - 14584548*x^15 - 2890975*x^14 + 2234645*x^13 - 281190*x^12 + 1365*x^11)*y^9 + (1287*x^34 + 33495*x^33 + 347292*x^32 + 1867395*x^31 + 5358797*x^30 + 5973705*x^29 - 9196637*x^28 - 35433633*x^27 - 20292369*x^26 + 61990159*x^25 + 93767536*x^24 - 25178067*x^23 - 118156487*x^22 - 18848216*x^21 + 77831955*x^20 + 20072051*x^19 - 33279843*x^18 - 6300189*x^17 + 9140510*x^16 + 227571*x^15 - 1214910*x^14 + 198415*x^13 - 455*x^12)*y^8 - (1716*x^33 + 38148*x^32 + 337557*x^31 + 1528250*x^30 + 3528670*x^29 + 2262086*x^28 - 7929558*x^27 - 17763697*x^26 - 2394521*x^25 + 29527670*x^24 + 23832819*x^23 - 19088475*x^22 - 26177764*x^21 + 5994786*x^20 + 13715220*x^19 - 1522177*x^18 - 3946982*x^17 + 536357*x^16 + 511486*x^15 - 114930*x^14 + 105*x^13)*y^7 + (1716*x^32 + 32637*x^31 + 245718*x^30 + 928930*x^29 + 1684600*x^28 + 329139*x^27 - 4168813*x^26 - 5837646*x^25 + 1580425*x^24 + 8717835*x^23 + 2997354*x^22 - 5400258*x^21 - 3031812*x^20 + 1880935*x^19 + 1108525*x^18 - 427814*x^17 - 157443*x^16 + 54047*x^15 - 15*x^14)*y^6 - (1287*x^31 + 20845*x^30 + 132396*x^29 + 412148*x^28 + 566281*x^27 - 132807*x^26 - 1400437*x^25 - 1195639*x^24 + 815982*x^23 + 1532268*x^22 + 46691*x^21 - 754551*x^20 - 142625*x^19 + 184765*x^18 + 30045*x^17 - 20333*x^16 + x^15)*y^5 + (715*x^30 + 9757*x^29 + 51545*x^28 + 129581*x^27 + 128426*x^26 - 83606*x^25 - 294603*x^24 - 141433*x^23 + 161386*x^22 + 152519*x^21 - 24892*x^20 - 50540*x^19 - 665*x^18 + 5985*x^17)*y^4 - (286*x^29 + 3230*x^28 + 13906*x^27 + 27575*x^26 + 18696*x^25 - 18977*x^24 - 36784*x^23 - 9397*x^22 + 14775*x^21 + 8141*x^20 - 1610*x^19 - 1330*x^18)*y^3 + (78*x^28 + 709*x^27 + 2421*x^26 + 3710*x^25 + 1730*x^24 - 1941*x^23 - 2531*x^22 - 464*x^21 + 525*x^20 + 210*x^19)*y^2 - (13*x^27 + 91*x^26 + 239*x^25 + 285*x^24 + 115*x^23 - 67*x^22 - 79*x^21 - 21*x^20)*y + x^21*(x+1)^5; r47:=1-x*y-y; s47:=(x*y+2*y-1)/(y-1); X48:=y^19 + (2*x^3 + 10*x^2 + 13*x - 6)*y^18 + (x^6 + 18*x^5 + 73*x^4 + 108*x^3 + 14*x^2 - 78*x + 15)*y^17 + (8*x^8 + 91*x^7 + 344*x^6 + 535*x^5 + 170*x^4 - 432*x^3 - 278*x^2 + 195*x - 20)*y^16 + (33*x^10 + 302*x^9 + 1081*x^8 + 1710*x^7 + 552*x^6 - 1718*x^5 - 1758*x^4 + 374*x^3 + 815*x^2 - 260*x + 15)*y^15 + (x^13 + 83*x^12 + 673*x^11 + 2296*x^10 + 3522*x^9 + 571*x^8 - 5445*x^7 - 5785*x^6 + 702*x^5 + 3674*x^4 + 558*x^3 - 1089*x^2 + 195*x - 6)*y^14 + (4*x^15 + 131*x^14 + 984*x^13 + 3232*x^12 + 4482*x^11 - 1486*x^10 - 12802*x^9 - 12243*x^8 + 4244*x^7 + 11697*x^6 + 2272*x^5 - 3515*x^4 - 1042*x^3 + 709*x^2 - 78*x + 1)*y^13 + (6*x^17 + 126*x^16 + 895*x^15 + 2834*x^14 + 3028*x^13 - 5904*x^12 - 20831*x^11 - 16015*x^10 + 16718*x^9 + 30379*x^8 + 1525*x^7 - 15544*x^6 - 2151*x^5 + 3090*x^4 - 46*x^3 - 139*x^2 + 13*x)*y^12 + (4*x^19 + 67*x^18 + 454*x^17 + 1336*x^16 + 334*x^15 - 8547*x^14 - 21528*x^13 - 10336*x^12 + 36680*x^11 + 55386*x^10 - 5016*x^9 - 52468*x^8 - 10832*x^7 + 22863*x^6 + 1694*x^5 - 5017*x^4 + 1242*x^3 - 87*x^2)*y^11 + (x^21 + 15*x^20 + 95*x^19 + 196*x^18 - 846*x^17 - 5924*x^16 - 12070*x^15 + 1493*x^14 + 46204*x^13 + 62728*x^12 - 18854*x^11 - 103720*x^10 - 39124*x^9 + 66312*x^8 + 33548*x^7 - 26281*x^6 - 6567*x^5 + 6314*x^4 - 1144*x^3 + 55*x^2)*y^10 - (2*x^21 + 43*x^20 + 382*x^19 + 1590*x^18 + 2146*x^17 - 6835*x^16 - 31406*x^15 - 37137*x^14 + 32882*x^13 + 121096*x^12 + 61248*x^11 - 102771*x^10 - 102888*x^9 + 38595*x^8 + 54096*x^7 - 13695*x^6 - 10714*x^5 + 4378*x^4 - 462*x^3 + 11*x^2)*y^9 + (x^21 + 40*x^20 + 529*x^19 + 3137*x^18 + 8696*x^17 + 5603*x^16 - 30340*x^15 - 78535*x^14 - 38831*x^13 + 102621*x^12 + 139887*x^11 - 20616*x^10 - 114258*x^9 - 15319*x^8 + 43623*x^7 + 2592*x^6 - 8056*x^5 + 1636*x^4 - 90*x^3 + x^2)*y^8 - (13*x^20 + 328*x^19 + 2845*x^18 + 11506*x^17 + 20870*x^16 - 290*x^15 - 67125*x^14 - 94260*x^13 + 10339*x^12 + 121140*x^11 + 57175*x^10 - 56918*x^9 - 37127*x^8 + 15742*x^7 + 6809*x^6 - 3124*x^5 + 317*x^4 - 8*x^3)*y^7 + (x^20 + 97*x^19 + 1362*x^18 + 7803*x^17 + 21545*x^16 + 23571*x^15 - 18336*x^14 - 74031*x^13 - 49070*x^12 + 41384*x^11 + 57773*x^10 - 3486*x^9 - 21799*x^8 + 129*x^7 + 3340*x^6 - 623*x^5 + 28*x^4)*y^6 - (14*x^19 + 364*x^18 + 3036*x^17 + 11676*x^16 + 21520*x^15 + 10956*x^14 - 24852*x^13 - 39513*x^12 - 5564*x^11 + 22367*x^10 + 8976*x^9 - 5211*x^8 - 1700*x^7 + 735*x^6 - 56*x^5)*y^5 + (x^19 + 55*x^18 + 707*x^17 + 3753*x^16 + 9692*x^15 + 11218*x^14 - 106*x^13 - 13103*x^12 - 9145*x^11 + 2670*x^10 + 3907*x^9 - 118*x^8 - 511*x^7 + 70*x^6)*y^4 - (4*x^18 + 96*x^17 + 737*x^16 + 2564*x^15 + 4342*x^14 + 2772*x^13 - 1500*x^12 - 2900*x^11 - 678*x^10 + 604*x^9 + 175*x^8 - 56*x^7)*y^3 + (6*x^17 + 83*x^16 + 405*x^15 + 921*x^14 + 981*x^13 + 267*x^12 - 347*x^11 - 251*x^10 + 3*x^9 + 28*x^8)*y^2 - (4*x^16 + 34*x^15 + 106*x^14 + 156*x^13 + 104*x^12 + 10*x^11 - 22*x^10 - 8*x^9)*y + x^10*(x+1)^5; r48:=(-x^3 - x^2 - x - y)/(x^2*y + x*y - x - y); s48:=(-x^2 - x - y)/(x*y - x - y); X49:=y^31 + (x^21 + 2*x^20 - 17*x^19 - 33*x^18 + 124*x^17 + 230*x^16 - 508*x^15 - 880*x^14 + 1285*x^13 + 2011*x^12 - 2075*x^11 - 2797*x^10 + 2129*x^9 + 2311*x^8 - 1327*x^7 - 1057*x^6 + 455*x^5 + 238*x^4 - 63*x^3 - 7*x^2 + 28*x - 10)*y^30 - (38*x^21 + 134*x^20 - 453*x^19 - 1923*x^18 + 2031*x^17 + 11523*x^16 - 3928*x^15 - 37570*x^14 + 1530*x^13 + 72677*x^12 + 5849*x^11 - 85236*x^10 - 8769*x^9 + 59166*x^8 + 3825*x^7 - 22708*x^6 - 133*x^5 + 3927*x^4 - 483*x^3 - 441*x^2 + 273*x - 45)*y^29 + (703*x^21 + 3610*x^20 - 2811*x^19 - 39923*x^18 - 20757*x^17 + 181596*x^16 + 173184*x^15 - 443480*x^14 - 506505*x^13 + 645091*x^12 + 756763*x^11 - 590316*x^10 - 608708*x^9 + 349851*x^8 + 253065*x^7 - 124180*x^6 - 43064*x^5 + 24444*x^4 + 1687*x^3 - 3843*x^2 + 1197*x - 120)*y^28 + (x^35 + 8*x^34 + 5*x^33 - 116*x^32 - 244*x^31 + 736*x^30 + 2413*x^29 - 2440*x^28 - 12995*x^27 + 3484*x^26 + 45839*x^25 + 5016*x^24 - 113405*x^23 - 35356*x^22 + 197559*x^21 + 29850*x^20 - 334343*x^19 + 257721*x^18 + 1098022*x^17 - 816556*x^16 - 3460506*x^15 + 720544*x^14 + 6552150*x^13 + 346166*x^12 - 7263814*x^11 - 804166*x^10 + 4772747*x^9 + 252793*x^8 - 1742164*x^7 + 120113*x^6 + 308791*x^5 - 63735*x^4 - 27384*x^3 + 15918*x^2 - 3108*x + 210)*y^27 - (21*x^35 + 198*x^34 + 347*x^33 - 2233*x^32 - 8373*x^31 + 7486*x^30 + 67153*x^29 + 18672*x^28 - 301069*x^27 - 253315*x^26 + 877446*x^25 + 1077206*x^24 - 1751941*x^23 - 2685327*x^22 + 2516207*x^21 + 4057190*x^20 - 4127109*x^19 - 4460302*x^18 + 10658231*x^17 + 9000570*x^16 - 21830632*x^15 - 22120246*x^14 + 27269661*x^13 + 31279267*x^12 - 22203602*x^11 - 23719278*x^10 + 12706779*x^9 + 8981523*x^8 - 4880685*x^7 - 1303855*x^6 + 1007657*x^5 - 2646*x^4 - 122535*x^3 + 39606*x^2 - 5292*x + 252)*y^26 + (210*x^35 + 2310*x^34 + 6622*x^33 - 15926*x^32 - 113481*x^31 - 57266*x^30 + 704798*x^29 + 1074474*x^28 - 2297205*x^27 - 5722010*x^26 + 4098168*x^25 + 17630634*x^24 - 2422490*x^23 - 35159190*x^22 - 3865708*x^21 + 48973756*x^20 + 1529997*x^19 - 65916733*x^18 + 15646180*x^17 + 112966125*x^16 - 13435631*x^15 - 166273376*x^14 - 15793428*x^13 + 162282827*x^12 + 24441407*x^11 - 99468072*x^10 - 6016212*x^9 + 35780868*x^8 - 3598089*x^7 - 6273085*x^6 + 1637461*x^5 + 454146*x^4 - 306355*x^3 + 64974*x^2 - 6174*x + 210)*y^25 - (1330*x^35 + 16940*x^34 + 67760*x^33 - 18183*x^32 - 826147*x^31 - 1499219*x^30 + 3236092*x^29 + 12071997*x^28 - 2532751*x^27 - 46798910*x^26 - 23136173*x^25 + 109962161*x^24 + 100405816*x^23 - 168069341*x^22 - 197195890*x^21 + 202437511*x^20 + 238381657*x^19 - 283570108*x^18 - 284688459*x^17 + 397449821*x^16 + 418632309*x^15 - 395564529*x^14 - 478904629*x^13 + 277360643*x^12 + 327635037*x^11 - 155277206*x^10 - 117179276*x^9 + 63252399*x^8 + 15546909*x^7 - 13454889*x^6 + 526477*x^5 + 1444198*x^4 - 494557*x^3 + 73206*x^2 - 4998*x + 120)*y^24 + (5985*x^35 + 87780*x^34 + 454685*x^33 + 575036*x^32 - 3312243*x^31 - 12200521*x^30 + 589319*x^29 + 64871562*x^28 + 68522776*x^27 - 170722310*x^26 - 330402282*x^25 + 226431072*x^24 + 799256751*x^23 - 100370724*x^22 - 1207575278*x^21 - 24634823*x^20 + 1441087494*x^19 - 36092388*x^18 - 1715397750*x^17 - 39497748*x^16 + 1859428628*x^15 + 305607287*x^14 - 1514443149*x^13 - 311249930*x^12 + 857008780*x^11 + 80332809*x^10 - 305045797*x^9 + 29556434*x^8 + 53460201*x^7 - 14800583*x^6 - 3394265*x^5 + 2482431*x^4 - 543837*x^3 + 57288*x^2 - 2772*x + 45)*y^23 + (x^42 + 18*x^41 + 138*x^40 + 573*x^39 + 1350*x^38 + 1917*x^37 + 4015*x^36 - 1440*x^35 - 278433*x^34 - 2055530*x^33 - 5322778*x^32 + 4500345*x^31 + 53458218*x^30 + 71635901*x^29 - 164775369*x^28 - 494274855*x^27 + 82761169*x^26 + 1471312242*x^25 + 751891654*x^24 - 2517906087*x^23 - 2190042471*x^22 + 3009153822*x^21 + 3161063434*x^20 - 3285389595*x^19 - 3556906704*x^18 + 3367748871*x^17 + 3870532170*x^16 - 2630858542*x^15 - 3497604601*x^14 + 1554052083*x^13 + 2132403820*x^12 - 834486245*x^11 - 735974517*x^10 + 358452573*x^9 + 97898132*x^8 - 79367121*x^7 + 3405941*x^6 + 8098258*x^5 - 2760030*x^4 + 413714*x^3 - 30723*x^2 + 1008*x - 10)*y^22 - (9*x^42 + 178*x^41 + 1505*x^40 + 6938*x^39 + 18212*x^38 + 26629*x^37 + 40111*x^36 + 153701*x^35 - 153668*x^34 - 5652377*x^33 - 24663698*x^32 - 25606404*x^31 + 123634317*x^30 + 399274125*x^29 + 30715624*x^28 - 1543602669*x^27 - 1699962476*x^26 + 2730360166*x^25 + 5611209206*x^24 - 2208384444*x^23 - 9676230639*x^22 + 505875949*x^21 + 11733920279*x^20 + 547022334*x^19 - 12024390455*x^18 - 1502408832*x^17 + 10447856517*x^16 + 2435855261*x^15 - 7125437819*x^14 - 1924570554*x^13 + 3676589255*x^12 + 557790417*x^11 - 1291199284*x^10 + 80739781*x^9 + 230783742*x^8 - 58891505*x^7 - 14543970*x^6 + 9854607*x^5 - 2078524*x^4 + 215180*x^3 - 10801*x^2 + 217*x - 1)*y^21 + (36*x^42 + 792*x^41 + 7461*x^40 + 38540*x^39 + 114182*x^38 + 180888*x^37 + 180842*x^36 + 790109*x^35 + 2771178*x^34 - 5115880*x^33 - 65636788*x^32 - 170488698*x^31 + 36954675*x^30 + 1052346567*x^29 + 1563518598*x^28 - 1870253387*x^27 - 6822355001*x^26 - 1098992688*x^25 + 13672373130*x^24 + 9004645854*x^23 - 17173656876*x^22 - 16313102881*x^21 + 16904836322*x^20 + 19136828676*x^19 - 14075954450*x^18 - 18062856581*x^17 + 8928203571*x^16 + 13604153937*x^15 - 4366062543*x^14 - 7419046128*x^13 + 2186475798*x^12 + 2496262377*x^11 - 1001297166*x^10 - 355888799*x^9 + 235908178*x^8 - 3797091*x^7 - 24432240*x^6 + 7604814*x^5 - 1059114*x^4 + 73248*x^3 - 2247*x^2 + 21*x)*y^20 - (84*x^42 + 2088*x^41 + 22194*x^40 + 129870*x^39 + 440110*x^38 + 792756*x^37 + 554067*x^36 + 1437235*x^35 + 12041877*x^34 + 24269057*x^33 - 75838370*x^32 - 470623191*x^31 - 684901745*x^30 + 1120243062*x^29 + 4848050052*x^28 + 2604831631*x^27 - 11258379022*x^26 - 16019700579*x^25 + 11736190467*x^24 + 33135077142*x^23 - 4215407553*x^22 - 42554626211*x^21 - 3800064941*x^20 + 41105552178*x^19 + 8543008503*x^18 - 31152232423*x^17 - 9547766679*x^16 + 18330706851*x^15 + 6379033590*x^14 - 8557534665*x^13 - 2018567266*x^12 + 2947598715*x^11 + 461748*x^10 - 545993138*x^9 + 111133652*x^8 + 37915065*x^7 - 20639080*x^6 + 3864336*x^5 - 351120*x^4 + 14735*x^3 - 210*x^2)*y^19 + (126*x^42 + 3612*x^41 + 44016*x^40 + 295665*x^39 + 1162480*x^38 + 2478685*x^37 + 1665647*x^36 - 1161014*x^35 + 19829809*x^34 + 105255332*x^33 + 104116254*x^32 - 597261859*x^31 - 2137848010*x^30 - 1349140941*x^29 + 6440056722*x^28 + 13234884494*x^27 - 3237694145*x^26 - 33016857654*x^25 - 16181478796*x^24 + 44889497982*x^23 + 39735218598*x^22 - 42067986563*x^21 - 50299399010*x^20 + 30089263771*x^19 + 44708754458*x^18 - 15746401747*x^17 - 29750854513*x^16 + 6105623626*x^15 + 14671780735*x^14 - 2753901220*x^13 - 4814334952*x^12 + 1421786727*x^11 + 751235055*x^10 - 370933606*x^9 - 15927083*x^8 + 41288916*x^7 - 10759315*x^6 + 1260154*x^5 - 68530*x^4 + 1330*x^3)*y^18 - (126*x^42 + 4284*x^41 + 61110*x^40 + 479076*x^39 + 2219910*x^38 + 5778729*x^37 + 5380441*x^36 - 10082585*x^35 - 6292668*x^34 + 168449634*x^33 + 537483327*x^32 + 138222792*x^31 - 2825484300*x^30 - 6223610475*x^29 + 515796414*x^28 + 20207212231*x^27 + 20655495388*x^26 - 25969501566*x^25 - 55222858732*x^24 + 11276437454*x^23 + 77031281310*x^22 + 10029726021*x^21 - 73088490720*x^20 - 21423082275*x^19 + 50868370156*x^18 + 20228544490*x^17 - 26582442987*x^16 - 11993564687*x^15 + 11169351208*x^14 + 3968853630*x^13 - 3742074308*x^12 - 351269966*x^11 + 724085901*x^10 - 93517380*x^9 - 57841446*x^8 + 23174172*x^7 - 3501813*x^6 + 240009*x^5 - 5985*x^4)*y^17 + (84*x^42 + 3528*x^41 + 60606*x^40 + 566496*x^39 + 3150444*x^38 + 10247688*x^37 + 14993682*x^36 - 15106147*x^35 - 83926782*x^34 + 43503873*x^33 + 825174978*x^32 + 1691071692*x^31 - 688212273*x^30 - 8605943934*x^29 - 11402456835*x^28 + 10237559815*x^27 + 39211214369*x^26 + 12729235407*x^25 - 59538974121*x^24 - 49871128148*x^23 + 54540117747*x^22 + 69758333971*x^21 - 33788516430*x^20 - 61040267361*x^19 + 13772463120*x^18 + 37482213194*x^17 - 3344838156*x^16 - 16909564695*x^15 + 1189357583*x^14 + 5370886017*x^13 - 947891371*x^12 - 906261454*x^11 + 304452675*x^10 + 45161776*x^9 - 38600670*x^8 + 7687914*x^7 - 656173*x^6 + 20349*x^5)*y^16 - (35*x^42 + 1960*x^41 + 42434*x^40 + 487340*x^39 + 3321129*x^38 + 13670304*x^37 + 30122099*x^36 + 6705237*x^35 - 144851396*x^34 - 281499987*x^33 + 403671984*x^32 + 2549923080*x^31 + 3338877203*x^30 - 4040476154*x^29 - 17475735232*x^28 - 11763335713*x^27 + 28247908113*x^26 + 47567466247*x^25 - 14500859767*x^24 - 74231154477*x^23 - 12728132989*x^22 + 70725899552*x^21 + 27560389426*x^20 - 46275737275*x^19 - 24032788759*x^18 + 21733272594*x^17 + 13068425848*x^16 - 8108440318*x^15 - 4357663367*x^14 + 2611213269*x^13 + 611238824*x^12 - 529620385*x^11 + 17348093*x^10 + 48706551*x^9 - 13480257*x^8 + 1432803*x^7 - 54264*x^6)*y^15 + (7*x^42 + 658*x^41 + 19782*x^40 + 294070*x^39 + 2528785*x^38 + 13284768*x^37 + 41167236*x^36 + 54508062*x^35 - 92069433*x^34 - 500543918*x^33 - 524115566*x^32 + 1483286760*x^31 + 5263901460*x^30 + 3914437860*x^29 - 10354822455*x^28 - 23854222204*x^27 - 2632073731*x^26 + 42481438932*x^25 + 33198014898*x^24 - 38922113382*x^23 - 53022671355*x^22 + 20249104200*x^21 + 46930364142*x^20 - 4764860691*x^19 - 27311753146*x^18 - 937680196*x^17 + 11337783990*x^16 + 695471775*x^15 - 3433048068*x^14 + 151100502*x^13 + 608366346*x^12 - 116580828*x^11 - 43428483*x^10 + 18932340*x^9 - 2535525*x^8 + 116280*x^7)*y^14 - (98*x^41 + 5397*x^40 + 115780*x^39 + 1324820*x^38 + 9054528*x^37 + 37866493*x^36 + 88274274*x^35 + 45418734*x^34 - 365164178*x^33 - 1046935267*x^32 - 495148182*x^31 + 3275156752*x^30 + 7457646060*x^29 + 1828249590*x^28 - 16218333866*x^27 - 21375462890*x^26 + 10360457604*x^25 + 39308639616*x^24 + 7956464838*x^23 - 38249804979*x^22 - 18995617442*x^21 + 23552491425*x^20 + 16118266998*x^19 - 9747117296*x^18 - 8220941060*x^17 + 3071146302*x^16 + 2680233258*x^15 - 929284866*x^14 - 448420413*x^13 + 200354630*x^12 + 20263278*x^11 - 21160167*x^10 + 3667825*x^9 - 203490*x^8)*y^13 + (637*x^40 + 26208*x^39 + 445200*x^38 + 4148536*x^37 + 23298891*x^36 + 78917762*x^35 + 135558298*x^34 - 44355211*x^33 - 768716032*x^32 - 1465393774*x^31 + 46171743*x^30 + 4830551190*x^29 + 7261670700*x^28 - 1932432754*x^27 - 16725091649*x^26 - 11453678063*x^25 + 15950116471*x^24 + 22319572636*x^23 - 6581568571*x^22 - 20410839782*x^21 - 504719507*x^20 + 11376644108*x^19 + 1965488298*x^18 - 4308733100*x^17 - 941251490*x^16 + 1208062492*x^15 + 137638580*x^14 - 216002486*x^13 + 10469732*x^12 + 18418946*x^11 - 4353167*x^10 + 293930*x^9)*y^12 - (2548*x^39 + 85267*x^38 + 1203720*x^37 + 9409008*x^36 + 44208738*x^35 + 122026674*x^34 + 146487642*x^33 - 202048746*x^32 - 1070803470*x^31 - 1407808944*x^30 + 813936750*x^29 + 4953469425*x^28 + 4707667384*x^27 - 4307496767*x^26 - 11497197642*x^25 - 2291988515*x^24 + 11719493929*x^23 + 7050407007*x^22 - 6668591119*x^21 - 6043404220*x^20 + 2233827330*x^19 + 2921422832*x^18 - 479587522*x^17 - 902726823*x^16 + 125090358*x^15 + 158411091*x^14 - 32352915*x^13 - 11795511*x^12 + 4233957*x^11 - 352716*x^10)*y^11 + (7007*x^38 + 198198*x^37 + 2382226*x^36 + 15857688*x^35 + 62830866*x^34 + 140856240*x^33 + 104370474*x^32 - 330145410*x^31 - 1048976807*x^30 - 913096614*x^29 + 1205300259*x^28 + 3573870818*x^27 + 1814072519*x^26 - 3861783744*x^25 - 5134215499*x^24 + 1234883669*x^23 + 4981327182*x^22 + 756843703*x^21 - 2643310187*x^20 - 885531990*x^19 + 877834135*x^18 + 377378134*x^17 - 212941425*x^16 - 72723368*x^15 + 36206271*x^14 + 4577748*x^13 - 3351257*x^12 + 352716*x^11)*y^10 - (14014*x^37 + 341341*x^36 + 3533684*x^35 + 20156290*x^34 + 67402160*x^33 + 121216690*x^32 + 37653992*x^31 - 337177367*x^30 - 737195006*x^29 - 367673551*x^28 + 1006512194*x^27 + 1800535161*x^26 + 211499962*x^25 - 2042339567*x^24 - 1380436902*x^23 + 1042925506*x^22 + 1239414364*x^21 - 213007221*x^20 - 564718693*x^19 - 17276973*x^18 + 157517412*x^17 + 9575954*x^16 - 26079712*x^15 + 260305*x^14 + 2125445*x^13 - 293930*x^12)*y^9 + (21021*x^36 + 444444*x^35 + 3977820*x^34 + 19443270*x^33 + 54621588*x^32 + 77087304*x^31 - 8961384*x^30 - 236771472*x^29 - 372344871*x^28 - 60678694*x^27 + 547498907*x^26 + 615739500*x^25 - 160465529*x^24 - 669608462*x^23 - 181318155*x^22 + 330451868*x^21 + 175806134*x^20 - 85542471*x^19 - 67619223*x^18 + 14119644*x^17 + 12764826*x^16 - 1953798*x^15 - 1046535*x^14 + 203490*x^13)*y^8 - (24024*x^35 + 441441*x^34 + 3409560*x^33 + 14214354*x^32 + 33251400*x^31 + 35630805*x^30 - 20279148*x^29 - 117338922*x^28 - 133882168*x^27 + 21572257*x^26 + 199477590*x^25 + 134923518*x^24 - 91114804*x^23 - 134314122*x^22 - 480336*x^21 + 56023681*x^20 + 13094550*x^19 - 12653221*x^18 - 3840963*x^17 + 1648290*x^16 + 372097*x^15 - 116280*x^14)*y^7 + (21021*x^34 + 334334*x^33 + 2214058*x^32 + 7805462*x^31 + 15028853*x^30 + 11691624*x^29 - 12727992*x^28 - 41143141*x^27 - 33601257*x^26 + 16473107*x^25 + 47934787*x^24 + 17176782*x^23 - 21266243*x^22 - 16372752*x^21 + 2807266*x^20 + 5438986*x^19 + 291270*x^18 - 831516*x^17 - 74613*x^16 + 54264*x^15)*y^6 - (14014*x^33 + 191191*x^32 + 1073772*x^31 + 3164224*x^30 + 4958632*x^29 + 2660889*x^28 - 4587486*x^27 - 10099266*x^26 - 5700333*x^25 + 4676077*x^24 + 7295731*x^23 + 1162854*x^22 - 2601180*x^21 - 1236774*x^20 + 328986*x^19 + 276108*x^18 - 7182*x^17 - 20349*x^16)*y^5 + (7007*x^32 + 80808*x^31 + 378952*x^30 + 921620*x^29 + 1171275*x^28 + 422506*x^27 - 1032906*x^26 - 1688130*x^25 - 634028*x^24 + 676787*x^23 + 685758*x^22 + 53456*x^21 - 170646*x^20 - 55650*x^19 + 11970*x^18 + 5985*x^17)*y^4 - (2548*x^31 + 24297*x^30 + 93240*x^29 + 185500*x^28 + 194586*x^27 + 51548*x^26 - 142742*x^25 - 180901*x^24 - 50993*x^23 + 47973*x^22 + 38939*x^21 + 3731*x^20 - 4760*x^19 - 1330*x^18)*y^3 + (637*x^30 + 4858*x^29 + 14910*x^28 + 24444*x^27 + 22218*x^26 + 5628*x^25 - 10470*x^24 - 11436*x^23 - 3468*x^22 + 1194*x^21 + 1071*x^20 + 210*x^19)*y^2 - (98*x^29 + 567*x^28 + 1372*x^27 + 1932*x^26 + 1596*x^25 + 546*x^24 - 240*x^23 - 336*x^22 - 138*x^21 - 21*x^20)*y + x^21*(x+1)^8-x^28*(x+1); r49:=1-x*y-y; s49:=(x*y+2*y-1)/(y-1); X50:=5*y^23 - (15*x^3 + 60*x^2 + 70*x - 45)*y^22 + (20*x^6 + 155*x^5 + 500*x^4 + 645*x^3 - 65*x^2 - 620*x + 185)*y^21 - (15*x^9 + 175*x^8 + 900*x^7 + 2520*x^6 + 3475*x^5 + 415*x^4 - 4260*x^3 - 1900*x^2 + 2505*x - 460)*y^20 + (6*x^12 + 111*x^11 + 779*x^10 + 3230*x^9 + 8330*x^8 + 11771*x^7 + 2546*x^6 - 17426*x^5 - 17370*x^4 + 8860*x^3 + 10764*x^2 - 6116*x + 771)*y^19 - (x^15 + 37*x^14 + 385*x^13 + 2096*x^12 + 7471*x^11 + 18207*x^10 + 25982*x^9 + 5485*x^8 - 49644*x^7 - 69214*x^6 + 8494*x^5 + 67308*x^4 + 2085*x^3 - 29616*x^2 + 10064*x - 917)*y^18 + (5*x^17 + 99*x^16 + 775*x^15 + 3516*x^14 + 11024*x^13 + 25427*x^12 + 36571*x^11 + 3484*x^10 - 102069*x^9 - 170098*x^8 - 21046*x^7 + 201896*x^6 + 112515*x^5 - 120166*x^4 - 48199*x^3 + 51523*x^2 - 11760*x + 791)*y^17 - (10*x^19 + 145*x^18 + 934*x^17 + 3557*x^16 + 9489*x^15 + 20230*x^14 + 29712*x^13 - 5682*x^12 - 146264*x^11 - 279409*x^10 - 80075*x^9 + 398286*x^8 + 414686*x^7 - 193092*x^6 - 354919*x^5 + 96040*x^4 + 117848*x^3 - 61992*x^2 + 9982*x - 495)*y^16 + (10*x^21 + 120*x^20 + 640*x^19 + 1865*x^18 + 3240*x^17 + 5156*x^16 + 10072*x^15 - 8389*x^14 - 131866*x^13 - 309401*x^12 - 132641*x^11 + 565258*x^10 + 838204*x^9 - 122655*x^8 - 938480*x^7 - 183771*x^6 + 533268*x^5 + 33864*x^4 - 164599*x^3 + 53511*x^2 - 6160*x + 220)*y^15 - (5*x^23 + 52*x^22 + 207*x^21 + 183*x^20 - 1385*x^19 - 4390*x^18 - 372*x^17 + 7123*x^16 - 56408*x^15 - 228270*x^14 - 158140*x^13 + 565753*x^12 + 1129343*x^11 + 81152*x^10 - 1539080*x^9 - 938350*x^8 + 956151*x^7 + 750941*x^6 - 449866*x^5 - 182500*x^4 + 154475*x^3 - 33374*x^2 + 2706*x - 66)*y^14 + (x^25 + 9*x^24 + 10*x^23 - 228*x^22 - 1423*x^21 - 3037*x^20 + 2546*x^19 + 21560*x^18 + 6553*x^17 - 121442*x^16 - 167621*x^15 + 360721*x^14 + 1072850*x^13 + 300638*x^12 - 1788867*x^11 - 1798593*x^10 + 1002682*x^9 + 1980195*x^8 - 223489*x^7 - 1021864*x^6 + 157282*x^5 + 237697*x^4 - 101650*x^3 + 14766*x^2 - 804*x + 12)*y^13 + (5*x^25 + 58*x^24 + 249*x^23 + 74*x^22 - 3756*x^21 - 14809*x^20 - 11378*x^19 + 64342*x^18 + 145485*x^17 - 126339*x^16 - 740704*x^15 - 423823*x^14 + 1479100*x^13 + 2184217*x^12 - 636550*x^11 - 2980243*x^10 - 714461*x^9 + 1928897*x^8 + 661472*x^7 - 782879*x^6 - 101322*x^5 + 183614*x^4 - 46664*x^3 + 4408*x^2 - 145*x + 1)*y^12 + (10*x^25 + 150*x^24 + 953*x^23 + 2638*x^22 - 1724*x^21 - 33024*x^20 - 74905*x^19 + 34829*x^18 + 392666*x^17 + 367960*x^16 - 847626*x^15 - 1827620*x^14 + 115170*x^13 + 3039799*x^12 + 1730846*x^11 - 2156680*x^10 - 2047040*x^9 + 841564*x^8 + 966825*x^7 - 314479*x^6 - 174576*x^5 + 92740*x^4 - 14293*x^3 + 797*x^2 - 12*x)*y^11 + (10*x^25 + 200*x^24 + 1721*x^23 + 7491*x^22 + 12371*x^21 - 27268*x^20 - 156414*x^19 - 174169*x^18 + 364861*x^17 + 1053679*x^16 + 169948*x^15 - 2132196*x^14 - 1996183*x^13 + 1559357*x^12 + 2915620*x^11 - 129955*x^10 - 1864620*x^9 - 205952*x^8 + 653043*x^7 + 1879*x^6 - 115082*x^5 + 30194*x^4 - 2629*x^3 + 66*x^2)*y^10 + (5*x^25 + 145*x^24 + 1715*x^23 + 10358*x^22 + 31108*x^21 + 21387*x^20 - 142035*x^19 - 395730*x^18 - 107241*x^17 + 1033929*x^16 + 1361551*x^15 - 722545*x^14 - 2530400*x^13 - 661967*x^12 + 1945273*x^11 + 1090892*x^10 - 777495*x^9 - 497090*x^8 + 220393*x^7 + 74778*x^6 - 42858*x^5 + 5775*x^4 - 220*x^3)*y^9 + (x^25 + 54*x^24 + 965*x^23 + 8132*x^22 + 35387*x^21 + 70245*x^20 - 16973*x^19 - 356000*x^18 - 530539*x^17 + 261506*x^16 + 1390751*x^15 + 759739*x^14 - 1250965*x^13 - 1420198*x^12 + 366882*x^11 + 912118*x^10 - 1006*x^9 - 281490*x^8 + 8852*x^7 + 39927*x^6 - 8844*x^5 + 495*x^4)*y^8 + (8*x^24 + 289*x^23 + 3704*x^22 + 22810*x^21 + 71136*x^20 + 84414*x^19 - 118743*x^18 - 479498*x^17 - 347362*x^16 + 542773*x^15 + 958558*x^14 + 23976*x^13 - 799193*x^12 - 309866*x^11 + 300475*x^10 + 148688*x^9 - 66460*x^8 - 21102*x^7 + 9570*x^6 - 792*x^5)*y^7 + (38*x^23 + 937*x^22 + 8658*x^21 + 38990*x^20 + 85440*x^19 + 45029*x^18 - 183477*x^17 - 357725*x^16 - 65413*x^15 + 410435*x^14 + 325882*x^13 - 141819*x^12 - 223487*x^11 + 4196*x^10 + 61450*x^9 + 930*x^8 - 7194*x^7 + 924*x^6)*y^6 + (x^23 + 116*x^22 + 1885*x^21 + 12540*x^20 + 41055*x^19 + 60788*x^18 - 3572*x^17 - 137018*x^16 - 145196*x^15 + 37497*x^14 + 147545*x^13 + 46155*x^12 - 50264*x^11 - 25198*x^10 + 7716*x^9 + 3498*x^8 - 792*x^7)*y^5 + (5*x^22 + 215*x^21 + 2345*x^20 + 11235*x^19 + 26410*x^18 + 24713*x^17 - 15627*x^16 - 53998*x^15 - 30400*x^14 + 20360*x^13 + 25518*x^12 + 1088*x^11 - 5958*x^10 - 825*x^9 + 495*x^8)*y^4 + (10*x^21 + 236*x^20 + 1769*x^19 + 6080*x^18 + 10102*x^17 + 5442*x^16 - 6792*x^15 - 11171*x^14 - 3160*x^13 + 3292*x^12 + 2027*x^11 - 143*x^10 - 220*x^9)*y^3 + (10*x^20 + 148*x^19 + 769*x^18 + 1884*x^17 + 2210*x^16 + 671*x^15 - 1137*x^14 - 1166*x^13 - 206*x^12 + 175*x^11 + 66*x^10)*y^2 + (5*x^19 + 48*x^18 + 172*x^17 + 303*x^16 + 265*x^15 + 70*x^14 - 62*x^13 - 53*x^12 - 12*x^11)*y + x^12*(x+1)^6; r50:=(x^3 + x^2 + x - y)/(x^2*y + x*y + x - y); s50:=(x^2 + x - y)/(x*y + x - y);