newa1p = a1 + d
newa3p = a3 + d^3
newb4p = (2*b4 + a3*d - a1*d^3)/2
newa5p = a5 + d^5
newb5p = (12*b5 - a1*a3*d + 6*b4*d + a3*d^2 + a1^2*d^3 - a1*d^4)/12
newb6p = (2*b6 + a5*d - a1*d^5)/2
newc6p = (24*c6 - 2*a1*b4*d + 12*b5*d - a1*a3*d^2 + 2*b4*d^2 + a1^2*d^4)/24
newa7p = a7 + d^7
newb7p = (12*b7 - a1*a5*d + 6*b6*d + a5*d^2 + a1^2*d^5 - a1*d^6)/12
newc7p = (720*c7 + a1^3*a3*d - 60*a1*b5*d + 360*c6*d + 4*a1^2*a3*d^2 - 
     30*a1*b4*d^2 + 60*b5*d^2 - a1^4*d^3 - 4*a1*a3*d^3 - 4*a1^3*d^4 - 
     a3*d^4 + 4*a1^2*d^5 + a1*d^6)/720
newd7p = (-(a3^2*d) + a1*a3*d^3 + 6*b4*d^3 + a3*d^4 - a1*d^6 + 12*d7)/12
newb8p = (2*b8 + a7*d - a1*d^7)/2
newc8p = (24*c8 - 2*a1*b6*d + 12*b7*d - a1*a5*d^2 + 2*b6*d^2 + a1^2*d^6)/24
newd8p = (2*a1^3*b4*d - 120*a1*c6*d + 720*c7*d + a1^3*a3*d^2 + 
     8*a1^2*b4*d^2 - 60*a1*b5*d^2 + 120*c6*d^2 + 4*a1^2*a3*d^3 - 
     8*a1*b4*d^3 - a1^4*d^4 + a1*a3*d^4 - 2*b4*d^4 - 4*a1^3*d^5 - a1^2*d^6 + 
     1440*d8)/1440
newe8p = (a5*d^3 - a3*d^5 + 2*e8)/2
newf8p = (-2*a3*b4*d - a3^2*d^2 - 2*a1*b4*d^3 + 12*b5*d^3 + 4*b4*d^4 + 
     a1^2*d^6 + 12*d*d7 + 24*f8)/24
newa9p = a9 + d^9
newb9p = (12*b9 - a1*a7*d + 6*b8*d + a7*d^2 + a1^2*d^7 - a1*d^8)/12
newc9p = (720*c9 + a1^3*a5*d - 60*a1*b7*d + 360*c8*d + 4*a1^2*a5*d^2 - 
     30*a1*b6*d^2 + 60*b7*d^2 - 4*a1*a5*d^3 - a5*d^4 - a1^4*d^5 - 
     4*a1^3*d^6 + 4*a1^2*d^7 + a1*d^8)/720
newd9p = (a3*a5*d - 2*a1*a5*d^3 + a5*d^4 + a1*a3*d^5 - 6*b4*d^5 - 2*a3*d^6 + 
     a1*d^8 + 12*d9 + 6*d*e8)/12
newe9p = (-2*a3*a5*d + a1*a5*d^3 + 6*b6*d^3 + a5*d^4 + a1*a3*d^5 + 6*b4*d^5 + 
     a3*d^6 - 2*a1*d^8 + 12*e9)/12
newf9p = (a1^2*a3^2*d - 30*b4^2*d + 30*a3*b5*d + a1*a3^2*d^2 - 15*a3*b4*d^2 - 
     a1^3*a3*d^3 - 3*a3^2*d^3 - 60*a1*b5*d^3 + 2*a1^2*a3*d^4 - 15*a1*b4*d^4 + 
     30*b5*d^4 + 2*a1*a3*d^5 - 3*a1^3*d^6 - a3*d^6 + a1^2*d^7 + a1*d^8 - 
     30*a1*d*d7 + 30*d^2*d7 + 180*d*f8 + 360*f9)/360
newg9p = (a1^2*a3^2*d + 60*b4^2*d - 120*a3*b5*d + 6*a1*a3^2*d^2 - 
     a1^3*a3*d^3 + 2*a3^2*d^3 + 60*a1*b5*d^3 + 360*c6*d^3 - 8*a1^2*a3*d^4 - 
     30*a1*b4*d^4 + 60*b5*d^4 - 8*a1*a3*d^5 + 2*a1^3*d^6 - a3*d^6 + 
     6*a1^2*d^7 + a1*d^8 + 720*g9)/720
newh9p = (-(a1^5*a3*d) + 42*a1^3*b5*d - 2520*a1*c7*d - 6*a1^4*a3*d^2 + 
     21*a1^3*b4*d^2 + 168*a1^2*b5*d^2 - 1260*a1*c6*d^2 + 2520*c7*d^2 + 
     a1^6*d^3 - 8*a1^3*a3*d^3 + 84*a1^2*b4*d^3 - 168*a1*b5*d^3 + 6*a1^5*d^4 + 
     8*a1^2*a3*d^4 + 21*a1*b4*d^4 - 42*b5*d^4 + 8*a1^4*d^5 + 6*a1*a3*d^5 - 
     8*a1^3*d^6 + a3*d^6 - 6*a1^2*d^7 - a1*d^8 + 15120*d*d8 + 30240*h9)/30240
newb10p = (2*b10 + a9*d - a1*d^9)/2
newc10p = (24*c10 - 2*a1*b8*d + 12*b9*d - a1*a7*d^2 + 2*b8*d^2 + a1^2*d^8)/24
newd10p = (2*a1^3*b6*d - 120*a1*c8*d + 720*c9*d + a1^3*a5*d^2 + 
     8*a1^2*b6*d^2 - 60*a1*b7*d^2 + 120*c8*d^2 + 4*a1^2*a5*d^3 - 
     8*a1*b6*d^3 + a1*a5*d^4 - 2*b6*d^4 - a1^4*d^6 - 4*a1^3*d^7 - a1^2*d^8 + 
     1440*d10)/1440
newe10p = (-4*a1^5*b4*d + 168*a1^3*c6*d - 2*a1^5*a3*d^2 - 24*a1^4*b4*d^2 + 
     84*a1^3*b5*d^2 + 672*a1^2*c6*d^2 - 5040*a1*c7*d^2 - 12*a1^4*a3*d^3 - 
     32*a1^3*b4*d^3 + 336*a1^2*b5*d^3 - 672*a1*c6*d^3 + 2*a1^6*d^4 - 
     23*a1^3*a3*d^4 + 32*a1^2*b4*d^4 + 84*a1*b5*d^4 - 168*c6*d^4 + 
     12*a1^5*d^5 - 12*a1^2*a3*d^5 + 24*a1*b4*d^5 + 23*a1^4*d^6 - 
     2*a1*a3*d^6 + 4*b4*d^6 + 12*a1^3*d^7 + 2*a1^2*d^8 - 10080*a1*d*d8 + 
     10080*d^2*d8 + 120960*e10 + 60480*d*h9)/120960
newf10p = (a7*d^3 - a3*d^7 + 2*f10)/2
newg10p = (2*a5*b4*d + a3*a5*d^2 - 2*a1*a5*d^4 + 2*a1*b4*d^5 - 12*b5*d^5 + 
     2*a1*a3*d^6 - 4*b4*d^6 - a1^2*d^8 + 12*d*d9 - 2*a1*d*e8 + 2*d^2*e8 + 
     24*g10)/24
newh10p = (4*a5*b4*d - 4*a3*b6*d + 2*a1*b6*d^3 + 12*b7*d^3 - a1*a5*d^4 + 
     2*b6*d^4 - 2*a1*b4*d^5 - 12*b5*d^5 + a1*a3*d^6 - 2*b4*d^6 + 24*h10)/24
newi10p = (-6*a5*b4*d + 2*a3*b6*d - 2*a3*a5*d^2 - 4*a1*b6*d^3 + a1*a5*d^4 + 
     2*b6*d^4 + 24*b5*d^5 - a1*a3*d^6 + 6*b4*d^6 + 2*a1^2*d^8 + 12*d*e9 + 
     24*i10)/24
newj10p = (-2*a3*b4*d^3 - a3^2*d^4 + a1*a3*d^6 + 2*b4*d^6 + 12*d^3*d7 + 
     24*j10)/24
newk10p = (-4*a1^2*a3*b4*d + 120*b4*b5*d - 240*a3*c6*d - 2*a1^2*a3^2*d^2 - 
     4*a1*a3*b4*d^2 + 60*b4^2*d^2 - 60*a3*b5*d^2 - 2*a1*a3^2*d^3 + 
     2*a1^3*b4*d^3 + 12*a3*b4*d^3 + 120*a1*c6*d^3 + 720*c7*d^3 + 
     3*a1^3*a3*d^4 + a3^2*d^4 - 4*a1^2*b4*d^4 + 60*a1*b5*d^4 + 120*c6*d^4 - 
     4*a1*b4*d^5 - a1^4*d^6 - 3*a1*a3*d^6 + 2*b4*d^6 + 2*a1^3*d^7 + 
     2*a1^2*d^8 + 60*a1*d^2*d7 + 120*a1*d*f8 - 120*d^2*f8 - 720*d*f9 + 
     1440*k10)/1440
newl10p = (2*a1^2*a3*b4*d - 24*b4*b5*d + 24*a3*c6*d + a1^2*a3^2*d^2 + 
     4*a1*a3*b4*d^2 - 12*b4^2*d^2 + 2*a1*a3^2*d^3 - 4*a3*b4*d^3 - 
     48*a1*c6*d^3 - a1^3*a3*d^4 + 4*a1^2*b4*d^4 - 36*a1*b5*d^4 + 24*c6*d^4 - 
     4*a1*b4*d^5 + a1*a3*d^6 - 2*b4*d^6 - 2*a1^3*d^7 - a1^2*d^8 - 
     24*a1*d^2*d7 - 48*a1*d*f8 + 48*d^2*f8 + 288*d*f9 + 144*d*g9 + 288*l10)/
   288
newa11p = a11 + d^11
newb11p = (12*b11 - a1*a9*d + 6*b10*d + a9*d^2 + a1^2*d^9 - a1*d^10)/12
newc11p = (720*c11 + a1^3*a7*d - 60*a1*b9*d + 360*c10*d + 4*a1^2*a7*d^2 - 
     30*a1*b8*d^2 + 60*b9*d^2 - 4*a1*a7*d^3 - a7*d^4 - a1^4*d^7 - 
     4*a1^3*d^8 + 4*a1^2*d^9 + a1*d^10)/720
newd11p = (-(a1^5*a5*d) + 42*a1^3*b7*d - 2520*a1*c9*d - 6*a1^4*a5*d^2 + 
     21*a1^3*b6*d^2 + 168*a1^2*b7*d^2 - 1260*a1*c8*d^2 + 2520*c9*d^2 - 
     8*a1^3*a5*d^3 + 84*a1^2*b6*d^3 - 168*a1*b7*d^3 + 8*a1^2*a5*d^4 + 
     21*a1*b6*d^4 - 42*b7*d^4 + a1^6*d^5 + 6*a1*a5*d^5 + 6*a1^5*d^6 + 
     a5*d^6 + 8*a1^4*d^7 - 8*a1^3*d^8 - 6*a1^2*d^9 - a1*d^10 + 15120*d*d10 + 
     30240*d11)/30240
newe11p = (3*a1^7*a3*d - 120*a1^5*b5*d + 5040*a1^3*c7*d + 24*a1^6*a3*d^2 - 
     60*a1^5*b4*d^2 - 720*a1^4*b5*d^2 + 2520*a1^3*c6*d^2 + 
     20160*a1^2*c7*d^2 - 3*a1^8*d^3 + 64*a1^5*a3*d^3 - 360*a1^4*b4*d^3 - 
     960*a1^3*b5*d^3 + 10080*a1^2*c6*d^3 - 20160*a1*c7*d^3 - 24*a1^7*d^4 + 
     48*a1^4*a3*d^4 - 690*a1^3*b4*d^4 + 960*a1^2*b5*d^4 + 2520*a1*c6*d^4 - 
     5040*c7*d^4 - 64*a1^6*d^5 - 48*a1^3*a3*d^5 - 360*a1^2*b4*d^5 + 
     720*a1*b5*d^5 - 48*a1^5*d^6 - 64*a1^2*a3*d^6 - 60*a1*b4*d^6 + 
     120*b5*d^6 + 48*a1^4*d^7 - 24*a1*a3*d^7 + 64*a1^3*d^8 - 3*a3*d^8 + 
     24*a1^2*d^9 + 3*a1*d^10 - 151200*a1*d^2*d8 + 1814400*d*e10 + 
     3628800*e11 - 302400*a1*d*h9 + 302400*d^2*h9)/3628800
newf11p = (a3*a7*d - 2*a1*a7*d^3 + a7*d^4 + a1*a3*d^7 - 6*b4*d^7 - 2*a3*d^8 + 
     a1*d^10 + 6*d*f10 + 12*f11)/12
newg11p = (-2*a3*a7*d + a1*a7*d^3 + 6*b8*d^3 + a7*d^4 + a1*a3*d^7 + 
     6*b4*d^7 + a3*d^8 - 2*a1*d^10 + 12*g11)/12
newh11p = (-(a5^2*d) + a1*a5*d^5 + 6*b6*d^5 + a5*d^6 - a1*d^10 + 12*h11)/12
newi11p = (-(a3*a5*d^3) + a3^2*d^5 + a5*d^6 - a3*d^8 + 6*d^3*e8 + 12*i11)/12
newj11p = (-3*a1^2*a3*a5*d + 60*a5*b5*d - 8*a1*a3*a5*d^2 + 30*a5*b4*d^2 + 
     4*a1^3*a5*d^3 + 4*a3*a5*d^3 + 12*a1^2*a5*d^4 - a1^3*a3*d^5 - 
     8*a1*a5*d^5 + 60*a1*b5*d^5 - 360*c6*d^5 - 8*a1^2*a3*d^6 - a5*d^6 + 
     60*a1*b4*d^6 - 120*b5*d^6 + 12*a1*a3*d^7 + 4*a1^3*d^8 + 4*a3*d^8 - 
     8*a1^2*d^9 - 3*a1*d^10 - 60*a1*d*d9 + 60*d^2*d9 - 30*a1*d^2*e8 + 
     360*d*g10 + 720*j11)/720
newk11p = (2*a1^2*a3*a5*d - 120*a5*b5*d + 120*b4*b6*d - 120*a3*b7*d + 
     12*a1*a3*a5*d^2 - a1^3*a5*d^3 + 4*a3*a5*d^3 + 60*a1*b7*d^3 + 
     360*c8*d^3 - 8*a1^2*a5*d^4 - 30*a1*b6*d^4 + 60*b7*d^4 - a1^3*a3*d^5 - 
     8*a1*a5*d^5 + 60*a1*b5*d^5 + 360*c6*d^5 - 8*a1^2*a3*d^6 - a5*d^6 - 
     30*a1*b4*d^6 + 60*b5*d^6 - 8*a1*a3*d^7 + 4*a1^3*d^8 - a3*d^8 + 
     12*a1^2*d^9 + 2*a1*d^10 + 720*k11)/720
newl11p = (-3*a1^2*a3*a5*d + 300*a5*b5*d - 180*b4*b6*d + 60*a3*b7*d - 
     18*a1*a3*a5*d^2 + 60*a5*b4*d^2 - 60*a3*b6*d^2 + 4*a1^3*a5*d^3 - 
     6*a3*a5*d^3 - 120*a1*b7*d^3 + 22*a1^2*a5*d^4 + 30*a1*b6*d^4 + 
     60*b7*d^4 - a1^3*a3*d^5 + 2*a1*a5*d^5 - 60*a1*b5*d^5 - 1080*c6*d^5 + 
     2*a1^2*a3*d^6 - a5*d^6 + 60*a1*b4*d^6 - 240*b5*d^6 + 22*a1*a3*d^7 - 
     6*a1^3*d^8 + 4*a3*d^8 - 18*a1^2*d^9 - 3*a1*d^10 + 360*d*h10 + 720*l11)/
   720
newm11p = (7*a1^2*a3*a5*d - 240*a5*b5*d + 60*b4*b6*d + 22*a1*a3*a5*d^2 - 
     90*a5*b4*d^2 + 30*a3*b6*d^2 - 6*a1^3*a5*d^3 - 6*a3*a5*d^3 - 
     18*a1^2*a5*d^4 - 60*a1*b6*d^4 - a1^3*a3*d^5 + 2*a1*a5*d^5 - 
     60*a1*b5*d^5 + 1080*c6*d^5 + 2*a1^2*a3*d^6 - a5*d^6 - 90*a1*b4*d^6 + 
     300*b5*d^6 - 18*a1*a3*d^7 - 6*a1^3*d^8 - 6*a3*d^8 + 22*a1^2*d^9 + 
     7*a1*d^10 - 60*a1*d*e9 + 60*d^2*e9 + 360*d*i10 + 720*m11)/720
newn11p = (a1*a3^3*d - 2*a3^3*d^2 - a1^2*a3^2*d^3 - 60*b4^2*d^3 + 
     8*a1*a3^2*d^4 - 30*a3*b4*d^4 - 6*a3^2*d^5 - 6*a1^2*a3*d^6 + 
     8*a1*a3*d^7 - a3*d^8 - 2*a1^2*d^9 + a1*d^10 + 60*a3*d*d7 - 
     120*a1*d^3*d7 + 60*d^4*d7 + 360*d*j10 + 720*n11)/720
newo11p = (a1*a3^3*d + 3*a3^3*d^2 - a1^2*a3^2*d^3 + 30*b4^2*d^3 - 
     30*a3*b5*d^3 - 2*a1*a3^2*d^4 - 15*a3*b4*d^4 - a3^2*d^5 - a1^2*a3*d^6 - 
     15*a1*b4*d^6 + 30*b5*d^6 - 2*a1*a3*d^7 - a3*d^8 + 3*a1^2*d^9 + a1*d^10 - 
     60*a3*d*d7 + 30*a1*d^3*d7 + 30*d^4*d7 + 180*d^3*f8 + 360*o11)/360
newp11p = (-(a1^4*a3^2*d) - 42*a1^2*b4^2*d + 84*a1^2*a3*b5*d - 2520*b5^2*d + 
     5040*b4*c6*d - 5040*a3*c7*d - 9*a1^3*a3^2*d^2 - 252*a1*b4^2*d^2 + 
     504*a1*a3*b5*d^2 + a1^5*a3*d^3 - 23*a1^2*a3^2*d^3 - 84*b4^2*d^3 - 
     42*a1^3*b5*d^3 + 168*a3*b5*d^3 + 2520*a1*c7*d^3 + 12*a1^4*a3*d^4 - 
     15*a1*a3^2*d^4 + 21*a1^3*b4*d^4 - 336*a1^2*b5*d^4 - 1260*a1*c6*d^4 + 
     2520*c7*d^4 + 38*a1^3*a3*d^5 - 3*a3^2*d^5 + 84*a1^2*b4*d^5 - 
     336*a1*b5*d^5 - 3*a1^5*d^6 + 38*a1^2*a3*d^6 + 21*a1*b4*d^6 - 42*b5*d^6 - 
     15*a1^4*d^7 + 12*a1*a3*d^7 - 23*a1^3*d^8 + a3*d^8 - 9*a1^2*d^9 - 
     a1*d^10 + 15120*d^3*d8 + 30240*p11)/30240
newq11p = (a1^4*a3^2*d - 42*a1^2*b4^2*d + 5040*b5^2*d - 7560*b4*c6*d + 
     2520*a3*c7*d + 9*a1^3*a3^2*d^2 - 42*a1^2*a3*b4*d^2 + 168*a1*b4^2*d^2 - 
     420*a1*a3*b5*d^2 + 1260*b4*b5*d^2 - 2520*a3*c6*d^2 - a1^5*a3*d^3 + 
     16*a1^2*a3^2*d^3 - 42*a1*a3*b4*d^3 + 336*b4^2*d^3 - 420*a3*b5*d^3 - 
     5040*a1*c7*d^3 - 12*a1^4*a3*d^4 + 8*a1*a3^2*d^4 + 21*a1^3*b4*d^4 + 
     21*a3*b4*d^4 + 420*a1^2*b5*d^4 + 1260*a1*c6*d^4 + 2520*c7*d^4 - 
     24*a1^3*a3*d^5 + 3*a3^2*d^5 - 42*a1^2*b4*d^5 + 420*a1*b5*d^5 + 
     3*a1^5*d^6 - 24*a1^2*a3*d^6 - 42*a1*b4*d^6 + 8*a1^4*d^7 - 12*a1*a3*d^7 + 
     16*a1^3*d^8 - a3*d^8 + 9*a1^2*d^9 + a1*d^10 - 42*a1^3*d*d7 - 
     168*a1^2*d^2*d7 + 168*a1*d^3*d7 + 42*d^4*d7 + 1260*a1*d^2*f8 + 
     2520*a1*d*f9 - 2520*d^2*f9 + 15120*d*k10 + 30240*q11)/30240
newr11p = (-5*a1^4*a3^2*d + 84*a1^2*b4^2*d + 42*a1^2*a3*b5*d - 2520*b5^2*d + 
     2520*b4*c6*d - 24*a1^3*a3^2*d^2 + 105*a1^2*a3*b4*d^2 + 84*a1*b4^2*d^2 + 
     252*a1*a3*b5*d^2 - 1260*b4*b5*d^2 + 1260*a3*c6*d^2 + 5*a1^5*a3*d^3 - 
     17*a1^2*a3^2*d^3 + 210*a1*a3*b4*d^3 - 252*b4^2*d^3 + 84*a1^3*b5*d^3 + 
     84*a3*b5*d^3 + 18*a1^4*a3*d^4 + 23*a1*a3^2*d^4 + 252*a1^2*b5*d^4 - 
     2520*a1*c6*d^4 - 6*a1^3*a3*d^5 + 6*a3^2*d^5 + 210*a1^2*b4*d^5 - 
     588*a1*b5*d^5 + 6*a1^5*d^6 - 6*a1^2*a3*d^6 + 105*a1*b4*d^6 - 
     126*b5*d^6 + 23*a1^4*d^7 + 18*a1*a3*d^7 - 17*a1^3*d^8 + 5*a3*d^8 - 
     24*a1^2*d^9 - 5*a1*d^10 + 84*a1^3*d*d7 + 336*a1^2*d^2*d7 - 
     336*a1*d^3*d7 - 84*d^4*d7 - 2520*a1*d^2*f8 - 5040*a1*d*f9 + 
     5040*d^2*f9 - 2520*a1*d*g9 + 2520*d^2*g9 + 15120*d*l10 + 30240*r11)/30240
