newa1 = a1 + d
newb1 = b1
newa2 = a2 + (b1*d)/2
newa3 = a3 + (a2*d)/2 - (a1*b1*d)/12 + (b1*d^2)/12
newb3 = b3 - (b1^2*d)/12
newa4 = a4 - (a1*a2*d)/12 + (a3*d)/2 + (a2*d^2)/12 - (a1*b1*d^2)/24
newb4 = b4 - (a2*b1*d)/12 + (b3*d)/2 - (b1^2*d^2)/24
newc4 = c4
newa5 = a5 - (a1*a3*d)/12 + (a4*d)/2 + (a1^3*b1*d)/720 - (a1*a2*d^2)/24 + 
   (a3*d^2)/12 + (a1^2*b1*d^2)/180 - (a1*b1*d^3)/180 - (b1*d^4)/720
newb5 = b5 + (a2^2*d)/12 - (a3*b1*d)/6 + (a1^2*b1^2*d)/720 + 
   (a1*b1^2*d^2)/120 + (b1^2*d^3)/360
newc5 = c5 - (a2^2*d)/12 + (a3*b1*d)/12 + (a1^2*b1^2*d)/360 - (a1*b3*d)/12 + 
   (b4*d)/2 - (a2*b1*d^2)/24 + (a1*b1^2*d^2)/360 + (b3*d^2)/12 - 
   (b1^2*d^3)/120
newd5 = (a1*b1^3*d)/720 + (b1*b3*d)/12 + (c4*d)/2 - (b1^3*d^2)/360 + d5
newe5 = (a1*b1^3*d)/360 - (b1*b3*d)/6 + (b1^3*d^2)/120 + e5
newf5 = (b1^4*d)/720 + f5
newa6 = a6 + (a1^3*a2*d)/720 - (a1*a4*d)/12 + (a5*d)/2 + (a1^2*a2*d^2)/180 - 
   (a1*a3*d^2)/24 + (a4*d^2)/12 + (a1^3*b1*d^2)/1440 - (a1*a2*d^3)/180 + 
   (a1^2*b1*d^3)/360 - (a2*d^4)/720 + (a1*b1*d^4)/1440
newb6 = b6 + (a2*a3*d)/12 - (a1^2*a2*b1*d)/360 - (a4*b1*d)/6 + (a1*b4*d)/12 - 
   (c5*d)/2 + (a2^2*d^2)/24 - (a1*a2*b1*d^2)/360 - (a3*b1*d^2)/24 - 
   (a1^2*b1^2*d^2)/720 + (a1*b3*d^2)/24 - (b4*d^2)/12 + (a2*b1*d^3)/120 - 
   (a1*b1^2*d^3)/720 + (b1^2*d^4)/1440
newc6 = c6 - (a2*a3*d)/12 + (a1^2*a2*b1*d)/144 + (a4*b1*d)/12 - (a1*b4*d)/6 + 
   (b5*d)/2 + c5*d - (a2^2*d^2)/24 + (a1*a2*b1*d^2)/72 + 
   (a1^2*b1^2*d^2)/288 - (a1*b3*d^2)/12 + (b4*d^2)/6 - (a2*b1*d^3)/72 + 
   (a1*b1^2*d^3)/144
newd6 = (a1*a2*b1^2*d)/720 + (a2*b3*d)/36 + (b1*b4*d)/18 - (a1*c4*d)/12 - 
   (a2*b1^2*d^2)/360 + (a1*b1^3*d^2)/1440 + (b1*b3*d^2)/24 + (c4*d^2)/12 - 
   (b1^3*d^3)/720 + (d*d5)/2 + d6
newe6 = (a1*a2*b1^2*d)/360 - (a2*b3*d)/12 - (b1*b4*d)/12 + 
   (a2*b1^2*d^2)/120 + (a1*b1^3*d^2)/720 - (b1*b3*d^2)/12 + (b1^3*d^3)/240 + 
   (d*e5)/2 + e6
newf6 = (a2*b3*d)/18 - (b1*b4*d)/18 + f6
newg6 = (a2*b1^3*d)/720 + (b1*c4*d)/12 + (b1^4*d^2)/1440 + (d*f5)/2 + g6
newh6 = -(b1*c4*d)/6 + h6
newi6 = i6
newa7 = a7 + (a1^3*a3*d)/720 - (a1*a5*d)/12 + (a6*d)/2 - (a1^5*b1*d)/30240 + 
   (a1^3*a2*d^2)/1440 + (a1^2*a3*d^2)/180 - (a1*a4*d^2)/24 + (a5*d^2)/12 - 
   (a1^4*b1*d^2)/5040 + (a1^2*a2*d^3)/360 - (a1*a3*d^3)/180 - 
   (a1^3*b1*d^3)/3780 + (a1*a2*d^4)/1440 - (a3*d^4)/720 + 
   (a1^2*b1*d^4)/3780 + (a1*b1*d^5)/5040 + (b1*d^6)/30240
newb7 = b7 - (a1^2*a2^2*d)/720 - (a3^2*d)/12 + (a2*a4*d)/6 + 
   (a1^2*a3*b1*d)/360 - (a5*b1*d)/6 - (a1^4*b1^2*d)/30240 - 
   (a1*a2^2*d^2)/120 + (a1*a3*b1*d^2)/60 - (a1^3*b1^2*d^2)/3360 - 
   (a2^2*d^3)/360 + (a3*b1*d^3)/180 - (23*a1^2*b1^2*d^3)/30240 - 
   (a1*b1^2*d^4)/2016 - (b1^2*d^5)/10080
newc7 = c7 - (a1^2*a2^2*d)/720 + (a3^2*d)/6 - (a2*a4*d)/4 + (a5*b1*d)/12 + 
   (a1^4*b1^2*d)/30240 - (a1^3*b3*d)/720 + (b6*d)/2 + (a1*c5*d)/12 + 
   (a1*a2^2*d^2)/180 + (a2*a3*d^2)/24 - (a1^2*a2*b1*d^2)/720 - 
   (a1*a3*b1*d^2)/72 - (a4*b1*d^2)/12 + (a1^3*b1^2*d^2)/3360 - 
   (a1^2*b3*d^2)/180 + (a1*b4*d^2)/24 - (c5*d^2)/12 + (a2^2*d^3)/90 - 
   (a1*a2*b1*d^3)/720 - (a3*b1*d^3)/72 + (a1^2*b1^2*d^3)/1890 + 
   (a1*b3*d^3)/180 + (a2*b1*d^4)/1440 + (a1*b1^2*d^4)/3780 + (b3*d^4)/720 + 
   (b1^2*d^5)/10080
newd7 = (a1^2*a2^2*d)/360 - (a3^2*d)/12 + (a2*a4*d)/12 + (a1^2*a3*b1*d)/720 - 
   (a1^4*b1^2*d)/6048 + (a1^3*b3*d)/360 - (a1*b5*d)/12 - (a1*c5*d)/6 + 
   (c6*d)/2 + (a1*a2^2*d^2)/360 - (a2*a3*d^2)/24 + (a1^2*a2*b1*d^2)/288 + 
   (a1*a3*b1*d^2)/120 + (a4*b1*d^2)/24 - (a1^3*b1^2*d^2)/1260 + 
   (a1^2*b3*d^2)/90 - (a1*b4*d^2)/12 + (b5*d^2)/12 + (c5*d^2)/6 - 
   (a2^2*d^3)/120 + (a1*a2*b1*d^3)/144 + (a3*b1*d^3)/360 - 
   (17*a1^2*b1^2*d^3)/30240 - (a1*b3*d^3)/90 + (23*a1*b1^2*d^4)/30240 - 
   (b3*d^4)/360 + (b1^2*d^5)/5040 + d7
newe7 = (a1^3*b1^3*d)/30240 + (a3*b3*d)/6 - (a1^2*b1*b3*d)/360 - 
   (a2*b4*d)/6 + (b1*c5*d)/6 + (a1^2*b1^3*d^2)/2520 - (a1*b1*b3*d^2)/60 + 
   (11*a1*b1^3*d^3)/15120 - (b1*b3*d^3)/180 + (b1^3*d^4)/3360 + e7
newf7 = -(a1*a2^2*b1*d)/360 + (a1*a3*b1^2*d)/180 - (a1^3*b1^3*d)/6048 - 
   (a3*b3*d)/3 + (a1^2*b1*b3*d)/180 + (a2*b4*d)/3 - (b1*b5*d)/6 - 
   (b1*c5*d)/3 - (a2^2*b1*d^2)/120 + (a3*b1^2*d^2)/60 - 
   (13*a1^2*b1^3*d^2)/10080 + (a1*b1*b3*d^2)/30 - (17*a1*b1^3*d^3)/7560 + 
   (b1*b3*d^3)/90 - (b1^3*d^4)/1260 + f7
newg7 = -(a1*a2^2*b1*d)/2160 + (a1*a3*b1^2*d)/1080 - (a1^3*b1^3*d)/18144 + 
   (5*a3*b3*d)/36 - (a1^2*b1*b3*d)/720 - (a2*b4*d)/12 + (b1*b5*d)/12 + 
   (b1*c5*d)/36 + (a2^2*b1*d^2)/180 - (a3*b1^2*d^2)/90 + 
   (a1^2*b1^3*d^2)/30240 + (a2*b3*d^2)/36 - (a1*b1*b3*d^2)/120 - 
   (b1*b4*d^2)/36 + (17*a1*b1^3*d^3)/30240 - (b1*b3*d^3)/360 + 
   (b1^3*d^4)/5040 + (d*f6)/2 + g7
newh7 = (a1*a2^2*b1*d)/240 - (a1*a3*b1^2*d)/180 - (a1^3*b1^3*d)/7560 + 
   (a3*b3*d)/12 + (a1^2*b1*b3*d)/180 - (a2*b4*d)/6 + (b1*c5*d)/12 + 
   (a2^2*b1*d^2)/180 + (a1*a2*b1^2*d^2)/720 - (a3*b1^2*d^2)/360 - 
   (a1^2*b1^3*d^2)/5040 - (a2*b3*d^2)/24 + (a1*b1*b3*d^2)/180 - 
   (b1*b4*d^2)/24 + (a2*b1^2*d^3)/240 + (a1*b1^3*d^3)/10080 - 
   (b1*b3*d^3)/60 + (b1^3*d^4)/1120 - (a1*d*e5)/12 + (d^2*e5)/12 + (d*e6)/2 + 
   h7
newi7 = -(a1*a2^2*b1*d)/1080 + (7*a1*a3*b1^2*d)/2160 - (a1^3*b1^3*d)/90720 - 
   (a3*b3*d)/18 - (a1^2*b1*b3*d)/360 + (a2*b4*d)/12 - (b1*c5*d)/36 - 
   (a2^2*b1*d^2)/360 + (a1*a2*b1^2*d^2)/1440 + (a3*b1^2*d^2)/360 - 
   (a1^2*b1^3*d^2)/7560 + (a2*b3*d^2)/72 - (a1*b1*b3*d^2)/360 + 
   (b1*b4*d^2)/36 - (a1*c4*d^2)/24 - (a2*b1^2*d^3)/720 + 
   (a1*b1^3*d^3)/15120 + (b1*b3*d^3)/120 - (b1^3*d^4)/3024 - (a1*d*d5)/12 + 
   (d^2*d5)/12 + (d*d6)/2 + i7
newj7 = (a3*b1^3*d)/720 + (a1^2*b1^4*d)/30240 - (b3^2*d)/12 + (a2*c4*d)/12 + 
   (a2*b1^3*d^2)/1440 - (a1*b1^4*d^2)/5040 + (b1^2*b3*d^2)/72 + 
   (b1*c4*d^2)/24 - (b1^4*d^3)/3360 - (b1*d*e5)/12 - (a1*d*f5)/12 + 
   (d^2*f5)/12 + (d*g6)/2 + j7
newk7 = (a2^2*b1^2*d)/720 - (a3*b1^3*d)/360 - (a1^2*b1^4*d)/6048 - 
   (a1*b1^2*b3*d)/720 + (b3^2*d)/6 - (a2*c4*d)/4 + (a1*b1^4*d^2)/3360 - 
   (b1^2*b3*d^2)/40 - (b1*c4*d^2)/12 + (b1^4*d^3)/1260 + (b1*d*d5)/12 + 
   (b1*d*e5)/6 + (d*h6)/2 + k7
newl7 = -(a2^2*b1^2*d)/720 + (a3*b1^3*d)/360 - (a1^2*b1^4*d)/90720 - 
   (a1*b1^2*b3*d)/540 - (b3^2*d)/36 + (a2*c4*d)/6 - (a1*b1^4*d^2)/6048 - 
   (b1^2*b3*d^2)/180 + (b1^4*d^3)/10080 - (b1*d*d5)/6 + l7
newm7 = (a2^2*b1^2*d)/720 - (a3*b1^3*d)/360 - (a1^2*b1^4*d)/7560 + 
   (a1*b1^2*b3*d)/120 - (b3^2*d)/12 - (a1*b1^4*d^2)/1680 + (b1^2*b3*d^2)/40 - 
   (b1^4*d^3)/1120 - (b1*d*e5)/6 + m7
newn7 = -(a2^2*b1^2*d)/720 + (a3*b1^3*d)/360 - (a1^2*b1^4*d)/18144 - 
   (a1*b1^2*b3*d)/1080 + (b3^2*d)/36 - (a1*b1^4*d^2)/7560 - 
   (b1^2*b3*d^2)/360 + (b1^4*d^3)/30240 + n7
newo7 = -(a1*b1^5*d)/30240 - (b1^3*b3*d)/720 + (b1^5*d^2)/10080 + 
   (b1*d*f5)/12 + (d*i6)/2 + o7
newp7 = (a1*b1^5*d)/30240 - (b1^5*d^2)/10080 - (b1*d*f5)/6 + p7
newq7 = -(a1*b1^5*d)/6048 + (b1^3*b3*d)/360 - (b1^5*d^2)/5040 + q7
newr7 = -(b1^6*d)/30240 + r7
