newa1 = a1 + 2*d
newb1 = b1
newa3 = a3 - (a1*b1*d)/6 - (b1*d^2)/6
newb3 = b3 - (b1^2*d)/6
newa5 = a5 + (a3*b1*d)/6 + (a1^2*b1^2*d)/180 - (a1*b3*d)/6 + 
   (a1*b1^2*d^2)/90 - (b3*d^2)/6 + (b1^2*d^3)/60
newb5 = b5 + (a1*b1^3*d)/360 + (b1*b3*d)/6 - (b1^3*d^2)/90
newc5 = c5 + (a1*b1^3*d)/180 - (b1*b3*d)/3 + (b1^3*d^2)/30
newd5 = (b1^4*d)/360 + d5
newa7 = a7 + (a5*b1*d)/6 - (a1*a3*b1^2*d)/90 - (a1^3*b1^3*d)/3780 + 
   (a3*b3*d)/6 + (a1^2*b1*b3*d)/90 - (a1*c5*d)/6 - (a3*b1^2*d^2)/90 - 
   (a1^2*b1^3*d^2)/1260 + (a1*b1*b3*d^2)/45 - (c5*d^2)/6 - 
   (a1*b1^3*d^3)/504 + (b1*b3*d^3)/30 - (b1^3*d^4)/420
newb7 = b7 - (a5*b1*d)/18 + (7*a1*a3*b1^2*d)/1080 - (a1^3*b1^3*d)/45360 - 
   (a3*b3*d)/9 - (a1^2*b1*b3*d)/180 - (a1*b5*d)/6 + (a3*b1^2*d^2)/90 - 
   (a1^2*b1^3*d^2)/1890 - (a1*b1*b3*d^2)/90 - (b5*d^2)/6 - 
   (13*a1*b1^3*d^3)/15120 - (b1*b3*d^3)/60 + (b1^3*d^4)/3780
newc7 = c7 + (a3*b1^3*d)/360 + (a1^2*b1^4*d)/15120 - (b3^2*d)/6 - 
   (b1*c5*d)/6 - (a1*b1^4*d^2)/1260 + (b1^2*b3*d^2)/18 - (19*b1^4*d^3)/5040 - 
   (a1*d*d5)/6 - (d^2*d5)/6
newd7 = -(a3*b1^3*d)/180 - (a1^2*b1^4*d)/3024 - (a1*b1^2*b3*d)/360 + 
   (b3^2*d)/3 + (b1*b5*d)/6 + (b1*c5*d)/3 + (a1*b1^4*d^2)/840 - 
   (b1^2*b3*d^2)/10 + (2*b1^4*d^3)/315 + d7
newe7 = (a3*b1^3*d)/180 - (a1^2*b1^4*d)/45360 - (a1*b1^2*b3*d)/270 - 
   (b3^2*d)/18 - (b1*b5*d)/3 - (a1*b1^4*d^2)/1512 - (b1^2*b3*d^2)/45 + 
   (b1^4*d^3)/1260 + e7
newf7 = -(a3*b1^3*d)/180 - (a1^2*b1^4*d)/3780 + (a1*b1^2*b3*d)/60 - 
   (b3^2*d)/6 - (b1*c5*d)/3 - (a1*b1^4*d^2)/420 + (b1^2*b3*d^2)/10 - 
   (b1^4*d^3)/140 + f7
newg7 = -(a1*b1^5*d)/15120 - (b1^3*b3*d)/360 + (b1^5*d^2)/2520 + 
   (b1*d*d5)/6 + g7
newh7 = (a1*b1^5*d)/15120 - (b1^5*d^2)/2520 - (b1*d*d5)/3 + h7
newi7 = -(a1*b1^5*d)/3024 + (b1^3*b3*d)/180 - (b1^5*d^2)/1260 + i7
newj7 = -(b1^6*d)/15120 + j7
