newa1 = a1 + 2*d
newb1 = b1
newa3 = a3 - (a1*b1*d)/6 - (b1*d^2)/6
newb3 = b3 - (b1^2*d)/6
newa5 = a5 - (a1*a3*d)/6 + (a1^3*b1*d)/360 - (a3*d^2)/6 + (a1^2*b1*d^2)/45 + 
   (7*a1*b1*d^3)/180 + (7*b1*d^4)/360
newb5 = b5 - (a3*b1*d)/3 + (a1^2*b1^2*d)/360 + (a1*b1^2*d^2)/30 + 
   (b1^2*d^3)/45
newc5 = c5 + (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
newd5 = (a1*b1^3*d)/360 + (b1*b3*d)/6 - (b1^3*d^2)/90 + d5
newe5 = (a1*b1^3*d)/180 - (b1*b3*d)/3 + (b1^3*d^2)/30 + e5
newf5 = (b1^4*d)/360 + f5
newa7 = a7 + (a1^3*a3*d)/360 - (a1*a5*d)/6 - (a1^5*b1*d)/15120 + 
   (a1^2*a3*d^2)/45 - (a5*d^2)/6 - (a1^4*b1*d^2)/1260 + (7*a1*a3*d^3)/180 - 
   (53*a1^3*b1*d^3)/15120 + (7*a3*d^4)/360 - (13*a1^2*b1*d^4)/1890 - 
   (31*a1*b1*d^5)/5040 - (31*b1*d^6)/15120
newb7 = b7 - (a3^2*d)/6 + (a1^2*a3*b1*d)/180 - (a5*b1*d)/3 - 
   (a1^4*b1^2*d)/15120 + (a1*a3*b1*d^2)/15 - (a1^3*b1^2*d^2)/840 + 
   (2*a3*b1*d^3)/45 - (23*a1^2*b1^2*d^3)/3780 - (a1*b1^2*d^4)/126 - 
   (b1^2*d^5)/315
newc7 = c7 + (a3^2*d)/3 + (a5*b1*d)/6 + (a1^4*b1^2*d)/15120 - 
   (a1^3*b3*d)/360 + (a1*c5*d)/6 - (a1*a3*b1*d^2)/18 + (a1^3*b1^2*d^2)/840 - 
   (a1^2*b3*d^2)/45 + (c5*d^2)/6 - (a3*b1*d^3)/36 + (53*a1^2*b1^2*d^3)/7560 - 
   (7*a1*b3*d^3)/180 + (37*a1*b1^2*d^4)/3780 - (7*b3*d^4)/360 + 
   (23*b1^2*d^5)/5040
newd7 = -(a3^2*d)/6 + (a1^2*a3*b1*d)/360 - (a1^4*b1^2*d)/3024 + 
   (a1^3*b3*d)/180 - (a1*b5*d)/6 - (a1*c5*d)/3 + (a1*a3*b1*d^2)/30 - 
   (a1^3*b1^2*d^2)/315 + (2*a1^2*b3*d^2)/45 - (b5*d^2)/6 - (c5*d^2)/3 + 
   (a3*b1*d^3)/45 - (173*a1^2*b1^2*d^3)/15120 + (7*a1*b3*d^3)/90 - 
   (59*a1*b1^2*d^4)/3780 + (7*b3*d^4)/180 - (19*b1^2*d^5)/2520 + d7
newe7 = (a1^3*b1^3*d)/15120 + (a3*b3*d)/3 - (a1^2*b1*b3*d)/180 + 
   (b1*c5*d)/3 + (a1^2*b1^3*d^2)/630 - (a1*b1*b3*d^2)/15 + 
   (11*a1*b1^3*d^3)/1890 - (2*b1*b3*d^3)/45 + (b1^3*d^4)/210 + e7
newf7 = (a1*a3*b1^2*d)/90 - (a1^3*b1^3*d)/3024 - (2*a3*b3*d)/3 + 
   (a1^2*b1*b3*d)/90 - (b1*b5*d)/3 - (2*b1*c5*d)/3 + (a3*b1^2*d^2)/15 - 
   (13*a1^2*b1^3*d^2)/2520 + (2*a1*b1*b3*d^2)/15 - (17*a1*b1^3*d^3)/945 + 
   (4*b1*b3*d^3)/45 - (4*b1^3*d^4)/315 + f7
newg7 = (a1*a3*b1^2*d)/540 - (a1^3*b1^3*d)/9072 + (5*a3*b3*d)/18 - 
   (a1^2*b1*b3*d)/360 + (b1*b5*d)/6 + (b1*c5*d)/18 - (2*a3*b1^2*d^2)/45 + 
   (a1^2*b1^3*d^2)/7560 - (a1*b1*b3*d^2)/30 + (17*a1*b1^3*d^3)/3780 - 
   (b1*b3*d^3)/45 + (b1^3*d^4)/315 + g7
newh7 = -(a1*a3*b1^2*d)/90 - (a1^3*b1^3*d)/3780 + (a3*b3*d)/6 + 
   (a1^2*b1*b3*d)/90 + (b1*c5*d)/6 - (a3*b1^2*d^2)/90 - 
   (a1^2*b1^3*d^2)/1260 + (a1*b1*b3*d^2)/45 - (a1*b1^3*d^3)/504 + 
   (b1*b3*d^3)/30 - (b1^3*d^4)/420 - (a1*d*e5)/6 - (d^2*e5)/6 + h7
newi7 = (7*a1*a3*b1^2*d)/1080 - (a1^3*b1^3*d)/45360 - (a3*b3*d)/9 - 
   (a1^2*b1*b3*d)/180 - (b1*c5*d)/18 + (a3*b1^2*d^2)/90 - 
   (a1^2*b1^3*d^2)/1890 - (a1*b1*b3*d^2)/90 - (13*a1*b1^3*d^3)/15120 - 
   (b1*b3*d^3)/60 + (b1^3*d^4)/3780 - (a1*d*d5)/6 - (d^2*d5)/6 + i7
newj7 = (a3*b1^3*d)/360 + (a1^2*b1^4*d)/15120 - (b3^2*d)/6 - 
   (a1*b1^4*d^2)/1260 + (b1^2*b3*d^2)/18 - (19*b1^4*d^3)/5040 - (b1*d*e5)/6 - 
   (a1*d*f5)/6 - (d^2*f5)/6 + j7
newk7 = -(a3*b1^3*d)/180 - (a1^2*b1^4*d)/3024 - (a1*b1^2*b3*d)/360 + 
   (b3^2*d)/3 + (a1*b1^4*d^2)/840 - (b1^2*b3*d^2)/10 + (2*b1^4*d^3)/315 + 
   (b1*d*d5)/6 + (b1*d*e5)/3 + k7
newl7 = (a3*b1^3*d)/180 - (a1^2*b1^4*d)/45360 - (a1*b1^2*b3*d)/270 - 
   (b3^2*d)/18 - (a1*b1^4*d^2)/1512 - (b1^2*b3*d^2)/45 + (b1^4*d^3)/1260 - 
   (b1*d*d5)/3 + l7
newm7 = -(a3*b1^3*d)/180 - (a1^2*b1^4*d)/3780 + (a1*b1^2*b3*d)/60 - 
   (b3^2*d)/6 - (a1*b1^4*d^2)/420 + (b1^2*b3*d^2)/10 - (b1^4*d^3)/140 - 
   (b1*d*e5)/3 + m7
newn7 = (a3*b1^3*d)/180 - (a1^2*b1^4*d)/9072 - (a1*b1^2*b3*d)/540 + 
   (b3^2*d)/18 - (a1*b1^4*d^2)/1890 - (b1^2*b3*d^2)/90 + (b1^4*d^3)/3780 + n7
newo7 = -(a1*b1^5*d)/15120 - (b1^3*b3*d)/360 + (b1^5*d^2)/2520 + 
   (b1*d*f5)/6 + o7
newp7 = (a1*b1^5*d)/15120 - (b1^5*d^2)/2520 - (b1*d*f5)/3 + p7
newq7 = -(a1*b1^5*d)/3024 + (b1^3*b3*d)/180 - (b1^5*d^2)/1260 + q7
newr7 = -(b1^6*d)/15120 + r7
