x=var('x')
|
|
def recurse_find_parking_function(T,root):
if T.order()==1:
return (exp(x)-1)/x
else:
temp_T=copy(T)
temp_T.delete_vertex(root)
poly(x)=1
for v in T.neighbors(root):
poly(x)=poly*recurse_find_parking_function(temp_T.subgraph(temp_T.connected_component_containing_vertex(v)),v)
pt=poly.limit(x=0)
p=(exp(x)*poly-pt)/x
return p.rational_simplify()
|
|
%time
html('<!--notruncate-->')
for num_vertices in range(2,9):
for T in graphs.trees(num_vertices):
T.show()
for v in T.automorphism_group().orbits():
s=recurse_find_parking_function(T,v[0]).limit(x=0)*factorial(T.order())
print "Placing the root at "+str(v[0]%T.order())+": "+str(s(x=0))
print recurse_find_parking_function(T,v[0])
print ""
orbited=[]
for b in T.automorphism_group().orbits():
orbited.extend(b)
for i in range(T.order()):
if (i not in orbited) and ((i+T.order()) not in orbited):
s=recurse_find_parking_function(T,i).limit(x=0)*factorial(T.order())
print "Placing the root at "+str(i)+": "+str(s(x=0))
print recurse_find_parking_function(T,i)
print ""
 Placing the root at 1: 3 x |--> -(x - e^(2*x) + e^x)/x^2  Placing the root at 1: 16 x |--> -1/2*(3*x^2 + 2*x*e^x + 2*e^(2*x) - 2*e^(3*x))/x^3 Placing the root at 0: 12 x |--> -(x^2 + 2*e^(2*x) - e^(3*x) - e^x)/x^3  Placing the root at 1: 82 x |--> -1/2*(3*x^3 + 2*(x - 1)*e^(2*x) - 2*x*e^x + 4*e^(3*x) - 2*e^(4*x))/x^4 Placing the root at 2: 125 x |--> -1/6*(16*x^3 + 9*x^2*e^x + 6*x*e^(2*x) + 6*e^(3*x) - 6*e^(4*x))/x^4  Placing the root at 1: 98 x |--> -(2*x^3 + x^2*e^x - e^(2*x) + 2*e^(3*x) - e^(4*x))/x^4 Placing the root at 0: 60 x |--> -(x^3 - 3*e^(2*x) + 3*e^(3*x) - e^(4*x) + e^x)/x^4  Placing the root at 1: 785 x |--> -1/6*(16*x^4 - 9*x^2*e^x + 6*(x - 1)*e^(3*x) + 3*(3*x^2 - 2*x)*e^(2*x) + 12*e^(4*x) - 6*e^(5*x))/x^5 Placing the root at 2: 1296 x |--> -1/24*(125*x^4 + 64*x^3*e^x + 36*x^2*e^(2*x) + 24*x*e^(3*x) + 24*e^(4*x) - 24*e^(5*x))/x^5 Placing the root at 0: 690 x |--> -1/4*(9*x^4 - 4*x^2*e^x + 4*(2*x - 1)*e^(3*x) - 8*x*e^(2*x) + 8*e^(4*x) - 4*e^(5*x))/x^5  Placing the root at 1: 610 x |--> -(2*x^4 - x^2*e^x + (x^2 + 1)*e^(2*x) - 3*e^(3*x) + 3*e^(4*x) - e^(5*x))/x^5 Placing the root at 2: 1040 x |--> -1/12*(49*x^4 + 24*x^3*e^x + 12*x^2*e^(2*x) - 12*e^(3*x) + 24*e^(4*x) - 12*e^(5*x))/x^5 Placing the root at 3: 905 x |--> -1/12*(41*x^4 + 18*x^3*e^x + 12*(x - 1)*e^(3*x) - 12*x*e^(2*x) + 24*e^(4*x) - 12*e^(5*x))/x^5 Placing the root at 0: 500 x |--> -1/2*(3*x^4 + 2*(x - 3)*e^(3*x) - 2*(2*x - 1)*e^(2*x) + 2*x*e^x + 6*e^(4*x) - 2*e^(5*x))/x^5  Placing the root at 1: 690 x |--> -1/2*(5*x^4 + 2*x^3*e^x + 2*e^(2*x) - 6*e^(3*x) + 6*e^(4*x) - 2*e^(5*x))/x^5 Placing the root at 0: 360 x |--> -(x^4 + 4*e^(2*x) - 6*e^(3*x) + 4*e^(4*x) - e^(5*x) - e^x)/x^5  Placing the root at 1: 7865 x |--> -1/2*(8*x^5 - 3*x^3*e^x - 5*x^2*e^(2*x) + 2*(2*x - 1)*e^(4*x) + (3*x^2 - 4*x)*e^(3*x) + 4*e^(5*x) - 2*e^(6*x))/x^6 Placing the root at 2: 9651 x |--> -1/24*(125*x^5 - 64*x^3*e^x + 24*(x - 1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 4*(16*x^3 - 9*x^2)*e^(2*x) + 48*e^(5*x) - 24*e^(6*x))/x^6 Placing the root at 3: 16807 x |--> -1/120*(1296*x^5 + 625*x^4*e^x + 320*x^3*e^(2*x) + 180*x^2*e^(3*x) + 120*x*e^(4*x) + 120*e^(5*x) - 120*e^(6*x))/x^6  Placing the root at 1: 5670 x |--> -1/6*(16*x^5 + 9*x^2*e^x + 6*(x - 3)*e^(4*x) + 3*(3*x^2 - 4*x + 2)*e^(3*x) - 6*(3*x^2 - x)*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6 Placing the root at 2: 10931 x |--> -1/24*(157*x^5 + 64*x^4*e^x - 36*x^2*e^(2*x) + 24*(x - 1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6 Placing the root at 0: 6090 x |--> -(3*x^5 - x^3*e^x + (x - 3)*e^(4*x) + (x^2 - 2*x + 1)*e^(3*x) - (x^2 - x)*e^(2*x) + 3*e^(5*x) - e^(6*x))/x^6 Placing the root at 4: 7710 x |--> -1/12*(49*x^5 - 24*x^3*e^x + 12*(x^2 + 1)*e^(3*x) + 12*(2*x^3 - x^2)*e^(2*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6 Placing the root at 5: 13682 x |--> -1/12*(104*x^5 + 49*x^4*e^x + 24*x^3*e^(2*x) + 12*x^2*e^(3*x) - 12*e^(4*x) + 24*e^(5*x) - 12*e^(6*x))/x^6  Placing the root at 1: 4380 x |--> -(2*x^5 + x^2*e^x + (x^2 + 4)*e^(3*x) - (2*x^2 + 1)*e^(2*x) - 6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6 Placing the root at 2: 8670 x |--> -1/12*(61*x^5 + 24*x^4*e^x - 12*x^2*e^(2*x) + 12*(x^2 + 1)*e^(3*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6  Placing the root at 1: 6660 x |--> -1/12*(41*x^5 - 18*x^3*e^x + 12*(x - 3)*e^(4*x) - 12*(2*x - 1)*e^(3*x) + 6*(3*x^3 + 2*x)*e^(2*x) + 36*e^(5*x) - 12*e^(6*x))/x^6 Placing the root at 2: 12146 x |--> -1/24*(181*x^5 + 82*x^4*e^x + 36*x^3*e^(2*x) + 24*(x - 1)*e^(4*x) - 24*x*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6 Placing the root at 0: 4950 x |--> -1/4*(9*x^5 + 4*x^2*e^x + 4*(2*x - 3)*e^(4*x) - 4*(4*x - 1)*e^(3*x) - 4*(x^2 - 2*x)*e^(2*x) + 12*e^(5*x) - 4*e^(6*x))/x^6 Placing the root at 5: 9800 x |--> -1/4*(23*x^5 + 9*x^4*e^x - 4*x^2*e^(2*x) + 4*(2*x - 1)*e^(4*x) - 8*x*e^(3*x) + 8*e^(5*x) - 4*e^(6*x))/x^6  Placing the root at 1: 5040 x |--> -1/2*(5*x^5 - 2*x^3*e^x + 2*(x^3 - 1)*e^(2*x) + 8*e^(3*x) - 12*e^(4*x) + 8*e^(5*x) - 2*e^(6*x))/x^6 Placing the root at 2: 9480 x |--> -1/4*(23*x^5 + 10*x^4*e^x + 4*x^3*e^(2*x) + 4*e^(3*x) - 12*e^(4*x) + 12*e^(5*x) - 4*e^(6*x))/x^6 Placing the root at 3: 7380 x |--> -1/6*(25*x^5 + 9*x^4*e^x + 6*(x - 3)*e^(4*x) - 6*(2*x - 1)*e^(3*x) + 6*x*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6 Placing the root at 0: 3540 x |--> -1/2*(3*x^5 + 2*(x - 6)*e^(4*x) - 2*(3*x - 4)*e^(3*x) + 2*(3*x - 1)*e^(2*x) - 2*x*e^x + 8*e^(5*x) - 2*e^(6*x))/x^6  Placing the root at 1: 5520 x |--> -(3*x^5 + x^4*e^x - e^(2*x) + 4*e^(3*x) - 6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6 Placing the root at 0: 2520 x |--> -(x^5 - 5*e^(2*x) + 10*e^(3*x) - 10*e^(4*x) + 5*e^(5*x) - e^(6*x) + e^x)/x^6  Placing the root at 1: 112273 x |--> -1/48*(375*x^6 - 128*x^4*e^x - 200*x^3*e^(2*x) + 48*(2*x - 1)*e^(5*x) + 24*(3*x^2 - 4*x)*e^(4*x) + 8*(16*x^3 - 15*x^2)*e^(3*x) + 96*e^(6*x) - 48*e^(7*x))/x^7 Placing the root at 2: 144865 x |--> -1/120*(1296*x^6 - 625*x^4*e^x + 120*(x - 1)*e^(5*x) + 60*(3*x^2 - 2*x)*e^(4*x) + 20*(16*x^3 - 9*x^2)*e^(3*x) + 5*(125*x^4 - 64*x^3)*e^(2*x) + 240*e^(6*x) - 120*e^(7*x))/x^7 Placing the root at 3: 262144 x |--> -1/720*(16807*x^6 + 7776*x^5*e^x + 3750*x^4*e^(2*x) + 1920*x^3*e^(3*x) + 1080*x^2*e^(4*x) + 720*x*e^(5*x) + 720*e^(6*x) - 720*e^(7*x))/x^7 Placing the root at 0: 104160 x |--> -1/36*(256*x^6 - 81*x^4*e^x - 108*x^3*e^(2*x) - 144*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) + 36*(3*x^2 - 2*x)*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7  Placing the root at 1: 89530 x |--> -1/8*(49*x^6 - 16*x^4*e^x - 24*x^3*e^(2*x) + 8*(x - 3)*e^(5*x) + 8*(x^2 - 2*x + 1)*e^(4*x) + 8*(2*x^3 - x^2 + x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 2: 117614 x |--> -1/12*(104*x^6 - 49*x^4*e^x + 12*(x^2 + 1)*e^(4*x) + 12*(2*x^3 - x^2)*e^(3*x) + (49*x^4 - 24*x^3)*e^(2*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 3: 215488 x |--> -1/360*(6841*x^6 + 3120*x^5*e^x + 1470*x^4*e^(2*x) + 720*x^3*e^(3*x) + 360*x^2*e^(4*x) - 360*e^(5*x) + 720*e^(6*x) - 360*e^(7*x))/x^7 Placing the root at 4: 80682 x |--> -1/24*(125*x^6 + 64*x^3*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 4*(32*x^3 - 9*x^2)*e^(2*x) + 8*(8*x^3 - 9*x^2 + 3*x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 5: 162365 x |--> -1/240*(3217*x^6 + 1250*x^5*e^x - 640*x^3*e^(2*x) + 240*(x - 1)*e^(5*x) + 120*(3*x^2 - 2*x)*e^(4*x) + 40*(16*x^3 - 9*x^2)*e^(3*x) + 480*e^(6*x) - 240*e^(7*x))/x^7 Placing the root at 0: 80500 x |--> -1/6*(32*x^6 - 9*x^4*e^x + 6*(x - 3)*e^(5*x) - 6*(4*x^2 - x)*e^(3*x) + 3*(5*x^2 - 4*x + 2)*e^(4*x) - 3*(2*x^3 - 3*x^2)*e^(2*x) + 18*e^(6*x) - 6*e^(7*x))/x^7  Placing the root at 1: 77105 x |--> -1/8*(41*x^6 - 12*x^4*e^x + 8*(2*x - 3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 4*(3*x^3 - 2*x^2)*e^(2*x) + 4*(3*x^3 - 2*x^2 + 4*x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 0: 65135 x |--> -1/2*(8*x^6 + 3*x^3*e^x + 2*(2*x - 3)*e^(5*x) - 4*(2*x^2 - x)*e^(3*x) + (3*x^2 - 8*x + 2)*e^(4*x) - (3*x^3 - 5*x^2)*e^(2*x) + 6*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 2: 104027 x |--> -1/24*(181*x^6 - 82*x^4*e^x + 24*(x - 3)*e^(5*x) - 24*(2*x - 1)*e^(4*x) + 12*(3*x^3 + 2*x)*e^(3*x) + 2*(41*x^4 - 18*x^3)*e^(2*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 3: 193613 x |--> -1/360*(6073*x^6 + 2715*x^5*e^x + 1230*x^4*e^(2*x) + 540*x^3*e^(3*x) + 360*(x - 1)*e^(5*x) - 360*x*e^(4*x) + 720*e^(6*x) - 360*e^(7*x))/x^7 Placing the root at 4: 93002 x |--> -1/24*(157*x^6 - 64*x^4*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 4*(16*x^4 + 9*x^2)*e^(2*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 5: 177485 x |--> -1/720*(10931*x^6 + 4710*x^5*e^x + 1920*x^4*e^(2*x) - 1080*x^2*e^(3*x) + 720*(x - 1)*e^(5*x) + 360*(3*x^2 - 2*x)*e^(4*x) + 1440*e^(6*x) - 720*e^(7*x))/x^7 Placing the root at 6: 136353 x |--> -1/144*(1573*x^6 + 576*x^5*e^x - 216*x^3*e^(2*x) - 360*x^2*e^(3*x) + 144*(2*x - 1)*e^(5*x) + 72*(3*x^2 - 4*x)*e^(4*x) + 288*e^(6*x) - 144*e^(7*x))/x^7  Placing the root at 1: 46410 x |--> -1/6*(16*x^6 - 9*x^2*e^x + 6*(x - 6)*e^(5*x) + 3*(3*x^2 - 6*x + 8)*e^(4*x) - 3*(9*x^2 - 6*x + 2)*e^(3*x) + 3*(9*x^2 - 2*x)*e^(2*x) + 24*e^(6*x) - 6*e^(7*x))/x^7 Placing the root at 2: 101962 x |--> -1/24*(189*x^6 + 64*x^5*e^x + 36*x^2*e^(2*x) + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 0: 58170 x |--> -1/4*(15*x^6 - 4*x^4*e^x + 4*(x - 6)*e^(5*x) - 4*(3*x - 4)*e^(4*x) - 4*(x^3 + x)*e^(2*x) + 4*(x^3 + 3*x - 1)*e^(3*x) + 16*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 5: 80850 x |--> -1/4*(23*x^6 - 10*x^4*e^x + 4*(x^3 - 1)*e^(3*x) + 2*(5*x^4 - 2*x^3)*e^(2*x) + 16*e^(4*x) - 24*e^(5*x) + 16*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 6: 153426 x |--> -1/12*(158*x^6 + 69*x^5*e^x + 30*x^4*e^(2*x) + 12*x^3*e^(3*x) + 12*e^(4*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7  Placing the root at 1: 64260 x |--> -1/12*(49*x^6 + 24*x^3*e^x + 12*(x^2 + 4)*e^(4*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(3*x) - 12*(4*x^3 - x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 2: 131334 x |--> -1/24*(257*x^6 + 98*x^5*e^x - 48*x^3*e^(2*x) + 24*(x^2 + 1)*e^(4*x) + 24*(2*x^3 - x^2)*e^(3*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 0: 62160 x |--> -(4*x^6 - x^4*e^x + 2*x^2*e^(2*x) + 2*(x^2 + 2)*e^(4*x) - (4*x^2 + 1)*e^(3*x) - 6*e^(5*x) + 4*e^(6*x) - e^(7*x))/x^7  Placing the root at 1: 55230 x |--> -1/12*(41*x^6 + 18*x^3*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x - 4)*e^(4*x) - 12*(3*x^3 + x)*e^(2*x) + 6*(3*x^3 + 6*x - 2)*e^(3*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 2: 115507 x |--> -1/12*(111*x^6 + 41*x^5*e^x - 18*x^3*e^(2*x) + 12*(x - 3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 6*(3*x^3 + 2*x)*e^(3*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 0: 50190 x |--> -(3*x^6 + x^3*e^x + (x - 6)*e^(5*x) + (x^2 - 3*x + 4)*e^(4*x) - (2*x^2 - 3*x + 1)*e^(3*x) - (x^3 - x^2 + x)*e^(2*x) + 4*e^(6*x) - e^(7*x))/x^7 Placing the root at 4: 73500 x |--> -1/12*(61*x^6 - 24*x^4*e^x + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) + 12*(2*x^4 + x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 5: 142674 x |--> -1/24*(289*x^6 + 122*x^5*e^x + 48*x^4*e^(2*x) - 24*x^2*e^(3*x) + 24*(x^2 + 1)*e^(4*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 6: 107590 x |--> -1/24*(203*x^6 + 72*x^5*e^x - 24*x^3*e^(2*x) + 24*(x - 3)*e^(5*x) + 24*(x^2 - 2*x + 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7  Placing the root at 1: 41580 x |--> -1/2*(5*x^6 + 2*x^3*e^x + 2*(x^3 - 5)*e^(3*x) - 2*(2*x^3 - 1)*e^(2*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 2: 89250 x |--> -1/2*(14*x^6 + 5*x^5*e^x - 2*x^3*e^(2*x) + 2*(x^3 - 1)*e^(3*x) + 8*e^(4*x) - 12*e^(5*x) + 8*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 4: 80220 x |--> -1/12*(73*x^6 + 24*x^5*e^x + 12*x^2*e^(2*x) + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 0: 35700 x |--> -(2*x^6 - x^2*e^x + (x^2 + 10)*e^(4*x) + (3*x^2 + 1)*e^(2*x) - (3*x^2 + 5)*e^(3*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7  Placing the root at 1: 83090 x |--> -1/4*(23*x^6 - 9*x^4*e^x + 4*(2*x - 3)*e^(5*x) - 4*(4*x - 1)*e^(4*x) - 4*(x^2 - 2*x)*e^(3*x) + (9*x^4 + 4*x^2)*e^(2*x) + 12*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 2: 160986 x |--> -1/36*(490*x^6 + 207*x^5*e^x + 81*x^4*e^(2*x) - 36*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) - 72*x*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7 Placing the root at 0: 56700 x |--> -1/8*(27*x^6 + 8*x^3*e^x + 24*x^2*e^(2*x) + 24*(x - 1)*e^(5*x) - 8*(6*x - 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7  Placing the root at 1: 62160 x |--> -1/6*(25*x^6 - 9*x^4*e^x + 6*(x - 6)*e^(5*x) - 6*(3*x - 4)*e^(4*x) + 6*(3*x - 1)*e^(3*x) + 3*(3*x^4 - 2*x)*e^(2*x) + 24*e^(6*x) - 6*e^(7*x))/x^7 Placing the root at 2: 124012 x |--> -1/12*(123*x^6 + 50*x^5*e^x + 18*x^4*e^(2*x) + 12*(x - 3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 12*x*e^(3*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 5: 90650 x |--> -1/8*(55*x^6 + 18*x^5*e^x + 8*x^2*e^(2*x) + 8*(2*x - 3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 8*(x^2 - 2*x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 0: 40320 x |--> -1/4*(9*x^6 - 4*x^2*e^x + 8*(x - 3)*e^(5*x) - 8*(3*x - 2)*e^(4*x) - 4*(x^2 - 6*x + 1)*e^(3*x) + 8*(x^2 - x)*e^(2*x) + 16*e^(6*x) - 4*e^(7*x))/x^7  Placing the root at 1: 46200 x |--> -(3*x^6 - x^4*e^x + (x^4 + 1)*e^(2*x) - 5*e^(3*x) + 10*e^(4*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7 Placing the root at 2: 94920 x |--> -1/3*(23*x^6 + 9*x^5*e^x + 3*x^4*e^(2*x) - 3*e^(3*x) + 12*e^(4*x) - 18*e^(5*x) + 12*e^(6*x) - 3*e^(7*x))/x^7 Placing the root at 3: 67200 x |--> -1/12*(59*x^6 + 18*x^5*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x - 4)*e^(4*x) + 12*(3*x - 1)*e^(3*x) - 12*x*e^(2*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 0: 28560 x |--> -1/2*(3*x^6 + 2*(x - 10)*e^(5*x) - 4*(2*x - 5)*e^(4*x) - 2*(4*x - 1)*e^(2*x) + 2*(6*x - 5)*e^(3*x) + 2*x*e^x + 10*e^(6*x) - 2*e^(7*x))/x^7  Placing the root at 1: 49560 x |--> -1/2*(7*x^6 + 2*x^5*e^x + 2*e^(2*x) - 10*e^(3*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 0: 20160 x |--> -(x^6 + 6*e^(2*x) - 15*e^(3*x) + 20*e^(4*x) - 15*e^(5*x) + 6*e^(6*x) - e^(7*x) - e^x)/x^7  Placing the root at 1: 1694966 x |--> -1/36*(500*x^7 - 144*x^5*e^x - 177*x^4*e^(2*x) - 204*x^3*e^(3*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) + 48*(2*x^3 - 3*x^2)*e^(4*x) + 72*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 2: 1919820 x |--> -1/120*(1944*x^7 - 625*x^5*e^x - 945*x^4*e^(2*x) + 120*(2*x - 1)*e^(6*x) + 60*(3*x^2 - 4*x)*e^(5*x) + 20*(16*x^3 - 15*x^2)*e^(4*x) + 125*(5*x^4 - 4*x^3)*e^(3*x) + 240*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 3: 2567748 x |--> -1/720*(16807*x^7 - 7776*x^5*e^x + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 - 64*x^3)*e^(3*x) + 6*(1296*x^5 - 625*x^4)*e^(2*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 4: 4782969 x |--> -1/5040*(262144*x^7 + 117649*x^6*e^x + 54432*x^5*e^(2*x) + 26250*x^4*e^(3*x) + 13440*x^3*e^(4*x) + 7560*x^2*e^(5*x) + 5040*x*e^(6*x) + 5040*e^(7*x) - 5040*e^(8*x))/x^8  Placing the root at 1: 1308412 x |--> -1/12*(125*x^7 - 32*x^5*e^x + 12*(x - 3)*e^(6*x) + 6*(5*x^2 - 4*x + 2)*e^(5*x) - 2*(38*x^3 - 9*x^2)*e^(3*x) - 2*(9*x^4 - 16*x^3)*e^(2*x) + 4*(8*x^3 - 12*x^2 + 3*x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1376648 x |--> -1/120*(1296*x^7 + 625*x^4*e^x + 120*(x - 3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 10*(125*x^4 - 32*x^3)*e^(2*x) + 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 5*(125*x^4 - 128*x^3 + 36*x^2)*e^(3*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 3: 2858052 x |--> -1/720*(20695*x^7 + 7776*x^6*e^x - 3750*x^4*e^(2*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 - 64*x^3)*e^(3*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 1350300 x |--> -1/18*(196*x^7 - 54*x^5*e^x - 63*x^4*e^(2*x) + 18*(x - 3)*e^(6*x) + 9*(5*x^2 - 4*x + 2)*e^(5*x) - 27*(2*x^3 - x^2)*e^(3*x) + 18*(2*x^3 - 4*x^2 + x)*e^(4*x) + 54*e^(7*x) - 18*e^(8*x))/x^8 Placing the root at 5: 1556968 x |--> -1/12*(156*x^7 - 49*x^5*e^x - 73*x^4*e^(2*x) + 12*(x - 3)*e^(6*x) + 12*(x^2 - 2*x + 1)*e^(5*x) + (49*x^4 - 36*x^3)*e^(3*x) + 12*(2*x^3 - x^2 + x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 6: 2107000 x |--> -1/360*(6841*x^7 - 3120*x^5*e^x + 360*(x^2 + 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) + 30*(104*x^5 - 49*x^4)*e^(2*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 7: 3959426 x |--> -1/360*(15392*x^7 + 6841*x^6*e^x + 3120*x^5*e^(2*x) + 1470*x^4*e^(3*x) + 720*x^3*e^(4*x) + 360*x^2*e^(5*x) - 360*e^(6*x) + 720*e^(7*x) - 360*e^(8*x))/x^8  Placing the root at 1: 1041880 x |--> -1/6*(49*x^7 - 12*x^5*e^x + 12*(x^2 + 2)*e^(5*x) + 6*(2*x^3 - 4*x^2 - 1)*e^(4*x) - 12*(2*x^3 - x^2)*e^(3*x) - 6*(x^4 - 2*x^3)*e^(2*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 2: 1115632 x |--> -1/12*(104*x^7 + 49*x^4*e^x + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 2*(49*x^4 - 12*x^3)*e^(2*x) + (49*x^4 - 48*x^3 + 12*x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2339960 x |--> -1/360*(8401*x^7 + 3120*x^6*e^x - 1470*x^4*e^(2*x) + 360*(x^2 + 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8  Placing the root at 1: 1055684 x |--> -1/48*(375*x^7 + 128*x^4*e^x + 48*(2*x - 3)*e^(6*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(41*x^3 - 15*x^2)*e^(3*x) - 8*(16*x^4 - 25*x^3)*e^(2*x) + 32*(4*x^3 - 6*x^2 + 3*x)*e^(4*x) + 144*e^(7*x) - 48*e^(8*x))/x^8 Placing the root at 0: 1161020 x |--> -1/36*(328*x^7 - 81*x^5*e^x + 36*(2*x - 3)*e^(6*x) + 18*(3*x^2 - 8*x + 2)*e^(5*x) - 18*(6*x^3 - 5*x^2)*e^(3*x) - 54*(x^4 - x^3)*e^(2*x) + 18*(3*x^3 - 8*x^2 + 4*x)*e^(4*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 2: 1569148 x |--> -1/240*(3217*x^7 - 1250*x^5*e^x + 240*(x - 3)*e^(6*x) + 120*(3*x^2 - 4*x + 2)*e^(5*x) - 40*(32*x^3 - 9*x^2)*e^(3*x) + 10*(125*x^5 + 64*x^3)*e^(2*x) + 80*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 720*e^(7*x) - 240*e^(8*x))/x^8 Placing the root at 3: 3094302 x |--> -1/720*(23195*x^7 + 9651*x^6*e^x + 3750*x^5*e^(2*x) - 1920*x^3*e^(3*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 4: 2296070 x |--> -1/720*(16039*x^7 + 5625*x^6*e^x - 1920*x^4*e^(2*x) - 3000*x^3*e^(3*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) + 120*(16*x^3 - 15*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 5: 1375024 x |--> -1/48*(543*x^7 - 164*x^5*e^x - 236*x^4*e^(2*x) + 48*(2*x - 3)*e^(6*x) - 48*(4*x - 1)*e^(5*x) + 24*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 4*(41*x^4 - 18*x^3 + 12*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8 Placing the root at 6: 1888992 x |--> -1/360*(6073*x^7 - 2715*x^5*e^x + 360*(x - 3)*e^(6*x) - 360*(2*x - 1)*e^(5*x) + 180*(3*x^3 + 2*x)*e^(4*x) + 30*(41*x^4 - 18*x^3)*e^(3*x) + 15*(181*x^5 - 82*x^4)*e^(2*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 7: 3586178 x |--> -1/720*(27659*x^7 + 12146*x^6*e^x + 5430*x^5*e^(2*x) + 2460*x^4*e^(3*x) + 1080*x^3*e^(4*x) + 720*(x - 1)*e^(6*x) - 720*x*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8  Placing the root at 1: 839720 x |--> -1/8*(49*x^7 + 16*x^4*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x + 4)*e^(5*x) - 8*(2*x^4 - 3*x^3)*e^(2*x) + 8*(2*x^3 - 2*x^2 + 3*x - 1)*e^(4*x) - 8*(5*x^3 - x^2 + x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1266552 x |--> -1/24*(257*x^7 - 98*x^5*e^x + 24*(x^2 + 4)*e^(5*x) + 24*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 24*(4*x^3 - x^2)*e^(3*x) + 2*(49*x^5 + 24*x^3)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 3: 2525180 x |--> -1/120*(3127*x^7 + 1285*x^6*e^x + 490*x^5*e^(2*x) - 240*x^3*e^(3*x) + 120*(x^2 + 1)*e^(5*x) + 120*(2*x^3 - x^2)*e^(4*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 4: 1851948 x |--> -1/72*(1279*x^7 + 441*x^6*e^x - 144*x^4*e^(2*x) - 216*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) + 72*(2*x^3 - x^2 + x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 5: 984256 x |--> -1/24*(181*x^7 + 82*x^4*e^x + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) - 4*(41*x^4 - 9*x^3)*e^(2*x) + 2*(41*x^4 - 36*x^3 - 12*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 6: 2091712 x |--> -1/720*(14861*x^7 + 5430*x^6*e^x - 2460*x^4*e^(2*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) + 60*(41*x^4 - 18*x^3)*e^(3*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 895160 x |--> -1/6*(41*x^7 - 9*x^5*e^x + 15*x^3*e^(2*x) + 6*(x - 6)*e^(6*x) + 6*(x^2 - 3*x + 4)*e^(5*x) + 3*(3*x^3 - 4*x^2 + 6*x - 2)*e^(4*x) - 6*(4*x^3 - x^2 + x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8  Placing the root at 1: 720160 x |--> -1/8*(41*x^7 + 12*x^4*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x - 2)*e^(5*x) - 8*(3*x^3 - 2*x^2 + 2*x)*e^(3*x) + 4*(3*x^3 - 2*x^2 + 12*x - 2)*e^(4*x) - 4*(3*x^4 - 3*x^3 + 2*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1110536 x |--> -1/12*(111*x^7 - 41*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) - 12*(3*x^3 + x)*e^(3*x) + 6*(3*x^3 + 6*x - 2)*e^(4*x) + (41*x^5 + 18*x^3)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2246692 x |--> -1/720*(16501*x^7 + 6660*x^6*e^x + 2460*x^5*e^(2*x) - 1080*x^3*e^(3*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 4: 1621844 x |--> -1/144*(2203*x^7 + 738*x^6*e^x - 216*x^4*e^(2*x) + 144*(2*x - 3)*e^(6*x) - 144*(4*x - 1)*e^(5*x) - 72*(3*x^3 - 2*x^2)*e^(3*x) + 72*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 432*e^(7*x) - 144*e^(8*x))/x^8  Placing the root at 1: 1225924 x |--> -1/48*(471*x^7 - 128*x^5*e^x + 48*(2*x - 3)*e^(6*x) - 96*(2*x^2 - x)*e^(4*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(16*x^4 - 9*x^3)*e^(2*x) + 8*(16*x^4 - 9*x^3 + 15*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8 Placing the root at 2: 1725948 x |--> -1/720*(10931*x^7 - 4710*x^5*e^x + 720*(x - 3)*e^(6*x) + 360*(3*x^2 - 4*x + 2)*e^(5*x) - 720*(3*x^2 - x)*e^(4*x) + 120*(16*x^4 + 9*x^2)*e^(3*x) + 30*(157*x^5 - 64*x^4)*e^(2*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 3: 3323678 x |--> -1/720*(25355*x^7 + 10931*x^6*e^x + 4710*x^5*e^(2*x) + 1920*x^4*e^(3*x) - 1080*x^2*e^(4*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 976640 x |--> -1/36*(256*x^7 + 81*x^4*e^x + 36*(2*x - 3)*e^(6*x) + 36*(3*x^2 - 4*x + 1)*e^(5*x) - 36*(7*x^2 - 2*x)*e^(4*x) - 36*(3*x^3 - 4*x^2)*e^(3*x) - 27*(3*x^4 - 4*x^3)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 7: 2152822 x |--> -1/36*(744*x^7 + 256*x^6*e^x - 81*x^4*e^(2*x) - 108*x^3*e^(3*x) - 144*x^2*e^(4*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) + 72*e^(7*x) - 36*e^(8*x))/x^8  Placing the root at 1: 1066800 x |--> -1/8*(69*x^7 - 20*x^5*e^x - 28*x^4*e^(2*x) + 8*(x - 6)*e^(6*x) - 8*(3*x - 4)*e^(5*x) + 8*(x^3 + 3*x - 1)*e^(4*x) + 4*(5*x^4 - 2*x^3 - 2*x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1492848 x |--> -1/12*(158*x^7 - 69*x^5*e^x + 12*(x^3 - 1)*e^(4*x) + 6*(5*x^4 - 2*x^3)*e^(3*x) + 3*(23*x^5 - 10*x^4)*e^(2*x) + 48*e^(5*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2872212 x |--> -1/120*(3653*x^7 + 1580*x^6*e^x + 690*x^5*e^(2*x) + 300*x^4*e^(3*x) + 120*x^3*e^(4*x) + 120*e^(5*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 4: 750456 x |--> -1/24*(125*x^7 - 64*x^3*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) + 12*(16*x^3 - 3*x^2)*e^(2*x) + 4*(16*x^3 - 27*x^2 + 18*x - 6)*e^(4*x) - 12*(16*x^3 - 9*x^2 + 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 1709148 x |--> -1/120*(1921*x^7 + 625*x^6*e^x + 320*x^3*e^(2*x) + 120*(x - 3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 20*(32*x^3 - 9*x^2)*e^(3*x) + 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 0: 874440 x |--> -1/6*(40*x^7 - 9*x^5*e^x + 6*(x - 6)*e^(6*x) + 3*(3*x^2 - 6*x + 8)*e^(5*x) - 3*(2*x^4 + 3*x^2)*e^(2*x) - 3*(2*x^3 - 9*x^2 + 2*x)*e^(3*x) + 3*(2*x^3 - 9*x^2 + 6*x - 2)*e^(4*x) + 24*e^(7*x) - 6*e^(8*x))/x^8  Placing the root at 1: 967400 x |--> -1/8*(61*x^7 - 16*x^5*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x + 4)*e^(5*x) - 8*(2*x^2 - 3*x + 1)*e^(4*x) - 8*(2*x^4 - x^3)*e^(2*x) + 8*(2*x^4 - x^3 + x^2 - x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1384152 x |--> -1/24*(289*x^7 - 122*x^5*e^x + 24*(x^2 + 4)*e^(5*x) - 24*(2*x^2 + 1)*e^(4*x) + 24*(2*x^4 + x^2)*e^(3*x) + 2*(61*x^5 - 24*x^4)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 3: 2697212 x |--> -1/120*(3397*x^7 + 1445*x^6*e^x + 610*x^5*e^(2*x) + 240*x^4*e^(3*x) - 120*x^2*e^(4*x) + 120*(x^2 + 1)*e^(5*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 4: 875896 x |--> -1/24*(157*x^7 + 64*x^4*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) - 4*(32*x^4 + 9*x^2)*e^(2*x) + 4*(16*x^4 + 27*x^2 - 6*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 1901788 x |--> -1/360*(6643*x^7 + 2355*x^6*e^x - 960*x^4*e^(2*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) + 60*(16*x^4 + 9*x^2)*e^(3*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 0: 751520 x |--> -1/6*(32*x^7 + 9*x^4*e^x + 6*(x - 6)*e^(6*x) + 3*(5*x^2 - 6*x + 8)*e^(5*x) - 3*(13*x^2 - 6*x + 2)*e^(4*x) - 3*(2*x^3 - 11*x^2 + 2*x)*e^(3*x) - 3*(3*x^4 - 2*x^3 + 3*x^2)*e^(2*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 7: 1693692 x |--> -1/36*(575*x^7 + 192*x^6*e^x - 54*x^4*e^(2*x) + 36*(x - 3)*e^(6*x) - 36*(4*x^2 - x)*e^(4*x) + 18*(5*x^2 - 4*x + 2)*e^(5*x) - 18*(2*x^3 - 3*x^2)*e^(3*x) + 108*e^(7*x) - 36*e^(8*x))/x^8  Placing the root at 1: 1093680 x |--> -1/8*(69*x^7 - 18*x^5*e^x + 24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 6*(3*x^4 + 4*x^2)*e^(3*x) - 2*(9*x^4 - 4*x^3)*e^(2*x) + 24*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1562288 x |--> -1/36*(490*x^7 - 207*x^5*e^x + 36*(2*x - 3)*e^(6*x) - 36*(4*x - 1)*e^(5*x) - 36*(x^2 - 2*x)*e^(4*x) + 9*(9*x^4 + 4*x^2)*e^(3*x) + 9*(23*x^5 - 9*x^4)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 3: 3037930 x |--> -1/360*(11499*x^7 + 4900*x^6*e^x + 2070*x^5*e^(2*x) + 810*x^4*e^(3*x) - 360*x^2*e^(4*x) + 360*(2*x - 1)*e^(6*x) - 720*x*e^(5*x) + 720*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 4: 1311044 x |--> -1/144*(1573*x^7 - 576*x^5*e^x + 144*(2*x - 3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 - 5*x^2)*e^(3*x) + 72*(8*x^5 + 3*x^3)*e^(2*x) + 432*e^(7*x) - 144*e^(8*x))/x^8 Placing the root at 5: 2646406 x |--> -1/720*(19479*x^7 + 7865*x^6*e^x + 2880*x^5*e^(2*x) - 1080*x^3*e^(3*x) - 1800*x^2*e^(4*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 848820 x |--> -1/2*(12*x^7 + 3*x^4*e^x + 8*x^3*e^(2*x) + 6*(x - 1)*e^(6*x) - 6*(2*x^2 - x)*e^(4*x) + (3*x^2 - 12*x + 2)*e^(5*x) - 3*(2*x^3 - 3*x^2)*e^(3*x) + 6*e^(7*x) - 2*e^(8*x))/x^8  Placing the root at 1: 815920 x |--> -1/4*(25*x^7 - 6*x^5*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(3*x^4 + 2*x^2)*e^(2*x) + 2*(3*x^4 + 4*x^2 - 4*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 2: 1198736 x |--> -1/12*(123*x^7 - 50*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) + 6*(3*x^4 - 2*x)*e^(3*x) + 2*(25*x^5 - 9*x^4)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2375716 x |--> -1/180*(4429*x^7 + 1845*x^6*e^x + 750*x^5*e^(2*x) + 270*x^4*e^(3*x) + 180*(x - 3)*e^(6*x) - 180*(2*x - 1)*e^(5*x) + 180*x*e^(4*x) + 540*e^(7*x) - 180*e^(8*x))/x^8 Placing the root at 4: 974456 x |--> -1/24*(189*x^7 - 64*x^5*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 - 2*x)*e^(3*x) + 4*(16*x^5 - 9*x^2)*e^(2*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 2022748 x |--> -1/360*(7283*x^7 + 2835*x^6*e^x + 960*x^5*e^(2*x) + 540*x^2*e^(3*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 6: 1418564 x |--> -1/144*(1861*x^7 + 576*x^6*e^x + 216*x^3*e^(2*x) + 144*(2*x - 3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 - 5*x^2)*e^(3*x) + 432*e^(7*x) - 144*e^(8*x))/x^8 Placing the root at 0: 601720 x |--> -1/2*(8*x^7 - 3*x^3*e^x + 4*(x - 3)*e^(6*x) + (3*x^2 - 12*x + 8)*e^(5*x) - (11*x^2 - 12*x + 2)*e^(4*x) + (6*x^3 - 5*x^2)*e^(2*x) - (3*x^3 - 13*x^2 + 4*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8  Placing the root at 1: 425040 x |--> -1/6*(16*x^7 + 9*x^2*e^x + 6*(x - 10)*e^(6*x) + 3*(3*x^2 - 8*x + 20)*e^(5*x) - 6*(6*x^2 - 6*x + 5)*e^(4*x) - 6*(6*x^2 - x)*e^(2*x) + 6*(9*x^2 - 4*x + 1)*e^(3*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 2: 1046136 x |--> -1/24*(221*x^7 + 64*x^6*e^x - 36*x^2*e^(2*x) + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 - 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 604800 x |--> -1/2*(9*x^7 - 2*x^5*e^x + 2*(x - 10)*e^(6*x) - 4*(2*x - 5)*e^(5*x) + 2*(6*x - 5)*e^(4*x) + 2*(x^4 - 4*x + 1)*e^(3*x) - 2*(x^4 - x)*e^(2*x) + 10*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 6: 913920 x |--> -1/3*(23*x^7 - 9*x^5*e^x + 3*(x^4 + 1)*e^(3*x) + 3*(3*x^5 - x^4)*e^(2*x) - 15*e^(4*x) + 30*e^(5*x) - 30*e^(6*x) + 15*e^(7*x) - 3*e^(8*x))/x^8 Placing the root at 7: 1846824 x |--> -1/6*(113*x^7 + 46*x^6*e^x + 18*x^5*e^(2*x) + 6*x^4*e^(3*x) - 6*e^(4*x) + 24*e^(5*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8  Placing the root at 1: 596400 x |--> -1/12*(49*x^7 - 24*x^3*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(2*x^3 - 3*x^2 - 5)*e^(4*x) - 12*(6*x^3 - 3*x^2 - 1)*e^(3*x) + 12*(6*x^3 - x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1376312 x |--> -1/12*(153*x^7 + 49*x^6*e^x + 24*x^3*e^(2*x) + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 12*(4*x^3 - x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 5: 762720 x |--> -1/4*(23*x^7 + 10*x^4*e^x + 4*(x^3 - 5)*e^(4*x) + 2*(5*x^4 - 4*x^3 + 2)*e^(3*x) - 4*(5*x^4 - x^3)*e^(2*x) + 40*e^(5*x) - 40*e^(6*x) + 20*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 6: 1647408 x |--> -1/24*(385*x^7 + 138*x^6*e^x - 60*x^4*e^(2*x) + 24*(x^3 - 1)*e^(4*x) + 12*(5*x^4 - 2*x^3)*e^(3*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 673680 x |--> -(5*x^7 - x^5*e^x + (x^2 + 10)*e^(5*x) + (x^3 - 3*x^2 - 5)*e^(4*x) + (x^3 - x^2)*e^(2*x) - (2*x^3 - 3*x^2 - 1)*e^(3*x) - 10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8  Placing the root at 1: 510720 x |--> -1/12*(41*x^7 - 18*x^3*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x - 5)*e^(5*x) + 6*(3*x^3 + 12*x - 10)*e^(4*x) + 6*(9*x^3 + 2*x)*e^(2*x) - 6*(9*x^3 + 8*x - 2)*e^(3*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1202376 x |--> -1/24*(263*x^7 + 82*x^6*e^x + 36*x^3*e^(2*x) + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(3*x^3 + x)*e^(3*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 540960 x |--> -1/4*(15*x^7 + 4*x^4*e^x + 4*(x - 10)*e^(6*x) - 8*(2*x - 5)*e^(5*x) + 4*(x^3 + 6*x - 5)*e^(4*x) - 4*(2*x^3 + 4*x - 1)*e^(3*x) - 4*(x^4 - x^3 - x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 5: 855120 x |--> -1/2*(14*x^7 - 5*x^5*e^x + 2*(x^3 - 5)*e^(4*x) - 2*(2*x^3 - 1)*e^(3*x) + (5*x^5 + 2*x^3)*e^(2*x) + 20*e^(5*x) - 20*e^(6*x) + 10*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 6: 1760808 x |--> -1/24*(425*x^7 + 168*x^6*e^x + 60*x^5*e^(2*x) - 24*x^3*e^(3*x) + 24*(x^3 - 1)*e^(4*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 7: 1247400 x |--> -1/24*(277*x^7 + 90*x^6*e^x - 24*x^4*e^(2*x) + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(x^3 + x)*e^(3*x) + 24*(x^3 + 3*x - 1)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8  Placing the root at 1: 383040 x |--> -1/2*(5*x^7 - 2*x^3*e^x + 2*(x^3 - 15)*e^(4*x) - 6*(x^3 - 2)*e^(3*x) + 2*(3*x^3 - 1)*e^(2*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 2: 922320 x |--> -1/4*(33*x^7 + 10*x^6*e^x + 4*x^3*e^(2*x) + 4*(x^3 - 5)*e^(4*x) - 4*(2*x^3 - 1)*e^(3*x) + 40*e^(5*x) - 40*e^(6*x) + 20*e^(7*x) - 4*e^(8*x))/x^8  Placing the root at 1: 690480 x |--> -1/12*(61*x^7 + 24*x^4*e^x + 12*(x^2 + 10)*e^(5*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^4 + 3*x^2 + 1)*e^(3*x) - 12*(4*x^4 + x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1520792 x |--> -1/12*(175*x^7 + 61*x^6*e^x - 24*x^4*e^(2*x) + 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) + 12*(2*x^4 + x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 0: 577920 x |--> -(4*x^7 + x^4*e^x + 2*(x^2 + 5)*e^(5*x) + (6*x^2 + 1)*e^(3*x) - (6*x^2 + 5)*e^(4*x) - (x^4 + 2*x^2)*e^(2*x) - 10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8 Placing the root at 7: 1330840 x |--> -1/3*(37*x^7 + 12*x^6*e^x - 3*x^4*e^(2*x) + 6*x^2*e^(3*x) + 6*(x^2 + 2)*e^(5*x) - 3*(4*x^2 + 1)*e^(4*x) - 18*e^(6*x) + 12*e^(7*x) - 3*e^(8*x))/x^8  Placing the root at 1: 780640 x |--> -1/4*(23*x^7 + 9*x^4*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(9*x^4 + 2*x^2)*e^(2*x) + (9*x^4 + 8*x^2 - 8*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 2: 1716848 x |--> -1/72*(1187*x^7 + 414*x^6*e^x - 162*x^4*e^(2*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 18*(9*x^4 + 4*x^2)*e^(3*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 4: 1031240 x |--> -1/24*(203*x^7 - 72*x^5*e^x + 24*(x - 6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) + 24*(3*x^5 + x^3)*e^(2*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 2114700 x |--> -1/72*(1537*x^7 + 609*x^6*e^x + 216*x^5*e^(2*x) - 72*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) - 72*(x^2 - x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 0: 652680 x |--> -1/2*(9*x^7 + 2*x^4*e^x + 4*(x - 3)*e^(6*x) + 2*(x^2 - 6*x + 4)*e^(5*x) - 2*(3*x^2 - 6*x + 1)*e^(4*x) + 2*(2*x^3 - x^2)*e^(2*x) - 2*(2*x^3 - 3*x^2 + 2*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8  Placing the root at 1: 581280 x |--> -1/6*(25*x^7 + 9*x^4*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x - 5)*e^(5*x) + 6*(6*x - 5)*e^(4*x) + 3*(3*x^4 - 8*x + 2)*e^(3*x) - 6*(3*x^4 - x)*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 2: 1310736 x |--> -1/6*(74*x^7 + 25*x^6*e^x - 9*x^4*e^(2*x) + 6*(x - 6)*e^(6*x) - 6*(3*x - 4)*e^(5*x) + 6*(3*x - 1)*e^(4*x) + 3*(3*x^4 - 2*x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 4: 764400 x |--> -1/12*(73*x^7 - 24*x^5*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^5 - x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 5: 1611512 x |--> -1/12*(191*x^7 + 73*x^6*e^x + 24*x^5*e^(2*x) + 12*x^2*e^(3*x) + 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 6: 1111880 x |--> -1/24*(239*x^7 + 72*x^6*e^x + 24*x^3*e^(2*x) + 24*(x - 6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 462000 x |--> -(3*x^7 - x^3*e^x + (x - 10)*e^(6*x) + (x^2 - 4*x + 10)*e^(5*x) - (3*x^2 - 6*x + 5)*e^(4*x) - (x^3 - 3*x^2 + 4*x - 1)*e^(3*x) + (2*x^3 - x^2 + x)*e^(2*x) + 5*e^(7*x) - e^(8*x))/x^8  Placing the root at 1: 430080 x |--> -(3*x^7 + x^4*e^x + (x^4 + 6)*e^(3*x) - (2*x^4 + 1)*e^(2*x) - 15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8 Placing the root at 2: 994560 x |--> -1/6*(55*x^7 + 18*x^6*e^x - 6*x^4*e^(2*x) + 6*(x^4 + 1)*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 4: 818160 x |--> -1/12*(85*x^7 + 24*x^6*e^x - 12*x^2*e^(2*x) + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 0: 325920 x |--> -(2*x^7 + x^2*e^x + 6*(x^2 + 1)*e^(3*x) + (x^2 + 20)*e^(5*x) - (4*x^2 + 1)*e^(2*x) - (4*x^2 + 15)*e^(4*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8  Placing the root at 1: 863800 x |--> -1/8*(55*x^7 - 18*x^5*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x - 2)*e^(5*x) - 8*(x^2 - 6*x + 1)*e^(4*x) + 16*(x^2 - x)*e^(3*x) + 2*(9*x^5 - 4*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1818908 x |--> -1/72*(1295*x^7 + 495*x^6*e^x + 162*x^5*e^(2*x) + 72*x^2*e^(3*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 0: 521640 x |--> -1/8*(27*x^7 - 8*x^3*e^x + 24*(x - 2)*e^(6*x) - 8*(9*x - 4)*e^(5*x) + 24*(2*x^2 - x)*e^(3*x) - 8*(3*x^2 - 9*x + 1)*e^(4*x) + 8*(x^3 - 3*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 7: 1256220 x |--> -1/8*(90*x^7 + 27*x^6*e^x + 8*x^3*e^(2*x) + 24*x^2*e^(3*x) + 24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 24*e^(7*x) - 8*e^(8*x))/x^8  Placing the root at 1: 636720 x |--> -1/12*(59*x^7 - 18*x^5*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x - 5)*e^(5*x) - 12*(4*x - 1)*e^(3*x) + 12*(6*x - 5)*e^(4*x) + 6*(3*x^5 + 2*x)*e^(2*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1378776 x |--> -1/12*(160*x^7 + 59*x^6*e^x + 18*x^5*e^(2*x) + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) - 12*x*e^(3*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 5: 924280 x |--> -1/4*(32*x^7 + 9*x^6*e^x - 4*x^2*e^(2*x) + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) + 8*(x^2 - x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 0: 367920 x |--> -1/4*(9*x^7 + 4*x^2*e^x + 8*(x - 5)*e^(6*x) - 8*(4*x - 5)*e^(5*x) - 4*(x^2 - 12*x + 5)*e^(4*x) + 4*(3*x^2 - 8*x + 1)*e^(3*x) - 4*(3*x^2 - 2*x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8  Placing the root at 1: 467040 x |--> -1/2*(7*x^7 - 2*x^5*e^x + 2*(x^5 - 1)*e^(2*x) + 12*e^(3*x) - 30*e^(4*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 2: 1039920 x |--> -1/6*(59*x^7 + 21*x^6*e^x + 6*x^5*e^(2*x) + 6*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 3: 677040 x |--> -1/6*(34*x^7 + 9*x^6*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x - 5)*e^(5*x) - 6*(4*x - 1)*e^(3*x) + 6*(6*x - 5)*e^(4*x) + 6*x*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 0: 258720 x |--> -1/2*(3*x^7 + 2*(x - 15)*e^(6*x) - 10*(x - 4)*e^(5*x) + 10*(2*x - 3)*e^(4*x) - 4*(5*x - 3)*e^(3*x) + 2*(5*x - 1)*e^(2*x) - 2*x*e^x + 12*e^(7*x) - 2*e^(8*x))/x^8  Placing the root at 1: 493920 x |--> -(4*x^7 + x^6*e^x - e^(2*x) + 6*e^(3*x) - 15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8 Placing the root at 0: 181440 x |--> -(x^7 - 7*e^(2*x) + 21*e^(3*x) - 35*e^(4*x) + 35*e^(5*x) - 21*e^(6*x) + 7*e^(7*x) - e^(8*x) + e^x)/x^8 CPU time: 1185.43 s, Wall time: 1188.21 s Placing the root at 1: 3 x |--> -(x - e^(2*x) + e^x)/x^2 Placing the root at 1: 16 x |--> -1/2*(3*x^2 + 2*x*e^x + 2*e^(2*x) - 2*e^(3*x))/x^3 Placing the root at 0: 12 x |--> -(x^2 + 2*e^(2*x) - e^(3*x) - e^x)/x^3 Placing the root at 1: 82 x |--> -1/2*(3*x^3 + 2*(x - 1)*e^(2*x) - 2*x*e^x + 4*e^(3*x) - 2*e^(4*x))/x^4 Placing the root at 2: 125 x |--> -1/6*(16*x^3 + 9*x^2*e^x + 6*x*e^(2*x) + 6*e^(3*x) - 6*e^(4*x))/x^4 Placing the root at 1: 98 x |--> -(2*x^3 + x^2*e^x - e^(2*x) + 2*e^(3*x) - e^(4*x))/x^4 Placing the root at 0: 60 x |--> -(x^3 - 3*e^(2*x) + 3*e^(3*x) - e^(4*x) + e^x)/x^4 Placing the root at 1: 785 x |--> -1/6*(16*x^4 - 9*x^2*e^x + 6*(x - 1)*e^(3*x) + 3*(3*x^2 - 2*x)*e^(2*x) + 12*e^(4*x) - 6*e^(5*x))/x^5 Placing the root at 2: 1296 x |--> -1/24*(125*x^4 + 64*x^3*e^x + 36*x^2*e^(2*x) + 24*x*e^(3*x) + 24*e^(4*x) - 24*e^(5*x))/x^5 Placing the root at 0: 690 x |--> -1/4*(9*x^4 - 4*x^2*e^x + 4*(2*x - 1)*e^(3*x) - 8*x*e^(2*x) + 8*e^(4*x) - 4*e^(5*x))/x^5 Placing the root at 1: 610 x |--> -(2*x^4 - x^2*e^x + (x^2 + 1)*e^(2*x) - 3*e^(3*x) + 3*e^(4*x) - e^(5*x))/x^5 Placing the root at 2: 1040 x |--> -1/12*(49*x^4 + 24*x^3*e^x + 12*x^2*e^(2*x) - 12*e^(3*x) + 24*e^(4*x) - 12*e^(5*x))/x^5 Placing the root at 3: 905 x |--> -1/12*(41*x^4 + 18*x^3*e^x + 12*(x - 1)*e^(3*x) - 12*x*e^(2*x) + 24*e^(4*x) - 12*e^(5*x))/x^5 Placing the root at 0: 500 x |--> -1/2*(3*x^4 + 2*(x - 3)*e^(3*x) - 2*(2*x - 1)*e^(2*x) + 2*x*e^x + 6*e^(4*x) - 2*e^(5*x))/x^5 Placing the root at 1: 690 x |--> -1/2*(5*x^4 + 2*x^3*e^x + 2*e^(2*x) - 6*e^(3*x) + 6*e^(4*x) - 2*e^(5*x))/x^5 Placing the root at 0: 360 x |--> -(x^4 + 4*e^(2*x) - 6*e^(3*x) + 4*e^(4*x) - e^(5*x) - e^x)/x^5 Placing the root at 1: 7865 x |--> -1/2*(8*x^5 - 3*x^3*e^x - 5*x^2*e^(2*x) + 2*(2*x - 1)*e^(4*x) + (3*x^2 - 4*x)*e^(3*x) + 4*e^(5*x) - 2*e^(6*x))/x^6 Placing the root at 2: 9651 x |--> -1/24*(125*x^5 - 64*x^3*e^x + 24*(x - 1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 4*(16*x^3 - 9*x^2)*e^(2*x) + 48*e^(5*x) - 24*e^(6*x))/x^6 Placing the root at 3: 16807 x |--> -1/120*(1296*x^5 + 625*x^4*e^x + 320*x^3*e^(2*x) + 180*x^2*e^(3*x) + 120*x*e^(4*x) + 120*e^(5*x) - 120*e^(6*x))/x^6 Placing the root at 1: 5670 x |--> -1/6*(16*x^5 + 9*x^2*e^x + 6*(x - 3)*e^(4*x) + 3*(3*x^2 - 4*x + 2)*e^(3*x) - 6*(3*x^2 - x)*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6 Placing the root at 2: 10931 x |--> -1/24*(157*x^5 + 64*x^4*e^x - 36*x^2*e^(2*x) + 24*(x - 1)*e^(4*x) + 12*(3*x^2 - 2*x)*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6 Placing the root at 0: 6090 x |--> -(3*x^5 - x^3*e^x + (x - 3)*e^(4*x) + (x^2 - 2*x + 1)*e^(3*x) - (x^2 - x)*e^(2*x) + 3*e^(5*x) - e^(6*x))/x^6 Placing the root at 4: 7710 x |--> -1/12*(49*x^5 - 24*x^3*e^x + 12*(x^2 + 1)*e^(3*x) + 12*(2*x^3 - x^2)*e^(2*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6 Placing the root at 5: 13682 x |--> -1/12*(104*x^5 + 49*x^4*e^x + 24*x^3*e^(2*x) + 12*x^2*e^(3*x) - 12*e^(4*x) + 24*e^(5*x) - 12*e^(6*x))/x^6 Placing the root at 1: 4380 x |--> -(2*x^5 + x^2*e^x + (x^2 + 4)*e^(3*x) - (2*x^2 + 1)*e^(2*x) - 6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6 Placing the root at 2: 8670 x |--> -1/12*(61*x^5 + 24*x^4*e^x - 12*x^2*e^(2*x) + 12*(x^2 + 1)*e^(3*x) - 36*e^(4*x) + 36*e^(5*x) - 12*e^(6*x))/x^6 Placing the root at 1: 6660 x |--> -1/12*(41*x^5 - 18*x^3*e^x + 12*(x - 3)*e^(4*x) - 12*(2*x - 1)*e^(3*x) + 6*(3*x^3 + 2*x)*e^(2*x) + 36*e^(5*x) - 12*e^(6*x))/x^6 Placing the root at 2: 12146 x |--> -1/24*(181*x^5 + 82*x^4*e^x + 36*x^3*e^(2*x) + 24*(x - 1)*e^(4*x) - 24*x*e^(3*x) + 48*e^(5*x) - 24*e^(6*x))/x^6 Placing the root at 0: 4950 x |--> -1/4*(9*x^5 + 4*x^2*e^x + 4*(2*x - 3)*e^(4*x) - 4*(4*x - 1)*e^(3*x) - 4*(x^2 - 2*x)*e^(2*x) + 12*e^(5*x) - 4*e^(6*x))/x^6 Placing the root at 5: 9800 x |--> -1/4*(23*x^5 + 9*x^4*e^x - 4*x^2*e^(2*x) + 4*(2*x - 1)*e^(4*x) - 8*x*e^(3*x) + 8*e^(5*x) - 4*e^(6*x))/x^6 Placing the root at 1: 5040 x |--> -1/2*(5*x^5 - 2*x^3*e^x + 2*(x^3 - 1)*e^(2*x) + 8*e^(3*x) - 12*e^(4*x) + 8*e^(5*x) - 2*e^(6*x))/x^6 Placing the root at 2: 9480 x |--> -1/4*(23*x^5 + 10*x^4*e^x + 4*x^3*e^(2*x) + 4*e^(3*x) - 12*e^(4*x) + 12*e^(5*x) - 4*e^(6*x))/x^6 Placing the root at 3: 7380 x |--> -1/6*(25*x^5 + 9*x^4*e^x + 6*(x - 3)*e^(4*x) - 6*(2*x - 1)*e^(3*x) + 6*x*e^(2*x) + 18*e^(5*x) - 6*e^(6*x))/x^6 Placing the root at 0: 3540 x |--> -1/2*(3*x^5 + 2*(x - 6)*e^(4*x) - 2*(3*x - 4)*e^(3*x) + 2*(3*x - 1)*e^(2*x) - 2*x*e^x + 8*e^(5*x) - 2*e^(6*x))/x^6 Placing the root at 1: 5520 x |--> -(3*x^5 + x^4*e^x - e^(2*x) + 4*e^(3*x) - 6*e^(4*x) + 4*e^(5*x) - e^(6*x))/x^6 Placing the root at 0: 2520 x |--> -(x^5 - 5*e^(2*x) + 10*e^(3*x) - 10*e^(4*x) + 5*e^(5*x) - e^(6*x) + e^x)/x^6 Placing the root at 1: 112273 x |--> -1/48*(375*x^6 - 128*x^4*e^x - 200*x^3*e^(2*x) + 48*(2*x - 1)*e^(5*x) + 24*(3*x^2 - 4*x)*e^(4*x) + 8*(16*x^3 - 15*x^2)*e^(3*x) + 96*e^(6*x) - 48*e^(7*x))/x^7 Placing the root at 2: 144865 x |--> -1/120*(1296*x^6 - 625*x^4*e^x + 120*(x - 1)*e^(5*x) + 60*(3*x^2 - 2*x)*e^(4*x) + 20*(16*x^3 - 9*x^2)*e^(3*x) + 5*(125*x^4 - 64*x^3)*e^(2*x) + 240*e^(6*x) - 120*e^(7*x))/x^7 Placing the root at 3: 262144 x |--> -1/720*(16807*x^6 + 7776*x^5*e^x + 3750*x^4*e^(2*x) + 1920*x^3*e^(3*x) + 1080*x^2*e^(4*x) + 720*x*e^(5*x) + 720*e^(6*x) - 720*e^(7*x))/x^7 Placing the root at 0: 104160 x |--> -1/36*(256*x^6 - 81*x^4*e^x - 108*x^3*e^(2*x) - 144*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) + 36*(3*x^2 - 2*x)*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7 Placing the root at 1: 89530 x |--> -1/8*(49*x^6 - 16*x^4*e^x - 24*x^3*e^(2*x) + 8*(x - 3)*e^(5*x) + 8*(x^2 - 2*x + 1)*e^(4*x) + 8*(2*x^3 - x^2 + x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 2: 117614 x |--> -1/12*(104*x^6 - 49*x^4*e^x + 12*(x^2 + 1)*e^(4*x) + 12*(2*x^3 - x^2)*e^(3*x) + (49*x^4 - 24*x^3)*e^(2*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 3: 215488 x |--> -1/360*(6841*x^6 + 3120*x^5*e^x + 1470*x^4*e^(2*x) + 720*x^3*e^(3*x) + 360*x^2*e^(4*x) - 360*e^(5*x) + 720*e^(6*x) - 360*e^(7*x))/x^7 Placing the root at 4: 80682 x |--> -1/24*(125*x^6 + 64*x^3*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 4*(32*x^3 - 9*x^2)*e^(2*x) + 8*(8*x^3 - 9*x^2 + 3*x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 5: 162365 x |--> -1/240*(3217*x^6 + 1250*x^5*e^x - 640*x^3*e^(2*x) + 240*(x - 1)*e^(5*x) + 120*(3*x^2 - 2*x)*e^(4*x) + 40*(16*x^3 - 9*x^2)*e^(3*x) + 480*e^(6*x) - 240*e^(7*x))/x^7 Placing the root at 0: 80500 x |--> -1/6*(32*x^6 - 9*x^4*e^x + 6*(x - 3)*e^(5*x) - 6*(4*x^2 - x)*e^(3*x) + 3*(5*x^2 - 4*x + 2)*e^(4*x) - 3*(2*x^3 - 3*x^2)*e^(2*x) + 18*e^(6*x) - 6*e^(7*x))/x^7 Placing the root at 1: 77105 x |--> -1/8*(41*x^6 - 12*x^4*e^x + 8*(2*x - 3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 4*(3*x^3 - 2*x^2)*e^(2*x) + 4*(3*x^3 - 2*x^2 + 4*x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 0: 65135 x |--> -1/2*(8*x^6 + 3*x^3*e^x + 2*(2*x - 3)*e^(5*x) - 4*(2*x^2 - x)*e^(3*x) + (3*x^2 - 8*x + 2)*e^(4*x) - (3*x^3 - 5*x^2)*e^(2*x) + 6*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 2: 104027 x |--> -1/24*(181*x^6 - 82*x^4*e^x + 24*(x - 3)*e^(5*x) - 24*(2*x - 1)*e^(4*x) + 12*(3*x^3 + 2*x)*e^(3*x) + 2*(41*x^4 - 18*x^3)*e^(2*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 3: 193613 x |--> -1/360*(6073*x^6 + 2715*x^5*e^x + 1230*x^4*e^(2*x) + 540*x^3*e^(3*x) + 360*(x - 1)*e^(5*x) - 360*x*e^(4*x) + 720*e^(6*x) - 360*e^(7*x))/x^7 Placing the root at 4: 93002 x |--> -1/24*(157*x^6 - 64*x^4*e^x + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 4*(16*x^4 + 9*x^2)*e^(2*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 5: 177485 x |--> -1/720*(10931*x^6 + 4710*x^5*e^x + 1920*x^4*e^(2*x) - 1080*x^2*e^(3*x) + 720*(x - 1)*e^(5*x) + 360*(3*x^2 - 2*x)*e^(4*x) + 1440*e^(6*x) - 720*e^(7*x))/x^7 Placing the root at 6: 136353 x |--> -1/144*(1573*x^6 + 576*x^5*e^x - 216*x^3*e^(2*x) - 360*x^2*e^(3*x) + 144*(2*x - 1)*e^(5*x) + 72*(3*x^2 - 4*x)*e^(4*x) + 288*e^(6*x) - 144*e^(7*x))/x^7 Placing the root at 1: 46410 x |--> -1/6*(16*x^6 - 9*x^2*e^x + 6*(x - 6)*e^(5*x) + 3*(3*x^2 - 6*x + 8)*e^(4*x) - 3*(9*x^2 - 6*x + 2)*e^(3*x) + 3*(9*x^2 - 2*x)*e^(2*x) + 24*e^(6*x) - 6*e^(7*x))/x^7 Placing the root at 2: 101962 x |--> -1/24*(189*x^6 + 64*x^5*e^x + 36*x^2*e^(2*x) + 24*(x - 3)*e^(5*x) + 12*(3*x^2 - 4*x + 2)*e^(4*x) - 24*(3*x^2 - x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 0: 58170 x |--> -1/4*(15*x^6 - 4*x^4*e^x + 4*(x - 6)*e^(5*x) - 4*(3*x - 4)*e^(4*x) - 4*(x^3 + x)*e^(2*x) + 4*(x^3 + 3*x - 1)*e^(3*x) + 16*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 5: 80850 x |--> -1/4*(23*x^6 - 10*x^4*e^x + 4*(x^3 - 1)*e^(3*x) + 2*(5*x^4 - 2*x^3)*e^(2*x) + 16*e^(4*x) - 24*e^(5*x) + 16*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 6: 153426 x |--> -1/12*(158*x^6 + 69*x^5*e^x + 30*x^4*e^(2*x) + 12*x^3*e^(3*x) + 12*e^(4*x) - 36*e^(5*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 1: 64260 x |--> -1/12*(49*x^6 + 24*x^3*e^x + 12*(x^2 + 4)*e^(4*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(3*x) - 12*(4*x^3 - x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 2: 131334 x |--> -1/24*(257*x^6 + 98*x^5*e^x - 48*x^3*e^(2*x) + 24*(x^2 + 1)*e^(4*x) + 24*(2*x^3 - x^2)*e^(3*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 0: 62160 x |--> -(4*x^6 - x^4*e^x + 2*x^2*e^(2*x) + 2*(x^2 + 2)*e^(4*x) - (4*x^2 + 1)*e^(3*x) - 6*e^(5*x) + 4*e^(6*x) - e^(7*x))/x^7 Placing the root at 1: 55230 x |--> -1/12*(41*x^6 + 18*x^3*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x - 4)*e^(4*x) - 12*(3*x^3 + x)*e^(2*x) + 6*(3*x^3 + 6*x - 2)*e^(3*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 2: 115507 x |--> -1/12*(111*x^6 + 41*x^5*e^x - 18*x^3*e^(2*x) + 12*(x - 3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 6*(3*x^3 + 2*x)*e^(3*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 0: 50190 x |--> -(3*x^6 + x^3*e^x + (x - 6)*e^(5*x) + (x^2 - 3*x + 4)*e^(4*x) - (2*x^2 - 3*x + 1)*e^(3*x) - (x^3 - x^2 + x)*e^(2*x) + 4*e^(6*x) - e^(7*x))/x^7 Placing the root at 4: 73500 x |--> -1/12*(61*x^6 - 24*x^4*e^x + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) + 12*(2*x^4 + x^2)*e^(2*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 5: 142674 x |--> -1/24*(289*x^6 + 122*x^5*e^x + 48*x^4*e^(2*x) - 24*x^2*e^(3*x) + 24*(x^2 + 1)*e^(4*x) - 72*e^(5*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 6: 107590 x |--> -1/24*(203*x^6 + 72*x^5*e^x - 24*x^3*e^(2*x) + 24*(x - 3)*e^(5*x) + 24*(x^2 - 2*x + 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 72*e^(6*x) - 24*e^(7*x))/x^7 Placing the root at 1: 41580 x |--> -1/2*(5*x^6 + 2*x^3*e^x + 2*(x^3 - 5)*e^(3*x) - 2*(2*x^3 - 1)*e^(2*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 2: 89250 x |--> -1/2*(14*x^6 + 5*x^5*e^x - 2*x^3*e^(2*x) + 2*(x^3 - 1)*e^(3*x) + 8*e^(4*x) - 12*e^(5*x) + 8*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 4: 80220 x |--> -1/12*(73*x^6 + 24*x^5*e^x + 12*x^2*e^(2*x) + 12*(x^2 + 4)*e^(4*x) - 12*(2*x^2 + 1)*e^(3*x) - 72*e^(5*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 0: 35700 x |--> -(2*x^6 - x^2*e^x + (x^2 + 10)*e^(4*x) + (3*x^2 + 1)*e^(2*x) - (3*x^2 + 5)*e^(3*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7 Placing the root at 1: 83090 x |--> -1/4*(23*x^6 - 9*x^4*e^x + 4*(2*x - 3)*e^(5*x) - 4*(4*x - 1)*e^(4*x) - 4*(x^2 - 2*x)*e^(3*x) + (9*x^4 + 4*x^2)*e^(2*x) + 12*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 2: 160986 x |--> -1/36*(490*x^6 + 207*x^5*e^x + 81*x^4*e^(2*x) - 36*x^2*e^(3*x) + 36*(2*x - 1)*e^(5*x) - 72*x*e^(4*x) + 72*e^(6*x) - 36*e^(7*x))/x^7 Placing the root at 0: 56700 x |--> -1/8*(27*x^6 + 8*x^3*e^x + 24*x^2*e^(2*x) + 24*(x - 1)*e^(5*x) - 8*(6*x - 1)*e^(4*x) - 24*(x^2 - x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 1: 62160 x |--> -1/6*(25*x^6 - 9*x^4*e^x + 6*(x - 6)*e^(5*x) - 6*(3*x - 4)*e^(4*x) + 6*(3*x - 1)*e^(3*x) + 3*(3*x^4 - 2*x)*e^(2*x) + 24*e^(6*x) - 6*e^(7*x))/x^7 Placing the root at 2: 124012 x |--> -1/12*(123*x^6 + 50*x^5*e^x + 18*x^4*e^(2*x) + 12*(x - 3)*e^(5*x) - 12*(2*x - 1)*e^(4*x) + 12*x*e^(3*x) + 36*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 5: 90650 x |--> -1/8*(55*x^6 + 18*x^5*e^x + 8*x^2*e^(2*x) + 8*(2*x - 3)*e^(5*x) - 8*(4*x - 1)*e^(4*x) - 8*(x^2 - 2*x)*e^(3*x) + 24*e^(6*x) - 8*e^(7*x))/x^7 Placing the root at 0: 40320 x |--> -1/4*(9*x^6 - 4*x^2*e^x + 8*(x - 3)*e^(5*x) - 8*(3*x - 2)*e^(4*x) - 4*(x^2 - 6*x + 1)*e^(3*x) + 8*(x^2 - x)*e^(2*x) + 16*e^(6*x) - 4*e^(7*x))/x^7 Placing the root at 1: 46200 x |--> -(3*x^6 - x^4*e^x + (x^4 + 1)*e^(2*x) - 5*e^(3*x) + 10*e^(4*x) - 10*e^(5*x) + 5*e^(6*x) - e^(7*x))/x^7 Placing the root at 2: 94920 x |--> -1/3*(23*x^6 + 9*x^5*e^x + 3*x^4*e^(2*x) - 3*e^(3*x) + 12*e^(4*x) - 18*e^(5*x) + 12*e^(6*x) - 3*e^(7*x))/x^7 Placing the root at 3: 67200 x |--> -1/12*(59*x^6 + 18*x^5*e^x + 12*(x - 6)*e^(5*x) - 12*(3*x - 4)*e^(4*x) + 12*(3*x - 1)*e^(3*x) - 12*x*e^(2*x) + 48*e^(6*x) - 12*e^(7*x))/x^7 Placing the root at 0: 28560 x |--> -1/2*(3*x^6 + 2*(x - 10)*e^(5*x) - 4*(2*x - 5)*e^(4*x) - 2*(4*x - 1)*e^(2*x) + 2*(6*x - 5)*e^(3*x) + 2*x*e^x + 10*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 1: 49560 x |--> -1/2*(7*x^6 + 2*x^5*e^x + 2*e^(2*x) - 10*e^(3*x) + 20*e^(4*x) - 20*e^(5*x) + 10*e^(6*x) - 2*e^(7*x))/x^7 Placing the root at 0: 20160 x |--> -(x^6 + 6*e^(2*x) - 15*e^(3*x) + 20*e^(4*x) - 15*e^(5*x) + 6*e^(6*x) - e^(7*x) - e^x)/x^7 Placing the root at 1: 1694966 x |--> -1/36*(500*x^7 - 144*x^5*e^x - 177*x^4*e^(2*x) - 204*x^3*e^(3*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) + 48*(2*x^3 - 3*x^2)*e^(4*x) + 72*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 2: 1919820 x |--> -1/120*(1944*x^7 - 625*x^5*e^x - 945*x^4*e^(2*x) + 120*(2*x - 1)*e^(6*x) + 60*(3*x^2 - 4*x)*e^(5*x) + 20*(16*x^3 - 15*x^2)*e^(4*x) + 125*(5*x^4 - 4*x^3)*e^(3*x) + 240*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 3: 2567748 x |--> -1/720*(16807*x^7 - 7776*x^5*e^x + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 - 64*x^3)*e^(3*x) + 6*(1296*x^5 - 625*x^4)*e^(2*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 4: 4782969 x |--> -1/5040*(262144*x^7 + 117649*x^6*e^x + 54432*x^5*e^(2*x) + 26250*x^4*e^(3*x) + 13440*x^3*e^(4*x) + 7560*x^2*e^(5*x) + 5040*x*e^(6*x) + 5040*e^(7*x) - 5040*e^(8*x))/x^8 Placing the root at 1: 1308412 x |--> -1/12*(125*x^7 - 32*x^5*e^x + 12*(x - 3)*e^(6*x) + 6*(5*x^2 - 4*x + 2)*e^(5*x) - 2*(38*x^3 - 9*x^2)*e^(3*x) - 2*(9*x^4 - 16*x^3)*e^(2*x) + 4*(8*x^3 - 12*x^2 + 3*x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1376648 x |--> -1/120*(1296*x^7 + 625*x^4*e^x + 120*(x - 3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 10*(125*x^4 - 32*x^3)*e^(2*x) + 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 5*(125*x^4 - 128*x^3 + 36*x^2)*e^(3*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 3: 2858052 x |--> -1/720*(20695*x^7 + 7776*x^6*e^x - 3750*x^4*e^(2*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 30*(125*x^4 - 64*x^3)*e^(3*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 1350300 x |--> -1/18*(196*x^7 - 54*x^5*e^x - 63*x^4*e^(2*x) + 18*(x - 3)*e^(6*x) + 9*(5*x^2 - 4*x + 2)*e^(5*x) - 27*(2*x^3 - x^2)*e^(3*x) + 18*(2*x^3 - 4*x^2 + x)*e^(4*x) + 54*e^(7*x) - 18*e^(8*x))/x^8 Placing the root at 5: 1556968 x |--> -1/12*(156*x^7 - 49*x^5*e^x - 73*x^4*e^(2*x) + 12*(x - 3)*e^(6*x) + 12*(x^2 - 2*x + 1)*e^(5*x) + (49*x^4 - 36*x^3)*e^(3*x) + 12*(2*x^3 - x^2 + x)*e^(4*x) + 36*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 6: 2107000 x |--> -1/360*(6841*x^7 - 3120*x^5*e^x + 360*(x^2 + 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) + 30*(104*x^5 - 49*x^4)*e^(2*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 7: 3959426 x |--> -1/360*(15392*x^7 + 6841*x^6*e^x + 3120*x^5*e^(2*x) + 1470*x^4*e^(3*x) + 720*x^3*e^(4*x) + 360*x^2*e^(5*x) - 360*e^(6*x) + 720*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 1: 1041880 x |--> -1/6*(49*x^7 - 12*x^5*e^x + 12*(x^2 + 2)*e^(5*x) + 6*(2*x^3 - 4*x^2 - 1)*e^(4*x) - 12*(2*x^3 - x^2)*e^(3*x) - 6*(x^4 - 2*x^3)*e^(2*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 2: 1115632 x |--> -1/12*(104*x^7 + 49*x^4*e^x + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 2*(49*x^4 - 12*x^3)*e^(2*x) + (49*x^4 - 48*x^3 + 12*x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2339960 x |--> -1/360*(8401*x^7 + 3120*x^6*e^x - 1470*x^4*e^(2*x) + 360*(x^2 + 1)*e^(5*x) + 360*(2*x^3 - x^2)*e^(4*x) + 30*(49*x^4 - 24*x^3)*e^(3*x) - 1080*e^(6*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 1: 1055684 x |--> -1/48*(375*x^7 + 128*x^4*e^x + 48*(2*x - 3)*e^(6*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(41*x^3 - 15*x^2)*e^(3*x) - 8*(16*x^4 - 25*x^3)*e^(2*x) + 32*(4*x^3 - 6*x^2 + 3*x)*e^(4*x) + 144*e^(7*x) - 48*e^(8*x))/x^8 Placing the root at 0: 1161020 x |--> -1/36*(328*x^7 - 81*x^5*e^x + 36*(2*x - 3)*e^(6*x) + 18*(3*x^2 - 8*x + 2)*e^(5*x) - 18*(6*x^3 - 5*x^2)*e^(3*x) - 54*(x^4 - x^3)*e^(2*x) + 18*(3*x^3 - 8*x^2 + 4*x)*e^(4*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 2: 1569148 x |--> -1/240*(3217*x^7 - 1250*x^5*e^x + 240*(x - 3)*e^(6*x) + 120*(3*x^2 - 4*x + 2)*e^(5*x) - 40*(32*x^3 - 9*x^2)*e^(3*x) + 10*(125*x^5 + 64*x^3)*e^(2*x) + 80*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 720*e^(7*x) - 240*e^(8*x))/x^8 Placing the root at 3: 3094302 x |--> -1/720*(23195*x^7 + 9651*x^6*e^x + 3750*x^5*e^(2*x) - 1920*x^3*e^(3*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 120*(16*x^3 - 9*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 4: 2296070 x |--> -1/720*(16039*x^7 + 5625*x^6*e^x - 1920*x^4*e^(2*x) - 3000*x^3*e^(3*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) + 120*(16*x^3 - 15*x^2)*e^(4*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 5: 1375024 x |--> -1/48*(543*x^7 - 164*x^5*e^x - 236*x^4*e^(2*x) + 48*(2*x - 3)*e^(6*x) - 48*(4*x - 1)*e^(5*x) + 24*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 4*(41*x^4 - 18*x^3 + 12*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8 Placing the root at 6: 1888992 x |--> -1/360*(6073*x^7 - 2715*x^5*e^x + 360*(x - 3)*e^(6*x) - 360*(2*x - 1)*e^(5*x) + 180*(3*x^3 + 2*x)*e^(4*x) + 30*(41*x^4 - 18*x^3)*e^(3*x) + 15*(181*x^5 - 82*x^4)*e^(2*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 7: 3586178 x |--> -1/720*(27659*x^7 + 12146*x^6*e^x + 5430*x^5*e^(2*x) + 2460*x^4*e^(3*x) + 1080*x^3*e^(4*x) + 720*(x - 1)*e^(6*x) - 720*x*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 1: 839720 x |--> -1/8*(49*x^7 + 16*x^4*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x + 4)*e^(5*x) - 8*(2*x^4 - 3*x^3)*e^(2*x) + 8*(2*x^3 - 2*x^2 + 3*x - 1)*e^(4*x) - 8*(5*x^3 - x^2 + x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1266552 x |--> -1/24*(257*x^7 - 98*x^5*e^x + 24*(x^2 + 4)*e^(5*x) + 24*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 24*(4*x^3 - x^2)*e^(3*x) + 2*(49*x^5 + 24*x^3)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 3: 2525180 x |--> -1/120*(3127*x^7 + 1285*x^6*e^x + 490*x^5*e^(2*x) - 240*x^3*e^(3*x) + 120*(x^2 + 1)*e^(5*x) + 120*(2*x^3 - x^2)*e^(4*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 4: 1851948 x |--> -1/72*(1279*x^7 + 441*x^6*e^x - 144*x^4*e^(2*x) - 216*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) + 72*(2*x^3 - x^2 + x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 5: 984256 x |--> -1/24*(181*x^7 + 82*x^4*e^x + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) - 4*(41*x^4 - 9*x^3)*e^(2*x) + 2*(41*x^4 - 36*x^3 - 12*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 6: 2091712 x |--> -1/720*(14861*x^7 + 5430*x^6*e^x - 2460*x^4*e^(2*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) + 60*(41*x^4 - 18*x^3)*e^(3*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 895160 x |--> -1/6*(41*x^7 - 9*x^5*e^x + 15*x^3*e^(2*x) + 6*(x - 6)*e^(6*x) + 6*(x^2 - 3*x + 4)*e^(5*x) + 3*(3*x^3 - 4*x^2 + 6*x - 2)*e^(4*x) - 6*(4*x^3 - x^2 + x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 1: 720160 x |--> -1/8*(41*x^7 + 12*x^4*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x - 2)*e^(5*x) - 8*(3*x^3 - 2*x^2 + 2*x)*e^(3*x) + 4*(3*x^3 - 2*x^2 + 12*x - 2)*e^(4*x) - 4*(3*x^4 - 3*x^3 + 2*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1110536 x |--> -1/12*(111*x^7 - 41*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) - 12*(3*x^3 + x)*e^(3*x) + 6*(3*x^3 + 6*x - 2)*e^(4*x) + (41*x^5 + 18*x^3)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2246692 x |--> -1/720*(16501*x^7 + 6660*x^6*e^x + 2460*x^5*e^(2*x) - 1080*x^3*e^(3*x) + 720*(x - 3)*e^(6*x) - 720*(2*x - 1)*e^(5*x) + 360*(3*x^3 + 2*x)*e^(4*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 4: 1621844 x |--> -1/144*(2203*x^7 + 738*x^6*e^x - 216*x^4*e^(2*x) + 144*(2*x - 3)*e^(6*x) - 144*(4*x - 1)*e^(5*x) - 72*(3*x^3 - 2*x^2)*e^(3*x) + 72*(3*x^3 - 2*x^2 + 4*x)*e^(4*x) + 432*e^(7*x) - 144*e^(8*x))/x^8 Placing the root at 1: 1225924 x |--> -1/48*(471*x^7 - 128*x^5*e^x + 48*(2*x - 3)*e^(6*x) - 96*(2*x^2 - x)*e^(4*x) + 24*(3*x^2 - 8*x + 2)*e^(5*x) - 8*(16*x^4 - 9*x^3)*e^(2*x) + 8*(16*x^4 - 9*x^3 + 15*x^2)*e^(3*x) + 144*e^(7*x) - 48*e^(8*x))/x^8 Placing the root at 2: 1725948 x |--> -1/720*(10931*x^7 - 4710*x^5*e^x + 720*(x - 3)*e^(6*x) + 360*(3*x^2 - 4*x + 2)*e^(5*x) - 720*(3*x^2 - x)*e^(4*x) + 120*(16*x^4 + 9*x^2)*e^(3*x) + 30*(157*x^5 - 64*x^4)*e^(2*x) + 2160*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 3: 3323678 x |--> -1/720*(25355*x^7 + 10931*x^6*e^x + 4710*x^5*e^(2*x) + 1920*x^4*e^(3*x) - 1080*x^2*e^(4*x) + 720*(x - 1)*e^(6*x) + 360*(3*x^2 - 2*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 976640 x |--> -1/36*(256*x^7 + 81*x^4*e^x + 36*(2*x - 3)*e^(6*x) + 36*(3*x^2 - 4*x + 1)*e^(5*x) - 36*(7*x^2 - 2*x)*e^(4*x) - 36*(3*x^3 - 4*x^2)*e^(3*x) - 27*(3*x^4 - 4*x^3)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 7: 2152822 x |--> -1/36*(744*x^7 + 256*x^6*e^x - 81*x^4*e^(2*x) - 108*x^3*e^(3*x) - 144*x^2*e^(4*x) + 36*(2*x - 1)*e^(6*x) + 36*(3*x^2 - 2*x)*e^(5*x) + 72*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 1: 1066800 x |--> -1/8*(69*x^7 - 20*x^5*e^x - 28*x^4*e^(2*x) + 8*(x - 6)*e^(6*x) - 8*(3*x - 4)*e^(5*x) + 8*(x^3 + 3*x - 1)*e^(4*x) + 4*(5*x^4 - 2*x^3 - 2*x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1492848 x |--> -1/12*(158*x^7 - 69*x^5*e^x + 12*(x^3 - 1)*e^(4*x) + 6*(5*x^4 - 2*x^3)*e^(3*x) + 3*(23*x^5 - 10*x^4)*e^(2*x) + 48*e^(5*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2872212 x |--> -1/120*(3653*x^7 + 1580*x^6*e^x + 690*x^5*e^(2*x) + 300*x^4*e^(3*x) + 120*x^3*e^(4*x) + 120*e^(5*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 4: 750456 x |--> -1/24*(125*x^7 - 64*x^3*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) + 12*(16*x^3 - 3*x^2)*e^(2*x) + 4*(16*x^3 - 27*x^2 + 18*x - 6)*e^(4*x) - 12*(16*x^3 - 9*x^2 + 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 1709148 x |--> -1/120*(1921*x^7 + 625*x^6*e^x + 320*x^3*e^(2*x) + 120*(x - 3)*e^(6*x) + 60*(3*x^2 - 4*x + 2)*e^(5*x) - 20*(32*x^3 - 9*x^2)*e^(3*x) + 40*(8*x^3 - 9*x^2 + 3*x)*e^(4*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 0: 874440 x |--> -1/6*(40*x^7 - 9*x^5*e^x + 6*(x - 6)*e^(6*x) + 3*(3*x^2 - 6*x + 8)*e^(5*x) - 3*(2*x^4 + 3*x^2)*e^(2*x) - 3*(2*x^3 - 9*x^2 + 2*x)*e^(3*x) + 3*(2*x^3 - 9*x^2 + 6*x - 2)*e^(4*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 1: 967400 x |--> -1/8*(61*x^7 - 16*x^5*e^x + 8*(x - 6)*e^(6*x) + 8*(x^2 - 3*x + 4)*e^(5*x) - 8*(2*x^2 - 3*x + 1)*e^(4*x) - 8*(2*x^4 - x^3)*e^(2*x) + 8*(2*x^4 - x^3 + x^2 - x)*e^(3*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1384152 x |--> -1/24*(289*x^7 - 122*x^5*e^x + 24*(x^2 + 4)*e^(5*x) - 24*(2*x^2 + 1)*e^(4*x) + 24*(2*x^4 + x^2)*e^(3*x) + 2*(61*x^5 - 24*x^4)*e^(2*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 3: 2697212 x |--> -1/120*(3397*x^7 + 1445*x^6*e^x + 610*x^5*e^(2*x) + 240*x^4*e^(3*x) - 120*x^2*e^(4*x) + 120*(x^2 + 1)*e^(5*x) - 360*e^(6*x) + 360*e^(7*x) - 120*e^(8*x))/x^8 Placing the root at 4: 875896 x |--> -1/24*(157*x^7 + 64*x^4*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) - 4*(32*x^4 + 9*x^2)*e^(2*x) + 4*(16*x^4 + 27*x^2 - 6*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 1901788 x |--> -1/360*(6643*x^7 + 2355*x^6*e^x - 960*x^4*e^(2*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) + 60*(16*x^4 + 9*x^2)*e^(3*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 0: 751520 x |--> -1/6*(32*x^7 + 9*x^4*e^x + 6*(x - 6)*e^(6*x) + 3*(5*x^2 - 6*x + 8)*e^(5*x) - 3*(13*x^2 - 6*x + 2)*e^(4*x) - 3*(2*x^3 - 11*x^2 + 2*x)*e^(3*x) - 3*(3*x^4 - 2*x^3 + 3*x^2)*e^(2*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 7: 1693692 x |--> -1/36*(575*x^7 + 192*x^6*e^x - 54*x^4*e^(2*x) + 36*(x - 3)*e^(6*x) - 36*(4*x^2 - x)*e^(4*x) + 18*(5*x^2 - 4*x + 2)*e^(5*x) - 18*(2*x^3 - 3*x^2)*e^(3*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 1: 1093680 x |--> -1/8*(69*x^7 - 18*x^5*e^x + 24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 6*(3*x^4 + 4*x^2)*e^(3*x) - 2*(9*x^4 - 4*x^3)*e^(2*x) + 24*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1562288 x |--> -1/36*(490*x^7 - 207*x^5*e^x + 36*(2*x - 3)*e^(6*x) - 36*(4*x - 1)*e^(5*x) - 36*(x^2 - 2*x)*e^(4*x) + 9*(9*x^4 + 4*x^2)*e^(3*x) + 9*(23*x^5 - 9*x^4)*e^(2*x) + 108*e^(7*x) - 36*e^(8*x))/x^8 Placing the root at 3: 3037930 x |--> -1/360*(11499*x^7 + 4900*x^6*e^x + 2070*x^5*e^(2*x) + 810*x^4*e^(3*x) - 360*x^2*e^(4*x) + 360*(2*x - 1)*e^(6*x) - 720*x*e^(5*x) + 720*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 4: 1311044 x |--> -1/144*(1573*x^7 - 576*x^5*e^x + 144*(2*x - 3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 - 5*x^2)*e^(3*x) + 72*(8*x^5 + 3*x^3)*e^(2*x) + 432*e^(7*x) - 144*e^(8*x))/x^8 Placing the root at 5: 2646406 x |--> -1/720*(19479*x^7 + 7865*x^6*e^x + 2880*x^5*e^(2*x) - 1080*x^3*e^(3*x) - 1800*x^2*e^(4*x) + 720*(2*x - 1)*e^(6*x) + 360*(3*x^2 - 4*x)*e^(5*x) + 1440*e^(7*x) - 720*e^(8*x))/x^8 Placing the root at 0: 848820 x |--> -1/2*(12*x^7 + 3*x^4*e^x + 8*x^3*e^(2*x) + 6*(x - 1)*e^(6*x) - 6*(2*x^2 - x)*e^(4*x) + (3*x^2 - 12*x + 2)*e^(5*x) - 3*(2*x^3 - 3*x^2)*e^(3*x) + 6*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 1: 815920 x |--> -1/4*(25*x^7 - 6*x^5*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(3*x^4 + 2*x^2)*e^(2*x) + 2*(3*x^4 + 4*x^2 - 4*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 2: 1198736 x |--> -1/12*(123*x^7 - 50*x^5*e^x + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) + 6*(3*x^4 - 2*x)*e^(3*x) + 2*(25*x^5 - 9*x^4)*e^(2*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 3: 2375716 x |--> -1/180*(4429*x^7 + 1845*x^6*e^x + 750*x^5*e^(2*x) + 270*x^4*e^(3*x) + 180*(x - 3)*e^(6*x) - 180*(2*x - 1)*e^(5*x) + 180*x*e^(4*x) + 540*e^(7*x) - 180*e^(8*x))/x^8 Placing the root at 4: 974456 x |--> -1/24*(189*x^7 - 64*x^5*e^x + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 - 2*x)*e^(3*x) + 4*(16*x^5 - 9*x^2)*e^(2*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 2022748 x |--> -1/360*(7283*x^7 + 2835*x^6*e^x + 960*x^5*e^(2*x) + 540*x^2*e^(3*x) + 360*(x - 3)*e^(6*x) + 180*(3*x^2 - 4*x + 2)*e^(5*x) - 360*(3*x^2 - x)*e^(4*x) + 1080*e^(7*x) - 360*e^(8*x))/x^8 Placing the root at 6: 1418564 x |--> -1/144*(1861*x^7 + 576*x^6*e^x + 216*x^3*e^(2*x) + 144*(2*x - 3)*e^(6*x) - 288*(2*x^2 - x)*e^(4*x) + 72*(3*x^2 - 8*x + 2)*e^(5*x) - 72*(3*x^3 - 5*x^2)*e^(3*x) + 432*e^(7*x) - 144*e^(8*x))/x^8 Placing the root at 0: 601720 x |--> -1/2*(8*x^7 - 3*x^3*e^x + 4*(x - 3)*e^(6*x) + (3*x^2 - 12*x + 8)*e^(5*x) - (11*x^2 - 12*x + 2)*e^(4*x) + (6*x^3 - 5*x^2)*e^(2*x) - (3*x^3 - 13*x^2 + 4*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 1: 425040 x |--> -1/6*(16*x^7 + 9*x^2*e^x + 6*(x - 10)*e^(6*x) + 3*(3*x^2 - 8*x + 20)*e^(5*x) - 6*(6*x^2 - 6*x + 5)*e^(4*x) - 6*(6*x^2 - x)*e^(2*x) + 6*(9*x^2 - 4*x + 1)*e^(3*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 2: 1046136 x |--> -1/24*(221*x^7 + 64*x^6*e^x - 36*x^2*e^(2*x) + 24*(x - 6)*e^(6*x) + 12*(3*x^2 - 6*x + 8)*e^(5*x) - 12*(9*x^2 - 6*x + 2)*e^(4*x) + 12*(9*x^2 - 2*x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 604800 x |--> -1/2*(9*x^7 - 2*x^5*e^x + 2*(x - 10)*e^(6*x) - 4*(2*x - 5)*e^(5*x) + 2*(6*x - 5)*e^(4*x) + 2*(x^4 - 4*x + 1)*e^(3*x) - 2*(x^4 - x)*e^(2*x) + 10*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 6: 913920 x |--> -1/3*(23*x^7 - 9*x^5*e^x + 3*(x^4 + 1)*e^(3*x) + 3*(3*x^5 - x^4)*e^(2*x) - 15*e^(4*x) + 30*e^(5*x) - 30*e^(6*x) + 15*e^(7*x) - 3*e^(8*x))/x^8 Placing the root at 7: 1846824 x |--> -1/6*(113*x^7 + 46*x^6*e^x + 18*x^5*e^(2*x) + 6*x^4*e^(3*x) - 6*e^(4*x) + 24*e^(5*x) - 36*e^(6*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 1: 596400 x |--> -1/12*(49*x^7 - 24*x^3*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(2*x^3 - 3*x^2 - 5)*e^(4*x) - 12*(6*x^3 - 3*x^2 - 1)*e^(3*x) + 12*(6*x^3 - x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1376312 x |--> -1/12*(153*x^7 + 49*x^6*e^x + 24*x^3*e^(2*x) + 12*(x^2 + 4)*e^(5*x) + 12*(2*x^3 - 2*x^2 - 1)*e^(4*x) - 12*(4*x^3 - x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 5: 762720 x |--> -1/4*(23*x^7 + 10*x^4*e^x + 4*(x^3 - 5)*e^(4*x) + 2*(5*x^4 - 4*x^3 + 2)*e^(3*x) - 4*(5*x^4 - x^3)*e^(2*x) + 40*e^(5*x) - 40*e^(6*x) + 20*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 6: 1647408 x |--> -1/24*(385*x^7 + 138*x^6*e^x - 60*x^4*e^(2*x) + 24*(x^3 - 1)*e^(4*x) + 12*(5*x^4 - 2*x^3)*e^(3*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 673680 x |--> -(5*x^7 - x^5*e^x + (x^2 + 10)*e^(5*x) + (x^3 - 3*x^2 - 5)*e^(4*x) + (x^3 - x^2)*e^(2*x) - (2*x^3 - 3*x^2 - 1)*e^(3*x) - 10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8 Placing the root at 1: 510720 x |--> -1/12*(41*x^7 - 18*x^3*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x - 5)*e^(5*x) + 6*(3*x^3 + 12*x - 10)*e^(4*x) + 6*(9*x^3 + 2*x)*e^(2*x) - 6*(9*x^3 + 8*x - 2)*e^(3*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1202376 x |--> -1/24*(263*x^7 + 82*x^6*e^x + 36*x^3*e^(2*x) + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(3*x^3 + x)*e^(3*x) + 12*(3*x^3 + 6*x - 2)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 540960 x |--> -1/4*(15*x^7 + 4*x^4*e^x + 4*(x - 10)*e^(6*x) - 8*(2*x - 5)*e^(5*x) + 4*(x^3 + 6*x - 5)*e^(4*x) - 4*(2*x^3 + 4*x - 1)*e^(3*x) - 4*(x^4 - x^3 - x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 5: 855120 x |--> -1/2*(14*x^7 - 5*x^5*e^x + 2*(x^3 - 5)*e^(4*x) - 2*(2*x^3 - 1)*e^(3*x) + (5*x^5 + 2*x^3)*e^(2*x) + 20*e^(5*x) - 20*e^(6*x) + 10*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 6: 1760808 x |--> -1/24*(425*x^7 + 168*x^6*e^x + 60*x^5*e^(2*x) - 24*x^3*e^(3*x) + 24*(x^3 - 1)*e^(4*x) + 96*e^(5*x) - 144*e^(6*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 7: 1247400 x |--> -1/24*(277*x^7 + 90*x^6*e^x - 24*x^4*e^(2*x) + 24*(x - 6)*e^(6*x) - 24*(3*x - 4)*e^(5*x) - 24*(x^3 + x)*e^(3*x) + 24*(x^3 + 3*x - 1)*e^(4*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 1: 383040 x |--> -1/2*(5*x^7 - 2*x^3*e^x + 2*(x^3 - 15)*e^(4*x) - 6*(x^3 - 2)*e^(3*x) + 2*(3*x^3 - 1)*e^(2*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 2: 922320 x |--> -1/4*(33*x^7 + 10*x^6*e^x + 4*x^3*e^(2*x) + 4*(x^3 - 5)*e^(4*x) - 4*(2*x^3 - 1)*e^(3*x) + 40*e^(5*x) - 40*e^(6*x) + 20*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 1: 690480 x |--> -1/12*(61*x^7 + 24*x^4*e^x + 12*(x^2 + 10)*e^(5*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^4 + 3*x^2 + 1)*e^(3*x) - 12*(4*x^4 + x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1520792 x |--> -1/12*(175*x^7 + 61*x^6*e^x - 24*x^4*e^(2*x) + 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) + 12*(2*x^4 + x^2)*e^(3*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 0: 577920 x |--> -(4*x^7 + x^4*e^x + 2*(x^2 + 5)*e^(5*x) + (6*x^2 + 1)*e^(3*x) - (6*x^2 + 5)*e^(4*x) - (x^4 + 2*x^2)*e^(2*x) - 10*e^(6*x) + 5*e^(7*x) - e^(8*x))/x^8 Placing the root at 7: 1330840 x |--> -1/3*(37*x^7 + 12*x^6*e^x - 3*x^4*e^(2*x) + 6*x^2*e^(3*x) + 6*(x^2 + 2)*e^(5*x) - 3*(4*x^2 + 1)*e^(4*x) - 18*e^(6*x) + 12*e^(7*x) - 3*e^(8*x))/x^8 Placing the root at 1: 780640 x |--> -1/4*(23*x^7 + 9*x^4*e^x + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) - 2*(9*x^4 + 2*x^2)*e^(2*x) + (9*x^4 + 8*x^2 - 8*x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 2: 1716848 x |--> -1/72*(1187*x^7 + 414*x^6*e^x - 162*x^4*e^(2*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 18*(9*x^4 + 4*x^2)*e^(3*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 4: 1031240 x |--> -1/24*(203*x^7 - 72*x^5*e^x + 24*(x - 6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) + 24*(3*x^5 + x^3)*e^(2*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 5: 2114700 x |--> -1/72*(1537*x^7 + 609*x^6*e^x + 216*x^5*e^(2*x) - 72*x^3*e^(3*x) + 72*(x - 3)*e^(6*x) + 72*(x^2 - 2*x + 1)*e^(5*x) - 72*(x^2 - x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 0: 652680 x |--> -1/2*(9*x^7 + 2*x^4*e^x + 4*(x - 3)*e^(6*x) + 2*(x^2 - 6*x + 4)*e^(5*x) - 2*(3*x^2 - 6*x + 1)*e^(4*x) + 2*(2*x^3 - x^2)*e^(2*x) - 2*(2*x^3 - 3*x^2 + 2*x)*e^(3*x) + 8*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 1: 581280 x |--> -1/6*(25*x^7 + 9*x^4*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x - 5)*e^(5*x) + 6*(6*x - 5)*e^(4*x) + 3*(3*x^4 - 8*x + 2)*e^(3*x) - 6*(3*x^4 - x)*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 2: 1310736 x |--> -1/6*(74*x^7 + 25*x^6*e^x - 9*x^4*e^(2*x) + 6*(x - 6)*e^(6*x) - 6*(3*x - 4)*e^(5*x) + 6*(3*x - 1)*e^(4*x) + 3*(3*x^4 - 2*x)*e^(3*x) + 24*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 4: 764400 x |--> -1/12*(73*x^7 - 24*x^5*e^x + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) + 12*(2*x^5 - x^2)*e^(2*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 5: 1611512 x |--> -1/12*(191*x^7 + 73*x^6*e^x + 24*x^5*e^(2*x) + 12*x^2*e^(3*x) + 12*(x^2 + 4)*e^(5*x) - 12*(2*x^2 + 1)*e^(4*x) - 72*e^(6*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 6: 1111880 x |--> -1/24*(239*x^7 + 72*x^6*e^x + 24*x^3*e^(2*x) + 24*(x - 6)*e^(6*x) + 24*(x^2 - 3*x + 4)*e^(5*x) - 24*(2*x^2 - 3*x + 1)*e^(4*x) - 24*(x^3 - x^2 + x)*e^(3*x) + 96*e^(7*x) - 24*e^(8*x))/x^8 Placing the root at 0: 462000 x |--> -(3*x^7 - x^3*e^x + (x - 10)*e^(6*x) + (x^2 - 4*x + 10)*e^(5*x) - (3*x^2 - 6*x + 5)*e^(4*x) - (x^3 - 3*x^2 + 4*x - 1)*e^(3*x) + (2*x^3 - x^2 + x)*e^(2*x) + 5*e^(7*x) - e^(8*x))/x^8 Placing the root at 1: 430080 x |--> -(3*x^7 + x^4*e^x + (x^4 + 6)*e^(3*x) - (2*x^4 + 1)*e^(2*x) - 15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8 Placing the root at 2: 994560 x |--> -1/6*(55*x^7 + 18*x^6*e^x - 6*x^4*e^(2*x) + 6*(x^4 + 1)*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 4: 818160 x |--> -1/12*(85*x^7 + 24*x^6*e^x - 12*x^2*e^(2*x) + 12*(x^2 + 10)*e^(5*x) + 12*(3*x^2 + 1)*e^(3*x) - 12*(3*x^2 + 5)*e^(4*x) - 120*e^(6*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 0: 325920 x |--> -(2*x^7 + x^2*e^x + 6*(x^2 + 1)*e^(3*x) + (x^2 + 20)*e^(5*x) - (4*x^2 + 1)*e^(2*x) - (4*x^2 + 15)*e^(4*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8 Placing the root at 1: 863800 x |--> -1/8*(55*x^7 - 18*x^5*e^x + 16*(x - 3)*e^(6*x) - 16*(3*x - 2)*e^(5*x) - 8*(x^2 - 6*x + 1)*e^(4*x) + 16*(x^2 - x)*e^(3*x) + 2*(9*x^5 - 4*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 2: 1818908 x |--> -1/72*(1295*x^7 + 495*x^6*e^x + 162*x^5*e^(2*x) + 72*x^2*e^(3*x) + 72*(2*x - 3)*e^(6*x) - 72*(4*x - 1)*e^(5*x) - 72*(x^2 - 2*x)*e^(4*x) + 216*e^(7*x) - 72*e^(8*x))/x^8 Placing the root at 0: 521640 x |--> -1/8*(27*x^7 - 8*x^3*e^x + 24*(x - 2)*e^(6*x) - 8*(9*x - 4)*e^(5*x) + 24*(2*x^2 - x)*e^(3*x) - 8*(3*x^2 - 9*x + 1)*e^(4*x) + 8*(x^3 - 3*x^2)*e^(2*x) + 32*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 7: 1256220 x |--> -1/8*(90*x^7 + 27*x^6*e^x + 8*x^3*e^(2*x) + 24*x^2*e^(3*x) + 24*(x - 1)*e^(6*x) - 8*(6*x - 1)*e^(5*x) - 24*(x^2 - x)*e^(4*x) + 24*e^(7*x) - 8*e^(8*x))/x^8 Placing the root at 1: 636720 x |--> -1/12*(59*x^7 - 18*x^5*e^x + 12*(x - 10)*e^(6*x) - 24*(2*x - 5)*e^(5*x) - 12*(4*x - 1)*e^(3*x) + 12*(6*x - 5)*e^(4*x) + 6*(3*x^5 + 2*x)*e^(2*x) + 60*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 2: 1378776 x |--> -1/12*(160*x^7 + 59*x^6*e^x + 18*x^5*e^(2*x) + 12*(x - 6)*e^(6*x) - 12*(3*x - 4)*e^(5*x) + 12*(3*x - 1)*e^(4*x) - 12*x*e^(3*x) + 48*e^(7*x) - 12*e^(8*x))/x^8 Placing the root at 5: 924280 x |--> -1/4*(32*x^7 + 9*x^6*e^x - 4*x^2*e^(2*x) + 8*(x - 3)*e^(6*x) - 8*(3*x - 2)*e^(5*x) - 4*(x^2 - 6*x + 1)*e^(4*x) + 8*(x^2 - x)*e^(3*x) + 16*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 0: 367920 x |--> -1/4*(9*x^7 + 4*x^2*e^x + 8*(x - 5)*e^(6*x) - 8*(4*x - 5)*e^(5*x) - 4*(x^2 - 12*x + 5)*e^(4*x) + 4*(3*x^2 - 8*x + 1)*e^(3*x) - 4*(3*x^2 - 2*x)*e^(2*x) + 20*e^(7*x) - 4*e^(8*x))/x^8 Placing the root at 1: 467040 x |--> -1/2*(7*x^7 - 2*x^5*e^x + 2*(x^5 - 1)*e^(2*x) + 12*e^(3*x) - 30*e^(4*x) + 40*e^(5*x) - 30*e^(6*x) + 12*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 2: 1039920 x |--> -1/6*(59*x^7 + 21*x^6*e^x + 6*x^5*e^(2*x) + 6*e^(3*x) - 30*e^(4*x) + 60*e^(5*x) - 60*e^(6*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 3: 677040 x |--> -1/6*(34*x^7 + 9*x^6*e^x + 6*(x - 10)*e^(6*x) - 12*(2*x - 5)*e^(5*x) - 6*(4*x - 1)*e^(3*x) + 6*(6*x - 5)*e^(4*x) + 6*x*e^(2*x) + 30*e^(7*x) - 6*e^(8*x))/x^8 Placing the root at 0: 258720 x |--> -1/2*(3*x^7 + 2*(x - 15)*e^(6*x) - 10*(x - 4)*e^(5*x) + 10*(2*x - 3)*e^(4*x) - 4*(5*x - 3)*e^(3*x) + 2*(5*x - 1)*e^(2*x) - 2*x*e^x + 12*e^(7*x) - 2*e^(8*x))/x^8 Placing the root at 1: 493920 x |--> -(4*x^7 + x^6*e^x - e^(2*x) + 6*e^(3*x) - 15*e^(4*x) + 20*e^(5*x) - 15*e^(6*x) + 6*e^(7*x) - e^(8*x))/x^8 Placing the root at 0: 181440 x |--> -(x^7 - 7*e^(2*x) + 21*e^(3*x) - 35*e^(4*x) + 35*e^(5*x) - 21*e^(6*x) + 7*e^(7*x) - e^(8*x) + e^x)/x^8 CPU time: 1185.43 s, Wall time: 1188.21 s |
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