Waldek Hebisch schrieb:
Hooray! Hooray! Hooray! So FriCAS has a better pivoting strategy and
more efficient multivariate gcd computations, I guess.
Appended below is a solution as rendered by the Derive 6.10 simplifier
(Derive simplification excludes rational factorization which would here
collapse the denominators). This solution is 10389 Byte in size (tildes
and line breaks and tildes counted too).
Another 6-by-6 system, whose solution is even noticeably smaller:
SOLVE([-j*e*i*z-3*k*e*i*z+c*i-e*(e^2*w+3*i*z),-j*e*(h*z+i*y)-k*(~
3*d*i*z+e*(2*h*z+3*i*y))+b*i+c*h-d*(3*e^2*w+2*i*z)-e*(e^2*v+3*h*~
z+2*i*y),a*i-j*e*(g*z+h*y+i*x)-k*(d*(2*h*z+3*i*y)+e*(g*z+2*h*y+3~
*i*x))+b*h+c*g-3*d^2*e*w-d*(3*e^2*v+2*h*z+i*y)-e*(e^2*u+3*g*z+2*~
h*y+i*x),a*h-j*e*(f*z+g*y+h*x)-k*(d*(g*z+2*h*y+3*i*x)+e*(g*y+2*h~
*x))+b*g+c*f-d^3*w-3*d^2*e*v-d*(3*e^2*u+2*g*z+h*y)-e*(3*f*z+2*g*~
y+h*x),a*g-j*e*(f*y+g*x)-k*(d*(g*y+2*h*x)+e*g*x)+b*f-d^3*v-3*d^2~
*e*u-d*(2*f*z+g*y)-e*(2*f*y+g*x),a*f-j*e*f*x-k*d*g*x-d^3*u-d*f*y~
-e*f*x],[u,v,w,x,y,z])
Here I have abandoned the Derive calculation when the intermediate
result reached 10 MByte in size.
Martin.
[u=(a*(d^6*i^3*(j^3+6*j^2+11*j+6)-3*d^5*e*h*i^2*(j^3+6*j^2+11*j+~
6)+d^4*e^2*i*(g*i*(3*j^3+2*j^2*(5*k+14)+j*(15*k^2+65*k+83)+3*(3*~
k^3+17*k^2+34*k+26))+3*h^2*(j^3+6*j^2+11*j+6))+d^3*e^3*(f*i^2*(7~
*j^3+3*j^2*(5*k+19)+j*(9*k^2+84*k+152)+3*(9*k^2+39*k+44))-h*(g*i~
*(6*j^3+3*j^2*(5*k+17)+3*j*(7*k^2+32*k+47)+12*k^3+71*k^2+149*k+1~
26)+h^2*(j^3+6*j^2+11*j+6)))+d^2*e^4*(g*(g*i*(3*j^3+9*j^2*(k+3)+~
j*(10*k^2+55*k+78)+6*(k^3+6*k^2+14*k+12))+h^2*(3*j^3+6*j^2*(k+4)~
+j*(8*k^2+38*k+63)+2*(2*k^3+13*k^2+29*k+27)))-3*f*h*i*(3*j^3+j^2~
*(7*k+25)+j*(4*k^2+39*k+68)+6*(2*k^2+9*k+10)))+d*e^5*(f*(g*i*(3*~
j^3+2*j^2*(4*k+13)+j*(9*k^2+49*k+73)+3*(7*k^2+23*k+22))+h^2*(3*j~
^3+2*j^2*(4*k+13)+j*(4*k^2+44*k+73)+6*(2*k^2+10*k+11)))-g^2*h*(3~
*j^3+2*j^2*(4*k+13)+j*(9*k^2+49*k+73)+4*k^3+29*k^2+73*k+66))+e^6~
*(f^2*i*(j+2)*(j+3)*(j+3*k+4)-2*f*g*h*(j+k+3)*(j^2+2*j*(k+3)+5*k~
+8)+g^3*(j+k+2)*(j+k+3)*(j+k+4)))-b*e*(d^5*g*i^2*(k+1)*(6*j^2+2*~
j*(6*k+17)+3*(3*k^2+13*k+16))+d^4*e*i*(3*f*i*(2*j^3+4*j^2*(k+4)+~
j*(3*k^2+24*k+43)+3*(3*k^2+12*k+13))-g*h*(k+1)*(8*j^2+j*(16*k+47~
)+3*(4*k^2+18*k+23)))+d^3*e^2*(g*(k+1)*(g*i*(3*j^2+3*j*(2*k+7)+2~
*(3*k^2+13*k+18))+h^2*(3*j^2+6*j*(k+3)+4*k^2+20*k+27))-f*h*i*(8*~
j^3+16*j^2*(k+4)+j*(12*k^2+97*k+173)+3*(12*k^2+49*k+53)))+d^2*e^~
3*(f*(g*i*(3*j^3+9*j^2*(k+3)+j*(12*k^2+56*k+77)+3*(8*k^2+25*k+23~
))+h^2*(3*j^3+6*j^2*(k+4)+j*(2*k+5)*(2*k+13)+6*(k+2)*(2*k+5)))-g~
^2*h*(k+1)*(3*j^2+2*j*(3*k+10)+4*k^2+22*k+33))+d*e^4*(3*f^2*i*(j~
+3)*(j^2+j*(2*k+5)+3*k+5)-f*g*h*(3*j^3+j^2*(7*k+25)+j*(6*k^2+40*~
k+67)+3*(4*k^2+17*k+19))+g^3*(j+k+3)*(j+k+4)*(k+1))+e^5*f*(j+1)*~
(g^2*(j+k+3)*(j+k+4)-f*h*(j+3)*(j+2*(k+2))))-c*(d^6*g*i^2*(k+1)*~
(-3*j^2-3*j*(3*k+7)-9*k^2-36*k-38)+d^5*e*i*(g*h*(k+1)*(3*j^2+j*(~
11*k+25)+12*k^2+49*k+52)-3*f*i*(j^3+3*j^2*(k+3)+j*(k+2)*(3*k+14)~
+3*(k+2)*(3*k+5)))+d^4*e^2*(f*h*i*(3*j^3+j^2*(11*k+29)+j*(12*k^2~
+77*k+98)+6*(6*k^2+22*k+19))+g*(k+1)*(g*i*(j^2-j*(2*k+3)-2*(3*k^~
2+11*k+11))-h^2*(j^2+j*(4*k+9)+2*(2*k^2+9*k+10))))+d^3*e^3*(f*(g~
*i*(j^3-2*j^2*(4*k+1)-j*(15*k^2+57*k+31)-27*k^2-77*k-44)-h^2*(j^~
3+2*j^2*(2*k+5)+j*(4*k^2+28*k+35)+6*(2*k^2+8*k+7)))+g^2*h*(k^2+3~
*k+2)*(3*j+4*k+11))-d^2*e^4*(3*f^2*i*(2*j^3+3*j^2*(k+5)+j*(13*k+~
35)+12*(k+2))-2*f*g*h*(k+1)*(3*j^2+4*j*(k+4)+7*k+19)+g^3*(j+k+4)~
*(k+1)*(k+2))+d*e^5*f*(j+1)*(f*h*(3*j^2+j*(4*k+19)+6*(2*k+5))-2*~
g^2*(j+k+4)*(k+1))-e^6*f^2*g*(j+1)*(j+2)*(j+k+4)))/((j+1)*(j+2)*~
(j+3)*(d^9*i^3-3*d^8*e*h*i^2+3*d^7*e^2*i*(g*i+h^2)-d^6*e^3*(3*f*~
i^2+h*(6*g*i+h^2))+3*d^5*e^4*(2*f*h*i+g*(g*i+h^2))-3*d^4*e^5*(f*~
(2*g*i+h^2)+g^2*h)+d^3*e^6*(3*f^2*i+6*f*g*h+g^3)-3*d^2*e^7*f*(f*~
h+g^2)+3*d*e^8*f^2*g-e^9*f^3)) AND v=-(a*e*(3*d^5*i^3*(j^3+6*j^2~
+11*j+6)-d^4*e*h*i^2*(9*j^3+2*j^2*(10*k+37)+j*(30*k^2+130*k+199)~
+6*(3*k^3+17*k^2+34*k+29))+d^3*e^2*i*(h^2*(9*j^3+6*j^2*(5*k+14)+~
3*j*(14*k^2+64*k+83)+2*(12*k^3+71*k^2+149*k+117))-g*i*(j^3+2*j^2~
*(5*k+8)+j*(6*k^2+56*k+61)+6*(3*k^2+13*k+11)))+d^2*e^3*(3*f*i^2*~
(2*j^3+6*j^2*(k+3)+j*(3*k^2+33*k+52)+3*(3*k^2+15*k+16))-h*(g*i*(~
3*j^3+6*j^2*(k+4)+j*(13*k^2+43*k+63)+3*(4*k^3+17*k^2+25*k+18))+h~
^2*(j+2*k+5)*(3*j^2+3*j*(2*k+5)+2*(2*k^2+8*k+9))))-d*e^4*(2*f*h*~
i*(3*j^3+j^2*(11*k+29)+j*(9*k^2+64*k+88)+3*(7*k^2+29*k+28))+g*(2~
*g*i*(j+3)*(j+k+2)*(k+1)-h^2*(j+2*k+5)*(3*j^2+3*j*(2*k+5)+2*(2*k~
^2+8*k+9))))+e^5*(f*(g*i*(j+3)*(j+k+2)*(j+3*k+5)+h^2*(j+2)*(j+2*~
k+3)*(j+2*k+5))-g^2*h*(j+k+2)*(j+k+3)*(j+2*k+5)))-b*(d^6*i^3*(j^~
3+6*j^2+11*j+6)-d^5*e*h*i^2*(3*j^3+6*j^2*(2*k+5)+j*(24*k^2+92*k+~
101)+6*(3*k^3+16*k^2+29*k+19))+d^4*e^2*i*(h^2*(3*j^3+2*j^2*(8*k+~
17)+j*(32*k^2+126*k+127)+6*(4*k^3+22*k^2+41*k+26))-g*i*(3*j^3+2*~
j^2*(4*k+13)+3*j*(2*k^2+16*k+25)+18*(k+2)^2))+d^3*e^3*(f*i^2*(7*~
j^3+3*j^2*(5*k+19)+j*(9*k^2+87*k+155)+3*(9*k^2+42*k+47))+h*(g*i*~
(2*j^3+3*j^2*(k+5)-j*(5*k^2-k-28)-12*k^3-43*k^2-40*k+3)-h^2*(j+2~
*k+3)*(j+2*k+5)*(j+2*(k+2))))-d^2*e^4*(f*h*i*(9*j^3+27*j^2*(k+3)~
+j*(24*k^2+154*k+229)+3*(16*k^2+65*k+67))+g*(k+1)*(2*g*i*(j+3)*(~
k+1)-h^2*(j+2*k+5)*(3*j+4*k+9)))-d*e^5*(f*(g*i*(j^2-3*j*k-9*(k+1~
))*(k+1)-h^2*(j+2*k+5)*(3*j^2+j*(4*k+13)+6*(k+2)))+g^2*h*(j+k+3)~
*(j+2*k+5)*(k+1))+e^6*f*(j+1)*(f*i*(j+3)*(j+3*k+5)-g*h*(j+k+3)*(~
j+2*k+5)))-c*(2*d^6*h*i^2*(k+1)*(3*j^2+3*j*(3*k+7)+9*k^2+36*k+38~
)+d^5*e*i*(g*i*(3*j^3+6*j^2*(k+4)+j*(6*k^2+40*k+67)+6*(3*k^2+11*~
k+11))-2*h^2*(k+1)*(3*j^2+j*(11*k+25)+12*k^2+49*k+52))-d^4*e^2*(~
3*f*i^2*(2*j^3+4*j^2*(k+4)+j*(3*k^2+25*k+44)+3*(k+2)*(3*k+7))+h*~
(g*i*(3*j^3+2*j^2*(4*k+13)+3*j*(k^2+11*k+21)-12*k^3-35*k^2-13*k+~
28)-2*h^2*(j+2*k+5)*(j+2*(k+2))*(k+1)))+d^3*e^3*(2*f*h*i*(4*j^3+~
2*j^2*(7*k+19)+j*(15*k^2+84*k+113)+27*k^2+104*k+101)-g*(g*i*(j^3~
+2*j^2*(k+4)-j*(2*k^2-4*k-17)-6*(k^2+k-1))-h^2*(j+2*k+5)*(j^2+3*~
j-2*(2*k^2+5*k+2))))+d^2*e^4*(f*(g*i*(3*j^3+6*j^2*(k+4)-j*(3*k^2~
-17*k-53)-3*(3*k^2+k-8))-h^2*(j+2*k+5)*(3*j^2+3*j*(2*k+5)+2*(4*k~
+7)))+g^2*h*(j+2*k+5)*(k^2+3*k+2))+d*e^5*f*(j+1)*(2*g*h*(j+2*k+5~
)*(k+1)-3*f*i*(j^2+j*(2*k+7)+6*(k+2)))+e^6*f^2*h*(j+1)*(j+2)*(j+~
2*k+5)))/((j+1)*(j+2)*(j+3)*(d^9*i^3-3*d^8*e*h*i^2+3*d^7*e^2*i*(~
g*i+h^2)-d^6*e^3*(3*f*i^2+h*(6*g*i+h^2))+3*d^5*e^4*(2*f*h*i+g*(g~
*i+h^2))-3*d^4*e^5*(f*(2*g*i+h^2)+g^2*h)+d^3*e^6*(3*f^2*i+6*f*g*~
h+g^3)-3*d^2*e^7*f*(f*h+g^2)+3*d*e^8*f^2*g-e^9*f^3)) AND w=i*(j+~
3*(k+2))*(a*e^2*(3*d^4*i^2*(2*j^2+2*j*(2*k+5)+3*k^2+11*k+12)-4*d~
^3*e*h*i*(2*j^2+2*j*(2*k+5)+3*k^2+11*k+12)+d^2*e^2*(3*g*i*(j^2+j~
*(2*k+5)+2*(k^2+3*k+3))+h^2*(3*j^2+3*j*(2*k+5)+2*(2*k^2+8*k+9)))~
+d*e^3*(3*f*i*(j+2)*(j+2*k+3)-g*h*(3*j^2+3*j*(2*k+5)+2*(2*k^2+8*~
k+9)))+e^4*(g^2*(j+k+2)*(j+k+3)-f*h*(j+2)*(j+2*k+3)))-b*e*(3*d^5~
*i^2*(j^2+3*j*(k+2)+3*k^2+10*k+9)-d^4*e*h*i*(3*j^2+j*(11*k+20)+3~
*(4*k^2+13*k+11))+d^3*e^2*(h^2*(j+2*k+3)*(j+2*(k+2))-g*i*(j^2+j*~
(1-2*k)-2*(3*k^2+7*k+3)))+d^2*e^3*(3*f*i*(2*j^2+3*j*(k+3)+5*k+9)~
-g*h*(k+1)*(3*j+4*k+9))+d*e^4*(g^2*(j+k+3)*(k+1)-f*h*(3*j^2+j*(4~
*k+13)+6*(k+2)))+e^5*f*g*(j+1)*(j+k+3))+c*(d^6*i^2*(j+3*k+4)*(j+~
3*k+5)-2*d^5*e*h*i*(3*j*(k+1)+6*k^2+17*k+11)+d^4*e^2*(2*h^2*(j*(~
k+1)+2*(k^2+3*k+2))-g*i*(3*j^2+j*(2*k+11)-6*k^2-10*k+2))+d^3*e^3~
*(f*i*(7*j^2+3*j*(4*k+11)+18*k+32)+g*h*(j^2+3*j-2*(2*k^2+5*k+2))~
)+d^2*e^4*(g^2*(k^2+3*k+2)-f*h*(3*j^2+3*j*(2*k+5)+2*(4*k+7)))+2*~
d*e^5*f*g*(j+1)*(k+1)+e^6*f^2*(j+1)*(j+2)))/((j+1)*(j+2)*(j+3)*(~
d^9*i^3-3*d^8*e*h*i^2+3*d^7*e^2*i*(g*i+h^2)-d^6*e^3*(3*f*i^2+h*(~
6*g*i+h^2))+3*d^5*e^4*(2*f*h*i+g*(g*i+h^2))-3*d^4*e^5*(f*(2*g*i+~
h^2)+g^2*h)+d^3*e^6*(3*f^2*i+6*f*g*h+g^3)-3*d^2*e^7*f*(f*h+g^2)+~
3*d*e^8*f^2*g-e^9*f^3)) AND x=(d*(b*e*(d^6*i^2*(6*j^2+2*j*(6*k+1~
7)+3*(3*k^2+13*k+16))-d^5*e*h*i*(8*j^2+j*(16*k+47)+3*(4*k^2+18*k~
+23))+d^4*e^2*(g*i*(3*j^2+3*j*(2*k+7)+6*k^2+26*k+36)+h^2*(3*j^2+~
6*j*(k+3)+4*k^2+20*k+27))+d^3*e^3*(f*i*(3*j^2+2*j*(3*k+5)+3*(2*k~
+1))-g*h*(3*j^2+2*j*(3*k+10)+4*k^2+22*k+33))+d^2*e^4*(g^2*(j^2+j~
*(2*k+7)+k^2+7*k+12)-f*h*(j^2+j*(2*k+1)-6))-d*e^5*f*g*(3*j+2*k+9~
)+e^6*f^2*(j+3))-c*d*(d^6*i^2*(3*j^2+3*j*(3*k+7)+9*k^2+36*k+38)-~
d^5*e*h*i*(3*j^2+j*(11*k+25)+12*k^2+49*k+52)+d^4*e^2*(h^2*(j^2+j~
*(4*k+9)+4*k^2+18*k+20)-g*i*(j^2-j*(2*k+3)-6*k^2-22*k-22))+d^3*e~
^3*(f*i*(6*j^2+3*j*(3*k+8)+9*k+14)-g*h*(3*j*(k+2)+4*k^2+19*k+22)~
)+d^2*e^4*(g^2*(j+k+4)*(k+2)-f*h*(3*j^2+j*(4*k+11)+2*(k+1)))+d*e~
^5*f*g*(j^2+j*(k+3)-k-4)+2*e^6*f^2))-a*e^2*(d^6*i^2*(10*j^2+5*j*~
(3*k+10)+3*(3*k^2+14*k+20))-d^5*e*h*i*(15*j^2+3*j*(7*k+25)+12*k^~
2+59*k+90)+d^4*e^2*(g*i*(9*j^2+5*j*(2*k+9)+6*(k^2+5*k+9))+2*h^2*~
(3*j^2+j*(4*k+15)+2*k^2+11*k+18))-d^3*e^3*(f*i*(2*j^2+j*(10-3*k)~
-3*(k-4))+g*h*(8*j^2+j*(9*k+40)+4*k^2+25*k+48))+d^2*e^4*(f*h*(3*~
j^2+15*j+2*(k+9))+g^2*(3*j^2+3*j*(k+5)+k^2+8*k+18))-d*e^5*f*g*(3~
*j^2+j*(k+15)+3*(k+6))+e^6*f^2*(j+2)*(j+3)))/((j+1)*(j+2)*(j+3)*~
(d^9*i^3-3*d^8*e*h*i^2+3*d^7*e^2*i*(g*i+h^2)-d^6*e^3*(3*f*i^2+h*~
(6*g*i+h^2))+3*d^5*e^4*(2*f*h*i+g*(g*i+h^2))-3*d^4*e^5*(f*(2*g*i~
+h^2)+g^2*h)+d^3*e^6*(3*f^2*i+6*f*g*h+g^3)-3*d^2*e^7*f*(f*h+g^2)~
+3*d*e^8*f^2*g-e^9*f^3)) AND y=-e*(a*e^2*(3*d^5*i^2*(5*j^2+j*(9*~
k+25)+6*k^2+25*k+30)-d^4*e*h*i*(21*j^2+j*(37*k+105)+24*k^2+103*k~
+126)+2*d^3*e^2*(g*i*(5*j^2+j*(8*k+25)+6*(k^2+4*k+5))+h^2*(4*j^2~
+j*(7*k+20)+4*k^2+19*k+24))+d^2*e^3*(3*f*i*(j^2+j*(3*k+5)+5*k+6)~
-g*h*(9*j^2+15*j*(k+3)+8*k^2+41*k+54))+d*e^4*(g^2*(j+k+2)*(3*j+2~
*k+9)-2*f*h*k*(j+1))-e^5*f*g*(j+3)*(j+k+2))-b*e*(d^6*i^2*(8*j^2+~
j*(21*k+47)+3*(6*k^2+23*k+23))-3*d^5*e*h*i*(3*j^2+j*(9*k+19)+8*k~
^2+31*k+30)+d^4*e^2*(2*g*i*(j*(4*k+5)+6*k^2+20*k+15)+h^2*(3*j^2+~
10*j*(k+2)+8*k^2+34*k+33))+d^3*e^3*(f*i*(11*j^2+j*(15*k+47)+21*(~
k+2))-g*h*(j^2+j*(9*k+13)+8*k^2+35*k+30))+d^2*e^4*(g^2*(3*j*(k+1~
)+2*k^2+11*k+9)-6*f*h*(j^2+j*(k+4)+k+3))+d*e^5*f*g*(3*j^2+j*(k+1~
1)-k+6)-e^6*f^2*(j^2+4*j+3))+c*d*(d^6*i^2*(3*j^2+5*j*(3*k+5)+18*~
k^2+63*k+52)-d^5*e*h*i*(j^2+j*(17*k+21)+24*k^2+83*k+62)+2*d^4*e^~
2*(h^2*(3*j*(k+1)+4*k^2+15*k+11)-g*i*(3*j^2+9*j-2*(3*k^2+8*k+2))~
)+d^3*e^3*(f*i*(15*j^2+j*(21*k+67)+27*k+58)+g*h*(3*j^2+j*(7-3*k)~
-8*k^2-29*k-14))-d^2*e^4*(2*f*h*(4*j^2+j*(5*k+18)+5*k+14)+g^2*(j~
^2+j*(3-k)-2*k^2-9*k-4))+d*e^5*f*g*(3*j^2+3*j*(k+5)+k+10)-2*e^6*~
f^2*(j+1)))/((j+1)*(j+2)*(j+3)*(d^9*i^3-3*d^8*e*h*i^2+3*d^7*e^2*~
i*(g*i+h^2)-d^6*e^3*(3*f*i^2+h*(6*g*i+h^2))+3*d^5*e^4*(2*f*h*i+g~
*(g*i+h^2))-3*d^4*e^5*(f*(2*g*i+h^2)+g^2*h)+d^3*e^6*(3*f^2*i+6*f~
*g*h+g^3)-3*d^2*e^7*f*(f*h+g^2)+3*d*e^8*f^2*g-e^9*f^3)) AND z=-e~
^2*(a*e^2*(3*d^4*i^2*(2*j^2+2*j*(2*k+5)+3*k^2+11*k+12)-4*d^3*e*h~
*i*(2*j^2+2*j*(2*k+5)+3*k^2+11*k+12)+d^2*e^2*(3*g*i*(j^2+j*(2*k+~
5)+2*(k^2+3*k+3))+h^2*(3*j^2+3*j*(2*k+5)+2*(2*k^2+8*k+9)))+d*e^3~
*(3*f*i*(j+2)*(j+2*k+3)-g*h*(3*j^2+3*j*(2*k+5)+2*(2*k^2+8*k+9)))~
+e^4*(g^2*(j+k+2)*(j+k+3)-f*h*(j+2)*(j+2*k+3)))-b*e*(3*d^5*i^2*(~
j^2+3*j*(k+2)+3*k^2+10*k+9)-d^4*e*h*i*(3*j^2+j*(11*k+20)+3*(4*k^~
2+13*k+11))+d^3*e^2*(h^2*(j+2*k+3)*(j+2*(k+2))-g*i*(j^2+j*(1-2*k~
)-2*(3*k^2+7*k+3)))+d^2*e^3*(3*f*i*(2*j^2+3*j*(k+3)+5*k+9)-g*h*(~
k+1)*(3*j+4*k+9))+d*e^4*(g^2*(j+k+3)*(k+1)-f*h*(3*j^2+j*(4*k+13)~
+6*(k+2)))+e^5*f*g*(j+1)*(j+k+3))+c*(d^6*i^2*(j+3*k+4)*(j+3*k+5)~
-2*d^5*e*h*i*(3*j*(k+1)+6*k^2+17*k+11)+d^4*e^2*(2*h^2*(j*(k+1)+2~
*(k^2+3*k+2))-g*i*(3*j^2+j*(2*k+11)-6*k^2-10*k+2))+d^3*e^3*(f*i*~
(7*j^2+3*j*(4*k+11)+18*k+32)+g*h*(j^2+3*j-2*(2*k^2+5*k+2)))+d^2*~
e^4*(g^2*(k^2+3*k+2)-f*h*(3*j^2+3*j*(2*k+5)+2*(4*k+7)))+2*d*e^5*~
f*g*(j+1)*(k+1)+e^6*f^2*(j+1)*(j+2)))/((j+1)*(j+2)*(j+3)*(d^9*i^~
3-3*d^8*e*h*i^2+3*d^7*e^2*i*(g*i+h^2)-d^6*e^3*(3*f*i^2+h*(6*g*i+~
h^2))+3*d^5*e^4*(2*f*h*i+g*(g*i+h^2))-3*d^4*e^5*(f*(2*g*i+h^2)+g~
^2*h)+d^3*e^6*(3*f^2*i+6*f*g*h+g^3)-3*d^2*e^7*f*(f*h+g^2)+3*d*e^~
8*f^2*g-e^9*f^3))]