# Test cases for hypergeomdeg3. # L[38] has non trivial gauge transformation. # L[39] and L[40] resp. are solved when extension field {RootOf(x^2-2)} and {RootOf(x^2+2)} resp. are specified in the input. L:= [Dx^2+(1/20)*(13+70*x^3)*Dx/(x*(2*x^3-1))-(1089/1600)/(x^2*(2*x^3-1)), Dx^2+(1/2)*(5*x^6+3*x^3-24)*Dx/(x*(x^3+2)*(x^3+3))+(1/16)*x^4/((x^3+3)*(x^3+2)^2), Dx^2+(1/2)*(4*x^3+12*x^2+12*x+5)*Dx/((x+1)*(x^2+3*x+3)*x)+(1/16)*(x+1)/(x^2*(x^2+3*x+3)^2), Dx^2+(1/2)*(5*x^3+15*x^2+15*x+4)*Dx/((x+1)*(x^2+3*x+3)*x)-(1/16)/((x+1)^2*(x^2+3*x+3)*x), Dx^2+(1/4)*(10*x^3+30*x^2+30*x+11)*Dx/((x+1)*(x^2+3*x+3)*x)-(25/64)/((x+1)^2*(x^2+3*x+3)*x), Dx^2+(4*x^3-6*x^2+1+2*x)*Dx/(x*(x-1)*(2*x+1)*(2*x-3))+3/((x-1)^2*(2*x+1)^2*(-2*x+3)), Dx^2+(25*x^3-155*x^2+346*x-288)*Dx/((x-2)*(5*x-2)*(x-4)*(5*x-8))-(5/36)*(5*x-8)^2/((5*x-2)*(x-1)^2*(x-2)^2*(x-4)), Dx^2+(1/2)*(400*x^3-1695*x^2+2403*x-1064)*Dx/((8*x-7)*(5*x-4)*(5*x-7)*(x-2))-(1/2)*(5*x-7)^2/(x^2*(8*x-7)^2*(x-2)), Dx^2+(1/10)*(173*x^3-162*x^2-4*x+104+140*x^4)*Dx/(x*(x+2)*(x-2)*(7*x^2+8*x+4))-(1089/400)*(x+2)/(x^2*(x-2)*(7*x^2+8*x+4)), Dx^2+(1/10)*(120*x^5-102*x^4-1609*x^3-2682*x^2-1836*x-536)*Dx/((x+2)*(2+3*x)*(x+1)*(2*x^3-15*x^2+4-12*x))+(243/400)*(2+3*x)^2/((2*x^3-15*x^2+4-12*x)*(x+2)^2*(x+1)), Dx^2+(1/6)*(567*x^6+2880*x^5-1706*x^4-44060*x^3-154889*x^2-288764*x-236460)*Dx/((9*x^2+43+41*x)*(9*x^2+10*x-35)*(x+3)*(x^2+7))+(1/144)*(x+4)*(9*x^2+10*x-35)^2/((9*x^2+43+41*x)^2*(x+3)*(x^2+7)), Dx^2+2*x*(x^2-2)*Dx/((x+2)*(x-2)*(x-1)*(x+1))+4/((x-1)^2*(x+2)^2*(-4*x+8)), Dx^2+(2/15)*(150*x^4-728*x^3+1170*x^2-639*x+27)*Dx/(x*(5*x-9)*(2*x-3)*(x-1)*(x-2))+(72/25)*(2*x-3)/(x^2*(5*x-9)^2*(x-1)), Dx^2+(4/15)*(27*x^5-9*x^4-32*x^3-4*x^2+5*x+3)*Dx/((3*x+1)*(x^2-1-x)*x*(x+1)*(x-1))+(2/75)*(3*x+1)^2/((x+1)*x*(x^2-1-x)), Dx^2+(2/15)*(441*x^5+1904*x^4+2359*x^3+651*x^2-380*x-115)*Dx/((x+2)*(7*x+5)*(x-1)*(x+1)*(7*x^2+13*x+7))-(2/75)*(7*x+5)^2/((7*x^2+13*x+7)*(x+1)*(x+2)^2), Dx^2+(2/3)*(15*x^6-80*x^5+177*x^4-208*x^3+60*x^2+4*x+24)*Dx/((3*x^2+x+2)*(x-2)*(2*x^2-3*x+2)*x*(x-3))-(2/9)*(2*x^2-3*x+2)^2/((x-3)*(3*x^2+x+2)^2*(x-2)^2*x), Dx^2+(1/20)*(6622*x^4-4983*x^5-168*x^3+741*x^6-2625*x^2+1628*x-36+125*x^7)*Dx/(x*(x-2)*(5*x+x^2-2)*(x+1)*(5*x^3-21*x^2+18*x-1))-(121/1600)*(5*x+x^2-2)^2/(x^2*(5*x^3-21*x^2+18*x-1)*(x-2)^2), Dx^2+(1/3)*(-249*x^5-300*x^7-30*x^4-37*x^9+408*x^6+150*x^3+102*x^8-96*x^2+21*x-8+12*x^10)*Dx/((x^3+2)*(3*x+x^3-1)*(x-1)*x*(2*x^3-2-6*x^2+3*x))+(1/12)*(3*x+x^3-1)^2/((2*x^3-2-6*x^2+3*x)*(x^3+2)^2*x), Dx^2+(2/3)*(5*x^5+155*x^4+1481*x^3+5593*x^2+4138*x-2624)*Dx/((x+11)*(x+2)*(2*x+7)*(x-1)*(x+1)*(x+26))+6*(2*x+7)^2/((x+1)*(x-1)^2*(x+26)^2*(x+2)), Dx^2+(1/6)*(-80801*x^5-854294*x^4+408016*x^3+10376*x^2-34384*x+6272+392940*x^6)*Dx/((2+3*x)*(5*x-2)*(59*x-14)*(x-1)*x*(37*x^2+66*x-28))-(1/18)*(x-1)*(59*x-14)^2/((37*x^2+66*x-28)*x*(2+3*x)^2*(5*x-2)^2), Dx^2+(1/3)*(-34*x^6-888*x^4-316*x^5-1312*x^2-1648*x^3+960*x+1152+3*x^7)*Dx/((x+2)*(x-2)*(x^2-12-8*x)*(x+1)*x*(x^2+4*x+12))-(1/9)*(x^2-12-8*x)^2/((x^2+4*x+12)*x*(x+2)^2*(x+1)^2), Dx^2+(1/6)*(8*x^9+93*x^8+36*x^7-66*x^6+240*x^5+81*x^4+276*x^3+552*x^2+288*x+80)*Dx/(x*(x^2-1-x)*(x+2)*(x^3+6*x^2-3*x-2)*(x+1)*(x^2-x+4))+(1/144)*(x^3+6*x^2-3*x-2)^2/(x^2*(x^2-1-x)^2*(x+1)*(x^2-x+4)), Dx^2+(1/6)*(480-896*x+1584*x^2-1664*x^3+432*x^4+1504*x^5-1848*x^6+1184*x^7-450*x^8+80*x^9-9*x^10+8*x^11)*Dx/(x*(x-1)*(x-2)*(x^3+2*x+6)*(x^2+2)*(x^4+4*x^2-12*x+4))+(1/48)*(x^4+4*x^2-12*x+4)^2/(x^2*(x^3+2*x+6)*(x-1)^2*(x-2)^2*(x^2+2)), Dx^2+(1/6)*(155520-99072*x-26208*x^2-768*x^3+13968*x^4+10304*x^5-9220*x^6-148*x^7+1360*x^8-248*x^9-25*x^10+7*x^11)*Dx/((x^2-6)*(-4*x^2+18+x^3-4*x)*(x-3)*(x-2)*(x+2)*(x^4-14*x^2+24+12*x))+(1/144)*(x^4-14*x^2+24+12*x)^2/((-4*x^2+18+x^3-4*x)*(x^2-6)^2*(x-3)*(x-2)*(x+2)), Dx^2+(1/10)*(355*x^7-2400*x^6-14376*x^5-21648*x^4+1344*x^3+27008*x^2+22016*x+6144+100*x^8)*Dx/((x+2)*(x+3)*(5*x^2+16*x+8)*(x-2)*x*(x+1)*(x^2-8*x-8))+(363/800)*(5*x^2+16*x+8)^2/((x^2-8*x-8)*x*(x+2)^2*(x+3)^2*(x+1)), Dx^2+(1/3)*(2430+5103*x-2970*x^2-10962*x^3-6582*x^4-890*x^5+242*x^6+90*x^7+32*x^8+7*x^9)*Dx/(x*(2*x+3)*(x^3+2*x^2+3*x+9)*(x-6)*(x+1)*(x-1)*(x+2)*(x+3))+(1/36)*(x^3+2*x^2+3*x+9)^2/(x^2*(x-1)*(x+2)*(x+3)*(2*x+3)^2*(x-6)), Dx^2+(1/6)*(1183*x^9-36998*x^8+538776*x^7-4508224*x^6+20675360*x^5-44675328*x^4+18922368*x^3+86321664*x^2-139044096*x+58129920)*Dx/(x*(13*x-58)*(x+2)*(13*x^3-142*x^2+660*x-696)*(x-12)*(x-2)*(x-1)*(x-6))+(1/144)*(13*x^3-142*x^2+660*x-696)^2/(x^2*(x-6)*(13*x-58)^2*(x-12)*(x-2)*(x-1)), Dx^2+(1/6)*(-4230144+1575936*x+14688000*x^2-19369728*x^3+9732480*x^4-2494336*x^5+357920*x^6+41312*x^7-45644*x^8+9388*x^9-593*x^10+9*x^11)*Dx/((x+2)*(x-2)*(x-3)*(x^2-16*x+12)*(x-6)*(x-1)*(x+6)*(144-96*x+88*x^2-32*x^3+x^4))+(1/72)*(144-96*x+88*x^2-32*x^3+x^4)^2/((x^2-16*x+12)*(x+2)^2*(x-2)^2*(x-3)^2*(x-6)*(x-1)*(x+6)), 64*(x+4)*(x-2)*x*(3*x-4)*Dx^2+(1280+528*x^3+96*x^2-2368*x)*Dx+99*x^2-30*x-120, 9*(x+4)*(x-2)*(3*x-4)*Dx^2+(12*x-192+63*x^2)*Dx+9*x-4, 16*(x-2)*(x+1)*(x+2)*(x-1)*Dx^2+8*x*(7*x^2-17)*Dx+21*(x-1)*(x+1), 4*(7*x+3)*(7*x+2)*(7*x-6)*Dx^2+(-140*x-456+3136*x^2)*Dx+45+455*x, 4*(x^3-2)*x*Dx^2+(12*x^3-4)*Dx+3*x^2, 9*(x+1)*(x^2-x+1)*Dx^2+18*x^2*Dx+2*x, 16*(x^3+4)*x*Dx^2+(56*x^3+48)*Dx+21*x^2, 98*x*(18*x^3+49)*Dx^2+(4788*x^3+686)*Dx+855*x^2, 49*x*(8*x^3-49)*Dx^2+(1064*x^3-1372)*Dx+190*x^2, (x-37)*(x^2+3)*Dx^2+(x^2+3)*Dx-(9/16)*x-81/16, 2*(2*x^2-1)*(8*x^2-1)*Dx^2+4*x*(24*x^2-7)*Dx+24*x^2-3, 64*(x^2+2)*(x^2+8)*Dx^2+16*x*(13*x^2+62)*Dx+65*x^2+130]: