f := (1-t)*(1-s)*(1-u)/(1-2*(s+t+u)+3*(s*t+t*u+u*s)-4*s*t*u): F := normal(eval(f, {t=t/s, u=x/t})/s/t); P2 := x*(x-1)*(64*x-1)*(3*x-2)*(6*x+1)*dx^2 +(4608*x^4-6372*x^3+813*x^2+514*x-4)*dx +4*(576*x^3-801*x^2-108*x+74): q := denom(F): q1 := q/s/t: disc := factor(discrim(q1, t)); U := 93312*s^2*x^5*t^2+130974*t*x^3*s^4-32256*s^6*t^2*x^4+18432*x^3*s^7*t^2-972*x^3 *s*t-3312*s^8*x*t+71496*x^3*s^7*t-123732*t^2*x^4*s^2+25164*t^2*x^4*s+13542*t^2 *x^3*s^3-83858*t*x^3*s^3-9972*t^2*x^3*s+27054*x^4*s^2*t-4509*x^4*s*t+203904*s^ 4*x^5*t-225504*s^3*x^5*t-20412*s*x^5*t+110808*s^2*x^5*t-7776*t^3*x^3*s-46656*s *x^5*t^2-69120*t*x^5*s^5-82944*x^5*s^3*t^2+268140*x^4*s^3*t^2+27648*x^5*s^4*t^ 2-292720*t^2*x^4*s^4+20148*t*x^3*s^2-54324*t*x^4*s^3-18096*t^2*x*s^7+10464*s^7 *x*t+24472*t^2*x*s^6+150736*t^2*x^3*s^5+88836*t^2*x^2*s^6-93528*t^3*x^3*s^3+ 88128*t^3*x^3*s^4+37224*t^3*x*s^6-121536*t^3*x^2*s^5-67920*t^3*x*s^5-18432*t*x ^3*s^8-53272*x^3*s^5*t+23204*x^4*s^4*t-65872*t*x^3*s^6+22266*t^2*x^3*s^2+32256 *s^7*x^4*t-84096*t*x^4*s^6+60688*x^4*s^5*t+5184*t^2*x*s^8+10080*t*x^2*s^8-\ 31104*t^3*x^3*s^5-30816*t^2*x^2*s^7-7776*t^3*x*s^7-87048*t^2*x^3*s^6+38880*t^3 *x^2*s^6+3168*t^2*x*s^3+11038*t^2*x^2*s^2-4864*s^4*t*x-14006*t*x^2*s^3-450*x*s ^4*t^2+11482*x*s^5*t-13230*s^5*x*t^2-14814*s^6*x*t-1620*x^2*s*t^2+1620*t*x^2*s ^2-72*t*x*s^2+1008*t*x*s^3+44064*t^3*x^3*s^2+72*x*s*t^2-3816*t^3*x^2*s+4240*t^ 3*x*s^2-107748*t^2*x^2*s^5+81372*t*x^2*s^6-108928*t^2*x^3*s^4+152544*t^3*x^2*s ^4-96010*x^2*s^3*t^3-43764*t*x^2*s^7+75408*x^2*s^4*t^2-82428*x^2*s^5*t+47126*x ^2*s^4*t+30264*x^2*t^3*s^2+59684*t^3*x*s^4-56*s^2*t^2+56*s^3*t+616*s^3*t^2-\ 152544*x^4*s^5-424*t^3*s^3-2343*s^4*t^2+2555*s^5*t-616*s^4*t+2968*s^4*t^3+3522 *s^5*t^2-7738*s^5*t^3-556*s^6*t^2+424*x^2*s^4-2968*x^2*s^5+7738*x^2*s^6-4240*x ^3*s^3+25456*x^3*s^4-59684*x^3*s^5+8904*s^6*t^3-3816*t^3*s^7+67920*x^3*s^6-\ 37224*s^7*x^3-3568*s^7*t^2-8904*x^2*s^7-30264*x^4*s^3+7776*s^8*x^3-88128*x^5*s ^5+31104*x^5*s^6+3816*x^4*s^2+121536*x^4*s^6+3816*x^2*s^8+972*t^2*x^3-44064*x^ 5*s^3+7776*x^5*s^2+2544*s^8*t^2-5112*t*s^6+5008*t*s^7-1944*s^8*t-1215*t^2*x^4+ 93528*x^5*s^4-38880*x^4*s^7+8748*x^5*t^2+96010*x^4*s^4-35530*x^2*s^3*t^2+ 156672*t^2*x^4*s^5-1008*t^2*x*s^2-25456*t^3*x*s^3 : V := 60448512*x^7*s^9-15683328*x^8*s^8-23946240*x^6*s^10+1929744*x^5*s^11+3888*s^4* x^5-288*s^5*x^3+9216*s^5*x^4-152472*s^6*x^4-2144*s^6*x^3+160*s^6*x^2+42944*s^7 *x^3-2000*s^7*x^2-151668*x^6*s^4+133688*x^5*s^5+1411782*x^6*s^5-1378968*x^5*s^ 6+972348*x^4*s^7+5453876*x^5*s^7-3339516*x^4*s^8-230966*x^3*s^8+10756*x^2*s^8+ 640331*x^3*s^9-31726*x^2*s^9+68688*x^7*s^3-975942*s^4*x^7-5804536*s^6*x^6+ 5983065*s^5*x^7+14117630*s^7*x^6-20898942*s^6*x^7-11450508*s^8*x^5+6976068*s^9 *x^4+13665486*s^9*x^5-23127160*s^8*x^6-9275888*s^10*x^4-1046242*s^10*x^3+54172 *s^10*x^2+1039326*s^11*x^3-51042*s^11*x^2+139968*x^8*s^3-1358856*x^8*s^4+ 5677452*x^8*s^5+45887180*x^7*s^7-13230216*s^6*x^8+27437316*s^9*x^6-65513024*s^ 8*x^7+18565632*s^7*x^8-8719744*s^10*x^5+7837100*s^11*x^4-611912*s^12*x^3+20328 *s^12*x^2+2808*s^13*x^2+14502528*s^11*x^6-34371072*s^10*x^7+714528*s^12*x^5-\ 3991056*s^12*x^4+1057824*s^13*x^4+195000*s^13*x^3+7382016*s^9*x^8+10699776*s^ 11*x^7-1492992*s^10*x^8-5270400*s^12*x^6-351648*s^13*x^5-3456*s^14*x^2-93312*s ^14*x^4-26208*s^14*x^3-1327104*s^12*x^7+829440*s^13*x^6+56*s^6*t^2-104*s^5*t^3 -232*s^7*t^2-104*s^6*t^3-1891*s^8*t^2+9509*s^7*t^3+17826*s^9*t^2-60962*s^8*t^3 -16*s^7*t+184*s^8*t-2304*x^2*s^5*t+4320*x^3*s^4*t+192*x*s^6*t-1296*x^4*s^3*t+ 3240*x^4*s^2*t^2-71352*s^4*x^4*t+145728*s^3*x^4*t^2+23328*s^3*x^5*t-9648*s^3*x ^3*t^2+1168336*s^5*x^4*t-2189309*s^4*x^4*t^2-1219344*s^4*x^5*t-22160*s^5*x^3*t +46192*s^4*x^3*t^2+4256*s^4*x^2*t^2-6923396*s^6*x^4*t+11777982*s^5*x^4*t^2+ 8986609*s^5*x^5*t-40710*s^6*x^3*t+113903*s^5*x^3*t^2+26632*s^6*x^2*t-10100*s^5 *x^2*t^2-208*s^5*x*t^2+607650*s^7*x^3*t-1430682*s^6*x^3*t^2-140458*s^7*x^2*t-\ 134077*s^6*x^2*t^2-1600*s^7*x*t-8696*s^6*x*t^2+433237*s^8*x^2*t+950091*s^7*x^2 *t^2+4768*s^8*x*t+109297*s^7*x*t^2-384*x^2*s^3*t^3-125684*x^2*s^4*t^3-368*x*s^ 4*t^3+36728*x*s^5*t^3+1253747*x^2*s^5*t^3-368779*x*s^6*t^3+21456*x^3*s^3*t^3-\ 657917*x^3*s^4*t^3+5616*x^3*s^2*t^3-5447173*x^2*s^6*t^3+3984344*x^3*s^5*t^3-\ 529933*x*s^8*t^2+1635121*x*s^7*t^3-32530752*s^6*x^4*t^2-27897914*s^6*x^5*t-\ 2041631*s^8*x^3*t+4602848*s^7*x^3*t^2-830884*s^9*x^2*t-3011129*s^8*x^2*t^2-\ 4869*s^9*x*t+13677317*x^2*s^7*t^3-11815068*x^3*s^6*t^3+1390745*x*s^9*t^2-\ 4018979*x*s^8*t^3+21587620*s^7*x^4*t-39497270*t*x^4*s^8+3296702*t*x^3*s^9-\ 56376*x^5*s^2*t^2+2156895*s^3*x^5*t^2-13914699*s^4*x^5*t^2+35004915*s^5*x^5*t^ 2-896*t*s^9-6693702*s^8*x^3*t^2+50092610*s^7*x^4*t^2+731538*x^6*t*s^3+43740*x^ 6*t^2*s-41029714*s^8*x^4*t^2-17496*x^6*t*s^2-4301109*s^4*x^6*t-950211*s^2*x^6* t^2+7751544*s^5*x^6*t+1241433*s^3*x^6*t^2+7878190*s^6*x^6*t-24704588*s^6*x^5*t ^2+25571277*s^4*x^6*t^2+40063390*s^7*x^5*t-11074862*s^8*x^5*t+42996312*s^9*x^4 *t+2384934*s^9*x^3*t^2+5840812*s^9*x^2*t^2-2307310*t*x^3*s^10+13128476*s^9*x^4 *t^2-62380*s^10*t^2+2392*t*s^10-2606*s^10*x*t-54580252*s^7*x^6*t-61285110*s^7* x^5*t^2-141462870*s^5*x^6*t^2-48256532*s^9*x^5*t-25556084*s^10*x^4*t+6244576*s ^10*x^3*t^2-7443782*s^10*x^2*t^2+974144*s^10*x^2*t-2181978*x*s^10*t^2+14580*x^ 5*t^5+34992*x^5*t^4-11664*x^4*t^5+80514*x^5*t^5*s^2-120042*x^5*t^5*s-96*x*t^4* s^3-30416*x*t^4*s^4+3984*x*t^5*s^3-53892*x*t^5*s^4+480*x*t^5*s^2-20415465*x^5* t^3*s^4+18251586*x^5*t^4*s^3+7185807*x^5*t^3*s^3-2901825*x^5*t^4*s^2-973053*x^ 5*t^3*s^2+78246*x^5*t^4*s-5832*x^5*t^3*s+28355090*x^5*t^3*s^5-24550830*x^5*t^3 *s^6-63609810*x^5*t^4*s^4+144154300*x^5*t^4*s^5+2190852*x^5*t^5*s^3-10406112*x ^5*t^5*s^4-4383072*s^11*x^3*t^4+1421964*x^4*t^4*s^3+3631760*s^11*x^4*t^2-\ 37958384*s^10*x^4*t^3+20131392*s^9*x^4*t^4-1313683*s^6*x*t^4+1332243*s^3*x^4*t ^3-349002*s^2*x^4*t^4-6479622*x^4*t^3*s^4-14552972*s^10*x^2*t^3-3687948*s^9*x^ 2*t^4-17526564*s^4*x^7*t^2-28670436*s^3*x^7*t^3+5758128*s^2*x^7*t^4+5234353*s^ 5*x^2*t^4-11062752*s^6*x^2*t^4-95904*s^2*x^4*t^3+23976*s*x^4*t^4-728*s^5*t^4-\ 14045184*s^4*x^7*t^4-122807268*s^6*x^7*t+58562352*s^5*x^7*t^2-242160*s^12*x*t^ 3-2220576*s^11*x*t^4+35590444*s^8*x^3*t^4+156322944*s^4*x^6*t^3+34975964*s^7*x ^5*t^3-219784676*s^6*x^5*t^4+9414008*s^5*x^3*t^4+324405*s*x^6*t^3-43740*x^6*t^ 4+313482*s^5*x*t^4-9896800*s^11*x^3*t^3+22107120*s^10*x^3*t^4+314928*x^7*t^4-\ 184194*s^2*x^7*t+99873*s*x^7*t^2-3254*s^6*t^4+160*s^4*t^4+30592*s^7*t^4-3776*s ^11*t+183322*s^9*t^3-83209*s^8*t^4+3520*s^12*t+118152*s^11*t^2-303764*s^10*t^3 +79908*s^9*t^4-1792*s^13*t-128480*s^12*t^2+271360*s^11*t^3+61312*s^10*t^4+384* s^14*t+75840*s^13*t^2-97168*s^12*t^3-217008*s^11*t^4-18944*s^14*t^2-22176*s^13 *t^3+192912*s^12*t^4-1944*s*x^4*t^3+810936*x^3*t^4*s^3-69264*x^3*t^4*s^2+ 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53969400*s^5*x^7*t-15163713*s^4*x^7*t+3775572*s^3*x^7*t^2+9873576*s^2*x^7*t^3-\ 2271564*s*x^7*t^4+2492694*s^3*x^7*t-748926*s^2*x^7*t^2-1417176*s*x^7*t^3+32805 *x^7*t^3+344578512*s^6*x^6*t^2-329659752*s^5*x^6*t^3+16315812*s^4*x^6*t^4-\ 12769164*s^3*x^6*t^4+94449620*s^8*x^6*t-467910428*s^7*x^6*t^2+400367924*s^6*x^ 6*t^3+1655808*s^5*x^6*t^4-78902504*s^9*x^6*t+363624328*s^8*x^6*t^2-272493920*s ^7*x^6*t^3-29647424*s^6*x^6*t^4+74753488*s^10*x^5*t-164124352*s^9*x^5*t^2-\ 67251544*s^8*x^5*t^3+222469720*s^7*x^5*t^4+29685504*s^10*x^6*t-146447296*s^9*x ^6*t^2+83630656*s^8*x^6*t^3+35810304*s^7*x^6*t^4-47695488*s^11*x^5*t+77306496* s^10*x^5*t^2+74845248*s^9*x^5*t^3-142389888*s^8*x^5*t^4+2202432*s^12*x^4*t+ 13259232*s^12*x^5*t-11890944*s^11*x^5*t^2-40958784*s^10*x^5*t^3+51772032*s^9*x ^5*t^4-1017504*s^13*x^4*t-5359680*s^12*x^4*t^2+21532896*s^11*x^4*t^3-14753088* s^10*x^4*t^4-1320336*s^13*x^3*t+4850128*s^12*x^3*t^2+51792*s^13*x^2*t-2888952* s^12*x^2*t^2+4533960*s^11*x^2*t^3+7966152*s^10*x^2*t^4-16656*s^13*x*t-1224104* s^12*x*t^2+2217832*s^11*x*t^3+1949472*s^10*x*t^4+276480*s^14*x^3*t-631296*s^13 *x^3*t^2+1447776*s^12*x^3*t^3-23616*s^14*x^2*t+570912*s^13*x^2*t^2+196176*s^12 *x^2*t^3-4977360*s^11*x^2*t^4+7488*s^14*x*t+406832*s^13*x*t^2-63936*s^14*x*t^2 -154848*s^13*x*t^3+919872*s^12*x*t^4+183873520*s^7*x^7*t-123658224*s^6*x^7*t^2 +1874880*s^5*x^7*t^3+35952768*s^4*x^7*t^3-3110400*s^3*x^7*t^4-179895488*s^8*x^ 7*t+161246464*s^7*x^7*t^2-63211776*s^6*x^7*t^3+34182144*s^5*x^7*t^4+110116608* s^9*x^7*t-126447872*s^8*x^7*t^2+80181248*s^7*x^7*t^3-34689024*s^6*x^7*t^4-\ 1090944*s^11*x^6*t+18691200*s^10*x^6*t^2+3262464*s^9*x^6*t^3-18671616*s^8*x^6* t^4-37933056*s^10*x^7*t+54798336*s^9*x^7*t^2-44052480*s^8*x^7*t^3+17399808*s^7 *x^7*t^4-1603584*s^12*x^6*t+3022848*s^11*x^6*t^2-6008832*s^10*x^6*t^3+3760128* s^9*x^6*t^4-940032*s^13*x^5*t-1437696*s^12*x^5*t^2+8792064*s^11*x^5*t^3-\ 8073216*s^10*x^5*t^4+1695744*s^13*x^4*t^2-4626432*s^12*x^4*t^3+3594240*s^11*x^ 4*t^4-147456*s^14*x^3*t^2+368640*s^13*x^3*t^3-221184*s^12*x^3*t^4+18432*s^14*x ^2*t^2-398592*s^13*x^2*t^3+1178496*s^12*x^2*t^4-9818871*x^4*t^5*s^3+33377378*x ^4*t^5*s^4+1404774*x^4*t^5*s^2-20736*x^4*t^5*s-253668*x^3*t^5*s^3+4604848*x^3* t^5*s^4-143016*x^3*t^5*s^2+25920*x^3*t^5*s+333528*x^2*t^5*s^3-758800*x^2*t^5*s ^4-45744*x^2*t^5*s^2+20352*s^14*t^3-104976*x^6*t^5+880*s^4*t^5-3680*s^5*t^5-\ 26901504*x^8*s^8*t+29749248*x^8*s^7*t^2+5308416*x^8*s^9*t-5750784*x^8*s^8*t^2+ 58530816*s^7*x^8*t+5511240*x^8*s^3*t-22601916*x^8*s^4*t-6665976*x^8*t^2*s^2+ 26908848*x^8*t^2*s^3+51617088*x^8*s^5*t-60419520*x^8*s^4*t^2-8817984*s^2*x^8*t ^3+19595520*s^3*x^8*t^3+1032264*x^6*t^5*s-4321512*x^6*t^5*s^2+2204496*x^8*t^3* s+41086000*s^6*x^3*t^5-54627748*s^7*x^3*t^5-45829*s^7*t^5+133878*s^8*t^5+ 1658880*s^9*x^5*t^5+9988272*s^3*x^6*t^5-13768704*s^4*x^6*t^5-26127360*s^4*x^8* t^3-66282258*x^4*s^5*t^5+80422432*x^4*s^6*t^5+23092596*x^5*t^5*s^5-57987744*s^ 7*x^4*t^5-29489952*s^6*x^5*t^5-9289728*s^6*x^8*t^3+1769472*s^7*x^8*t^3-\ 12823272*s^9*x^2*t^5+5240160*s^10*x^2*t^5+44224272*s^8*x^3*t^5-20145456*s^9*x^ 3*t^5+9437184*s^9*x^7*t^3-3538944*s^8*x^7*t^4+161946*x*s^5*t^5-5142528*s^6*x^6 *t^5+995328*s^7*x^6*t^5-1195940*s^7*x*t^5+3026976*s^8*x*t^5+41472*s^14*x*t^3-\ 124416*x*s^13*t^4-457020*x^2*t^5*s^5+28118*x*t^5*s^6-3722160*x*t^5*s^9+2472480 *x*t^5*s^10-815616*x*t^5*s^11+93312*x*t^5*s^12+5948532*x^2*t^5*s^6-18744244*x^ 3*t^5*s^5+17517456*x^2*t^5*s^8-14022062*x^2*t^5*s^7+3974400*x^3*t^5*s^10-\ 933120*x^2*t^5*s^11+5529600*s^11*x^7*t-10100736*s^10*x^7*t^2-66023424*s^6*x^8* t^2+20901888*x^8*t^3*s^5+11321856*x^6*t^5*s^5-9289728*x^5*t^5*s^8+22268736*x^5 *t^5*s^7-70886016*s^6*x^8*t+81492480*s^5*x^8*t^2-252432*s^9*t^5+284592*s^10*t^ 5-175536*s^11*t^5-61056*s^13*t^4+45792*s^12*t^5+21650976*s^8*x^4*t^5-2071872*s ^9*x^4*t^5-663552*s^10*x^4*t^5+12590*s^6*t^5-236196*x^8*t^3-577368*x^8*s^2*t+ 708588*x^8*s*t^2-96*t^5*s^3 : S := (s-t) * U / (2 * s*t * q1^2 * disc): T := (s-t) * V / (2 * s^2 * q1^3 * disc^2): with(Ore_algebra): Alg := diff_algebra([dx, x]): P := skew_product(P2, dx, Alg): normal( applyopr(P, F, Alg) - diff(S, s) - diff(T, t) );