(* THIS FILE DEFINES p40: a degree 40 polynomial in Q[a,b,c,d,x] with 1673 terms *)

p40[{a_,b_,c_,d_},x_] := 
557256278016*a^6*b^4*c^4 + 7522959753216*a^3*b^6*c^4 + 25389989167104*b^8*c^4 - 4458050224128*a^7*b^2*c^5 - 
 70214291030016*a^4*b^4*c^5 - 270826551115776*a*b^6*c^5 + 8916100448256*a^8*c^6 + 196154209861632*a^5*b^2*c^6 + 
 962938848411648*a^2*b^4*c^6 - 142657607172096*a^6*c^7 - 1355247268134912*a^3*b^2*c^7 - 481469424205824*b^4*c^7 + 
 855945643032576*a^4*c^8 + 2567836929097728*a*b^2*c^8 - 2282521714753536*a^2*c^9 + 2282521714753536*c^10 - 
 4458050224128*a^6*b^5*c^2*d - 60183678025728*a^3*b^7*c^2*d - 203119913336832*b^9*c^2*d + 37893426905088*a^7*b^3*c^3*d + 
 591806167252992*a^4*b^5*c^3*d + 2268172365594624*a*b^7*c^3*d - 80244904034304*a^8*b*c^4*d - 1723036411625472*a^5*b^3*c^4*d - 
 8335439406563328*a^2*b^5*c^4*d + 1266086263652352*a^6*b*c^5*d + 11965406801559552*a^3*b^3*c^5*d + 4935061598109696*b^5*c^5*d - 
 8060154805223424*a^4*b*c^6*d - 27283267371663360*a*b^3*c^6*d + 24251793219256320*a^2*b*c^7*d - 28531521434419200*b*c^8*d + 
 8916100448256*a^6*b^6*d^2 + 120367356051456*a^3*b^8*d^2 + 406239826673664*b^10*d^2 - 80244904034304*a^7*b^4*c*d^2 - 
 1243796012531712*a^4*b^6*c*d^2 - 4739464644526080*a*b^8*c*d^2 + 150459195064320*a^8*b^2*c^2*d^2 + 3350781999710208*a^5*b^4*c^2*d^2 + 
 16484685559234560*a^2*b^6*c^2*d^2 + 120367356051456*a^9*c^3*d^2 - 555027252903936*a^6*b^2*c^3*d^2 - 
 17017213589913600*a^3*b^4*c^3*d^2 - 16268400466329600*b^6*c^3*d^2 - 1966000148840448*a^7*c^4*d^2 + 4513775851929600*a^4*b^2*c^4*d^2 + 
 89021690413056000*a*b^4*c^4*d^2 + 12179393212317696*a^5*c^5*d^2 - 47701137398169600*a^2*b^2*c^5*d^2 - 33881181703372800*a^3*c^6*d^2 + 
 129283456499712000*b^2*c^6*d^2 + 35664401793024000*a*c^7*d^2 + 120367356051456*a^8*b^3*d^3 + 1731952512073728*a^5*b^5*d^3 + 
 6206441796403200*a^2*b^7*d^3 - 541653102231552*a^9*b*c*d^3 - 9880153809223680*a^6*b^3*c*d^3 - 40467254339174400*a^3*b^5*c*d^3 + 
 16926659444736000*b^7*c*d^3 + 8726633313730560*a^7*b*c^2*d^3 + 63666529763328000*a^4*b^3*c^2*d^3 - 76640152485888000*a*b^5*c^2*d^3 - 
 61353916209561600*a^5*b*c^3*d^3 - 129562084638720000*a^2*b^3*c^3*d^3 + 211757385646080000*a^3*b*c^4*d^3 - 
 250765325107200000*b^3*c^4*d^3 - 289773264568320000*a*b*c^5*d^3 + 406239826673664*a^10*d^4 + 6206441796403200*a^7*b^2*d^4 + 
 19525737553920000*a^4*b^4*d^4 - 28211099074560000*a*b^6*d^4 - 6770663777894400*a^8*c*d^4 - 15986289475584000*a^5*b^2*c*d^4 + 
 293865615360000000*a^2*b^4*c*d^4 + 43257018580992000*a^6*c^2*d^4 - 173271873945600000*a^3*b^2*c^2*d^4 + 
 170442056908800000*b^4*c^2*d^4 - 121899810816000000*a^4*c^3*d^4 + 762744530534400000*a*b^2*c^3*d^4 + 111451255603200000*a^2*c^4*d^4 + 
 55725627801600000*c^5*d^4 - 28211099074560000*a^6*b*d^5 - 212018599526400000*a^3*b^3*d^5 + 23509249228800000*b^5*d^5 + 
 219419659468800000*a^4*b*c*d^5 - 724868517888000000*a*b^3*c*d^5 - 400527949824000000*a^2*b*c^2*d^5 - 348285173760000000*b*c^3*d^5 + 
 23509249228800000*a^5*d^6 + 669360568320000000*a^2*b^2*d^6 - 195910410240000000*a^3*c*d^6 + 489776025600000000*b^2*c*d^6 + 
 435356467200000000*a*c^2*d^6 - 816293376000000000*a*b*d^7 + 340122240000000000*d^8 + 21134460321792*a^6*b^9*x + 
 285315214344192*a^3*b^11*x + 962938848411648*b^13*x - 285315214344192*a^7*b^7*c*x - 4232175679438848*a^4*b^9*c*x - 
 15567511382654976*a*b^11*c*x + 1404285820600320*a^8*b^5*c^2*x + 23924456753725440*a^5*b^7*c^2*x + 99219201672609792*a^2*b^9*c^2*x - 
 2949000223260672*a^9*b^3*c^3*x - 63611547143897088*a^6*b^5*c^3*x - 320179731507707904*a^3*b^7*c^3*x - 24143128245043200*b^9*c^3*x + 
 2166612408926208*a^10*b*c^4*x + 78512951522230272*a^7*b^3*c^4*x + 565677576167620608*a^4*b^5*c^4*x + 258177762365276160*a*b^7*c^4*x - 
 36752166047711232*a^8*b*c^5*x - 554322220516638720*a^5*b^3*c^5*x - 954100351059886080*a^2*b^5*c^5*x + 
 242517932192563200*a^6*b*c^6*x + 1376348705862451200*a^3*b^3*c^6*x + 135052503715676160*b^5*c^6*x - 694584038475694080*a^4*b*c^7*x - 
 876366815318507520*a*b^3*c^7*x + 897369185263288320*a^2*b*c^8*x - 807336384292454400*b*c^9*x + 374476218826752*a^8*b^6*d*x + 
 5309042478022656*a^5*b^8*d*x + 18773964006359040*a^2*b^10*d*x - 3370285969440768*a^9*b^4*c*d*x - 54153422089224192*a^6*b^6*c*d*x - 
 207111725808353280*a^3*b^8*c*d*x + 48247248550625280*b^10*c*d*x + 9208102737936384*a^10*b^2*c^2*d*x + 
 187123314620104704*a^7*b^4*c^2*d*x + 834129807916400640*a^4*b^6*c^2*d*x - 433341985754972160*a*b^8*c^2*d*x - 
 6499837226778624*a^11*c^3*d*x - 247515406493810688*a^8*b^2*c^3*d*x - 1592636894635622400*a^5*b^4*c^3*d*x + 
 835194193206312960*a^2*b^6*c^3*d*x + 123496907308793856*a^9*c^4*d*x + 1819397167219998720*a^6*b^2*c^4*d*x + 
 1942706836419379200*a^3*b^4*c^4*d*x - 135199660651315200*b^6*c^4*d*x - 937973767156531200*a^7*c^5*d*x - 
 5469172339813908480*a^4*b^2*c^5*d*x + 1075966932890419200*a*b^4*c^5*d*x + 3495798245676810240*a^5*c^6*d*x + 
 5001668170717593600*a^2*b^2*c^6*d*x - 6412195261631692800*a^3*c^7*d*x + 6719437478559744000*b^2*c^7*d*x + 
 4786955262885888000*a*c^8*d*x + 1805510340771840*a^10*b^3*d^2*x + 25444321654210560*a^7*b^5*d^2*x + 70202062350581760*a^4*b^7*d^2*x - 
 152632494548582400*a*b^9*d^2*x - 8124796533473280*a^11*b*c*d^2*x - 141381490295439360*a^8*b^3*c*d^2*x - 
 362819114061004800*a^5*b^5*c*d^2*x + 2000299272752332800*a^2*b^7*c*d^2*x + 97196640011550720*a^9*b*c^2*d^2*x - 
 112682791977615360*a^6*b^3*c^2*d^2*x - 9258022709880422400*a^3*b^5*c^2*d^2*x - 1273957508579328000*b^7*c^2*d^2*x + 
 209673247166300160*a^7*b*c^3*d^2*x + 11471997645619200000*a^4*b^3*c^3*d^2*x + 5302935877976064000*a*b^5*c^3*d^2*x - 
 4533019768730419200*a^5*b*c^4*d^2*x - 27018261052784640000*a^2*b^3*c^4*d^2*x + 17793399348264960000*a^3*b*c^5*d^2*x - 
 23172779952046080000*b^3*c^5*d^2*x - 30615247131770880000*a*b*c^6*d^2*x + 8124796533473280*a^12*d^3*x + 
 149405980698869760*a^9*b^2*d^3*x + 828852539365785600*a^6*b^4*d^3*x + 1241301258731520000*a^3*b^6*d^3*x + 
 2199769157468160000*b^8*d^3*x - 157079399647150080*a^10*c*d^3*x - 1306738109133619200*a^7*b^2*c*d^3*x + 
 1140866134179840000*a^4*b^4*c*d^3*x - 8382295371939840000*a*b^6*c*d^3*x + 1268371014392217600*a^8*c^2*d^3*x + 
 1740450670313472000*a^5*b^2*c^2*d^3*x + 34373779483852800000*a^2*b^4*c^2*d^3*x - 6904962540896256000*a^6*c^3*d^3*x - 
 22089019686912000000*a^3*b^2*c^3*d^3*x + 28854136700928000000*b^4*c^3*d^3*x + 24426400186368000000*a^4*c^4*d^3*x + 
 131378327322624000000*a*b^2*c^4*d^3*x - 45827105174323200000*a^2*c^5*d^3*x + 39462000132096000000*c^6*d^3*x - 
 592433080565760000*a^8*b*d^4*x - 8424234711613440000*a^5*b^3*d^4*x - 15896412551577600000*a^2*b^5*d^4*x + 
 14337507463004160000*a^6*b*c*d^4*x + 28719740547072000000*a^3*b^3*c*d^4*x + 2806598025216000000*b^5*c*d^4*x - 
 71415874879488000000*a^4*b*c^2*d^4*x - 270370233040896000000*a*b^3*c^2*d^4*x + 120289959346176000000*a^2*b*c^3*d^4*x - 
 206958789918720000000*b*c^4*d^4*x - 2868128405913600000*a^7*d^5*x + 24077389418496000000*a^4*b^2*d^5*x + 
 93538755624960000000*a*b^4*d^5*x + 17631936921600000000*a^5*c*d^5*x + 78864824033280000000*a^2*b^2*c*d^5*x - 
 27514528727040000000*a^3*c^2*d^5*x + 320825467699200000000*b^2*c^2*d^5*x + 36505445990400000000*a*c^3*d^5*x - 
 84078217728000000000*a^3*b*d^6*x - 133065897984000000000*b^3*d^6*x - 148383995904000000000*a*b*c*d^6*x + 
 127885962240000000000*a^2*d^7*x - 163258675200000000000*c*d^7*x - 722204136308736*a^10*b^6*x^2 - 13173538412298240*a^7*b^8*x^2 - 
 75766111493160960*a^4*b^10*x^2 - 174398924767887360*a*b^12*x^2 + 6499837226778624*a^11*b^4*c*x^2 + 133808377477201920*a^8*b^6*c*x^2 + 
 842339405439959040*a^5*b^8*c*x^2 + 2240381995009966080*a^2*b^10*c*x^2 - 21479930835369984*a^12*b^2*c^2*x^2 - 
 534926635842207744*a^9*b^4*c^2*x^2 - 3934992508000985088*a^6*b^6*c^2*x^2 - 13023128947196952576*a^3*b^8*c^2*x^2 - 
 2232230450175148032*b^10*c^2*x^2 + 27421188300472320*a^13*c^3*x^2 + 982727994042482688*a^10*b^2*c^3*x^2 + 
 9493586609375969280*a^7*b^4*c^3*x^2 + 41869221850432585728*a^4*b^6*c^3*x^2 + 21524480874268065792*a*b^8*c^3*x^2 - 
 594125746510233600*a^11*c^4*x^2 - 10929452474122371072*a^8*b^2*c^4*x^2 - 73096207548039954432*a^5*b^4*c^4*x^2 - 
 83145651147503566848*a^2*b^6*c^4*x^2 + 5310457289795174400*a^9*c^5*x^2 + 68187625733725618176*a^6*b^2*c^5*x^2 + 
 176040138015241666560*a^3*b^4*c^5*x^2 + 678941405850894336*b^6*c^5*x^2 - 25005961575672053760*a^7*c^6*x^2 - 
 176251024760572477440*a^4*b^2*c^6*x^2 + 13060798307773710336*a*b^4*c^6*x^2 + 65460985790673715200*a^5*c^7*x^2 + 
 58401265497503956992*a^2*b^2*c^7*x^2 - 84820362154047700992*a^3*c^8*x^2 + 85597433844392263680*b^2*c^8*x^2 + 
 55142720795427471360*a*c^9*x^2 + 7921676620136448*a^12*b^3*d*x^2 + 177718639730098176*a^9*b^5*d*x^2 + 
 1508582120369651712*a^6*b^7*d*x^2 + 4411949402925563904*a^3*b^9*d*x^2 + 5062677743825584128*b^11*d*x^2 - 
 35647544790614016*a^13*b*c*d*x^2 - 1000958006264463360*a^10*b^3*c*d*x^2 - 10274556110704459776*a^7*b^5*c*d*x^2 - 
 30155089861692555264*a^4*b^7*c*d*x^2 - 36997276336109125632*a*b^9*c*d*x^2 + 894438538378739712*a^11*b*c^2*d*x^2 + 
 18226000185750061056*a^8*b^3*c^2*d*x^2 + 54865914435679076352*a^5*b^5*c^2*d*x^2 + 91025640232987262976*a^2*b^7*c^2*d*x^2 - 
 12158648929426341888*a^9*b*c^3*d*x^2 - 48857920180269613056*a^6*b^3*c^3*d*x^2 - 164115555981271105536*a^3*b^5*c^3*d*x^2 + 
 18493838473293987840*b^7*c^3*d*x^2 + 21077630253325615104*a^7*b*c^4*d*x^2 + 72413966657865646080*a^4*b^3*c^4*d*x^2 - 
 260755018138020741120*a*b^5*c^4*d*x^2 + 79838670812149186560*a^5*b*c^5*d*x^2 + 50165736387096084480*a^2*b^3*c^5*d*x^2 + 
 96316001907124469760*a^3*b*c^6*d*x^2 - 580537185866455449600*b^3*c^6*d*x^2 - 951177351237363302400*a*b*c^7*d*x^2 + 
 53471317185921024*a^14*d^2*x^2 + 1149633319497302016*a^11*b^2*d^2*x^2 + 8230661072857571328*a^8*b^4*d^2*x^2 + 
 10755423501735886848*a^5*b^6*d^2*x^2 - 15376018157178716160*a^2*b^8*d^2*x^2 - 1176368978090262528*a^12*c*d^2*x^2 - 
 13990325064589836288*a^9*b^2*c*d^2*x^2 + 50571185221090050048*a^6*b^4*c*d^2*x^2 + 270060221131271700480*a^3*b^6*c*d^2*x^2 + 
 41106608398349107200*b^8*c*d^2*x^2 + 10618099111902707712*a^10*c^2*d^2*x^2 - 106987872749948043264*a^7*b^2*c^2*d^2*x^2 - 
 531893551798020096000*a^4*b^4*c^2*d^2*x^2 - 318874125067399987200*a*b^6*c^2*d^2*x^2 + 6020794792977629184*a^8*c^3*d^2*x^2 + 
 612691439310742487040*a^5*b^2*c^3*d^2*x^2 + 2575016295959937024000*a^2*b^4*c^3*d^2*x^2 - 395123095178229841920*a^6*c^4*d^2*x^2 - 
 2634828227828121600000*a^3*b^2*c^4*d^2*x^2 + 644587601811701760000*b^4*c^4*d^2*x^2 + 1661638158455301734400*a^4*c^5*d^2*x^2 + 
 8041186901126283264000*a*b^2*c^5*d^2*x^2 - 2454529299185664000000*a^2*c^6*d^2*x^2 + 1785456116776304640000*c^7*d^2*x^2 - 
 3783700818979061760*a^10*b*d^3*x^2 - 85634413264342056960*a^7*b^3*d^3*x^2 - 232907575848512716800*a^4*b^5*d^3*x^2 + 
 87498283323359232000*a*b^7*d^3*x^2 + 183703097791583354880*a^8*b*c*d^3*x^2 + 559527774037984051200*a^5*b^3*c*d^3*x^2 - 
 653301126058475520000*a^2*b^5*c*d^3*x^2 - 805464239129277235200*a^6*b*c^2*d^3*x^2 - 3224009688987893760000*a^3*b^3*c^2*d^3*x^2 - 
 881483037449748480000*b^5*c^2*d^3*x^2 + 958349107693486080000*a^4*b*c^3*d^3*x^2 - 13094565283042099200000*a*b^3*c^3*d^3*x^2 + 
 460280528201318400000*a^2*b*c^4*d^3*x^2 - 12659503856143564800000*b*c^5*d^3*x^2 - 63968631887690956800*a^9*d^4*x^2 + 
 39457925538204672000*a^6*b^2*d^4*x^2 + 2113446677151744000000*a^3*b^4*d^4*x^2 + 2696930183194214400000*b^6*d^4*x^2 + 
 608756042081341440000*a^7*c*d^4*x^2 + 1398749854973184000000*a^4*b^2*c*d^4*x^2 + 1220119038192844800000*a*b^4*c*d^4*x^2 - 
 2202436107650580480000*a^5*c^2*d^4*x^2 + 10894655890626969600000*a^2*b^2*c^2*d^4*x^2 + 5224937316566630400000*a^3*c^3*d^4*x^2 + 
 37605320240615424000000*b^2*c^3*d^4*x^2 - 453344536461312000000*a*c^4*d^4*x^2 - 257778836164454400000*a^5*b*d^5*x^2 - 
 5630344620742656000000*a^2*b^3*d^5*x^2 - 13296101053335552000000*a^3*b*c*d^5*x^2 - 39508142677217280000000*b^3*c*d^5*x^2 - 
 5691384056401920000000*a*b*c^2*d^5*x^2 + 7887563311806720000000*a^4*d^6*x^2 + 32773495778611200000000*a*b^2*d^6*x^2 - 
 13534370922240000000000*a^2*c*d^6*x^2 + 16942894612992000000000*c^2*d^6*x^2 + 17320384949760000000000*b*d^7*x^2 + 
 8226356490141696*a^14*b^3*x^3 + 189053859338256384*a^11*b^5*x^3 + 1510038024955379712*a^8*b^7*x^3 + 6299283251571720192*a^5*b^9*x^3 + 
 12010992841795829760*a^2*b^11*x^3 - 37018604205637632*a^15*b*c*x^3 - 1050003002005585920*a^12*b^3*c*x^3 - 
 9576095249493467136*a^9*b^5*c*x^3 - 50287291642972864512*a^6*b^7*c*x^3 - 123576761720651120640*a^3*b^9*c*x^3 - 
 8992630310436864000*b^11*c*x^3 + 837717302579429376*a^13*b*c^2*x^3 + 12536431280093528064*a^10*b^3*c^2*x^3 + 
 134268001493171724288*a^7*b^5*c^2*x^3 + 558403165638574571520*a^4*b^7*c^2*x^3 + 276784719038612766720*a*b^9*c^2*x^3 - 
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