LIB "tst.lib";tst_init();

ring r= 43051,(x1,x2,x3),dp;

poly p1=
-497483226+12559018132*x2^5*x3^2+2991288707*x2^4*x3^2-12097910584*x2^2*x3^5-
166407768*x1*x2*x3-1026571994*x2^3*x3+791181496*x1^5*x2^3*x3^2+508861933*x1-
30342370*x1^10-157295309*x1^9+883876786*x1^8+867051798*x1^7+1170603482*x1^3+
1238771399*x1^2-15880056120*x1^2*x2^4*x3^2-1466257261*x1^2*x3^7*x2-5966682244*x1
^2*x2^2*x3^5+4932092509*x1^6+3877044241*x1^5+277804530*x1^4-4530117663*x1^7*x3-
1123338940*x1^7*x3^3-847225537*x1^7*x3^2-3332109179*x1^5*x3+3392611857*x1^5*x3^4
-5741778920*x1^5*x3^5+2364134543*x1^5*x3^3-10262782434*x1^8*x2*x3+3539988475*x1*
x2^7*x3^2-3854795862*x1*x2^4*x3^2+7444563183*x1^3*x2^4*x3^3-11461427653*x1^5*x2*
x3^2-2348195114*x1^8*x3^2+1449285570*x1^8*x3+10965245575*x1^3*x2^2*x3^4+
10860178438*x1^4*x2*x3^3+655470572*x1^5*x2*x3^4+707001612*x1^6*x2*x3^3+
2491910209*x1*x2^4*x3^5+1284596861*x1^5*x2^2*x3^2+9280224066*x3^8+8211566775*x3^
6+2484928609*x3^9+9424821619*x3^7+2283286458*x1*x2^2*x3^4+2225462690*x1^3*x2*x3^
2+14329904528*x1^3*x2^2*x3^2+5524691994*x2^5*x3^3-15058694111*x1*x2^4*x3+
24924148341*x1*x2^6*x3+557470115*x1^9*x3+1948051699*x1^2*x2^5*x3^2+1047685084*x2
^7*x3^3-5148318330*x2^8*x3^2+7157438081*x2^6*x3^4+730467829*x1*x2*x3^2-
6194015856*x1^2*x2^3*x3^5+7602939529*x1^3*x2^4*x3-4647532061*x1^2*x2^3*x3+
11381342452*x1*x2*x3^3+4636680230*x1^3*x2^2+321937752*x1*x2^5+10970018609*x1^5*
x2^3+3211682439*x1^5*x2-16086048069*x1^5*x2^5+15356688076*x1^4*x2^6-3445358004*
x1^6*x2^3+10849400982*x1^4*x2^5-17249506741*x1^4*x2^4-6329482634*x1^4*x2^3+
3267034360*x1^4*x2^2+456435762*x1^7*x2^2-83779949*x2^3+6138008929*x1^7*x2^3-
2866093271*x1^7*x2+6892830742*x1^8*x2-5323655763*x1^8*x2^2-2295277131*x2^2+
9858042987*x1^3*x3^2+10640751353*x1*x3^3-6064660115*x1^2*x2^2+3252427423*x1*x2^6
+2081515052*x1^6*x2^4+7439334176*x1^5*x2^4+4371125347*x1^2*x2^6-7276010880*x1^2*
x2^8-249547350*x1^2*x2^7+4021242232*x1^2*x2^3-11105846897*x1^5*x2^2+3461006128*
x1*x2^7-747943815*x1^3*x2^7-1542766850*x1^6*x2^2+7635334378*x1^6*x2+1086347612*
x1^9*x2+3602856476*x1^3*x2-12413588104*x1^2*x2^5-9370037407*x1^2*x2^4-1763056789
*x1^2*x2+3603825963*x1*x2^9+7873269589*x1*x2^8-5179491038*x1^3*x2^6+1136896797*
x2-5008504565*x1^3*x2^5-1063221776*x1^3*x2^4+5816189675*x1^3*x2^3+656608663*x2^2
*x3^3-637943099*x3-2871993693*x1^2*x2^5*x3^3+14531417356*x1^2*x2^2*x3^3-
1003007137*x1^2*x3^4+641420037*x1^2*x3^5+5869148009*x1^4*x2^4*x3-11023061816*x1^
4*x2*x3+485198545*x1*x2^7*x3-5254161821*x1*x2^2*x3^6-24200446391*x1*x2^3*x3^4-
10684479821*x1*x2^8*x3+1893743620*x1^2*x2^7*x3-12246201296*x2^4*x3^6+1954017338*
x3^8*x2^2-8835688265*x3^7*x2^3+23131311616*x1^4*x2^3*x3-23282331189*x1^4*x2^5*x3
+8887596448*x1*x2^2*x3^7+4340009201*x1^2*x2^4*x3^3+14959089355*x1^3*x2*x3+
7477911912*x1*x2^6*x3^3-9437554350*x1*x3^5-32194338433*x1*x2^5*x3^2+25231754637*
x1^4*x2^2*x3^4+2057200855*x1*x2^2*x3^5+10725156805*x1^6*x2^2*x3-2157700945*x1^2*
x3^8+8805673215*x1^2*x3^6+12215928425*x1^2*x3^7-23764490525*x1^2*x2^3*x3^2-
5932005555*x2^3*x3^2-15710871923*x2*x3^4-1078923593*x2^2*x3-6808218316*x2^6-
5940747392*x2^7-9086669504*x2^8-3791194272*x2^9+701328985*x2^10-1865893092*x3^8*
x2-14793578318*x3^5*x2-1810735193*x1^3*x2^3*x3^2-9144913569*x2^6*x3^2+6866739996
*x2^4*x3^5-24426874913*x2^4*x3^3-23715789967*x1^2*x2*x3^4-8789056315*x1*x2^6*x3^
2-7005243491*x1^3*x2*x3^4-25334104671*x1^3*x2*x3^3+7163019353*x1*x2^3*x3^5-
865854775*x1^6*x3-7538890496*x1^6*x3^4+19146191569*x1^6*x3^3-4345106193*x1^6*x3^
2-10747825256*x1*x2^3*x3+18580935513*x2^7*x3-8255922779*x2^3*x3^5+3879036214*x2^
6*x3^3-1457255737*x2^2*x3^4-2352503017*x2^2*x3^7-8636680121*x1^3*x2^3*x3+
1627612855*x1^4*x2^2*x3+4007674788*x1^3*x2^5*x3+2133252917*x1^4*x3+511642704*x1*
x3^7*x2+3360716544*x1^5*x2^4*x3-1156115482*x1^3*x3^6*x2-884900133*x2^4+232103666
*x2^5+10029236610*x2^8*x3+3573440850*x2^5*x3^4-12712034259*x2^3*x3^6-12969913673
*x2^3*x3^3-16255234348*x1*x2^3*x3^3+5930078975*x1^3*x2^6*x3-258856703*x2^9*x3+
11496889735*x2^5*x3^5-1036961150*x1^2*x2^4*x3+8109625642*x3^4-6627513228*x1^4*x2
^3*x3^2-2302687957*x1^5*x2*x3^3+3300323926*x1^2*x2^6*x3-3958217038*x1*x3^6-
2582079856*x1*x3^9+1746597940*x1*x3^7-14918866520*x1*x2^2*x3^3-1028570709*x1^5*
x2^3*x3-2355486048*x1^4*x2^3*x3^3-12354829241*x1^2*x2^2*x3^4+2937310424*x1*x2^2*
x3+8531613805*x1^2*x2^6*x3^2-6809045799*x1^2*x3^5*x2+18208335839*x1*x2^4*x3^3+
10302271997*x1^4*x2*x3^4+2097206565*x2^2*x3^6-10022339840*x2^3*x3^4-4990366668*
x3^6*x2-13422076920*x3^7*x2-6901954893*x1^3*x2^3*x3^4+6998572446*x1^5*x2^2*x3+
3776285467*x1^3*x3^5*x2+11610806874*x1^5*x2^2*x3^3-18615401125*x1^3*x2^5*x3^2+
14855896209*x1^3*x2^4*x3^2+2790387590*x1^2*x2^2*x3-2526820*x1^2*x2^2*x3^2-
625501378*x2*x3-10606063192*x1^4*x2^2*x3^3-11538296097*x2^4*x3^4-1308706331*x1*
x3^8-28996594569*x1^4*x2*x3^2-2188034660*x1*x2^5*x3+6223853439*x1^4*x3^4+
27657939677*x1^4*x3^5+343107665*x1^4*x3^3+2083940176*x1^4*x3^2-2884805942*x1*x2^
2*x3^2-521130116*x1*x2^3*x3^2+15440254019*x1*x2*x3^4+30738574398*x1^3*x2^2*x3^5+
12842163710*x1^4*x2^4*x3^2-721528400*x1^2*x2^3*x3^4+22394769649*x1^6*x2*x3^2-
10438487911*x2^7*x3^2-6861805893*x1^3*x3^6-25513384947*x1^3*x3^4-2031798956*x1^3
*x3^5-15530315935*x1^3*x3^3-10612907588*x1^3*x3^7+9900026432*x1*x2^5*x3^4-
1682460414*x1^7*x2*x3^2+12204850338*x1*x2^4*x3^4+6427819491*x1^2*x2^5*x3+
19018794167*x1^3*x2^2*x3^3+4857514217*x1*x2^4+2449377907*x1*x2^3-2674312087*x1*
x2^2+787131320*x1*x2+8681839839*x1^4*x2-981443120*x2^2*x3^2+2211451997*x1*x3^2+
7396134233*x1^2*x3^3+4882347237*x1^2*x3+4977649875*x1*x3^4+591555644*x3^10+
2199230286*x2^6*x3-5497674010*x2^5*x3+15309022414*x1^3*x2^3*x3^3+3689574348*x1*
x2^5*x3^3-972162119*x1^7*x2^2*x3+9334967204*x1^2*x2*x3+18008802516*x1^3*x2^2*x3-
3638425870*x1^2*x2*x3^3+2277307938*x1^2*x2^3*x3^3+1907944332*x3^9*x2+7278724908*
x1^3*x3-6078794417*x2*x3^3-6767876076*x2^4*x3-4456246073*x2*x3^2+14262953353*x3^
5+1551355778*x3^3+165000047*x1*x3+317536317*x3^2+7909278409*x1^2*x3^2+
17065514826*x1^2*x2^2*x3^6-448392881*x1^6*x2^2*x3^2-10099469490*x1^4*x3^6+
4567139939*x1^2*x2^4*x3^4-9893277167*x1^2*x3^6*x2-10168977622*x1*x2^3*x3^6-
2419987848*x1^6*x2^3*x3+2444334710*x1^6*x2*x3+6508433896*x1^4*x3^5*x2+
31126272301*x1^2*x2*x3^2-11091185478*x1^7*x2*x3-55331044338*x1^4*x2^2*x3^2-
16975642681*x1^5*x2*x3-1361985271*x1*x3^8*x2-2756429927*x1*x3^6*x2-10245709023*
x1*x3^5*x2-16842341493*x1^5*x3^2;

poly p2=
-17029644228*x2^5*x3^2+3929262129*x2^4*x3^2-5541893490*x2^2*x3^5+876684364*x1*x2
*x3+7206451365*x2^3*x3-14689453988*x1^5*x2^3*x3^2+3722821939*x1-107676439*x1^10+
435205454*x1^9-755544*x1^8+1606401775*x1^7-6260568221*x1^3+2139123115*x1^2-
17734052863*x1^2*x2^4*x3^2-7693857226*x1^2*x3^7*x2+15950288809*x1^2*x2^2*x3^5-
605115362*x1^6-4591997734*x1^5-5085282369*x1^4+481867609*x1^7*x3+4385509072*x1^7
*x3^3-3633372250*x1^7*x3^2-2613425489*x1^5*x3-11181530681*x1^5*x3^4+10055479424*
x1^5*x3^5+4611688766*x1^5*x3^3-1851652611*x1^8*x2*x3+1942457213*x1*x2^7*x3^2-
24172590666*x1*x2^4*x3^2-2853537015*x1^3*x2^4*x3^3-9237582543*x1^5*x2*x3^2-
58704802*x1^8*x3^2-2042235559*x1^8*x3+1301518*x1^3*x2^2*x3^4+36615705097*x1^4*x2
*x3^3-9305104117*x1^5*x2*x3^4-4494868348*x1^6*x2*x3^3-4392823766*x1*x2^4*x3^5-
271928245*x1^5*x2^2*x3^2+8115472030*x3^8-3726112094*x3^6-7757275363*x3^9-
11076852956*x3^7+7429846138*x1*x2^2*x3^4+7769652714*x1^3*x2*x3^2+12529023779*x1^
3*x2^2*x3^2+21653861258*x2^5*x3^3-1085713330*x1*x2^4*x3+10988970553*x1*x2^6*x3+
1019676093*x1^9*x3-3307983766*x1^2*x2^5*x3^2+7376293327*x2^7*x3^3-185134079*x2^8
*x3^2+13333446281*x2^6*x3^4+2956589334*x1*x2*x3^2+20239926927*x1^2*x2^3*x3^5-
1240796142+9502147615*x1^3*x2^4*x3-7859258409*x1^2*x2^3*x3+12686331599*x1*x2*x3^
3+14215087320*x1^3*x2^2-10679308069*x1*x2^5+14131816150*x1^5*x2^3-5961032398*x1^
5*x2-6251192046*x1^5*x2^5-8804402271*x1^4*x2^6-6333634963*x1^6*x2^3+11466369779*
x1^4*x2^5+7041972442*x1^4*x2^4-5581970075*x1^4*x2^3+5985463046*x1^4*x2^2-
2569969761*x1^7*x2^2-2338510043*x2^3-1440794841*x1^7*x2^3+824362217*x1^7*x2-
3634851027*x1^8*x2+1627215432*x1^8*x2^2-3348302913*x2^2+5742099297*x1^3*x3^2-
6130993101*x1*x3^3-8349322394*x1^2*x2^2-8862947105*x1*x2^6+9110875843*x1^6*x2^4-
12154940153*x1^5*x2^4-905653543*x1^2*x2^6-3658193770*x1^2*x2^8-10296427374*x1^2*
x2^7+11399465771*x1^2*x2^3-5769031537*x1^5*x2^2+9474272034*x1*x2^7+13137759719*
x1^3*x2^7+7785141559*x1^6*x2^2-4414652137*x1^6*x2+3201460403*x1^9*x2-17270980782
*x1^3*x2-10076159962*x1^2*x2^5+10002631932*x1^2*x2^4-8126513359*x1^2*x2-
4614855793*x1*x2^9+14897942576*x1*x2^8+458425417*x1^3*x2^6+2379631161*x2-
16663299660*x1^3*x2^5-8208618779*x1^3*x2^4+19259372492*x1^3*x2^3-9677341311*x2^2
*x3^3+24406396*x3+8794489713*x1^2*x2^5*x3^3-8509878331*x1^2*x2^2*x3^3+7393811197
*x1^2*x3^4-12368273876*x1^2*x3^5+5354277145*x1^4*x2^4*x3+4808136038*x1^4*x2*x3-
7467859952*x1*x2^7*x3-11086222792*x1*x2^2*x3^6-18947532019*x1*x2^3*x3^4-
9727107339*x1*x2^8*x3+4696299577*x1^2*x2^7*x3-1554408419*x2^4*x3^6-8329503550*x3
^8*x2^2+1997816405*x3^7*x2^3-12679217197*x1^4*x2^3*x3-5500011613*x1^4*x2^5*x3-
19557799143*x1*x2^2*x3^7+23018873674*x1^2*x2^4*x3^3-5487267334*x1^3*x2*x3+
4636995082*x1*x2^6*x3^3-25739481403*x1*x3^5-5756009881*x1*x2^5*x3^2+5740135560*
x1^4*x2^2*x3^4+15120038686*x1*x2^2*x3^5-4703680696*x1^6*x2^2*x3-836717953*x1^2*
x3^8+21662184160*x1^2*x3^6-13443250702*x1^2*x3^7+3749914564*x1^2*x2^3*x3^2+
8690196161*x2^3*x3^2-7231729953*x2*x3^4+4015919313*x2^2*x3-6391572694*x2^6-
6881749000*x2^7-3296183898*x2^8+4745533934*x2^9-565629701*x2^10+5788747533*x3^8*
x2-7456720491*x3^5*x2-30203096254*x1^3*x2^3*x3^2-8804601352*x2^6*x3^2+
20508506613*x2^4*x3^5+4023820076*x2^4*x3^3-9502895260*x1^2*x2*x3^4+10256851068*
x1*x2^6*x3^2-1587324371*x1^3*x2*x3^4-16324435747*x1^3*x2*x3^3+10159637682*x1*x2^
3*x3^5+1031125339*x1^6*x3+1066871935*x1^6*x3^4-8086829456*x1^6*x3^3+4227034459*
x1^6*x3^2-17127278164*x1*x2^3*x3+15140864082*x2^7*x3-1185979294*x2^3*x3^5+
12425563539*x2^6*x3^3+13025091285*x2^2*x3^4+19723028134*x2^2*x3^7+8850219117*x1^
3*x2^3*x3-35521386840*x1^4*x2^2*x3+18007446441*x1^3*x2^5*x3+2734526234*x1^4*x3+
13032279291*x1*x3^7*x2-5202577564*x1^5*x2^4*x3-11288911667*x1^3*x3^6*x2+
1259203615*x2^4+10615897400*x2^5+8466454151*x2^8*x3-12146118801*x2^5*x3^4-
9505420627*x2^3*x3^6+4783903558*x2^3*x3^3+10842027345*x1*x2^3*x3^3-2587330240*x1
^3*x2^6*x3-2211293049*x2^9*x3+13801377422*x2^5*x3^5+3731220259*x1^2*x2^4*x3-
1250179786*x3^4+10373067065*x1^4*x2^3*x3^2+13397654851*x1^5*x2*x3^3+3115648058*
x1^2*x2^6*x3-355644282*x1*x3^6+7598207808*x1*x3^9+6820291991*x1*x3^7+22835648836
*x1*x2^2*x3^3+18259677864*x1^5*x2^3*x3-9143917547*x1^4*x2^3*x3^3-3839412986*x1^2
*x2^2*x3^4-2461440044*x1*x2^2*x3-10987992069*x1^2*x2^6*x3^2-3513502517*x1^2*x3^5
*x2+5169421488*x1*x2^4*x3^3+3714924726*x1^4*x2*x3^4-16563594885*x2^2*x3^6+
8116506149*x2^3*x3^4+4746590380*x3^6*x2+1879596544*x3^7*x2+4258733240*x1^3*x2^3*
x3^4-1779638621*x1^5*x2^2*x3+28196512275*x1^3*x3^5*x2+8204239212*x1^5*x2^2*x3^3+
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^8*x3^18-33394937321*x1^14*x2^12*x3^12-15277702603*x2^4*x3^24*x1^2+10708359014*
x3^21*x1^3+49142328634*x2^6*x3^19*x1-84906295491*x1^9*x2^2*x3^24+40067426406*x1^
9*x2^2*x3^22-38024274921*x1^9*x2^2*x3^25-33644218026*x1^9*x2^2*x3^23-31555490271
*x1^22*x2^9-59596671486*x1^22*x2^10+31885090378*x1^22*x2^4-44068903524*x1^22*x2^
5-41801778146*x3^15*x2^6*x1^19-18035646702*x2^29*x3^7+14736691246*x1^26*x3^12+
3009976318*x1^25*x3^11+40124446525*x2^6*x3^6*x1^10+112642879215*x2^7*x3^4*x1^20-
89536484341*x2^16*x3^5*x1^5-48690901342*x2^12*x3^3*x1^16+54529407366*x2^23*x3^4*
x1+46178285861*x2^27*x3^3*x1^4+13455217236*x2^22*x3^3*x1^4-10898496120*x2^23*x3^
3*x1^4-16321281425*x2^16*x3^3*x1^5+75268002520*x2^10*x3^5*x1^6+37834683284*x1^4*
x2^5*x3^12-35660157590*x2^9*x3^3*x1^16+34941890800*x2^8*x3^3*x1^16+18657839759*
x2^20*x3^4*x1-33898286919*x2^24*x3^3*x1^4+38121611428*x1^11*x3^12*x2+21452238192
*x3^33*x1^3+11030243964*x1^28*x3^12-61043411008*x2^9*x3^21*x1^4-3966943079*x1^14
*x3^21*x2^2-20964529880*x1^4*x2^29*x3^6-19612459282*x3^21*x1^8*x2^9-1000763472*
x3^22*x1^3*x2^4-2934440427*x3^23+7666103364*x1^11*x2^28*x3+10625693141*x2^6*x3^
17*x1^2+14795533312*x1^11*x2^27*x3-36139339874*x1^8*x2^20*x3^12+36017184842*x1^
11*x2^22*x3^7+54065209785*x2^8*x3^17*x1^2-10371095295*x2^9*x3^16*x1^2-
18087039570*x1^5*x2^11*x3^15-62419931544*x2^8*x3^16*x1^3-105261282396*x2^12*x3^
10*x1^4+18682913942*x2^9*x3^15*x1^2-8232224654*x2^10*x3^14*x1^2-79737289079*x2^
21*x1*x3^6-31030328456*x2^27*x3^4*x1+162106553507*x1^7*x2^17*x3^6-15889617772*x1
^6*x2^22*x3^10+33384638211*x1^6*x2^19*x3^6-14614777384*x1^25*x3^12+5487113984*x3
^36*x2+41620855250*x3^21*x2^15*x1^3+25565422803*x1^22*x2^17+21237235443*x1^22*x2
^12-32804164322*x1^22*x2^13+2494748411*x1^22*x2^18-36151803293*x1^22*x2^14+
40952008952*x1^22*x2^15-6169695959*x1^22*x2^16-59933960368*x1^22*x2^11-
42214514715*x1^22*x2^3-20221050491*x1^22*x2^2+5358661045*x1^22*x2+24530164804*x1
^6*x2^17*x3^8+10372779274*x1^7*x2^15*x3^8+52040025490*x3^26*x1^7*x2+17228122701*
x3^27*x1^4*x2^2-4077522616*x3^29*x1^8*x2-16420972585*x3^33*x1^3*x2^2-17898710820
*x3^28*x1^4*x2^2+3372949679*x3^26*x1^4*x2^2+9149802394*x3^25*x1^2*x2^2+
32643093067*x3^28*x1^8*x2-54532099373*x1^5*x3^16+5411516646*x1^2*x3^19+
22201479913*x2^14*x3^4*x1^5+13963673637*x1^10*x2^23*x3^7-985644774*x1^11*x2^13*
x3^16-16421723416*x1^11*x2^14*x3^15+93109162011*x2^10*x3^19*x1^4-21323018712*x2^
10*x3^22*x1+30416774052*x1^12*x3^22*x2^5-67990644355*x1^3*x2^24*x3^10-7411143072
*x1^9*x3^19*x2^3-159667161439*x1^10*x3^13*x2^7-129542022778*x1^10*x3^15*x2^2-
73307549128*x1^8*x3^18*x2^4-17604430381*x1^8*x3^17*x2^5+99702449322*x1^12*x3^15*
x2^3+113595224307*x1^12*x3^16*x2^3-133894549863*x1^13*x3^12*x2^2-122367628811*x1
^20*x3^9*x2^9-83471964403*x1^8*x3^19*x2^4;

tst_status();
gcd (p1,p2);
tst_status();
gcd (q1,q2);
tst_status();
gcd (r1,r2);
tst_status();
tst_status(1);

$