i1 : P9 := ZZ/10000019[x_0..x_9] ZZ o1 = --------[x , x , x , x , x , x , x , x , x , x ] 10000019 0 1 2 3 4 5 6 7 8 9 o1 : PolynomialRing |
i2 : L = trim ideal(random(1,P9),random(1,P9),random(1,P9),random(1,P9)) o2 = ideal (x - 1112016x - 3901361x - 3193863x + 4143040x - 1964417x + 3 4 5 6 7 8 ------------------------------------------------------------------------ 1074958x , x + 632284x + 492458x + 3869254x + 2840266x + 4883974x 9 2 4 5 6 7 8 ------------------------------------------------------------------------ + 3340961x , x + 4724709x - 3505386x + 2469206x - 1381515x + 9 1 4 5 6 7 ------------------------------------------------------------------------ 2331280x - 4936229x , x - 2094456x - 3936498x - 4665404x - 736943x 8 9 0 4 5 6 7 ------------------------------------------------------------------------ - 849671x + 3034137x ) 8 9 ZZ o2 : Ideal of --------[x , x , x , x , x , x , x , x , x , x ] 10000019 0 1 2 3 4 5 6 7 8 9 |
i3 : time parametrize L -- used 0.0204937 seconds o3 = -- rational map -- ZZ source: Proj(--------[t , t , t , t , t , t ]) 10000019 0 1 2 3 4 5 ZZ target: Proj(--------[x , x , x , x , x , x , x , x , x , x ]) 10000019 0 1 2 3 4 5 6 7 8 9 defining forms: { 2094456t + 3936498t + 4665404t + 736943t + 849671t - 3034137t , 0 1 2 3 4 5 - 4724709t + 3505386t - 2469206t + 1381515t - 2331280t + 4936229t , 0 1 2 3 4 5 - 632284t - 492458t - 3869254t - 2840266t - 4883974t - 3340961t , 0 1 2 3 4 5 1112016t + 3901361t + 3193863t - 4143040t + 1964417t - 1074958t , 0 1 2 3 4 5 t , 0 t , 1 t , 2 t , 3 t , 4 t 5 } o3 : RationalMap (linear rational map from PP^5 to PP^9) |
i4 : Q = trim ideal(random(2,P9),random(1,P9),random(1,P9)) o4 = ideal (x - 3731285x + 569485x + 4255201x - 2098712x - 4248990x - 1 2 3 4 5 6 ------------------------------------------------------------------------ 1801342x + 4050229x - 2319263x , x - 3094689x - 4410186x + 7 8 9 0 2 3 ------------------------------------------------------------------------ 2 3196146x + 2713771x + 2261412x - 1267196x - 4210403x + 285932x , x 4 5 6 7 8 9 2 ------------------------------------------------------------------------ 2 2 + 1045421x x + 718532x - 3701628x x + 3903798x x + 2842397x - 2 3 3 2 4 3 4 4 ------------------------------------------------------------------------ 2 2997962x x + 4189835x x + 1489225x x - 2279955x + 2520782x x + 2 5 3 5 4 5 5 2 6 ------------------------------------------------------------------------ 2 4494280x x + 3101255x x - 681950x x + 1307490x + 2690767x x + 3 6 4 6 5 6 6 2 7 ------------------------------------------------------------------------ 2 4503651x x + 1762528x x + 137682x x - 2229093x x - 4018967x + 3 7 4 7 5 7 6 7 7 ------------------------------------------------------------------------ 4536117x x - 2541309x x + 3810968x x - 4208194x x - 1643560x x + 2 8 3 8 4 8 5 8 6 8 ------------------------------------------------------------------------ 2 3330573x x - 2280516x - 1532056x x + 1883935x x + 1887667x x + 7 8 8 2 9 3 9 4 9 ------------------------------------------------------------------------ 2 1211601x x - 2168594x x - 1801762x x + 3022242x x + 3618789x ) 5 9 6 9 7 9 8 9 9 ZZ o4 : Ideal of --------[x , x , x , x , x , x , x , x , x , x ] 10000019 0 1 2 3 4 5 6 7 8 9 |
i5 : time parametrize Q -- used 0.685375 seconds o5 = -- rational map -- ZZ source: Proj(--------[t , t , t , t , t , t , t ]) 10000019 0 1 2 3 4 5 6 ZZ target: Proj(--------[x , x , x , x , x , x , x , x , x , x ]) 10000019 0 1 2 3 4 5 6 7 8 9 defining forms: { 2 2 2 2 2 2 2 - 3919443t - 4515761t t - 4802607t + 769772t t + 1742271t t - 1038543t + 3799724t t - 1149614t t - 950065t t - 1869735t + 3129608t t + 3268176t t - 2460210t t - 2164949t t + 2844186t - 1998621t t + 4603959t t - 3573200t t + 2622867t t - 1309755t t - 854520t - 1942100t t + 4313071t t + 677243t t + 1205223t t + 2969838t t - 3992471t t - 573413t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 339676t - 1843502t t - 3515859t - 1881741t t - 1435813t t + 3853220t - 1591439t t + 2222028t t - 831231t t + 506515t + 1977134t t - 318964t t + 3502926t t - 1501752t t + 381060t - 2631833t t + 2915500t t + 1965604t t + 307902t t - 4753876t t - 928778t - 710730t t + 1441791t t + 2220746t t - 2073572t t + 2499905t t + 4037923t t - 3144492t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 - 3797516t - 3261835t t + 4469990t + 2612518t t + 1089371t t - 1898627t - 2905764t t - 3313431t t + 2328126t t + 528460t + 3284231t t - 2410627t t + 269261t t + 3157218t t - 9101t + 3173097t t - 3940755t t + 4104247t t + 1427249t t - 2110993t t - 3512949t - 3198809t t + 3708441t t + 2235127t t + 446685t t - 1973588t t + 1189419t t + 1546877t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 2909824t + 704743t t + 683148t + 4039608t t + 4553303t t + 4644113t - 3502175t t - 3106852t t + 949266t t + 3198523t - 2016334t t - 2762895t t + 472212t t - 1329029t t - 1786955t - 3245058t t + 4306055t t - 4704077t t - 1128640t t + 3866702t t - 4650216t + 2782612t t - 2204016t t + 3402448t t + 368687t t - 1382880t t - 4282016t t + 4292390t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 2130730t + 4534219t t + 1261110t - 1200141t t + 866465t t + 4734784t + 1670123t t + 3982546t t - 3704928t t - 1869595t - 1147417t t + 2887743t t - 1274150t t + 2769050t t + 3563916t + 1781510t t + 4911359t t - 4333786t t - 4108403t t + 2287250t t - 1441305t - 3468167t t + 4126t t + 238325t t - 2048349t t + 3544421t t + 2226516t t - 77164t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 - 3359480t - 63377t t + 1993010t + 1690141t t - 3917183t t + 3331914t + 487752t t + 1518121t t + 4731396t t - 811904t - 4806382t t - 2532717t t - 909302t t + 2243484t t + 4638897t - 2411777t t + 4685691t t - 2238070t t - 3323904t t + 2734300t t + 1515599t - 3156194t t - 4041114t t - 2810029t t - 2851810t t + 3835177t t - 113258t t + 4866994t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 1742205t - 4742261t t - 4734909t + 3426242t t + 1139456t t - 1055499t - 1629160t t - 3200359t t - 1491054t t - 777812t + 4042731t t - 2394359t t - 1413747t t - 4259569t t + 1331666t + 3493892t t + 2150329t t + 2815419t t - 2481194t t - 4202417t t + 53909t + 3315142t t + 2245426t t - 2139703t t + 3090805t t - 4348058t t + 3457936t t - 4712981t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 3913925t + 344157t t + 284425t - 955585t t - 3573346t t + 2638272t - 3975919t t - 199465t t - 769771t t - 3450281t - 1790509t t - 1485590t t - 930127t t + 2641206t t - 3998191t - 927224t t + 2323166t t - 2305340t t - 1015315t t + 4353120t t - 4376126t - 2408746t t - 1897589t t + 2602224t t - 414496t t + 1313611t t - 2789292t t + 1550914t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 - 2570676t - 360063t t - 422687t + 1146156t t + 1539218t t + 4015746t - 3399631t t + 974029t t + 610022t t + 3532378t - 4663382t t + 3973301t t + 3770101t t + 586024t t - 4135569t - 692081t t - 3642736t t + 173656t t + 1926543t t + 1500356t t - 968137t - 1636697t t + 4613837t t + 1064895t t - 4517045t t + 3208482t t - 47442t t + 1267079t , 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 2 2 2 2 2 2 2 t + 2557201t t + 897582t - 1955667t t - 4162832t t + 2917974t - 2414045t t - 3133456t t + 130269t t - 921025t + 4924767t t + 268844t t - 1179881t t - 1984252t t + 85259t - 989568t t - 2303912t t - 4074596t t - 1741629t t - 1251685t t - 2195520t + 1090392t t - 4221350t t - 3633875t t + 286385t t - 4128258t t - 2812768t t - 2652542t 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 } o5 : RationalMap (quadratic rational map from PP^6 to PP^9) |