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 0.00519894 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 0.329951 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 - 682809t + 3459943t t + 4096634t + 4491457t t + 3754509t t + 4876632t - 1479422t t - 2107241t t + 1323384t t + 2964353t + 1158570t t + 1245987t t + 1835032t t + 2549634t t + 4498087t + 4652720t t - 1140139t t - 4465959t t - 2303619t t + 159311t t - 2032648t - 1312082t t + 3706671t t - 2270713t t - 2442511t t - 3356670t t + 1661576t t + 1564174t , 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 4103505t - 2848088t t - 4773227t - 4065202t t + 529963t t - 1851540t + 3093732t t + 2067167t t - 1522819t t - 3511727t - 2388328t t + 602140t t + 1616211t t - 2532757t t + 68061t - 2776090t t - 3037765t t - 3402041t t + 3710646t t + 4385373t t + 1825455t + 522562t t + 2080620t t + 4100165t t + 46583t t + 4842280t t - 166760t t + 1321220t , 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 1737729t + 3893480t t + 1307753t - 2803264t t - 144194t t - 1593170t + 1966600t t + 2984247t t + 1788998t t + 1188706t + 918591t t + 538658t t + 354108t t - 2250928t t - 2962346t + 2256168t t + 2910935t t - 179477t t - 3470248t t - 3185347t t - 1525181t + 2199648t t + 1623395t t + 2028017t t - 1425889t t - 4560981t t + 762986t t - 399277t , 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 2874317t + 2341356t t + 299627t + 3775841t t + 3948288t t - 3661865t - 654258t t + 4673879t t + 3578624t t + 656392t + 4614050t t + 1411342t t + 4427288t t + 1862847t t + 927489t + 3279171t t - 846000t t + 1701222t t - 2325665t t - 2638458t t + 1530319t - 3692583t t + 4985662t t + 1156916t t - 4835040t t + 395424t t - 1518393t t - 2077777t , 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 - 2372546t + 4523687t t - 537627t - 2153189t t - 4944054t t - 4499317t + 1926472t t + 4373901t t + 4833787t t + 27827t - 4046783t t - 3544928t t - 3089335t t + 200924t t - 515082t + 1139327t t - 3185695t t + 79197t t - 2933537t t + 4597637t t + 2296896t - 262732t t - 1972027t t + 4669800t t - 295236t t + 3395394t t - 1212151t t - 4045281t , 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 1297307t - 4801047t t + 610262t + 4331721t t - 943782t t + 903568t - 1526490t t - 3237988t t - 1435517t t + 90540t + 2563521t t + 2822792t t - 4972213t t + 881578t t - 3112646t - 1054213t t - 3480765t t - 1869591t t - 3200205t t + 3372963t t + 1947054t + 486661t t - 1044409t t - 2517569t t - 1440712t t + 2174453t t + 3317362t t - 4766209t , 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 567434t + 1473334t t + 4978354t - 1068566t t + 4315634t t - 1183092t - 988513t t - 3860316t t - 3210583t t + 2720158t + 4127604t t - 2685021t t - 593322t t - 1061777t t + 4111419t - 4322904t t + 2678437t t - 538473t t + 3691782t t + 3595267t t + 3965155t + 698714t t + 719273t t + 439669t t - 3657140t t + 293622t t + 2430882t t + 4463926t , 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 2709382t + 3971019t t + 2001285t - 4322393t t - 4546445t t + 3859985t - 2090474t t - 1192533t t - 655282t t + 3432959t - 2812564t t - 2390207t t - 3164797t t - 823959t t - 1217738t + 3230081t t + 4397155t t - 871527t t + 1380223t t - 1612670t t - 3261705t - 3629885t t + 348918t t - 2313683t t + 3828352t t + 2103388t t - 1907739t t - 3790233t , 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 - 4267374t - 2054631t t + 1778625t - 3360715t t - 1607780t t - 4858102t - 4672480t t - 1400351t t - 3300435t t + 4427649t + 4546238t t - 996600t t - 275531t t - 3653171t t + 3734431t + 1214211t t + 3776085t t + 3540077t t + 2050999t t - 2757378t t + 4100511t - 4184559t t + 2524520t t - 4185103t t - 2179409t t - 4949382t t + 4531450t t - 2452562t , 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 3836175t + 1907460t t - 4913382t + 3400588t t - 1705892t t - 2358846t - 1482583t t - 2731926t t + 3731588t t + 3633724t + 2150988t t + 672173t t - 1395357t t - 3453452t t - 2177108t + 1190285t t - 2824039t t - 3611723t t - 934833t t - 3581702t t - 2933478t - 3416967t t + 3431989t t - 3941840t t + 889997t t - 43439t t + 219075t t + 4026790t 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) |