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 0.0174462 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 1.06625 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 - 504829t + 3229176t t - 4562550t - 4459889t t + 4322859t t + 4902406t - 2392187t t - 3546510t t - 3444057t t - 753699t - 476139t t + 10192t t - 2986367t t - 3950341t t - 1133935t + 1674708t t - 618804t t + 315841t t + 3155923t t - 4313726t t + 60196t + 4436333t t + 445658t t - 938211t t + 3387775t t - 1601930t t + 2461433t t + 2001752t , 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 1487252t - 4924428t t - 1911703t - 4130820t t + 1545559t t + 4421923t + 3567211t t + 151525t t + 2462682t t - 3670699t - 4346000t t - 1983008t t + 2957070t t + 2851548t t + 1377348t + 702578t t + 3376029t t - 2471380t t + 2274186t t + 517265t t + 2995696t + 4601592t t + 698380t t + 2407012t t - 4145247t t + 1698509t t - 2464618t t - 899103t , 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 - 2645998t + 4124448t t + 4335664t + 1138774t t + 4218178t t + 1301734t - 3894435t t + 2555998t t - 858551t t - 4322407t - 3980348t t - 4739225t t + 3899459t t - 4585874t t + 3285060t - 26077t t + 4961529t t + 2382243t t - 1905104t t - 1983390t t + 491233t + 430607t t + 2434946t t - 2286649t t - 2697467t t - 3922195t t + 4361600t t - 2508443t , 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 1300350t + 2375t t - 1463923t + 3248345t t + 1693747t t + 281578t - 2558052t t + 2827624t t + 2037235t t - 4016977t - 1398979t t + 631179t t + 4656744t t + 814120t t - 3670003t - 2303918t t + 3722991t t - 841659t t - 4664497t t + 4502747t t + 992386t - 1456791t t - 2042982t t - 378180t t + 4447876t t - 90777t t + 4080602t t + 3563837t , 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 1755735t - 1232809t t + 3138541t - 1582940t t - 1359259t t - 3588226t + 4754923t t + 2082709t t - 4025615t t - 2755942t - 639738t t - 2076498t t + 3568331t t - 4065981t t + 1925954t + 4128618t t - 1249725t t + 1087035t t - 3182438t t - 2987997t t - 3983194t - 4239316t t + 2139714t t - 4980249t t - 4787383t t - 3288221t t + 4158613t t - 1979785t , 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 3230006t + 3773089t t + 4332553t - 4142082t t + 275239t t - 4379770t + 4980733t t - 3884484t t - 1147849t t - 623821t - 3264698t t + 4083082t t + 4531652t t - 3688165t t - 3441687t - 4504438t t + 2858329t t - 4521790t t - 1431400t t - 2378524t t + 700787t - 3989391t t + 4499010t t + 4247848t t + 3510772t t - 2774435t t - 254652t t - 296603t , 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 - 1857074t - 513714t t + 3323746t + 4020863t t - 1813353t t + 1020751t + 790421t t - 2328028t t + 656053t t - 1629478t - 3393663t t + 1757333t t + 2737318t t - 339621t t + 128767t - 4615880t t + 710105t t + 2112127t t - 4031886t t + 4790173t t + 1795943t - 3880433t t + 3253627t t + 213558t t + 1444271t t - 3191486t t - 2879596t t + 3402237t , 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 - 2899302t - 2622888t t - 1114117t + 725869t t + 775021t t - 3333412t + 3111511t t + 3014162t t - 2082844t t - 1098013t + 3824880t t - 3242917t t + 4760521t t + 320501t t - 3998075t - 3302670t t - 645279t t - 2798786t t + 4363171t t + 1874533t t + 3379649t + 2260922t t - 1691718t t - 2021154t t - 718336t t + 753075t t + 1406452t t - 2063190t , 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 - 1176583t + 11786t t + 262829t - 3797888t t + 3876083t t + 1979905t - 3825529t t - 975389t t - 4516356t t - 3076034t - 2980490t t - 1101683t t + 4367802t t + 3785614t t + 2223475t - 1377679t t + 1138586t t - 4962588t t - 3324451t t + 2323683t t + 4384016t + 2632722t t - 3213844t t + 692945t t + 1150283t t + 29776t t + 1372978t t - 210547t , 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) |