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 0.00613374 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 0.391913 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 3810457t - 4062914t t + 1116613t - 851076t t - 2195930t t + 3328417t + 2808775t t + 3336380t t + 3479811t t + 509663t - 2766083t t - 3444690t t + 2726555t t - 2557473t t - 4863909t + 851754t t - 927798t t - 3350896t t + 194688t t - 2808033t t + 1342608t - 65040t t + 3674385t t - 2921914t t + 836688t t + 2019408t t - 2550783t t - 2358913t , 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 4992910t + 185995t t - 2371306t - 768515t t + 3969639t t + 3882955t + 3479921t t - 4071403t t + 156992t t + 3804571t + 1683117t t + 1345651t t + 1549247t t - 2829697t t - 295121t + 1424766t t + 2361539t t + 2739585t t + 4853729t t + 3046102t t - 4335217t - 1223298t t - 582618t t + 3646552t t + 1813559t t - 1488018t t + 4877251t t + 1686152t , 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 4272529t + 4672518t t - 2161508t + 1903854t t + 3350873t t + 4848756t + 2326909t t + 3806520t t - 2977201t t + 1454465t - 4152392t t - 2626580t t - 1010785t t - 2923446t t + 2583224t + 55633t t - 2130779t t + 3503436t t + 3728444t t - 1700286t t + 4952699t + 2589800t t + 3973889t t + 3179164t t - 4107156t t - 2843390t t - 16813t t - 1085942t , 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 - 3411911t + 4356256t t - 4080528t - 928208t t - 4694109t t + 1327801t - 2959248t t - 1549219t t - 189335t t + 4540257t - 4774360t t - 58071t t + 1313875t t + 87746t t + 4432761t + 1529459t t - 2239555t t + 2498909t t + 452870t t - 294162t t + 4606010t - 3390523t t + 3134454t t + 4528108t t - 2606448t t + 2119120t t - 4154462t t + 32344t , 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 - 2308806t + 205727t t + 1230354t + 3124734t t - 993233t t + 2121544t + 990525t t - 1732071t t - 95233t t + 4005876t + 5387t t + 2539085t t + 2881603t t + 4218756t t + 3883261t - 3805160t t - 4257560t t + 2418423t t - 4155078t t + 2347319t t + 117982t + 1191298t t - 309794t t + 2131218t t + 3849989t t - 1269579t t + 3296180t t + 3248891t , 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 - 3256308t - 2252482t t - 2124576t + 1997780t t + 2589170t t - 4026572t - 889774t t + 3635973t t + 4819128t t - 4622666t + 2289171t t + 4520710t t - 1360547t t + 3385108t t + 963725t + 2072517t t + 1422823t t + 4342159t t - 329681t t + 4134846t t - 4243472t + 4553499t t - 4672822t t + 3750819t t + 4005284t t + 4010049t t + 1538026t t - 2676276t , 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 - 679742t + 1681922t t - 833288t + 633807t t - 3661008t t + 1328095t + 623025t t + 3159301t t + 4403961t t - 3764145t + 4308759t t - 3912479t t + 1943290t t - 1445564t t + 3836197t + 856111t t - 4971256t t + 4302507t t - 3370199t t + 909570t t + 4211631t - 4403133t t - 2999917t t + 164864t t - 4921165t t - 2321529t t - 186745t t - 3639087t , 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 590428t - 1823110t t - 3700910t - 1892560t t + 3849888t t + 1246977t - 579913t t + 550043t t - 3820821t t - 3303851t - 3294831t t + 3528513t t - 2749998t t + 1659688t t + 2692588t + 3074251t t + 90453t t + 393626t t + 3268947t t + 3477949t t - 2072315t - 2060503t t - 514816t t - 3026326t t - 2256663t t - 4176322t t - 1842815t t - 4070214t , 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 4919161t + 3453790t t - 4531279t + 875390t t - 4523064t t + 1687013t - 4733481t t - 4811003t t - 810756t t + 502692t - 1538014t t + 2406716t t + 2420012t t + 2931529t t + 319119t + 1346947t t + 1504285t t + 571506t t + 1834909t t + 4786863t t + 4008310t + 4319679t t - 4627633t t - 804179t t - 3369396t t + 93319t t + 3289390t t + 2351630t , 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 - 4625543t - 711145t t + 3751394t + 4614781t t + 1832668t t + 1434779t - 2264440t t - 2071821t t - 3716203t t + 2647138t + 1757911t t + 2880453t t - 69019t t - 4489801t t + 1578666t + 638592t t + 3776258t t + 3195986t t + 4523223t t + 1789506t t + 2872005t + 4500079t t - 1156350t t + 3132766t t - 3615163t t - 1387166t t + 4612979t t + 3768408t 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) |