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
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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
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i3 : time parametrize L
-- used 0.00556162 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)
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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
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i5 : time parametrize Q
-- used 0.355945 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
3595775t + 1955085t t - 3216200t + 4854122t t + 1205502t t - 1975634t + 3832790t t - 1340758t t - 2876523t t - 2376974t + 413617t t + 697370t t + 1458127t t - 178971t t + 1598242t + 2885494t t - 3431573t t - 2594430t t - 4118744t t + 920588t t - 928298t - 1355233t t - 2841870t t + 4503191t t + 4578965t t - 4703003t t - 2255578t t + 3369687t ,
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
196923t + 735740t t + 4204361t + 4919087t t + 4191608t t - 4897776t - 80313t t + 1616507t t + 2913552t t - 661472t - 1950679t t + 1466426t t + 4735302t t - 4114190t t - 573844t + 3471476t t + 713534t t - 3588772t t + 4356229t t - 1094071t t + 1819413t + 2855848t t + 673382t t - 2207004t t - 4313805t t + 2594471t t + 1797216t t + 4464199t ,
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
- 4465202t + 2675358t t + 2673408t + 1608117t t + 455149t t + 1414960t - 1918352t t - 2585719t t + 3705854t t + 4858205t + 4123629t t + 2628647t t + 3545835t t - 323076t t - 3931135t + 2617377t t + 2924145t t - 359942t t + 518309t t - 4870860t t + 1668542t - 1288445t t + 4649334t t - 4911574t t - 4445126t t + 312193t t + 3435991t t + 3339675t ,
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
730764t - 3118985t t - 633600t + 1675759t t - 1983772t t - 3699329t - 2028122t t + 624554t t + 2269469t t - 122152t - 4405808t t + 1143542t t - 2920885t t - 3170637t t + 4089506t + 704014t t - 2749909t t - 2413980t t + 2026520t t - 4599448t t - 3928920t - 2294470t t - 4750280t t + 14950t t - 1091822t t + 3402770t t + 4310641t t + 1480834t ,
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
- 4315118t - 3098978t t - 4885672t - 359755t t + 278623t t - 1652496t - 759743t t - 3302491t t - 4526561t t + 4004742t - 350777t t - 1379421t t + 70322t t - 4746577t t - 1946552t + 4575853t t + 3252519t t - 1481191t t + 368114t t - 1788374t t - 129069t - 1206452t t - 1240321t t - 913163t t - 2720448t t - 3441947t t + 2765564t t - 17463t ,
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
4437767t + 2448998t t - 4674501t + 2014093t t + 3178605t t + 4120464t + 1117090t t - 700111t t + 2370933t t + 3414676t - 3049078t t - 1232613t t + 2982730t t - 1314587t t - 1142231t - 3870882t t + 4164403t t - 3311199t t + 982524t t + 4166497t t + 2308221t - 3559246t t - 2674453t t + 82769t t - 2512434t t - 2311487t t + 4707485t t - 988168t ,
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
- 437502t - 3720847t t - 4825935t - 527348t t + 4523783t t - 1306564t - 3597282t t - 3264013t t - 35115t t - 97631t + 570254t t + 1228457t t - 4317755t t - 4288159t t + 1658388t - 2526156t t - 83660t t + 3701572t t - 861625t t + 1939090t t + 273554t - 1207486t t - 3084758t t - 3174489t t + 4738002t t - 1560900t t + 1883185t t - 1461027t ,
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
723816t + 4353780t t + 4582020t + 4681410t t - 2761246t t - 1717794t + 4053489t t + 4253348t t + 4652620t t + 4003848t + 4173348t t - 1551664t t - 3977382t t - 351623t t - 2947146t - 3378384t t + 61740t t + 369478t t + 4209042t t - 945255t t - 2702875t + 2487074t t - 2645391t t - 1291715t t + 2838290t t - 271417t t - 4299261t t + 4539436t ,
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
1105636t + 884462t t + 858814t - 314377t t - 1521147t t - 3344493t + 4782364t t - 33386t t + 4054274t t - 2734383t - 4083729t t - 3802210t t - 2325347t t + 4622529t t + 4519057t + 4236565t t - 4508343t t + 1442297t t + 4717591t t - 2796257t t + 2305249t - 1559784t t + 3348653t t + 1454428t t + 2907444t t + 4195869t t - 582563t t + 3805702t ,
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)
|