|
|
D.15.20.15 grtranspose1
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grtranspose1(M), graded object or list M
- Return:
- same as input
- Purpose:
- graded transpose of graded object or chain complex M
- Assume:
- M must be a graded object or a list of graded objects
Example:
| | LIB "gradedModules.lib";
"Surface Name: 'k3.d10.g9.quart2' in P^4";
==> Surface Name: 'k3.d10.g9.quart2' in P^4
int @p=31991; ring R = (@p),(x,y,z,u,v), dp;
ideal J = x3yz2+31/15x2y2z2-7231xy3z2+99/37y4z2+28/95x3z3+97/32x2yz3+13247xy2z3+12717y3z3-113/31x2z4-61/30xyz4-6844y2z4+104/3xz5-13849yz5+43/39z6+13061x3yzu-8463x2y2zu+94/69xy3zu-8/61y4zu-13297x3z2u+7217x2yz2u-7830xy2z2u-75/14y3z2u+2839x2z3u-14657xyz3u-52/7y2z3u-6/89xz4u-6169yz4u+44/7z5u-98/33x3yu2+41/30x2y2u2-65/98xy3u2+122/13y4u2+9906x3zu2-11587x2yzu2+17/53xy2zu2+6504y3zu2+49/106x2z2u2+11480xyz2u2+97/71y2z2u2+12560xz3u2-114/83yz3u2-13761z4u2-67/112x3u3-18/49x2yu3+21/67xy2u3-44/43y3u3+123/116x2zu3+4459xyzu3-13841y2zu3-805xz2u3-1382yz2u3-5293z3u3+133x2u4-122/79xyu4+9724y2u4+61/24xzu4+113/119yzu4-19/108z2u4+15893xu5+57/22yu5+4600zu5-618u6-27/53x3yzv+44/103x2y2zv-142xy3zv+19/84y4zv+105/8x3z2v+10532x2yz2v-75/74xy2z2v-70/19y3z2v+31/80x2z3v-481xyz3v+47/30y2z3v+14318xz4v+51/28yz4v-15/113z5v-46/17x3yuv-99/100x2y2uv-106/5xy3uv+14384y4uv+7/100x3zuv-15/64x2yzuv-6976xy2zuv+12051y3zuv-67/42x2z2uv-2627xyz2uv-49/104y2z2uv+77/16xz3uv+15766yz3uv+85/117z4uv-107/101x3u2v-6699x2yu2v+2443xy2u2v-27/28y3u2v+11945x2zu2v-14467xyzu2v-4873y2zu2v-63/124xz2u2v-8270yz2u2v+11900z3u2v+47/14x2u3v+53/8xyu3v-10/51y2u3v-87/119xzu3v+114/73yzu3v+86/57z2u3v+52/63xu4v-11587yu4v+1/18zu4v-121/109u5v+116/11x3yv2+19/108x2y2v2-31/3xy3v2-43/9y4v2-81/100x3zv2-7728x2yzv2-1037xy2zv2+24/101y3zv2-61/103x2z2v2-8/51xyz2v2+117/109y2z2v2+98/23xz3v2+1646yz3v2-3356z4v2+105/59x3uv2+117/31x2yuv2+519xy2uv2+12633y3uv2+25/6x2zuv2-963xyzuv2-49/23y2zuv2-116/25xz2uv2+14146yz2uv2+11480z3uv2-95/8x2u2v2-10928xyu2v2-51/23y2u2v2-12770xzu2v2-92/91yzu2v2+3872z2u2v2+3183xu3v2+6871yu3v2+90/37zu3v2+10019u4v2-69/88x3v3-1398x2yv3-97/72xy2v3-46/97y3v3+107/14x2zv3-20/89xyzv3-11367y2zv3+120/29xz2v3-86/81yz2v3+107/69z3v3-39/17x2uv3+83/11xyuv3+169y2uv3-11/71xzuv3-22/17yzuv3-14862z2uv3-13009xu2v3-101/12yu2v3+10617zu2v3+2567u3v3-23/85x2v4+27/50xyv4+113/51y2v4+97/16xzv4+4438yzv4-11857z2v4+14580xuv4-6426yuv4+9421zuv4-10585u2v4+14670xv5+1807yv5+10298zv5-116/53uv5+7869v6,x3yzu+31/15x2y2zu-7231xy3zu+99/37y4zu+28/95x3z2u+97/32x2yz2u+13247xy2z2u+12717y3z2u-113/31x2z3u-61/30xyz3u-6844y2z3u+104/3xz4u-13849yz4u+43/39z5u-124/43x3yu2-90/13x2y2u2-13244xy3u2-78/73y4u2+118/43x3zu2+37/67x2yzu2-10426xy2zu2+2412y3zu2-32/113x2z2u2+35/104xyz2u2+3952y2z2u2+9028xz3u2-1990yz3u2-59/109z4u2+15499x3u3+116/23x2yu3+95/58xy2u3+8/47y3u3+59/109x2zu3-29xyzu3+12412y2zu3+20/81xz2u3+2200yz2u3-13809z3u3+3889x2u4-8136xyu4+8922y2u4-4/121xzu4+82/113yzu4-65/23z2u4+101/53xu5+103/113yu5-99/118zu5-9524u6-2749x3yzv-7814x2y2zv+73/113xy3zv+9937y4zv-59/62x3z2v-23/12x2yz2v-10245xy2z2v+7130y3z2v-4427x2z3v+6656xyz3v+3448y2z3v-46/79xz4v+1611yz4v+8453z5v+12013x3yuv+49/17x2y2uv-4/115xy3uv-121/91y4uv-63/29x3zuv+64/7x2yzuv-8785xy2zuv-87/14y3zuv+36/121x2z2uv+9525xyz2uv+4215y2z2uv-17/13xz3uv-117/125yz3uv+101/122z4uv+42/37x3u2v-8747x2yu2v-105/79xy2u2v+10799y3u2v-58/49x2zu2v-8/75xyzu2v-67/49y2zu2v-38/11xz2u2v+53/27yz2u2v+113/52z3u2v+18/59x2u3v+71/106xyu3v+47/2y2u3v-4594xzu3v+95/4yzu3v-121/46z2u3v-55/62xu4v-101/72yu4v+40/53zu4v+15227u5v-15553x3yv2+29/94x2y2v2-4076xy3v2-7133y4v2+27/125x3zv2+33/29x2yzv2-63/95xy2zv2+9166y3zv2-480x2z2v2+9941xyz2v2+107/46y2z2v2+13018xz3v2+53/98yz3v2+92/35z4v2+17/30x3uv2+77/95x2yuv2+11/67xy2uv2+8262y3uv2+65/11x2zuv2+2567xyzuv2-33/94y2zuv2+85/92xz2uv2+103/25yz2uv2-27/100z3uv2+13210x2u2v2-109/90xyu2v2+141y2u2v2-124/51xzu2v2-3/109yzu2v2-4910z2u2v2+205xu3v2+14357yu3v2+85/57zu3v2-109/28u4v2-68/39x3v3+10545x2yv3-2176xy2v3-8743y3v3+15111x2zv3+25/119xyzv3+8/103y2zv3-6046xz2v3+8658yz2v3+106/5z3v3-31/126x2uv3-7762xyuv3+2315y2uv3+124/67xzuv3-77/104yzuv3+95/71z2uv3+69/119xu2v3+13069yu2v3-8620zu2v3+105/41u3v3-15772x2v4-11212xyv4-61/36y2v4+38/125xzv4-15860yzv4+8/63z2v4+7519xuv4-94/41yuv4+45/32zuv4+9417u2v4-71/35xv5-6287yv5+6481zv5+106/99uv5+3/41v6,-8036x3yu2+7966x2y2u2-151xy3u2-14/111y4u2-111/76x3zu2-102/11x2yzu2+7956xy2zu2-7397y3zu2-113/16x2z2u2-8049xyz2u2+7230y2z2u2+3978xz3u2-36/113yz3u2-8147z4u2-107/83x3u3+78/97x2yu3+12700xy2u3+11/72y3u3+88/31x2zu3-63/40xyzu3+101/35y2zu3-220xz2u3+3/103yz2u3-49/45z3u3-21/113x2u4+104/123xyu4+98/47y2u4-56/61xzu4-87/50yzu4+5913z2u4-120/17xu5+64/11yu5-109/80zu5+10371u6-118/25x3yzv+58/99x2y2zv-5/64xy3zv+7/46y4zv-49/103x3z2v-77/106x2yz2v-44/7xy2z2v-7559y3z2v-17/35x2z3v+948xyz3v-15043y2z3v-3576xz4v-2/109yz4v+74/11z5v+6436x3yuv+7316x2y2uv+29/5xy3uv-1326y4uv+34/49x3zuv-122/27x2yzuv-632xy2zuv+46/49y3zuv-13463x2z2uv-808xyz2uv-17/32y2z2uv-13149xz3uv-117/88yz3uv-45/79z4uv-65/94x3u2v+6/67x2yu2v+34/39xy2u2v-14026y3u2v+42/107x2zu2v-3287xyzu2v-70/43y2zu2v+29/104xz2u2v-47/18yz2u2v-11038z3u2v+6262x2u3v-5255xyu3v-7/10y2u3v+7065xzu3v+5608yzu3v+4675z2u3v-73/90xu4v-15822yu4v-71/63zu4v+110/97u5v-69/5x3yv2+4315x2y2v2-124/45xy3v2-79/16y4v2-10739x3zv2-93/46x2yzv2+12499xy2zv2-73/86y3zv2+6367x2z2v2-12876xyz2v2-306y2z2v2-89xz3v2-70/51yz3v2+13120z4v2+61/57x3uv2+14782x2yuv2-91/9xy2uv2-2625y3uv2+14747x2zuv2-5899xyzuv2-12944y2zuv2-47/14xz2uv2-4551yz2uv2-99/101z3uv2-12618x2u2v2+1507xyu2v2-11951y2u2v2+68/49xzu2v2+49/39yzu2v2-56/103z2u2v2-31/85xu3v2-32/49yu3v2-65/14zu3v2+15/7u4v2+5749x3v3-3667x2yv3-107/29xy2v3+11301y3v3+95/18x2zv3-121/74xyzv3+75/26y2zv3+101/98xz2v3-111/76yz2v3-11335z3v3-15923x2uv3-36/83xyuv3-4134y2uv3-87/118xzuv3-41/11yzuv3+104/61z2uv3+12583xu2v3-50/23yu2v3-31/44zu2v3-29/23u3v3+108/107x2v4-8216xyv4-5009y2v4+101/26xzv4-9779yzv4+71/74z2v4-3358xuv4+83/84yuv4-34/39zuv4+44/47u2v4-112/83xv5+113/74yv5+82/79zv5-115/99uv5+12/109v6,-x4y-31/15x3y2+7231x2y3-99/37xy4-28/95x4z-53/107x3yz-4623x2y2z+5300xy3z-41/111y4z+12205x3z2+113/120x2yz2+54/49xy2z2-85/63y3z2+104/89x2z3-52/121xyz3-22/49y2z3+14367xz4+71/93yz4+55/56z5-5/81x4u-67/81x3yu-83/13x2y2u+98/55xy3u+15289y4u-94/111x3zu+40/29x2yzu-16/59xy2zu-107/14y3zu+2965x2z2u-459xyz2u-2/47y2z2u+35/22xz3u+119/39yz3u-12180z4u-13679x3u2+1534x2yu2+11305xy2u2-62/9y3u2-68/39x2zu2+11/90xyzu2-36/101y2zu2-2896xz2u2-15114yz2u2-49/114z3u2+19/16x2u3-11401xyu3-109/3y2u3+67/80xzu3+53/92yzu3+2894z2u3+119/74xu4+407yu4-65/53zu4+95/94u5-9309x4v+21/40x3yv+1436x2y2v+2194xy3v+6994y4v-116/81x3zv+13/2x2yzv-12/13xy2zv-23/84y3zv-61/83x2z2v+2023xyz2v+19/40y2z2v+43/26xz3v-59/113yz3v-47/53z4v+15580x3uv+21x2yuv+113/97xy2uv-15419y3uv-15243x2zuv+5128xyzuv-34/47y2zuv+13206xz2uv-4833yz2uv+107/91z3uv-1693x2u2v+54/53xyu2v-86/67y2u2v+98/9xzu2v+86/17yzu2v+64/89z2u2v+25/113xu3v+7884yu3v+14089zu3v-12027u4v-9471x3v2-36/85x2yv2-21/13xy2v2+15888y3v2+76/109x2zv2+4547xyzv2+115/12y2zv2-11/107xz2v2+6764yz2v2-8321z3v2+84/101x2uv2-202xyuv2+3251y2uv2+91/4xzuv2+7124yzuv2-53/81z2uv2+47/84xu2v2-8833yu2v2+117/14zu2v2-3/113u3v2+126/97x2v3-78/115xyv3+68/63y2v3-34/109xzv3+5913yzv3+6226z2v3-2365xuv3+91/120yuv3+14120zuv3-69/8u2v3+71/12xv4-13094yv4-7262zv4-33uv4+5367v5,-9533x4y-318x3y2+8/49x2y3+83/29xy4+13129y5+221x4z+115/48x3yz+12508x2y2z+97/52xy3z+11479y4z+8941x3z2+104/109x2yz2+9191xy2z2+103/64y3z2+10584x2z3-7728xyz3+3979y2z3+15/82xz4+5409yz4-1326z5+3756x4u-57/62x3yu+63/47x2y2u-14600xy3u+159y4u-11/4x3zu-113/57x2yzu-26/125xy2zu-32/87y3zu-10/21x2z2u+12927xyz2u-73/62y2z2u+115/99xz3u-13/3yz3u-126/25z4u-3969x3u2-122/57x2yu2-5003xy2u2-100/117y3u2-71/30x2zu2+7356xyzu2-2211y2zu2+31/40xz2u2-6722yz2u2-139z3u2+4426x2u3+1/115xyu3-72/85y2u3+15260xzu3+7938yzu3+4/115z2u3-33/89xu4+31/108yu4-50/83zu4+14/107u5+24/95x4v-113/17x3yv+81/14x2y2v-9957xy3v-10075y4v-122/113x3zv+65/118x2yzv-96/29xy2zv-19/41y3zv+113/35x2z2v+121/31xyz2v-9/68y2z2v+91/45xz3v-23/116yz3v-67/99z4v-5355x3uv-3112x2yuv-12824xy2uv-58/123y3uv-13/22x2zuv-19/85xyzuv-121/24y2zuv-14093xz2uv+99/95yz2uv+89/50z3uv+13096x2u2v-109/120xyu2v+121/61y2u2v+80/41xzu2v-39yzu2v-8/99z2u2v+5/17xu3v+112/69yu3v+14346zu3v-7173u4v+125/13x3v2+43/53x2yv2-78/103xy2v2-109/111y3v2+33/13x2zv2-15333xyzv2+87/49y2zv2-7212xz2v2+7729yz2v2-86/123z3v2-119/103x2uv2-71/122xyuv2-81/113y2uv2+6133xzuv2+55/72yzuv2+69/31z2uv2+12828xu2v2+94/15yu2v2-7588zu2v2+21/41u3v2-8712x2v3+74/9xyv3-11/87y2v3+1446xzv3-3/95yzv3-87/55z2v3-717xuv3-110/97yuv3-13/113zuv3-95/81u2v3-37/68xv4+5112yv4-56/11zv4-6/115uv4+7910v5,25/42x4y-42/79x3y2-59/21x2y3+2736xy4-107/115x4z-203x3yz+47/101x2y2z+7686xy3z-63/64y4z+103/57x3z2-12082x2yz2+11/102xy2z2-83/43y3z2+13/49x2z3-2685xyz3+123/44y2z3+31/12xz4+126/83yz4+14745z5+83/37x4u+7362x3yu-14615x2y2u-14109xy3u+49/47y4u+1929x3zu+83/71x2yzu-13640xy2zu-97/58y3zu-11141x2z2u-61/49xyz2u-3745y2z2u-74/21xz3u+3493yz3u-7540z4u-103/118x3u2-43/32x2yu2-9200xy2u2-23/65y3u2+15895x2zu2-13924xyzu2-14291y2zu2-11039xz2u2-31/37yz2u2-101/93z3u2-39/83x2u3-4536xyu3-78/47y2u3+75/44xzu3-24/121yzu3-81/113z2u3-81/89xu4+15825yu4-4111zu4+5850u5-12534x4v-69/94x3yv-10076x2y2v+3952xy3v+25/12y4v+21/34x3zv+11002x2yzv-54xy2zv+20/23y3zv+4991x2z2v+549xyz2v+2687y2z2v-110/9xz3v+11359yz3v+49/24z4v+62/107x3uv-27/41x2yuv-17/52xy2uv-10972y3uv+12/103x2zuv-318xyzuv-77/40y2zuv-114/53xz2uv+17/28yz2uv-8084z3uv+85/36x2u2v+7/100xyu2v-5772y2u2v-89/114xzu2v-40/121yzu2v+3340z2u2v+36/113xu3v-38/93yu3v+2519zu3v-7084u4v+8136x3v2-55/23x2yv2+27/7xy2v2+74/39y3v2+63/16x2zv2-8661xyzv2+2/91y2zv2+3773xz2v2-75/122yz2v2+447z3v2-59/109x2uv2-119/9xyuv2-67/49y2uv2-11334xzuv2-10482yzuv2-60/91z2uv2+94/65xu2v2-108/17yu2v2-69/70zu2v2-23/20u3v2+8/115x2v3+29/41xyv3+8/15y2v3-95/6xzv3-9714yzv3+2550z2v3-121/80xuv3+67/18yuv3+43/5zuv3+23/124u2v3-12509xv4-104/79yv4-73/21zv4-1238uv4+9038v5,94/107x4y+47/14x3y2-6362x2y3-20/59xy4-43/120y5-3028x4z-15141x3yz-2028x2y2z+84/115xy3z-3024y4z+2811x3z2+47/45x2yz2+121/101xy2z2-100/57y3z2+8/115x2z3+1/101xyz3-13/112y2z3+3618xz4+88/67yz4-52/63z5+102/97x4u-12/89x3yu-102x2y2u-3846xy3u-61/86y4u+85/54x3zu+78/29x2yzu-13381xy2zu-49/95y3zu-77/2x2z2u-5784xyz2u+1557y2z2u-9163xz3u-114/121yz3u-57/103z4u+36/31x3u2-9062x2yu2-23/111xy2u2+7362y3u2-7671x2zu2+14945xyzu2+7901y2zu2+51/5xz2u2-109/48yz2u2+7696z3u2+11280x2u3-44/57xyu3-13736y2u3-13458xzu3-14723yzu3-707z2u3+899xu4-10381yu4+99/25zu4-7788u5-237x4v+45/43x3yv-7666x2y2v-4/109xy3v+4303y4v-13107x3zv-108/91x2yzv-7707xy2zv-73/47y3zv+61/118x2z2v-11/65xyz2v+2970y2z2v-104/37xz3v-15408yz3v-64/55z4v+47/113x3uv+2185x2yuv+7941xy2uv-61/37y3uv+6482x2zuv-11/70xyzuv+83/110y2zuv-109/83xz2uv-86/95yz2uv-7583z3uv+83/45x2u2v+89/38xyu2v-2/11y2u2v+3577xzu2v+124/125yzu2v-1151z2u2v+109/85xu3v+70/13yu3v+37/104zu3v-210u4v+51/29x3v2-104/111x2yv2+105/58xy2v2-13459y3v2-80/79x2zv2-3006xyzv2-115/16y2zv2+8208xz2v2+35/38yz2v2+49/27z3v2-1647x2uv2+10482xyuv2-34/93y2uv2+97/18xzuv2+101/20yzuv2+1711z2uv2+91/36xu2v2-96/23yu2v2+7006zu2v2+86/31u3v2-10734x2v3-43/18xyv3-4597y2v3-11174xzv3-7334yzv3+7/96z2v3+4/97xuv3-5/82yuv3-15600zuv3-69/94u2v3-71/25xv4+21/97yv4+117/23zv4-6557uv4-67/83v5,8164x4y+19/73x3y2-1592x2y3-28/87xy4-63/103x4z+11/42x3yz-52/67x2y2z-13766xy3z+11378y4z+10/37x3z2+115/41x2yz2+11/100xy2z2-49/40y3z2+86/111x2z3+124/5xyz3-25/79y2z3-14525xz4+11380yz4-53/42z5-12169x4u-14/51x3yu+68/33x2y2u-3/62xy3u-31/22y4u-74/93x3zu+12924x2yzu-103/123xy2zu-74/97y3zu-2789x2z2u-95/32xyz2u+45/13y2z2u+40/71xz3u+49/110yz3u+34/75z4u+9829x3u2-59/92x2yu2+106/65xy2u2+123/86y3u2+7133x2zu2-73/46xyzu2-7/29y2zu2-937xz2u2-65/67yz2u2-88/111z3u2-61/119x2u3+975xyu3-54/7y2u3-37/33xzu3+61/59yzu3+51/115z2u3+117/43xu4+8506yu4+13941zu4-14945u5-115/63x4v-14237x3yv-74/87x2y2v+104/47xy3v-95/104y4v+11535x3zv-119/75x2yzv-44xy2zv+11299y3zv-21/113x2z2v-2852xyz2v+95/77y2z2v-75/19xz3v-4864yz3v-79/88z4v+139x3uv-10068x2yuv+2049xy2uv+7515y3uv+97/56x2zuv+109/113xyzuv+7778y2zuv-71/11xz2uv-80/19yz2uv+55/59z3uv-69/98x2u2v-15679xyu2v+114/11y2u2v+69/65xzu2v+879yzu2v+45/104z2u2v+47/97xu3v-1373yu3v+15885zu3v+11121u4v-5042x3v2+4/25x2yv2-8607xy2v2-25/33y3v2+93/55x2zv2+68xyzv2-4167y2zv2+14180xz2v2-115/47yz2v2-81/67z3v2-12099x2uv2+34/107xyuv2+122/59y2uv2+775xzuv2-91yzuv2-85/96z2uv2-59/95xu2v2+174yu2v2+11/16zu2v2+66/37u3v2-121/36x2v3+6070xyv3-83/52y2v3-121/59xzv3-55/12yzv3+8088z2v3-20/29xuv3+76/125yuv3-10858zuv3+1833u2v3-103/50xv4+76/93yv4-119/18zv4+37/114uv4+51/7v5,85/56x4y-7839x3y2+12/37x2y3+6558xy4-8191x4z+115/7x3yz+81/23x2y2z-4121xy3z-1131y4z-23/37x3z2-71/32x2yz2+30/97xy2z2+5070y3z2-49/123x2z3+103/88xyz3-45/19y2z3+5132xz4+7277yz4+1896z5-103/75x4u-12020x3yu+12337x2y2u+6248xy3u+14290y4u-87/44x3zu-5364x2yzu-11801xy2zu-59/37y3zu+34/109x2z2u-14482xyz2u-10338y2z2u+118/73xz3u+7/8yz3u+158z4u+10590x3u2-5182x2yu2+83/62xy2u2+11557y3u2-92/119x2zu2-37/94xyzu2+5383y2zu2-365xz2u2+7/62yz2u2-7965z3u2-10/43x2u3+119/101xyu3-113/83y2u3-121/41xzu3+61/104yzu3+37/60z2u3-74/95xu4-113/66yu4-205zu4+4787u5-94/93x4v+14871x3yv-14723x2y2v+10730xy3v+112/17y4v-35/19x3zv-3487x2yzv-65/43xy2zv-7445y3zv-79/124x2z2v+7423xyz2v+91/2y2z2v+91/34xz3v-6970yz3v-50/113z4v+75/43x3uv-127x2yuv+11978xy2uv+48/113y3uv+113/62x2zuv-8941xyzuv-101/112y2zuv-5737xz2uv-31/123yz2uv+9490z3uv+19/92x2u2v-107/73xyu2v-23/121y2u2v+38/65xzu2v-672yzu2v+13/77z2u2v+46/119xu3v-103/18yu3v+107/59zu3v-52/21u4v-94/87x3v2-74/31x2yv2-9/22xy2v2-2896y3v2+113/3x2zv2-5386xyzv2-11391y2zv2+42/97xz2v2+77/64yz2v2-1610z3v2-102/43x2uv2+124/39xyuv2+14829y2uv2+88/113xzuv2-10411yzuv2-51/43z2uv2-36/121xu2v2+9487yu2v2-5589zu2v2+4335u3v2-5/91x2v3+6084xyv3-56/39y2v3-84/101xzv3-81/85yzv3-6521z2v3-2432xuv3+14317yuv3-43/82zuv3+121/8u2v3+14783xv4-92/45yv4+112/27zv4-8410uv4+31/105v5,-6691x4y-10158x3y2-5372x2y3+4132xy4+106/9y5+15600x4z-803x3yz+43/29x2y2z+9/91xy3z-92/61y4z+4807x3z2-12562x2yz2+14234xy2z2-91/17y3z2-91/30x2z3-10615xyz3-4206y2z3-29/45xz4-11/86yz4-115/9z5+125/112x4u+52/59x3yu+92/49x2y2u+121/85xy3u-51/14y4u-73/48x3zu-1/110x2yzu+12/65xy2zu+15045y3zu+12826x2z2u-123/89xyz2u+9465y2z2u-67/31xz3u-5080yz3u-7944z4u-107/72x3u2+1473x2yu2+7965xy2u2+15753y3u2-95/98x2zu2-9827xyzu2-25/53y2zu2-83/54xz2u2-13217yz2u2-117/110z3u2+230x2u3-12120xyu3+11/36y2u3-2071xzu3+109/59yzu3+6909z2u3-15/64xu4+45/82yu4-3091zu4-15711u5+5957x4v-45/86x3yv+26/29x2y2v-40/57xy3v+25/43y4v+126/37x3zv-38/33x2yzv+65/109xy2zv-33/68y3zv-7287x2z2v-4842xyz2v+35/118y2z2v+6157xz3v-97/89yz3v-91/50z4v-70/27x3uv+32/9x2yuv+78/125xy2uv+38/7y3uv-3214x2zuv-68/101xyzuv+87/55y2zuv-69/98xz2uv+5805yz2uv+41/102z3uv-43/54x2u2v-42/73xyu2v-13/49y2u2v+11864xzu2v+121/37yzu2v-100/109z2u2v-12609xu3v-9114yu3v-8746zu3v+11659u4v+3799x3v2-9581x2yv2+60/91xy2v2+2029y3v2+12075x2zv2+210xyzv2-1/22y2zv2+17/58xz2v2+1212yz2v2+118/27z3v2-3571x2uv2-3139xyuv2-23/100y2uv2-1240xzuv2+71/49yzuv2-21/103z2uv2-110/71xu2v2-40/77yu2v2-103/29zu2v2+10737u3v2+2828x2v3+14/39xyv3+7564y2v3+113/50xzv3+38/79yzv3+59/66z2v3+2726xuv3+91/94yuv3-15730zuv3-13408u2v3-97/42xv4+54/29yv4-33/73zv4+4823uv4+57/71v5,-14556x3yz-9751x2y2z-45/28xy3z+85/23y4z+5623x3z2+5369x2yz2-19/60xy2z2-36/5y3z2-95/36x2z3+5862xyz3-5/93y2z3+2949xz4+11357yz4-5679z5-52/45x3yu+4448x2y2u-9/22xy3u+2427y4u+3296x3zu+16/39x2yzu+53/57xy2zu+15/41y3zu+9473x2z2u+37xyz2u-58/69y2z2u-23/56xz3u-13/90yz3u-54/29z4u-41/67x3u2+10258x2yu2+23/44xy2u2-12952y3u2+2124x2zu2-1677xyzu2+12911y2zu2+22/45xz2u2+17/84yz2u2+5910z3u2+4782x2u3+119/39xyu3-17/84y2u3-120/91xzu3+35/59yzu3+17/77z2u3-4467xu4-77/4yu4-26/53zu4-3580u5-11977x3yv-118/77x2y2v+6040xy3v+9724y4v-47/5x3zv+59/101x2yzv+1212xy2zv-7/121y3zv+93/53x2z2v-56/23xyz2v-4470y2z2v+110/111xz3v-41/99yz3v-81/10z4v-71/24x3uv+26/115x2yuv+59/39xy2uv-10029y3uv+11748x2zuv+5749xyzuv+6887y2zuv+38/3xz2uv-116/61yz2uv-55/118z3uv+105/22x2u2v+70/87xyu2v-28/13y2u2v-109/123xzu2v-102/47yzu2v-52/71z2u2v+101/95xu3v+51/16yu3v+15/97zu3v-78/125u4v+35/46x3v2-9526x2yv2+10781xy2v2-119/44y3v2-23/10x2zv2+59/29xyzv2-15144y2zv2+29/120xz2v2-53/126yz2v2-93/85z3v2+53/8x2uv2-487xyuv2-12143y2uv2+13825xzuv2+55/6yzuv2-4250z2uv2+4237xu2v2-109/9yu2v2+67/53zu2v2+82/33u3v2+8660x2v3+15046xyv3-79/84y2v3-10310xzv3+110yzv3-7636z2v3+57/92xuv3-22/119yuv3-95/103zuv3+5138u2v3+123/49xv4-7587yv4+30/41zv4-124/121uv4+54/71v5,-29/60x4y-108/77x3y2-109/37x2y3-3619xy4+109/6x4z-37/67x3yz+53/45x2y2z+5291xy3z-2927y4z+34/5x3z2+87/17x2yz2+100/89xy2z2-114/29y3z2-4057x2z3-1/42xyz3-14/61y2z3-398xz4-122/73yz4+66/37z5+99/37x4u-5691x3yu-8778x2y2u+17/115xy3u+51/113y4u-71/101x3zu+85/91x2yzu-92/9xy2zu-3442y3zu+109/26x2z2u+50/37xyz2u+77/94y2z2u+16/35xz3u+9985yz3u+5/102z4u-5932x3u2+89/125x2yu2-895xy2u2-12455y3u2-630x2zu2-64/47xyzu2+25/9y2zu2+7906xz2u2+6827yz2u2+9808z3u2-113/118x2u3+79/8xyu3+9484y2u3+62/39xzu3+6/85yzu3-23/49z2u3-93/115xu4-11/93yu4-15177zu4-13/2u5-7623x4v-103/73x3yv-96/115x2y2v+39/76xy3v+80/79y4v+43/68x3zv+45/97x2yzv+101/87xy2zv+4632y3zv-918x2z2v+8248xyz2v-4276y2z2v+8853xz3v-39/61yz3v-121/87z4v+9968x3uv+473x2yuv+117/56xy2uv-19/21y3uv+121/119x2zuv+3/98xyzuv-65/42y2zuv-3723xz2uv+7/34yz2uv-112/87z3uv+103x2u2v+25/41xyu2v-14459y2u2v-56/41xzu2v-59/81yzu2v-109/102z2u2v-87/16xu3v-13011yu3v+49/123zu3v+106/89u4v-61/51x3v2+14107x2yv2+8035xy2v2-8853y3v2+5723x2zv2+123/53xyzv2-9727y2zv2-102/83xz2v2+1111yz2v2-15745z3v2+83/118x2uv2-57/35xyuv2-48/73y2uv2-28/37xzuv2-27/97yzuv2-27/58z2uv2+71/93xu2v2+117/8yu2v2+12344zu2v2-2497u3v2-118/71x2v3-11/19xyv3+21/./examples/grtranspose1.sing 5. 104y2v3+32/113xzv3+15544yzv3+31/18z2v3+5909xuv3-67/58yuv3+27/35zuv3+115/9u2v3+79/13xv4+6722yv4-37/114zv4-71/124uv4+4657v5,-77/61x4y-88/101x3y2+93/88x2y3-11/70xy4+9806y5+7896x4z-4699x3yz+55/122x2y2z-63/122xy3z-125/74y4z+47/45x3z2+101/17x2yz2+92/47xy2z2+69/82y3z2+12402x2z3+113/98xyz3-101/33y2z3-15376xz4+47/71yz4-73/10z5+65/74x4u-14409x3yu-14478x2y2u+13593xy3u+102/97y4u+39/62x3zu-34/125x2yzu-83/9xy2zu+45/113y3zu+14484x2z2u-15293xyz2u-26/55y2z2u-958xz3u+67/35yz3u-93/19z4u+25/16x3u2+107/52x2yu2-4599xy2u2-86/51y3u2-9885x2zu2-77/47xyzu2+33/65y2zu2+90/109xz2u2-61/26yz2u2+6198z3u2-38/37x2u3-13935xyu3-142y2u3-64/5xzu3-7228yzu3+1251z2u3+1556xu4+117/121yu4-92/35zu4+99/92u5+13493x4v+12654x3yv+32/101x2y2v-11118xy3v+43/51y4v-575x3zv+103/21x2yzv+85/24xy2zv+1788y3zv+85/3x2z2v-64/25xyz2v+57/35y2z2v+37/120xz3v-69/110yz3v+48/49z4v+55/114x3uv-6439x2yuv+31/51xy2uv-90/49y3uv-45/104x2zuv-12018xyzuv+6/119y2zuv+40/63xz2uv+20/91yz2uv+50/43z3uv+1/26x2u2v-109/47xyu2v+99/7y2u2v+72/83xzu2v+61/118yzu2v+3530z2u2v+6146xu3v+117yu3v-9921zu3v-8708u4v-10/47x3v2-15294x2yv2-7336xy2v2+1/66y3v2-3057x2zv2+74/123xyzv2+146y2zv2-103/34xz2v2-117/76yz2v2+8472z3v2-7/92x2uv2+10033xyuv2+43/53y2uv2+4694xzuv2-49/2yzuv2-71/73z2uv2-125/17xu2v2-9817yu2v2+7218zu2v2+6897u3v2-19/90x2v3+11899xyv3-11779y2v3-5456xzv3+17/42yzv3+15340z2v3+12/7xuv3+9580yuv3-502zuv3-14069u2v3-4371xv4+14452yv4-9423zv4-117/122uv4+1126v5,49/108x4-39/4x3y-67/21x2y2-8/69xy3-9779y4+57/14x3z-11145x2yz+6928xy2z-7824y3z+1/79x2z2+5173xyz2-62/15y2z2-123/112xz3+88/79yz3+1/125z4+57/23x3u-11856x2yu-7444xy2u+115/8y3u-11133x2zu+71/73xyzu-7941y2zu+69/65xz2u+22/75yz2u+65/121z3u+9471x2u2+9167xyu2+51/59y2u2+12835xzu2+15047yzu2+11102z2u2-10059xu3+19/28yu3+65/21zu3-39/28u4-3/73x3v+94/61x2yv+8778xy2v-12922y3v-8711x2zv-37/97xyzv+14270y2zv+4487xz2v-59/112yz2v-14183z3v+15553x2uv+3579xyuv+114/91y2uv-4/97xzuv+13/85yzuv-89/15z2uv+58/75xu2v-34/7yu2v-90/61zu2v+90/101u3v-14673x2v2+90/19xyv2-45/37y2v2+23/49xzv2-71/11yzv2+119/8z2v2+89/10xuv2+109/91yuv2+36/49zuv2-7/31u2v2-40/113xv3-21/121yv3+9910zv3+33/14uv3-23/79v4,93/70x4-43/125x3y+9582x2y2+7565xy3-11511y4-3/79x3z-36/107x2yz-2038xy2z+879y3z-4700x2z2+103/14xyz2+102/79y2z2-67/68xz3-44/25yz3+105/79z4-29/24x3u-74/83x2yu+67/43xy2u+49/12y3u-115/11x2zu+23/67xyzu-61/27y2zu+12257xz2u+14068yz2u+23/15z3u+607x2u2+73/8xyu2+14237y2u2-13/33xzu2+110/71yzu2+41/101z2u2+5708xu3+88/67yu3+1460zu3-2472u4-1629x3v-51/70x2yv-88/73xy2v-36/97y3v+38/11x2zv+15899xyzv+54/19y2zv+9460xz2v-5150yz2v+3462z3v+5522x2uv-19/123xyuv+14871y2uv+53/5xzuv-7535yzuv-13430z2uv+107/47xu2v-8307yu2v-55/79zu2v-11945u3v-16/83x2v2+115/48xyv2+12389y2v2+11545xzv2-25/26yzv2-3755z2v2+4724xuv2-31/21yuv2+7872zuv2+89/45u2v2+87/47xv3+7625yv3+13494zv3-15376uv3-25/126v4;
def I = grobj( groebner(J), intvec(0) ); // ASSUME: no zero entries in J!
ASSUME(0, grtest(I));
"Input degrees: "; grview(I);
==> Input degrees:
==> Graded homomorphism: R <- R(-4)^2 + R(-5)^5 + R(-6)^3, given by a matrix,\
with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 ....
==> --- --- --- --- --- --- --- --- --- --- +...
==> 0 : 4 4 5 5 5 5 5 6 6 6 |..1
==> === === === === === === === === === ===
==> 4 4 5 5 5 5 5 6 6 6
def RR = grres(I, 0, 1); list L = RR;
" = Non-minimal betti numbers: "; print(betti(L, 0), "betti");
==> = Non-minimal betti numbers:
==> 0 1 2 3 4
==> ------------------------------------
==> 0: 1 - - - -
==> 1: - - - - -
==> 2: - - - - -
==> 3: - 2 - - -
==> 4: - 4 7 2 -
==> 5: - 3 8 7 2
==> ------------------------------------
==> total: 1 9 15 9 2
==>
"Graded (original) structure of 'res(Input,0)': "; grview(L);
==> Graded (original) structure of 'res(Input,0)':
==> Graded resolution:
==> R <-- d_1 --
==> R(-4)^2 + R(-5)^4 + R(-6)^3 <-- d_2 --
==> R(-7)^2 + R(-6)^7 + R(-7)^6 <-- d_3 --
==> R(-7)^2 + R(-8)^7 <-- d_4 --
==> R(-9)^2 <-- d_5 --
==> 0, given by maps:
==> d_1 :
==> Graded homomorphism: R <- R(-4)^2 + R(-5)^4 + R(-6)^3, given by a matrix,\
with degrees:
==> .1 .2 .3 .4 .5 .6 .7 .8 .9 ...
==> -- -- -- -- -- -- -- -- -- +..
==> 0 : 4 4 5 5 5 5 6 6 6 |.1
==> == == == == == == == == ==
==> 4 4 5 5 5 5 6 6 6
==> d_2 :
==> Graded homomorphism: R(-4)^2 + R(-5)^4 + R(-6)^3 <- R(-7)^2 + R(-6)^7 + R\
(-7)^6
==> , given by a matrix, with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 .11 .12 .13 .14 .15 ....
==> --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- +...
==> 4 : - - 2 2 2 2 2 2 2 3 3 3 3 3 3 |..1
==> 4 : - - 2 2 2 2 2 2 2 3 3 3 3 3 3 |..2
==> 5 : 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 |..3
==> 5 : 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 |..4
==> 5 : - - 1 1 1 1 1 1 1 2 2 2 2 2 2 |..5
==> 5 : - - 1 1 1 1 1 1 1 2 2 2 2 2 2 |..6
==> 6 : 1 1 - - - - - - - 1 1 1 1 1 1 |..7
==> 6 : 1 1 - - - - - - - 1 1 1 1 1 1 |..8
==> 6 : 1 1 - - - - - - - 1 1 1 1 1 1 |..9
==> === === === === === === === === === === === === === === ===
==> 7 7 6 6 6 6 6 6 6 7 7 7 7 7 7
==> d_3 :
==> Graded homomorphism: R(-7)^2 + R(-6)^7 + R(-7)^6 <- R(-7)^2 + R(-8)^7, gi\
ven by a matrix, with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 ....
==> --- --- --- --- --- --- --- --- --- +...
==> 7 : - - 1 1 1 1 1 1 1 |..1
==> 7 : - - 1 1 1 1 1 1 1 |..2
==> 6 : 1 1 2 2 2 2 2 2 2 |..3
==> 6 : 1 1 2 2 2 2 2 2 2 |..4
==> 6 : 1 1 2 2 2 2 2 2 2 |..5
==> 6 : 1 1 2 2 2 2 2 2 2 |..6
==> 6 : 1 1 2 2 2 2 2 2 2 |..7
==> 6 : 1 1 2 2 2 2 2 2 2 |..8
==> 6 : 1 1 2 2 2 2 2 2 2 |..9
==> 7 : - - 1 1 1 1 1 1 1 |.10
==> 7 : - - 1 1 1 1 1 1 1 |.11
==> 7 : - - 1 1 1 1 1 1 1 |.12
==> 7 : - - 1 1 1 1 1 1 1 |.13
==> 7 : - - 1 1 1 1 1 1 1 |.14
==> 7 : - - 1 1 1 1 1 1 1 |.15
==> === === === === === === === === ===
==> 7 7 8 8 8 8 8 8 8
==> d_4 :
==> Graded homomorphism: R(-7)^2 + R(-8)^7 <- R(-9)^2, given by a matrix, wit\
h degrees:
==> .1 .2 ...
==> -- -- +..
==> 7 : 2 2 |.1
==> 7 : 2 2 |.2
==> 8 : 1 1 |.3
==> 8 : 1 1 |.4
==> 8 : 1 1 |.5
==> 8 : 1 1 |.6
==> 8 : 1 1 |.7
==> 8 : 1 1 |.8
==> 8 : 1 1 |.9
==> == ==
==> 9 9
==> d_5 :
==> Graded homomorphism: R(-9)^2 <- 0, given by zero (2 x 0) matrix.
"Graded transpose of the previous resolution "; list LLL = grtranspose1( L ); grview( LLL );
==> Graded transpose of the previous resolution
==> Graded resolution:
==> R(9)^2 <-- d_1 --
==> R(8)^7 + R(7)^2 <-- d_2 --
==> R(7)^8 + R(6)^7 <-- d_3 --
==> R(6)^3 + R(5)^4 + R(4)^2 <-- d_4 --
==> R, given by maps:
==> d_1 :
==> Graded homomorphism: R(9)^2 <- R(8)^7 + R(7)^2, given by a matrix, with d\
egrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 ....
==> --- --- --- --- --- --- --- --- --- +...
==> -9 : 1 1 1 1 1 1 1 2 2 |..1
==> -9 : 1 1 1 1 1 1 1 2 2 |..2
==> === === === === === === === === ===
==> -8 -8 -8 -8 -8 -8 -8 -7 -7
==> d_2 :
==> Graded homomorphism: R(8)^7 + R(7)^2 <- R(7)^8 + R(6)^7, given by a matri\
x, with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 .11 .12 .13 .14 .15 ....
==> --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- +...
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..1
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..2
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..3
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..4
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..5
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..6
==> -8 : 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 |..7
==> -7 : - - - - - - - - 1 1 1 1 1 1 1 |..8
==> -7 : - - - - - - - - 1 1 1 1 1 1 1 |..9
==> === === === === === === === === === === === === === === ===
==> -7 -7 -7 -7 -7 -7 -7 -7 -6 -6 -6 -6 -6 -6 -6
==> d_3 :
==> Graded homomorphism: R(7)^8 + R(6)^7 <- R(6)^3 + R(5)^4 + R(4)^2, given b\
y a matrix, with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 ....
==> --- --- --- --- --- --- --- --- --- +...
==> -7 : 1 1 1 2 2 - - - - |..1
==> -7 : 1 1 1 2 2 - - - - |..2
==> -7 : 1 1 1 2 2 2 2 3 3 |..3
==> -7 : 1 1 1 2 2 2 2 3 3 |..4
==> -7 : 1 1 1 2 2 2 2 3 3 |..5
==> -7 : 1 1 1 2 2 2 2 3 3 |..6
==> -7 : 1 1 1 2 2 2 2 3 3 |..7
==> -7 : 1 1 1 2 2 2 2 3 3 |..8
==> -6 : - - - 1 1 1 1 2 2 |..9
==> -6 : - - - 1 1 1 1 2 2 |.10
==> -6 : - - - 1 1 1 1 2 2 |.11
==> -6 : - - - 1 1 1 1 2 2 |.12
==> -6 : - - - 1 1 1 1 2 2 |.13
==> -6 : - - - 1 1 1 1 2 2 |.14
==> -6 : - - - 1 1 1 1 2 2 |.15
==> === === === === === === === === ===
==> -6 -6 -6 -5 -5 -5 -5 -4 -4
==> d_4 :
==> Graded homomorphism: R(6)^3 + R(5)^4 + R(4)^2 <- R, given by a matrix, wi\
th degrees:
==> ..1 ....
==> --- +...
==> -6 : 6 |..1
==> -6 : 6 |..2
==> -6 : 6 |..3
==> -5 : 5 |..4
==> -5 : 5 |..5
==> -5 : 5 |..6
==> -5 : 5 |..7
==> -4 : 4 |..8
==> -4 : 4 |..9
==> ===
==> 0
"Its non-minimal betti numbers: "; print(betti(LLL, 0), "betti");
==> Its non-minimal betti numbers:
==> 0 1 2 3 4
==> ------------------------------------
==> -9: 2 7 8 3 -
==> -8: - 2 7 4 -
==> -7: - - - 2 -
==> -6: - - - - -
==> -5: - - - - -
==> -4: - - - - 1
==> ------------------------------------
==> total: 2 9 15 9 1
==>
|
|
Online Manual
