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D.15.5.14 grorder
Procedure from library gradedModules.lib (see gradedModules_lib).
- Usage:
- grorder(M), graded object or list M
- Return:
- same as input
- Purpose:
- reorder/transform graded object or chain complex M into block form
- Assume:
- M must be a graded object or a list of graded objects
Example:
| | LIB "gradedModules.lib";
"Surface Name: 'rat.d10.g9.quart2' in P^4";
==> Surface Name: 'rat.d10.g9.quart2' in P^4
int @p=31991; ring R = (@p),(x,y,z,u,v), dp;
ideal J = 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+76/101xy3u+123/88y4u-5932x3zu-11857x2yzu+7128xy2zu-45/79y3zu+119/18x2z2u+9/74xyz2u+7042y2z2u-1114xz3u-11/82yz3u-1466z4u-6/85x3u2+27/106x2yu2+14246xy2u2-6216y3u2+47/6x2zu2-45/59xyzu2+89/41y2zu2+41/80xz2u2-7583yz2u2-75/113z3u2-14808x2u3-10873xyu3-90/67y2u3-11081xzu3-7369yzu3-7131z2u3-1402xu4-15386yu4-108/73zu4-5039u5+120/113x4v+10617x3yv-50/87x2y2v-2395xy3v-20/69y4v-8587x3zv+12960x2yzv-41/50xy2zv-13844y3zv-65/32x2z2v-77/122xyz2v-85/66y2z2v+13/100xz3v-20/51yz3v-13676z4v+76/97x3uv+1046x2yuv-8059xy2uv-117/59y3uv-29/105x2zuv+7287xyzuv-107/119y2zuv-35/118xz2uv+79/86yz2uv-2211z3uv+5448x2u2v+62/35xyu2v-2275y2u2v+29/121xzu2v-1674yzu2v-56/43z2u2v-3377xu3v-43/110yu3v+23/10zu3v-24/61u4v+121/53x3v2-4745x2yv2-57/64xy2v2+9554y3v2-12741x2zv2+10449xyzv2+37/108y2zv2+8621xz2v2-11/57yz2v2+1566z3v2+125/49x2uv2-121/118xyuv2+109/84y2uv2-335xzuv2+10167yzuv2-59/109z2uv2-103/119xu2v2+43/13yu2v2-73/87zu2v2+2037u3v2+13002x2v3+83/48xyv3-10713y2v3+1026xzv3-105/64yzv3-37/6z2v3+14779xuv3-6448yuv3+19/69zuv3-1/110u2v3+10010xv4+79/12yv4+12/19zv4-35/61uv4-11/57v5,-1592x3y2-75/121x2y3-40/19xy4+2651y5+39/121x3yz+122/77x2y2z-114/31xy3z+1544y4z+2/3x3z2-10271x2yz2-8373xy2z2+56/61y3z2+55/48x2z3-116xyz3-25/7y2z3-108/113xz4-34/53yz4+5548z5-122x3yu-9690x2y2u+43/87xy3u-5/19y4u+97/54x3zu-17/19x2yzu+4355xy2zu+12/5y3zu-1/100x2z2u+12754xyz2u+13600y2z2u+17/45xz3u-12091yz3u+5145z4u-63/64x3u2-8./examples/grorder.sing 5. 4/31x2yu2-97/41xy2u2+7/13y3u2-79/62x2zu2-80/103xyzu2-69/14y2zu2+119/4xz2u2-35/87yz2u2-13840z3u2+14101x2u3+7952xyu3-1857y2u3-9861xzu3+3180yzu3+75/107z2u3-250xu4-15134yu4+4717zu4-2/41u5+22/27x3yv-8983x2y2v+10520xy3v-113/2y4v+10/73x3zv-1986x2yzv-110/13xy2zv+1550y3zv+32/111x2z2v-111/35xyz2v+101/98y2z2v+8045xz3v-2/89yz3v+2924z4v-79/11x3uv-15178x2yuv+10874xy2uv+54/11y3uv-8950x2zuv+70/53xyzuv-2403y2zuv-8249xz2uv+6935yz2uv+20/89z3uv+885x2u2v-76/71xyu2v-4/17y2u2v-31/52xzu2v-4/99yzu2v+10333z2u2v-93/104xu3v+82/101yu3v-71/37zu3v+9397u4v-15/112x3v2-6614x2yv2+119/2xy2v2+88/119y3v2+306x2zv2+2790xyzv2+10992y2zv2-115/74xz2v2-14711yz2v2+11612z3v2-1788x2uv2-75/97xyuv2+79/30y2uv2+99/59xzuv2-11439yzuv2-121/113z2uv2+108/37xu2v2+37/36yu2v2-3/65zu2v2-55/42u3v2+13/100x2v3-209xyv3-1272y2v3-117/68xzv3+63/94yzv3+32/59z2v3+1013xuv3-3463yuv3+6946zuv3-37/86u2v3+67/117xv4+85/28yv4-3024zv4-82/9uv4-32/65v5,-35/52x4y-12140x3y2+23/83x2y3+69/5xy4-80/79y5+120/43x4z-11865x3yz-3487x2y2z+53/59xy3z+53/102y4z-14083x3z2-14430x2yz2-2442xy2z2-33/104y3z2-91/38x2z3+4/87xyz3-26/57y2z3+4097xz4-9/122yz4+6364z5+9634x4u-97/95x3yu-46/99x2y2u+3847xy3u+121/106y4u+12765x3zu-5292x2yzu+1607xy2zu-67/121y3zu-12/35x2z2u+4/55xyz2u-17/27y2z2u+91/122xz3u-23/31yz3u+65/49z4u+73/46x3u2-124/27x2yu2-9933xy2u2+46/75y3u2+53/114x2zu2+3503xyzu2-14147y2zu2-11283xz2u2+11889yz2u2+99/104z3u2+3117x2u3+12624xyu3-10060y2u3+2193xzu3-80/47yzu3-77/13z2u3+11/31xu4-47/90yu4+49/48zu4-2/105u5-92/61x4v+7443x3yv+35/76x2y2v+114/67xy3v-73/126y4v+97/107x3zv+9464x2yzv+10869xy2zv+15718y3zv-37/33x2z2v+124/13xyz2v-11/26y2z2v-61/40xz3v+91/100yz3v-18/103z4v+60/29x3uv+21/125x2yuv-11117xy2uv+11748y3uv-16/117x2zuv+18/103xyzuv-1711y2zuv+1872xz2uv-109/123yz2uv-18/113z3uv-26/103x2u2v+14140xyu2v+11065y2u2v+8686xzu2v-5/111yzu2v+30/101z2u2v-10501xu3v-36/113yu3v-73/74zu3v+12753u4v-43/52x3v2-76/15x2yv2-5793xy2v2+18/13y3v2+1/79x2zv2+84/23xyzv2-172y2zv2+86/77xz2v2+15/37yz2v2+11835z3v2-6482x2uv2+94/113xyuv2+10727y2uv2-102/41xzuv2+15914yzuv2-12973z2uv2-9038xu2v2-13107yu2v2+1533zu2v2+12549u3v2-13528x2v3+903xyv3+23/114y2v3-123/64xzv3-81/5yzv3+111/103z2v3+4734xuv3-33/20yuv3-7954zuv3-2478u2v3+15518xv4-6723yv4-14/31zv4-3482uv4+10919v5,-3/94x4y-12936x3y2+2/11x2y3+32/23xy4-15921y5+61/93x4z+82/111x3yz-93/2x2y2z-6659xy3z-97/90y4z+402x3z2-14586x2yz2-121/39xy2z2+68/7y3z2+1212x2z3-2980xyz3+49/52y2z3-72/89xz4+92/47yz4+8478z5+2733x4u-103/89x3yu+1166x2y2u-7/53xy3u-106/23y4u+677x3zu+907x2yzu+7891xy2zu-9014y3zu+76/47x2z2u+49/116xyz2u-49/78y2z2u+12261xz3u+118/105yz3u-126/13z4u-8812x3u2-97/120x2yu2-9534xy2u2+92/5y3u2-54/71x2zu2+94/103xyzu2+2256y2zu2+4182xz2u2-5798yz2u2-31/115z3u2-73/98x2u3+15822xyu3+1004y2u3-578xzu3+9494yzu3-6779z2u3+14506xu4+10/121yu4+58/27zu4-2817u5-19/119x4v+7128x3yv+75/64x2y2v-65/109xy3v+5129y4v-53/55x3zv+54/125x2yzv-3009xy2zv+6144y3zv+15601x2z2v+123/55xyz2v-58/77y2z2v-56/61xz3v+121/10yz3v-103/86z4v-93/25x3uv+94/123x2yuv-25/107xy2uv+14807y3uv+65/7x2zuv+87/44xyzuv+6605y2zuv+23/99xz2uv-413yz2uv-17/15z3uv-79/46x2u2v+15240xyu2v-42/67y2u2v+8932xzu2v-5888yzu2v-4204z2u2v+7002xu3v-36/97yu3v-1634zu3v+61/102u4v-14/33x3v2-6520x2yv2+9004xy2v2-67/36y3v2-7/8x2zv2-24/11xyzv2-9373y2zv2+1556xz2v2-79/74yz2v2-6691z3v2+108x2uv2-76/61xyuv2+220y2uv2-1191xzuv2-4/9yzuv2+4546z2uv2+12205xu2v2+9/22yu2v2+64/93zu2v2-44/125u3v2+292x2v3+41/74xyv3+16/79y2v3-15892xzv3+5733yzv3+6796z2v3-42/55xuv3+71/79yuv3-19/104zuv3-38/15u2v3+6436xv4+28/15yv4+87/55zv4+2270uv4-30/41v5,-117/4x3y+97/122x2y2-3618xy3+6566y4+97/113x3z-12634x2yz+9865xy2z-1764y3z+114/31x2z2+5006xyz2+7/44y2z2-15040xz3+8/125yz3+11134z4-12980x3u-79/41x2yu-79/98xy2u+89/65y3u-1217x2zu+89/87xyzu+83/66y2zu+115/11xz2u+123/107yz2u+10920z3u-86/73x2u2-11/94xyu2-14054y2u2+6752xzu2-123/124yzu2+12129z2u2-13310xu3-52/63yu3+12847zu3-1545u4-11064x3v+11499x2yv-37/64xy2v+50/103y3v+123/94x2zv-126xyzv-111/44y2zv+95/14xz2v+113/83yz2v-77/103z3v+41/64x2uv+91/90xyuv-4932y2uv+103/31xzuv+62/63yzuv+1161z2uv-99/106xu2v-3181yu2v-11741zu2v-33/8u3v-3/118x2v2-9369xyv2+527y2v2-113/39xzv2-88/49yzv2-113/101z2v2+95/68xuv2-5930yuv2-20/43zuv2+7/41u2v2+109/93xv3-107/61yv3-8352zv3-5255uv3+12021v4,-2159x4-94/3x3y-4602x2y2+1609xy3+10721y4+28/9x3z-99/35x2yz+1/110xy2z+113/114y3z-118/75x2z2-103/93xyz2-68/67y2z2+13687xz3-1531yz3+61/107z4+6076x3u+9004x2yu+2211xy2u+110/53y3u+47/102x2zu+8495xyzu-9238y2zu+57/121xz2u-8543yz2u+8/19z3u-13527x2u2-13293xyu2+1138y2u2+26/115xzu2+78/53yzu2-12556z2u2+7299xu3+70/19yu3-14687zu3+13559u4+113/9x3v-85/126x2yv-83/3xy2v-3/46y3v+1814x2zv+28/79xyzv+103/51y2zv+78/31xz2v-14387yz2v+1/88z3v+116/75x2uv-101/59xyuv-70/3y2uv+109/71xzuv+13/88yzuv-147z2uv-113/76xu2v-9661yu2v+13855zu2v-6162u3v-1857x2v2-8208xyv2-4634y2v2-6178xzv2-7352yzv2-8247z2v2-113/15xuv2+99/40yuv2+21/97zuv2+11/37u2v2-6605xv3+8964yv3+35/121zv3+8543uv3-6008v4;
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)^6 + R(-6), given by a matrix, w\
ith degrees:
==> .1 .2 .3 .4 .5 .6 .7 .8 .9 ...
==> -- -- -- -- -- -- -- -- -- +..
==> 0 : 4 4 5 5 5 5 5 5 6 |.1
==> == == == == == == == == ==
==> 4 4 5 5 5 5 5 5 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: - 5 9 3 -
==> 5: - 1 3 3 1
==> ------------------------------------
==> total: 1 8 12 6 1
==>
"Graded reordered structure of 'res(Input,0)': "; grview(grorder(L));
==> Graded reordered structure of 'res(Input,0)':
==> Graded resolution:
==> R <-- d_1 --
==> R(-4)^2 + R(-5)^5 + R(-6) <-- d_2 --
==> R(-6)^9 + R(-7)^3 <-- d_3 --
==> R(-7)^3 + R(-8)^3 <-- d_4 --
==> R(-9), given by maps:
==> d_1 :
==> Graded homomorphism: R <- R(-4)^2 + R(-5)^5 + R(-6), given by a matrix, w\
ith degrees:
==> .1 .2 .3 .4 .5 .6 .7 .8 ...
==> -- -- -- -- -- -- -- -- +..
==> 0 : 4 4 5 5 5 5 5 6 |.1
==> == == == == == == == ==
==> 4 4 5 5 5 5 5 6
==> d_2 :
==> Graded homomorphism: R(-4)^2 + R(-5)^5 + R(-6) <- R(-6)^9 + R(-7)^3, give\
n by a matrix, with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ..7 ..8 ..9 .10 .11 .12 ....
==> --- --- --- --- --- --- --- --- --- --- --- --- +...
==> 4 : 2 2 2 2 2 2 2 2 2 - 3 3 |..1
==> 4 : 2 2 2 2 2 2 2 2 2 - 3 3 |..2
==> 5 : 1 1 1 1 1 1 1 1 1 2 2 2 |..3
==> 5 : 1 1 1 1 1 1 1 1 1 2 2 2 |..4
==> 5 : 1 1 1 1 1 1 1 1 1 2 2 2 |..5
==> 5 : 1 1 1 1 1 1 1 1 1 - 2 2 |..6
==> 5 : 1 1 1 1 1 1 1 1 1 - 2 2 |..7
==> 6 : - - - - - - - - - 1 1 1 |..8
==> === === === === === === === === === === === ===
==> 6 6 6 6 6 6 6 6 6 7 7 7
==> d_3 :
==> Graded homomorphism: R(-6)^9 + R(-7)^3 <- R(-7)^3 + R(-8)^3, given by a m\
atrix, with degrees:
==> ..1 ..2 ..3 ..4 ..5 ..6 ....
==> --- --- --- --- --- --- +...
==> 6 : 1 1 1 2 2 2 |..1
==> 6 : 1 1 1 2 2 2 |..2
==> 6 : 1 1 1 2 2 2 |..3
==> 6 : 1 1 1 2 2 2 |..4
==> 6 : 1 1 1 2 2 2 |..5
==> 6 : 1 1 1 2 2 2 |..6
==> 6 : 1 1 1 2 2 2 |..7
==> 6 : 1 1 1 2 2 2 |..8
==> 6 : 1 1 1 - - 2 |..9
==> 7 : - - - 1 1 1 |.10
==> 7 : - - - 1 1 1 |.11
==> 7 : - - - 1 1 1 |.12
==> === === === === === ===
==> 7 7 7 8 8 8
==> d_4 :
==> Graded homomorphism: R(-7)^3 + R(-8)^3 <- R(-9), given by a matrix, with \
degrees:
==> .1 ...
==> -- +..
==> 7 : 2 |.1
==> 7 : 2 |.2
==> 7 : 2 |.3
==> 8 : 1 |.4
==> 8 : 1 |.5
==> 8 : 1 |.6
==> ==
==> 9
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