| | LIB "modwalk.lib";
ring R1 = 0, (x,y,z,t), dp;
ideal I = 3x3+x2+1, 11y5+y3+2, 5z4+z2+4;
I = std(I);
ring R2 = 0, (x,y,z,t), lp;
ideal I = fetch(R1, I);
int radius = 2;
ideal J = modrWalk(I,radius);
J;
==> J[1]=x3+1/3x2+1/3
==> J[2]=z4+1/5z2+4/5
==> J[3]=y5+1/11y3+2/11
ring S1 = 0, (a,b,c,d), Dp;
ideal I = 5b2, ac2+9d3+3a2+5b, 2a2c+7abd+bcd+4a2, 2ad2+6b2d+7c3+8ad+4c;
I = std(I);
ring S2 = 0, (c,d,b,a), lp;
ideal I = fetch(S1,I);
// I is assumed to be a Dp-Groebner basis.
// We compute a lp-Groebner basis.
ideal J = modrWalk(I,radius,"Dp");
J;
==> J[1]=a25+16a24+96a23+256a22+256a21+256/9a20+1024/3a19+2048a18+65536/9a17+\
32768/3a16+16384/81a15+131072/81a14+1048576/81a13+1048576/27a12+1048576/9\
a11
==> J[2]=ba11+1522867351997104938459/91668001658017308797687087104a24+4293036\
9782248629690765/91668001658017308797687087104a23+80925218629630777478637\
/22917000414504327199421771776a22+7108535670237178684767/2864625051813040\
899927721472a21-3255817194541612658349/89519532869157528122741296a20+5380\
8965391546362724459/358078131476630112490965184a19+1534729815590907963215\
01/358078131476630112490965184a18-260815719913165309506063/44759766434578\
764061370648a17-1485276141860757031491027/89519532869157528122741296a16-4\
92332725360316960775/22379883217289382030685324a15+7423992361030571232440\
/16784912412967036523013993a14-17640364913371983121693/167849124129670365\
23013993a13-37723213977586186442564/5594970804322345507671331a12+92047580\
41857159721472414/5594970804322345507671331a11
==> J[3]=b2a6-63/2ba10+41087306587333357057895823883/924013456712814472680685\
83800832a24+93915562116924232413944264677/1320019223875449246686694054297\
6a23+1314662746341964624103002499857/30800448557093815756022861266944a22+\
2628268795042931967685617407557/23100336417820361817017145950208a21+32861\
7969148352577032114618159/2887542052227545227127143243776a20+175631724829\
284757906915538269/12993939235023953522072144596992a19+303812212296039043\
29090032467/206253003730538944794795945984a18+581332950565269518541458030\
9/6445406366579342024837373312a17+1392577308804410648719627124495/4060606\
01094498547564754518656a16+728489619081836101063651608791/135353533698166\
182521584839552a15+80182830319998353431517995037/913636352462621732020697\
666976a14+22597043807001043905240513127/32629869730807919000739202392a13+\
2699689128255025271541196980091/456818176231310866010348833488a12+6291773\
289016174025274735397/352483160672307766983293853a11+4/7a6
==> J[4]=b3a5+4/7ba5-5398327059462849163101023479/739210765370251578144548670\
406656a24+3500067651845908053488406611/92401345671281447268068583800832a2\
3+81936880336538263803253409291/46200672835640723634034291900416a22+85587\
506267677081700930548967/6600096119377246233433470271488a21+4349147060430\
84846670081811347/11550168208910180908508572975104a20+1021713731964491721\
016405426709/25987878470047907044144289193984a19+189087309367688338214840\
3875/812121202188997095129509037312a18+3873208423822126582196454031/10312\
6501865269472397397972992a17+104243440049859097996976327663/4060606010944\
98547564754518656a16+52530075262606982469983545909/5075757513681231844559\
4314832a15+6154556265260978917193662164647/365454540985048692808279066790\
4a14+138400848395446486358821423/5639730570756924271732701648a13+68577767\
53456717192310999393/38068181352609238834195736124a12+3439955547980759942\
57860510037/228409088115655433005174416744a11+9/2a10+18a9
==> J[5]=b4-63/2b3a4+4/7b2+3859043113737/128ba10-61261515/8ba9-525086793/32ba\
8+3969/16ba7-19845/4ba6+9/2ba5-317530772199391516703685862633925319890715\
5/9853890705461273608546303647569412096a24-889000025950798002413919214249\
17407047623059/17244308734557228814956031383246471168a23-4443358152931308\
1841158459544460024461570519/1437025727879769067913002615270539264a22-443\
94201884268758058296712245149507940575423/5388846479549134004673759807264\
52224a21-88794706503699382133468723144783169844707611/1077769295909826800\
934751961452904448a20-1763218978464215084468461907410740543335425/1732129\
22556936450150227993804931072a19-4436403904696107325808495191699219229446\
85/4210036312147760941151374849425408a18-21791665871565292166347154127869\
734967876143/33680290497182087529210998795403264a17-382244791239220889094\
021792022832016196677083/151561307237319393881449494579314688a16-25381669\
887869257097552146559952295821945667/6315054468221641411727062274138112a1\
5-3081988985408645474889243822837753592680251/487161344691383766047516232\
57636864a14-42991086686519981772739427292780808208480959/8525323532099215\
9058315340700864512a13-44791324614077928834488691100822888689474979/10656\
654415124019882289417587608064a12-250969820105414481651193596059252574282\
0133/197345452131926294116470696066816a11+771901337907/64a10-1701/4a9+437\
53689/4a8-19845/8a7-19845/2a6
==> J[6]=da-1323/800b3a4+63/20b2a4+2701701074331/1280ba10-61269453/320ba9+306\
291699/160ba8-27783/16ba6-189/200ba4-685883099436497069901143509465258298\
0621641/123173633818265920106828795594617651200a24-5486790468650205133145\
8584531975294116209709/61586816909132960053414397797308825600a23-60954530\
98260341081175657932145681344303369/1140496609428388149137303662913126400\
a22-54839253809480536502430419967744127237862429/384917605682081000333839\
9862331801600a21-6855741428155530311932580353074238311128479/481147007102\
601250417299982791475200a20-2878029541644786739384025698911163129301521/1\
732129225569364501502279938049310720a19-539637460347386518746735121876349\
5466944867/288688204261560750250379989674885120a18-1360851075145362976080\
2370233473935440353147/120286751775650312604324995697868800a17-2261317453\
3404843047583509526614944559001629/54129038299042640671946248064040960a16\
-19899168362053216404911620136404443756991/309379505595808417192193918976\
00a15-3443170203569948104100043669593479708510001/30447584043211485377969\
7645360230400a14-27203224432640761938740031635681832222207391/30447584043\
2114853779697645360230400a13-11007706754707314979975768772869745826795967\
3/152237920216057426889848822680115200a12-1380727908059280736173048219943\
2331439121223/6343246675669059453743700945004800a11-1929592445193/640a10+\
437570343/1600a9+164090367/100a8+3969/8a6+9/5a4
==> J[7]=db2+4/7d+81/160b3a4-189/200b3a3+9/5b2a3+250047/32ba10+4750893/320ba9\
-567/40ba8-567/10ba7+81/280ba4-27/50ba3-627430952592078879073202920720376\
153131/5173292620367168644486809414973941350400a24-2906859466655459274817\
4299538370243493/18476045072739888016024319339192647680a23-69048240138740\
571289193103124930690109/11975214398998075565941688460587827200a22+488085\
08639174871490992992380443024047/11547528170462430010015199586995404800a2\
1+5093069077149293873574182379116672811143/808326971932370100701063971089\
67833600a20+3286117544936595300844164893345508176887/36374713736956654531\
547878699035525120a19-57124126734867585149642894515011901057/189451634046\
6492423518118682241433600a18-296407013643924816106633846582502767991/2526\
021787288656564690824909655244800a17-193831832299525900077669479610197531\
4379/11367098042798954541108712093448601600a16+49045157132492520042165362\
0398209599/433131307834131784069071486566400a15+9565278519988924726047202\
0815175898220317/25575970596297647717494602210259353600a14-51800242230268\
556716933919846651112061/456713760648172280669546468040345600a13-15498981\
08498974500694541229046869490537/1598498162268602982343412638141209600a12\
-700479417253540849801700529315888259/26641636037810049705723543969020160\
a11+20611017/1600a10+21504771/320a9+243/50a8-1701/100a7+36/35a3
==> J[8]=d2
==> J[9]=ca-1630191535/8275968d2ba2-36060437345/409660416d2ba+38107475/568972\
8d2a2-456425375/60690432d2a+92575/2844864d2+91285075/182071296db4a+35/921\
6db4-1088785/5689728db3a2+2258752616171/182071296db3a+24027/2528768db3-81\
62999/79656192db2a3-6539063/79656192db2a2+25495277/45517824db2a+5095/1264\
384db2-5243/158048dba4-753114969703/1486915584dba3-753467060575/223037337\
6dba2+30870844232377/2230373376dba+24027/4425344db-7/256da5+5/96da3+34222\
8711385/101380608da2+342235311685/25345152da+2645/2489256d-68441518085/57\
931776b6+8617/1896576b5a-752908955671/318624768b5+7/256b4a2-2163/79024b4a\
-752734601911/1115186688b4+529/316096b3a3+7/128b3a2-12811/59268b3a-752421\
061495/557593344b3+311787/632192b2a4+529/158048b2a3+1/64b2a2-309/19756b2a\
+309/4939b2+68441518085/22529024ba5+752978795959/61954816ba4+529/553168ba\
3+1/32ba2-1/8ba+1/2b+3/32a6+68445742277/11264512a5+68447062337/2816128a4+\
529/276584a3
==> J[10]=cb-452831001/4597760d2ba2-3340189909/75863040d2ba-3176523/158048d2a\
2-76214943/20230144d2a+5145/316096d2+25404981/101150720db4a-7203/1024db4+\
453789/790240db3a2+125486265849/20230144db3a-25399101/12643840db3-324051/\
6321920db2a3+194523/790240db2a2+11921259/25287680db2a-9921275/1264384db2-\
27783/632192dba4-12813612147/50575360dba3-12806449187/75863040dba2+104952\
523865/15172608dba-31286843/3160960db+1163396585/689664da2+1163396585/172\
416da-172823/79024d-1628855795/2758656b6+64827/3160960b5a-89587760437/758\
63040b5+64827/1580480b4a-12804376067/37931520b4+1323/1580480b3a3+9261/790\
240b3a-12798251491/18965760b3-583443/395120b2a4-10887849/1580480b2a3+9261\
/395120b2a-9261/98780b2+698081055/459776ba5+38375787849/6321920ba4-622295\
1/395120ba3+698037951/229888a5+698037951/57472a4-1555407/395120a3
==> J[11]=cd+66199/8d2ba2+6818809/2304d2ba+35/64d2b+47/96d2a2-155/768d2a-7/19\
2db5+7/256db4a+7/320db4-1/80db3a2-133413949/256db3a-23/96db3+441/128db2a3\
+1/64db2a+1/80db2+667316711/31360dba3+667069751/47040dba2-27349858321/470\
40dba-1/8db+141/160da5+141/40da4+63/32da3-667069751/4704da2-667069751/117\
6da+667069751/13440b6+667069751/6720b5-63/80b4a2+667069751/23520b4-63/40b\
3a2+667069751/11760b3-9/20b2a2-2001209253/15680ba5-2001209253/3920ba4-9/1\
0ba2-2001209253/7840a5-2001209253/1960a4
==> J[12]=c2+1/3cb2+5/3d+3a3
intvec w = 3,2,1,2;
ring S3 = 0, (c,d,b,a), (a(w),lp);
ideal I = fetch(S1,I);
// I is assumed to be a Dp-Groebner basis.
// We compute a (a(w),lp)-Groebner basis.
ideal J = modrWalk(I,radius,"Dp",w);
J;
==> J[1]=d2
==> J[2]=c2+3a3+1/3cb2+5/3d
==> J[3]=ca2+4ca+7/2b3+2b
==> J[4]=cda-6/7ba3+4/7c2-2/21cb3+1/7dba-10/21db
==> J[5]=db4a-192/49b2a3+128/49c2b-64/7cda-64/147cb4+4/63d2ba+2db3a-4db4+60/4\
9db2a-8db3+8/7dba-656/147db2-32/7db
==> J[6]=db6+333576da3-189/4b8+15876b4a2-5186640/2401b2a3+44514592/2470629c2b\
+772122956311640/155649627cd2+1815960/49cdb2-3535382608/352947cda+8395442\
084/7203cb4-2304/49cb2a-826877376/2401ca2+308820941902337/311299254d2ba-4\
3215/7db5+199982018/49db3a-4664160/7dba2-126b7+72/7b5a+31752b3a2+1728/240\
1ba3-7028226304/2470629c2-1012272/49cdb+5598114168/2401cb3-4608/49cba-191\
05043/21609d2b2-129552/49db4+864216/2401db2a-117b6+144/7b4a+9072b2a2-2016\
0cd+4663152/7cb2-3307509504/2401ca-128772920/352947d2b-172796/49db3+57587\
01763736/2470629dba-1296/7b5+288/49b3a+18144ba2+9326304/7cb+185320d2-1952\
9120/7203db2-1188/7b4+576/49b2a+2752/2401db-413460864/343b3-3312/49b2-165\
3754752/2401b
==> J[7]=cb3a-5/8da3-245/1024b8-7/32b6a+2/343b2a3-1833054229/38118276c2b-3473\
26678687775/9605805552cd2+5/112cdb2-916402091/5445468cda-108013/49392cb4+\
25/7cb2a-966391/1372ca2-2222840154809345/307385777664d2ba-3/256db5-15431/\
2016db3a+5/4dba2-245/256b7-25/32b5a+5/1372ba3-916476179/9529569c2+5/84cdb\
-108035/24696cb3+16/7cba-3313805/790272d2b2-47/2688db4+53/24696db2a-91/25\
6b6-5/8b4a-5/84cd-5/4cb2-966979/343ca-80483075/43563744d2b+1/192db3-21666\
16927/76236552dba+65/32b5-1/14b3a-5/2cb-25/72d2-667/98784db2+85/64b4-2/7b\
2a+109/12348db-1932803/784b3+3/14ba+93/112b2-966979/686b
==> J[8]=cb5-4/7db2a2+96/7b2a3-64/7c2b-4/441cdb2+32cda+116/21cb4+1152/7ca2-8/\
7dba2-8/441cdb+32/7cb3+14db4-16/7db2a+16/7cb2+4608/7ca+28db3+16/7cb+328/2\
1db2+16db+576b3+2304/7b
==> J[9]=cdb3+18da3+2cdb2+63cb4+441/2db3a-36dba2+126cb3+36cb2+126dba+72cb+10d\
2
==> J[10]=ba4-2/3c2a+1/9cb3a+14/3cda-1/6dba2+49/12db3+5/9dba+7/3db
==> J[11]=b3a3+2744/5c2d+382/15c2b2-1127/15cdb3+693167/15cdba+129659/45cb5+23\
52/5cb3a-8647/27d2b2a-49/15db4a-8232/5db2a2-1029/10b6a+616/15c2b+86470/27\
cd2+161/5cdb2+1382932/15cda+28812/5cb4+1680cb2a+686/5d2ba-98/15db5-121045\
/6db3a-735/2b5a-112/5c2-224/15cdb+8232/5cb3+5376/5cba+201698/5db4+38/3db2\
a+2058/5b6-294b4a-28cd+16464/5cb2-4032/5ca+3631597/45db3-173024/15dba+147\
0b5-168/5b3a+115256/5db2+1176b4-672/5b2a+138352/3db+672/5b3+504/5ba+2688/\
5b2-2016/5b
==> J[12]=b5a2+2420474/3c2d+32/9c2b2-1210217/9cdb3-689428/147cdba+931/2cb5+64\
cb3a-345872/7cba2-6173/81d2b4-1867616522/3969d2b2a-7/18db6+669815/252db4a\
-117310/441db2a2-14b6a+4b4a2+395552/63c2b+18676165220/3969cd2+194/63cdb2+\
1844168/147cda-8469797cb4+1600/7cb2a-128/7ca2+7471160423/7938d2ba-11/6db5\
-622555298/21db3a+2134623448/441dba2-50b5a+32/7b3a2+790208/63c2-124/21cdb\
-16941190cb3-1382464/7cba-24692/567d2b2-259351/63db4+74519/49db2a+56b6-40\
b4a+16/7b2a2-400/63cd-4839884cb2-1280/7ca-518474/63db3-7469280824/441dba+\
200b5-32/7b3a+16/7ba2-9680832cb-1037348/441db2-172776b4-128/7b2a-2073632/\
441db-320/7b3+96/7ba-691232/7b2-640/7b
==> J[13]=b7a-13606662/245c2d+1024/735c2b2-864700/27783cd2b+23004293/2205cdb3\
+29189312/12005cdba+758/5cb5+3904/245cb3a+12618cba2+12600644807/388962d2b\
2a+4/63db6+537472/15435db4a-3032/35db2a2-52/35b6a-1008b4a2+1266752/15435c\
2b-21001940345/64827cd2+20176/15435cdb2+554322208/108045cda+20430577/35cb\
4+26496/343cb2a+9216ca2-2334414076/36015d2ba+863872/2205db5+12600769819/6\
174db3a-16335524/49dba2-4b7-772/49b5a-2016b3a2+2447488/15435c2+2892256/22\
05cdb+40842962/35cb3+12382792/245cba+33193268/15435db4+49664/2401db2a+208\
/35b6-736/49b4a-576b2a2+3946912/3087cd+81722308/245cb2+63150592/1715ca+10\
0/441d2b+9239464/2205db3+126015926254/108045dba+3088/49b5-432/1715b3a-115\
2ba2+32671944/49cb+44256944/36015db2+2166931/49b4-1984/245b2a+16325536/72\
03db+55320768/1715b3+8896/1715ba+6190756/245b2+31575296/1715b
==> J[14]=b9-48392128/5145c2d+469223949568/2334744405c2b2+4446618588746560/29\
417779503cd2b+8065888/5145cdb3+293190604544/333534915cdba+384/35cb5+3072/\
1715cb3a-11648320/16807cba2+1050576605312618/29417779503d2b2a-4/441db6-15\
04/108045db4a-1536/245db2a2+4b8-96/245b6a-256/16807b2a3+767602156544/2334\
744405c2b-10670463200/194481cd2+7936/36015cdb2+23968768/252105cda+7472643\
9712/756315cb4+16384/2401cb2a+2651044/151263d2b3-74705512256/6806835d2ba-\
664/15435db5+7469324432/21609db3a-19361152/343dba2+36/7b7-512/343b5a-1757\
184/12005c2+256/108045cdb+48404416/245cb3-232478976/84035cba+515091680/66\
706983d2b2+16596304/108045db4+46922869120/466948881db2a+1504/245b6-512/34\
3b4a-1024/21609cd+96827264/1715cb2-16384/12005ca-640/3087d2b+33201824/108\
045db3+49786270144/252105dba+3728/343b5-6656/12005b3a+38722304/343cb+9483\
008/108045db2-5806688/2401b4-8704/12005b2a+8854528/50421db+42304/12005b3+\
2048/12005ba-116239488/84035b2-8192/12005b
==> J[15]=dba3-2/3c2d+1/9cdb3-1/6d2ba+5/9d2b
==> J[16]=db3a2-147/2cdb3-10cdba-288cba2+63b4a2-32c2b-132cda-576ca2-49/2db5+4\
db3a+126b3a2-64c2-82cdb-1152cba-21/2db4+36b2a2-80cd-2304ca-14db3-16dba+72\
ba2-6db2-1008b4-2016b3-576b2-1152b
==> J[17]=a5+1/9cb2a2-4/3c2a-7/6cb3+5/9da2-2/3cb
==> J[18]=da4-4/21c3+11/63cdba+8/63c2b-1/63db3a+10/63cdb+32/7cba+5/9d2a+2/63d\
b2a-b4a+4b4-4/7b2a+16/7b2
|
