01342_01432_10342_10432_20341_20431_30421
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3125, 17354, 98386, 566333, 3298562, 19395029, 114936956, 685659248, 4113735616, 24804490702, 150223886163, 913392450022, 5573340531740, 34116974406237, 209459712729750, 1289439088573261, 7957570605048522, 49222058346077014, 305118275742300744, 1895148427125600082, 11793121055669711847, 73514731254392163220, 459023022193610999929, 2870566356732461540386, 17977774169692726491137, 112746953679295077921706, 708014967581994712255494, 4451633821972072839509171, 28022614948028321082543698, 176597665353901346481838229, 1114101995785062294476254753, 7035692896468518820670978263, 44474432468212033344203742288, 281395137798355930171021922302, 1781999683477624024925164168420, 11294495780925917053678773162730, 71643799754439598879852004380322, 454808104863183958054180245559151, 2889360570350720141113046509821074, 18369028525442656778392353843897633, 116860895363769291514763455572112949, 743942143046264614113936700165635409, 4738981745246384201664654323435529605, 30206222282393890551008074560443724163, 192647522153395861615635462669153151109, 1229353326851322449808994332514200957199, 7849236561436458235222499612567898734078, 50142627979721706768947400774435946890688, 320485019220183943260132887550359750168038, 2049376396112511963929082677001143216386812, 13111181679206990158490963298446381577105750, 83919164603996018459944290823816211218494515, 537369616413494248624821691754154853988331096, 3442480078099806959004197936615860047966405421, 22062268223579554179312945085127524010337130886, 141450203336055439584928514120024025296987449176, 907248449604392827155512203644525844333649435000, 5821205481375096342797598757708806811110889532118, 37364457653808156082027318967815802942457140900323, 239915734977933896771685155201428172249570110415594, 1541020868554035706762646336140007198438706156459362, 9901561311541608924330009973398301681219294418488335, 63641445197011480267370570744361449135234936937719896, 409179217609695901062600959512215296263912417981335279, 2631603401682023815066827600268848666548652921792982202, 16930000007705785210989809642926411482383692109780079612, 108948080565899218006647883176189013745882880565431126337, 701301733286556432617438809554522377817237678922487159305, 4515539819912948543306001982525646187491939966946142531897, 29082432807354129053014547997271238965487136085573382476004, 187354902138253727163620334661672283505150814033458505827126, 1207284850834346855497506006658251387728215171734629423924134, 7781476403225529085389888908323200427479530052064975522579023, 50167115013301408331604988768409193377664027141262636466210724, 323503154115180969136427277562566553594309997030766889144738951, 2086592684009618114424253451918286964864992100897336000286455276, 13461522959832315144800943456722773503683616100258141402818223247, 86865183098586736099201325832438448737385651132993090077875838918, 560647724290298972353066349742676298565810396720553714977698754545, 3619303483215050075270662461494553427973431150094068999059063168624, 23369448149052398952026830415488148399672799991933044486142518954234, 150924035676694108636627359373534509584994762303042762087920536933111, 974883913084123157212310069159203434079027928124737759390338795446358, 6298397273792352027625697131251404416397350074733436538742633268996141, 40699401383048605461265410692598928434526760930086700382133590536709466, 263041970612200130712878910678251695708978804651188598228644311296289032, 1700354297011583716151407461835788177850877849596604969635014986146569359, 10993335617329663963314907965116385009529359574500957284921526112924553355, 71087564657981343781778587786122231748642115657806379439837142830577867575, 459759083094151080962236096805013148893717962421750801576807313915386124434, 2973979883397759730163102750412133734958927144262786452710656403186899768987, 19240453429841451886830642929130917073562620256694554667921203545148322167367, 124497528882647443543577308888215697635492409359309584971649836373991626742983, 805699214702898431468456980588578322058151817493660028372166926365721496065962
Implicit equation for the generating function in Maple syntax:
(2*x^6-4*x^5+7*x^4-8*x^3+6*x^2-3*x+1)*F(x)^6+(7*x^5-25*x^4+37*x^3-33*x^2+19*x-7)*F(x)^5+(-4*x^5+28*x^4-57*x^3+65*x^2-46*x+20)*F(x)^4+(x^5-11*x^4+35*x^3-57*x^2+54*x-30)*F(x)^3+(x^4-7*x^3+21*x^2-31*x+25)*F(x)^2+(-2*x^2+7*x-11)*F(x)+2 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{6}-4 x^{5}+7 x^{4}-8 x^{3}+6 x^{2}-3 x +1\right) F \! \left(x \right)^{6}+\left(7 x^{5}-25 x^{4}+37 x^{3}-33 x^{2}+19 x -7\right) F \! \left(x \right)^{5}+\left(-4 x^{5}+28 x^{4}-57 x^{3}+65 x^{2}-46 x +20\right) F \! \left(x \right)^{4}+\left(x^{5}-11 x^{4}+35 x^{3}-57 x^{2}+54 x -30\right) F \! \left(x \right)^{3}+\left(x^{4}-7 x^{3}+21 x^{2}-31 x +25\right) F \! \left(x \right)^{2}+\left(-2 x^{2}+7 x -11\right) F \! \left(x \right)+2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 580
a(7) = 3125
a(8) = 17354
a(9) = 98386
a(10) = 566333
a(11) = 3298562
a(12) = 19395029
a(13) = 114936956
a(14) = 685659248
a(15) = 4113735616
a(16) = 24804490702
a(17) = 150223886163
a(18) = 913392450022
a(19) = 5573340531740
a(20) = 34116974406237
a(21) = 209459712729750
a(22) = 1289439088573261
a(23) = 7957570605048522
a(24) = 49222058346077014
a(25) = 305118275742300744
a(26) = 1895148427125600082
a(27) = 11793121055669711847
a(28) = 73514731254392163220
a(29) = 459023022193610999929
a(30) = 2870566356732461540386
a(31) = 17977774169692726491137
a(32) = 112746953679295077921706
a(33) = 708014967581994712255494
a(34) = 4451633821972072839509171
a(35) = 28022614948028321082543698
a(36) = 176597665353901346481838229
a(37) = 1114101995785062294476254753
a(38) = 7035692896468518820670978263
a(39) = 44474432468212033344203742288
a(40) = 281395137798355930171021922302
a(41) = 1781999683477624024925164168420
a(42) = 11294495780925917053678773162730
a(43) = 71643799754439598879852004380322
a(44) = 454808104863183958054180245559151
a(45) = 2889360570350720141113046509821074
a(46) = 18369028525442656778392353843897633
a(47) = 116860895363769291514763455572112949
a(48) = 743942143046264614113936700165635409
a(49) = 4738981745246384201664654323435529605
a(50) = 30206222282393890551008074560443724163
a(51) = 192647522153395861615635462669153151109
a(52) = 1229353326851322449808994332514200957199
a(53) = 7849236561436458235222499612567898734078
a(54) = 50142627979721706768947400774435946890688
a(55) = 320485019220183943260132887550359750168038
a(56) = 2049376396112511963929082677001143216386812
a(57) = 13111181679206990158490963298446381577105750
a(58) = 83919164603996018459944290823816211218494515
a(59) = 537369616413494248624821691754154853988331096
a(60) = 3442480078099806959004197936615860047966405421
a(n+61) = -1/56*(300739*n^2+33505009*n+933161028)/(n+61)/(n+60)*a(n+59)+3/560*(1163819863607620034154*n^5+129385472831070068189105*n^4+5728758459982505247147920*n^3+126193871230279988230002875*n^2+1381859626924111848374797826*n+6011406674668954180004622360)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+23)-3/560*(716661322512404481196*n^5+78999047236498874148355*n^4+3429167848467747201436410*n^3+72915352623086259873385765*n^2+753783537118564323626431714*n+2992895346732730918034299680)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+24)+3/560*(67499376199238371971*n^5-581609585451240005675*n^4-523776110894868142838265*n^3-26588834698643188335424785*n^2-515601567844458834350525246*n-3569645236884940156824773040)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+25)+3/560*(529169700627688282053*n^5+54501882224255738308370*n^4+2230129474287349486188415*n^3+45364316437762418589475810*n^2+459103583074201292659758392*n+1850445415238228584687413120)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+19)-1/560*(2650147584463405431043*n^5+277050991410122796668350*n^4+11540067562183821295111385*n^3+239494326691098272880280430*n^2+2477132962872744483027272592*n+10217791037227646139770468520)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+20)+1/560*(3580599563103981966976*n^5+382126414482740759608705*n^4+16270185805266983612898650*n^3+345512982967959818361444635*n^2+3659687125343268482147770674*n+15467617546146293057883687600)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+21)-1/112*(787069896753116145160*n^5+85814347822910968000789*n^4+3732627784986230178040370*n^3+80949554590021529119277027*n^2+875105705068828518121613502*n+3771509573410058100879302112)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+22)-1/35*(6424886614563620197*n^5+423996147821662443325*n^4+10915631739897377075795*n^3+135384728805951088768655*n^2+791155288297393607913648*n+1660072366324985073462000)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+15)+3/7*(142740453104009383*n^5-96507247531661019*n^4-391326382901582140266*n^3-12836685040283746643913*n^2-158595615687107661256141*n-698219755869709900186248)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+16)+3/70*(8774215922668546863*n^5+991302343602632230580*n^4+42397100956741426075035*n^3+875231642941332086923510*n^2+8816633443589614450340352*n+34901484578612163015199440)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+17)-1/280*(379080983515276852933*n^5+39158847891792463101235*n^4+1595352730541006388449585*n^3+32143831054017972751653485*n^2+321017880351847364144779362*n+1273380185867396262886325880)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+18)+24/35*(1890945100950999*n^5+89826619360096255*n^4+1703268325489206955*n^3+16115435434059330765*n^2+76083283589896853706*n+143387930290061328120)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+8)-4/35*(37463083431103933*n^5+1903137036705694420*n^4+38697089033988351695*n^3+393621470171421310820*n^2+2002648784966189937972*n+4076388353054427220080)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+9)+6/35*(69572057380081133*n^5+3785598394217053385*n^4+82599551999111850145*n^3+903196133464395260295*n^2+4948229990813776261082*n+10863513888463574586600)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+10)-1/35*(1013841752997311659*n^5+59131500222632901190*n^4+1384516718126015461265*n^3+16263362107885178015870*n^2+95817237683962871698416*n+226451142010431969360480)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+11)+3/35*(693218683979738863*n^5+42970295895724061420*n^4+1069758252104255565845*n^3+13367716309049725597360*n^2+83830820836133913190152*n+211023915215397353980440)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+12)-1/7*(759246631185245537*n^5+49850706808954071581*n^4+1315053914724499901641*n^3+17422575691844497685755*n^2+115925177485172369725470*n+309902137084004000167152)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+13)+3/35*(2008026729241615389*n^5+138075578518375956115*n^4+3809227027658288043495*n^3+52706856295429974962005*n^2+365804384758861876399796*n+1018887776587093833612720)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+14)+256/7*(202149157*n^5+11576184286*n^4+148113071255*n^3+793835503406*n^2+1946449346424*n+1807449521472)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+3)-384/7*(7111448969*n^5+202822399411*n^4+2197573275081*n^3+11458036491653*n^2+28958189959150*n+28498017026088)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+4)+64/7*(4567462781*n^5-1362421244806*n^4-39367152990929*n^3-401284933777310*n^2-1769712188534376*n-2873971503456336)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+5)+192/7*(1160217411795*n^5+48305920956134*n^4+793069269991350*n^3+6424576557582000*n^2+25708158168532067*n+40692123121592670)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+6)-96/7*(20316754508467*n^5+898251302447109*n^4+15789592081613712*n^3+137989744643193778*n^2+599744281774739094*n+1037374818355734852)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+7)+3/112*(2322065448741637*n^5+553690138320695869*n^4+52783079352356203977*n^3+2514637681117932540067*n^2+59870869990319844371386*n+569916758659972988741976)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+48)-1/56*(1578147804948908*n^5+379450595143142195*n^4+36490405993267534666*n^3+1754399982024706820959*n^2+42170188917042330410688*n+405415199440577297294460)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+49)+1/56*(482171898043363*n^5+117742205362134499*n^4+11500208958820913603*n^3+561607785745023198407*n^2+13712443550348005703808*n+133918767725315545261980)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+50)-1/56*(113450447441005*n^5+28184582221278952*n^4+2800674324135184937*n^3+139145728930908785714*n^2+3456480006738449803956*n+34343594449786723099392)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+51)+1/56*(21399553442777*n^5+5411366126542754*n^4+547331728362722035*n^3+27678750995308349074*n^2+699834205931509144620*n+7077621028552973017416)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+52)-1/112*(6556960173175*n^5+1687869778287868*n^4+173784464057412089*n^3+8946006277736752364*n^2+230247168149143622568*n+2370264709419840785472)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+53)+1/112*(816435228707*n^5+213919911567110*n^4+22418684887332085*n^3+1174651531896575422*n^2+30771488190426107388*n+322417806186912375600)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+54)-3/112*(27332637923*n^5+7288306741199*n^4+777311672726147*n^3+41447434588368829*n^2+1104929316138617294*n+11781380028130053216)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+55)+1/112*(6542235485*n^5+1774979198417*n^4+192609693253897*n^3+10449395547581023*n^2+283421459318262906*n+3074632315834593456)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+56)-3/560*(9271057637818180713*n^5+1873693690173574039145*n^4+151480205313022804955925*n^3+6123840888321724097444835*n^2+123798831642630765496634582*n+1001241894100432158330919920)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+42)+1/112*(2855573938664358907*n^5+590708901056164699276*n^4+48887558357902432427729*n^3+2023452340528852209581840*n^2+41886454938691208648817768*n+346934592160962738347248992)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+43)-1/560*(5570560507424285861*n^5+1175873689601563404230*n^4+99301319628779982466015*n^3+4193796805191331364372290*n^2+88579745048327772627398124*n+748590113025095600508316200)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+44)+3/560*(534646532578353984*n^5+114709801269171791755*n^4+9844321696842939257490*n^3+422422735611970694685805*n^2+9063612157758438014974646*n+77795764763417828785297920)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+45)-3/560*(93011902256866884*n^5+19990291681062530965*n^4+1716549361313639629910*n^3+73611031641973856228515*n^2+1576383019317738824923686*n+13486080981043280934486840)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+46)-3/112*(1091284188975031*n^5+297614247173911403*n^4+31584755546637848407*n^3+1642337090981023165425*n^2+42038411199972748631502*n+425124779267915459666760)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+47)+3/560*(32313638638316388663*n^5+6909470244978582313655*n^4+582780913192768894228015*n^3+24311129683553000755094125*n^2+502687271703840604640391662*n+4128394081141580361634522560)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+38)-1/560*(17837085491708728907*n^5+4443466999115133986360*n^4+421128839634691208513425*n^3+19306944550901233025140660*n^2+432329091814105866573575808*n+3805553847596238315142781760)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+39)-1/112*(6066053748609241231*n^5+1109467191531978194758*n^4+80607992453834109053909*n^3+2904134594237145826347686*n^2+51790646224842689188190184*n+364849942225843744187867712)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+40)+3/112*(2606787360619572427*n^5+511281922180530625859*n^4+40089699998591224855303*n^3+1570822175038767494745993*n^2+30756536098961174258582034*n+240740107872286584362374704)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+41)+1/560*(13959125856373083397*n^5-10976297241462517399190*n^4-1696046565074757204581305*n^3-91532942580459961957399630*n^2-2161463688568726633108618032*n-19036942589452465348627890600)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+35)+3/560*(30684165375606162561*n^5+8769680227458696301090*n^4+860748928832017101656775*n^3+39113305212417941434891550*n^2+848491380719476188893310624*n+7139619540747208228762131480)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+36)-1/560*(145757944713491138873*n^5+32271232050042733849775*n^4+2773109064381073896204085*n^3+116620300304769862933679485*n^2+2413372408943385585965818302*n+19733853385824875258374864800)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+37)-3/560*(1413040119118650146583*n^5+222902853388955078880655*n^4+14075106252035620725240275*n^3+444677366312212067656038905*n^2+7028627643007883569962683782*n+44462657005535639992163267280)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+31)+1/112*(469541602276852974719*n^5+76641561943999388468891*n^4+5008364069761471574668471*n^3+163776283487235695337672937*n^2+2679818736478227887474993430*n+17552051684808546978341521272)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+32)-1/280*(422797678885944023722*n^5+74748334748345972127355*n^4+5272377678034235338023470*n^3+185523116375217696165720575*n^2+3257604234326038024873847118*n+22840429893006286002108622140)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+33)+1/28*(5366323997138996113*n^5+1585621681239771216625*n^4+153704449527551121848621*n^3+6793724667077996292204761*n^2+142355923658291870297523618*n+1152654089467082650968069018)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+34)+1/560*(1943489397171213444113*n^5+286509826625269840596275*n^4+16838326812139527987824305*n^3+492937221154879434183668845*n^2+7187032035789990594085653462*n+41750833709188770425284719600)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+26)-3/560*(1337650292700272668161*n^5+194102912488716011537330*n^4+11277016436471266802798155*n^3+327718274805075960446371190*n^2+4761782962648531940270765964*n+27666558252347653444894780920)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+27)+1/560*(5601762295111622101693*n^5+826584056460280697358700*n^4+48828252990035099103389135*n^3+1443011321549103039720596000*n^2+21329870209497312563089991592*n+126136694971320561163599214680)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+28)-3/112*(417345770056089426260*n^5+62892681614651686874089*n^4+3793391341434080712541386*n^3+114455374771069490873171327*n^2+1727355013641774615218923450*n+10430783114580988803023780160)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+29)+3/112*(383723720583143606728*n^5+59084527687790540588475*n^4+3641270336920314269202786*n^3+112262358739013535587748333*n^2+1731366563627636950618301606*n+10685188658356647421567237464)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+30)+1/56*(6023*n+338321)/(n+61)*a(n+60)+512/7*(n+3)*(97345187*n^4+1048540628*n^3+4109247703*n^2+6926608894*n+4229860488)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+2)+1/56*(9326185*n^3+1545216411*n^2+85335875180*n+1570837667688)/(n+60)/(n+59)/(n+61)*a(n+58)-135168/7*(n+3)*(n+2)*(42781*n^3+262364*n^2+491003*n+289972)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n+1)+3244032*(3*n+2)*(3*n+1)*(n+3)*(n+2)*(n+1)/(n+60)/(n+59)/(n+58)/(n+57)/(n+61)*a(n)-3/56*(67426823*n^4+14765696581*n^3+1212481061596*n^2+44246845242000*n+605466474043408)/(n+60)/(n+59)/(n+58)/(n+61)*a(n+57), n >= 61
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 580
a(7) = 3125
a(8) = 17354
a(9) = 98386
a(10) = 566333
a(11) = 3298562
a(12) = 19395029
a(13) = 114936956
a(14) = 685659248
a(15) = 4113735616
a(16) = 24804490702
a(17) = 150223886163
a(18) = 913392450022
a(19) = 5573340531740
a(20) = 34116974406237
a(21) = 209459712729750
a(22) = 1289439088573261
a(23) = 7957570605048522
a(24) = 49222058346077014
a(25) = 305118275742300744
a(26) = 1895148427125600082
a(27) = 11793121055669711847
a(28) = 73514731254392163220
a(29) = 459023022193610999929
a(30) = 2870566356732461540386
a(31) = 17977774169692726491137
a(32) = 112746953679295077921706
a(33) = 708014967581994712255494
a(34) = 4451633821972072839509171
a(35) = 28022614948028321082543698
a(36) = 176597665353901346481838229
a(37) = 1114101995785062294476254753
a(38) = 7035692896468518820670978263
a(39) = 44474432468212033344203742288
a(40) = 281395137798355930171021922302
a(41) = 1781999683477624024925164168420
a(42) = 11294495780925917053678773162730
a(43) = 71643799754439598879852004380322
a(44) = 454808104863183958054180245559151
a(45) = 2889360570350720141113046509821074
a(46) = 18369028525442656778392353843897633
a(47) = 116860895363769291514763455572112949
a(48) = 743942143046264614113936700165635409
a(49) = 4738981745246384201664654323435529605
a(50) = 30206222282393890551008074560443724163
a(51) = 192647522153395861615635462669153151109
a(52) = 1229353326851322449808994332514200957199
a(53) = 7849236561436458235222499612567898734078
a(54) = 50142627979721706768947400774435946890688
a(55) = 320485019220183943260132887550359750168038
a(56) = 2049376396112511963929082677001143216386812
a(57) = 13111181679206990158490963298446381577105750
a(58) = 83919164603996018459944290823816211218494515
a(59) = 537369616413494248624821691754154853988331096
a(60) = 3442480078099806959004197936615860047966405421
a{\left(n + 61 \right)} = \frac{3244032 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(3 n + 1\right) \left(3 n + 2\right) a{\left(n \right)}}{\left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{135168 \left(n + 2\right) \left(n + 3\right) \left(42781 n^{3} + 262364 n^{2} + 491003 n + 289972\right) a{\left(n + 1 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{512 \left(n + 3\right) \left(97345187 n^{4} + 1048540628 n^{3} + 4109247703 n^{2} + 6926608894 n + 4229860488\right) a{\left(n + 2 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(6023 n + 338321\right) a{\left(n + 60 \right)}}{56 \left(n + 61\right)} - \frac{\left(300739 n^{2} + 33505009 n + 933161028\right) a{\left(n + 59 \right)}}{56 \left(n + 60\right) \left(n + 61\right)} + \frac{\left(9326185 n^{3} + 1545216411 n^{2} + 85335875180 n + 1570837667688\right) a{\left(n + 58 \right)}}{56 \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(67426823 n^{4} + 14765696581 n^{3} + 1212481061596 n^{2} + 44246845242000 n + 605466474043408\right) a{\left(n + 57 \right)}}{56 \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{256 \left(202149157 n^{5} + 11576184286 n^{4} + 148113071255 n^{3} + 793835503406 n^{2} + 1946449346424 n + 1807449521472\right) a{\left(n + 3 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{64 \left(4567462781 n^{5} - 1362421244806 n^{4} - 39367152990929 n^{3} - 401284933777310 n^{2} - 1769712188534376 n - 2873971503456336\right) a{\left(n + 5 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(6542235485 n^{5} + 1774979198417 n^{4} + 192609693253897 n^{3} + 10449395547581023 n^{2} + 283421459318262906 n + 3074632315834593456\right) a{\left(n + 56 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{384 \left(7111448969 n^{5} + 202822399411 n^{4} + 2197573275081 n^{3} + 11458036491653 n^{2} + 28958189959150 n + 28498017026088\right) a{\left(n + 4 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(27332637923 n^{5} + 7288306741199 n^{4} + 777311672726147 n^{3} + 41447434588368829 n^{2} + 1104929316138617294 n + 11781380028130053216\right) a{\left(n + 55 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(816435228707 n^{5} + 213919911567110 n^{4} + 22418684887332085 n^{3} + 1174651531896575422 n^{2} + 30771488190426107388 n + 322417806186912375600\right) a{\left(n + 54 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{192 \left(1160217411795 n^{5} + 48305920956134 n^{4} + 793069269991350 n^{3} + 6424576557582000 n^{2} + 25708158168532067 n + 40692123121592670\right) a{\left(n + 6 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(6556960173175 n^{5} + 1687869778287868 n^{4} + 173784464057412089 n^{3} + 8946006277736752364 n^{2} + 230247168149143622568 n + 2370264709419840785472\right) a{\left(n + 53 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{96 \left(20316754508467 n^{5} + 898251302447109 n^{4} + 15789592081613712 n^{3} + 137989744643193778 n^{2} + 599744281774739094 n + 1037374818355734852\right) a{\left(n + 7 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(21399553442777 n^{5} + 5411366126542754 n^{4} + 547331728362722035 n^{3} + 27678750995308349074 n^{2} + 699834205931509144620 n + 7077621028552973017416\right) a{\left(n + 52 \right)}}{56 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(113450447441005 n^{5} + 28184582221278952 n^{4} + 2800674324135184937 n^{3} + 139145728930908785714 n^{2} + 3456480006738449803956 n + 34343594449786723099392\right) a{\left(n + 51 \right)}}{56 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(482171898043363 n^{5} + 117742205362134499 n^{4} + 11500208958820913603 n^{3} + 561607785745023198407 n^{2} + 13712443550348005703808 n + 133918767725315545261980\right) a{\left(n + 50 \right)}}{56 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(1091284188975031 n^{5} + 297614247173911403 n^{4} + 31584755546637848407 n^{3} + 1642337090981023165425 n^{2} + 42038411199972748631502 n + 425124779267915459666760\right) a{\left(n + 47 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(1578147804948908 n^{5} + 379450595143142195 n^{4} + 36490405993267534666 n^{3} + 1754399982024706820959 n^{2} + 42170188917042330410688 n + 405415199440577297294460\right) a{\left(n + 49 \right)}}{56 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{24 \left(1890945100950999 n^{5} + 89826619360096255 n^{4} + 1703268325489206955 n^{3} + 16115435434059330765 n^{2} + 76083283589896853706 n + 143387930290061328120\right) a{\left(n + 8 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(2322065448741637 n^{5} + 553690138320695869 n^{4} + 52783079352356203977 n^{3} + 2514637681117932540067 n^{2} + 59870869990319844371386 n + 569916758659972988741976\right) a{\left(n + 48 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{4 \left(37463083431103933 n^{5} + 1903137036705694420 n^{4} + 38697089033988351695 n^{3} + 393621470171421310820 n^{2} + 2002648784966189937972 n + 4076388353054427220080\right) a{\left(n + 9 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{6 \left(69572057380081133 n^{5} + 3785598394217053385 n^{4} + 82599551999111850145 n^{3} + 903196133464395260295 n^{2} + 4948229990813776261082 n + 10863513888463574586600\right) a{\left(n + 10 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(93011902256866884 n^{5} + 19990291681062530965 n^{4} + 1716549361313639629910 n^{3} + 73611031641973856228515 n^{2} + 1576383019317738824923686 n + 13486080981043280934486840\right) a{\left(n + 46 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(142740453104009383 n^{5} - 96507247531661019 n^{4} - 391326382901582140266 n^{3} - 12836685040283746643913 n^{2} - 158595615687107661256141 n - 698219755869709900186248\right) a{\left(n + 16 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(534646532578353984 n^{5} + 114709801269171791755 n^{4} + 9844321696842939257490 n^{3} + 422422735611970694685805 n^{2} + 9063612157758438014974646 n + 77795764763417828785297920\right) a{\left(n + 45 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(693218683979738863 n^{5} + 42970295895724061420 n^{4} + 1069758252104255565845 n^{3} + 13367716309049725597360 n^{2} + 83830820836133913190152 n + 211023915215397353980440\right) a{\left(n + 12 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(759246631185245537 n^{5} + 49850706808954071581 n^{4} + 1315053914724499901641 n^{3} + 17422575691844497685755 n^{2} + 115925177485172369725470 n + 309902137084004000167152\right) a{\left(n + 13 \right)}}{7 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(1013841752997311659 n^{5} + 59131500222632901190 n^{4} + 1384516718126015461265 n^{3} + 16263362107885178015870 n^{2} + 95817237683962871698416 n + 226451142010431969360480\right) a{\left(n + 11 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(2008026729241615389 n^{5} + 138075578518375956115 n^{4} + 3809227027658288043495 n^{3} + 52706856295429974962005 n^{2} + 365804384758861876399796 n + 1018887776587093833612720\right) a{\left(n + 14 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(2606787360619572427 n^{5} + 511281922180530625859 n^{4} + 40089699998591224855303 n^{3} + 1570822175038767494745993 n^{2} + 30756536098961174258582034 n + 240740107872286584362374704\right) a{\left(n + 41 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(2855573938664358907 n^{5} + 590708901056164699276 n^{4} + 48887558357902432427729 n^{3} + 2023452340528852209581840 n^{2} + 41886454938691208648817768 n + 346934592160962738347248992\right) a{\left(n + 43 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(5366323997138996113 n^{5} + 1585621681239771216625 n^{4} + 153704449527551121848621 n^{3} + 6793724667077996292204761 n^{2} + 142355923658291870297523618 n + 1152654089467082650968069018\right) a{\left(n + 34 \right)}}{28 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(5570560507424285861 n^{5} + 1175873689601563404230 n^{4} + 99301319628779982466015 n^{3} + 4193796805191331364372290 n^{2} + 88579745048327772627398124 n + 748590113025095600508316200\right) a{\left(n + 44 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(6066053748609241231 n^{5} + 1109467191531978194758 n^{4} + 80607992453834109053909 n^{3} + 2904134594237145826347686 n^{2} + 51790646224842689188190184 n + 364849942225843744187867712\right) a{\left(n + 40 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(6424886614563620197 n^{5} + 423996147821662443325 n^{4} + 10915631739897377075795 n^{3} + 135384728805951088768655 n^{2} + 791155288297393607913648 n + 1660072366324985073462000\right) a{\left(n + 15 \right)}}{35 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(8774215922668546863 n^{5} + 991302343602632230580 n^{4} + 42397100956741426075035 n^{3} + 875231642941332086923510 n^{2} + 8816633443589614450340352 n + 34901484578612163015199440\right) a{\left(n + 17 \right)}}{70 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(9271057637818180713 n^{5} + 1873693690173574039145 n^{4} + 151480205313022804955925 n^{3} + 6123840888321724097444835 n^{2} + 123798831642630765496634582 n + 1001241894100432158330919920\right) a{\left(n + 42 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(13959125856373083397 n^{5} - 10976297241462517399190 n^{4} - 1696046565074757204581305 n^{3} - 91532942580459961957399630 n^{2} - 2161463688568726633108618032 n - 19036942589452465348627890600\right) a{\left(n + 35 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(17837085491708728907 n^{5} + 4443466999115133986360 n^{4} + 421128839634691208513425 n^{3} + 19306944550901233025140660 n^{2} + 432329091814105866573575808 n + 3805553847596238315142781760\right) a{\left(n + 39 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(30684165375606162561 n^{5} + 8769680227458696301090 n^{4} + 860748928832017101656775 n^{3} + 39113305212417941434891550 n^{2} + 848491380719476188893310624 n + 7139619540747208228762131480\right) a{\left(n + 36 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(32313638638316388663 n^{5} + 6909470244978582313655 n^{4} + 582780913192768894228015 n^{3} + 24311129683553000755094125 n^{2} + 502687271703840604640391662 n + 4128394081141580361634522560\right) a{\left(n + 38 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(67499376199238371971 n^{5} - 581609585451240005675 n^{4} - 523776110894868142838265 n^{3} - 26588834698643188335424785 n^{2} - 515601567844458834350525246 n - 3569645236884940156824773040\right) a{\left(n + 25 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(145757944713491138873 n^{5} + 32271232050042733849775 n^{4} + 2773109064381073896204085 n^{3} + 116620300304769862933679485 n^{2} + 2413372408943385585965818302 n + 19733853385824875258374864800\right) a{\left(n + 37 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(379080983515276852933 n^{5} + 39158847891792463101235 n^{4} + 1595352730541006388449585 n^{3} + 32143831054017972751653485 n^{2} + 321017880351847364144779362 n + 1273380185867396262886325880\right) a{\left(n + 18 \right)}}{280 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(383723720583143606728 n^{5} + 59084527687790540588475 n^{4} + 3641270336920314269202786 n^{3} + 112262358739013535587748333 n^{2} + 1731366563627636950618301606 n + 10685188658356647421567237464\right) a{\left(n + 30 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(417345770056089426260 n^{5} + 62892681614651686874089 n^{4} + 3793391341434080712541386 n^{3} + 114455374771069490873171327 n^{2} + 1727355013641774615218923450 n + 10430783114580988803023780160\right) a{\left(n + 29 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(422797678885944023722 n^{5} + 74748334748345972127355 n^{4} + 5272377678034235338023470 n^{3} + 185523116375217696165720575 n^{2} + 3257604234326038024873847118 n + 22840429893006286002108622140\right) a{\left(n + 33 \right)}}{280 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(469541602276852974719 n^{5} + 76641561943999388468891 n^{4} + 5008364069761471574668471 n^{3} + 163776283487235695337672937 n^{2} + 2679818736478227887474993430 n + 17552051684808546978341521272\right) a{\left(n + 32 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(529169700627688282053 n^{5} + 54501882224255738308370 n^{4} + 2230129474287349486188415 n^{3} + 45364316437762418589475810 n^{2} + 459103583074201292659758392 n + 1850445415238228584687413120\right) a{\left(n + 19 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(716661322512404481196 n^{5} + 78999047236498874148355 n^{4} + 3429167848467747201436410 n^{3} + 72915352623086259873385765 n^{2} + 753783537118564323626431714 n + 2992895346732730918034299680\right) a{\left(n + 24 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(787069896753116145160 n^{5} + 85814347822910968000789 n^{4} + 3732627784986230178040370 n^{3} + 80949554590021529119277027 n^{2} + 875105705068828518121613502 n + 3771509573410058100879302112\right) a{\left(n + 22 \right)}}{112 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{3 \left(1163819863607620034154 n^{5} + 129385472831070068189105 n^{4} + 5728758459982505247147920 n^{3} + 126193871230279988230002875 n^{2} + 1381859626924111848374797826 n + 6011406674668954180004622360\right) a{\left(n + 23 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(1337650292700272668161 n^{5} + 194102912488716011537330 n^{4} + 11277016436471266802798155 n^{3} + 327718274805075960446371190 n^{2} + 4761782962648531940270765964 n + 27666558252347653444894780920\right) a{\left(n + 27 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{3 \left(1413040119118650146583 n^{5} + 222902853388955078880655 n^{4} + 14075106252035620725240275 n^{3} + 444677366312212067656038905 n^{2} + 7028627643007883569962683782 n + 44462657005535639992163267280\right) a{\left(n + 31 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(1943489397171213444113 n^{5} + 286509826625269840596275 n^{4} + 16838326812139527987824305 n^{3} + 492937221154879434183668845 n^{2} + 7187032035789990594085653462 n + 41750833709188770425284719600\right) a{\left(n + 26 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} - \frac{\left(2650147584463405431043 n^{5} + 277050991410122796668350 n^{4} + 11540067562183821295111385 n^{3} + 239494326691098272880280430 n^{2} + 2477132962872744483027272592 n + 10217791037227646139770468520\right) a{\left(n + 20 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(3580599563103981966976 n^{5} + 382126414482740759608705 n^{4} + 16270185805266983612898650 n^{3} + 345512982967959818361444635 n^{2} + 3659687125343268482147770674 n + 15467617546146293057883687600\right) a{\left(n + 21 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)} + \frac{\left(5601762295111622101693 n^{5} + 826584056460280697358700 n^{4} + 48828252990035099103389135 n^{3} + 1443011321549103039720596000 n^{2} + 21329870209497312563089991592 n + 126136694971320561163599214680\right) a{\left(n + 28 \right)}}{560 \left(n + 57\right) \left(n + 58\right) \left(n + 59\right) \left(n + 60\right) \left(n + 61\right)}, \quad n \geq 61
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24464/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[38,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]*F[23,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[27,x]+F[13,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]+F[9,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[11,x]*F[2,x]
F[26,x] = -F[33,x]+F[27,x]
F[27,x] = -F[25,x]+F[28,x]
F[28,x] = 1/F[23,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[32,x]+F[15,x]
F[32,x] = 2+F[32,x]^2+(-2+x)*F[32,x]
F[33,x] = F[31,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[23,x]*F[36,x]
F[36,x] = 1/F[23,x]*F[37,x]
F[37,x] = F[30,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[15,x]*F[2,x]
F[40,x] = F[41,x]
F[41,x] = F[23,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[11,x]*F[18,x]*F[2,x]
F[44,x] = F[32,x]*F[45,x]*F[5,x]
F[45,x] = F[46,x]+F[61,x]
F[46,x] = F[15,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[2,x]*F[32,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[21,x]*F[31,x]
F[53,x] = F[54,x]
F[54,x] = F[15,x]*F[23,x]*F[32,x]*F[55,x]
F[55,x] = 1/F[14,x]/F[23,x]/F[32,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[23,x]*F[59,x]
F[59,x] = F[26,x]
F[60,x] = F[21,x]*F[33,x]
F[61,x] = F[62,x]
F[62,x] = F[23,x]*F[32,x]*F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{38}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{9}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{15}\! \left(x \right)
F_{32}\! \left(x \right) = F_{32}\! \left(x \right) x +F_{32} \left(x \right)^{2}-2 F_{32}\! \left(x \right)+2
F_{33}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{2}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right) F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right) F_{31}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{14}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{26}\! \left(x \right)
F_{60}\! \left(x \right) = F_{21}\! \left(x \right) F_{33}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{23}\! \left(x \right) F_{32}\! \left(x \right) F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_38(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x)*F_23(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_27(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x) + F_9(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_11(x)*F_2(x))
Eq(F_26(x), F_27(x) - F_33(x))
Eq(F_27(x), -F_25(x) + F_28(x))
Eq(F_28(x), F_29(x)/F_23(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_15(x) - F_32(x))
Eq(F_32(x), (x - 2)*F_32(x) + F_32(x)**2 + 2)
Eq(F_33(x), F_31(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_23(x)*F_36(x))
Eq(F_36(x), F_37(x)/F_23(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_15(x)*F_2(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_23(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_11(x)*F_18(x)*F_2(x))
Eq(F_44(x), F_32(x)*F_45(x)*F_5(x))
Eq(F_45(x), F_46(x) + F_61(x))
Eq(F_46(x), F_15(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_2(x)*F_32(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_21(x)*F_31(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_15(x)*F_23(x)*F_32(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_14(x)*F_23(x)*F_32(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_23(x))
Eq(F_59(x), F_26(x))
Eq(F_60(x), F_21(x)*F_33(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_23(x)*F_32(x)*F_55(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 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3, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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{"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24545/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[26,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[26,x]
F[12,x] = F[13,x]+F[43,x]
F[13,x] = F[0,x]*F[14,x]*F[21,x]
F[14,x] = 1/F[0,x]*F[15,x]
F[15,x] = -F[32,x]+F[16,x]
F[16,x] = F[17,x]+F[29,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[0,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[26,x]
F[21,x] = 1/F[26,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[26,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = x
F[27,x] = F[28,x]
F[28,x] = F[14,x]*F[21,x]*F[26,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[14,x]*F[2,x]
F[31,x] = -F[37,x]+F[32,x]
F[32,x] = -F[30,x]+F[33,x]
F[33,x] = 1/F[26,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = -F[36,x]+F[19,x]
F[36,x] = (1+F[36,x])*x+F[36,x]^2
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[2,x]+F[35,x]
F[39,x] = F[40,x]
F[40,x] = F[14,x]*F[26,x]*F[41,x]
F[41,x] = 1/F[26,x]*F[42,x]
F[42,x] = F[35,x]
F[43,x] = F[44,x]*F[45,x]*F[5,x]
F[44,x] = 2+F[44,x]^2+(-2+x)*F[44,x]
F[45,x] = F[46,x]+F[61,x]
F[46,x] = F[18,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[2,x]*F[44,x]
F[49,x] = F[50,x]
F[50,x] = F[26,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[24,x]*F[38,x]
F[53,x] = F[54,x]
F[54,x] = F[18,x]*F[26,x]*F[44,x]*F[55,x]
F[55,x] = 1/F[17,x]/F[26,x]/F[44,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[26,x]*F[59,x]
F[59,x] = F[31,x]
F[60,x] = F[24,x]*F[37,x]
F[61,x] = F[62,x]
F[62,x] = F[26,x]*F[44,x]*F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{15}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right) F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{19}\! \left(x \right)
F_{36}\! \left(x \right) = F_{36}\! \left(x \right) x +F_{36} \left(x \right)^{2}+x
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{44}\! \left(x \right) x +F_{44} \left(x \right)^{2}-2 F_{44}\! \left(x \right)+2
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right) F_{38}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right) F_{26}\! \left(x \right) F_{44}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{17}\! \left(x \right) F_{26}\! \left(x \right) F_{44}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{31}\! \left(x \right)
F_{60}\! \left(x \right) = F_{24}\! \left(x \right) F_{37}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{26}\! \left(x \right) F_{44}\! \left(x \right) F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_26(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_26(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_26(x))
Eq(F_12(x), F_13(x) + F_43(x))
Eq(F_13(x), F_0(x)*F_14(x)*F_21(x))
Eq(F_14(x), F_15(x)/F_0(x))
Eq(F_15(x), F_16(x) - F_32(x))
Eq(F_16(x), F_17(x) + F_29(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_0(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_26(x))
Eq(F_21(x), F_22(x)/F_26(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_26(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), x)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_14(x)*F_21(x)*F_26(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_14(x)*F_2(x))
Eq(F_31(x), F_32(x) - F_37(x))
Eq(F_32(x), -F_30(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_26(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_19(x) - F_36(x))
Eq(F_36(x), (x - 3)*(F_36(x) + 1) + (F_36(x) + 1)**2 + F_36(x) + 2)
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_2(x) + F_35(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_14(x)*F_26(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_26(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_44(x)*F_45(x)*F_5(x))
Eq(F_44(x), (x - 2)*F_44(x) + F_44(x)**2 + 2)
Eq(F_45(x), F_46(x) + F_61(x))
Eq(F_46(x), F_18(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_2(x)*F_44(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_26(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_24(x)*F_38(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_18(x)*F_26(x)*F_44(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_17(x)*F_26(x)*F_44(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_26(x))
Eq(F_59(x), F_31(x))
Eq(F_60(x), F_24(x)*F_37(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_26(x)*F_44(x)*F_55(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 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{"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24551/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[26,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[26,x]
F[12,x] = F[13,x]+F[43,x]
F[13,x] = F[0,x]*F[14,x]*F[21,x]
F[14,x] = 1/F[0,x]*F[15,x]
F[15,x] = -F[32,x]+F[16,x]
F[16,x] = F[17,x]+F[29,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[0,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[26,x]
F[21,x] = 1/F[26,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[26,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = x
F[27,x] = F[28,x]
F[28,x] = F[14,x]*F[21,x]*F[26,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[14,x]*F[2,x]
F[31,x] = -F[37,x]+F[32,x]
F[32,x] = -F[30,x]+F[33,x]
F[33,x] = 1/F[26,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = -F[36,x]+F[19,x]
F[36,x] = (1+F[36,x])*x+F[36,x]^2
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[2,x]+F[35,x]
F[39,x] = F[40,x]
F[40,x] = F[14,x]*F[26,x]*F[41,x]
F[41,x] = 1/F[26,x]*F[42,x]
F[42,x] = F[35,x]
F[43,x] = F[44,x]*F[45,x]*F[5,x]
F[44,x] = 2+F[44,x]^2+(-2+x)*F[44,x]
F[45,x] = F[46,x]+F[61,x]
F[46,x] = F[18,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[2,x]*F[44,x]
F[49,x] = F[50,x]
F[50,x] = F[26,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[24,x]*F[38,x]
F[53,x] = F[54,x]
F[54,x] = F[18,x]*F[26,x]*F[44,x]*F[55,x]
F[55,x] = 1/F[17,x]/F[26,x]/F[44,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[26,x]*F[59,x]
F[59,x] = F[31,x]
F[60,x] = F[24,x]*F[37,x]
F[61,x] = F[62,x]
F[62,x] = F[26,x]*F[44,x]*F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{15}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right) F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{19}\! \left(x \right)
F_{36}\! \left(x \right) = F_{36}\! \left(x \right) x +F_{36} \left(x \right)^{2}+x
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{44}\! \left(x \right) = F_{44}\! \left(x \right) x +F_{44} \left(x \right)^{2}-2 F_{44}\! \left(x \right)+2
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right) F_{38}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right) F_{26}\! \left(x \right) F_{44}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{17}\! \left(x \right) F_{26}\! \left(x \right) F_{44}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{31}\! \left(x \right)
F_{60}\! \left(x \right) = F_{24}\! \left(x \right) F_{37}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{26}\! \left(x \right) F_{44}\! \left(x \right) F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_26(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_26(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_26(x))
Eq(F_12(x), F_13(x) + F_43(x))
Eq(F_13(x), F_0(x)*F_14(x)*F_21(x))
Eq(F_14(x), F_15(x)/F_0(x))
Eq(F_15(x), F_16(x) - F_32(x))
Eq(F_16(x), F_17(x) + F_29(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_0(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_26(x))
Eq(F_21(x), F_22(x)/F_26(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_26(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), x)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_14(x)*F_21(x)*F_26(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_14(x)*F_2(x))
Eq(F_31(x), F_32(x) - F_37(x))
Eq(F_32(x), -F_30(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_26(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_19(x) - F_36(x))
Eq(F_36(x), (x - 3)*(F_36(x) + 1) + (F_36(x) + 1)**2 + F_36(x) + 2)
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_2(x) + F_35(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_14(x)*F_26(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_26(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_44(x)*F_45(x)*F_5(x))
Eq(F_44(x), (x - 2)*F_44(x) + F_44(x)**2 + 2)
Eq(F_45(x), F_46(x) + F_61(x))
Eq(F_46(x), F_18(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_2(x)*F_44(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_26(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_24(x)*F_38(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_18(x)*F_26(x)*F_44(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_17(x)*F_26(x)*F_44(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_26(x))
Eq(F_59(x), F_31(x))
Eq(F_60(x), F_24(x)*F_37(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_26(x)*F_44(x)*F_55(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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[0, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24626/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[38,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]*F[23,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[27,x]+F[13,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]+F[9,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[11,x]*F[2,x]
F[26,x] = -F[33,x]+F[27,x]
F[27,x] = -F[25,x]+F[28,x]
F[28,x] = 1/F[23,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[32,x]+F[15,x]
F[32,x] = 2+F[32,x]^2+(-2+x)*F[32,x]
F[33,x] = F[31,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[23,x]*F[36,x]
F[36,x] = 1/F[23,x]*F[37,x]
F[37,x] = F[30,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[15,x]*F[2,x]
F[40,x] = F[41,x]
F[41,x] = F[23,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[11,x]*F[18,x]*F[2,x]
F[44,x] = F[32,x]*F[45,x]*F[5,x]
F[45,x] = F[46,x]+F[61,x]
F[46,x] = F[15,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[2,x]*F[32,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[21,x]*F[31,x]
F[53,x] = F[54,x]
F[54,x] = F[15,x]*F[23,x]*F[32,x]*F[55,x]
F[55,x] = 1/F[14,x]/F[23,x]/F[32,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[23,x]*F[59,x]
F[59,x] = F[26,x]
F[60,x] = F[21,x]*F[33,x]
F[61,x] = F[62,x]
F[62,x] = F[23,x]*F[32,x]*F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{38}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{9}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{15}\! \left(x \right)
F_{32}\! \left(x \right) = F_{32}\! \left(x \right) x +F_{32} \left(x \right)^{2}-2 F_{32}\! \left(x \right)+2
F_{33}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{2}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right) F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right) F_{31}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{14}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{26}\! \left(x \right)
F_{60}\! \left(x \right) = F_{21}\! \left(x \right) F_{33}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{23}\! \left(x \right) F_{32}\! \left(x \right) F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_38(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x)*F_23(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_27(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x) + F_9(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_11(x)*F_2(x))
Eq(F_26(x), F_27(x) - F_33(x))
Eq(F_27(x), -F_25(x) + F_28(x))
Eq(F_28(x), F_29(x)/F_23(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_15(x) - F_32(x))
Eq(F_32(x), (x - 2)*F_32(x) + F_32(x)**2 + 2)
Eq(F_33(x), F_31(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_23(x)*F_36(x))
Eq(F_36(x), F_37(x)/F_23(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_15(x)*F_2(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_23(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_11(x)*F_18(x)*F_2(x))
Eq(F_44(x), F_32(x)*F_45(x)*F_5(x))
Eq(F_45(x), F_46(x) + F_61(x))
Eq(F_46(x), F_15(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_2(x)*F_32(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_21(x)*F_31(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_15(x)*F_23(x)*F_32(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_14(x)*F_23(x)*F_32(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_23(x))
Eq(F_59(x), F_26(x))
Eq(F_60(x), F_21(x)*F_33(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_23(x)*F_32(x)*F_55(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], 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0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25186/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[38,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]*F[23,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[27,x]+F[13,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]+F[9,x]
F[15,x] = F[0,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[0,x]+F[21,x]
F[21,x] = 1/F[23,x]*F[22,x]
F[22,x] = F[2,x]
F[23,x] = x
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[11,x]*F[2,x]
F[26,x] = -F[33,x]+F[27,x]
F[27,x] = -F[25,x]+F[28,x]
F[28,x] = 1/F[23,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[32,x]+F[15,x]
F[32,x] = 2+F[32,x]^2+(-2+x)*F[32,x]
F[33,x] = F[31,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[23,x]*F[36,x]
F[36,x] = 1/F[23,x]*F[37,x]
F[37,x] = F[30,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[15,x]*F[2,x]
F[40,x] = F[41,x]
F[41,x] = F[23,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[11,x]*F[18,x]*F[2,x]
F[44,x] = F[32,x]*F[45,x]*F[5,x]
F[45,x] = F[46,x]+F[61,x]
F[46,x] = F[15,x]+F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[2,x]*F[32,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[21,x]*F[31,x]
F[53,x] = F[54,x]
F[54,x] = F[15,x]*F[23,x]*F[32,x]*F[55,x]
F[55,x] = 1/F[14,x]/F[23,x]/F[32,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[23,x]*F[59,x]
F[59,x] = F[26,x]
F[60,x] = F[21,x]*F[33,x]
F[61,x] = F[62,x]
F[62,x] = F[23,x]*F[32,x]*F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{38}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{9}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{15}\! \left(x \right)
F_{32}\! \left(x \right) = F_{32}\! \left(x \right) x +F_{32} \left(x \right)^{2}-2 F_{32}\! \left(x \right)+2
F_{33}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{30}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{2}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right) F_{45}\! \left(x \right) F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{61}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{32}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right) F_{31}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{14}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{26}\! \left(x \right)
F_{60}\! \left(x \right) = F_{21}\! \left(x \right) F_{33}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{23}\! \left(x \right) F_{32}\! \left(x \right) F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_38(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x)*F_23(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_27(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x) + F_9(x))
Eq(F_15(x), F_0(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), -F_0(x) + F_21(x))
Eq(F_21(x), F_22(x)/F_23(x))
Eq(F_22(x), F_2(x))
Eq(F_23(x), x)
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_11(x)*F_2(x))
Eq(F_26(x), F_27(x) - F_33(x))
Eq(F_27(x), -F_25(x) + F_28(x))
Eq(F_28(x), F_29(x)/F_23(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_15(x) - F_32(x))
Eq(F_32(x), (x - 2)*F_32(x) + F_32(x)**2 + 2)
Eq(F_33(x), F_31(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_23(x)*F_36(x))
Eq(F_36(x), F_37(x)/F_23(x))
Eq(F_37(x), F_30(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_15(x)*F_2(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_23(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_11(x)*F_18(x)*F_2(x))
Eq(F_44(x), F_32(x)*F_45(x)*F_5(x))
Eq(F_45(x), F_46(x) + F_61(x))
Eq(F_46(x), F_15(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_2(x)*F_32(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_21(x)*F_31(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_15(x)*F_23(x)*F_32(x)*F_55(x))
Eq(F_55(x), F_56(x)/(F_14(x)*F_23(x)*F_32(x)))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_23(x))
Eq(F_59(x), F_26(x))
Eq(F_60(x), F_21(x)*F_33(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_23(x)*F_32(x)*F_55(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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