02341_02431_03241_20341_20431_24031
Counting sequence:
1, 1, 2, 6, 24, 114, 597, 3314, 19105, 113090, 682679, 4184123, 25957984, 162655987, 1027772600, 6540508805, 41878317633, 269581609701, 1743563874521, 11324091171784, 73823641257577, 482894670510517, 3168371392624789, 20846229957323139, 137506587944721395, 909146396515401890, 6023919380965409084, 39993493824230661258, 266012501041853451818, 1772399229315281005954, 11828179092170658821225, 79054400267178141534581, 529109208070161345085135, 3546000340504107912301321, 23794292050789194873909424, 159851481380932023721219066, 1075083743300236456200739721, 7238088127047504529162115557, 48779531423620194955761324537, 329049813903505874747854277204, 2221650175941634466443385110139, 15012773130372166989484250884081, 101531301116370787091570924994824, 687189547886906589159174616109139, 4654527356908591423199423320959463, 31548808916407566199245399881414549, 213986065815560108957869844578094466, 1452348407793488093174935625147977070, 9863415726622866729461125688177162917, 67026137007118639830618361639042606155, 455733691217946554427445189437556181049, 3100405812200074284347347310505535462022, 21103637878378201732109652863742827360379, 143720564474269627796419420606420242086642, 979253665330905841622944044338540609677990, 6675419104706319552417201276858013937844241, 45526226212195786055745517435739475660533769, 310625904629867488759033391683484575040655492, 2120313443719817385081203248403180841108196253, 14479135804829987030880943401991081508231741278, 98914395706534874550506048519636783243619894815, 675997426663789710528932450243169697812021734457, 4621616714592019307000920808023864704636235054335, 31608294465914824442477612270783295496752912418139, 216252732296539148395576122579799577738401943839790, 1480031357555449133023787658270118885631522368435241, 10132685904979317809479916610251604402335905891166087, 69393431963810845626441268243376723818388447117071212, 475388019102123218999983101533426986508250176472082112, 3257694144005577411215578306627635944301884255387718932, 22330625336973349267391603748006059299530705078881426866, 153114532957711263703459375483945440584960524570203339482, 1050155202014202129730233792977985605089582151194172816344, 7204582837609636895849724791328396941376695805581072109955, 49440098823137542192837898568655962157846115487631001740225, 339361012798440017250538456004786085933395223039068397969068, 2329988589602989652752001921566379419991585241421641128379528, 16001182766263854290950795707629122857659283913491032952989299, 109914285835234867623505812163534944868700011911213996096866856, 755192007371644982633413385806407685688478005760141663348624149, 5189904056566247545585438453916078692335109695742179660498007073, 35674474321829597239948453748213889834124731080308700062961787251, 245273053026140608039994742903676414855871343718414439189142106694, 1686684556384017638432594654083589705581268110991569851140903516524, 11601323316473179340162851236904184570819971602112508398645276956499, 79812102309939751431321357709985089190893740711550528811318003115544, 549181031910562933889615102686907478817401533747068008131726154752972, 3779600799765582825771509834079140412527841077727197241654285236532878, 26017052491657462491791719654086547124420771990551010736981936173125750, 179122526395725347975839841983445717093673029854640180843807324811592017, 1233447089156036675976562410027060516635109721597050656258871087206667253, 8495077763516128047252499651348430029182646585919600555993172124617497768, 58517945980038716413028195273645329554850209449526892937069409793477017549, 403166172785982696947653593856104183966952898273459270967500295532555605836, 2778119111131491876364758342881493290380993534047246138053640695878060914544, 19146434757811064346344640542228578936073895723840935098058272269966027492401, 131975649619279860078904120674160026623714405444820059539404550636337879600549, 909844433773323279364185174667855446021394882298355845457003751589494539835673, 6273451785553399223516421905856554702638478149360905216818994013036471737472136, 43262415205644238013549589470437654479191504201944778073351159679947345576603732, 298386010140736847866566043217235367478890292172341872986465289750120316932357427
Implicit equation for the generating function in Maple syntax:
x^2*(x-1)*(4*x^2-6*x+3)*F(x)^8-x*(x-1)*(4*x^3-9*x^2+5*x+2)*F(x)^7+x*(x^4-3*x^2+10*x-7)*F(x)^6+(-4*x^4+13*x^3-20*x^2+10*x-1)*F(x)^5+(x^4-6*x^3+15*x^2-10*x+5)*F(x)^4+(x^3-7*x^2+10*x-10)*F(x)^3+(2*x^2-7*x+10)*F(x)^2+(2*x-5)*F(x)+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x -1\right) \left(4 x^{2}-6 x +3\right) F \! \left(x \right)^{8}-x \left(x -1\right) \left(4 x^{3}-9 x^{2}+5 x +2\right) F \! \left(x \right)^{7}+x \left(x^{4}-3 x^{2}+10 x -7\right) F \! \left(x \right)^{6}+\left(-4 x^{4}+13 x^{3}-20 x^{2}+10 x -1\right) F \! \left(x \right)^{5}+\left(x^{4}-6 x^{3}+15 x^{2}-10 x +5\right) F \! \left(x \right)^{4}+\left(x^{3}-7 x^{2}+10 x -10\right) F \! \left(x \right)^{3}+\left(2 x^{2}-7 x +10\right) F \! \left(x \right)^{2}+\left(2 x -5\right) F \! \left(x \right)+1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a(6) = 597
a(7) = 3314
a(8) = 19105
a(9) = 113090
a(10) = 682679
a(11) = 4184123
a(12) = 25957984
a(13) = 162655987
a(14) = 1027772600
a(15) = 6540508805
a(16) = 41878317633
a(17) = 269581609701
a(18) = 1743563874521
a(19) = 11324091171784
a(20) = 73823641257577
a(21) = 482894670510517
a(22) = 3168371392624789
a(23) = 20846229957323139
a(24) = 137506587944721395
a(25) = 909146396515401890
a(26) = 6023919380965409084
a(27) = 39993493824230661258
a(28) = 266012501041853451818
a(29) = 1772399229315281005954
a(30) = 11828179092170658821225
a(31) = 79054400267178141534581
a(32) = 529109208070161345085135
a(33) = 3546000340504107912301321
a(34) = 23794292050789194873909424
a(35) = 159851481380932023721219066
a(36) = 1075083743300236456200739721
a(37) = 7238088127047504529162115557
a(38) = 48779531423620194955761324537
a(39) = 329049813903505874747854277204
a(40) = 2221650175941634466443385110139
a(41) = 15012773130372166989484250884081
a(42) = 101531301116370787091570924994824
a(43) = 687189547886906589159174616109139
a(44) = 4654527356908591423199423320959463
a(45) = 31548808916407566199245399881414549
a(46) = 213986065815560108957869844578094466
a(47) = 1452348407793488093174935625147977070
a(48) = 9863415726622866729461125688177162917
a(49) = 67026137007118639830618361639042606155
a(50) = 455733691217946554427445189437556181049
a(51) = 3100405812200074284347347310505535462022
a(52) = 21103637878378201732109652863742827360379
a(53) = 143720564474269627796419420606420242086642
a(54) = 979253665330905841622944044338540609677990
a(55) = 6675419104706319552417201276858013937844241
a(56) = 45526226212195786055745517435739475660533769
a(57) = 310625904629867488759033391683484575040655492
a(58) = 2120313443719817385081203248403180841108196253
a(59) = 14479135804829987030880943401991081508231741278
a(60) = 98914395706534874550506048519636783243619894815
a(61) = 675997426663789710528932450243169697812021734457
a(62) = 4621616714592019307000920808023864704636235054335
a(63) = 31608294465914824442477612270783295496752912418139
a(64) = 216252732296539148395576122579799577738401943839790
a(65) = 1480031357555449133023787658270118885631522368435241
a(66) = 10132685904979317809479916610251604402335905891166087
a(67) = 69393431963810845626441268243376723818388447117071212
a(68) = 475388019102123218999983101533426986508250176472082112
a(69) = 3257694144005577411215578306627635944301884255387718932
a(70) = 22330625336973349267391603748006059299530705078881426866
a(71) = 153114532957711263703459375483945440584960524570203339482
a(72) = 1050155202014202129730233792977985605089582151194172816344
a(73) = 7204582837609636895849724791328396941376695805581072109955
a(74) = 49440098823137542192837898568655962157846115487631001740225
a(75) = 339361012798440017250538456004786085933395223039068397969068
a(76) = 2329988589602989652752001921566379419991585241421641128379528
a(77) = 16001182766263854290950795707629122857659283913491032952989299
a(78) = 109914285835234867623505812163534944868700011911213996096866856
a(79) = 755192007371644982633413385806407685688478005760141663348624149
a(n+80) = -1/31436823281394348195840*(59403581113701314860589477333444138104603000373188001*n^7+21591873032041411656599181724929172981789214570891540145*n^6+3363726189286631376014351526800241021433239186457230586955*n^5+291144415907664116870636612642407768399538671429801033850535*n^4+15120917904620027824599347372175758468046449398662800387943404*n^3+471227146899765221729704128705826175300742439369434489226235400*n^2+8159090244471532596304984799582433757772329607516340892885074120*n+60549249418687738829729342661923488253795832346446538611234613440)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+52)+1/31436823281394348195840*(24252332447845045381286573302926852444865173806145995*n^7+8973167311191986366926375952583839713284202928695159937*n^6+1422942756215182214351376742846926036430851858538895845499*n^5+125367058983939460818259809161204971653664225893692041164035*n^4+6627629156090316999075769310599806378862508131788439956694850*n^3+210238556828378041476344212391229034517333162937556213840997948*n^2+3705295359542215086475471385211067680259953305760264023957317176*n+27988908640931220857625841638650544416636732731084569490386773760)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+53)-1/31436823281394348195840*(8998605409723600232466247423565212341141426431944405*n^7+3388398647785939463231536560996255646351973278407310887*n^6+546840439368327201271060580378143260966270448010199084925*n^5+49031882093529634979909568751583838189049632215173375439925*n^4+2637987795203780618850154761299512097225810165837320417870630*n^3+85161633632740178475689357129204926518700168006977179644408068*n^2+1527457450881953113751706783623761056038827035608179492186136040*n+11742068829010891885232349948562562676889381702010305665615446400)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+54)+9555019576400861901/222817534607360*n*(2*n+1)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n)-1/15718411640697174097920*(1176508121074838569636126839622975885700393020907311267*n^7+367705748153604520672695001948325473920556341306111405700*n^6+49257477331206440924983372459712371671776342523905928847423*n^5+3666183887728736495148826578437228941145031428235639910993120*n^4+163738263925134465378615427200242546932038245748186654820105978*n^3+4388132449576686938638033158232188418949667251719339891801042960*n^2+65339958983116415117947992091644453953387339902956128433428506752*n+417006668132220017050334575470574349979106803256709039985561099120)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+44)+1/62873646562788696391680*(4215685430946765845664705966667845575259597479325069053*n^7+1343485132872880977380865726965330254352635696943788722209*n^6+183513794610314972752925469967995085619269284105581413447691*n^5+13927716452153488197227647198755585764074223710900152537780395*n^4+634293251294179042932742480533354524985950625162144766435467272*n^3+17334011630402330967762424007844777083614906921371179885391648116*n^2+263198230642420806641349666885344723326851607725176093533750846224*n+1712920711467186889759967774126854986640300066283381785015061836800)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+45)-1/62873646562788696391680*(3397440051439347029199827479497464934591664606549672401*n^7+1104017998162420522762466706009371480717474201491493171303*n^6+153770225880506553682675608371299899854709001513327065189453*n^5+11899929989936300074913936348239294726641347763981608603592005*n^4+552606995841561520192792999374576671892231910314594597222744954*n^3+15398845334806794818670968282661364599608800396519401966433358372*n^2+238416305365862912338789983691094248362624490577524776234528028152*n+1582178345763003553419580884556698900195043013456986519937103225600)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+46)+1/62873646562788696391680*(2475650856763491492100479841504923159602466421505873695*n^7+820172860398848895748473039798873243515211041754778374525*n^6+116463945483387996961006018457911227085600769031221661600823*n^5+9188659405248393733486785336451346350259468614603123312305615*n^4+435022041433541574066633374191003147979107692715219057772297650*n^3+12358590779099527406804329019769951983039132821788898026830043300*n^2+195074983380733580437729726309762279796683530230968881462709901832*n+1319790365479474624708711909787251166687607330719161553835630941760)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+47)+1/7859205820348587048960*(65912602082998013371772650912528291177766474277847*n^7+26142253828300929832727031062120753474816368097050452*n^6+4443880461826644181713180216322345740347351817816678511*n^5+419692876508908772074014381717018921741116040288470271960*n^4+23783475332256673055075887239131441855147951843832026186938*n^3+808712899369657716740112863454361870893563439879395200070508*n^2+15277977308168043000534724018733790213053784869343614899287504*n+123704746927435645850654455446626253982216000345625409925302240)/(4*n+315)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2158347283026754747131362820235682536160708*n+6519723449278083549309852283059724358895845520)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+72)+1/54144660909588480*(2062937430812865277089359144704*n^7+1039406311241287025183550137998768*n^6+224424897819856940846946698892083290*n^5+26918270297101605834708862215343408795*n^4+1937033779319255001763001833703566366516*n^3+83625920806223042862152894646113443042417*n^2+2005553663665695943525407597781031809758510*n+20611650439260120559385993930554945784894280)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+73)-1/1128013768949760*(1254231985948752183198086084*n^7+639356768988977699411002264428*n^6+139663645058095845136592200790633*n^5+16947357427967676732282570057021180*n^4+1233736413381219350870693837166912896*n^3+53882042793132527714319981054517600632*n^2+1307202072034436262026660140024195878267*n+13589816757035257549523542717955351466000)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+74)+1/564006884474880*(10924658846552973481660864*n^7+5625295685297940183283328784*n^6+1241171899369646683694548733758*n^5+152114546659061496940441419812985*n^4+11183670414580033469470380733656286*n^3+493255053012459874668547106012541231*n^2+12083904175833647366463055647926959212*n+126848681766357871954376192705119257120)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+75)-1/11750143426560*(696942673647003096224*n^7+353994662526450381044656*n^6+76948327548342376033403114*n^5+9278185324923910149860676925*n^4+670132716996020572956825140936*n^3+28989108248656875480000573499369*n^2+695338300427731375013287938543636*n+7132901408965760219981854356384000)/(4*n+315)/(n+81)/(n+80)/(n+77)/(4*n+313)/(2*n+161)/(2*n+157)*a(n+76), n >= 80
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a(6) = 597
a(7) = 3314
a(8) = 19105
a(9) = 113090
a(10) = 682679
a(11) = 4184123
a(12) = 25957984
a(13) = 162655987
a(14) = 1027772600
a(15) = 6540508805
a(16) = 41878317633
a(17) = 269581609701
a(18) = 1743563874521
a(19) = 11324091171784
a(20) = 73823641257577
a(21) = 482894670510517
a(22) = 3168371392624789
a(23) = 20846229957323139
a(24) = 137506587944721395
a(25) = 909146396515401890
a(26) = 6023919380965409084
a(27) = 39993493824230661258
a(28) = 266012501041853451818
a(29) = 1772399229315281005954
a(30) = 11828179092170658821225
a(31) = 79054400267178141534581
a(32) = 529109208070161345085135
a(33) = 3546000340504107912301321
a(34) = 23794292050789194873909424
a(35) = 159851481380932023721219066
a(36) = 1075083743300236456200739721
a(37) = 7238088127047504529162115557
a(38) = 48779531423620194955761324537
a(39) = 329049813903505874747854277204
a(40) = 2221650175941634466443385110139
a(41) = 15012773130372166989484250884081
a(42) = 101531301116370787091570924994824
a(43) = 687189547886906589159174616109139
a(44) = 4654527356908591423199423320959463
a(45) = 31548808916407566199245399881414549
a(46) = 213986065815560108957869844578094466
a(47) = 1452348407793488093174935625147977070
a(48) = 9863415726622866729461125688177162917
a(49) = 67026137007118639830618361639042606155
a(50) = 455733691217946554427445189437556181049
a(51) = 3100405812200074284347347310505535462022
a(52) = 21103637878378201732109652863742827360379
a(53) = 143720564474269627796419420606420242086642
a(54) = 979253665330905841622944044338540609677990
a(55) = 6675419104706319552417201276858013937844241
a(56) = 45526226212195786055745517435739475660533769
a(57) = 310625904629867488759033391683484575040655492
a(58) = 2120313443719817385081203248403180841108196253
a(59) = 14479135804829987030880943401991081508231741278
a(60) = 98914395706534874550506048519636783243619894815
a(61) = 675997426663789710528932450243169697812021734457
a(62) = 4621616714592019307000920808023864704636235054335
a(63) = 31608294465914824442477612270783295496752912418139
a(64) = 216252732296539148395576122579799577738401943839790
a(65) = 1480031357555449133023787658270118885631522368435241
a(66) = 10132685904979317809479916610251604402335905891166087
a(67) = 69393431963810845626441268243376723818388447117071212
a(68) = 475388019102123218999983101533426986508250176472082112
a(69) = 3257694144005577411215578306627635944301884255387718932
a(70) = 22330625336973349267391603748006059299530705078881426866
a(71) = 153114532957711263703459375483945440584960524570203339482
a(72) = 1050155202014202129730233792977985605089582151194172816344
a(73) = 7204582837609636895849724791328396941376695805581072109955
a(74) = 49440098823137542192837898568655962157846115487631001740225
a(75) = 339361012798440017250538456004786085933395223039068397969068
a(76) = 2329988589602989652752001921566379419991585241421641128379528
a(77) = 16001182766263854290950795707629122857659283913491032952989299
a(78) = 109914285835234867623505812163534944868700011911213996096866856
a(79) = 755192007371644982633413385806407685688478005760141663348624149
a{\left(n + 80 \right)} = \frac{9555019576400861901 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(2 n + 1\right) a{\left(n \right)}}{222817534607360 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{4563 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(201384828358980013 n^{2} + 2670483831480622522 n + 3547898335298632668\right) a{\left(n + 1 \right)}}{445635069214720 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{1521 \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(1134800993628230307522 n^{3} + 19384774712853355430947 n^{2} + 97815581644152806472931 n + 141155776121843408231166\right) a{\left(n + 2 \right)}}{6238890969006080 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{3 \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(38241299524697679354116043 n^{4} + 904271208727419306918521021 n^{3} + 7796087439196217312425854576 n^{2} + 29036306389765691253778763116 n + 39164893493263041878151319248\right) a{\left(n + 3 \right)}}{12477781938012160 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(n + 4\right) \left(n + 5\right) \left(2083331065530270607578867301 n^{5} + 62435679045814142390164261224 n^{4} + 741879437492308054753589577887 n^{3} + 4375898542275846655894183734192 n^{2} + 12823692691064209891494126648516 n + 14940983099018473687604602627488\right) a{\left(n + 4 \right)}}{12477781938012160 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(n + 5\right) \left(2971283871009948930763943774 n^{6} + 98313772321170790411874255851 n^{5} + 1277103331273030283200358915247 n^{4} + 8010244841498845733544212739795 n^{3} + 22921202347363559277258254594871 n^{2} + 14953529655759535053304028640094 n - 34495752531837861808988849128272\right) a{\left(n + 5 \right)}}{1782540276858880 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(1580706112 n^{6} + 741491267072 n^{5} + 144922522611020 n^{4} + 15106039036348860 n^{3} + 885674128473506373 n^{2} + 27693772499874297343 n + 360798799159717606020\right) a{\left(n + 79 \right)}}{344960 \left(n + 77\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(59185155377504 n^{7} + 33033481298343216 n^{6} + 7895106937446992590 n^{5} + 1047482180551047177865 n^{4} + 83322266332372708874091 n^{3} + 3973901408009643623473049 n^{2} + 105221751882897144563270415 n + 1193261547134519543745706950\right) a{\left(n + 78 \right)}}{1274972160 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(2693969190610953664 n^{7} + 1424016216419539023104 n^{6} + 322518200383415020680412 n^{5} + 40570647519185396996038340 n^{4} + 3061320844623840554054226961 n^{3} + 138561265039212161088578560781 n^{2} + 3483243950957579561480424013908 n + 37516930592619496872498524053020\right) a{\left(n + 77 \right)}}{734383964160 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(696942673647003096224 n^{7} + 353994662526450381044656 n^{6} + 76948327548342376033403114 n^{5} + 9278185324923910149860676925 n^{4} + 670132716996020572956825140936 n^{3} + 28989108248656875480000573499369 n^{2} + 695338300427731375013287938543636 n + 7132901408965760219981854356384000\right) a{\left(n + 76 \right)}}{11750143426560 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(10924658846552973481660864 n^{7} + 5625295685297940183283328784 n^{6} + 1241171899369646683694548733758 n^{5} + 152114546659061496940441419812985 n^{4} + 11183670414580033469470380733656286 n^{3} + 493255053012459874668547106012541231 n^{2} + 12083904175833647366463055647926959212 n + 126848681766357871954376192705119257120\right) a{\left(n + 75 \right)}}{564006884474880 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(1254231985948752183198086084 n^{7} + 639356768988977699411002264428 n^{6} + 139663645058095845136592200790633 n^{5} + 16947357427967676732282570057021180 n^{4} + 1233736413381219350870693837166912896 n^{3} + 53882042793132527714319981054517600632 n^{2} + 1307202072034436262026660140024195878267 n + 13589816757035257549523542717955351466000\right) a{\left(n + 74 \right)}}{1128013768949760 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(483135482542353754732646053566 n^{7} - 256179671870025744476281457744009 n^{6} - 11854735423751711090283707289386421 n^{5} - 220980382045995980741064809012171285 n^{4} - 2175635707693194487113162456791775441 n^{3} - 11984573441266174153574030809039791986 n^{2} - 35066530365091615248786966351521100264 n - 42596132751446148124530179002217392320\right) a{\left(n + 6 \right)}}{898400299536875520 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(2062937430812865277089359144704 n^{7} + 1039406311241287025183550137998768 n^{6} + 224424897819856940846946698892083290 n^{5} + 26918270297101605834708862215343408795 n^{4} + 1937033779319255001763001833703566366516 n^{3} + 83625920806223042862152894646113443042417 n^{2} + 2005553663665695943525407597781031809758510 n + 20611650439260120559385993930554945784894280\right) a{\left(n + 73 \right)}}{54144660909588480 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(239066242781991762254002626061131 n^{7} + 17464913748452139851999073328987571 n^{6} + 521581722433512915833267450917778859 n^{5} + 8383812570854215301154177871653168965 n^{4} + 79026233229163380064770988294991669274 n^{3} + 439203760158292010654075513112873326264 n^{2} + 1337335226692901879113327577677913155776 n + 1725202056113961989210104547537259678720\right) a{\left(n + 7 \right)}}{770057399603036160 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(710910757296623851350783110436916 n^{7} + 353813419522320211837441002098884604 n^{6} + 75461892044480981204022121999760341897 n^{5} + 8940862450559711112522977016896916294020 n^{4} + 635554948954975625693390664797106200050159 n^{3} + 27104951766915880631017910112082895006942936 n^{2} + 642158347283026754747131362820235682536160708 n + 6519723449278083549309852283059724358895845520\right) a{\left(n + 72 \right)}}{758025252734238720 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(27144062927847867349662110092597684 n^{7} + 13338998244070771893726466534898684708 n^{6} + 2809130041058572414142884525998363122345 n^{5} + 328643452632087455296024512060242654194210 n^{4} + 23067809455165966225419334685960067753587691 n^{3} + 971439859241488316837465424675517854838337682 n^{2} + 22726359962015640528672098738491380634981623480 n + 227847318231686827198055639249612903632485274080\right) a{\left(n + 71 \right)}}{1516050505468477440 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(30362212753176916429146122957329358 n^{7} + 2172063670300119127868092660935655153 n^{6} + 65708717725605503909536039211278724003 n^{5} + 1092809425708427606591211520405973113855 n^{4} + 10812822788295819770530932876158276798987 n^{3} + 63743703433069638364203964864356713210512 n^{2} + 207527711343415663755721354380974416744212 n + 288066509759619373651787730740572209219120\right) a{\left(n + 8 \right)}}{4620344397618216960 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(2425690043909788597630959150452267041 n^{7} + 180398334565027289534611320971853634117 n^{6} + 5722461177646398486615395138579274687193 n^{5} + 100445890611645782041749971184976449938875 n^{4} + 1054312167720556327706261366354859101114494 n^{3} + 6620651931956793777150797176936028421491368 n^{2} + 23039061204432486740820350192545438248045792 n + 34283365227244221758501728408556460596346240\right) a{\left(n + 9 \right)}}{27722066385709301760 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(2516447966973530387833140296926850788 n^{7} + 1220647546130035186761299795122547745164 n^{6} + 253745347515076248105733102110689612137867 n^{5} + 29303242548884390387128595650629728332479275 n^{4} + 2030330976345996415348034110767689904609733507 n^{3} + 84401778399045460495152933646181775182040425621 n^{2} + 1949154308093144713374399445805566661859287303778 n + 19290632193749026773594859257978070616175133889640\right) a{\left(n + 70 \right)}}{9096303032810864640 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(32354134569420483856709703190047338044 n^{7} + 15486835582277987026083443715879234853878 n^{6} + 3176916403789929056232363725268134845867814 n^{5} + 362045743032394505249016486092837297019137995 n^{4} + 24754804304060162317698964458775125156645450306 n^{3} + 1015532959164633744858992420741856249862920982787 n^{2} + 23144262512584034659772283162101700007125689201736 n + 226049352946373964565778652267169941117264050549280\right) a{\left(n + 69 \right)}}{9096303032810864640 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(256728318779959348302435753900055057105 n^{7} + 20111318902863332407838302204917944047831 n^{6} + 674161538892860102159001519486726878419276 n^{5} + 12538449172588073179538251070324239044465640 n^{4} + 139760028800703473469048382040455085248988245 n^{3} + 933784706448432527733690448800102319523057329 n^{2} + 3463099499070818749467297991459006537717103094 n + 5500179548869173084020704563399819928358955960\right) a{\left(n + 10 \right)}}{291081697049947668480 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - 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\frac{\left(817736404589237783849013979934679168097588398511239180 n^{7} + 276133657536765827991478236694670178509493244495951309181 n^{6} + 39966179742696156019895246826696246447721859728528649542863 n^{5} + 3213940067377495807314048486072455774512429101178276095133295 n^{4} + 155088209212297010262406987432088394047592944333502964806314505 n^{3} + 4490719344191745144968954153717536057150997708358548562759397364 n^{2} + 72247970995240862529633523562792232797700001099464343118020942812 n + 498200256291250626065017236392150079003091213179920828503404901440\right) a{\left(n + 48 \right)}}{31436823281394348195840 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(980815411922352084029541995857444451672398496169854357 n^{7} + 337494153616731994499551865820098373693884201737453901765 n^{6} + 49774744734141340178299236553903021750987511170033876876031 n^{5} + 4078686372922193983057670079559119212832287771411212909228175 n^{4} + 200550706369139676116009447660034236942214493670516279780926748 n^{3} + 5917265499094671740171031260219801123956940741856806468090638700 n^{2} + 97003518015683473567002866494821469946582541166914681793955709264 n + 681584238148588127870186837396915465545980407181264203907192286080\right) a{\left(n + 49 \right)}}{62873646562788696391680 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(993398405521651708378383987155284584501335263397075779 n^{7} + 294743582855514975351528189625331987847256827002109152435 n^{6} + 37467915646169382281296221004674851761647100590155633884297 n^{5} + 2645330024573206028036630930326389459630073730417204160792825 n^{4} + 112030236948996500643201646299429612531152442820890887097603716 n^{3} + 2845977526340325109000243651710387688360699542595495971343814260 n^{2} + 40155969613167482393353919098286660424631311766505711421188541008 n + 242768285917722822931498194036404174143409392417934588197074221760\right) a{\left(n + 41 \right)}}{20957882187596232130560 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(1018945980558883687198822838167232134590076604856158387 n^{7} + 306833954780455917350411961521064535451628070092719287975 n^{6} + 39597583779279865469188290325500936404885439501613335673649 n^{5} + 2838913571387842343629729730374816511111919121311753816534535 n^{4} + 122117662631618719821177338145389742325902972649973842322279228 n^{3} + 3151725702602925913032569537775705546288792721028284085317889950 n^{2} + 45189645387106962326719908795421284993905377386600086689455462636 n + 277681168866549000160576368852972803614507169943549348684814408320\right) a{\left(n + 42 \right)}}{15718411640697174097920 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(1170511580855651417611600066982818083940417251957910386 n^{7} + 358894071820939170049226948913682205336625902684556661735 n^{6} + 47163785216131340872473429783929092866332552363992857854619 n^{5} + 3443554903642506085074186341813377282922918519120500997031415 n^{4} + 150863786011502630843676004663165755820944527072434018722069399 n^{3} + 3965906624838047709749475973467971790912362193097173192345030310 n^{2} + 57923598931469257859356210892477077876643482797305467945983642936 n + 362593229702856442531289563145157487098164808263634402505582167120\right) a{\left(n + 43 \right)}}{15718411640697174097920 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(1176508121074838569636126839622975885700393020907311267 n^{7} + 367705748153604520672695001948325473920556341306111405700 n^{6} + 49257477331206440924983372459712371671776342523905928847423 n^{5} + 3666183887728736495148826578437228941145031428235639910993120 n^{4} + 163738263925134465378615427200242546932038245748186654820105978 n^{3} + 4388132449576686938638033158232188418949667251719339891801042960 n^{2} + 65339958983116415117947992091644453953387339902956128433428506752 n + 417006668132220017050334575470574349979106803256709039985561099120\right) a{\left(n + 44 \right)}}{15718411640697174097920 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(2475650856763491492100479841504923159602466421505873695 n^{7} + 820172860398848895748473039798873243515211041754778374525 n^{6} + 116463945483387996961006018457911227085600769031221661600823 n^{5} + 9188659405248393733486785336451346350259468614603123312305615 n^{4} + 435022041433541574066633374191003147979107692715219057772297650 n^{3} + 12358590779099527406804329019769951983039132821788898026830043300 n^{2} + 195074983380733580437729726309762279796683530230968881462709901832 n + 1319790365479474624708711909787251166687607330719161553835630941760\right) a{\left(n + 47 \right)}}{62873646562788696391680 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} - \frac{\left(3397440051439347029199827479497464934591664606549672401 n^{7} + 1104017998162420522762466706009371480717474201491493171303 n^{6} + 153770225880506553682675608371299899854709001513327065189453 n^{5} + 11899929989936300074913936348239294726641347763981608603592005 n^{4} + 552606995841561520192792999374576671892231910314594597222744954 n^{3} + 15398845334806794818670968282661364599608800396519401966433358372 n^{2} + 238416305365862912338789983691094248362624490577524776234528028152 n + 1582178345763003553419580884556698900195043013456986519937103225600\right) a{\left(n + 46 \right)}}{62873646562788696391680 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)} + \frac{\left(4215685430946765845664705966667845575259597479325069053 n^{7} + 1343485132872880977380865726965330254352635696943788722209 n^{6} + 183513794610314972752925469967995085619269284105581413447691 n^{5} + 13927716452153488197227647198755585764074223710900152537780395 n^{4} + 634293251294179042932742480533354524985950625162144766435467272 n^{3} + 17334011630402330967762424007844777083614906921371179885391648116 n^{2} + 263198230642420806641349666885344723326851607725176093533750846224 n + 1712920711467186889759967774126854986640300066283381785015061836800\right) a{\left(n + 45 \right)}}{62873646562788696391680 \left(n + 77\right) \left(n + 80\right) \left(n + 81\right) \left(2 n + 157\right) \left(2 n + 161\right) \left(4 n + 313\right) \left(4 n + 315\right)}, \quad n \geq 80
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24555/
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[11,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[11,x]*F[8,x]
F[8,x] = F[71,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]
F[11,x] = x
F[12,x] = F[13,x]+F[56,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[53,x]
F[15,x] = F[16,x]+F[35,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[15,x]+F[20,x]
F[20,x] = F[21,x]+F[47,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[23,x]*F[4,x]
F[23,x] = 1/F[11,x]/F[46,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[6,x]
F[28,x] = F[29,x]+F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[43,x]
F[32,x] = 1/F[11,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[5,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[16,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[11,x]*F[16,x]*F[41,x]
F[41,x] = 1/F[11,x]*F[42,x]
F[42,x] = F[20,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[23,x]*F[45,x]
F[45,x] = F[19,x]+F[32,x]
F[46,x] = F[28,x]+F[4,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[43,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[11,x]*F[23,x]*F[52,x]
F[52,x] = F[43,x]+F[45,x]
F[53,x] = F[0,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[0,x]*F[11,x]*F[23,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[69,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = 1/F[11,x]/F[65,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[53,x]*F[65,x]
F[65,x] = 1/F[11,x]*F[66,x]
F[66,x] = F[2,x]
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[23,x]*F[63,x]
F[69,x] = F[53,x]*F[70,x]
F[70,x] = -F[12,x]+F[41,x]
F[71,x] = F[72,x]
F[72,x] = F[11,x]*F[73,x]
F[73,x] = 1/F[11,x]*F[74,x]
F[74,x] = F[28,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_{11}\! \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_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{71}\! \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_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{56}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{20}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{11}\! \left(x \right) F_{65}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{63}\! \left(x \right)
F_{69}\! \left(x \right) = F_{53}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{41}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{28}\! \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_11(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_11(x)*F_8(x))
Eq(F_8(x), F_71(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_56(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_53(x))
Eq(F_15(x), F_16(x) + F_35(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_15(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_47(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_23(x)*F_4(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_46(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_6(x))
Eq(F_28(x), F_29(x) + F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_43(x))
Eq(F_32(x), F_33(x)/F_11(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_16(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_11(x)*F_16(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_11(x))
Eq(F_42(x), F_20(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_23(x)*F_45(x))
Eq(F_45(x), F_19(x) + F_32(x))
Eq(F_46(x), F_28(x) + F_4(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_11(x)*F_23(x)*F_52(x))
Eq(F_52(x), F_43(x) + F_45(x))
Eq(F_53(x), F_0(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_0(x)*F_11(x)*F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_69(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_11(x)*F_65(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_53(x)*F_65(x))
Eq(F_65(x), F_66(x)/F_11(x))
Eq(F_66(x), F_2(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_23(x)*F_63(x))
Eq(F_69(x), F_53(x)*F_70(x))
Eq(F_70(x), -F_12(x) + F_41(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_11(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_11(x))
Eq(F_74(x), F_28(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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 4, 0, 3, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 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"FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [0, 2]], [[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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], 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{"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [3, 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[1, 2, 0], "pos": [[1, 3], [3, 3], [3, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 6], [0, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 6], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 6], [0, 3], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 6], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 6], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 6], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 6], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 6], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 6], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 6], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"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"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24587/
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[11,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[11,x]*F[8,x]
F[8,x] = F[71,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]
F[11,x] = x
F[12,x] = F[13,x]+F[56,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[53,x]
F[15,x] = F[16,x]+F[35,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[15,x]+F[20,x]
F[20,x] = F[21,x]+F[47,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[23,x]*F[4,x]
F[23,x] = 1/F[11,x]/F[46,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[6,x]
F[28,x] = F[29,x]+F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[43,x]
F[32,x] = 1/F[11,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[5,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[16,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[11,x]*F[16,x]*F[41,x]
F[41,x] = 1/F[11,x]*F[42,x]
F[42,x] = F[20,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[23,x]*F[45,x]
F[45,x] = F[19,x]+F[32,x]
F[46,x] = F[28,x]+F[4,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[43,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[11,x]*F[23,x]*F[52,x]
F[52,x] = F[43,x]+F[45,x]
F[53,x] = F[0,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[0,x]*F[11,x]*F[23,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[69,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = 1/F[11,x]/F[65,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[53,x]*F[65,x]
F[65,x] = 1/F[11,x]*F[66,x]
F[66,x] = F[2,x]
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[23,x]*F[63,x]
F[69,x] = F[53,x]*F[70,x]
F[70,x] = -F[12,x]+F[41,x]
F[71,x] = F[72,x]
F[72,x] = F[11,x]*F[73,x]
F[73,x] = 1/F[11,x]*F[74,x]
F[74,x] = F[28,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_{11}\! \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_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{71}\! \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_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{56}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{20}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{11}\! \left(x \right) F_{65}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{63}\! \left(x \right)
F_{69}\! \left(x \right) = F_{53}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{41}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{28}\! \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_11(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_11(x)*F_8(x))
Eq(F_8(x), F_71(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_56(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_53(x))
Eq(F_15(x), F_16(x) + F_35(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_15(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_47(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_23(x)*F_4(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_46(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_6(x))
Eq(F_28(x), F_29(x) + F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_43(x))
Eq(F_32(x), F_33(x)/F_11(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_16(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_11(x)*F_16(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_11(x))
Eq(F_42(x), F_20(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_23(x)*F_45(x))
Eq(F_45(x), F_19(x) + F_32(x))
Eq(F_46(x), F_28(x) + F_4(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_11(x)*F_23(x)*F_52(x))
Eq(F_52(x), F_43(x) + F_45(x))
Eq(F_53(x), F_0(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_0(x)*F_11(x)*F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_69(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_11(x)*F_65(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_53(x)*F_65(x))
Eq(F_65(x), F_66(x)/F_11(x))
Eq(F_66(x), F_2(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_23(x)*F_63(x))
Eq(F_69(x), F_53(x)*F_70(x))
Eq(F_70(x), -F_12(x) + F_41(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_11(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_11(x))
Eq(F_74(x), F_28(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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 4, 0, 3, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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], [0, 2]], [[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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"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": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, 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"requirements": [[{"patt": [0], "pos": [[2, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 7]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[1, 7]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[2, 7]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[3, 7]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 5]]}, {"patt": [0], "pos": [[4, 6]]}, {"patt": [0, 1], "pos": [[0, 6], [0, 6]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 5]]}, {"patt": [1, 0], "pos": [[0, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[0, 6], [0, 6]]}, {"patt": [1, 0], "pos": [[0, 6], [4, 4]]}, {"patt": [1, 0], "pos": [[2, 5], [2, 5]]}, {"patt": [1, 0], "pos": [[4, 7], [4, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 6], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 3], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 4], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 7], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 6], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [3, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [3, 3], [3, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 6], [0, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 6], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 6], [0, 3], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 6], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 6], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 6], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 6], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 6], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 6], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 6], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"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"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24827/
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[11,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[11,x]*F[8,x]
F[8,x] = F[71,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]
F[11,x] = x
F[12,x] = F[13,x]+F[56,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[53,x]
F[15,x] = F[16,x]+F[35,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[15,x]+F[20,x]
F[20,x] = F[21,x]+F[47,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[23,x]*F[4,x]
F[23,x] = 1/F[11,x]/F[46,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[6,x]
F[28,x] = F[29,x]+F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[43,x]
F[32,x] = 1/F[11,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[5,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[16,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[11,x]*F[16,x]*F[41,x]
F[41,x] = 1/F[11,x]*F[42,x]
F[42,x] = F[20,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[23,x]*F[45,x]
F[45,x] = F[19,x]+F[32,x]
F[46,x] = F[28,x]+F[4,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[43,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[11,x]*F[23,x]*F[52,x]
F[52,x] = F[43,x]+F[45,x]
F[53,x] = F[0,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[0,x]*F[11,x]*F[23,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[69,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = 1/F[11,x]/F[65,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[53,x]*F[65,x]
F[65,x] = 1/F[11,x]*F[66,x]
F[66,x] = F[2,x]
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[23,x]*F[63,x]
F[69,x] = F[53,x]*F[70,x]
F[70,x] = -F[12,x]+F[41,x]
F[71,x] = F[72,x]
F[72,x] = F[11,x]*F[73,x]
F[73,x] = 1/F[11,x]*F[74,x]
F[74,x] = F[28,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_{11}\! \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_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{71}\! \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_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{56}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{20}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{11}\! \left(x \right) F_{65}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{63}\! \left(x \right)
F_{69}\! \left(x \right) = F_{53}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{41}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{28}\! \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_11(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_11(x)*F_8(x))
Eq(F_8(x), F_71(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_56(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_53(x))
Eq(F_15(x), F_16(x) + F_35(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_15(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_47(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_23(x)*F_4(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_46(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_6(x))
Eq(F_28(x), F_29(x) + F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_43(x))
Eq(F_32(x), F_33(x)/F_11(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_16(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_11(x)*F_16(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_11(x))
Eq(F_42(x), F_20(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_23(x)*F_45(x))
Eq(F_45(x), F_19(x) + F_32(x))
Eq(F_46(x), F_28(x) + F_4(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_11(x)*F_23(x)*F_52(x))
Eq(F_52(x), F_43(x) + F_45(x))
Eq(F_53(x), F_0(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_0(x)*F_11(x)*F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_69(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_11(x)*F_65(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_53(x)*F_65(x))
Eq(F_65(x), F_66(x)/F_11(x))
Eq(F_66(x), F_2(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_23(x)*F_63(x))
Eq(F_69(x), F_53(x)*F_70(x))
Eq(F_70(x), -F_12(x) + F_41(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_11(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_11(x))
Eq(F_74(x), F_28(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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 4, 0, 3, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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": 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"requirements": [[{"patt": [0], "pos": [[2, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 7]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[1, 7]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[2, 7]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[3, 7]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 5]]}, {"patt": [0], "pos": [[4, 6]]}, {"patt": [0, 1], "pos": [[0, 6], [0, 6]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 5]]}, {"patt": [1, 0], "pos": [[0, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[0, 6], [0, 6]]}, {"patt": [1, 0], "pos": [[0, 6], [4, 4]]}, {"patt": [1, 0], "pos": [[2, 5], [2, 5]]}, {"patt": [1, 0], "pos": [[4, 7], [4, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 6], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 3], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 4], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 7], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 6], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [3, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [3, 3], [3, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 6], [0, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 6], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 6], [0, 3], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 6], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 6], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 6], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 7], [4, 7], [4, 7], [4, 7]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 6], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 6], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 6], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"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, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 6], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 3], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 6], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"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"}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25026/
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[34,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = k[0]*x*(1+F[7,x,k[0]])*(F[7,x,k[0]]^2+F[7,x,k[0]]+1)
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[34,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]+F[14,x,k[0]]
F[13,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[21,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[7,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[20,x,k[0]]
F[19,x,k[0]] = F[11,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[66,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[34,x]*F[58,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[34,x]*F[35,x,k[0]]
F[27,x,k[0]] = F[26,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[20,x,k[0]]*F[27,x,k[0]]
F[28,x,k[0]] = F[6,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[34,x]
F[31,x,k[0]] = F[18,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[23,x,k[0]]*F[7,x,k[0]]
F[34,x] = x
F[36,x,k[0]] = F[34,x]*F[35,x,k[0]]*F[43,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[64,x,k[0]]
F[38,x,k[0]] = F[2,x]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[20,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[52,x,k[0]]
F[42,x,k[0]] = F[2,x]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[45,x,k[0]] = F[0,x]*F[44,x,k[0]]
F[46,x,k[0]] = F[45,x,k[0]]+F[48,x,k[0]]
F[47,x,k[0]] = F[20,x,k[0]]*F[46,x,k[0]]
F[47,x,k[0]] = F[6,x,k[0]]
F[49,x,k[0]] = F[48,x,k[0]]+F[51,x,k[0]]
F[50,x,k[0]] = F[20,x,k[0]]*F[49,x,k[0]]
F[50,x,k[0]] = F[8,x,k[0]]
F[51,x,k[0]] = F[2,x]*F[44,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[34,x]*F[43,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[59,x,k[0]]
F[55,x,k[0]] = F[0,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[34,x]*F[56,x,k[0]]*F[58,x,k[0]]
F[57,x,k[0]] = F[38,x,k[0]]
F[58,x,k[0]] = 1+x*F[58,x,k[0]]*(F[58,x,k[0]]^2-F[58,x,k[0]]+1)*k[0]
F[59,x,k[0]] = F[60,x,k[0]]*F[61,x]
F[60,x,k[0]] = F[38,x,k[0]]+F[58,x,k[0]]
F[61,x] = -F[0,x]+F[62,x]
F[62,x] = 1/F[34,x]*F[63,x]
F[63,x] = F[2,x]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[20,x,k[0]]*F[38,x,k[0]]*F[43,x,k[0]]*F[58,x,k[0]]
F[44,x,k[0]] = F[58,x,k[0]]+F[66,x,k[0]]
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_{34}\! \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_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x F_{7}\! \left(x , y\right)^{3} y +2 x F_{7}\! \left(x , y\right)^{2} y +2 x F_{7}\! \left(x , y\right) y +y x
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{34}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{34}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{34}\! \left(x \right) = x
F_{36}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{35}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{43}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{34}\! \left(x \right) F_{56}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = x F_{58}\! \left(x , y\right)^{3} y -x F_{58}\! \left(x , y\right)^{2} y +x F_{58}\! \left(x , y\right) y +1
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{61}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{61}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{34}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{38}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{66}\! \left(x , y\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_34(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(F_7(x, k_0) + 1)**3 - k_0*x*(F_7(x, k_0) + 1)**2 + (k_0*x - 1)*(F_7(x, k_0) + 1) + F_7(x, k_0) + 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_34(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0) + F_14(x, k_0))
Eq(F_13(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_20(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_21(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_7(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_20(x, k_0))
Eq(F_19(x, k_0), F_11(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_66(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_34(x)*F_58(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_34(x)*F_35(x, k_0))
Eq(F_27(x, k_0), F_26(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_20(x, k_0)*F_27(x, k_0))
Eq(F_28(x, k_0), F_6(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_34(x))
Eq(F_31(x, k_0), F_18(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_23(x, k_0)*F_7(x, k_0))
Eq(F_34(x), x)
Eq(F_36(x, k_0), F_34(x)*F_35(x, k_0)*F_43(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_64(x, k_0))
Eq(F_38(x, k_0), F_2(x) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_20(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_52(x, k_0))
Eq(F_42(x, k_0), F_2(x)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_45(x, k_0), F_0(x)*F_44(x, k_0))
Eq(F_46(x, k_0), F_45(x, k_0) + F_48(x, k_0))
Eq(F_47(x, k_0), F_20(x, k_0)*F_46(x, k_0))
Eq(F_47(x, k_0), F_6(x, k_0))
Eq(F_49(x, k_0), F_48(x, k_0) + F_51(x, k_0))
Eq(F_50(x, k_0), F_20(x, k_0)*F_49(x, k_0))
Eq(F_50(x, k_0), F_8(x, k_0))
Eq(F_51(x, k_0), F_2(x)*F_44(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_34(x)*F_43(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_59(x, k_0))
Eq(F_55(x, k_0), F_0(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_34(x)*F_56(x, k_0)*F_58(x, k_0))
Eq(F_57(x, k_0), F_38(x, k_0))
Eq(F_58(x, k_0), k_0*x*F_58(x, k_0)**3 - k_0*x*F_58(x, k_0)**2 + k_0*x*F_58(x, k_0) + 1)
Eq(F_59(x, k_0), F_60(x, k_0)*F_61(x))
Eq(F_60(x, k_0), F_38(x, k_0) + F_58(x, k_0))
Eq(F_61(x), -F_0(x) + F_62(x))
Eq(F_62(x), F_63(x)/F_34(x))
Eq(F_63(x), F_2(x))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_20(x, k_0)*F_38(x, k_0)*F_43(x, k_0)*F_58(x, k_0))
Eq(F_44(x, k_0), F_58(x, k_0) + F_66(x, k_0))
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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 4, 0, 3, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 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": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [[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": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, 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3], [4, 3], [4, 3], [4, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 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, 3], [4, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [4, 3], [4, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 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": [[0, 3], [0, 3], [0, 3], [0, 3], [4, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [4, 3]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [3, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[5, 2], [5, 3], [5, 2]]}, {"patt": [1, 2, 0], "pos": [[5, 3], [5, 3], [5, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[5, 3], [5, 3], [5, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [5, 3], [5, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [5, 3], [5, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [5, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [5, 3], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 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, 3], [5, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [5, 3], [5, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 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": [[0, 3], [0, 3], [0, 3], [0, 3], [5, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [5, 3]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[5, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": true}}, {"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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25450/
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[11,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[11,x]*F[8,x]
F[8,x] = F[71,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]
F[11,x] = x
F[12,x] = F[13,x]+F[56,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[53,x]
F[15,x] = F[16,x]+F[35,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[15,x]+F[20,x]
F[20,x] = F[21,x]+F[47,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[23,x]*F[4,x]
F[23,x] = 1/F[11,x]/F[46,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[11,x]*F[27,x]
F[27,x] = F[6,x]
F[28,x] = F[29,x]+F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[43,x]
F[32,x] = 1/F[11,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[5,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[16,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[11,x]*F[16,x]*F[41,x]
F[41,x] = 1/F[11,x]*F[42,x]
F[42,x] = F[20,x]
F[43,x] = F[44,x]
F[44,x] = F[11,x]*F[23,x]*F[45,x]
F[45,x] = F[19,x]+F[32,x]
F[46,x] = F[28,x]+F[4,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[49,x]
F[49,x] = F[43,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[11,x]*F[23,x]*F[52,x]
F[52,x] = F[43,x]+F[45,x]
F[53,x] = F[0,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[0,x]*F[11,x]*F[23,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[69,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = 1/F[11,x]/F[65,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[53,x]*F[65,x]
F[65,x] = 1/F[11,x]*F[66,x]
F[66,x] = F[2,x]
F[67,x] = F[68,x]
F[68,x] = F[11,x]*F[23,x]*F[63,x]
F[69,x] = F[53,x]*F[70,x]
F[70,x] = -F[12,x]+F[41,x]
F[71,x] = F[72,x]
F[72,x] = F[11,x]*F[73,x]
F[73,x] = 1/F[11,x]*F[74,x]
F[74,x] = F[28,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_{11}\! \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_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{71}\! \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_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{56}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{20}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{53}\! \left(x \right) = F_{0}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{11}\! \left(x \right) F_{65}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{63}\! \left(x \right)
F_{69}\! \left(x \right) = F_{53}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{41}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{28}\! \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_11(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_11(x)*F_8(x))
Eq(F_8(x), F_71(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_56(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_53(x))
Eq(F_15(x), F_16(x) + F_35(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_15(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_47(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_23(x)*F_4(x))
Eq(F_23(x), F_24(x)/(F_11(x)*F_46(x)))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_11(x))
Eq(F_27(x), F_6(x))
Eq(F_28(x), F_29(x) + F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_43(x))
Eq(F_32(x), F_33(x)/F_11(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_16(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_11(x)*F_16(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_11(x))
Eq(F_42(x), F_20(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_11(x)*F_23(x)*F_45(x))
Eq(F_45(x), F_19(x) + F_32(x))
Eq(F_46(x), F_28(x) + F_4(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_49(x))
Eq(F_49(x), F_43(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_11(x)*F_23(x)*F_52(x))
Eq(F_52(x), F_43(x) + F_45(x))
Eq(F_53(x), F_0(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_0(x)*F_11(x)*F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_69(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_11(x)*F_65(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_53(x)*F_65(x))
Eq(F_65(x), F_66(x)/F_11(x))
Eq(F_66(x), F_2(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_11(x)*F_23(x)*F_63(x))
Eq(F_69(x), F_53(x)*F_70(x))
Eq(F_70(x), -F_12(x) + F_41(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_11(x)*F_73(x))
Eq(F_73(x), F_74(x)/F_11(x))
Eq(F_74(x), F_28(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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 4, 0, 3, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], 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