02341_02413_02431_03241_20341_20413_20431_24013_24031
Counting sequence:
1, 1, 2, 6, 24, 111, 547, 2783, 14452, 76204, 406705, 2191970, 11909334, 65141671, 358343731, 1980874998, 10996351039, 61269693828, 342499962757, 1920157417231, 10793029539469, 60809129755532, 343334833148072, 1942265134866358, 11007013015216027, 62479641377058714, 355190203115894672, 2022034363099045175, 11525991980376447536, 65779730130492917838, 375833607338435075092, 2149602206250070061697, 12306987527321197752962, 70526353733012293447937, 404514641356305194335529, 2322091686566488575785761, 13340365738237281258587322, 76697622781148483816196641, 441271439341125621043350226, 2540532192501009715867846218, 14636084343253806041116898726, 84371115370443754168207496968, 486653272215511705095897330901, 2808610975531684285356347194965, 16218081388116703366200059007770, 93698761847313428184501742110215, 541609010991261456551337439971163, 3132184174612487615848294081392205, 18122175208605031935764202054533456, 104898118735020406413816852880008604, 607452836687872909206661299836786856, 3519155584288614800412154017858461385, 20395733275927907425805983780198329694, 118252242585793032516936802590506505265, 685872228020484562592637059754905860413, 3979565661641737833081175917618713467580, 23098398928809420900184237173241125347410, 134114951405125062167064221837087358987004, 778963722088183847536939848063259885609320, 4525825447299739846961701518344794083462120, 26303583290762453059671551235391966801220900, 152920173302032041228935734500163285340927053, 889290748382820100154861533269611276891019670, 5173070934009148002387418178086335912930187968, 30100620764638951689996126540905478079466154018, 175194983155110144622787404791220986231084172269, 1019962122992878498568112299363073240097835055516, 5939633995464556075222532786055655991844211258259, 34597586267369996938083891747967466204952644309255, 201576416848723891236726595850818865199414078319822, 1174732210793229889589122220743298787916922138073532, 6847638118792202432746111662395675231422228084762528, 39924833888190812895415766161285768879491556296961422, 232832468511348442548083401550025603499755868430520821, 1358125405696850793497286795335944232062809263223177488, 7923735829434622013671262270280200812984292022454876916, 46239362722106842427844113126730171332108029107027466264, 269887924562738279248427349937996813933195496059109053986, 1575588933024661093826751527612397831199009256291481314184, 9200012154423453363620597370547144362688511569928299178996, 53730157089852791126403700734096862221204647456136638601904, 313855920836703630518046984653301440668639849816541479374125, 1833679291298421084238851714051410510252777924363632970686317, 10715085938417984063282259009528752332016010657606010262809475, 62624691074315185951765220115721033504260594307304281982570754, 366076354618883123586733979156897097376652251788036374666626391, 2140289068528453876009768210466709714229235652306112130495819064, 12515449042124880127255872136843743908320288087246787539745833106, 73196835054893069984074028823900565327848037102463509275682209090, 428162561729536792661707411162402337819421521910316587877155288300, 2504922493530584202567401891266012131279904375902047140034285825609, 14657092964687293922021650890758095431085404928435464018880958193623, 85776457672027596863227745325671483373952978770621712758866424083381, 502057995977984873295286605523684492621362416320912803721242671806481, 2939030005248139919979515069519010662087100178676604989366956029383509, 17207483737576652228484851348485625435249490512986476691821002751726901, 100761083197614232504550573988991410766558486334406021613439488445210335, 590105040233173186246293925092359636467868789664290696746963166568108522, 3456414432619873798130181269011800583081581161343160132895575126372873264, 20247959554258457815966768375113621304151386924709193949144760090340483810, 118630044601152837052625365052079252578849037053993748029967762045482304740
Implicit equation for the generating function in Maple syntax:
x^2*(x-1)*F(x)^9-x*(9*x^2-8*x+1)*F(x)^8+(4*x-1)*(5*x^2-x-1)*F(x)^7+(-13*x^3-20*x^2+18*x-3)*F(x)^6+(41*x^2-18*x+1)*F(x)^5+(-19*x^2-9*x+5)*F(x)^4+(21*x-5)*F(x)^3+(-8*x-1)*F(x)^2+3*F(x)-1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(x -1\right) F \! \left(x \right)^{9}-x \left(9 x^{2}-8 x +1\right) F \! \left(x \right)^{8}+\left(4 x -1\right) \left(5 x^{2}-x -1\right) F \! \left(x \right)^{7}+\left(-13 x^{3}-20 x^{2}+18 x -3\right) F \! \left(x \right)^{6}+\left(41 x^{2}-18 x +1\right) F \! \left(x \right)^{5}+\left(-19 x^{2}-9 x +5\right) F \! \left(x \right)^{4}+\left(21 x -5\right) F \! \left(x \right)^{3}+\left(-8 x -1\right) F \! \left(x \right)^{2}+3 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) = 111
a(6) = 547
a(7) = 2783
a(8) = 14452
a(9) = 76204
a(10) = 406705
a(11) = 2191970
a(12) = 11909334
a(13) = 65141671
a(14) = 358343731
a(15) = 1980874998
a(16) = 10996351039
a(17) = 61269693828
a(18) = 342499962757
a(19) = 1920157417231
a(20) = 10793029539469
a(21) = 60809129755532
a(22) = 343334833148072
a(23) = 1942265134866358
a(24) = 11007013015216027
a(25) = 62479641377058714
a(26) = 355190203115894672
a(27) = 2022034363099045175
a(28) = 11525991980376447536
a(29) = 65779730130492917838
a(30) = 375833607338435075092
a(31) = 2149602206250070061697
a(32) = 12306987527321197752962
a(33) = 70526353733012293447937
a(34) = 404514641356305194335529
a(35) = 2322091686566488575785761
a(36) = 13340365738237281258587322
a(37) = 76697622781148483816196641
a(38) = 441271439341125621043350226
a(39) = 2540532192501009715867846218
a(40) = 14636084343253806041116898726
a(41) = 84371115370443754168207496968
a(42) = 486653272215511705095897330901
a(43) = 2808610975531684285356347194965
a(44) = 16218081388116703366200059007770
a(45) = 93698761847313428184501742110215
a(46) = 541609010991261456551337439971163
a(47) = 3132184174612487615848294081392205
a(48) = 18122175208605031935764202054533456
a(49) = 104898118735020406413816852880008604
a(50) = 607452836687872909206661299836786856
a(51) = 3519155584288614800412154017858461385
a(52) = 20395733275927907425805983780198329694
a(53) = 118252242585793032516936802590506505265
a(54) = 685872228020484562592637059754905860413
a(55) = 3979565661641737833081175917618713467580
a(56) = 23098398928809420900184237173241125347410
a(57) = 134114951405125062167064221837087358987004
a(58) = 778963722088183847536939848063259885609320
a(59) = 4525825447299739846961701518344794083462120
a(60) = 26303583290762453059671551235391966801220900
a(61) = 152920173302032041228935734500163285340927053
a(62) = 889290748382820100154861533269611276891019670
a(63) = 5173070934009148002387418178086335912930187968
a(64) = 30100620764638951689996126540905478079466154018
a(65) = 175194983155110144622787404791220986231084172269
a(66) = 1019962122992878498568112299363073240097835055516
a(67) = 5939633995464556075222532786055655991844211258259
a(68) = 34597586267369996938083891747967466204952644309255
a(69) = 201576416848723891236726595850818865199414078319822
a(70) = 1174732210793229889589122220743298787916922138073532
a(71) = 6847638118792202432746111662395675231422228084762528
a(72) = 39924833888190812895415766161285768879491556296961422
a(73) = 232832468511348442548083401550025603499755868430520821
a(74) = 1358125405696850793497286795335944232062809263223177488
a(75) = 7923735829434622013671262270280200812984292022454876916
a(76) = 46239362722106842427844113126730171332108029107027466264
a(77) = 269887924562738279248427349937996813933195496059109053986
a(78) = 1575588933024661093826751527612397831199009256291481314184
a(79) = 9200012154423453363620597370547144362688511569928299178996
a(80) = 53730157089852791126403700734096862221204647456136638601904
a(81) = 313855920836703630518046984653301440668639849816541479374125
a(82) = 1833679291298421084238851714051410510252777924363632970686317
a(83) = 10715085938417984063282259009528752332016010657606010262809475
a(84) = 62624691074315185951765220115721033504260594307304281982570754
a(85) = 366076354618883123586733979156897097376652251788036374666626391
a(86) = 2140289068528453876009768210466709714229235652306112130495819064
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n >= 87
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 111
a(6) = 547
a(7) = 2783
a(8) = 14452
a(9) = 76204
a(10) = 406705
a(11) = 2191970
a(12) = 11909334
a(13) = 65141671
a(14) = 358343731
a(15) = 1980874998
a(16) = 10996351039
a(17) = 61269693828
a(18) = 342499962757
a(19) = 1920157417231
a(20) = 10793029539469
a(21) = 60809129755532
a(22) = 343334833148072
a(23) = 1942265134866358
a(24) = 11007013015216027
a(25) = 62479641377058714
a(26) = 355190203115894672
a(27) = 2022034363099045175
a(28) = 11525991980376447536
a(29) = 65779730130492917838
a(30) = 375833607338435075092
a(31) = 2149602206250070061697
a(32) = 12306987527321197752962
a(33) = 70526353733012293447937
a(34) = 404514641356305194335529
a(35) = 2322091686566488575785761
a(36) = 13340365738237281258587322
a(37) = 76697622781148483816196641
a(38) = 441271439341125621043350226
a(39) = 2540532192501009715867846218
a(40) = 14636084343253806041116898726
a(41) = 84371115370443754168207496968
a(42) = 486653272215511705095897330901
a(43) = 2808610975531684285356347194965
a(44) = 16218081388116703366200059007770
a(45) = 93698761847313428184501742110215
a(46) = 541609010991261456551337439971163
a(47) = 3132184174612487615848294081392205
a(48) = 18122175208605031935764202054533456
a(49) = 104898118735020406413816852880008604
a(50) = 607452836687872909206661299836786856
a(51) = 3519155584288614800412154017858461385
a(52) = 20395733275927907425805983780198329694
a(53) = 118252242585793032516936802590506505265
a(54) = 685872228020484562592637059754905860413
a(55) = 3979565661641737833081175917618713467580
a(56) = 23098398928809420900184237173241125347410
a(57) = 134114951405125062167064221837087358987004
a(58) = 778963722088183847536939848063259885609320
a(59) = 4525825447299739846961701518344794083462120
a(60) = 26303583290762453059671551235391966801220900
a(61) = 152920173302032041228935734500163285340927053
a(62) = 889290748382820100154861533269611276891019670
a(63) = 5173070934009148002387418178086335912930187968
a(64) = 30100620764638951689996126540905478079466154018
a(65) = 175194983155110144622787404791220986231084172269
a(66) = 1019962122992878498568112299363073240097835055516
a(67) = 5939633995464556075222532786055655991844211258259
a(68) = 34597586267369996938083891747967466204952644309255
a(69) = 201576416848723891236726595850818865199414078319822
a(70) = 1174732210793229889589122220743298787916922138073532
a(71) = 6847638118792202432746111662395675231422228084762528
a(72) = 39924833888190812895415766161285768879491556296961422
a(73) = 232832468511348442548083401550025603499755868430520821
a(74) = 1358125405696850793497286795335944232062809263223177488
a(75) = 7923735829434622013671262270280200812984292022454876916
a(76) = 46239362722106842427844113126730171332108029107027466264
a(77) = 269887924562738279248427349937996813933195496059109053986
a(78) = 1575588933024661093826751527612397831199009256291481314184
a(79) = 9200012154423453363620597370547144362688511569928299178996
a(80) = 53730157089852791126403700734096862221204647456136638601904
a(81) = 313855920836703630518046984653301440668639849816541479374125
a(82) = 1833679291298421084238851714051410510252777924363632970686317
a(83) = 10715085938417984063282259009528752332016010657606010262809475
a(84) = 62624691074315185951765220115721033504260594307304281982570754
a(85) = 366076354618883123586733979156897097376652251788036374666626391
a(86) = 2140289068528453876009768210466709714229235652306112130495819064
a{\left(n + 87 \right)} = \frac{39122438738332808459918740932444761258348297982873 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(2 n + 1\right) \left(2 n + 3\right) \left(2 n + 5\right) a{\left(n \right)}}{60910287516800000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{291395052929841516303921 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(2 n + 3\right) \left(2 n + 5\right) \left(14365096103148062082999067485 n^{2} + 118582064886263796829527188624 n + 246743593476714857906177083975\right) a{\left(n + 1 \right)}}{60910287516800000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{246318726060728247087 \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(2 n + 5\right) \left(3125977205185719539958532305881497 n^{4} + 56674558920807546248101326000451454 n^{3} + 385073595866310938334254630804859349 n^{2} + 1159110929252502017651085356650386572 n + 1300606574006347087417451618965809060\right) a{\left(n + 2 \right)}}{243641150067200000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{11729463145748964147 \left(n + 3\right) \left(n + 4\right) \left(3452470605614231958745688490200090627 n^{6} + 101999107608852831759679546324387687536 n^{5} + 1252575644022286505736808254115367716235 n^{4} + 8176195086312917902324288887435559702236 n^{3} + 29892965960473683839600988765236696483006 n^{2} + 57988742514423385088076053493851080973616 n + 46586782360354113804349479349184931695880\right) a{\left(n + 3 \right)}}{487282300134400000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{1675637592249852021 \left(n + 4\right) \left(189553857405830724531795522062153340500 n^{7} + 7265169060454855230465145688846778036105 n^{6} + 118944881987533672731784792868875890972524 n^{5} + 1077837519065789712203263555695261713993886 n^{4} + 5836319038917557086111746607848271867498706 n^{3} + 18878883998709487838492295314535935705217201 n^{2} + 33770513190492506211905418878316913818334182 n + 25765281127080835435858452576529852573958160\right) a{\left(n + 4 \right)}}{487282300134400000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{3 \left(634105905708036 n^{2} + 106152169017024763 n + 4442293179638156542\right) a{\left(n + 86 \right)}}{7613785939600 \left(n + 88\right) \left(2 n + 173\right)} - \frac{\left(72331916165301329800 n^{4} + 24078228959533044829964 n^{3} + 3005674219480276620129115 n^{2} + 166751019620373454273589637 n + 3469111960411764709665447726\right) a{\left(n + 85 \right)}}{2436411500672000 \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(107994960366858364704532 n^{5} + 44493005591585748111604849 n^{4} + 7332334948112939613047830895 n^{3} + 604178510872967000583855314798 n^{2} + 24892057608922217804463156911412 n + 410222019680097277698134494935192\right) a{\left(n + 84 \right)}}{97456460026880000 \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{\left(447352934344727277720751361 n^{6} + 219359933925600598052069478025 n^{5} + 44818581648071889367184791040559 n^{4} + 4883854637268195027378542984374415 n^{3} + 299360869094529191517649383127420996 n^{2} + 9786587397287252763720083878422791436 n + 133309643441735653642636028765549604720\right) a{\left(n + 83 \right)}}{15593033604300800000 \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(164389077454571155404875139902 n^{7} + 93426666025859774847553037627395 n^{6} + 22755850430584089876248610472762410 n^{5} + 3079242894697239803202916261087214417 n^{4} + 250004191669279155123692354431688864512 n^{3} + 12178762164590867597632915396039064817348 n^{2} + 329600469607316680508354870135207377215696 n + 3822936460952610334081074337743386541707520\right) a{\left(n + 82 \right)}}{311860672086016000000 \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{3 \left(105726715827128883895886682090921 n^{8} + 68451144639573705501661532851393878 n^{7} + 19387938296213570451406896090674490896 n^{6} + 3137774373378433622996335143395755299046 n^{5} + 317372547883382829745561305449000403301059 n^{4} + 20543519563222191559121385041762580585282452 n^{3} + 831071807384802081466967957010115548948734404 n^{2} + 19210678680411955105338450500499318283726047984 n + 194269106191942404184537215972182600376796235520\right) a{\left(n + 81 \right)}}{49897707533762560000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(2961580933484756795543605362513458 n^{8} + 1986092370851205642772796692082902268 n^{7} + 581078097092278275622539957481985163845 n^{6} + 96901862898005917661226681999445852464143 n^{5} + 10076578010362140816458235118438947454580717 n^{4} + 669215899144827795506750303717008710546029897 n^{3} + 27724853656380187289058500851705851044793348540 n^{2} + 655197257436490539083209571149295972190628559052 n + 6763177486730119061717606073890891727436778804160\right) a{\left(n + 80 \right)}}{124744268834406400000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{3 \left(14105733815699524291773042721662903477 n^{8} + 8622003819203654612234868229347733548036 n^{7} + 2304068208674512245425621566553376891700114 n^{6} + 351580156356678546255666223890778236375904032 n^{5} + 33503898521011115975129406934794017810166747133 n^{4} + 2041684692737749476225250452666988594927301114604 n^{3} + 77693203041321694504506099462694815416216925501436 n^{2} + 1687862218702831867828268406285335152521019288498608 n + 16026588375729364147233976560524407547486570242026240\right) a{\left(n + 79 \right)}}{39918166027010048000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{239376798892836003 \left(4316727043087716421654313490931184695733 n^{8} + 174000016736974432357190098308292799836901 n^{7} + 2820769721144442462642843086694902183213540 n^{6} + 22106760210953397359912767976206352232638306 n^{5} + 63991752175763060924333546385167144430891377 n^{4} - 249634675975255694194002721011478687000727311 n^{3} - 2626564020479201762207528722576019541848632650 n^{2} - 8075114612516576120309283262611308225261578776 n - 8994023584670895120087771467591481475374864480\right) a{\left(n + 5 \right)}}{487282300134400000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{\left(6746341402891648549917762252951263029939 n^{8} + 4125492690441459438207805956495732558148132 n^{7} + 1103532753257243074190176255302689122705462654 n^{6} + 168646921727810598211439854748490547452337134544 n^{5} + 16105394397215350170705738803289124432946628329611 n^{4} + 984151215767429878665701548653246084525766398077788 n^{3} + 37579204367724491771506696702777900910800073855194116 n^{2} + 819800445218476772691676075486794308509705060203100656 n + 7822708449727606523624352380960851215406472186805392640\right) a{\left(n + 78 \right)}}{199590830135050240000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(317980976217063938072692412430273711652100 n^{8} + 192742144128532911749804863786631172048351995 n^{7} + 51108455094670592110899091037894115562093700678 n^{6} + 7743415322647911644681958729780032632194781211324 n^{5} + 733184791371970834535022616206197429951265138597770 n^{4} + 44425739189829235152260764917336136856042804050868765 n^{3} + 1682269170239005362323423820820681186509358330725098892 n^{2} + 36397962136455597038030325415549404430849697114723879676 n + 344504347163088131206079972200784784369583107464959728720\right) a{\left(n + 77 \right)}}{498977075337625600000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{34196685556119429 \left(542467677282945738489758125205257634164895 n^{8} + 40585117032917080003908591832318334154688988 n^{7} + 1271182437160883994928873785285023334254005646 n^{6} + 22061781203640519193257107712911572723328714438 n^{5} + 233858225136436701967995498458324777996722902095 n^{4} + 1558036600525209456201461613519161820373354137422 n^{3} + 6392144677813205323636631931890862238516086884604 n^{2} + 14799407139873041091286507087815106792543802314872 n + 14829101157413066890976089463096797755915739748160\right) a{\left(n + 6 \right)}}{974564600268800000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{34196685556119429 \left(21260713772782591006896717810299618126081504 n^{8} + 1571738617424101985276810818274469817758557213 n^{7} + 50390702639967284189511535631935556059864288661 n^{6} + 916122018136270579525949725855942832776273327793 n^{5} + 10338819451330818188837904936810858497229985387511 n^{4} + 74213597257869274872052358031719381647709770125002 n^{3} + 331062779301439294480496023656949497120661338136644 n^{2} + 839475124016688583879754298175901136474422035999032 n + 926685575268930888342279476690209211603134061722560\right) a{\left(n + 7 \right)}}{1949129200537600000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - 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\frac{3 \left(748326675167109210114519007558218076893924798365575793324435844346299 n^{8} + 171475663633410730461406073107614986072069746428989616614012455691949116 n^{7} + 17197492009838929007102116426026335875400540603655713302926405864830414290 n^{6} + 985960215157968223718791846733038141504583605691656348454081321556828703740 n^{5} + 35342699285675520900235688913605885799950624599876552671869359790923708031951 n^{4} + 811114796721017888691097102977430193761170567191340252821651516746839588134824 n^{3} + 11638673618538426027027877431383898819469638883425653236390426579847182317338340 n^{2} + 95464375500877034936970712468730922894867848994733448416670161320094811271534240 n + 342695283810082421468330781397365290196208931222471331408442088829060967871583360\right) a{\left(n + 28 \right)}}{15593033604300800000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(1225462210291616330132045716755571307909584343771095795125020829957079 n^{8} + 323822072466751856502794867014005794823905548779192376904411962769147458 n^{7} + 37429404562013716336914611821973624777202016277510845853667770319136343716 n^{6} + 2471686498478819980939507595864722166882317110989015169654812343097304900062 n^{5} + 101989506602108101175032911361444926587563599966690643221415213556085098682001 n^{4} + 2692701056500654244550449474140073593107984567440500685074995265003790436159952 n^{3} + 44420112065130901118264728158553275780412732498583219145099546634148516280065844 n^{2} + 418600254577975891015313261012741996189403700910381767344663743137181410937617488 n + 1725243886945713272611071531714289146675559202921760978462371739444284609591645760\right) a{\left(n + 33 \right)}}{7796516802150400000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(1278406117679707796939499424127290262002840407485892496577657506028567 n^{8} + 349926836791502426652007592310557555635004251191994498660926992027384036 n^{7} + 41837670374716422656749180790098240702999186094433659358498317255901490610 n^{6} + 2853313005047395826989753204938124874099572689442793463721345185216005355356 n^{5} + 121382620360821083520525840209389565123943824938312193048876866152415725313163 n^{4} + 3297550963525552512144574514843807862365642992841606336149376909408893672200464 n^{3} + 55852415244532152122032327846649289032519142885031654779982546174413037373678700 n^{2} + 539086567761466351189060351576559926711216420495568595697495638233182117857018864 n + 2269357147582595532093525737854604199235525483855081991799165700759277602199098560\right) a{\left(n + 35 \right)}}{15593033604300800000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{\left(1300181510818848973081342517890082331959824104204863650435599887778965 n^{8} + 353016670208219036243845306370074744898346665806070216448921412316510972 n^{7} + 41674745968176798395843117663478659730500735002857329509854738859745410754 n^{6} + 2790696409942189447364488691595863590867137505399106196753028488257805199232 n^{5} + 115763310776668991189990482300211983142993785025310951663792455755547774277485 n^{4} + 3039946088073449783973430659697181851812732147483370137548144703143718542390708 n^{3} + 49213427922545775563364800245830996917727747845678105550073742473051932065279676 n^{2} + 447269904683515371362847021911102804204714024923481677427283843070512709345307088 n + 1736720409152472055162703351049198250036268369975592715793650292274833134792448640\right) a{\left(n + 36 \right)}}{31186067208601600000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} - \frac{\left(1446861740875706948395319136731332187532134709854169340597806215486519 n^{8} + 352862374033660933094444451090385019880631235667008834068357640275635404 n^{7} + 37659272523709208551952865036953932059759326174987818174061047882937811464 n^{6} + 2297245673299395361794345420694186898584049029721642835914004967914034655318 n^{5} + 87604557044215722657158110843698639742344105094996430262648026145673930647041 n^{4} + 2138584079592426560889712342621359910528979216715830309859187892063975035741886 n^{3} + 32636457342900339030402418198395726964357727497500516895093767621623032294689696 n^{2} + 284665779028525620536699853051328356844764055831845393983731978734676759785716832 n + 1086515028745102175736475083695797768610055223801991555043935212166747811026744160\right) a{\left(n + 30 \right)}}{7796516802150400000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(1484154057460065325145950326350508114334949282051929130215369244767849 n^{8} + 372506564170831584796971689696408883040238838527099245600799440686279700 n^{7} + 40910610301929328023012092968870753510445335995034039695496691878334678464 n^{6} + 2567823894617438168510774121054838458488502918448412738579955709475074122022 n^{5} + 100747901450824981777156703600143252102388633901741144320830252088541808175371 n^{4} + 2530138657477455990907293494077937490111071933181551132165206832990228063971630 n^{3} + 39717894586975110243951951783276635616027765627853703600989379201786971149711996 n^{2} + 356319462097768066532114210017181393073441710788208815735876703720014666486873608 n + 1398673121640309755492082403646147627409414811843735954611880867621877419829780640\right) a{\left(n + 31 \right)}}{7796516802150400000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)} + \frac{\left(2631838159707739781572570444568616748091482865325749451004423220650795 n^{8} + 622653336316100365917344616733449517946405722962717293596592697267586036 n^{7} + 64469636328048520403317991602872656688448812952632701223554846551285137946 n^{6} + 3815632363428586492285302100884390328388851145326129161660814957912624109380 n^{5} + 141187090459765913550265492165647547541232082001150279779746128376331663890655 n^{4} + 3344546331986979101650763701032215913068734704514937677252887478335543086469304 n^{3} + 49532455239260467998171860406439982113722603966805010808152760436003363506058044 n^{2} + 419306321563953204450269200038325895424637176734848955443676644794054886359742320 n + 1553368619638302711731371473810833581472532287446451580270489717198174548547502080\right) a{\left(n + 29 \right)}}{15593033604300800000000000000000000 \left(n + 83\right) \left(n + 84\right) \left(n + 85\right) \left(n + 86\right) \left(n + 87\right) \left(n + 88\right) \left(2 n + 171\right) \left(2 n + 173\right)}, \quad n \geq 87
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24473/
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[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[34,x]
F[15,x] = F[16,x]*F[18,x]
F[16,x] = F[17,x]+F[7,x]
F[17,x] = F[0,x]*F[2,x]*F[9,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[18,x]*F[19,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[19,x]*F[22,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[22,x]*F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]^2*F[22,x]
F[34,x] = F[35,x]
F[35,x] = F[18,x]^2*F[11,x]*F[16,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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{22}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{11}\! \left(x \right) F_{16}\! \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_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_34(x))
Eq(F_15(x), F_16(x)*F_18(x))
Eq(F_16(x), F_17(x) + F_7(x))
Eq(F_17(x), F_0(x)*F_2(x)*F_9(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_18(x)*F_19(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_19(x)*F_22(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_22(x)*F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)**2*F_22(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_16(x)*F_18(x)**2)
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, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [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, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [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:
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"pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "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": "Rule", "comb_class": {"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, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 6]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "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": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[2, 6]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24600/
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[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[34,x]
F[15,x] = F[16,x]*F[18,x]
F[16,x] = F[17,x]+F[7,x]
F[17,x] = F[0,x]*F[2,x]*F[9,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[18,x]*F[19,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[19,x]*F[22,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[22,x]*F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]^2*F[22,x]
F[34,x] = F[35,x]
F[35,x] = F[18,x]^2*F[11,x]*F[16,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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{22}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{11}\! \left(x \right) F_{16}\! \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_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_34(x))
Eq(F_15(x), F_16(x)*F_18(x))
Eq(F_16(x), F_17(x) + F_7(x))
Eq(F_17(x), F_0(x)*F_2(x)*F_9(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_18(x)*F_19(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_19(x)*F_22(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_22(x)*F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)**2*F_22(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_16(x)*F_18(x)**2)
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:
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"pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "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": "Rule", "comb_class": {"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, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 6]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "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": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[2, 6]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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://www.permpal.com/tree/25325/
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[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[34,x]
F[15,x] = F[16,x]*F[18,x]
F[16,x] = F[17,x]+F[7,x]
F[17,x] = F[0,x]*F[2,x]*F[9,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[18,x]*F[19,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[19,x]*F[22,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[22,x]*F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]^2*F[22,x]
F[34,x] = F[35,x]
F[35,x] = F[18,x]^2*F[11,x]*F[16,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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{22}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{11}\! \left(x \right) F_{16}\! \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_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_34(x))
Eq(F_15(x), F_16(x)*F_18(x))
Eq(F_16(x), F_17(x) + F_7(x))
Eq(F_17(x), F_0(x)*F_2(x)*F_9(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_18(x)*F_19(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_19(x)*F_22(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_22(x)*F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)**2*F_22(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_16(x)*F_18(x)**2)
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, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [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, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [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:
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"pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "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": "Rule", "comb_class": {"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, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 6]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "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": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[2, 6]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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://www.permpal.com/tree/25769/
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[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[34,x]
F[15,x] = F[16,x]*F[18,x]
F[16,x] = F[17,x]+F[7,x]
F[17,x] = F[0,x]*F[2,x]*F[9,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[18,x]*F[19,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[19,x]*F[22,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[22,x]*F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]^2*F[22,x]
F[34,x] = F[35,x]
F[35,x] = F[18,x]^2*F[11,x]*F[16,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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{22}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{11}\! \left(x \right) F_{16}\! \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_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_34(x))
Eq(F_15(x), F_16(x)*F_18(x))
Eq(F_16(x), F_17(x) + F_7(x))
Eq(F_17(x), F_0(x)*F_2(x)*F_9(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_18(x)*F_19(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_19(x)*F_22(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_22(x)*F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)**2*F_22(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_16(x)*F_18(x)**2)
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:
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"pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "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": "Rule", "comb_class": {"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, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 6]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "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": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[2, 6]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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 5
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25886/
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[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[34,x]
F[15,x] = F[16,x]*F[18,x]
F[16,x] = F[17,x]+F[7,x]
F[17,x] = F[0,x]*F[2,x]*F[9,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[18,x]*F[19,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[19,x]*F[22,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[22,x]*F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]^2*F[22,x]
F[34,x] = F[35,x]
F[35,x] = F[18,x]^2*F[11,x]*F[16,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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{22}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{11}\! \left(x \right) F_{16}\! \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_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_34(x))
Eq(F_15(x), F_16(x)*F_18(x))
Eq(F_16(x), F_17(x) + F_7(x))
Eq(F_17(x), F_0(x)*F_2(x)*F_9(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_18(x)*F_19(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_19(x)*F_22(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_22(x)*F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)**2*F_22(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_16(x)*F_18(x)**2)
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:
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