01243_01342_01432_02143_12043
Counting sequence:
1, 1, 2, 6, 24, 115, 619, 3614, 22425, 145949, 987202, 6893335, 49438329, 362740391, 2714363788, 20662617662, 159680428208, 1250616610866, 9912426144516, 79412985020237, 642403934275837, 5242541310220385, 43127658033271436, 357401452129797811, 2981844789342013211, 25033068597336342465, 211368946612653353598, 1794262398491511423332, 15306888618146833564376, 131189452840178548861565, 1129252305226827112765069, 9759881651912524746356972, 84674362085592572702721849, 737250432532110307066079223, 6440865724420045101899220182, 56449159317315195316773101261, 496225824569807885796611093825, 4374621870951685482326868783138, 38670247595900062818914108612813, 342712146121234297128726408000159, 3044691866660954973015220224431710, 27112379906334912015999083485776022, 241966414255960221101704933446758842, 2164021860188473826336891616125289331, 19393054383809145220551806332720781745, 174128720782854317792104051385251793883, 1566384211110269979656046625521032644140, 14115498059404196035282883046638985875509, 127418515588503055289989560745236407159685, 1152066662212119264053730709908115564075257, 10432862310502697299683486327488487837671710, 94620191965347832390738490187154659860909142, 859397010272997922192016988541440033199006236, 7816459542057360321970506838652892620149263051, 71188593774951986010702444939991124282403552921, 649193065459501686544496999815822042518286410448, 5927623489928743176205779188203256667981424821825, 54189084318015948610975073709969078961035881562217, 495963393376419356458058948107529024344899489050960, 4544405562518142852841839014813647041385372568547417, 41684833510484413944369253532615291074075389749222449, 382769434507401225543095808742768087484995912794791003, 3518357907277450401909603023318215719539533543780904288, 32372217636243285788252767228091744348233773762486559772, 298140711858453477282420478748861881348697467166969366676, 2748361446368383184877384255689058999597328835653992425540, 25358177953969446935186739939935815019920588968310130556570, 234175963269492137217458905144729405530162294290849016695379, 2164390411356318351965252781835966289913055872018382854303777, 20021071738026883267074295119609056735647964182472811862270259, 185347761114656504395098787911753646029432673937268888623104338, 1717220088553484286465924518592980204892027676363747148056684773, 15921862212722012630633514039020455276080749077507382884464305547, 147734564857713125447277472478845608074182875389573598104373462397, 1371772705357934573109222639293004552634909132336681505876348289936, 12746347352273971430321525394961470582524498780883433677384334779228, 118518182621526625632715016918236537513222046042804205755604552772274, 1102737781533626562557655855741124335872134914784791892067353095091704, 10266921644940991618727396113741253458419763999276328193879581131360268, 95649327921665896312225853149044845808450175027404812439061898492211863, 891641967945833803920713142359734259148784295248228430177810558376091159, 8316861221226233444002219836426721324876172689004236631400427935547396981, 77621581829844252705043347221045797886143785409159400423694657919036838814, 724859001894482887926513378854216305041436581069771115368853223751458595501, 6772776520180151434074441349789780055817375716208390452203739577037341250263, 63316436930722737694253698595514604510757519257435745273408523480863967927338, 592239336306891540307415232972099799766809663016292093783288680566778297685111, 5542476063621603554409576546263027745361012084497909245286954018883357016982335, 51895668261171155858637611658012752945991487156634331891517578666309526861689174, 486154353494645459009547051562430499136645443566792640977286807129885727208875842, 4556467553681558144869231859413802536604136650735297658562423887829520821286348258, 42725663645827642137185230875102003166827416418522072677024572363384105343868547571, 400821799513032653277736577728224157536188264101409443341272544186919417642575197015, 3761937032632801755275981420473299327992679355591230533415991362238332611259353136809, 35323620517856882058945321244055769213805339221131558096693032288620839820541294305590, 331824430082273128908941222567955282074554770071430316302950678131328709411775470431955, 3118437510036088177704505885279808067400466533946500598278277245686805918611663606380747, 29318887022961229241186305824067864123799533379986265167462820386921464529719735314547997, 275762989908203181547200907605860120643237913412494549027938111999909793414212122598010570, 2594770627702535885964765048214412524742884700895186144339117798518320134086669977994604520, 24424911460664794045356315653281799492338970823679465378257637265381703192158224514722245228
Specification 1
Strategy pack name: all_the_strategies_2_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24383/
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[4,x,1]
F[4,x,k[0]] = F[5,x]*F[6,x,k[0]]
F[5,x] = x
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[8,x,k[0]] = F[9,x,k[0],1]
F[9,x,k[0],k[1]] = F[10,x,k[0],k[0]*k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0]]*F[12,x,k[0],k[1]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[39,x,k[1],k[0]]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[14,x,k[0],k[1]]*k[0]-F[14,x,1,k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[5,x]
F[15,x,k[0],k[1]] = F[16,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[1,x]+F[17,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[17,x,k[0],k[1]] = F[13,x,k[1],k[0]]
F[18,x,k[0],k[1]] = F[19,x,k[1],k[0]]
F[19,x,k[0],k[1]] = F[11,x,k[0]]*F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[1],k[0]]
F[21,x,k[0],k[1]] = F[1,x]+F[22,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[38,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[1],k[0]]
F[23,x,k[0],k[1]] = (F[24,x,k[0],1]*k[0]-F[24,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[24,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[1],k[0]]
F[26,x,k[0],k[1]] = (F[27,x,k[0],1]*k[0]-F[27,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[27,x,k[0],k[1]] = F[19,x,k[0],k[0]*k[1]]
F[28,x,k[0],k[1]] = F[29,x,k[1],k[0]]
F[29,x,k[0],k[1]] = (F[30,x,k[0],1]*k[0]-F[30,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[11,x,k[0]]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[0]*k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[1],k[0]]
F[33,x,k[0],k[1]] = F[1,x]+F[22,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[34,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[11,x,k[1]]*F[33,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = k[0]*x
F[38,x,k[0],k[1]] = F[33,x,k[0],k[1]]*F[36,x,k[0]]
F[39,x,k[0],k[1]] = F[11,x,k[0]]*F[40,x,k[1],k[0]]
F[40,x,k[0],k[1]] = F[41,x,k[0],1,k[1]]
F[41,x,k[0],k[1],k[2]] = (F[15,x,k[0],k[1]*k[2]]*k[1]-F[15,x,k[0],k[2]])/(k[1]-1)
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_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{6}\! \left(x , y_{0}\right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{4}\! \left(x , y_{0}\right) y_{0}+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{9}\! \left(x , y_{0}, 1\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{12}\! \left(x , y_{0}, y_{1}\right)
F_{11}\! \left(x , y_{0}\right) = y_{0} x
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{14}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{14}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{1}, y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{1}, y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}, y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{1}, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{24}\! \left(x , y_{0}, 1\right) y_{0}-F_{24}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{1}, y_{0}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{27}\! \left(x , y_{0}, 1\right) y_{0}-F_{27}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{1}, y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{30}\! \left(x , y_{0}, 1\right) y_{0}-F_{30}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{1}, y_{0}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{1}\right) F_{33}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = y_{0} x
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{40}\! \left(x , y_{1}, y_{0}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, 1, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{15}\! \left(x , y_{0}, y_{2}\right)}{y_{1}-1}
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_4(x, 1))
Eq(F_4(x, k_0), F_5(x)*F_6(x, k_0))
Eq(F_5(x), x)
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_9(x, k_0, 1))
Eq(F_9(x, k_0, k_1), F_10(x, k_0, k_0*k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0)*F_12(x, k_0, k_1))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_19(x, k_0, k_1) + F_39(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), (k_0*F_14(x, k_0, k_1) - F_14(x, 1, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_5(x))
Eq(F_15(x, k_0, k_1), F_16(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_1(x) + F_17(x, k_0, k_1) + F_18(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), F_13(x, k_1, k_0))
Eq(F_18(x, k_0, k_1), F_19(x, k_1, k_0))
Eq(F_19(x, k_0, k_1), F_11(x, k_0)*F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_1, k_0))
Eq(F_21(x, k_0, k_1), F_1(x) + F_22(x, k_0, k_1) + F_25(x, k_0, k_1) + F_28(x, k_0, k_1) + F_38(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0, 1) + k_1*F_24(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_1, k_0))
Eq(F_26(x, k_0, k_1), (-k_0*F_27(x, k_0, 1) + k_1*F_27(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1), F_19(x, k_0, k_0*k_1))
Eq(F_28(x, k_0, k_1), F_29(x, k_1, k_0))
Eq(F_29(x, k_0, k_1), (-k_0*F_30(x, k_0, 1) + k_1*F_30(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_11(x, k_0)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_0*k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_1, k_0))
Eq(F_33(x, k_0, k_1), F_1(x) + F_22(x, k_0, k_1) + F_25(x, k_0, k_1) + F_34(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_11(x, k_1)*F_33(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_16(x, k_0, k_1)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), k_0*x)
Eq(F_38(x, k_0, k_1), F_33(x, k_0, k_1)*F_36(x, k_0))
Eq(F_39(x, k_0, k_1), F_11(x, k_0)*F_40(x, k_1, k_0))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, 1, k_1))
Eq(F_41(x, k_0, k_1, k_2), (-k_1*k_2*F_15(x, k_0, k_1*k_2) + k_2*F_15(x, k_0, k_2))/(-k_1*k_2 + k_2))
Pack JSON:
{"name": "all_the_strategies_2_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.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"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}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": "RequirementInsertionFactory", "ignore_parent": false, "maxreqlen": 2, "extra_basis": [], "limited_insertion": true, "allow_factorable_insertions": true}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "AllPlacementsFactory", "ignore_parent": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, 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[[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], 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[0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 2], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25080/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[31,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[30,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[9,x,k[0]]
F[17,x,k[0],k[1]] = F[1,x]+F[18,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[29,x,k[1],k[0]]
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]*F[3,x]
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[9,x,k[0]]
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[17,x,k[0],k[0]*k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]*F[9,x,k[0]]
F[25,x,k[0],k[1]] = (F[26,x,k[0],1]*k[0]-F[26,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1]] = F[27,x,k[0],k[0]*k[1]]
F[27,x,k[0],k[1]] = (F[28,x,k[0],1]*k[0]-F[28,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[28,x,k[0],k[1]] = F[15,x,k[0],k[0]*k[1]]
F[29,x,k[0],k[1]] = F[27,x,k[1],k[0]]*F[9,x,k[0]]
F[30,x,k[0],k[1]] = F[15,x,k[1],k[0]]*F[9,x,k[0]]
F[31,x,k[0],k[1]] = F[32,x,k[1],k[0]]*F[9,x,k[0]]
F[32,x,k[0],k[1]] = F[33,x,k[0],1,k[1]]
F[33,x,k[0],k[1],k[2]] = (F[15,x,k[0],k[1]*k[2]]*k[1]-F[15,x,k[0],k[2]])/(k[1]-1)
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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{1}, y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{20}\! \left(x , y_{0}, 1\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{23}\! \left(x , y_{0}, 1\right) y_{0}-F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{26}\! \left(x , y_{0}, 1\right) y_{0}-F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{28}\! \left(x , y_{0}, 1\right) y_{0}-F_{28}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, 1, y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{15}\! \left(x , y_{0}, y_{2}\right)}{y_{1}-1}
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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_31(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_30(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_9(x, k_0))
Eq(F_17(x, k_0, k_1), F_1(x) + F_18(x, k_0, k_1) + F_21(x, k_0, k_1) + F_24(x, k_0, k_1) + F_29(x, k_1, k_0))
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1)*F_3(x))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_9(x, k_0))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_17(x, k_0, k_0*k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1)*F_9(x, k_0))
Eq(F_25(x, k_0, k_1), (-k_0*F_26(x, k_0, 1) + k_1*F_26(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_0*k_1))
Eq(F_27(x, k_0, k_1), (-k_0*F_28(x, k_0, 1) + k_1*F_28(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_28(x, k_0, k_1), F_15(x, k_0, k_0*k_1))
Eq(F_29(x, k_0, k_1), F_27(x, k_1, k_0)*F_9(x, k_0))
Eq(F_30(x, k_0, k_1), F_15(x, k_1, k_0)*F_9(x, k_0))
Eq(F_31(x, k_0, k_1), F_32(x, k_1, k_0)*F_9(x, k_0))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, 1, k_1))
Eq(F_33(x, k_0, k_1, k_2), (-k_1*k_2*F_15(x, k_0, k_1*k_2) + k_2*F_15(x, k_0, k_2))/(-k_1*k_2 + k_2))
Pack JSON:
{"name": "col_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 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{"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 3
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25114/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[43,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[21,x,k[1],k[0]]
F[17,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[18,x,k[1],k[0]]
F[11,x,k[0],k[1]] = F[17,x,k[0]*k[1],k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[1],k[0]]*F[9,x,k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],1,k[1]]
F[20,x,k[0],k[1],k[2]] = (F[15,x,k[0],k[1]*k[2]]*k[1]-F[15,x,k[0],k[2]])/(k[1]-1)
F[21,x,k[0],k[1]] = F[15,x,k[1],k[0]]*F[9,x,k[0]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[9,x,k[1]]
F[23,x,k[0],k[1]] = F[1,x]+F[24,x,k[0],k[1]]+F[30,x,k[0],k[1]]+F[35,x,k[0],k[1]]+F[41,x,k[1],k[0]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]*F[3,x]
F[25,x,k[0],k[1]] = F[26,x,1,k[0],k[1]]
F[26,x,k[0],k[1],k[2]] = (-F[27,x,1,k[1],k[2]]*k[1]*k[2]+F[27,x,k[0]/k[1]/k[2],k[1],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2],1]
F[28,x,k[0],k[1],k[2],k[3]] = (F[29,x,k[0],k[1]*k[2],k[3]]*k[1]*k[3]-F[29,x,k[0],k[1]*k[2],1/k[1]])/(k[1]*k[3]-1)
F[29,x,k[0],k[1],k[2]] = F[15,x,k[0]*k[1],k[1]*k[2]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]*F[9,x,k[1]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1],1]
F[32,x,k[0],k[1],k[2]] = (F[33,x,k[0]*k[1],k[2]]*k[0]*k[2]-F[33,x,k[0]*k[1],1/k[0]])/(k[0]*k[2]-1)
F[33,x,k[0],k[1]] = F[34,x,k[0],k[0]*k[1]]
F[16,x,k[0],k[1]] = F[34,x,k[0],k[1]]*F[9,x,k[0]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]*F[9,x,k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[0],k[1],1]
F[37,x,k[0],k[1],k[2]] = (F[38,x,k[0]*k[1],k[2]]*k[0]*k[2]-F[38,x,k[0]*k[1],1/k[0]])/(k[0]*k[2]-1)
F[38,x,k[0],k[1]] = F[39,x,k[0],k[0]*k[1]]
F[39,x,k[0],k[1]] = (F[40,x,k[0],1]*k[0]-F[40,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[40,x,k[0],k[1]] = F[29,x,1,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,k[0],k[0]*k[1]]
F[42,x,k[0],k[1]] = F[39,x,k[1],k[0]]*F[9,x,k[0]]
F[43,x,k[0],k[1]] = F[18,x,k[0],k[0]*k[1]]
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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{1}, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{1}, y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, 1, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{15}\! \left(x , y_{0}, y_{2}\right)}{y_{1}-1}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{1}, y_{0}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , 1, y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{27}\! \left(x , 1, y_{1}, y_{2}\right) y_{1} y_{2}-F_{27}\! \left(x , \frac{y_{0}}{y_{1} y_{2}}, y_{1}, y_{2}\right) y_{0}}{-y_{1} y_{2}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{29}\! \left(x , y_{0}, y_{1} y_{2}, y_{3}\right) y_{1} y_{3}-F_{29}\! \left(x , y_{0}, y_{1} y_{2}, \frac{1}{y_{1}}\right)}{y_{1} y_{3}-1}
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{1}, 1\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{2} F_{33}\! \left(x , y_{0} y_{1}, y_{2}\right)-F_{33}\! \left(x , y_{0} y_{1}, \frac{1}{y_{0}}\right)}{y_{0} y_{2}-1}
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{37}\! \left(x , y_{0}, y_{1}, 1\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{38}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0} y_{2}-F_{38}\! \left(x , y_{0} y_{1}, \frac{1}{y_{0}}\right)}{y_{0} y_{2}-1}
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{40}\! \left(x , y_{0}, 1\right)-y_{1} F_{40}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , 1, y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}, y_{0} y_{1}\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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_22(x, k_0, k_1) + F_43(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_21(x, k_1, k_0))
Eq(F_17(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_0, k_1) + F_18(x, k_1, k_0))
Eq(F_11(x, k_0, k_1), F_17(x, k_0*k_1, k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_1, k_0)*F_9(x, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, 1, k_1))
Eq(F_20(x, k_0, k_1, k_2), (-k_1*k_2*F_15(x, k_0, k_1*k_2) + k_2*F_15(x, k_0, k_2))/(-k_1*k_2 + k_2))
Eq(F_21(x, k_0, k_1), F_15(x, k_1, k_0)*F_9(x, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_9(x, k_1))
Eq(F_23(x, k_0, k_1), F_1(x) + F_24(x, k_0, k_1) + F_30(x, k_0, k_1) + F_35(x, k_0, k_1) + F_41(x, k_1, k_0))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1)*F_3(x))
Eq(F_25(x, k_0, k_1), F_26(x, 1, k_0, k_1))
Eq(F_26(x, k_0, k_1, k_2), (-k_0*F_27(x, k_0/(k_1*k_2), k_1, k_2) + k_1*k_2*F_27(x, 1, k_1, k_2))/(-k_0 + k_1*k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2, 1))
Eq(F_28(x, k_0, k_1, k_2, k_3), (-k_1*k_3*F_29(x, k_0, k_1*k_2, k_3) + F_29(x, k_0, k_1*k_2, 1/k_1))/(-k_1*k_3 + 1))
Eq(F_29(x, k_0, k_1, k_2), F_15(x, k_0*k_1, k_1*k_2))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1)*F_9(x, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1, 1))
Eq(F_32(x, k_0, k_1, k_2), (-k_0*k_2*F_33(x, k_0*k_1, k_2) + F_33(x, k_0*k_1, 1/k_0))/(-k_0*k_2 + 1))
Eq(F_33(x, k_0, k_1), F_34(x, k_0, k_0*k_1))
Eq(F_16(x, k_0, k_1), F_34(x, k_0, k_1)*F_9(x, k_0))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1)*F_9(x, k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_0, k_1, 1))
Eq(F_37(x, k_0, k_1, k_2), (-k_0*k_2*F_38(x, k_0*k_1, k_2) + F_38(x, k_0*k_1, 1/k_0))/(-k_0*k_2 + 1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_0*k_1))
Eq(F_39(x, k_0, k_1), (-k_0*F_40(x, k_0, 1) + k_1*F_40(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_40(x, k_0, k_1), F_29(x, 1, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0, k_0*k_1))
Eq(F_42(x, k_0, k_1), F_39(x, k_1, k_0)*F_9(x, k_0))
Eq(F_43(x, k_0, k_1), F_18(x, k_0, k_0*k_1))
Pack JSON:
{"name": "col_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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