01342_01432_02341_02431_03241_03421_04231_04321_10342_10432
Counting sequence:
1, 1, 2, 6, 24, 110, 542, 2800, 14966, 82074, 459208, 2610938, 15042218, 87621664, 515190026, 3053559598, 18225049304, 109441034198, 660742323670, 4008361264080, 24421204151438, 149364648063826, 916748821025288, 5644655601477746, 34856968779353874, 215825236366301760, 1339624576181967122, 8333945571129071190, 51955591538427515160, 324536199857266542590, 2030883565843017320590, 12730501800158721556400, 79927692281814928997990, 502570890430761177122250, 3164511112655428189542600, 19952141757944194738785770, 125954422647091267564802490, 796064813980419699024815200, 5036943263814648078102791834, 31903915631584606770699227646, 202281343846460045364399908568, 1283751443454287129056970423654, 8154536264652527633428131864518, 51843243356274702158878946922640, 329869595204979822194810386237310, 2100552183775122147039073228793218, 13385994252805882826203057926573576, 85364962282279104154645805105416418, 544762640140142505624523005656680226, 3478734077892079746408606684603708544, 22228479834308013965250890194794655778, 142122215680098298140650601333935089318, 909217007639694348447405387389442842648, 5819917114647837537644892440428935242894, 37273532612143527333340520773460754204926, 238841705770574532156837505706743320987760, 1531219474183908100222783192138023650234198, 9821428244665472875545069189168125541195770, 63025229659406730242498087091100483609827784, 404622332173945154690502707050511225489822426, 2598808482126678735542632840567901865391261642, 16698652896241708689736121068439821912876490912, 107340932301661507506058610549769960445639792682, 690272177542606644523562068902880686147039969486, 4440593729010880714925757597258118628057793707224, 28577367486892155022699678191098363817582130002422, 183975071581873903085714580891035761624466106524086, 1184804306453250682713196139273738883447536158325072, 7632743354149387664008142432983411366460779239517550, 49187731637656338028440192473847356023398330632848050, 317081513726598254769797060006319401505105061571359752, 2044650637749470774774059131511618440590969145574419794, 13188566632256798659363427432370688242808875482241969202, 85094750717487164924093656368768027866293875740445753024, 549200809486887516478563089141683982486556390623247718706, 3545516179666409667253194086978013890879478689632117036278, 22895202566135178017245238592696225770248103497843615345944, 147884671750379942816711333035398805400436071923634116049438, 955460069021631039572852937973884022700954569028664526827374, 6174613792405890441313004715150247437950068336367033952187696, 39912801213543907707873453061345157953008495868368381681199430, 258057895190116429094440175682003100562610063609230096547085098, 1668868426541287667959082899618149013100043420823591602990679240, 10795049020234811804356390720962328584646148195553580920291619274, 69842916592778143082245522864139169906325901025327933104248532186, 451973613182750325103925308104598541772576586595739506947968263392, 2925462789823183126014896026599241378710439342564479611858793395642, 18939336208965465935366242952157703982593095049809191740238218383262, 122637015394119277353405880114177312747079297815633166029697421799640, 794260693655132119045999320540410792808714175070589446374568537538950, 5145023344149177479251735839566234099645356714312677673804847493918630, 33334394730954468352582066882359853416942543369126400030196408975199760, 216011547633958210333098513867303652315997842106707410304608958746344030, 1400034752915305735587898816657843647568368355171004415008408648215033570, 9075623171363016979897255082578105019197258901111698467311146333019292680, 58842115268425152230281261428230370046957977076543638664191008776914575810, 381568681610517527254258647029597549726573397686135927006918192578959327810, 2474732607114753155593374983575050453215265570519942336975100677938121058560, 16052899647401773153815115189711613147328729780521179606171247186011631396930, 104147040532505180360984508006922937937597758045005800369849163636407271507270, 675782954323736559733061503052494538525990616239303614272227428105681136891928
Implicit equation for the generating function in Maple syntax:
-F(x)^3+(x+2)*F(x)^2-3*x*F(x)+x-1 = 0
Implicit equation for the generating function in latex syntax:
-F \! \left(x \right)^{3}+\left(x +2\right) F \! \left(x \right)^{2}-3 x F \! \left(x \right)+x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(n+6) = 5/7*(n-1)*n/(n+6)/(n+5)*a(n)-3/7*n*(15*n+11)/(n+6)/(n+5)*a(n+1)+6/35*(71*n+120)*(n+1)/(n+6)/(n+5)*a(n+2)-1/35*(197*n^2+301*n-606)/(n+6)/(n+5)*a(n+3)+6/35*(3*n^2-55*n-254)/(n+6)/(n+5)*a(n+4)+3/5*(11*n+52)/(n+6)*a(n+5), n >= 6
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a{\left(n + 6 \right)} = \frac{5 n \left(n - 1\right) a{\left(n \right)}}{7 \left(n + 5\right) \left(n + 6\right)} - \frac{3 n \left(15 n + 11\right) a{\left(n + 1 \right)}}{7 \left(n + 5\right) \left(n + 6\right)} + \frac{6 \left(n + 1\right) \left(71 n + 120\right) a{\left(n + 2 \right)}}{35 \left(n + 5\right) \left(n + 6\right)} + \frac{3 \left(11 n + 52\right) a{\left(n + 5 \right)}}{5 \left(n + 6\right)} + \frac{6 \left(3 n^{2} - 55 n - 254\right) a{\left(n + 4 \right)}}{35 \left(n + 5\right) \left(n + 6\right)} - \frac{\left(197 n^{2} + 301 n - 606\right) a{\left(n + 3 \right)}}{35 \left(n + 5\right) \left(n + 6\right)}, \quad n \geq 6
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25040/
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]*F[5,x]
F[4,x] = x
F[5,x] = F[1,x]+F[41,x]+F[6,x]
F[6,x] = F[4,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[5,x]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[18,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[24,x,k[0]]+F[30,x,k[0]]+F[36,x,k[0]]
F[12,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,1])
F[13,x,k[0]] = F[0,x]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x]+F[16,x,k[0]]+F[17,x,k[0]]
F[15,x] = 0
F[16,x,k[0]] = F[4,x]*F[9,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[19,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[13,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[14,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[27,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]+F[8,x,k[0]]
F[29,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[32,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[34,x,k[0]]
F[35,x,k[0]] = F[12,x,k[0]]+F[34,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[18,x,k[0]]*F[38,x,k[0]]
F[39,x,k[0]] = F[18,x,k[0]]*F[38,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = -k[0]*(F[14,x,1]-F[14,x,k[0]])/(-1+k[0])
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x,1]
F[43,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,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 \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = -\frac{y \left(F_{14}\! \left(x , 1\right)-F_{14}\! \left(x , y\right)\right)}{-1+y}
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
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)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_1(x) + F_41(x) + F_6(x))
Eq(F_6(x), F_4(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_5(x) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_18(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_24(x, k_0) + F_30(x, k_0) + F_36(x, k_0))
Eq(F_12(x, k_0), (k_0*F_13(x, k_0) - F_13(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_0(x) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x) + F_16(x, k_0) + F_17(x, k_0))
Eq(F_15(x), 0)
Eq(F_16(x, k_0), F_4(x)*F_9(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_19(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_13(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_14(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_27(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0) + F_8(x, k_0))
Eq(F_29(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_32(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_35(x, k_0), F_12(x, k_0) + F_34(x, k_0))
Eq(F_35(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_18(x, k_0)*F_38(x, k_0))
Eq(F_39(x, k_0), F_18(x, k_0)*F_38(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), -F_14(x, 1) + (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x, 1))
Eq(F_43(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Pack JSON:
{"name": "point_and_col_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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}], [{"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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[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [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, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 1, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25407/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = -F[91,x]+F[8,x]
F[8,x] = -F[90,x]+F[9,x]
F[9,x] = 1/F[18,x]*F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[18,x]
F[13,x] = F[14,x]+F[86,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[18,x]*F[17,x]
F[17,x] = F[2,x]
F[18,x] = x
F[19,x] = F[20,x]*F[32,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]*F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[28,x]+F[24,x]
F[24,x] = 1/F[18,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[27,x]
F[27,x] = -F[0,x]+F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[30,x]
F[30,x] = 1/F[18,x]*F[31,x]
F[31,x] = F[11,x]
F[32,x] = 1/F[62,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[84,x]+F[35,x]
F[35,x] = 1/F[18,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[18,x]*F[38,x]
F[38,x] = F[39,x]+F[78,x]
F[39,x] = F[40,x]+F[77,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[0,x]^2
F[42,x] = F[43,x]
F[43,x] = F[18,x]*F[44,x]
F[44,x] = F[45,x]+F[76,x]
F[45,x] = F[46,x]+F[56,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[0,x]*F[48,x]
F[48,x] = 1/F[18,x]*F[49,x]
F[49,x] = F[2,x]
F[50,x] = -F[55,x]+F[51,x]
F[51,x] = 1/F[18,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[2,x]+F[54,x]
F[54,x] = -F[0,x]+F[48,x]
F[55,x] = F[2,x]*F[48,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]*F[58,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[18,x]*F[60,x]
F[60,x] = F[50,x]
F[61,x] = F[62,x]*F[63,x]
F[62,x] = F[3,x]
F[63,x] = 1/F[18,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[18,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[48,x]+F[65,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[18,x]*F[71,x]
F[71,x] = F[54,x]
F[72,x] = F[32,x]+F[73,x]
F[73,x] = F[54,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[18,x]*F[69,x]
F[76,x] = F[62,x]*F[68,x]
F[77,x] = F[0,x]*F[62,x]
F[78,x] = F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[0,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[18,x]*F[39,x]
F[84,x] = F[79,x]+F[85,x]
F[85,x] = F[0,x]*F[16,x]
F[86,x] = F[32,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[18,x]*F[89,x]
F[89,x] = F[11,x]+F[4,x]
F[90,x] = F[0,x]*F[87,x]
F[91,x] = F[0,x]*F[20,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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{86}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{62}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{78}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{77}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{18}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{76}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right) F_{48}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{50}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{3}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{48}\! \left(x \right)+F_{65}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)
F_{72}\! \left(x \right) = F_{32}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{54}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{18}\! \left(x \right) F_{69}\! \left(x \right)
F_{76}\! \left(x \right) = F_{62}\! \left(x \right) F_{68}\! \left(x \right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right) F_{62}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{0}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right) F_{39}\! \left(x \right)
F_{84}\! \left(x \right) = F_{79}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{4}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \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_18(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_18(x)*F_7(x))
Eq(F_7(x), F_8(x) - F_91(x))
Eq(F_8(x), F_9(x) - F_90(x))
Eq(F_9(x), F_10(x)/F_18(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_18(x))
Eq(F_13(x), F_14(x) + F_86(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x)/F_18(x))
Eq(F_17(x), F_2(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x)*F_32(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_18(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_28(x))
Eq(F_24(x), F_25(x)/F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_27(x))
Eq(F_27(x), -F_0(x) + F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_30(x))
Eq(F_30(x), F_31(x)/F_18(x))
Eq(F_31(x), F_11(x))
Eq(F_32(x), F_33(x)/F_62(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_84(x))
Eq(F_35(x), F_36(x)/F_18(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_18(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_78(x))
Eq(F_39(x), F_40(x) + F_77(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_0(x)**2)
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_18(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_76(x))
Eq(F_45(x), F_46(x) + F_56(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_0(x)*F_48(x))
Eq(F_48(x), F_49(x)/F_18(x))
Eq(F_49(x), F_2(x))
Eq(F_50(x), F_51(x) - F_55(x))
Eq(F_51(x), F_52(x)/F_18(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), -F_2(x) + F_54(x))
Eq(F_54(x), -F_0(x) + F_48(x))
Eq(F_55(x), F_2(x)*F_48(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x)*F_58(x))
Eq(F_58(x), F_59(x) - F_61(x))
Eq(F_59(x), F_60(x)/F_18(x))
Eq(F_60(x), F_50(x))
Eq(F_61(x), F_62(x)*F_63(x))
Eq(F_62(x), F_3(x))
Eq(F_63(x), F_64(x)/F_18(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_18(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_48(x) + F_65(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_18(x))
Eq(F_71(x), F_54(x))
Eq(F_72(x), F_32(x) + F_73(x))
Eq(F_73(x), F_54(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_18(x)*F_69(x))
Eq(F_76(x), F_62(x)*F_68(x))
Eq(F_77(x), F_0(x)*F_62(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_0(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_18(x)*F_39(x))
Eq(F_84(x), F_79(x) + F_85(x))
Eq(F_85(x), F_0(x)*F_16(x))
Eq(F_86(x), F_32(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_18(x)*F_89(x))
Eq(F_89(x), F_11(x) + F_4(x))
Eq(F_90(x), F_0(x)*F_87(x))
Eq(F_91(x), F_0(x)*F_20(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 2, 3, 1], "pos": [[1, 0], [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, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 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[2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 2], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 2], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 2], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 4], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 4], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25581/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = -F[91,x]+F[8,x]
F[8,x] = -F[90,x]+F[9,x]
F[9,x] = 1/F[18,x]*F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[18,x]
F[13,x] = F[14,x]+F[86,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[18,x]*F[17,x]
F[17,x] = F[2,x]
F[18,x] = x
F[19,x] = F[20,x]*F[32,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]*F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[28,x]+F[24,x]
F[24,x] = 1/F[18,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[27,x]
F[27,x] = -F[0,x]+F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[30,x]
F[30,x] = 1/F[18,x]*F[31,x]
F[31,x] = F[11,x]
F[32,x] = 1/F[62,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[84,x]+F[35,x]
F[35,x] = 1/F[18,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[18,x]*F[38,x]
F[38,x] = F[39,x]+F[78,x]
F[39,x] = F[40,x]+F[77,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[0,x]^2
F[42,x] = F[43,x]
F[43,x] = F[18,x]*F[44,x]
F[44,x] = F[45,x]+F[76,x]
F[45,x] = F[46,x]+F[56,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[0,x]*F[48,x]
F[48,x] = 1/F[18,x]*F[49,x]
F[49,x] = F[2,x]
F[50,x] = -F[55,x]+F[51,x]
F[51,x] = 1/F[18,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[2,x]+F[54,x]
F[54,x] = -F[0,x]+F[48,x]
F[55,x] = F[2,x]*F[48,x]
F[56,x] = F[57,x]
F[57,x] = F[18,x]*F[58,x]
F[58,x] = -F[61,x]+F[59,x]
F[59,x] = 1/F[18,x]*F[60,x]
F[60,x] = F[50,x]
F[61,x] = F[62,x]*F[63,x]
F[62,x] = F[3,x]
F[63,x] = 1/F[18,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[18,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[48,x]+F[65,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[18,x]*F[71,x]
F[71,x] = F[54,x]
F[72,x] = F[32,x]+F[73,x]
F[73,x] = F[54,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[18,x]*F[69,x]
F[76,x] = F[62,x]*F[68,x]
F[77,x] = F[0,x]*F[62,x]
F[78,x] = F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[0,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[18,x]*F[39,x]
F[84,x] = F[79,x]+F[85,x]
F[85,x] = F[0,x]*F[16,x]
F[86,x] = F[32,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[18,x]*F[89,x]
F[89,x] = F[11,x]+F[4,x]
F[90,x] = F[0,x]*F[87,x]
F[91,x] = F[0,x]*F[20,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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{86}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{32}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{62}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{78}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{77}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{18}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{76}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{0}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right) F_{48}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{50}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{3}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{48}\! \left(x \right)+F_{65}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)
F_{72}\! \left(x \right) = F_{32}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{54}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{18}\! \left(x \right) F_{69}\! \left(x \right)
F_{76}\! \left(x \right) = F_{62}\! \left(x \right) F_{68}\! \left(x \right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right) F_{62}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{0}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right) F_{39}\! \left(x \right)
F_{84}\! \left(x \right) = F_{79}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{4}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \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_18(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_18(x)*F_7(x))
Eq(F_7(x), F_8(x) - F_91(x))
Eq(F_8(x), F_9(x) - F_90(x))
Eq(F_9(x), F_10(x)/F_18(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_18(x))
Eq(F_13(x), F_14(x) + F_86(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x)/F_18(x))
Eq(F_17(x), F_2(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x)*F_32(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_18(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_28(x))
Eq(F_24(x), F_25(x)/F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_27(x))
Eq(F_27(x), -F_0(x) + F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_30(x))
Eq(F_30(x), F_31(x)/F_18(x))
Eq(F_31(x), F_11(x))
Eq(F_32(x), F_33(x)/F_62(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_84(x))
Eq(F_35(x), F_36(x)/F_18(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_18(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_78(x))
Eq(F_39(x), F_40(x) + F_77(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_0(x)**2)
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_18(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_76(x))
Eq(F_45(x), F_46(x) + F_56(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_0(x)*F_48(x))
Eq(F_48(x), F_49(x)/F_18(x))
Eq(F_49(x), F_2(x))
Eq(F_50(x), F_51(x) - F_55(x))
Eq(F_51(x), F_52(x)/F_18(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), -F_2(x) + F_54(x))
Eq(F_54(x), -F_0(x) + F_48(x))
Eq(F_55(x), F_2(x)*F_48(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_18(x)*F_58(x))
Eq(F_58(x), F_59(x) - F_61(x))
Eq(F_59(x), F_60(x)/F_18(x))
Eq(F_60(x), F_50(x))
Eq(F_61(x), F_62(x)*F_63(x))
Eq(F_62(x), F_3(x))
Eq(F_63(x), F_64(x)/F_18(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_18(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_48(x) + F_65(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_18(x))
Eq(F_71(x), F_54(x))
Eq(F_72(x), F_32(x) + F_73(x))
Eq(F_73(x), F_54(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_18(x)*F_69(x))
Eq(F_76(x), F_62(x)*F_68(x))
Eq(F_77(x), F_0(x)*F_62(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_0(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_18(x)*F_39(x))
Eq(F_84(x), F_79(x) + F_85(x))
Eq(F_85(x), F_0(x)*F_16(x))
Eq(F_86(x), F_32(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_18(x)*F_89(x))
Eq(F_89(x), F_11(x) + F_4(x))
Eq(F_90(x), F_0(x)*F_87(x))
Eq(F_91(x), F_0(x)*F_20(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, 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"pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25587/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = -F[91,x]+F[8,x]
F[8,x] = -F[90,x]+F[9,x]
F[9,x] = 1/F[18,x]*F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[18,x]
F[13,x] = F[14,x]+F[86,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[18,x]*F[17,x]
F[17,x] = F[2,x]
F[18,x] = x
F[19,x] = F[20,x]*F[31,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]*F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[27,x]+F[24,x]
F[24,x] = 1/F[18,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[5,x]
F[27,x] = F[28,x]
F[28,x] = F[18,x]*F[29,x]
F[29,x] = 1/F[18,x]*F[30,x]
F[30,x] = F[11,x]
F[31,x] = 1/F[61,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[84,x]+F[34,x]
F[34,x] = 1/F[18,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[18,x]*F[37,x]
F[37,x] = F[38,x]+F[78,x]
F[38,x] = F[39,x]+F[77,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[0,x]^2
F[41,x] = F[42,x]
F[42,x] = F[18,x]*F[43,x]
F[43,x] = F[44,x]+F[76,x]
F[44,x] = F[45,x]+F[55,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[0,x]*F[47,x]
F[47,x] = 1/F[18,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = -F[54,x]+F[50,x]
F[50,x] = 1/F[18,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[2,x]+F[53,x]
F[53,x] = -F[0,x]+F[47,x]
F[54,x] = F[2,x]*F[47,x]
F[55,x] = F[56,x]
F[56,x] = F[18,x]*F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[18,x]*F[59,x]
F[59,x] = F[49,x]
F[60,x] = F[61,x]*F[62,x]
F[61,x] = F[3,x]
F[62,x] = 1/F[18,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[47,x]+F[64,x]
F[68,x] = -F[72,x]+F[69,x]
F[69,x] = 1/F[18,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[2,x]+F[52,x]
F[72,x] = F[31,x]+F[73,x]
F[73,x] = F[71,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[18,x]*F[68,x]
F[76,x] = F[61,x]*F[67,x]
F[77,x] = F[0,x]*F[61,x]
F[78,x] = F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[0,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[18,x]*F[38,x]
F[84,x] = F[79,x]+F[85,x]
F[85,x] = F[0,x]*F[16,x]
F[86,x] = F[31,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[18,x]*F[89,x]
F[89,x] = F[11,x]+F[4,x]
F[90,x] = F[0,x]*F[87,x]
F[91,x] = F[0,x]*F[20,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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{86}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{31}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{61}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{78}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{77}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{76}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{55}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{0}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{49}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right) F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{3}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{47}\! \left(x \right)+F_{64}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{2}\! \left(x \right)+F_{52}\! \left(x \right)
F_{72}\! \left(x \right) = F_{31}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{18}\! \left(x \right) F_{68}\! \left(x \right)
F_{76}\! \left(x \right) = F_{61}\! \left(x \right) F_{67}\! \left(x \right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right) F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{0}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{84}\! \left(x \right) = F_{79}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right)
F_{86}\! \left(x \right) = F_{31}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{4}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \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_18(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_18(x)*F_7(x))
Eq(F_7(x), F_8(x) - F_91(x))
Eq(F_8(x), F_9(x) - F_90(x))
Eq(F_9(x), F_10(x)/F_18(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_18(x))
Eq(F_13(x), F_14(x) + F_86(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x)/F_18(x))
Eq(F_17(x), F_2(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x)*F_31(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_18(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_27(x))
Eq(F_24(x), F_25(x)/F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_5(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_18(x)*F_29(x))
Eq(F_29(x), F_30(x)/F_18(x))
Eq(F_30(x), F_11(x))
Eq(F_31(x), F_32(x)/F_61(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) - F_84(x))
Eq(F_34(x), F_35(x)/F_18(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_18(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_78(x))
Eq(F_38(x), F_39(x) + F_77(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_0(x)**2)
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_18(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_76(x))
Eq(F_44(x), F_45(x) + F_55(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_0(x)*F_47(x))
Eq(F_47(x), F_48(x)/F_18(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x) - F_54(x))
Eq(F_50(x), F_51(x)/F_18(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_2(x) + F_53(x))
Eq(F_53(x), -F_0(x) + F_47(x))
Eq(F_54(x), F_2(x)*F_47(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_18(x)*F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_18(x))
Eq(F_59(x), F_49(x))
Eq(F_60(x), F_61(x)*F_62(x))
Eq(F_61(x), F_3(x))
Eq(F_62(x), F_63(x)/F_18(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_47(x) + F_64(x))
Eq(F_68(x), F_69(x) - F_72(x))
Eq(F_69(x), F_70(x)/F_18(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_2(x) + F_52(x))
Eq(F_72(x), F_31(x) + F_73(x))
Eq(F_73(x), F_71(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_18(x)*F_68(x))
Eq(F_76(x), F_61(x)*F_67(x))
Eq(F_77(x), F_0(x)*F_61(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_0(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_18(x)*F_38(x))
Eq(F_84(x), F_79(x) + F_85(x))
Eq(F_85(x), F_0(x)*F_16(x))
Eq(F_86(x), F_31(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_18(x)*F_89(x))
Eq(F_89(x), F_11(x) + F_4(x))
Eq(F_90(x), F_0(x)*F_87(x))
Eq(F_91(x), F_0(x)*F_20(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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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{"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 2], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 4], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 4], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25709/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = -F[91,x]+F[8,x]
F[8,x] = -F[90,x]+F[9,x]
F[9,x] = 1/F[18,x]*F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[18,x]
F[13,x] = F[14,x]+F[86,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[18,x]*F[17,x]
F[17,x] = F[2,x]
F[18,x] = x
F[19,x] = F[20,x]*F[31,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]*F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[27,x]+F[24,x]
F[24,x] = 1/F[18,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[2,x]+F[5,x]
F[27,x] = F[28,x]
F[28,x] = F[18,x]*F[29,x]
F[29,x] = 1/F[18,x]*F[30,x]
F[30,x] = F[11,x]
F[31,x] = 1/F[61,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[84,x]+F[34,x]
F[34,x] = 1/F[18,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[18,x]*F[37,x]
F[37,x] = F[38,x]+F[78,x]
F[38,x] = F[39,x]+F[77,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[0,x]^2
F[41,x] = F[42,x]
F[42,x] = F[18,x]*F[43,x]
F[43,x] = F[44,x]+F[76,x]
F[44,x] = F[45,x]+F[55,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[0,x]*F[47,x]
F[47,x] = 1/F[18,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = -F[54,x]+F[50,x]
F[50,x] = 1/F[18,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = -F[2,x]+F[53,x]
F[53,x] = -F[0,x]+F[47,x]
F[54,x] = F[2,x]*F[47,x]
F[55,x] = F[56,x]
F[56,x] = F[18,x]*F[57,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[18,x]*F[59,x]
F[59,x] = F[49,x]
F[60,x] = F[61,x]*F[62,x]
F[61,x] = F[3,x]
F[62,x] = 1/F[18,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[18,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[47,x]+F[64,x]
F[68,x] = -F[72,x]+F[69,x]
F[69,x] = 1/F[18,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[2,x]+F[52,x]
F[72,x] = F[31,x]+F[73,x]
F[73,x] = F[71,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[18,x]*F[68,x]
F[76,x] = F[61,x]*F[67,x]
F[77,x] = F[0,x]*F[61,x]
F[78,x] = F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[81,x]
F[81,x] = F[0,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[18,x]*F[38,x]
F[84,x] = F[79,x]+F[85,x]
F[85,x] = F[0,x]*F[16,x]
F[86,x] = F[31,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[18,x]*F[89,x]
F[89,x] = F[11,x]+F[4,x]
F[90,x] = F[0,x]*F[87,x]
F[91,x] = F[0,x]*F[20,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_{18}\! \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_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{86}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{31}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{61}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{78}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{77}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{76}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{55}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{0}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{49}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right) F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{3}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{47}\! \left(x \right)+F_{64}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{2}\! \left(x \right)+F_{52}\! \left(x \right)
F_{72}\! \left(x \right) = F_{31}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{18}\! \left(x \right) F_{68}\! \left(x \right)
F_{76}\! \left(x \right) = F_{61}\! \left(x \right) F_{67}\! \left(x \right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right) F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{0}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{84}\! \left(x \right) = F_{79}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right)
F_{86}\! \left(x \right) = F_{31}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{11}\! \left(x \right)+F_{4}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right) F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \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_18(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_18(x)*F_7(x))
Eq(F_7(x), F_8(x) - F_91(x))
Eq(F_8(x), F_9(x) - F_90(x))
Eq(F_9(x), F_10(x)/F_18(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_18(x))
Eq(F_13(x), F_14(x) + F_86(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x)/F_18(x))
Eq(F_17(x), F_2(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x)*F_31(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_18(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_27(x))
Eq(F_24(x), F_25(x)/F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_2(x) + F_5(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_18(x)*F_29(x))
Eq(F_29(x), F_30(x)/F_18(x))
Eq(F_30(x), F_11(x))
Eq(F_31(x), F_32(x)/F_61(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) - F_84(x))
Eq(F_34(x), F_35(x)/F_18(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_18(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_78(x))
Eq(F_38(x), F_39(x) + F_77(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_0(x)**2)
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_18(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_76(x))
Eq(F_44(x), F_45(x) + F_55(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_0(x)*F_47(x))
Eq(F_47(x), F_48(x)/F_18(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x) - F_54(x))
Eq(F_50(x), F_51(x)/F_18(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), -F_2(x) + F_53(x))
Eq(F_53(x), -F_0(x) + F_47(x))
Eq(F_54(x), F_2(x)*F_47(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_18(x)*F_57(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_18(x))
Eq(F_59(x), F_49(x))
Eq(F_60(x), F_61(x)*F_62(x))
Eq(F_61(x), F_3(x))
Eq(F_62(x), F_63(x)/F_18(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_18(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_47(x) + F_64(x))
Eq(F_68(x), F_69(x) - F_72(x))
Eq(F_69(x), F_70(x)/F_18(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_2(x) + F_52(x))
Eq(F_72(x), F_31(x) + F_73(x))
Eq(F_73(x), F_71(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_18(x)*F_68(x))
Eq(F_76(x), F_61(x)*F_67(x))
Eq(F_77(x), F_0(x)*F_61(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_81(x))
Eq(F_81(x), F_0(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_18(x)*F_38(x))
Eq(F_84(x), F_79(x) + F_85(x))
Eq(F_85(x), F_0(x)*F_16(x))
Eq(F_86(x), F_31(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_18(x)*F_89(x))
Eq(F_89(x), F_11(x) + F_4(x))
Eq(F_90(x), F_0(x)*F_87(x))
Eq(F_91(x), F_0(x)*F_20(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 2, 3, 1], "pos": [[1, 0], [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, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 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