01324_01342_10324_10342_13024_13042_13204
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3121, 17266, 97200, 553626, 3179393, 18369558, 106621863, 621079038, 3628142778, 21243449076, 124621177137, 732230827648, 4308101009605, 25375784570794, 149616404513772, 882892998171510, 5213853992197697, 30810032921839426, 182169112089803851, 1077651641123697430, 6377919086267361798, 37762072728475338336, 223661326517528223953, 1325160860084821689948, 7853717552264386678905, 46558495376597784692706, 276076217737662512291016, 1637404917346042697027442, 9713413878636542263812993, 57632702416120851862149966, 342011508679352137500974991, 2029930379384348627243884206, 12049940172118284287630471154, 71539701663186807648450331884, 424779421490508699574886855025, 2522492920014853140189787966488, 14981075041498866677605571273421, 88981404367350717032708266318362, 528561819153137478115005339619140, 3140001371947272005844011971825806, 18655156391544662298806472764843841, 110841056059532050634646245506692666, 658617101976831628385513938144790643, 3913758212024182825437033771815898054, 23258506472236476350627275581192314238, 138227622911782982554896314712084101784, 821545283785064774177636448085651484433, 4883041389411192351994878763778499181492, 29024865714761620527507999515613655199425, 172532027614802226837078930447971745835858, 1025623094392263112442146474001531576861280, 6097100571315579485770234852829547402048714, 36247281816040933922138275437373180309335425, 215497944144180539672247165724513222182309382, 1281225470473181406358527150121112083374946807, 7617666266880541119682975137220032072454867294, 45293045006204351156395357287054364959998057898, 269310691032184891717114609428924818766905548644, 1601354604930489921271008798326473773939175779761, 9522098301177221622533207793296146946177883883824, 56622424390695820051721071637185261409307377285973, 336708725929378641881082974209150428304586199883914, 2002303398882812935480954302776976933879221295680796, 11907333609412418705881144008149903200032706996152870, 70812158357399109184325204595395046521847126478660161, 421123417265847982213811715934475202134227997243732146, 2504487113401860504573221934630890966265830157449959195, 14894834567294265103360754953769019006858146663517107830, 88584896863468742060408742923749214967480188856127552374, 526854222734070909210948768118166230609808498880080393040, 3133485655588992513675294629151002312796877473575743867217, 18636790402569854402632191881850405327076550354254893437068, 110846098516996071582806738372033304007880872288876789948297, 659288218173104449799859013437914494233154290547777251598018, 3921349718772669528185581635295203639059018935024317762627192, 23323888369021112432217002539293588874516020923482617554081442, 138730266803613404249934587642454050677794899683056739462384001, 825175189097322275271687483488777129821173365266754366592320574, 4908237490773380145754429857630962523551663593719525404254950111, 29195051632338552208778558130872339989974659051795244404008362510, 173658887290617861003611224968969566302399067404173607215210828258, 1032972337552717578825867033686288848570810755971565454646155198044, 6144465541781263941589362081127879810560650114484032737619332339185, 36549641342169512999852461605689688447012151171864501100053669721544, 217413025680292841877838339890312704954214200503033434916652581876317, 1293276214867127705769624472486003962358805017565036561216191200185082, 7693078670368198525229246221959077865012359620108859023413198822921588, 45762746294884366144067574128607796155756082907498165918714187647875134, 272224295795983651956538903934173177325273694771153497718790699494059841, 1619363948265108747016987822667335293187667089184603322379485815676143274, 9633070005435053059307260073881436556149321090809400766326753836468527171, 57304341368456763158895700356839581713918476346733274038567222698623691558, 340888845283669199018538878901977249652357910562658511309063213287678753774, 2027871414160336974852499420856130928073589924596364107379588871192564699272
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25060/
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[35,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (4*x*k[0]-1)*F[7,x,k[0]]^2+F[7,x,k[0]]+k[0]^2*x^2
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[35,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[14,x,k[0]]
F[13,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[25,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]^2*F[21,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = (F[23,x,k[0]]*k[0]-F[23,x,1])/(-1+k[0])
F[24,x,k[0]] = F[21,x,k[0]]*F[23,x,k[0]]
F[24,x,k[0]] = F[6,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[29,x,k[0]]
F[26,x,k[0]] = F[27,k[0]*x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = (F[18,x,k[0]]-F[18,x,1])/(-1+k[0])
F[29,x,k[0]] = F[30,x,k[0]]+F[36,x,k[0]]
F[30,x,k[0]] = (F[31,x,k[0]]*k[0]-F[31,x,1])/(-1+k[0])
F[31,x,k[0]] = F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = F[0,x]*F[20,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[20,x,k[0]]*F[29,x,k[0]]*F[35,x]
F[35,x] = x
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[35,x]*F[38,x,k[0]]*F[41,x]
F[38,x,k[0]] = F[1,x]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[21,x,k[0]]*F[38,x,k[0]]
F[41,x] = F[42,x,1]
F[43,x,k[0]] = F[21,x,k[0]]*F[42,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[23,x,k[0]] = F[31,x,k[0]]+F[44,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -F_{7}\! \left(x , y\right)^{2}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)^{2} F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = -\frac{-F_{23}\! \left(x , y\right) y +F_{23}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(y x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{29}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = x
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{35}\! \left(x \right) F_{38}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_35(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0**2*x**2 + 4*k_0*x + (-8*k_0*x + 2)*(F_7(x, k_0) + 1) + (4*k_0*x - 1)*(F_7(x, k_0) + 1)**2 + F_7(x, k_0) - 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_35(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_14(x, k_0))
Eq(F_13(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_25(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)**2*F_21(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), (-k_0*F_23(x, k_0) + F_23(x, 1))/(1 - k_0))
Eq(F_24(x, k_0), F_21(x, k_0)*F_23(x, k_0))
Eq(F_24(x, k_0), F_6(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_29(x, k_0))
Eq(F_26(x, k_0), F_27(k_0*x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), -F_18(x, k_0) + (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_36(x, k_0))
Eq(F_30(x, k_0), (-k_0*F_31(x, k_0) + F_31(x, 1))/(1 - k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), F_0(x)*F_20(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_20(x, k_0)*F_29(x, k_0)*F_35(x))
Eq(F_35(x), x)
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_35(x)*F_38(x, k_0)*F_41(x))
Eq(F_38(x, k_0), F_1(x) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_21(x, k_0)*F_38(x, k_0))
Eq(F_41(x), F_42(x, 1))
Eq(F_43(x, k_0), F_21(x, k_0)*F_42(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_23(x, k_0), F_31(x, k_0) + F_44(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "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, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "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, 0]]}, {"patt": [0], "pos": [[0, 2]]}, 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{"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25753/
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[35,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (4*x*k[0]-1)*F[7,x,k[0]]^2+F[7,x,k[0]]+k[0]^2*x^2
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[35,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[14,x,k[0]]
F[13,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[21,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[25,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[22,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]^2*F[21,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = (F[23,x,k[0]]*k[0]-F[23,x,1])/(-1+k[0])
F[24,x,k[0]] = F[21,x,k[0]]*F[23,x,k[0]]
F[24,x,k[0]] = F[6,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[29,x,k[0]]
F[26,x,k[0]] = F[27,k[0]*x]
F[27,x] = F[28,x,1]
F[28,x,k[0]] = (F[18,x,k[0]]-F[18,x,1])/(-1+k[0])
F[29,x,k[0]] = F[30,x,k[0]]+F[36,x,k[0]]
F[30,x,k[0]] = (F[31,x,k[0]]*k[0]-F[31,x,1])/(-1+k[0])
F[31,x,k[0]] = F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = F[0,x]*F[20,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[20,x,k[0]]*F[29,x,k[0]]*F[35,x]
F[35,x] = x
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[35,x]*F[38,x,k[0]]*F[41,x]
F[38,x,k[0]] = F[1,x]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[21,x,k[0]]*F[38,x,k[0]]
F[41,x] = F[42,x,1]
F[43,x,k[0]] = F[21,x,k[0]]*F[42,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[23,x,k[0]] = F[31,x,k[0]]+F[44,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -F_{7}\! \left(x , y\right)^{2}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)^{2} F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = -\frac{-F_{23}\! \left(x , y\right) y +F_{23}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(y x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{29}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = x
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{35}\! \left(x \right) F_{38}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_35(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0**2*x**2 + 4*k_0*x + (-8*k_0*x + 2)*(F_7(x, k_0) + 1) + (4*k_0*x - 1)*(F_7(x, k_0) + 1)**2 + F_7(x, k_0) - 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_35(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_14(x, k_0))
Eq(F_13(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_21(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_25(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_22(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)**2*F_21(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), (-k_0*F_23(x, k_0) + F_23(x, 1))/(1 - k_0))
Eq(F_24(x, k_0), F_21(x, k_0)*F_23(x, k_0))
Eq(F_24(x, k_0), F_6(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_29(x, k_0))
Eq(F_26(x, k_0), F_27(k_0*x))
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), -F_18(x, k_0) + (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_36(x, k_0))
Eq(F_30(x, k_0), (-k_0*F_31(x, k_0) + F_31(x, 1))/(1 - k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), F_0(x)*F_20(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_20(x, k_0)*F_29(x, k_0)*F_35(x))
Eq(F_35(x), x)
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_35(x)*F_38(x, k_0)*F_41(x))
Eq(F_38(x, k_0), F_1(x) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_21(x, k_0)*F_38(x, k_0))
Eq(F_41(x), F_42(x, 1))
Eq(F_43(x, k_0), F_21(x, k_0)*F_42(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_23(x, k_0), F_31(x, k_0) + F_44(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "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, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "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, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 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