01342_01423_01432_02413_10342_10423_10432_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 111, 549, 2817, 14809, 79256, 430166, 2361629, 13090327, 73155326, 411743737, 2331941355, 13280389668, 76006601896, 436941880341, 2521992575215, 14610087287607, 84920465585764, 495109410962987, 2894757899321494, 16968781369908426, 99708417387829704, 587191919796460503, 3465192916420713619, 20488614742162619007, 121361297746267969380, 720078817388705598939, 4279237556081032039924, 25468165409023868083575, 151787422695437112895283, 905828383557507370223833, 5412477303979715366642869, 32378509391428350430212617, 193910394753611906942923463, 1162528893785970926101069851, 6976565383772691956833385569, 41907653506377949575024385295, 251964196698144130712357101193, 1516210781156441211695959434504, 9131419622493476155577517247283, 55037521371118509148146906206325, 331975635413703108081765968483076, 2003854718872739668093000325111369, 12103910883105356953391142631170055, 73159760010150489156549191950594753, 442480616065174809925585375747023055, 2677815785768470168547338645375674199, 16215162240848304977054249764132810893, 98244065810195289296324037252858547367, 595561485909627736732391643609855647801, 3612213881621974546471812943541797952504, 21919905683000005958911794372475297707340, 133080526181384351201448105598856586157461, 808339090025234466050974349461479639482675, 4912119393778359781145079174629380896994963, 29863030611111460825965986287192235658537944, 181627739308505725580961188018983966934078051, 1105115873159635404896212440780540564793841290, 6726747024549178702720232751710318817883654671, 40960814165034931644700687094830360973505371091, 249512951426569241773174975757299459828456321100, 1520455428971606750309814476596256632809941148053, 9268419113459942487804019339133841441415204450477, 56517702408993526345165151887280618786084588097487, 344751280347041037217330578041171571677404898787931, 2103612343930440666921245006989024394778926994562874, 12839852096786321107614075099397864687257346045972303, 78394399855494091242670646347548519195827284678227877, 478781260703965840129228540192643285742065575049517310, 2924912372808859336746814817671619019966074877598610650, 17873469066119252992123008431523657003570147619016658119, 109250120183537827018599113340425115180472348200647005489, 667957754493870620829388058238689841168176497475350975159, 4084953485849137232692527420300374161038480645177409025021, 24988111807616855272150704082872430020494836393637425433796, 152892167016363318171986880784240574260438767477900060304467, 935706983514291604228708666724760041083069405391970469810022, 5727891853858723779377054745878368388268918097238468450625132, 35070956487834757021338106743994834524007443258826066708969852, 214781029321498585867048709374058091533714102283026416403167034, 1315641202288648315769864829839359835723158317451564347417621284, 8060649922695743763961222259478087053180139936665897471740205098, 49395977878667752941914164094640104079669116697280151014766501359, 302761053062753731136091241324427295961926765157246953881248183090, 1856065708936499117465615698402499368748099810342545941973324592449, 11380719045287193784821627442347417218198646671264897383307577163717, 69795468987136739949425207334402751739480768877257553539928334475596, 428118651583928349783825495271141622650680881549512193413575301619467, 2626508047624284140474200395313527698274568451086073088113839686333275, 16116447679498149402084379710316161605776684212143901029457624358100082, 98908654610314991211380067760391977103374933259367932382267249868913175, 607116571713885349730764062978497077626488939737033163424120497875738073, 3727187031663209829896438316283640026993707687546780877516605998077181401, 22885485119549544543609516076045166272108806323228780532578509047994261537, 140542434950220367884520867640178857388553165729753385791174339189564540702, 863220723498113395785739850937821106494439321840308537359762506892810112077, 5302759577897577619577969352765787960654768515327358099162609385067778139124
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24842/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[38,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[22,x]
F[13,x] = F[14,x]+F[33,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[32,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[0,x]*F[18,x]
F[18,x] = 1+x^2*F[18,x]^3+(-x^2+x)*F[18,x]^2
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = F[26,x]+F[28,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = x*(1+F[27,x])^2*(x*F[27,x]+1)
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[27,x]*F[30,x]
F[30,x] = F[31,x]+F[5,x]
F[31,x] = F[0,x]+F[20,x]
F[32,x] = F[18,x]*F[5,x]
F[33,x] = F[34,x]
F[34,x] = F[18,x]*F[30,x]*F[35,x]
F[35,x] = -F[0,x]+F[36,x]
F[36,x] = 1/F[22,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[22,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[2,x]*F[42,x]
F[42,x] = 1/F[22,x]*F[43,x]
F[43,x] = F[11,x]
F[44,x] = F[35,x]*F[45,x]
F[45,x] = 1/F[22,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{33}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{5}\! \left(x \right)
F_{31}\! \left(x \right) = F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right) F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{11}\! \left(x \right)
F_{44}\! \left(x \right) = F_{35}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_38(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_22(x))
Eq(F_13(x), F_14(x) + F_33(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_32(x))
Eq(F_16(x), F_17(x) + F_19(x))
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), x**2*F_18(x)**3 - x*(x - 1)*F_18(x)**2 + 1)
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_28(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), x**2*(F_27(x) + 1)**3 - x*(x - 1)*(F_27(x) + 1)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_27(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_5(x))
Eq(F_31(x), F_0(x) + F_20(x))
Eq(F_32(x), F_18(x)*F_5(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_18(x)*F_30(x)*F_35(x))
Eq(F_35(x), -F_0(x) + F_36(x))
Eq(F_36(x), F_37(x)/F_22(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_22(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_2(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_22(x))
Eq(F_43(x), F_11(x))
Eq(F_44(x), F_35(x)*F_45(x))
Eq(F_45(x), F_46(x)/F_22(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_22(x))
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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "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, 4, 1, 3], "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, 2, 3], "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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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", 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{"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25042/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[38,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[22,x]
F[13,x] = F[14,x]+F[33,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[32,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[0,x]*F[18,x]
F[18,x] = 1+x^2*F[18,x]^3+(-x^2+x)*F[18,x]^2
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = F[26,x]+F[28,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = x*(1+F[27,x])^2*(x*F[27,x]+1)
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[27,x]*F[30,x]
F[30,x] = F[31,x]+F[5,x]
F[31,x] = F[0,x]+F[20,x]
F[32,x] = F[18,x]*F[5,x]
F[33,x] = F[34,x]
F[34,x] = F[18,x]*F[30,x]*F[35,x]
F[35,x] = -F[0,x]+F[36,x]
F[36,x] = 1/F[22,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[22,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[2,x]*F[42,x]
F[42,x] = 1/F[22,x]*F[43,x]
F[43,x] = F[11,x]
F[44,x] = F[35,x]*F[45,x]
F[45,x] = 1/F[22,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{33}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{5}\! \left(x \right)
F_{31}\! \left(x \right) = F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right) F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{11}\! \left(x \right)
F_{44}\! \left(x \right) = F_{35}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_38(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_22(x))
Eq(F_13(x), F_14(x) + F_33(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_32(x))
Eq(F_16(x), F_17(x) + F_19(x))
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), x**2*F_18(x)**3 - x*(x - 1)*F_18(x)**2 + 1)
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_28(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), x**2*(F_27(x) + 1)**3 - x*(x - 1)*(F_27(x) + 1)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_27(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_5(x))
Eq(F_31(x), F_0(x) + F_20(x))
Eq(F_32(x), F_18(x)*F_5(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_18(x)*F_30(x)*F_35(x))
Eq(F_35(x), -F_0(x) + F_36(x))
Eq(F_36(x), F_37(x)/F_22(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_22(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_2(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_22(x))
Eq(F_43(x), F_11(x))
Eq(F_44(x), F_35(x)*F_45(x))
Eq(F_45(x), F_46(x)/F_22(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_22(x))
Pack JSON:
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Specification JSON:
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"pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 3], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25085/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[37,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[22,x]
F[13,x] = F[14,x]+F[32,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[31,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[0,x]*F[18,x]
F[18,x] = 1+x^2*F[18,x]^3+(-x^2+x)*F[18,x]^2
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = F[26,x]+F[28,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = x*(1+F[27,x])^2*(x*F[27,x]+1)
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[27,x]*F[30,x]
F[30,x] = F[20,x]+F[4,x]
F[31,x] = F[18,x]*F[5,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]*F[30,x]*F[34,x]
F[34,x] = -F[0,x]+F[35,x]
F[35,x] = 1/F[22,x]*F[36,x]
F[36,x] = F[2,x]
F[37,x] = F[38,x]
F[38,x] = F[22,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[2,x]*F[41,x]
F[41,x] = 1/F[22,x]*F[42,x]
F[42,x] = F[11,x]
F[43,x] = F[34,x]*F[44,x]
F[44,x] = 1/F[22,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[20,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{5}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{22}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{11}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_37(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_22(x))
Eq(F_13(x), F_14(x) + F_32(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_31(x))
Eq(F_16(x), F_17(x) + F_19(x))
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), x**2*F_18(x)**3 - x*(x - 1)*F_18(x)**2 + 1)
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_28(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), x**2*(F_27(x) + 1)**3 - x*(x - 1)*(F_27(x) + 1)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_27(x)*F_30(x))
Eq(F_30(x), F_20(x) + F_4(x))
Eq(F_31(x), F_18(x)*F_5(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)*F_30(x)*F_34(x))
Eq(F_34(x), -F_0(x) + F_35(x))
Eq(F_35(x), F_36(x)/F_22(x))
Eq(F_36(x), F_2(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_22(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_2(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_22(x))
Eq(F_42(x), F_11(x))
Eq(F_43(x), F_34(x)*F_44(x))
Eq(F_44(x), F_45(x)/F_22(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_20(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_22(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, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "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, 4, 1, 3], "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, 2, 3], "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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 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, 0]]}, {"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, 1, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 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"pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"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, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 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{"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [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, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"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, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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, 2, 3], "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, 4, 1, 3], "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, 2, 3], "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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 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0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25535/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[38,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[22,x]
F[13,x] = F[14,x]+F[33,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[32,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[0,x]*F[18,x]
F[18,x] = 1+x^2*F[18,x]^3+(-x^2+x)*F[18,x]^2
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = F[26,x]+F[28,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = x*(1+F[27,x])^2*(x*F[27,x]+1)
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[27,x]*F[30,x]
F[30,x] = F[31,x]+F[5,x]
F[31,x] = F[0,x]+F[20,x]
F[32,x] = F[18,x]*F[5,x]
F[33,x] = F[34,x]
F[34,x] = F[18,x]*F[30,x]*F[35,x]
F[35,x] = -F[0,x]+F[36,x]
F[36,x] = 1/F[22,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[22,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[2,x]*F[42,x]
F[42,x] = 1/F[22,x]*F[43,x]
F[43,x] = F[11,x]
F[44,x] = F[35,x]*F[45,x]
F[45,x] = 1/F[22,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[11,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{33}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{32}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{5}\! \left(x \right)
F_{31}\! \left(x \right) = F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right) F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{11}\! \left(x \right)
F_{44}\! \left(x \right) = F_{35}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_38(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_22(x))
Eq(F_13(x), F_14(x) + F_33(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_32(x))
Eq(F_16(x), F_17(x) + F_19(x))
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), x**2*F_18(x)**3 - x*(x - 1)*F_18(x)**2 + 1)
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_28(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), x**2*(F_27(x) + 1)**3 - x*(x - 1)*(F_27(x) + 1)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_27(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_5(x))
Eq(F_31(x), F_0(x) + F_20(x))
Eq(F_32(x), F_18(x)*F_5(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_18(x)*F_30(x)*F_35(x))
Eq(F_35(x), -F_0(x) + F_36(x))
Eq(F_36(x), F_37(x)/F_22(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_22(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_2(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_22(x))
Eq(F_43(x), F_11(x))
Eq(F_44(x), F_35(x)*F_45(x))
Eq(F_45(x), F_46(x)/F_22(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_11(x)*F_22(x))
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, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "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, 4, 1, 3], "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, 2, 3], "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]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 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, 0]]}, {"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, 1, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], 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2, 4, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25782/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]+F[37,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[22,x]
F[13,x] = F[14,x]+F[32,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[31,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[0,x]*F[18,x]
F[18,x] = 1+x^2*F[18,x]^3+(-x^2+x)*F[18,x]^2
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = F[26,x]+F[28,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = x*(1+F[27,x])^2*(x*F[27,x]+1)
F[28,x] = F[29,x]
F[29,x] = F[18,x]*F[27,x]*F[30,x]
F[30,x] = F[20,x]+F[4,x]
F[31,x] = F[18,x]*F[5,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]*F[30,x]*F[34,x]
F[34,x] = -F[0,x]+F[35,x]
F[35,x] = 1/F[22,x]*F[36,x]
F[36,x] = F[2,x]
F[37,x] = F[38,x]
F[38,x] = F[22,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[2,x]*F[41,x]
F[41,x] = 1/F[22,x]*F[42,x]
F[42,x] = F[11,x]
F[43,x] = F[34,x]*F[44,x]
F[44,x] = 1/F[22,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[20,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[11,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{5}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{22}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{11}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_37(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_22(x))
Eq(F_13(x), F_14(x) + F_32(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_31(x))
Eq(F_16(x), F_17(x) + F_19(x))
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), x**2*F_18(x)**3 - x*(x - 1)*F_18(x)**2 + 1)
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_28(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), x**2*(F_27(x) + 1)**3 - x*(x - 1)*(F_27(x) + 1)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_18(x)*F_27(x)*F_30(x))
Eq(F_30(x), F_20(x) + F_4(x))
Eq(F_31(x), F_18(x)*F_5(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)*F_30(x)*F_34(x))
Eq(F_34(x), -F_0(x) + F_35(x))
Eq(F_35(x), F_36(x)/F_22(x))
Eq(F_36(x), F_2(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_22(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_2(x)*F_41(x))
Eq(F_41(x), F_42(x)/F_22(x))
Eq(F_42(x), F_11(x))
Eq(F_43(x), F_34(x)*F_44(x))
Eq(F_44(x), F_45(x)/F_22(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_20(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_11(x)*F_22(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, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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