02341_02431_03241_12340_12430_13240_23140
Counting sequence:
1, 1, 2, 6, 24, 113, 582, 3168, 17906, 104016, 616950, 3719871, 22728729, 140408972, 875454265, 5501828010, 34813950036, 221615333051, 1418213151899, 9118538797433, 58876010741705, 381592972903518, 2481741599870229, 16190987324540110, 105933761962200574, 694924892940545260, 4569766023251397096, 30117791350500970431, 198909025720384217309, 1316208538239993849859, 8725229190790269571988, 57937478935198432295670, 385324411534715445524326, 2566465840828369692905289, 17117806479296687104179418, 114321879403400997986428278, 764446569720939057474579138, 5117666815448059840908044429, 34298638275277325731725190129, 230110674113287590654071031230, 1545356142403938080107280743199, 10387976460709453768308789403950, 69891451088932638028578643077799, 470640671400155332489678636265328, 3171830651413390824251080243608524, 21392900310825128313670416681179661, 144395459747257156105559198414481472, 975321109187972225951009341585830926, 6592328347407530703643330038693701248, 44587679746764134200983464181398112312, 301761766687851439754555652490183542736, 2043506389481796062397830781044817317255, 13846500099888525577676315012967383974323, 93874280054812704031092689221345979676316, 636776057405831491431462788336611622590476, 4321671389287037902517201303948682320957280, 29344961165128064236056140561870090697754014, 199353757735671111783048153171330079128536056, 1354930787385887337993809335188947413705961226, 9213076484703207816719596626239455862678351910, 62673010314335640622318423946742430161373415748, 426519121533712807602858540026747494851311391305, 2903839395645572140284110954272257282124327115472, 19777762860231522098767560474803303882987698434447, 134755605617905927976228896791060609668289266475365, 918494342192251422842470565267187942995881483574527, 6262694176384196753318094555823644745739524196435627, 42716564991394958068266065829254423642064199551882742, 291458933363735823607476008854494716286944888729671782, 1989299075925366343199636307884124849545639250014864212, 13581894882522987751921501264679818367523617519909288222, 92758626917514015420694018169869996202120177263381108140, 633691924119652481103563338932097782272221768811671284180, 4330403412287469450220512515222868983958765928897917942094, 29600661574234146603994787513219515528180494176366991785464, 202392330048556259328378511338258660620628336128400323898946, 1384213497023901631047398533010327678175676334716825056622947, 9469465275296139263615103359163502117453541971286772402821776, 64797499560810284447575460137499285038226309865973546610807322, 443505117182028537890597205962362636375831251422370734983813696, 3036294593173747479336799158928750052620972846732262819641609553, 20791769379514692626702660214882508838240477295159143448036257321, 142409430431317813893870340786108038634560574682450350045788255647, 975626039446524181773727997596822792440150733017547634624247624258, 6685332530413968787510462926899036245270901227775439388289486193863, 45820032115641886779968654837203026475046481939882098544486538252831, 314107520624628380919576780258085979217854443669114837605059284687576, 2153722535108718208697563316350011359708100943876478708041527907735698, 14770242150672616689452549539239304059852025192288754785697244360249645, 101314117722207707780945072764701331282145559974586751669641405977328771, 695080195630784246843452012930014706530954939923826889435625481945733582, 4769585409353327225832388653827242684180482077737514912781783679517835994, 32734472309955176329805608501037259271387291631117303021736342515042149844, 224702211094138683419031488136089018569443431076812195885367073310295327972, 1542712429355024044147410394891099150108289897975895381912134645280997599374, 10593430911514449987225528563448808541206201477030351305465166373280950132810, 72754652823149493296367916146364604059020942235018418454153742357446957066799, 499753536470491130958647011079919229011762618365053770813372558818725975046442, 3433369069001629596619455223736683170138423506013419681221386723648853864157259, 23591372140252446188815618904447460594108018545282085954898773371969006619159572, 162125988905544974544295892836435373096015212666534987697599933964737083347478619
Specification 1
Strategy pack name: point_placements_tracked_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24670/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,k[0]]+F[9,x,k[0]]
F[8,x,k[0]] = k[0]*x*(1+F[8,x,k[0]])*(F[8,x,k[0]]^2+F[8,x,k[0]]+1)
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[20,x,k[0]]
F[19,x,k[0]] = F[2,x]+F[9,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[15,x,k[0]]*F[22,x,k[0]]*F[28,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[25,x,k[0]]
F[23,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = 1+x*F[24,x,k[0]]*(F[24,x,k[0]]^2-F[24,x,k[0]]+1)*k[0]
F[25,x,k[0]] = F[19,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[2,x]*F[27,x,k[0]]
F[27,x,k[0]] = (F[8,x,k[0]]-F[8,x,1])/(-1+k[0])
F[29,x,k[0]] = F[0,x]*F[28,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[15,x,k[0]]*F[30,x,k[0]]
F[31,x,k[0]] = F[7,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]*F[33,x,k[0]]
F[34,x,k[0]] = F[9,x,k[0]]
F[35,x,k[0]] = F[2,x]*F[28,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = x F_{8}\! \left(x , y\right)^{3} y +2 x F_{8}\! \left(x , y\right)^{2} y +2 x F_{8}\! \left(x , y\right) y +y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x F_{24}\! \left(x , y\right)^{3}-y x F_{24}\! \left(x , y\right)^{2}+y x F_{24}\! \left(x , y\right)+1
F_{25}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{28}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, k_0) + F_9(x, k_0))
Eq(F_8(x, k_0), k_0*x*(F_8(x, k_0) + 1)**3 - k_0*x*(F_8(x, k_0) + 1)**2 + (k_0*x - 1)*(F_8(x, k_0) + 1) + F_8(x, k_0) + 1)
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_20(x, k_0))
Eq(F_19(x, k_0), F_2(x) + F_9(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_15(x, k_0)*F_22(x, k_0)*F_28(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_25(x, k_0))
Eq(F_23(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), k_0*x*F_24(x, k_0)**3 - k_0*x*F_24(x, k_0)**2 + k_0*x*F_24(x, k_0) + 1)
Eq(F_25(x, k_0), F_19(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_2(x)*F_27(x, k_0))
Eq(F_27(x, k_0), -F_8(x, k_0) + (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_0(x)*F_28(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_15(x, k_0)*F_30(x, k_0))
Eq(F_31(x, k_0), F_7(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0)*F_33(x, k_0))
Eq(F_34(x, k_0), F_9(x, k_0))
Eq(F_35(x, k_0), F_2(x)*F_28(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}], "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": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, 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{"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 1], [2, 3], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 5]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 6]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}}]}
Specification 2
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24697/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[4,x]*F[8,x,k[0]]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0]]+F[6,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[23,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[26,x,k[0]]+F[6,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[16,x,k[0]]*F[22,x]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x]*F[4,x]*F[6,x,k[0]]
F[21,x,k[0]] = 1+x*F[21,x,k[0]]*(F[21,x,k[0]]^2-F[21,x,k[0]]+1)*k[0]
F[22,x] = F[23,x,1]
F[23,x,k[0]] = F[21,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[21,x,k[0]]^2*F[10,x,k[0]]*F[23,x,k[0]]
F[26,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]*F[21,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{6}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = x F_{21}\! \left(x , y\right)^{3} y -x F_{21}\! \left(x , y\right)^{2} y +x F_{21}\! \left(x , y\right) y +1
F_{22}\! \left(x \right) = F_{23}\! \left(x , 1\right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{21}\! \left(x , y\right)^{2} F_{10}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{21}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_4(x)*F_8(x, k_0))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0) + F_6(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_23(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_26(x, k_0) + F_6(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_16(x, k_0)*F_22(x)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x)*F_4(x)*F_6(x, k_0))
Eq(F_21(x, k_0), k_0*x*F_21(x, k_0)**3 - k_0*x*F_21(x, k_0)**2 + k_0*x*F_21(x, k_0) + 1)
Eq(F_22(x), F_23(x, 1))
Eq(F_23(x, k_0), F_21(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_10(x, k_0)*F_21(x, k_0)**2*F_23(x, k_0))
Eq(F_26(x, k_0), F_10(x, k_0)*F_11(x, k_0)*F_21(x, k_0))
Pack JSON:
{"name": "point_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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3]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"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": "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.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25657/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,k[0]]+F[9,x,k[0]]
F[8,x,k[0]] = k[0]*x*(1+F[8,x,k[0]])*(F[8,x,k[0]]^2+F[8,x,k[0]]+1)
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[20,x,k[0]]
F[19,x,k[0]] = F[2,x]+F[9,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[15,x,k[0]]*F[22,x,k[0]]*F[28,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[25,x,k[0]]
F[23,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = 1+x*F[24,x,k[0]]*(F[24,x,k[0]]^2-F[24,x,k[0]]+1)*k[0]
F[25,x,k[0]] = F[19,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[2,x]*F[27,x,k[0]]
F[27,x,k[0]] = (F[8,x,k[0]]-F[8,x,1])/(-1+k[0])
F[29,x,k[0]] = F[0,x]*F[28,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[15,x,k[0]]*F[30,x,k[0]]
F[31,x,k[0]] = F[7,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]*F[33,x,k[0]]
F[34,x,k[0]] = F[9,x,k[0]]
F[35,x,k[0]] = F[2,x]*F[28,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = x F_{8}\! \left(x , y\right)^{3} y +2 x F_{8}\! \left(x , y\right)^{2} y +2 x F_{8}\! \left(x , y\right) y +y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x F_{24}\! \left(x , y\right)^{3}-y x F_{24}\! \left(x , y\right)^{2}+y x F_{24}\! \left(x , y\right)+1
F_{25}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{28}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, k_0) + F_9(x, k_0))
Eq(F_8(x, k_0), k_0*x*(F_8(x, k_0) + 1)**3 - k_0*x*(F_8(x, k_0) + 1)**2 + (k_0*x - 1)*(F_8(x, k_0) + 1) + F_8(x, k_0) + 1)
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_20(x, k_0))
Eq(F_19(x, k_0), F_2(x) + F_9(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_15(x, k_0)*F_22(x, k_0)*F_28(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_25(x, k_0))
Eq(F_23(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), k_0*x*F_24(x, k_0)**3 - k_0*x*F_24(x, k_0)**2 + k_0*x*F_24(x, k_0) + 1)
Eq(F_25(x, k_0), F_19(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_2(x)*F_27(x, k_0))
Eq(F_27(x, k_0), -F_8(x, k_0) + (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_0(x)*F_28(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_15(x, k_0)*F_30(x, k_0))
Eq(F_31(x, k_0), F_7(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0)*F_33(x, k_0))
Eq(F_34(x, k_0), F_9(x, k_0))
Eq(F_35(x, k_0), F_2(x)*F_28(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}], "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": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 3], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 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{"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 1], [2, 3], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 3], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[2, 1], [2, 1], [2, 3], [2, 3], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 3], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[1, 5]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 6]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "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, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 2, 4, 3, 0], [1, 3, 2, 4, 0], [2, 3, 1, 4, 0]], "symmetry": true}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25741/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,k[0]]+F[9,x,k[0]]
F[8,x,k[0]] = k[0]*x*(1+F[8,x,k[0]])*(F[8,x,k[0]]^2+F[8,x,k[0]]+1)
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[20,x,k[0]]
F[19,x,k[0]] = F[2,x]+F[9,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[15,x,k[0]]*F[22,x,k[0]]*F[28,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[25,x,k[0]]
F[23,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = 1+x*F[24,x,k[0]]*(F[24,x,k[0]]^2-F[24,x,k[0]]+1)*k[0]
F[25,x,k[0]] = F[19,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[2,x]*F[27,x,k[0]]
F[27,x,k[0]] = (F[8,x,k[0]]-F[8,x,1])/(-1+k[0])
F[29,x,k[0]] = F[0,x]*F[28,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]+F[32,x,k[0]]
F[31,x,k[0]] = F[15,x,k[0]]*F[30,x,k[0]]
F[31,x,k[0]] = F[7,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]*F[33,x,k[0]]
F[34,x,k[0]] = F[9,x,k[0]]
F[35,x,k[0]] = F[2,x]*F[28,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = x F_{8}\! \left(x , y\right)^{3} y +2 x F_{8}\! \left(x , y\right)^{2} y +2 x F_{8}\! \left(x , y\right) y +y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x F_{24}\! \left(x , y\right)^{3}-y x F_{24}\! \left(x , y\right)^{2}+y x F_{24}\! \left(x , y\right)+1
F_{25}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{28}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, k_0) + F_9(x, k_0))
Eq(F_8(x, k_0), k_0*x*(F_8(x, k_0) + 1)**3 - k_0*x*(F_8(x, k_0) + 1)**2 + (k_0*x - 1)*(F_8(x, k_0) + 1) + F_8(x, k_0) + 1)
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_20(x, k_0))
Eq(F_19(x, k_0), F_2(x) + F_9(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_15(x, k_0)*F_22(x, k_0)*F_28(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_25(x, k_0))
Eq(F_23(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), k_0*x*F_24(x, k_0)**3 - k_0*x*F_24(x, k_0)**2 + k_0*x*F_24(x, k_0) + 1)
Eq(F_25(x, k_0), F_19(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_2(x)*F_27(x, k_0))
Eq(F_27(x, k_0), -F_8(x, k_0) + (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_0(x)*F_28(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0) + F_32(x, k_0))
Eq(F_31(x, k_0), F_15(x, k_0)*F_30(x, k_0))
Eq(F_31(x, k_0), F_7(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0)*F_33(x, k_0))
Eq(F_34(x, k_0), F_9(x, k_0))
Eq(F_35(x, k_0), F_2(x)*F_28(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:
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