01234_01243_01324_01342_01423_01432_02314_02413_12304_12403
Counting sequence:
1, 1, 2, 6, 24, 110, 540, 2762, 14544, 78342, 429852, 2394858, 13514320, 77090282, 443819364, 2575488650, 15049106016, 88469158846, 522876526924, 3105118229874, 18518852749520, 110872508051890, 666116510805684, 4014735000614834, 24267513461897632, 147079240768468130, 893600729928649828, 5441523099273334858, 33205497188273969408, 203024025897030717402, 1243583162022416194276, 7630270596886231477378, 46891651461371163689472, 288601618871070177193030, 1778732631252336071507484, 10977304180690205581690394, 67829920774769306144476880, 419621436633272343102360474, 2598826771987757102690849412, 16112206638075252824670301242, 99992491159848942147722086816, 621144748155756704753287165082, 3861991136305078617958725015636, 24032787075042147221044534562034, 149676663069810846524474264960320, 932921248900962870744965323650082, 5819179305170435422516057701153140, 36323714694235131757889914598470186, 226891032365289816981954979087409664, 1418177474015258434533937115159945658, 8869893044993863413882718856363746004, 55509817355360915717903559319411245362, 347595812396916363405313418199243712704, 2177824570274013151553735762462989364338, 13652296629468952040097791916158068805780, 85627715004435281346012815461872885981162, 537329434784936195462139215165547368952064, 3373469624086803987525265767187441375439202, 21189247560955130630232268553318864147947460, 133152666008963924435869676602458653683211890, 837092001286111079486505240900186658610546912, 5264767965035215284342524059113631791448036130, 33125468273494883975808425602744072541820273588, 208504716728727770734808389719901216394426103674, 1312911329308583433723589573521695400250974916032, 8270188402374712397371285687476472870003311243326, 52113589066556927656528639210718169218679697189324, 328501562388745343609037485858165998811290874684242, 2071430088041396070561981713937546064289790735808720, 13066077039835673530512949455924840892189739585821778, 82443825748984278742092801478508768410992404063992308, 520361451395358436337433833740303146487864410118214930, 3285355638581427238246188880428400737780116022333280032, 20748482805227082433639930541782941443219768115386019506, 131073086249796829658732872388781762898685496308109569220, 828248405892880405352554126674376092457997524804251475562, 5235093065481270024173805239046498797161881576073215505600, 33098007998147471638475282184602544548195211184178402482842, 209310017837126602293394770505046995753908678777867442537828, 1323994101172555802292874534114259219513321332960810621479042, 8376975385534352902495502640977597317832167517803987212674688, 53014047193871881443402987357599673551238229376736676412935714, 335578932590510588892889930838383576185573183789950934533638052, 2124692037553128241326487537017990992886196236500982079231955818, 13455273234500552896506797068566936742341492376039549259884962688, 85227945548639629892102033680156881329975155639487444707112641130, 539960888802039109166023956376803608194305359493320522112681809668, 3421615989215590971539307957394335554859683494897417213688471587874, 21686370622931537212162632601842072616475135506980542013977683532544, 137476088155475969620560395655358446962209086984062213491489166216474, 871666266487724432009886767630906016326711781937951668874214523157620, 5527824672629638000775149787499355780752616686050926693906146836792330, 35062062017528399476730890418132384857737064352587117757186894000773728, 222432428167386584822302927123330203144625652786864675661308625470078650, 1411349409097841222658955444336672332302163753238777845194450495251013604, 8956641128936615221365494758320416294814122985979295775069346923275415410, 56849732766666168727493995813426271612282946484462105977490542112346642496, 360896606485334070699157364481470393835198801697732070312854437689394171618, 2291431204087102094147814798707597708543464868993442750462213878681792005348, 14551209135976283441595003479364607342489244485668289563387729288894565437050, 92418348189346866160080408873090323210007468416555383024535122680373613919040
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24206/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[1,x]+F[35,x]+F[4,x]
F[4,x] = F[13,x]*F[5,x]
F[5,x] = F[1,x]+F[31,x]+F[33,x]+F[6,x]
F[6,x] = F[13,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[14,x,k[0]]+F[30,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[8,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x]
F[12,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[13,x] = x
F[14,x,k[0]] = F[13,x]*F[15,x,k[0]]
F[15,x,k[0]] = (F[16,x,k[0]]*k[0]-F[16,x,1])/(-1+k[0])
F[16,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[19,x,k[0]]+F[20,x,k[0]]
F[18,x,k[0]] = F[10,x,k[0]]*F[17,x,k[0]]
F[19,x,k[0]] = F[13,x]*F[16,x,k[0]]
F[20,x,k[0]] = F[13,x]*F[21,x,k[0]]
F[21,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[22,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[23,x,k[0]]+F[24,x,k[0]]
F[23,x,k[0]] = F[13,x]*F[8,x,k[0]]
F[24,x,k[0]] = F[13,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[26,x,k[0]]+F[27,x,k[0]]+F[9,x,k[0]]
F[26,x,k[0]] = F[12,x,k[0]]*F[13,x]
F[21,x,k[0]] = F[1,x]+F[26,x,k[0]]+F[27,x,k[0]]+F[28,x,k[0]]+F[29,x]
F[28,x,k[0]] = F[10,x,k[0]]*F[16,x,k[0]]
F[29,x] = F[18,x,1]
F[16,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[28,x,k[0]]+F[29,x]+F[30,x,k[0]]
F[31,x] = F[13,x]*F[32,x]
F[32,x] = F[16,x,1]
F[33,x] = F[13,x]*F[34,x]
F[34,x] = F[21,x,1]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[1,x]+F[37,x]+F[38,x]+F[6,x]
F[37,x] = F[13,x]*F[7,x]
F[38,x] = F[24,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{13}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{13}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{8}\! \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_{13}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x \right) = x
F_{14}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{29}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{33}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_13(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_35(x) + F_4(x))
Eq(F_4(x), F_13(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_31(x) + F_33(x) + F_6(x))
Eq(F_6(x), F_13(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_11(x, k_0) + F_14(x, k_0) + F_30(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_8(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x))
Eq(F_12(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_13(x), x)
Eq(F_14(x, k_0), F_13(x)*F_15(x, k_0))
Eq(F_15(x, k_0), (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_16(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_19(x, k_0) + F_20(x, k_0))
Eq(F_18(x, k_0), F_10(x, k_0)*F_17(x, k_0))
Eq(F_19(x, k_0), F_13(x)*F_16(x, k_0))
Eq(F_20(x, k_0), F_13(x)*F_21(x, k_0))
Eq(F_21(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_1(x) + F_18(x, k_0) + F_23(x, k_0) + F_24(x, k_0))
Eq(F_23(x, k_0), F_13(x)*F_8(x, k_0))
Eq(F_24(x, k_0), F_13(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_1(x) + F_11(x, k_0) + F_26(x, k_0) + F_27(x, k_0) + F_9(x, k_0))
Eq(F_26(x, k_0), F_12(x, k_0)*F_13(x))
Eq(F_21(x, k_0), F_1(x) + F_26(x, k_0) + F_27(x, k_0) + F_28(x, k_0) + F_29(x))
Eq(F_28(x, k_0), F_10(x, k_0)*F_16(x, k_0))
Eq(F_29(x), F_18(x, 1))
Eq(F_16(x, k_0), F_1(x) + F_14(x, k_0) + F_28(x, k_0) + F_29(x) + F_30(x, k_0))
Eq(F_31(x), F_13(x)*F_32(x))
Eq(F_32(x), F_16(x, 1))
Eq(F_33(x), F_13(x)*F_34(x))
Eq(F_34(x), F_21(x, 1))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_1(x) + F_37(x) + F_38(x) + F_6(x))
Eq(F_37(x), F_13(x)*F_7(x))
Eq(F_38(x), F_24(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 3, 1, 4], "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, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 4, "original_rule": {"children": 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"pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 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[0, 4], [0, 1], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 3], [0, 4], [0, 4], [0, 0], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 3], [0, 4], [0, 4], [0, 1], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 3], [0, 4], [0, 4], [0, 2], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 3], [0, 4], [0, 4], [0, 3], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 0], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 2], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 4], [0, 4], [0, 0], [0, 4]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 0], [0, 4]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 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{"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 0, "strategy_class": "FusionStrategy", "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24207/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[21,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[3,x]
F[13,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[11,x,k[0],k[1]]*k[0]*k[1]-F[11,x,1/k[1],k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[16,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[3,x]
F[18,x,k[0],k[1]] = 1/(-1+k[0])*(F[16,x,k[0],k[1]]*k[0]-F[16,x,1,k[1]])
F[19,x,k[0],k[1]] = F[20,x,k[1],k[0]]*F[9,x,k[0]]
F[20,x,k[0],k[1]] = (-F[11,x,1,k[1]]*k[1]+F[11,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0]]*F[5,x,k[1]]*F[9,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[9,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[9,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{21}\! \left(x , z , y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{y z F_{11}\! \left(x , y , z\right)-F_{11}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = \frac{y F_{5}\! \left(x , y\right)-z F_{5}\! \left(x , z\right)}{-z +y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = -\frac{-y F_{16}\! \left(x , y , z\right)+F_{16}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , z , y\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = -\frac{z F_{11}\! \left(x , 1, z\right)-y F_{11}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y\right) F_{5}\! \left(x , z\right) F_{9}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{9}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_21(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_3(x))
Eq(F_13(x, k_0, k_1), (k_0*k_1*F_11(x, k_0, k_1) - F_11(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_3(x))
Eq(F_18(x, k_0, k_1), (k_0*F_16(x, k_0, k_1) - F_16(x, 1, k_1))/(k_0 - 1))
Eq(F_19(x, k_0, k_1), F_20(x, k_1, k_0)*F_9(x, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_11(x, k_0/k_1, k_1) + k_1*F_11(x, 1, k_1))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0)*F_5(x, k_1)*F_9(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_9(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 3, 1, 4], "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, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 3], [1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 3], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 4], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 3], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 3], [1, 2], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 3], [1, 2], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 3], [1, 3], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 4], [1, 2], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 4], [1, 3], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 3], [1, 4], [1, 3], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 3], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 4], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 3], [1, 2], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 2], [1, 4], 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