01243_01342_01432_02143_02341_02431_03142_03241_03421_04132_04231_04321_10243_10342_10432_12043_13042_14032_20143_21043
Counting sequence:
1, 1, 2, 6, 24, 100, 426, 1875, 8482, 39143, 183476, 871216, 4182214, 20263013, 98958258, 486628732, 2407534846, 11974896698, 59846748198, 300375063936, 1513416795510, 7651864234492, 38810915374498, 197423975782268, 1006934914639018, 5148335838218990, 26382456349669356, 135479732454915108, 697075294995103042, 3593134226768117892, 18552543155498626462, 95945054567898772567, 496921893816201451054, 2577277480602148064488, 13384626559939346373682, 69597062926132681709062, 362314210947911193586260, 1888262002099032525993219, 9851363440191010310580254, 51447506826553470366589069, 268933353951727081892127316, 1407075341192620654704914545, 7368240825333209323405363456, 38615953471990270852070338596, 202539666505503580157686387642, 1063111341230529647074693533735, 5584170571979731208580319954590, 29351931699585050421098005835956, 154383340041322449979687435943554, 812527942460974693057185924045841, 4278971510974728079103124010948170, 22547242206177654517950015573554686, 118875054252821005212329744541091246, 627078848642749386524043799769658288, 3309627153105838968457151353506163152, 17476454129182111449599803424796661767, 92328796826153889850461622587938839502, 488003922276464945952066108528151752459, 2580505478755366813621365565600959318496, 13651331126117885604780421726367433870952, 72248310188361273238051226580854164291014, 382522429572682943629592261070396768417285, 2026081750016432583499772017635171194289058, 10735504762706104475026905696188824564196934, 56904717062201827375780864396725368274233624, 301737612379435507078540987529335469633877884, 1600520796925195079760600451807897730370977614, 8492575242892371748155839645774342440911076952, 45077457226174196557681092937457810527384263592, 239341077896471635737576431047685769523833798910, 1271185637559865629615851424072954634985010906828, 6753530345944928639359472401933824777712524251786, 35890480675916369890348108883124010431949715584722, 190787878955085921669819864218632296285631637622824, 1014476649769885010438945543039207744901691081328240, 5395726376071731107708155890523906226401924708894092, 28705909393959572093545949040195609268861425041001266, 152757763530358816697797764165448054205697098947069462, 813098268816058835647664839156237566673063163166409638, 4329002385707261401263372109515900037932107050290541698, 23053402864617226239617601499627030157692789503730680000, 122795417201717326461676867515104967760427386151458900712, 654224424048838918385947385450850740631998115680214020370, 3486313853736885335211306705005465739297863389820116913112, 18582283649626684498890274509573616584007732417371417097406, 99065488371772092440057998272494633396490774542551188573174, 528243641230313478260080972316333327692337683092759297237762, 2817297652901861051612988008839671874148226233424788741000372, 15028505332587469421694482696204940751100204765143913050697106, 80182861517003532946184237386357890475249863242712370632997246, 427886105843598084878476197468817154687339242147935188382345172, 2283778171118741879775087526707673524709431142942134126599982076, 12191496979581929164203957761378612766299487019231314785754946062, 65093238399334391106245850337123951229119974687283599986657864612, 347607260783070366151243551272331155504352473671969395773616776410, 1856582969457663400847765453195753308505863466348409289666913638408, 9917699365413442535198744265947872919727888864327641830937407300310, 52987948967383534737643590724707281775409540693116327063807177313552, 283146668161008664663674434679848993517027223217819369498277060973536, 1513256695622880111681953263313159055479256229438906482641925132027264, 8088709205559757265758875038715094779380752930204275690907195519028142
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24325/
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[1,x]+F[43,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[1,x]+F[39,x]+F[40,x]+F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[35,x,k[0]]+F[38,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[31,x,k[0]]+F[33,x,k[0]]+F[34,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[16,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[17,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[20,x,k[0]]+F[8,x,k[0]]
F[19,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[24,x,k[0]]+F[30,x,k[0]]
F[23,x,k[0]] = F[17,x,k[0]]*F[3,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[3,x]
F[25,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[26,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[29,x,k[0]] = F[21,x,k[0]]*F[27,x,k[0]]
F[30,x,k[0]] = F[21,x,k[0]]*F[26,x,k[0]]
F[31,x,k[0]] = F[3,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[25,x,k[0]]*k[0]-F[25,x,1])
F[33,x,k[0]] = F[3,x]*F[32,x,k[0]]
F[34,x,k[0]] = F[21,x,k[0]]*F[25,x,k[0]]
F[35,x,k[0]] = F[3,x]*F[36,x,k[0]]
F[36,x,k[0]] = 1/(-1+k[0])*(F[37,x,k[0]]*k[0]-F[37,x,1])
F[37,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[38,x,k[0]] = F[21,x,k[0]]*F[37,x,k[0]]
F[39,x] = F[19,x,1]
F[40,x] = F[3,x]*F[41,x]
F[41,x] = F[42,x,1]
F[42,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[43,x] = F[3,x]*F[44,x]
F[44,x] = F[1,x]+F[45,x]+F[48,x]+F[51,x]
F[45,x] = F[3,x]*F[46,x]
F[46,x] = F[47,x,1]
F[47,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[48,x] = F[3,x]*F[49,x]
F[49,x] = F[50,x,1]
F[50,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[51,x] = F[3,x]*F[49,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)+F_{40}\! \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_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{3}\! \left(x \right)
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) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{26}\! \left(x , y\right) = -\frac{-y F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-y F_{37}\! \left(x , y\right)+F_{37}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{39}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{40}\! \left(x \right) = F_{3}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{42}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{43}\! \left(x \right) = F_{3}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)+F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{45}\! \left(x \right) = F_{3}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{47}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{48}\! \left(x \right) = F_{3}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{51}\! \left(x \right) = F_{3}\! \left(x \right) F_{49}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_43(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_39(x) + F_40(x) + F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_35(x, k_0) + F_38(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_31(x, k_0) + F_33(x, k_0) + F_34(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_16(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_20(x, k_0) + F_8(x, k_0))
Eq(F_19(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_1(x) + F_23(x, k_0) + F_24(x, k_0) + F_30(x, k_0))
Eq(F_23(x, k_0), F_17(x, k_0)*F_3(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_3(x))
Eq(F_25(x, k_0), (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
Eq(F_26(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_29(x, k_0), F_21(x, k_0)*F_27(x, k_0))
Eq(F_30(x, k_0), F_21(x, k_0)*F_26(x, k_0))
Eq(F_31(x, k_0), F_3(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (k_0*F_25(x, k_0) - F_25(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_3(x)*F_32(x, k_0))
Eq(F_34(x, k_0), F_21(x, k_0)*F_25(x, k_0))
Eq(F_35(x, k_0), F_3(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (k_0*F_37(x, k_0) - F_37(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), F_21(x, k_0)*F_37(x, k_0))
Eq(F_39(x), F_19(x, 1))
Eq(F_40(x), F_3(x)*F_41(x))
Eq(F_41(x), F_42(x, 1))
Eq(F_42(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_43(x), F_3(x)*F_44(x))
Eq(F_44(x), F_1(x) + F_45(x) + F_48(x) + F_51(x))
Eq(F_45(x), F_3(x)*F_46(x))
Eq(F_46(x), F_47(x, 1))
Eq(F_47(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_48(x), F_3(x)*F_49(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_50(x, k_0), (-k_0*F_26(x, k_0) + F_26(x, 1))/(1 - k_0))
Eq(F_51(x), F_3(x)*F_49(x))
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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 2, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 2
Strategy pack name: point_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24326/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[1,x]+F[44,x]+F[6,x]
F[6,x] = F[4,x]*F[7,x]
F[7,x] = F[1,x]+F[40,x]+F[41,x]+F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[36,x,k[0]]+F[39,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[4,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[13,x,k[0]] = F[14,x,k[0]]*F[4,x]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[32,x,k[0]]+F[34,x,k[0]]+F[35,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[4,x]
F[17,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
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[1,x]+F[20,x,k[0]]+F[21,x,k[0]]+F[9,x,k[0]]
F[20,x,k[0]] = F[15,x,k[0]]*F[4,x]
F[21,x,k[0]] = F[22,x,k[0]]*F[23,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]+F[25,x,k[0]]+F[31,x,k[0]]
F[24,x,k[0]] = F[18,x,k[0]]*F[4,x]
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[27,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[28,x,k[0]] = F[1,x]+F[29,x,k[0]]+F[30,x,k[0]]
F[29,x,k[0]] = F[19,x,k[0]]*F[4,x]
F[30,x,k[0]] = F[22,x,k[0]]*F[28,x,k[0]]
F[31,x,k[0]] = F[22,x,k[0]]*F[27,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[33,x,k[0]] = 1/(-1+k[0])*(F[26,x,k[0]]*k[0]-F[26,x,1])
F[34,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[35,x,k[0]] = F[22,x,k[0]]*F[26,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[4,x]
F[37,x,k[0]] = 1/(-1+k[0])*(F[38,x,k[0]]*k[0]-F[38,x,1])
F[38,x,k[0]] = 1/(-1+k[0])*(F[23,x,k[0]]*k[0]-F[23,x,1])
F[39,x,k[0]] = F[22,x,k[0]]*F[38,x,k[0]]
F[40,x] = F[20,x,1]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x,1]
F[43,x,k[0]] = 1/(-1+k[0])*(F[23,x,k[0]]*k[0]-F[23,x,1])
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[1,x]+F[46,x]+F[49,x]+F[52,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x,1]
F[51,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[52,x] = F[4,x]*F[50,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{14}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
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_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{-y F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = -\frac{-y F_{26}\! \left(x , y\right)+F_{26}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}
F_{38}\! \left(x , y\right) = -\frac{-y F_{23}\! \left(x , y\right)+F_{23}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{40}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = -\frac{-y F_{23}\! \left(x , y\right)+F_{23}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x , 1\right)
F_{51}\! \left(x , y\right) = -\frac{-y F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_1(x) + F_44(x) + F_6(x))
Eq(F_6(x), F_4(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_40(x) + F_41(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_36(x, k_0) + F_39(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_4(x))
Eq(F_12(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_14(x, k_0)*F_4(x))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_32(x, k_0) + F_34(x, k_0) + F_35(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_4(x))
Eq(F_17(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
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_1(x) + F_20(x, k_0) + F_21(x, k_0) + F_9(x, k_0))
Eq(F_20(x, k_0), F_15(x, k_0)*F_4(x))
Eq(F_21(x, k_0), F_22(x, k_0)*F_23(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0) + F_25(x, k_0) + F_31(x, k_0))
Eq(F_24(x, k_0), F_18(x, k_0)*F_4(x))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_27(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_1(x) + F_29(x, k_0) + F_30(x, k_0))
Eq(F_29(x, k_0), F_19(x, k_0)*F_4(x))
Eq(F_30(x, k_0), F_22(x, k_0)*F_28(x, k_0))
Eq(F_31(x, k_0), F_22(x, k_0)*F_27(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_33(x, k_0), (k_0*F_26(x, k_0) - F_26(x, 1))/(k_0 - 1))
Eq(F_34(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_35(x, k_0), F_22(x, k_0)*F_26(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_4(x))
Eq(F_37(x, k_0), (k_0*F_38(x, k_0) - F_38(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), (k_0*F_23(x, k_0) - F_23(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_22(x, k_0)*F_38(x, k_0))
Eq(F_40(x), F_20(x, 1))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x, 1))
Eq(F_43(x, k_0), (-k_0*F_23(x, k_0) + F_23(x, 1))/(1 - k_0))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_1(x) + F_46(x) + F_49(x) + F_52(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x, 1))
Eq(F_51(x, k_0), (-k_0*F_27(x, k_0) + F_27(x, 1))/(1 - k_0))
Eq(F_52(x), F_4(x)*F_50(x))
Pack JSON:
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Specification JSON:
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