1032_1302_2301
Counting sequence:
1, 1, 2, 6, 21, 77, 286, 1066, 3978, 14858, 55556, 208012, 780045, 2930085, 11025510, 41560770, 156938430, 593636670, 2249244060, 8535951060, 32444397570, 123501460914, 470783346732, 1797045948836, 6868463963956, 26284315603252, 100703763395592, 386263129337624, 1483156828673597, 5700803693467477, 21933622262363574, 84467779350804402, 325582066632106102, 1256035164222331766, 4849525364763282476, 18738631479060710532, 72460883742672747574, 280403360348653315270, 1085835610635292392260, 4207599207373905942060, 16314841195390520668620, 63299303038996598539980, 245738131342776717777720, 954540158704913182305960, 3709837323988668375720210, 14426001725413171386122370, 56125396511916591983226012, 218467821311091156218682996, 850790852811215945439595308, 3314808539738007945730983468, 12920750750005202811226655256, 50385362423677055895694785096, 196563255203746119257755404132, 767142152968499971272916140996, 2995155917203397642451807846936, 11698437572317285497570165034632, 45708410822614576988623174782696, 178656750692968938234545475075816, 698543106369717351437077612224528, 2732203737698068829396690984425008, 10689929595052979562300577298311581, 41838343540230521493600869259286197, 163797827124468250205056990354411350, 641463738060614347505520490911100050, 2512828538060471801623913450274416550, 9846388396539574819356371828511229350, 38593232647153651706006905820894781900, 151308139862964107063137053897143072100, 593372397605990060309932068774269741550, 2327573417000565688773950661420689711550, 9132456964407011883076885955046458054100, 35840773823972831109069094766590635758940, 140692199065326473188328690208012073961820, 552411928078029779009800347467908611232860, 2169472001575637889541994569160995672873560, 8521983559662859051603662709578790039232520, 33482719478461914607101254430779392227214470, 131580633740206525418354557985097595781666390, 517192647303228519530779988659740503747938420, 2033292233359192054008731292412994458903644220, 7995256354626233428991797230127168062001963140, 31444755469194805497613046223319264524122655620, 123693094521979414077152653805645509477658238920, 486656265181526262821367317688536563337261974360, 1915036684416446140333885768169207603562454250460, 7537166853774928792239087651357195496416091172220, 29669744383178785453885123112688056633345238091240, 116813372794928285532611871559210717705813441383800, 459984179406235554914577964753690070481010462429400, 1811604259373994671615454603180846869318539267421400, 7135960824384996828328050198518029790544263348402800, 28113109776326262854372920501998537938515769718053200, 110772329599085676516802368822533875157644994238384050, 436534287627275377314335848845409013561037871133551650, 1720556121964372756313160362490437044188806013415707900, 6782370515389206910486534623033172483712997054530001300, 26739616583000013372982304435416768856215754183156522940, 105435941536592895071198571743913500644753498279580338620, 415796570199354513243325403472144218820069190450574144760, 1639950537138601475664766267531321716529950075093434121960, 6469000112881766173027106602587798880878564922527776873820
Generating function in Maple syntax:
-1/2*(2*(-4*x+1)^(1/2)*x+2*x^2-(-4*x+1)^(1/2)-4*x+1)*(3*x-1)/x^4
Generating function in latex syntax:
-\frac{\left(2 \sqrt{-4 x +1}\, x +2 x^{2}-\sqrt{-4 x +1}-4 x +1\right) \left(3 x -1\right)}{2 x^{4}}
Generating function in sympy syntax:
(3*x - 1)*(-x**2 - x*sqrt(1 - 4*x) + 2*x + sqrt(1 - 4*x)/2 - 1/2)/x**4
Implicit equation for the generating function in Maple syntax:
x^4*F(x)^2+(3*x-1)*(2*x^2-4*x+1)*F(x)+(3*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
x^{4} F \! \left(x \right)^{2}+\left(3 x -1\right) \left(2 x^{2}-4 x +1\right) F \! \left(x \right)+\left(3 x -1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+3) = 12*(3+2*n)/(7+n)*a(n)-2*(44+13*n)/(7+n)*a(n+1)+(47+9*n)/(7+n)*a(n+2), n >= 3
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(n +3\right) = \frac{12 \left(3+2 n \right) a \! \left(n \right)}{7+n}-\frac{2 \left(44+13 n \right) a \! \left(n +1\right)}{7+n}+\frac{\left(47+9 n \right) a \! \left(n +2\right)}{7+n}, \quad n \geq 3
Specification 1
Strategy pack name: point_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/385/
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]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]*F[5,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x,1]
F[14,x,k[0]] = F[15,x,k[0]]
F[16,x,k[0]] = F[15,x,k[0]]+F[48,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[43,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[40,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]+F[23,x,k[0]]
F[19,x,k[0]] = F[1,x]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[19,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[19,x,k[0]]*F[25,x,k[0]]*F[4,x]
F[25,x,k[0]] = F[18,x,k[0]]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]*F[4,x]
F[28,x,k[0]] = F[29,x,k[0]]+F[38,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]+F[32,x]
F[31,x,k[0]] = F[19,x,k[0]]*F[30,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[14,x,k[0]]
F[32,x] = F[33,x]*F[36,x]
F[33,x] = F[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[33,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[4,x]*F[8,x]
F[38,x,k[0]] = F[39,x]
F[39,x] = F[33,x]*F[6,x]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[4,x]*F[42,x,k[0]]
F[42,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[19,x,k[0]]*F[45,x]
F[45,x] = -F[0,x]+F[46,x]
F[46,x] = 1/F[4,x]*F[47,x]
F[47,x] = F[2,x]
F[48,x,k[0]] = F[19,x,k[0]]*F[46,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_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\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)+F_{48}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{32}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right) F_{6}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{46}\! \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_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_5(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x, 1))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_16(x, k_0), F_15(x, k_0) + F_48(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_43(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_40(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0) + F_23(x, k_0))
Eq(F_19(x, k_0), F_1(x) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_19(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_19(x, k_0)*F_25(x, k_0)*F_4(x))
Eq(F_25(x, k_0), F_18(x, k_0) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0)*F_4(x))
Eq(F_28(x, k_0), F_29(x, k_0) + F_38(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0) + F_32(x))
Eq(F_31(x, k_0), F_19(x, k_0)*F_30(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_14(x, k_0))
Eq(F_32(x), F_33(x)*F_36(x))
Eq(F_33(x), F_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_33(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_4(x)*F_8(x))
Eq(F_38(x, k_0), F_39(x))
Eq(F_39(x), F_33(x)*F_6(x))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_4(x)*F_42(x, k_0))
Eq(F_42(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_19(x, k_0)*F_45(x))
Eq(F_45(x), -F_0(x) + F_46(x))
Eq(F_46(x), F_47(x)/F_4(x))
Eq(F_47(x), F_2(x))
Eq(F_48(x, k_0), F_19(x, k_0)*F_46(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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": "point_placements_tracked_fusion_expand_verified", "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], 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1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 4], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 3]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [2, 3], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 3], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [2, 0], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 4], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 3], [2, 2], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 3], [2, 2], [2, 4], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 3], [2, 3], [2, 4], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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: row_placements_tracked_fusion
Tree: http://permpal.com/tree/386/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[25,x]*F[3,x]
F[3,x] = F[1,x]+F[133,x]+F[4,x]
F[4,x] = F[25,x]*F[5,x]
F[5,x] = F[1,x]+F[107,x]+F[253,x]+F[6,x]
F[6,x] = F[25,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[250,x,k[0]]+F[251,x,k[0]]+F[252,x,k[0]]+F[9,x]
F[9,x] = F[10,x]*F[25,x]
F[10,x] = F[1,x]+F[11,x]+F[170,x]+F[27,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]*F[25,x]
F[13,x,k[0]] = F[1,x]+F[112,x]+F[122,x]+F[14,x,k[0]]+F[249,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[25,x]
F[15,x,k[0]] = F[1,x]+F[115,x,k[0]]+F[16,x]+F[231,x,k[0]]+F[233,x,k[0]]+F[235,x,k[0]]
F[16,x] = F[17,x]*F[25,x]
F[17,x] = F[1,x]+F[133,x]+F[18,x]+F[230,x]
F[18,x] = F[19,x]*F[25,x]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[1,x]+F[16,x]+F[172,x,k[0]]+F[184,x,k[0]]+F[21,x]
F[21,x] = F[22,x]*F[25,x]
F[22,x] = F[1,x]+F[16,x]+F[170,x]+F[23,x]+F[27,x]
F[23,x] = F[24,x]*F[25,x]
F[24,x] = F[15,x,1]
F[25,x] = F[26,x,1]
F[26,x,k[0]] = k[0]*x
F[27,x] = F[28,x,1]
F[28,x,k[0]] = F[25,x]*F[29,x,k[0]]
F[29,x,k[0]] = F[1,x]+F[217,x]+F[229,x,k[0]]+F[30,x,k[0]]+F[31,x]
F[30,x,k[0]] = F[25,x]*F[29,x,k[0]]
F[31,x] = F[25,x]*F[32,x]
F[32,x] = F[33,x,1]
F[33,x,k[0]] = F[1,x]+F[112,x]+F[228,x]+F[34,x,k[0]]+F[78,x,k[0]]
F[34,x,k[0]] = F[26,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[1,x]+F[226,x,k[0]]+F[36,x,k[0]]+F[50,x,k[0]]
F[36,x,k[0]] = F[26,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[38,x]+F[41,x,k[0]]
F[38,x] = F[1,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[25,x]*F[38,x]
F[41,x,k[0]] = F[42,x,k[0]]+F[45,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[26,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[42,x,k[0]]
F[45,x,k[0]] = F[46,x]+F[47,x,k[0]]+F[49,x,k[0]]
F[46,x] = 0
F[47,x,k[0]] = F[26,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[39,x]+F[45,x,k[0]]
F[49,x,k[0]] = F[25,x]*F[41,x,k[0]]
F[50,x,k[0]] = F[25,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[1,x]+F[227,x]+F[52,x,k[0]]+F[53,x,k[0]]+F[57,x,k[0]]
F[52,x,k[0]] = F[26,x,k[0]]*F[51,x,k[0]]
F[53,x,k[0]] = F[25,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[134,x,k[0]]+F[135,x]+F[225,x]+F[36,x,k[0]]+F[55,x,k[0]]
F[55,x,k[0]] = F[25,x]*F[56,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[133,x]+F[52,x,k[0]]+F[53,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[25,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[1,x]+F[127,x,k[0]]+F[129,x,k[0]]+F[131,x,k[0]]+F[59,x,k[0]]+F[73,x,k[0]]
F[59,x,k[0]] = F[26,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[61,x]+F[66,x,k[0]]
F[61,x] = F[38,x]+F[62,x]
F[62,x] = F[39,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[25,x]*F[65,x]
F[65,x] = F[39,x]+F[63,x]
F[66,x,k[0]] = F[41,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[45,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = 2*F[46,x]+F[69,x,k[0]]+F[71,x,k[0]]
F[69,x,k[0]] = F[26,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[63,x]+F[68,x,k[0]]
F[71,x,k[0]] = F[25,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[45,x,k[0]]+F[68,x,k[0]]
F[73,x,k[0]] = F[25,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[1,x]+F[125,x,k[0]]+F[126,x,k[0]]+F[75,x,k[0]]+F[76,x,k[0]]
F[75,x,k[0]] = F[26,x,k[0]]*F[74,x,k[0]]
F[76,x,k[0]] = F[25,x]*F[77,x,k[0]]
F[77,x,k[0]] = F[1,x]+F[112,x]+F[122,x]+F[34,x,k[0]]+F[78,x,k[0]]+F[83,x]
F[78,x,k[0]] = F[25,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[1,x]+F[36,x,k[0]]+F[80,x,k[0]]+F[81,x,k[0]]+F[82,x,k[0]]
F[80,x,k[0]] = F[25,x]*F[58,x,k[0]]
F[81,x,k[0]] = F[25,x]*F[54,x,k[0]]
F[82,x,k[0]] = F[25,x]*F[79,x,k[0]]
F[83,x] = F[84,x,1]
F[84,x,k[0]] = F[25,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[1,x]+F[113,x,k[0]]+F[115,x,k[0]]+F[16,x]+F[28,x,k[0]]+F[86,x]
F[86,x] = F[25,x]*F[87,x]
F[87,x] = F[1,x]+F[16,x]+F[86,x]+F[88,x]
F[88,x] = F[25,x]*F[89,x]
F[89,x] = F[90,x,1]
F[90,x,k[0]] = F[1,x]+F[104,x,k[0]]+F[110,x,k[0]]+F[112,x]+F[91,x,k[0]]
F[91,x,k[0]] = F[26,x,k[0]]*F[92,x,k[0]]
F[92,x,k[0]] = F[93,x]+F[96,x,k[0]]
F[93,x] = F[1,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[25,x]*F[93,x]
F[96,x,k[0]] = F[100,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[26,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[1,x]+F[97,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[103,x,k[0]]+F[46,x]
F[101,x,k[0]] = F[102,x,k[0]]*F[26,x,k[0]]
F[102,x,k[0]] = F[100,x,k[0]]+F[94,x]
F[103,x,k[0]] = F[25,x]*F[96,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[25,x]
F[105,x,k[0]] = F[1,x]+F[106,x,k[0]]+F[107,x]+F[109,x,k[0]]+F[6,x]
F[106,x,k[0]] = F[105,x,k[0]]*F[26,x,k[0]]
F[107,x] = F[108,x,1]
F[108,x,k[0]] = F[20,x,k[0]]*F[25,x]
F[109,x,k[0]] = F[105,x,k[0]]*F[25,x]
F[110,x,k[0]] = F[111,x,k[0]]*F[25,x]
F[111,x,k[0]] = (F[90,x,k[0]]*k[0]-F[90,x,1])/(-1+k[0])
F[112,x] = F[17,x]*F[25,x]
F[113,x,k[0]] = F[114,x,k[0]]*F[25,x]
F[114,x,k[0]] = 1/(-1+k[0])*(F[85,x,k[0]]*k[0]-F[85,x,1])
F[115,x,k[0]] = F[116,x,k[0]]*F[26,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[99,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[94,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[121,x,k[0]]+F[46,x]
F[119,x,k[0]] = F[120,x,k[0]]*F[25,x]
F[120,x,k[0]] = F[118,x,k[0]]+F[97,x,k[0]]
F[121,x,k[0]] = F[117,x,k[0]]*F[26,x,k[0]]
F[122,x] = F[123,x,1]
F[123,x,k[0]] = F[124,x,k[0]]*F[26,x,k[0]]
F[124,x,k[0]] = F[1,x]+F[115,x,k[0]]+F[12,x,k[0]]+F[28,x,k[0]]
F[125,x,k[0]] = F[25,x]*F[56,x,k[0]]
F[126,x,k[0]] = F[25,x]*F[74,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]*F[25,x]
F[128,x,k[0]] = (F[58,x,k[0]]*k[0]-F[58,x,1])/(-1+k[0])
F[129,x,k[0]] = F[130,x,k[0]]*F[25,x]
F[130,x,k[0]] = (F[54,x,k[0]]*k[0]-F[54,x,1])/(-1+k[0])
F[131,x,k[0]] = F[132,x,k[0]]*F[25,x]
F[132,x,k[0]] = (F[79,x,k[0]]*k[0]-F[79,x,1])/(-1+k[0])
F[133,x] = F[25,x]*F[87,x]
F[134,x,k[0]] = F[25,x]*F[77,x,k[0]]
F[135,x] = F[136,x]*F[25,x]
F[136,x] = F[1,x]+F[137,x]+F[157,x]+F[219,x]+F[222,x]
F[137,x] = F[138,x,1]
F[138,x,k[0]] = F[139,x,k[0]]*F[26,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]+F[145,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[38,x]
F[141,x,k[0]] = F[142,x,k[0]]+F[97,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]*F[26,x,k[0]]
F[144,x,k[0]] = F[142,x,k[0]]+F[39,x]
F[145,x,k[0]] = F[146,x]+F[151,x,k[0]]
F[146,x] = F[147,x]+F[94,x]
F[147,x] = F[148,x]+F[150,x]+F[46,x]
F[148,x] = F[149,x]*F[25,x]
F[149,x] = F[147,x]+F[39,x]
F[150,x] = F[146,x]*F[25,x]
F[151,x,k[0]] = F[118,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = 2*F[46,x]+F[153,x,k[0]]+F[155,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]*F[25,x]
F[154,x,k[0]] = F[142,x,k[0]]+F[152,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]*F[26,x,k[0]]
F[156,x,k[0]] = F[147,x]+F[152,x,k[0]]
F[157,x] = F[158,x]*F[25,x]
F[158,x] = F[159,x,1]
F[159,x,k[0]] = F[1,x]+F[160,x,k[0]]+F[161,x,k[0]]+F[217,x]+F[218,x,k[0]]
F[160,x,k[0]] = F[159,x,k[0]]*F[25,x]
F[161,x,k[0]] = F[162,x,k[0]]*F[25,x]
F[162,x,k[0]] = F[1,x]+F[112,x]+F[123,x,k[0]]+F[163,x]+F[164,x]+F[84,x,k[0]]
F[163,x] = F[34,x,1]
F[164,x] = F[165,x,1]
F[165,x,k[0]] = F[166,x,k[0]]*F[25,x]
F[166,x,k[0]] = F[1,x]+F[167,x,k[0]]+F[201,x,k[0]]+F[207,x,k[0]]+F[215,x,k[0]]
F[167,x,k[0]] = F[168,x,k[0]]*F[25,x]
F[168,x,k[0]] = 1/(-1+k[0])*(F[169,x,k[0]]*k[0]-F[169,x,1])
F[169,x,k[0]] = F[1,x]+F[170,x]+F[172,x,k[0]]+F[184,x,k[0]]
F[170,x] = F[171,x,1]
F[171,x,k[0]] = F[25,x]*F[37,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]*F[25,x]
F[173,x,k[0]] = F[1,x]+F[174,x,k[0]]+F[175,x,k[0]]+F[186,x,k[0]]+F[193,x,k[0]]
F[174,x,k[0]] = F[173,x,k[0]]*F[25,x]
F[175,x,k[0]] = F[176,x,k[0]]*F[25,x]
F[176,x,k[0]] = F[1,x]+F[163,x]+F[164,x]+F[177,x,k[0]]+F[185,x,k[0]]+F[186,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]*F[25,x]
F[178,x,k[0]] = F[1,x]+F[16,x]+F[172,x,k[0]]+F[179,x]+F[184,x,k[0]]+F[86,x]
F[179,x] = F[180,x]*F[25,x]
F[180,x] = F[181,x,1]
F[181,x,k[0]] = F[1,x]+F[104,x,k[0]]+F[112,x]+F[122,x]+F[182,x,k[0]]+F[91,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]*F[25,x]
F[183,x,k[0]] = (F[181,x,k[0]]*k[0]-F[181,x,1])/(-1+k[0])
F[184,x,k[0]] = F[169,x,k[0]]*F[26,x,k[0]]
F[185,x,k[0]] = F[25,x]*F[8,x,k[0]]
F[186,x,k[0]] = F[187,x,k[0]]*F[26,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]+F[44,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[39,x]
F[189,x,k[0]] = F[190,x,k[0]]+F[192,x,k[0]]+F[46,x]
F[190,x,k[0]] = F[191,x,k[0]]*F[25,x]
F[191,x,k[0]] = F[189,x,k[0]]+F[42,x,k[0]]
F[192,x,k[0]] = F[188,x,k[0]]*F[26,x,k[0]]
F[193,x,k[0]] = F[194,x,k[0]]*F[25,x]
F[194,x,k[0]] = F[1,x]+F[195,x,k[0]]+F[197,x,k[0]]+F[199,x,k[0]]+F[201,x,k[0]]+F[207,x,k[0]]
F[195,x,k[0]] = F[196,x,k[0]]*F[25,x]
F[196,x,k[0]] = 1/(-1+k[0])*(F[173,x,k[0]]*k[0]-F[173,x,1])
F[197,x,k[0]] = F[198,x,k[0]]*F[25,x]
F[198,x,k[0]] = 1/(-1+k[0])*(F[176,x,k[0]]*k[0]-F[176,x,1])
F[199,x,k[0]] = F[200,x,k[0]]*F[25,x]
F[200,x,k[0]] = 1/(-1+k[0])*(F[194,x,k[0]]*k[0]-F[194,x,1])
F[201,x,k[0]] = F[202,x,k[0]]*F[25,x]
F[202,x,k[0]] = F[1,x]+F[203,x,k[0]]+F[204,x,k[0]]+F[205,x,k[0]]+F[206,x,k[0]]
F[203,x,k[0]] = F[202,x,k[0]]*F[25,x]
F[204,x,k[0]] = F[25,x]*F[8,x,k[0]]
F[205,x,k[0]] = F[178,x,k[0]]*F[25,x]
F[206,x,k[0]] = F[202,x,k[0]]*F[26,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]*F[26,x,k[0]]
F[208,x,k[0]] = F[187,x,k[0]]+F[209,x,k[0]]
F[209,x,k[0]] = F[188,x,k[0]]+F[210,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]+F[63,x]
F[211,x,k[0]] = 2*F[46,x]+F[212,x,k[0]]+F[214,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]*F[25,x]
F[213,x,k[0]] = F[189,x,k[0]]+F[211,x,k[0]]
F[214,x,k[0]] = F[210,x,k[0]]*F[26,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]*F[25,x]
F[216,x,k[0]] = 1/(-1+k[0])*(F[166,x,k[0]]*k[0]-F[166,x,1])
F[217,x] = F[125,x,1]
F[218,x,k[0]] = F[159,x,k[0]]*F[26,x,k[0]]
F[219,x] = F[220,x,1]
F[220,x,k[0]] = F[221,x,k[0]]*F[25,x]
F[221,x,k[0]] = (F[51,x,k[0]]*k[0]-F[51,x,1])/(-1+k[0])
F[222,x] = F[223,x,1]
F[223,x,k[0]] = F[224,x,k[0]]*F[25,x]
F[224,x,k[0]] = (F[35,x,k[0]]*k[0]-F[35,x,1])/(-1+k[0])
F[225,x] = F[226,x,1]
F[226,x,k[0]] = F[25,x]*F[35,x,k[0]]
F[227,x] = F[186,x,1]
F[228,x] = F[25,x]*F[89,x]
F[229,x,k[0]] = F[26,x,k[0]]*F[29,x,k[0]]
F[230,x] = F[25,x]*F[7,x]
F[231,x,k[0]] = F[232,x,k[0]]*F[25,x]
F[232,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[233,x,k[0]] = F[234,x,k[0]]*F[25,x]
F[234,x,k[0]] = 1/(-1+k[0])*(F[29,x,k[0]]*k[0]-F[29,x,1])
F[235,x,k[0]] = F[236,x,k[0]]*F[25,x]
F[236,x,k[0]] = F[237,x,k[0]]+F[242,x,k[0]]
F[237,x,k[0]] = F[238,x,k[0]]+F[99,x,k[0]]
F[238,x,k[0]] = F[239,x,k[0]]+F[39,x]
F[239,x,k[0]] = F[240,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]*F[25,x]
F[241,x,k[0]] = F[239,x,k[0]]+F[97,x,k[0]]
F[242,x,k[0]] = F[117,x,k[0]]+F[243,x,k[0]]
F[243,x,k[0]] = F[147,x]+F[244,x,k[0]]
F[244,x,k[0]] = 2*F[46,x]+F[245,x,k[0]]+F[247,x,k[0]]
F[245,x,k[0]] = F[246,x,k[0]]*F[25,x]
F[246,x,k[0]] = F[239,x,k[0]]+F[244,x,k[0]]
F[247,x,k[0]] = F[248,x,k[0]]*F[25,x]
F[248,x,k[0]] = F[118,x,k[0]]+F[244,x,k[0]]
F[249,x,k[0]] = F[13,x,k[0]]*F[26,x,k[0]]
F[250,x,k[0]] = F[194,x,k[0]]*F[25,x]
F[251,x,k[0]] = F[176,x,k[0]]*F[25,x]
F[252,x,k[0]] = F[166,x,k[0]]*F[26,x,k[0]]
F[253,x] = F[25,x]*F[5,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_{25}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{133}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{25}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{107}\! \left(x \right)+F_{253}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{25}\! \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_{250}\! \left(x , y\right)+F_{251}\! \left(x , y\right)+F_{252}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{25}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{170}\! \left(x \right)+F_{27}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{122}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{115}\! \left(x , y\right)+F_{16}\! \left(x \right)+F_{231}\! \left(x , y\right)+F_{233}\! \left(x , y\right)+F_{235}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{133}\! \left(x \right)+F_{18}\! \left(x \right)+F_{230}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)+F_{170}\! \left(x \right)+F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{25}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x \right) = F_{28}\! \left(x , 1\right)
F_{28}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{217}\! \left(x \right)+F_{229}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{33}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{228}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{226}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{25}\! \left(x \right) F_{38}\! \left(x \right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{46}\! \left(x \right) = 0
F_{47}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{227}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{135}\! \left(x \right)+F_{225}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{133}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{127}\! \left(x , y\right)+F_{129}\! \left(x , y\right)+F_{131}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{61}\! \left(x \right) = F_{38}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{39}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{25}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{39}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{69}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{63}\! \left(x \right)+F_{68}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{125}\! \left(x , y\right)+F_{126}\! \left(x , y\right)+F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{122}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{78}\! \left(x , y\right)+F_{83}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{83}\! \left(x \right) = F_{84}\! \left(x , 1\right)
F_{84}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{16}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{25}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{25}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x , 1\right)
F_{90}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{112}\! \left(x \right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{93}\! \left(x \right) = F_{1}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{25}\! \left(x \right) F_{93}\! \left(x \right)
F_{96}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{94}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{106}\! \left(x , y\right)+F_{107}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{107}\! \left(x \right) = F_{108}\! \left(x , 1\right)
F_{108}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{111}\! \left(x , y\right) = -\frac{-y F_{90}\! \left(x , y\right)+F_{90}\! \left(x , 1\right)}{-1+y}
F_{112}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{114}\! \left(x , y\right) = -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{94}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{121}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{122}\! \left(x \right) = F_{123}\! \left(x , 1\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{115}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{128}\! \left(x , y\right) = -\frac{-y F_{58}\! \left(x , y\right)+F_{58}\! \left(x , 1\right)}{-1+y}
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{130}\! \left(x , y\right) = -\frac{-y F_{54}\! \left(x , y\right)+F_{54}\! \left(x , 1\right)}{-1+y}
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{132}\! \left(x , y\right) = -\frac{-y F_{79}\! \left(x , y\right)+F_{79}\! \left(x , 1\right)}{-1+y}
F_{133}\! \left(x \right) = F_{25}\! \left(x \right) F_{87}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{25}\! \left(x \right)
F_{136}\! \left(x \right) = F_{1}\! \left(x \right)+F_{137}\! \left(x \right)+F_{157}\! \left(x \right)+F_{219}\! \left(x \right)+F_{222}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x , 1\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{38}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{39}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x \right)+F_{151}\! \left(x , y\right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{94}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{150}\! \left(x \right)+F_{46}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{25}\! \left(x \right)
F_{149}\! \left(x \right) = F_{147}\! \left(x \right)+F_{39}\! \left(x \right)
F_{150}\! \left(x \right) = F_{146}\! \left(x \right) F_{25}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{147}\! \left(x \right)+F_{152}\! \left(x , y\right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{25}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x , 1\right)
F_{159}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{160}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{217}\! \left(x \right)+F_{218}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{123}\! \left(x , y\right)+F_{163}\! \left(x \right)+F_{164}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{163}\! \left(x \right) = F_{34}\! \left(x , 1\right)
F_{164}\! \left(x \right) = F_{165}\! \left(x , 1\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{167}\! \left(x , y\right)+F_{201}\! \left(x , y\right)+F_{207}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{168}\! \left(x , y\right) = -\frac{-y F_{169}\! \left(x , y\right)+F_{169}\! \left(x , 1\right)}{-1+y}
F_{169}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{170}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{170}\! \left(x \right) = F_{171}\! \left(x , 1\right)
F_{171}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{174}\! \left(x , y\right)+F_{175}\! \left(x , y\right)+F_{186}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{173}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{176}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{163}\! \left(x \right)+F_{164}\! \left(x \right)+F_{177}\! \left(x , y\right)+F_{185}\! \left(x , y\right)+F_{186}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{178}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{179}\! \left(x \right)+F_{184}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{25}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x , 1\right)
F_{181}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{112}\! \left(x \right)+F_{122}\! \left(x \right)+F_{182}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{183}\! \left(x , y\right) = -\frac{-y F_{181}\! \left(x , y\right)+F_{181}\! \left(x , 1\right)}{-1+y}
F_{184}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{39}\! \left(x \right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)+F_{192}\! \left(x , y\right)+F_{46}\! \left(x \right)
F_{190}\! \left(x , y\right) = F_{191}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{191}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{194}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{194}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{201}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{196}\! \left(x , y\right) = -\frac{-y F_{173}\! \left(x , y\right)+F_{173}\! \left(x , 1\right)}{-1+y}
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{198}\! \left(x , y\right) = -\frac{-y F_{176}\! \left(x , y\right)+F_{176}\! \left(x , 1\right)}{-1+y}
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{200}\! \left(x , y\right) = -\frac{-y F_{194}\! \left(x , y\right)+F_{194}\! \left(x , 1\right)}{-1+y}
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{203}\! \left(x , y\right)+F_{204}\! \left(x , y\right)+F_{205}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{204}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{178}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{206}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{63}\! \left(x \right)
F_{211}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{212}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{213}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{210}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{216}\! \left(x , y\right) = -\frac{-y F_{166}\! \left(x , y\right)+F_{166}\! \left(x , 1\right)}{-1+y}
F_{217}\! \left(x \right) = F_{125}\! \left(x , 1\right)
F_{218}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{219}\! \left(x \right) = F_{220}\! \left(x , 1\right)
F_{220}\! \left(x , y\right) = F_{221}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{221}\! \left(x , y\right) = -\frac{-y F_{51}\! \left(x , y\right)+F_{51}\! \left(x , 1\right)}{-1+y}
F_{222}\! \left(x \right) = F_{223}\! \left(x , 1\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{224}\! \left(x , y\right) = -\frac{-y F_{35}\! \left(x , y\right)+F_{35}\! \left(x , 1\right)}{-1+y}
F_{225}\! \left(x \right) = F_{226}\! \left(x , 1\right)
F_{226}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{227}\! \left(x \right) = F_{186}\! \left(x , 1\right)
F_{228}\! \left(x \right) = F_{25}\! \left(x \right) F_{89}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{230}\! \left(x \right) = F_{25}\! \left(x \right) F_{7}\! \left(x \right)
F_{231}\! \left(x , y\right) = F_{232}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{232}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{233}\! \left(x , y\right) = F_{234}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{234}\! \left(x , y\right) = -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}
F_{235}\! \left(x , y\right) = F_{236}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right)+F_{242}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{238}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{238}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{39}\! \left(x \right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{241}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{147}\! \left(x \right)+F_{244}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = 2 F_{46}\! \left(x \right)+F_{245}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{246}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{246}\! \left(x , y\right) = F_{239}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{248}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{244}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{194}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{251}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{252}\! \left(x , y\right) = F_{166}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{253}\! \left(x \right) = F_{25}\! \left(x \right) F_{5}\! \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_25(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_133(x) + F_4(x))
Eq(F_4(x), F_25(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_107(x) + F_253(x) + F_6(x))
Eq(F_6(x), F_25(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_250(x, k_0) + F_251(x, k_0) + F_252(x, k_0) + F_9(x))
Eq(F_9(x), F_10(x)*F_25(x))
Eq(F_10(x), F_1(x) + F_11(x) + F_170(x) + F_27(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_25(x))
Eq(F_13(x, k_0), F_1(x) + F_112(x) + F_122(x) + F_14(x, k_0) + F_249(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_25(x))
Eq(F_15(x, k_0), F_1(x) + F_115(x, k_0) + F_16(x) + F_231(x, k_0) + F_233(x, k_0) + F_235(x, k_0))
Eq(F_16(x), F_17(x)*F_25(x))
Eq(F_17(x), F_1(x) + F_133(x) + F_18(x) + F_230(x))
Eq(F_18(x), F_19(x)*F_25(x))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_1(x) + F_16(x) + F_172(x, k_0) + F_184(x, k_0) + F_21(x))
Eq(F_21(x), F_22(x)*F_25(x))
Eq(F_22(x), F_1(x) + F_16(x) + F_170(x) + F_23(x) + F_27(x))
Eq(F_23(x), F_24(x)*F_25(x))
Eq(F_24(x), F_15(x, 1))
Eq(F_25(x), F_26(x, 1))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x), F_28(x, 1))
Eq(F_28(x, k_0), F_25(x)*F_29(x, k_0))
Eq(F_29(x, k_0), F_1(x) + F_217(x) + F_229(x, k_0) + F_30(x, k_0) + F_31(x))
Eq(F_30(x, k_0), F_25(x)*F_29(x, k_0))
Eq(F_31(x), F_25(x)*F_32(x))
Eq(F_32(x), F_33(x, 1))
Eq(F_33(x, k_0), F_1(x) + F_112(x) + F_228(x) + F_34(x, k_0) + F_78(x, k_0))
Eq(F_34(x, k_0), F_26(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_1(x) + F_226(x, k_0) + F_36(x, k_0) + F_50(x, k_0))
Eq(F_36(x, k_0), F_26(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x) + F_41(x, k_0))
Eq(F_38(x), F_1(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_25(x)*F_38(x))
Eq(F_41(x, k_0), F_42(x, k_0) + F_45(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_26(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_42(x, k_0))
Eq(F_45(x, k_0), F_46(x) + F_47(x, k_0) + F_49(x, k_0))
Eq(F_46(x), 0)
Eq(F_47(x, k_0), F_26(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_39(x) + F_45(x, k_0))
Eq(F_49(x, k_0), F_25(x)*F_41(x, k_0))
Eq(F_50(x, k_0), F_25(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_1(x) + F_227(x) + F_52(x, k_0) + F_53(x, k_0) + F_57(x, k_0))
Eq(F_52(x, k_0), F_26(x, k_0)*F_51(x, k_0))
Eq(F_53(x, k_0), F_25(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_134(x, k_0) + F_135(x) + F_225(x) + F_36(x, k_0) + F_55(x, k_0))
Eq(F_55(x, k_0), F_25(x)*F_56(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_133(x) + F_52(x, k_0) + F_53(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_25(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_1(x) + F_127(x, k_0) + F_129(x, k_0) + F_131(x, k_0) + F_59(x, k_0) + F_73(x, k_0))
Eq(F_59(x, k_0), F_26(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x) + F_66(x, k_0))
Eq(F_61(x), F_38(x) + F_62(x))
Eq(F_62(x), F_39(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_25(x)*F_65(x))
Eq(F_65(x), F_39(x) + F_63(x))
Eq(F_66(x, k_0), F_41(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_45(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), 2*F_46(x) + F_69(x, k_0) + F_71(x, k_0))
Eq(F_69(x, k_0), F_26(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_63(x) + F_68(x, k_0))
Eq(F_71(x, k_0), F_25(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_45(x, k_0) + F_68(x, k_0))
Eq(F_73(x, k_0), F_25(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_1(x) + F_125(x, k_0) + F_126(x, k_0) + F_75(x, k_0) + F_76(x, k_0))
Eq(F_75(x, k_0), F_26(x, k_0)*F_74(x, k_0))
Eq(F_76(x, k_0), F_25(x)*F_77(x, k_0))
Eq(F_77(x, k_0), F_1(x) + F_112(x) + F_122(x) + F_34(x, k_0) + F_78(x, k_0) + F_83(x))
Eq(F_78(x, k_0), F_25(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_1(x) + F_36(x, k_0) + F_80(x, k_0) + F_81(x, k_0) + F_82(x, k_0))
Eq(F_80(x, k_0), F_25(x)*F_58(x, k_0))
Eq(F_81(x, k_0), F_25(x)*F_54(x, k_0))
Eq(F_82(x, k_0), F_25(x)*F_79(x, k_0))
Eq(F_83(x), F_84(x, 1))
Eq(F_84(x, k_0), F_25(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_1(x) + F_113(x, k_0) + F_115(x, k_0) + F_16(x) + F_28(x, k_0) + F_86(x))
Eq(F_86(x), F_25(x)*F_87(x))
Eq(F_87(x), F_1(x) + F_16(x) + F_86(x) + F_88(x))
Eq(F_88(x), F_25(x)*F_89(x))
Eq(F_89(x), F_90(x, 1))
Eq(F_90(x, k_0), F_1(x) + F_104(x, k_0) + F_110(x, k_0) + F_112(x) + F_91(x, k_0))
Eq(F_91(x, k_0), F_26(x, k_0)*F_92(x, k_0))
Eq(F_92(x, k_0), F_93(x) + F_96(x, k_0))
Eq(F_93(x), F_1(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_25(x)*F_93(x))
Eq(F_96(x, k_0), F_100(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_26(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_1(x) + F_97(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0) + F_46(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_26(x, k_0))
Eq(F_102(x, k_0), F_100(x, k_0) + F_94(x))
Eq(F_103(x, k_0), F_25(x)*F_96(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_25(x))
Eq(F_105(x, k_0), F_1(x) + F_106(x, k_0) + F_107(x) + F_109(x, k_0) + F_6(x))
Eq(F_106(x, k_0), F_105(x, k_0)*F_26(x, k_0))
Eq(F_107(x), F_108(x, 1))
Eq(F_108(x, k_0), F_20(x, k_0)*F_25(x))
Eq(F_109(x, k_0), F_105(x, k_0)*F_25(x))
Eq(F_110(x, k_0), F_111(x, k_0)*F_25(x))
Eq(F_111(x, k_0), (-k_0*F_90(x, k_0) + F_90(x, 1))/(1 - k_0))
Eq(F_112(x), F_17(x)*F_25(x))
Eq(F_113(x, k_0), F_114(x, k_0)*F_25(x))
Eq(F_114(x, k_0), (k_0*F_85(x, k_0) - F_85(x, 1))/(k_0 - 1))
Eq(F_115(x, k_0), F_116(x, k_0)*F_26(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_99(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_94(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_121(x, k_0) + F_46(x))
Eq(F_119(x, k_0), F_120(x, k_0)*F_25(x))
Eq(F_120(x, k_0), F_118(x, k_0) + F_97(x, k_0))
Eq(F_121(x, k_0), F_117(x, k_0)*F_26(x, k_0))
Eq(F_122(x), F_123(x, 1))
Eq(F_123(x, k_0), F_124(x, k_0)*F_26(x, k_0))
Eq(F_124(x, k_0), F_1(x) + F_115(x, k_0) + F_12(x, k_0) + F_28(x, k_0))
Eq(F_125(x, k_0), F_25(x)*F_56(x, k_0))
Eq(F_126(x, k_0), F_25(x)*F_74(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0)*F_25(x))
Eq(F_128(x, k_0), (-k_0*F_58(x, k_0) + F_58(x, 1))/(1 - k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_25(x))
Eq(F_130(x, k_0), (-k_0*F_54(x, k_0) + F_54(x, 1))/(1 - k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_25(x))
Eq(F_132(x, k_0), (-k_0*F_79(x, k_0) + F_79(x, 1))/(1 - k_0))
Eq(F_133(x), F_25(x)*F_87(x))
Eq(F_134(x, k_0), F_25(x)*F_77(x, k_0))
Eq(F_135(x), F_136(x)*F_25(x))
Eq(F_136(x), F_1(x) + F_137(x) + F_157(x) + F_219(x) + F_222(x))
Eq(F_137(x), F_138(x, 1))
Eq(F_138(x, k_0), F_139(x, k_0)*F_26(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0) + F_145(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_38(x))
Eq(F_141(x, k_0), F_142(x, k_0) + F_97(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0)*F_26(x, k_0))
Eq(F_144(x, k_0), F_142(x, k_0) + F_39(x))
Eq(F_145(x, k_0), F_146(x) + F_151(x, k_0))
Eq(F_146(x), F_147(x) + F_94(x))
Eq(F_147(x), F_148(x) + F_150(x) + F_46(x))
Eq(F_148(x), F_149(x)*F_25(x))
Eq(F_149(x), F_147(x) + F_39(x))
Eq(F_150(x), F_146(x)*F_25(x))
Eq(F_151(x, k_0), F_118(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_155(x, k_0) + 2*F_46(x))
Eq(F_153(x, k_0), F_154(x, k_0)*F_25(x))
Eq(F_154(x, k_0), F_142(x, k_0) + F_152(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0)*F_26(x, k_0))
Eq(F_156(x, k_0), F_147(x) + F_152(x, k_0))
Eq(F_157(x), F_158(x)*F_25(x))
Eq(F_158(x), F_159(x, 1))
Eq(F_159(x, k_0), F_1(x) + F_160(x, k_0) + F_161(x, k_0) + F_217(x) + F_218(x, k_0))
Eq(F_160(x, k_0), F_159(x, k_0)*F_25(x))
Eq(F_161(x, k_0), F_162(x, k_0)*F_25(x))
Eq(F_162(x, k_0), F_1(x) + F_112(x) + F_123(x, k_0) + F_163(x) + F_164(x) + F_84(x, k_0))
Eq(F_163(x), F_34(x, 1))
Eq(F_164(x), F_165(x, 1))
Eq(F_165(x, k_0), F_166(x, k_0)*F_25(x))
Eq(F_166(x, k_0), F_1(x) + F_167(x, k_0) + F_201(x, k_0) + F_207(x, k_0) + F_215(x, k_0))
Eq(F_167(x, k_0), F_168(x, k_0)*F_25(x))
Eq(F_168(x, k_0), (k_0*F_169(x, k_0) - F_169(x, 1))/(k_0 - 1))
Eq(F_169(x, k_0), F_1(x) + F_170(x) + F_172(x, k_0) + F_184(x, k_0))
Eq(F_170(x), F_171(x, 1))
Eq(F_171(x, k_0), F_25(x)*F_37(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0)*F_25(x))
Eq(F_173(x, k_0), F_1(x) + F_174(x, k_0) + F_175(x, k_0) + F_186(x, k_0) + F_193(x, k_0))
Eq(F_174(x, k_0), F_173(x, k_0)*F_25(x))
Eq(F_175(x, k_0), F_176(x, k_0)*F_25(x))
Eq(F_176(x, k_0), F_1(x) + F_163(x) + F_164(x) + F_177(x, k_0) + F_185(x, k_0) + F_186(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0)*F_25(x))
Eq(F_178(x, k_0), F_1(x) + F_16(x) + F_172(x, k_0) + F_179(x) + F_184(x, k_0) + F_86(x))
Eq(F_179(x), F_180(x)*F_25(x))
Eq(F_180(x), F_181(x, 1))
Eq(F_181(x, k_0), F_1(x) + F_104(x, k_0) + F_112(x) + F_122(x) + F_182(x, k_0) + F_91(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0)*F_25(x))
Eq(F_183(x, k_0), (-k_0*F_181(x, k_0) + F_181(x, 1))/(1 - k_0))
Eq(F_184(x, k_0), F_169(x, k_0)*F_26(x, k_0))
Eq(F_185(x, k_0), F_25(x)*F_8(x, k_0))
Eq(F_186(x, k_0), F_187(x, k_0)*F_26(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0) + F_44(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_39(x))
Eq(F_189(x, k_0), F_190(x, k_0) + F_192(x, k_0) + F_46(x))
Eq(F_190(x, k_0), F_191(x, k_0)*F_25(x))
Eq(F_191(x, k_0), F_189(x, k_0) + F_42(x, k_0))
Eq(F_192(x, k_0), F_188(x, k_0)*F_26(x, k_0))
Eq(F_193(x, k_0), F_194(x, k_0)*F_25(x))
Eq(F_194(x, k_0), F_1(x) + F_195(x, k_0) + F_197(x, k_0) + F_199(x, k_0) + F_201(x, k_0) + F_207(x, k_0))
Eq(F_195(x, k_0), F_196(x, k_0)*F_25(x))
Eq(F_196(x, k_0), (k_0*F_173(x, k_0) - F_173(x, 1))/(k_0 - 1))
Eq(F_197(x, k_0), F_198(x, k_0)*F_25(x))
Eq(F_198(x, k_0), (k_0*F_176(x, k_0) - F_176(x, 1))/(k_0 - 1))
Eq(F_199(x, k_0), F_200(x, k_0)*F_25(x))
Eq(F_200(x, k_0), (k_0*F_194(x, k_0) - F_194(x, 1))/(k_0 - 1))
Eq(F_201(x, k_0), F_202(x, k_0)*F_25(x))
Eq(F_202(x, k_0), F_1(x) + F_203(x, k_0) + F_204(x, k_0) + F_205(x, k_0) + F_206(x, k_0))
Eq(F_203(x, k_0), F_202(x, k_0)*F_25(x))
Eq(F_204(x, k_0), F_25(x)*F_8(x, k_0))
Eq(F_205(x, k_0), F_178(x, k_0)*F_25(x))
Eq(F_206(x, k_0), F_202(x, k_0)*F_26(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0)*F_26(x, k_0))
Eq(F_208(x, k_0), F_187(x, k_0) + F_209(x, k_0))
Eq(F_209(x, k_0), F_188(x, k_0) + F_210(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0) + F_63(x))
Eq(F_211(x, k_0), F_212(x, k_0) + F_214(x, k_0) + 2*F_46(x))
Eq(F_212(x, k_0), F_213(x, k_0)*F_25(x))
Eq(F_213(x, k_0), F_189(x, k_0) + F_211(x, k_0))
Eq(F_214(x, k_0), F_210(x, k_0)*F_26(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0)*F_25(x))
Eq(F_216(x, k_0), (k_0*F_166(x, k_0) - F_166(x, 1))/(k_0 - 1))
Eq(F_217(x), F_125(x, 1))
Eq(F_218(x, k_0), F_159(x, k_0)*F_26(x, k_0))
Eq(F_219(x), F_220(x, 1))
Eq(F_220(x, k_0), F_221(x, k_0)*F_25(x))
Eq(F_221(x, k_0), (-k_0*F_51(x, k_0) + F_51(x, 1))/(1 - k_0))
Eq(F_222(x), F_223(x, 1))
Eq(F_223(x, k_0), F_224(x, k_0)*F_25(x))
Eq(F_224(x, k_0), (-k_0*F_35(x, k_0) + F_35(x, 1))/(1 - k_0))
Eq(F_225(x), F_226(x, 1))
Eq(F_226(x, k_0), F_25(x)*F_35(x, k_0))
Eq(F_227(x), F_186(x, 1))
Eq(F_228(x), F_25(x)*F_89(x))
Eq(F_229(x, k_0), F_26(x, k_0)*F_29(x, k_0))
Eq(F_230(x), F_25(x)*F_7(x))
Eq(F_231(x, k_0), F_232(x, k_0)*F_25(x))
Eq(F_232(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_233(x, k_0), F_234(x, k_0)*F_25(x))
Eq(F_234(x, k_0), (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_235(x, k_0), F_236(x, k_0)*F_25(x))
Eq(F_236(x, k_0), F_237(x, k_0) + F_242(x, k_0))
Eq(F_237(x, k_0), F_238(x, k_0) + F_99(x, k_0))
Eq(F_238(x, k_0), F_239(x, k_0) + F_39(x))
Eq(F_239(x, k_0), F_240(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0)*F_25(x))
Eq(F_241(x, k_0), F_239(x, k_0) + F_97(x, k_0))
Eq(F_242(x, k_0), F_117(x, k_0) + F_243(x, k_0))
Eq(F_243(x, k_0), F_147(x) + F_244(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0) + F_247(x, k_0) + 2*F_46(x))
Eq(F_245(x, k_0), F_246(x, k_0)*F_25(x))
Eq(F_246(x, k_0), F_239(x, k_0) + F_244(x, k_0))
Eq(F_247(x, k_0), F_248(x, k_0)*F_25(x))
Eq(F_248(x, k_0), F_118(x, k_0) + F_244(x, k_0))
Eq(F_249(x, k_0), F_13(x, k_0)*F_26(x, k_0))
Eq(F_250(x, k_0), F_194(x, k_0)*F_25(x))
Eq(F_251(x, k_0), F_176(x, k_0)*F_25(x))
Eq(F_252(x, k_0), F_166(x, k_0)*F_26(x, k_0))
Eq(F_253(x), F_25(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "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": "row_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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"include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], 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