0231_3012
Counting sequence:
1, 1, 2, 6, 22, 87, 352, 1434, 5861, 24019, 98677, 406291, 1676009, 6924618, 28646875, 118638038, 491765865, 2039944740, 8467475533, 35166107745, 146115418937, 607353499821, 2525443862594, 10504254304765, 43702642447260, 181865873468907, 756979080521743, 3151341504417932, 13121308978429878, 54641335368897681, 227573261466380102, 947918780836065736, 3948806758399365512, 16451329514526911834, 68544485712562299906, 285612318293285057898, 1190175817636901778461, 4959893053233184483363, 20670835552622426440037, 86152139999671291043943, 359082668411282313031116, 1496722802515618694128687, 6238860327683618291689344, 26006665070355248544782715, 108412229910763387474567099, 451944310491754961618802502, 1884098203799209185718103482, 7854764083648823662642807673, 32747102124416661780544791838, 136528060611803074070834111100, 569219222064278249080437309952, 2373258900723312497401349528975, 9895050082416667234852249718215, 41256999261676578398806754719833, 172021817619410408348476444521757, 717257694290331216676445290791382, 2990695939421469361692256706255959, 12470224612362297895710231504127704, 51997312839753757122301619465122361, 216816237068603649296677806846932877, 904079617542366084543893509483330656, 3769860201612202413146966391805596272, 15719808295682361837124735008990239649, 65549961201649781641338495447324362960, 273338373010232660740398456794002588402, 1139807576594402075867216345560416990859, 4752969785901097989451275391734739295512, 19819877792905877507347897010196762860046, 82649291323567671177860432470790274043841, 344650877595711163035109052514017407731766, 1437214523131423786898237729321902213868434, 5993294660307074252072735238486675105301726, 24992595968593457323297697950317842939801643, 104221831349930642344378992979501792386374203, 434617813010829622814633042548931405019495875, 1812415376406188275516586669474440345955657229, 7558041260957855470288903072468133537785662120, 31518243044475891946388217118103508601152976293, 131436469613048924365508380601607711418191014040, 548113933140456626509082655811377663041878208513, 2285739864254095470143893833842193975215740213507, 9531992772140675603428138056927135208623518809462, 39750398661060653207215410410306236598761220374846, 165767772099839325276409319663801569520650319209031, 691288750236242176783942414819857778953513981102082, 2882833812067515106223548168718884180634084586384702, 12022102026120853133578973249942569026073371248614714, 50135096381392802225652245219227054506664620533716439, 209075865260291588094197864669453516268928052281898489, 871899680787612850583354205435588406500948838592481993, 3636048501571599204973397838255422816278825914999671683, 15163285701988903170592436444957088130843435288059706496, 63234987841109271670394631735419190727946061615788534915, 263707210102140366739279251985392441061227092195911335064, 1099732312855844007170325355261354889479407509185028195463, 4586193347456176905471198464483295116607541061842478631649, 19125733653824316476343113912509094507450272495633034022864, 79759825396380961117029385657078227601017806349822195422538, 332621726187778351565037854765850815628518416278502547088529, 1387130560088220441646575419871964845726441577516890610287512, 5784746833909570018367578900576827671232501384730009735538188
Generating function in Maple syntax:
((-6*x^5+15*x^4-14*x^3+6*x^2-x)*(1-4*x)^(1/2)-20*x^6+110*x^5-201*x^4+180*x^3-86*x^2+21*x-2)/(8*x^7-64*x^6+196*x^5-282*x^4+220*x^3-96*x^2+22*x-2)
Generating function in latex syntax:
\frac{\left(-6 x^{5}+15 x^{4}-14 x^{3}+6 x^{2}-x \right) \sqrt{1-4 x}-20 x^{6}+110 x^{5}-201 x^{4}+180 x^{3}-86 x^{2}+21 x -2}{8 x^{7}-64 x^{6}+196 x^{5}-282 x^{4}+220 x^{3}-96 x^{2}+22 x -2}
Generating function in sympy syntax:
(-20*x**6 + 110*x**5 - 201*x**4 + 180*x**3 - 86*x**2 + 21*x + sqrt(1 - 4*x)*(-6*x**5 + 15*x**4 - 14*x**3 + 6*x**2 - x) - 2)/(8*x**7 - 64*x**6 + 196*x**5 - 282*x**4 + 220*x**3 - 96*x**2 + 22*x - 2)
Implicit equation for the generating function in Maple syntax:
(4*x^7-32*x^6+98*x^5-141*x^4+110*x^3-48*x^2+11*x-1)*F(x)^2+(20*x^6-110*x^5+201*x^4-180*x^3+86*x^2-21*x+2)*F(x)+25*x^5-66*x^4+71*x^3-38*x^2+10*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{7}-32 x^{6}+98 x^{5}-141 x^{4}+110 x^{3}-48 x^{2}+11 x -1\right) F \! \left(x \right)^{2}+\left(20 x^{6}-110 x^{5}+201 x^{4}-180 x^{3}+86 x^{2}-21 x +2\right) F \! \left(x \right)+25 x^{5}-66 x^{4}+71 x^{3}-38 x^{2}+10 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 87
a(6) = 352
a(7) = 1434
a(8) = 5861
a(9) = 24019
a(10) = 98677
a(11) = 406291
a(n+12) = -48*(3+2*n)/(11+n)*a(n)+3*(71+7*n)/(11+n)*a(11+n)+1032*(n+2)/(11+n)*a(n+1)-4*(3089+1187*n)/(11+n)*a(n+2)+396*(103+31*n)/(11+n)*a(n+3)-2*(41453+10080*n)/(11+n)*a(n+4)+(111043+22471*n)/(11+n)*a(n+5)-4*(25509+4403*n)/(11+n)*a(n+6)+2*(32779+4923*n)/(11+n)*a(n+7)-8*(3682+489*n)/(11+n)*a(n+8)+(9067+1079*n)/(11+n)*a(n+9)-2*(909+98*n)/(11+n)*a(n+10), n >= 12
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 87
a \! \left(6\right) = 352
a \! \left(7\right) = 1434
a \! \left(8\right) = 5861
a \! \left(9\right) = 24019
a \! \left(10\right) = 98677
a \! \left(11\right) = 406291
a \! \left(n +12\right) = -\frac{48 \left(3+2 n \right) a \! \left(n \right)}{11+n}+\frac{3 \left(71+7 n \right) a \! \left(11+n \right)}{11+n}+\frac{1032 \left(n +2\right) a \! \left(n +1\right)}{11+n}-\frac{4 \left(3089+1187 n \right) a \! \left(n +2\right)}{11+n}+\frac{396 \left(103+31 n \right) a \! \left(n +3\right)}{11+n}-\frac{2 \left(41453+10080 n \right) a \! \left(n +4\right)}{11+n}+\frac{\left(111043+22471 n \right) a \! \left(n +5\right)}{11+n}-\frac{4 \left(25509+4403 n \right) a \! \left(n +6\right)}{11+n}+\frac{2 \left(32779+4923 n \right) a \! \left(n +7\right)}{11+n}-\frac{8 \left(3682+489 n \right) a \! \left(n +8\right)}{11+n}+\frac{\left(9067+1079 n \right) a \! \left(n +9\right)}{11+n}-\frac{2 \left(909+98 n \right) a \! \left(n +10\right)}{11+n}, \quad n \geq 12
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/188/
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[38,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[7,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[14,x,k[0]]+F[15,x]+F[22,x]
F[14,x,k[0]] = F[13,x,k[0]]*F[9,x,k[0]]
F[15,x] = F[16,x]*F[3,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[20,x,k[0]]+F[34,x,k[0]]+F[8,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[3,x]
F[19,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[20,x,k[0]] = F[21,x,k[0]]*F[3,x]
F[21,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[15,x]+F[20,x,k[0]]+F[22,x]+F[29,x,k[0]]
F[22,x] = F[23,x]*F[3,x]
F[23,x] = 2*F[22,x]+F[1,x]+F[15,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[3,x]*F[4,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[3,x]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[26,x]*F[3,x]*F[31,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[31,x,k[0]]*F[9,x,k[0]]
F[34,x,k[0]] = F[3,x]*F[35,x,k[0]]
F[35,x,k[0]] = F[1,x]+F[15,x]+F[22,x]+F[34,x,k[0]]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[31,x,k[0]]*F[4,x]*F[9,x,k[0]]
F[38,x] = F[3,x]*F[39,x]
F[39,x] = F[1,x]+F[15,x]+F[22,x]+F[38,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_{38}\! \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_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{7}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \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) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{3}\! \left(x \right)
F_{23}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{3}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{3}\! \left(x \right) F_{31}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{4}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{38}\! \left(x \right) = F_{3}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{38}\! \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_38(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_7(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_1(x) + F_12(x, k_0) + F_14(x, k_0) + F_15(x) + F_22(x))
Eq(F_14(x, k_0), F_13(x, k_0)*F_9(x, k_0))
Eq(F_15(x), F_16(x)*F_3(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_20(x, k_0) + F_34(x, k_0) + F_8(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_3(x))
Eq(F_19(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_3(x))
Eq(F_21(x, k_0), F_1(x) + F_14(x, k_0) + F_15(x) + F_20(x, k_0) + F_22(x) + F_29(x, k_0))
Eq(F_22(x), F_23(x)*F_3(x))
Eq(F_23(x), F_1(x) + F_15(x) + 2*F_22(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_3(x)*F_4(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_3(x))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_26(x)*F_3(x)*F_31(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_31(x, k_0)*F_9(x, k_0))
Eq(F_34(x, k_0), F_3(x)*F_35(x, k_0))
Eq(F_35(x, k_0), F_1(x) + F_15(x) + F_22(x) + F_34(x, k_0) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_31(x, k_0)*F_4(x)*F_9(x, k_0))
Eq(F_38(x), F_3(x)*F_39(x))
Eq(F_39(x), F_1(x) + F_15(x) + F_22(x) + F_38(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], 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"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, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "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": [{"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]]}], "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"}]}]}
Specification 2
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/189/
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[46,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[7,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,x,1])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = F[14,x]+F[44,x,k[0]]
F[14,x] = F[15,x]+F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[3,x]
F[17,x] = F[16,x]+F[18,x]+F[39,x]+F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[3,x]*F[4,x]
F[20,x] = F[21,x]+F[31,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[3,x]
F[25,x] = F[23,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[3,x]
F[29,x] = F[23,x]+F[26,x]
F[30,x] = F[25,x]*F[3,x]
F[31,x] = F[32,x]
F[32,x] = F[21,x]*F[3,x]*F[33,x]
F[33,x] = F[22,x]+F[34,x]
F[34,x] = F[23,x]+F[35,x]
F[35,x] = F[27,x]+F[36,x]+F[38,x]
F[36,x] = F[3,x]*F[37,x]
F[37,x] = F[23,x]+F[35,x]
F[38,x] = F[3,x]*F[34,x]
F[39,x] = F[40,x]
F[40,x] = F[22,x]*F[3,x]*F[41,x]
F[41,x] = F[18,x]+F[4,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[3,x]*F[33,x]*F[4,x]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[13,x,k[0]]*F[22,x]*F[9,x,k[0]]
F[46,x] = F[14,x]*F[3,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_{46}\! \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_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{7}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \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) = F_{14}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{3}\! \left(x \right)
F_{17}\! \left(x \right) = F_{16}\! \left(x \right)+F_{18}\! \left(x \right)+F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{31}\! \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_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{3}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{3}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{25}\! \left(x \right) F_{3}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{36}\! \left(x \right) = F_{3}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{3}\! \left(x \right) F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right) F_{3}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{3}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{22}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{46}\! \left(x \right) = F_{14}\! \left(x \right) F_{3}\! \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_46(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_7(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), F_14(x) + F_44(x, k_0))
Eq(F_14(x), F_15(x) + F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_3(x))
Eq(F_17(x), F_16(x) + F_18(x) + F_39(x) + F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_3(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_31(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_3(x))
Eq(F_25(x), F_23(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_3(x))
Eq(F_29(x), F_23(x) + F_26(x))
Eq(F_30(x), F_25(x)*F_3(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_21(x)*F_3(x)*F_33(x))
Eq(F_33(x), F_22(x) + F_34(x))
Eq(F_34(x), F_23(x) + F_35(x))
Eq(F_35(x), F_27(x) + F_36(x) + F_38(x))
Eq(F_36(x), F_3(x)*F_37(x))
Eq(F_37(x), F_23(x) + F_35(x))
Eq(F_38(x), F_3(x)*F_34(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_22(x)*F_3(x)*F_41(x))
Eq(F_41(x), F_18(x) + F_4(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_3(x)*F_33(x)*F_4(x))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_13(x, k_0)*F_22(x)*F_9(x, k_0))
Eq(F_46(x), F_14(x)*F_3(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": 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_and_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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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[0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: insertion_row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/190/
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[8,x]
F[4,x] = F[35,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[8,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[8,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[15,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[8,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]+F[6,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[8,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[8,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[27,x]
F[34,x] = F[30,x]
F[35,x] = F[2,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[8,x]
F[38,x] = F[116,x]+F[39,x]
F[39,x] = F[40,x,1]
F[40,x,k[0]] = F[2,x]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[49,x,k[0]]
F[43,x,k[0]] = F[40,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[50,x,k[0]]
F[45,x,k[0]] = F[2,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[46,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = k[0]*x
F[50,x,k[0]] = F[105,x,k[0]]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[8,x]
F[53,x] = F[54,x]+F[88,x]
F[54,x] = F[39,x]+F[55,x]
F[55,x] = F[15,x]+F[56,x]
F[56,x] = F[57,x]+F[58,x]+F[85,x]
F[57,x] = 0
F[58,x] = F[59,x]*F[8,x]
F[59,x] = F[55,x]+F[60,x]
F[60,x] = F[61,x]+F[73,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]*F[8,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[15,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[64,x]*F[8,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]*F[8,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[65,x]
F[72,x] = F[68,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = F[56,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[76,x]*F[8,x]
F[79,x] = F[73,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[8,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[77,x]
F[84,x] = F[80,x]
F[85,x] = F[8,x]*F[86,x]
F[86,x] = F[15,x]+F[87,x]
F[87,x] = F[57,x]+F[66,x]+F[85,x]
F[88,x] = F[104,x]+F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[15,x]*F[2,x]
F[91,x] = F[102,x]+F[57,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[15,x]*F[8,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[14,x]*F[35,x]
F[96,x] = F[14,x]*F[97,x]
F[97,x] = F[2,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[8,x]
F[100,x] = F[101,x]+F[96,x]
F[101,x] = F[14,x]*F[2,x]
F[102,x] = F[103,x]*F[8,x]
F[103,x] = F[36,x]+F[91,x]
F[104,x] = F[50,x,1]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[8,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[112,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[111,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[47,x,k[0]]*F[55,x]
F[111,x,k[0]] = -k[0]*(F[41,x,1]-F[41,x,k[0]])/(-1+k[0])
F[112,x,k[0]] = F[113,x,k[0]]+F[115,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[47,x,k[0]]*F[89,x]
F[115,x,k[0]] = -k[0]*(F[105,x,1]-F[105,x,k[0]])/(-1+k[0])
F[116,x] = F[104,x]+F[117,x]
F[117,x] = F[101,x]+F[103,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{116}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{40}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = y x
F_{50}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{88}\! \left(x \right)
F_{54}\! \left(x \right) = F_{39}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)+F_{85}\! \left(x \right)
F_{57}\! \left(x \right) = 0
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{73}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{8}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{64}\! \left(x \right) F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right) F_{8}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{56}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{79}\! \left(x \right) = F_{73}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{77}\! \left(x \right)
F_{84}\! \left(x \right) = F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{8}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{57}\! \left(x \right)+F_{66}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{104}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{91}\! \left(x \right) = F_{102}\! \left(x \right)+F_{57}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right)
F_{96}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{2}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{8}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{8}\! \left(x \right)
F_{103}\! \left(x \right) = F_{36}\! \left(x \right)+F_{91}\! \left(x \right)
F_{104}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{111}\! \left(x , y\right) = -\frac{y \left(F_{41}\! \left(x , 1\right)-F_{41}\! \left(x , y\right)\right)}{-1+y}
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{89}\! \left(x \right)
F_{115}\! \left(x , y\right) = -\frac{y \left(F_{105}\! \left(x , 1\right)-F_{105}\! \left(x , y\right)\right)}{-1+y}
F_{116}\! \left(x \right) = F_{104}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{101}\! \left(x \right)+F_{103}\! \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_8(x))
Eq(F_4(x), F_35(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_8(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_8(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_15(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_8(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x) + F_6(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_8(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_8(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_27(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_2(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_8(x))
Eq(F_38(x), F_116(x) + F_39(x))
Eq(F_39(x), F_40(x, 1))
Eq(F_40(x, k_0), F_2(x) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_49(x, k_0))
Eq(F_43(x, k_0), F_40(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_50(x, k_0))
Eq(F_45(x, k_0), F_2(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_46(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), k_0*x)
Eq(F_50(x, k_0), F_105(x, k_0) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_8(x))
Eq(F_53(x), F_54(x) + F_88(x))
Eq(F_54(x), F_39(x) + F_55(x))
Eq(F_55(x), F_15(x) + F_56(x))
Eq(F_56(x), F_57(x) + F_58(x) + F_85(x))
Eq(F_57(x), 0)
Eq(F_58(x), F_59(x)*F_8(x))
Eq(F_59(x), F_55(x) + F_60(x))
Eq(F_60(x), F_61(x) + F_73(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x)*F_8(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_15(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_64(x)*F_8(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x)*F_8(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_65(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_56(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_76(x)*F_8(x))
Eq(F_79(x), F_73(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_8(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_77(x))
Eq(F_84(x), F_80(x))
Eq(F_85(x), F_8(x)*F_86(x))
Eq(F_86(x), F_15(x) + F_87(x))
Eq(F_87(x), F_57(x) + F_66(x) + F_85(x))
Eq(F_88(x), F_104(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_15(x)*F_2(x))
Eq(F_91(x), F_102(x) + F_57(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_15(x)*F_8(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_14(x)*F_35(x))
Eq(F_96(x), F_14(x)*F_97(x))
Eq(F_97(x), F_2(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_8(x))
Eq(F_100(x), F_101(x) + F_96(x))
Eq(F_101(x), F_14(x)*F_2(x))
Eq(F_102(x), F_103(x)*F_8(x))
Eq(F_103(x), F_36(x) + F_91(x))
Eq(F_104(x), F_50(x, 1))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_8(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_112(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_111(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_47(x, k_0)*F_55(x))
Eq(F_111(x, k_0), -F_41(x, 1) + (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_112(x, k_0), F_113(x, k_0) + F_115(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_47(x, k_0)*F_89(x))
Eq(F_115(x, k_0), -F_105(x, 1) + (k_0*F_105(x, k_0) - F_105(x, 1))/(k_0 - 1))
Eq(F_116(x), F_104(x) + F_117(x))
Eq(F_117(x), F_101(x) + F_103(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": 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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_and_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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0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], 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Specification 4
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/191/
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[13,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[3,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[8,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0]]*F[3,x]
F[12,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[13,x] = F[14,x]+F[15,x]+F[56,x]
F[14,x] = 0
F[15,x] = F[16,x]*F[3,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x,1]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[14,x]+F[20,x,k[0]]+F[21,x,k[0]]+F[23,x,k[0]]
F[20,x,k[0]] = F[10,x,k[0]]*F[19,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[3,x]
F[22,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[23,x,k[0]] = F[24,x,k[0]]*F[3,x]
F[24,x,k[0]] = F[25,x]+F[54,x,k[0]]
F[25,x] = F[26,x]+F[4,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[3,x]
F[28,x] = F[27,x]+F[29,x]+F[4,x]+F[49,x]
F[29,x] = F[30,x]
F[30,x] = F[3,x]*F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[41,x]
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[3,x]*F[33,x]
F[36,x] = F[34,x]+F[37,x]
F[37,x] = F[14,x]+F[38,x]+F[40,x]
F[38,x] = F[3,x]*F[39,x]
F[39,x] = F[34,x]+F[37,x]
F[40,x] = F[3,x]*F[36,x]
F[41,x] = F[42,x]
F[42,x] = F[3,x]*F[32,x]*F[43,x]
F[43,x] = F[33,x]+F[44,x]
F[44,x] = F[34,x]+F[45,x]
F[45,x] = F[14,x]+F[46,x]+F[48,x]
F[46,x] = F[3,x]*F[47,x]
F[47,x] = F[34,x]+F[45,x]
F[48,x] = F[3,x]*F[44,x]
F[49,x] = F[50,x]
F[50,x] = F[3,x]*F[33,x]*F[51,x]
F[51,x] = F[29,x]+F[4,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[3,x]*F[32,x]*F[4,x]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[10,x,k[0]]*F[24,x,k[0]]*F[33,x]
F[56,x] = F[25,x]*F[3,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_{13}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{3}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{14}\! \left(x \right) = 0
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{3}\! \left(x \right)
F_{28}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)+F_{4}\! \left(x \right)+F_{49}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{3}\! \left(x \right) F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \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_{3}\! \left(x \right) F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{3}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{3}\! \left(x \right) F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{3}\! \left(x \right) F_{32}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{33}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right)+F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{3}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{34}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{3}\! \left(x \right) F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{3}\! \left(x \right) F_{33}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{29}\! \left(x \right)+F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{3}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{24}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{56}\! \left(x \right) = F_{25}\! \left(x \right) F_{3}\! \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_13(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_3(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_11(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_8(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_3(x))
Eq(F_12(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_13(x), F_14(x) + F_15(x) + F_56(x))
Eq(F_14(x), 0)
Eq(F_15(x), F_16(x)*F_3(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_14(x) + F_20(x, k_0) + F_21(x, k_0) + F_23(x, k_0))
Eq(F_20(x, k_0), F_10(x, k_0)*F_19(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_3(x))
Eq(F_22(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_3(x))
Eq(F_24(x, k_0), F_25(x) + F_54(x, k_0))
Eq(F_25(x), F_26(x) + F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_3(x))
Eq(F_28(x), F_27(x) + F_29(x) + F_4(x) + F_49(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_3(x)*F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_41(x))
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_3(x)*F_33(x))
Eq(F_36(x), F_34(x) + F_37(x))
Eq(F_37(x), F_14(x) + F_38(x) + F_40(x))
Eq(F_38(x), F_3(x)*F_39(x))
Eq(F_39(x), F_34(x) + F_37(x))
Eq(F_40(x), F_3(x)*F_36(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_3(x)*F_32(x)*F_43(x))
Eq(F_43(x), F_33(x) + F_44(x))
Eq(F_44(x), F_34(x) + F_45(x))
Eq(F_45(x), F_14(x) + F_46(x) + F_48(x))
Eq(F_46(x), F_3(x)*F_47(x))
Eq(F_47(x), F_34(x) + F_45(x))
Eq(F_48(x), F_3(x)*F_44(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_3(x)*F_33(x)*F_51(x))
Eq(F_51(x), F_29(x) + F_4(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_3(x)*F_32(x)*F_4(x))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_10(x, k_0)*F_24(x, k_0)*F_33(x))
Eq(F_56(x), F_25(x)*F_3(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"}, {"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": "point_and_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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"children": [{"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]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], 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"pos": [[2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "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": [0, 1], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 5
Strategy pack name: insertion_point_placements_tracked_fusion
Tree: http://permpal.com/tree/192/
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[8,x]
F[4,x] = F[35,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[8,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[8,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[15,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[8,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]+F[6,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[8,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[8,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[27,x]
F[34,x] = F[30,x]
F[35,x] = F[2,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[8,x]
F[38,x] = F[139,x]+F[39,x]
F[39,x] = F[40,x,1]
F[40,x,k[0]] = F[2,x]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[49,x,k[0]]
F[43,x,k[0]] = F[40,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[50,x,k[0]]
F[45,x,k[0]] = F[2,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[46,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = k[0]*x
F[50,x,k[0]] = F[128,x,k[0]]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[8,x]
F[53,x] = F[54,x]+F[88,x]
F[54,x] = F[39,x]+F[55,x]
F[55,x] = F[15,x]+F[56,x]
F[56,x] = F[57,x]+F[58,x]+F[85,x]
F[57,x] = 0
F[58,x] = F[59,x]*F[8,x]
F[59,x] = F[55,x]+F[60,x]
F[60,x] = F[61,x]+F[73,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]*F[8,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[15,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[64,x]*F[8,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]*F[8,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[65,x]
F[72,x] = F[68,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = F[56,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[76,x]*F[8,x]
F[79,x] = F[73,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[8,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[77,x]
F[84,x] = F[80,x]
F[85,x] = F[8,x]*F[86,x]
F[86,x] = F[15,x]+F[87,x]
F[87,x] = F[57,x]+F[66,x]+F[85,x]
F[88,x] = F[125,x]+F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[15,x]*F[2,x]
F[91,x] = F[92,x]
F[92,x] = F[8,x]*F[93,x]
F[93,x] = F[109,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[15,x]*F[39,x]
F[97,x] = F[14,x]*F[15,x]*F[98,x]
F[98,x] = F[2,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[8,x]
F[101,x] = F[102,x]+F[98,x]
F[102,x] = F[103,x]*F[2,x]
F[103,x] = F[104,x]+F[14,x]
F[104,x] = F[105,x]+F[15,x]
F[105,x] = F[106,x]+F[108,x]+F[57,x]
F[106,x] = F[107,x]*F[8,x]
F[107,x] = F[105,x]+F[15,x]
F[108,x] = F[104,x]*F[8,x]
F[109,x] = F[110,x]+F[122,x]
F[110,x] = F[111,x]+F[115,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[14,x]*F[2,x]
F[113,x] = F[114,x]+F[15,x]
F[114,x] = F[14,x]*F[15,x]
F[115,x] = F[116,x]+F[118,x]
F[116,x] = F[117,x]
F[117,x] = F[113,x]*F[36,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[15,x]*F[91,x]
F[120,x] = F[121,x]
F[121,x] = F[15,x]^2*F[14,x]*F[36,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[125,x]*F[15,x]
F[125,x] = F[50,x,1]
F[126,x] = F[127,x]
F[127,x] = F[15,x]^2*F[14,x]*F[98,x]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[8,x]
F[130,x,k[0]] = F[131,x,k[0]]+F[135,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[134,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]
F[133,x,k[0]] = F[47,x,k[0]]*F[55,x]
F[134,x,k[0]] = -k[0]*(F[41,x,1]-F[41,x,k[0]])/(-1+k[0])
F[135,x,k[0]] = F[136,x,k[0]]+F[138,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]
F[137,x,k[0]] = F[47,x,k[0]]*F[89,x]
F[138,x,k[0]] = -k[0]*(F[128,x,1]-F[128,x,k[0]])/(-1+k[0])
F[139,x] = F[125,x]+F[140,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[14,x]*F[2,x]
F[142,x] = F[36,x]+F[91,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{139}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{40}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = y x
F_{50}\! \left(x , y\right) = F_{128}\! \left(x , y\right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{88}\! \left(x \right)
F_{54}\! \left(x \right) = F_{39}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)+F_{85}\! \left(x \right)
F_{57}\! \left(x \right) = 0
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{73}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{8}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{64}\! \left(x \right) F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right) F_{8}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{56}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{79}\! \left(x \right) = F_{73}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{77}\! \left(x \right)
F_{84}\! \left(x \right) = F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{8}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{57}\! \left(x \right)+F_{66}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{125}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{8}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{109}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{15}\! \left(x \right) F_{39}\! \left(x \right)
F_{97}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{2}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{8}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{98}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{2}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{14}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{15}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{108}\! \left(x \right)+F_{57}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{8}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{15}\! \left(x \right)
F_{108}\! \left(x \right) = F_{104}\! \left(x \right) F_{8}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{122}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{115}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{15}\! \left(x \right)
F_{114}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{118}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{113}\! \left(x \right) F_{36}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{15}\! \left(x \right) F_{91}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{15} \left(x \right)^{2} F_{14}\! \left(x \right) F_{36}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{15}\! \left(x \right)
F_{125}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{15} \left(x \right)^{2} F_{14}\! \left(x \right) F_{98}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{55}\! \left(x \right)
F_{134}\! \left(x , y\right) = -\frac{y \left(F_{41}\! \left(x , 1\right)-F_{41}\! \left(x , y\right)\right)}{-1+y}
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{89}\! \left(x \right)
F_{138}\! \left(x , y\right) = -\frac{y \left(F_{128}\! \left(x , 1\right)-F_{128}\! \left(x , y\right)\right)}{-1+y}
F_{139}\! \left(x \right) = F_{125}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right)
F_{142}\! \left(x \right) = F_{36}\! \left(x \right)+F_{91}\! \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_8(x))
Eq(F_4(x), F_35(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_8(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_8(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_15(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_8(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x) + F_6(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_8(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_8(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_27(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_2(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_8(x))
Eq(F_38(x), F_139(x) + F_39(x))
Eq(F_39(x), F_40(x, 1))
Eq(F_40(x, k_0), F_2(x) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_49(x, k_0))
Eq(F_43(x, k_0), F_40(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_50(x, k_0))
Eq(F_45(x, k_0), F_2(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_46(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), k_0*x)
Eq(F_50(x, k_0), F_128(x, k_0) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_8(x))
Eq(F_53(x), F_54(x) + F_88(x))
Eq(F_54(x), F_39(x) + F_55(x))
Eq(F_55(x), F_15(x) + F_56(x))
Eq(F_56(x), F_57(x) + F_58(x) + F_85(x))
Eq(F_57(x), 0)
Eq(F_58(x), F_59(x)*F_8(x))
Eq(F_59(x), F_55(x) + F_60(x))
Eq(F_60(x), F_61(x) + F_73(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x)*F_8(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_15(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_64(x)*F_8(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x)*F_8(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_65(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_56(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_76(x)*F_8(x))
Eq(F_79(x), F_73(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_8(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_77(x))
Eq(F_84(x), F_80(x))
Eq(F_85(x), F_8(x)*F_86(x))
Eq(F_86(x), F_15(x) + F_87(x))
Eq(F_87(x), F_57(x) + F_66(x) + F_85(x))
Eq(F_88(x), F_125(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_15(x)*F_2(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_8(x)*F_93(x))
Eq(F_93(x), F_109(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_15(x)*F_39(x))
Eq(F_97(x), F_14(x)*F_15(x)*F_98(x))
Eq(F_98(x), F_2(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_8(x))
Eq(F_101(x), F_102(x) + F_98(x))
Eq(F_102(x), F_103(x)*F_2(x))
Eq(F_103(x), F_104(x) + F_14(x))
Eq(F_104(x), F_105(x) + F_15(x))
Eq(F_105(x), F_106(x) + F_108(x) + F_57(x))
Eq(F_106(x), F_107(x)*F_8(x))
Eq(F_107(x), F_105(x) + F_15(x))
Eq(F_108(x), F_104(x)*F_8(x))
Eq(F_109(x), F_110(x) + F_122(x))
Eq(F_110(x), F_111(x) + F_115(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_14(x)*F_2(x))
Eq(F_113(x), F_114(x) + F_15(x))
Eq(F_114(x), F_14(x)*F_15(x))
Eq(F_115(x), F_116(x) + F_118(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_113(x)*F_36(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_15(x)*F_91(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_14(x)*F_15(x)**2*F_36(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_125(x)*F_15(x))
Eq(F_125(x), F_50(x, 1))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_14(x)*F_15(x)**2*F_98(x))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_130(x, k_0)*F_8(x))
Eq(F_130(x, k_0), F_131(x, k_0) + F_135(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_134(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0))
Eq(F_133(x, k_0), F_47(x, k_0)*F_55(x))
Eq(F_134(x, k_0), -F_41(x, 1) + (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_135(x, k_0), F_136(x, k_0) + F_138(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0))
Eq(F_137(x, k_0), F_47(x, k_0)*F_89(x))
Eq(F_138(x, k_0), -F_128(x, 1) + (k_0*F_128(x, k_0) - F_128(x, 1))/(k_0 - 1))
Eq(F_139(x), F_125(x) + F_140(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_14(x)*F_2(x))
Eq(F_142(x), F_36(x) + F_91(x))
Pack JSON:
{"expansion_strats": [[{"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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "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], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": 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