02431_03421_12430_13420
Counting sequence:
1, 1, 2, 6, 24, 116, 632, 3720, 23072, 148528, 983072, 6647776, 45727616, 318947136, 2250473344, 16034726016, 115204555264, 833701020416, 6071393452544, 44460988694016, 327199429228544, 2418586647786496, 17948732704159744, 133679253739800576, 998872407282294784, 7485971546167586816, 56256199275671724032, 423820155289339944960, 3200352310745397952512, 24218334758348867452928, 183634568289554708529152, 1394981852859454730567680, 10615315699723740670722048, 80909403814431119158476800, 617622161151143299826974720, 4721332458192524983142318080, 36139965190171876699311439872, 276986774033975238982890684416, 2125435791576382294738966413312, 16327758950230142177042886033408, 125565114895348504884075028283392, 966610319941152310833961640132608, 7448208755069396026355567476867072, 57444681245799426628273624483627008, 443431382485652056866173254780321792, 3425815874103007045139313530155040768, 26487817430454910444610790902026207232, 204954551965103619117007426157971243008, 1587025379330436389340015985294428864512, 12297353959254492573408993157837590888448, 95351691358196158746218176692730747420672, 739813500177064172239520892487507038437376, 5743572849993728430868672099538913508458496, 44616716581783731039726666526632463214575616, 346783825717277473882941762710077965697286144, 2696848404688634464193741766801597742738046976, 20983694099520039558823951896511302895293956096, 163352875577657702190978731389975174890265772032, 1272281481894340799804010087793362120758511271936, 9913882898150704031294073730401745241726018125824, 77286114956885190947578179286804678462192343842816, 602767178687574196812433016725191581758939826487296, 4703073801811707292687343239983259060550403413245952, 36710646316983094772128766341863535972343309251117056, 286664927106557626729461280815045018891238319329378304, 2239359984049577593372309049347022849178825236200554496, 17499872000270312132739282650349112902686649060671094784, 136805155144173051729007446451324500363523544877656702976, 1069847651400452483800645485910067906480034062497359069184, 8369292776040914841371424199798638488542545507288262639616, 65493559859502841058666194895542676022199562236051129892864, 512681090544089711809610988996281119384811855769885575479296, 4014494798632613429002057544092532276028446970246148772593664, 31444565358073991653136208764672436196162512230517285465358336, 246369956225253333066429296336536824018413862368419563641503744, 1930873656892398337401361532702089172716455733678086020520738816, 15137026742573320900536103275988650210440195524493219592839102464, 118698352584236350541431040417382294783003935134220220575321686016, 931028781986913088772148061116667033500505390307302467836831596544, 7304539727341190169385782891941318240838737289650821688286894882816, 57323286428584740865190513805149356000882986775508398695755854905344, 449961170024815167017720928352891496171809704339762832015555387457536, 3532824635486296034258232344044106101755368084685031375385188068491264, 27744037555084301456162028387808190833000085471841762643229013144764416, 217929155079595932512916214048848610154478538384802607871004705023852544, 1712208821937879789513647543875312872651442719908336403804471100604153856, 13455243757737228423451968156894799098142969819600632633244325389432520704, 105759077669714588425882940250870420212015054485782382784125259698956926976, 831443729133279657385049398590074348762754378480594403548519994676167573504, 6537852875950458054589806989931466831217695292655257962514660188494491549696, 51418868867975138161488524747594484761329563303247571440293061319974279184384, 404476296502196840301485644092631407592058563623717482291461612264015607627776, 3182328189279362038816090473210410616650400160678451079070555167390897153245184, 25042426109727211825335010460330382572420967149187273175455903190949824997359616, 197099558650514508234541562416534688868000659300855859018030138746790084884824064, 1551568823370063086536633897607069370759032243235680564990382381726121473024720896, 12216054419963196033459228393366398280724893678200100550811177803217629439762366464, 96197508831063544549078658310028123040856513138781142690215068216397378408400551936, 757649122794759881491015875909006247755176020007792592289015375808715919904728940544, 5968186464527552780036403582243130945728156023930663227604542077698710121348507631616, 47020275941527453300110702025751443972851245542696846888382713411466624462660927750144
Generating function in Maple syntax:
(-x*(-8*x+1)^(1/2)-x+2)/(4*x^2-4*x+2)
Generating function in latex syntax:
\frac{-x \sqrt{-8 x +1}-x +2}{4 x^{2}-4 x +2}
Generating function in sympy syntax:
(-x*sqrt(1 - 8*x) - x + 2)/(4*x**2 - 4*x + 2)
Implicit equation for the generating function in Maple syntax:
(2*x^2-2*x+1)*F(x)^2+(-2+x)*F(x)+x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{2}-2 x +1\right) F \! \left(x \right)^{2}+\left(-2+x \right) F \! \left(x \right)+x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+3) = 8*(2*n+1)/(n+2)*a(n)-6*(3*n+2)/(n+2)*a(n+1)+2*(5*n+4)/(n+2)*a(n+2), n >= 3
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a{\left(n + 3 \right)} = \frac{8 \left(2 n + 1\right) a{\left(n \right)}}{n + 2} - \frac{6 \left(3 n + 2\right) a{\left(n + 1 \right)}}{n + 2} + \frac{2 \left(5 n + 4\right) a{\left(n + 2 \right)}}{n + 2}, \quad n \geq 3
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24967/
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[46,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[50,x]+F[7,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[46,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[17,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[47,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[46,x]
F[21,x,k[0]] = F[22,x,k[0]]+F[30,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[24,x,k[0]]
F[23,x,k[0]] = F[12,x,k[0]]*F[9,x]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]*F[26,x,k[0]]
F[27,x,k[0]] = F[16,x,k[0]]*F[26,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = -k[0]*(F[29,x,1]-F[29,x,k[0]])/(-1+k[0])
F[10,x,k[0]] = F[29,x,k[0]]+F[4,x]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[46,x]
F[32,x,k[0]] = F[33,x,k[0]]
F[34,x,k[0]] = F[33,x,k[0]]*F[46,x]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[39,x,k[0]]
F[36,x,k[0]] = F[12,x,k[0]]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[19,x,1]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[43,x,k[0]] = F[16,x,k[0]]*F[42,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = -k[0]*(F[45,x,1]-F[45,x,k[0]])/(-1+k[0])
F[19,x,k[0]] = F[45,x,k[0]]+F[6,x]
F[46,x] = x
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[46,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[30,x,k[0]]+F[35,x,k[0]]
F[50,x] = F[38,x]*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_{46}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x F_{5}\! \left(x \right)+F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{50}\! \left(x \right)+F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{46}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{46}\! \left(x \right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = -\frac{y \left(F_{29}\! \left(x , 1\right)-F_{29}\! \left(x , y\right)\right)}{y -1}
F_{10}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{46}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{46}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = -\frac{y \left(F_{45}\! \left(x , 1\right)-F_{45}\! \left(x , y\right)\right)}{y -1}
F_{19}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{46}\! \left(x \right) = x
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{46}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{50}\! \left(x \right) = F_{38}\! \left(x \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_46(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_50(x) + F_7(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_46(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_17(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_47(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_46(x))
Eq(F_21(x, k_0), F_22(x, k_0) + F_30(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_24(x, k_0))
Eq(F_23(x, k_0), F_12(x, k_0)*F_9(x))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_15(x, k_0)*F_16(x, k_0)*F_26(x, k_0))
Eq(F_27(x, k_0), F_16(x, k_0)*F_26(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), -F_29(x, 1) + (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_29(x, k_0) + F_4(x))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_46(x))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_34(x, k_0), F_33(x, k_0)*F_46(x))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_39(x, k_0))
Eq(F_36(x, k_0), F_12(x, k_0)*F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_19(x, 1))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_15(x, k_0)*F_16(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_43(x, k_0), F_16(x, k_0)*F_42(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), -F_45(x, 1) + (-k_0*F_45(x, k_0) + F_45(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), F_45(x, k_0) + F_6(x))
Eq(F_46(x), x)
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_46(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_30(x, k_0) + F_35(x, k_0))
Eq(F_50(x), F_38(x)*F_46(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]]}], "iterative": false}
Specification JSON:
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"pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25077/
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[58,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[62,x]+F[7,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[58,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[30,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[28,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[19,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[21,x,k[0]]+F[24,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[19,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[21,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[27,x,k[0]]+F[7,x]
F[25,x,k[0]] = F[19,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = F[17,x,k[0]]+F[24,x,k[0]]
F[27,x,k[0]] = F[19,x,k[0]]*F[20,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[30,x,k[0]] = F[29,x,k[0]]+F[59,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[58,x]
F[32,x,k[0]] = F[33,x,k[0]]+F[42,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[12,x,k[0]]*F[9,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[19,x,k[0]]*F[37,x,k[0]]*F[41,x,k[0]]
F[38,x,k[0]] = F[19,x,k[0]]*F[37,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = -k[0]*(F[40,x,1]-F[40,x,k[0]])/(-1+k[0])
F[10,x,k[0]] = F[4,x]+F[40,x,k[0]]
F[41,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]*F[58,x]
F[44,x,k[0]] = F[45,x,k[0]]
F[46,x,k[0]] = F[45,x,k[0]]*F[58,x]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[51,x,k[0]]
F[48,x,k[0]] = F[12,x,k[0]]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[30,x,1]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[19,x,k[0]]*F[41,x,k[0]]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[55,x,k[0]] = F[19,x,k[0]]*F[54,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = -k[0]*(F[57,x,1]-F[57,x,k[0]])/(-1+k[0])
F[30,x,k[0]] = F[57,x,k[0]]+F[6,x]
F[58,x] = x
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[58,x]*F[61,x,k[0]]
F[61,x,k[0]] = F[42,x,k[0]]+F[47,x,k[0]]
F[62,x] = F[50,x]*F[58,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_{58}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{62}\! \left(x \right)+F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{58}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{58}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = -\frac{y \left(F_{40}\! \left(x , 1\right)-F_{40}\! \left(x , y\right)\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{58}\! \left(x \right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{58}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{41}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = -\frac{y \left(F_{57}\! \left(x , 1\right)-F_{57}\! \left(x , y\right)\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{58}\! \left(x \right) = x
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{58}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{50}\! \left(x \right) F_{58}\! \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_58(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_62(x) + F_7(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_58(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_30(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_28(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_19(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_16(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_21(x, k_0) + F_24(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_19(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_21(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_27(x, k_0) + F_7(x))
Eq(F_25(x, k_0), F_19(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), F_17(x, k_0) + F_24(x, k_0))
Eq(F_27(x, k_0), F_19(x, k_0)*F_20(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_30(x, k_0), F_29(x, k_0) + F_59(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_58(x))
Eq(F_32(x, k_0), F_33(x, k_0) + F_42(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_12(x, k_0)*F_9(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_19(x, k_0)*F_37(x, k_0)*F_41(x, k_0))
Eq(F_38(x, k_0), F_19(x, k_0)*F_37(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), -F_40(x, 1) + (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_4(x) + F_40(x, k_0))
Eq(F_41(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0)*F_58(x))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_46(x, k_0), F_45(x, k_0)*F_58(x))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_51(x, k_0))
Eq(F_48(x, k_0), F_12(x, k_0)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_30(x, 1))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_19(x, k_0)*F_41(x, k_0)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_55(x, k_0), F_19(x, k_0)*F_54(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), -F_57(x, 1) + (-k_0*F_57(x, k_0) + F_57(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_57(x, k_0) + F_6(x))
Eq(F_58(x), x)
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_58(x)*F_61(x, k_0))
Eq(F_61(x, k_0), F_42(x, k_0) + F_47(x, k_0))
Eq(F_62(x), F_50(x)*F_58(x))
Pack JSON:
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Specification JSON:
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{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25196/
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[43,x]
F[4,x] = F[5,x]+F[7,x]
F[5,x] = F[6,x]
F[6,x] = 2+F[6,x]^2+(-2+x)*F[6,x]
F[7,x] = F[8,x]+F[9,x]
F[8,x] = (1+F[8,x])*x+F[8,x]^2
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[43,x]
F[11,x] = F[12,x]+F[59,x]
F[12,x] = F[13,x]+F[14,x]
F[13,x] = F[7,x]
F[14,x] = F[15,x,1]
F[16,x,k[0]] = F[13,x]+F[15,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[44,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[34,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[6,x]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[38,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[29,x,k[0]]*F[33,x,k[0]]*F[34,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[35,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[6,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[33,x,k[0]]*F[34,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[22,x,k[0]]*F[33,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = 2*F[27,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]*F[43,x]
F[41,x,k[0]] = F[33,x,k[0]]*F[40,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = -k[0]*(F[20,x,1]-F[20,x,k[0]])/(-1+k[0])
F[43,x] = x
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[43,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[55,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[12,x]*F[34,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[33,x,k[0]]*F[51,x,k[0]]*F[54,x,k[0]]
F[52,x,k[0]] = F[33,x,k[0]]*F[51,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = -k[0]*(F[15,x,1]-F[15,x,k[0]])/(-1+k[0])
F[54,x,k[0]] = F[27,x,k[0]]+F[34,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[43,x]*F[57,x,k[0]]
F[58,x,k[0]] = F[43,x]*F[57,x,k[0]]
F[58,x,k[0]] = F[47,x,k[0]]
F[59,x] = F[60,x]
F[60,x] = F[43,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = 1/F[43,x]*F[63,x]
F[63,x] = F[12,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_{43}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{7}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{6}\! \left(x \right) x +F_{6} \left(x \right)^{2}-2 F_{6}\! \left(x \right)+2
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = F_{8}\! \left(x \right) x +F_{8} \left(x \right)^{2}+x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{59}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{29}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = y x
F_{34}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{27}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{43}\! \left(x \right)
F_{41}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{y \left(F_{20}\! \left(x , 1\right)-F_{20}\! \left(x , y\right)\right)}{-1+y}
F_{43}\! \left(x \right) = x
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{51}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = -\frac{y \left(F_{15}\! \left(x , 1\right)-F_{15}\! \left(x , y\right)\right)}{-1+y}
F_{54}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{43}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{43}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{43}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{12}\! \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_43(x))
Eq(F_4(x), F_5(x) + F_7(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), (x - 2)*F_6(x) + F_6(x)**2 + 2)
Eq(F_7(x), F_8(x) + F_9(x))
Eq(F_8(x), (x - 3)*(F_8(x) + 1) + (F_8(x) + 1)**2 + F_8(x) + 2)
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_43(x))
Eq(F_11(x), F_12(x) + F_59(x))
Eq(F_12(x), F_13(x) + F_14(x))
Eq(F_13(x), F_7(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_16(x, k_0), F_13(x) + F_15(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_44(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_34(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_6(x))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_38(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_29(x, k_0)*F_33(x, k_0)*F_34(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_35(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_6(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_33(x, k_0)*F_34(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_30(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_22(x, k_0)*F_33(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), 2*F_27(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0)*F_43(x))
Eq(F_41(x, k_0), F_33(x, k_0)*F_40(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), -F_20(x, 1) + (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_43(x), x)
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_43(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_55(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_12(x)*F_34(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_33(x, k_0)*F_51(x, k_0)*F_54(x, k_0))
Eq(F_52(x, k_0), F_33(x, k_0)*F_51(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), -F_15(x, 1) + (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_54(x, k_0), F_27(x, k_0) + F_34(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_43(x)*F_57(x, k_0))
Eq(F_58(x, k_0), F_43(x)*F_57(x, k_0))
Eq(F_58(x, k_0), F_47(x, k_0))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_43(x)*F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x)/F_43(x))
Eq(F_63(x), F_12(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]]}], "iterative": false}
Specification JSON:
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"strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25606/
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[52,x]
F[4,x] = F[5,x]+F[7,x]
F[5,x] = F[6,x]
F[6,x] = 2+F[6,x]^2+(-2+x)*F[6,x]
F[7,x] = F[8,x]+F[9,x]
F[8,x] = (1+F[8,x])*x+F[8,x]^2
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[52,x]
F[11,x] = F[12,x]+F[68,x]
F[12,x] = F[13,x]+F[14,x]
F[13,x] = F[7,x]
F[14,x] = F[15,x,1]
F[16,x,k[0]] = F[13,x]+F[15,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[53,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[46,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[6,x]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[33,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[47,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[33,x,k[0]]*F[37,x,k[0]]*F[46,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[43,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[6,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[33,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[34,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[30,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = k[0]*x
F[34,x,k[0]] = F[35,x,k[0]]+F[38,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[33,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[30,x,k[0]]
F[38,x,k[0]] = F[39,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[39,x] = 0
F[40,x,k[0]] = F[33,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[31,x,k[0]]+F[38,x,k[0]]
F[42,x,k[0]] = F[33,x,k[0]]*F[34,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[22,x,k[0]]*F[33,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = 2*F[27,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[52,x]
F[50,x,k[0]] = F[33,x,k[0]]*F[49,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = -k[0]*(F[20,x,1]-F[20,x,k[0]])/(-1+k[0])
F[52,x] = x
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[52,x]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[64,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = F[12,x]*F[46,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[33,x,k[0]]*F[60,x,k[0]]*F[63,x,k[0]]
F[61,x,k[0]] = F[33,x,k[0]]*F[60,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = -k[0]*(F[15,x,1]-F[15,x,k[0]])/(-1+k[0])
F[63,x,k[0]] = F[27,x,k[0]]+F[46,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[52,x]*F[66,x,k[0]]
F[67,x,k[0]] = F[52,x]*F[66,x,k[0]]
F[67,x,k[0]] = F[56,x,k[0]]
F[68,x] = F[69,x]
F[69,x] = F[52,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = 1/F[52,x]*F[72,x]
F[72,x] = F[12,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_{52}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{7}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{6}\! \left(x \right) x +F_{6} \left(x \right)^{2}-2 F_{6}\! \left(x \right)+2
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = F_{8}\! \left(x \right) x +F_{8} \left(x \right)^{2}+x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{37}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = y x
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = 2 F_{27}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{52}\! \left(x \right)
F_{50}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{y \left(F_{20}\! \left(x , 1\right)-F_{20}\! \left(x , y\right)\right)}{-1+y}
F_{52}\! \left(x \right) = x
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{52}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{60}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = -\frac{y \left(F_{15}\! \left(x , 1\right)-F_{15}\! \left(x , y\right)\right)}{-1+y}
F_{63}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{52}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{52}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{52}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{52}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{12}\! \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_52(x))
Eq(F_4(x), F_5(x) + F_7(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), (x - 2)*F_6(x) + F_6(x)**2 + 2)
Eq(F_7(x), F_8(x) + F_9(x))
Eq(F_8(x), (x - 3)*(F_8(x) + 1) + (F_8(x) + 1)**2 + F_8(x) + 2)
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_52(x))
Eq(F_11(x), F_12(x) + F_68(x))
Eq(F_12(x), F_13(x) + F_14(x))
Eq(F_13(x), F_7(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_16(x, k_0), F_13(x) + F_15(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_53(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_46(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_6(x))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_33(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_47(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_33(x, k_0)*F_37(x, k_0)*F_46(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_43(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_6(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_33(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_34(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_30(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), k_0*x)
Eq(F_34(x, k_0), F_35(x, k_0) + F_38(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_33(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_30(x, k_0))
Eq(F_38(x, k_0), F_39(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_39(x), 0)
Eq(F_40(x, k_0), F_33(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_31(x, k_0) + F_38(x, k_0))
Eq(F_42(x, k_0), F_33(x, k_0)*F_34(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_22(x, k_0)*F_33(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), 2*F_27(x, k_0))
Eq(F_46(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_52(x))
Eq(F_50(x, k_0), F_33(x, k_0)*F_49(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), -F_20(x, 1) + (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_52(x), x)
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_52(x)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_64(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), F_12(x)*F_46(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_33(x, k_0)*F_60(x, k_0)*F_63(x, k_0))
Eq(F_61(x, k_0), F_33(x, k_0)*F_60(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), -F_15(x, 1) + (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_63(x, k_0), F_27(x, k_0) + F_46(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_52(x)*F_66(x, k_0))
Eq(F_67(x, k_0), F_52(x)*F_66(x, k_0))
Eq(F_67(x, k_0), F_56(x, k_0))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_52(x)*F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)/F_52(x))
Eq(F_72(x), F_12(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 3, 1], [0, 3, 4, 2, 1], [1, 2, 4, 3, 0], [1, 3, 4, 2, 0]]}], "iterative": false}
Specification JSON:
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