10342_13042_13402_31042_31402_34102
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3302, 19044, 113292, 691320, 4310192, 27374264, 176669540, 1156339560, 7662832862, 51341086820, 347374265620, 2371093368872, 16313319675896, 113045869171456, 788505339317016, 5532825410362992, 39036116875746456, 276805023095849104, 1971973561332140464, 14109074736466474016, 101352105803978191152, 730775591357448259344, 5287427848007126868680, 38381027505855890891216, 279455161636976740345166, 2040566535941652623838372, 14940297329489221199293316, 109665650543157392763085064, 806907063581082424742226840, 5950610612092963772643485216, 43977720687145843669155792872, 325678522996707329289713087120, 2416497723967415089210317753880, 17963188409492915962571819141008, 133764866068073594486652813912240, 997761617371619230967298690437600, 7454260255676305131095958312194048, 55775627627499454926646886139667744, 417943604896481800102833871776767024, 3136152685916997305336786743287279584, 23564470788762085324336464322541601208, 177286389721147645495509959619470263824, 1335451059982299140618360812557941842512, 10071505931260961257372087634300669650080, 76042239152389916163176288011478018809312, 574765570454457033840912590339270543974144, 4348948996991198213884451744454737242287840, 32939645775408637454732528772109476361022144, 249734642538333535158591849630235141336926560, 1895173435329318057052869529612905487757008192, 14395118859030407718379974216700378336697995584, 109437010180757114683437429880185551292037232640, 832689468082933885431631166700629498222316690336, 6341027829082071670084344999714478809045308682400, 48326174622033816772344852183798445074320194618768, 368587276098544481758686707075659397139421169405856, 2813344559984654978597824628215187620640115622037550, 21489196014706388020195949826279215668071685581617700, 164256480254596644750885366716116633693508799353927140, 1256379480740956123222990494840769788604073385141651400, 9616264777124386645063719655595355004408295502357453400, 73649686765164969879373925404642570643145242279586351840, 564425107960338901295879193134033036336007255051938885320, 4328177156340313464746051243440987436453461057274702186320, 33209297485063589814541083131985361299582361583406797756120, 254954850830134734752882511113823859150154607279840389063440, 1958434543878862743315474392106212383881860582881741728767920, 15051873609216912586120603471499859097222054972189342791830240, 115744821956359615720147185342053768812658930061684436701721152, 890504490994568570129902637126659479052174866533506482230563680, 6854699956410461125744497001392280263449581569991714977092940240, 52790169277144357037406665366974716290683095175860419451308267552, 406747238504263281694237076812612288638444746727261390597707765624, 3135436475849373882888676893245215988773749297739293626182291563408, 24180668502109553714209247547482789704595683073366396953161271072080, 186565248581496462442799669539539989463120788815248656142347135890080, 1440060596803012912611743811263781004746073674359451031316855809937888, 11120234129608775572373499380295513102183075812831660093910254227593728, 85906490311092860058972575763553906414055400110249582110189640517258080, 663915463667000735913833032741622042936580073763715353030012590968033216, 5132989504166994240606248473053060961716262566975590579141905410769842272, 39700402380021112940142234126191185499868626551868325249301236229583059520, 307172735618654048474709517972360192026399644153237745126503841382943106240, 2377552162998723983683980300009871749008501277622433784736195486397940435584, 18409144157738169854734621679463405771429118683862726812990146617500143255360, 142590284572898069079250745299934573194142096575814564871890700778289985855680, 1104830893672720009697845692511599026206996185220909325838138411876185172625504, 8563436217103780156186407344127354709699643941729238317913042973387884814887872, 66396265757456404612494436229055840166882206176590016362290945191399010059444472, 514967251546320437012946323233806303445905434203642642767691468251061382720240912, 3995333804119153273547673971507998485264071052114056453815468703995376431079340944, 31007106933801876804875184964158515523397854274873582765533427906466185706924445472, 240714052807038388647417771944085184427034628858628252615665304995512523562858167136, 1869265737494728643743767825866691308704649625539629583672356697844883072597351746176
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24367/
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[34,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[30,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[29,x,k[0],k[1]]
F[13,x,k[0],k[1]] = k[0]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[3,x]
F[15,x,k[0],k[1]] = F[16,x,k[1],k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],1,k[1]]
F[17,x,k[0],k[1],k[2]] = (F[18,x,k[0],k[1],k[2]]*k[0]-F[18,x,1,k[1],k[2]])/(-1+k[0])
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1],k[2]]*k[0]-F[19,x,1,k[1],k[2]])/(-1+k[0])
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[25,x,k[0],k[1]]
F[21,x,k[0],k[1]] = k[0]*F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[3,x]
F[23,x,k[0],k[1]] = F[24,x,k[1],k[0]]
F[24,x,k[0],k[1]] = 1/(-1+k[1])*(F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],1])
F[25,x,k[0],k[1]] = F[21,x,k[1],k[0]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[3,x]
F[27,x,k[0],k[1]] = 1/(-1+k[1])*(F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])
F[28,x,k[0],k[1]] = F[26,x,k[1],k[0]]
F[29,x,k[0],k[1]] = F[13,x,k[1],k[0]]
F[30,x,k[0]] = k[0]*F[31,x,k[0]]
F[31,x,k[0]] = F[3,x]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,1,k[0]]
F[33,x,k[0],k[1]] = (F[24,x,k[0],k[1]]*k[0]-F[24,x,1,k[1]])/(-1+k[0])
F[34,x] = F[5,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{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_{34}\! \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_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , 1, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{14}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{1}, y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, 1, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{19}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{20}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{22}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}, y_{0}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{20}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{20}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}, y_{0}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{12}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{1}, y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{1}, y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = y_{0} F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , 1, y_{0}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{34}\! \left(x \right) = F_{5}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_34(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_30(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_26(x, k_0, k_1) + F_28(x, k_0, k_1) + F_29(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), k_0*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_3(x))
Eq(F_15(x, k_0, k_1), F_16(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, 1, k_1))
Eq(F_17(x, k_0, k_1, k_2), (-k_0*F_18(x, k_0, k_1, k_2) + F_18(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_18(x, k_0, k_1, k_2), (-k_0*F_19(x, k_0, k_1, k_2) + F_19(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1) + k_2*F_20(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_25(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), k_0*F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_3(x))
Eq(F_23(x, k_0, k_1), F_24(x, k_1, k_0))
Eq(F_24(x, k_0, k_1), (k_1*F_20(x, k_0, k_1) - F_20(x, k_0, 1))/(k_1 - 1))
Eq(F_25(x, k_0, k_1), F_21(x, k_1, k_0))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_3(x))
Eq(F_27(x, k_0, k_1), (k_1*F_12(x, k_0, k_1) - F_12(x, k_0, 1))/(k_1 - 1))
Eq(F_28(x, k_0, k_1), F_26(x, k_1, k_0))
Eq(F_29(x, k_0, k_1), F_13(x, k_1, k_0))
Eq(F_30(x, k_0), k_0*F_31(x, k_0))
Eq(F_31(x, k_0), F_3(x)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, 1, k_0))
Eq(F_33(x, k_0, k_1), (-k_0*F_24(x, k_0, k_1) + F_24(x, 1, k_1))/(1 - k_0))
Eq(F_34(x), F_5(x))
Pack JSON:
{"name": "row_and_col_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": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 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[[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}], "strategy": {"class_module": "tilings.strategies.symmetry", "strategy_class": "TilingComplement", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 5], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 1], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 4]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 4]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 2], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 5], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 4], [1, 4], [1, 5], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 5], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 5], [1, 4], [1, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 4], [1, 0], [1, 4], [1, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 4], [1, 1], [1, 4], [1, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 4], [1, 2], [1, 4], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 0], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 1], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 2], [1, 4]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 5], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 4], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 5], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 5], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 0], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 1], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 1], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}], "strategy": {"class_module": "tilings.strategies.symmetry", "strategy_class": "TilingComplement", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false}}]}, {"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.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: all_the_strategies_2_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24368/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[1,x]+F[30,x]+F[6,x]
F[6,x] = F[4,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[28,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x,k[0]] = F[12,x,k[0]]*F[4,x]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[27,x,k[0],k[1]]
F[14,x,k[0],k[1]] = k[0]*F[15,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[4,x]
F[16,x,k[0],k[1]] = F[17,x,k[1],k[0]]
F[17,x,k[0],k[1]] = (F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])/(-1+k[0])
F[18,x,k[0],k[1]] = F[1,x]+F[19,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[19,x,k[0],k[1]] = k[0]*F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[4,x]
F[21,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[4,x]
F[22,x,k[0],k[1]] = F[21,x,k[1],k[0]]
F[23,x,k[0],k[1]] = F[19,x,k[1],k[0]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]*F[4,x]
F[25,x,k[0],k[1]] = 1/(-1+k[1])*(F[13,x,k[0],k[1]]*k[1]-F[13,x,k[0],1])
F[26,x,k[0],k[1]] = F[24,x,k[1],k[0]]
F[27,x,k[0],k[1]] = F[14,x,k[1],k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[19,x,k[0],1]
F[30,x] = F[6,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , 1, y\right)
F_{13}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = y F_{15}\! \left(x , y , z\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , z , y\right)
F_{17}\! \left(x , y , z\right) = -\frac{-y F_{18}\! \left(x , y , z\right)+F_{18}\! \left(x , 1, z\right)}{-1+y}
F_{18}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = y F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{21}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = F_{21}\! \left(x , z , y\right)
F_{23}\! \left(x , y , z\right) = F_{19}\! \left(x , z , y\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y , z\right) = -\frac{-z F_{13}\! \left(x , y , z\right)+F_{13}\! \left(x , y , 1\right)}{-1+z}
F_{26}\! \left(x , y , z\right) = F_{24}\! \left(x , z , y\right)
F_{27}\! \left(x , y , z\right) = F_{14}\! \left(x , z , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{19}\! \left(x , y , 1\right)
F_{30}\! \left(x \right) = F_{6}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_1(x) + F_30(x) + F_6(x))
Eq(F_6(x), F_4(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_28(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_12(x, k_0)*F_4(x))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_24(x, k_0, k_1) + F_26(x, k_0, k_1) + F_27(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), k_0*F_15(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_4(x))
Eq(F_16(x, k_0, k_1), F_17(x, k_1, k_0))
Eq(F_17(x, k_0, k_1), (-k_0*F_18(x, k_0, k_1) + F_18(x, 1, k_1))/(1 - k_0))
Eq(F_18(x, k_0, k_1), F_1(x) + F_19(x, k_0, k_1) + F_21(x, k_0, k_1) + F_22(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), k_0*F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_18(x, k_0, k_1)*F_4(x))
Eq(F_21(x, k_0, k_1), F_17(x, k_0, k_1)*F_4(x))
Eq(F_22(x, k_0, k_1), F_21(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), F_19(x, k_1, k_0))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1)*F_4(x))
Eq(F_25(x, k_0, k_1), (k_1*F_13(x, k_0, k_1) - F_13(x, k_0, 1))/(k_1 - 1))
Eq(F_26(x, k_0, k_1), F_24(x, k_1, k_0))
Eq(F_27(x, k_0, k_1), F_14(x, k_1, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_19(x, k_0, 1))
Eq(F_30(x), F_6(x))
Pack JSON:
{"name": "all_the_strategies_2_tracked_fusion_tracked_component_fusion_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.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"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.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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionFactory", "ignore_parent": false, "maxreqlen": 2, "extra_basis": [], "limited_insertion": true, "allow_factorable_insertions": true}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "AllPlacementsFactory", "ignore_parent": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": 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[[1, 0], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 5], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 4], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 5], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 5], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 0], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 1], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 1], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}], "strategy": {"class_module": "tilings.strategies.symmetry", "strategy_class": "TilingComplement", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false}}]}, {"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"}}]}
Specification 3
Strategy pack name: col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24369/
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[31,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[28,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[27,x,k[0],k[1]]
F[13,x,k[0],k[1]] = k[0]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[3,x]
F[15,x,k[0],k[1]] = F[16,x,k[1],k[0]]
F[16,x,k[0],k[1]] = (F[17,x,k[0],k[1]]*k[0]-F[17,x,1,k[1]])/(-1+k[0])
F[17,x,k[0],k[1]] = (F[18,x,k[0],k[1]]*k[0]-F[18,x,1,k[1]])/(-1+k[0])
F[18,x,k[0],k[1]] = 1/(-1+k[1])*(F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],1])
F[19,x,k[0],k[1]] = F[1,x]+F[20,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[20,x,k[0],k[1]] = k[0]*F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[3,x]
F[22,x,k[0],k[1]] = F[18,x,k[1],k[0]]
F[23,x,k[0],k[1]] = F[20,x,k[1],k[0]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]*F[3,x]
F[25,x,k[0],k[1]] = 1/(-1+k[1])*(F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])
F[26,x,k[0],k[1]] = F[24,x,k[1],k[0]]
F[27,x,k[0],k[1]] = F[13,x,k[1],k[0]]
F[28,x,k[0]] = k[0]*F[29,x,k[0]]
F[29,x,k[0]] = F[3,x]*F[30,x,k[0]]
F[30,x,k[0]] = F[17,x,1,k[0]]
F[31,x] = F[5,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{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_{31}\! \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_{28}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = y F_{14}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = -\frac{-F_{17}\! \left(x , y , z\right) y +F_{17}\! \left(x , 1, z\right)}{-1+y}
F_{17}\! \left(x , y , z\right) = -\frac{-y F_{18}\! \left(x , y , z\right)+F_{18}\! \left(x , 1, z\right)}{-1+y}
F_{18}\! \left(x , y , z\right) = -\frac{-F_{19}\! \left(x , y , z\right) z +F_{19}\! \left(x , y , 1\right)}{-1+z}
F_{19}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = y F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = F_{18}\! \left(x , z , y\right)
F_{23}\! \left(x , y , z\right) = F_{20}\! \left(x , z , y\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{25}\! \left(x , y , z\right) = -\frac{-z F_{12}\! \left(x , y , z\right)+F_{12}\! \left(x , y , 1\right)}{-1+z}
F_{26}\! \left(x , y , z\right) = F_{24}\! \left(x , z , y\right)
F_{27}\! \left(x , y , z\right) = F_{13}\! \left(x , z , y\right)
F_{28}\! \left(x , y\right) = y F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{17}\! \left(x , 1, y\right)
F_{31}\! \left(x \right) = F_{5}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_31(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_28(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_24(x, k_0, k_1) + F_26(x, k_0, k_1) + F_27(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), k_0*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_3(x))
Eq(F_15(x, k_0, k_1), F_16(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0, k_1) + F_17(x, 1, k_1))/(1 - k_0))
Eq(F_17(x, k_0, k_1), (-k_0*F_18(x, k_0, k_1) + F_18(x, 1, k_1))/(1 - k_0))
Eq(F_18(x, k_0, k_1), (k_1*F_19(x, k_0, k_1) - F_19(x, k_0, 1))/(k_1 - 1))
Eq(F_19(x, k_0, k_1), F_1(x) + F_20(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), k_0*F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_3(x))
Eq(F_22(x, k_0, k_1), F_18(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), F_20(x, k_1, k_0))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1)*F_3(x))
Eq(F_25(x, k_0, k_1), (k_1*F_12(x, k_0, k_1) - F_12(x, k_0, 1))/(k_1 - 1))
Eq(F_26(x, k_0, k_1), F_24(x, k_1, k_0))
Eq(F_27(x, k_0, k_1), F_13(x, k_1, k_0))
Eq(F_28(x, k_0), k_0*F_29(x, k_0))
Eq(F_29(x, k_0), F_3(x)*F_30(x, k_0))
Eq(F_30(x, k_0), F_17(x, 1, k_0))
Eq(F_31(x), F_5(x))
Pack JSON:
{"name": "col_placements_tracked_fusion_tracked_component_fusion_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.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": 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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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[0, 2, 1], "pos": [[1, 1], [1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 5], [1, 4]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 1], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 4]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 4]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 2], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 4], [1, 4], [1, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 5], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 4], [1, 4], [1, 5], [1, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 4], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 5], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 4], [1, 5], [1, 4], [1, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 4], [1, 0], [1, 4], [1, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 4], [1, 1], [1, 4], [1, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 4], [1, 2], [1, 4], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 0], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 1], [1, 4]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 4], [1, 4], [1, 2], [1, 4]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 4], [1, 4], [1, 4], [1, 4], [1, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 5], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 4], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 5], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 5], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 0], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 1], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 1], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}], "strategy": {"class_module": "tilings.strategies.symmetry", "strategy_class": "TilingComplement", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 4]]}]}]}], "strategy": {"class_module": "tilings.strategies.symmetry", "strategy_class": "TilingComplement", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false}}]}, {"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"}}]}
Specification 4
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24370/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[1,x]+F[35,x]+F[6,x]
F[6,x] = F[4,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[31,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x,k[0]] = F[12,x,k[0]]*F[4,x]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[27,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[14,x,k[0],k[1]] = k[0]*F[15,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[4,x]
F[16,x,k[0],k[1]] = F[17,x,k[1],k[0]]
F[17,x,k[0],k[1]] = F[18,x,k[0],1,k[1]]
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1],k[2]]*k[0]-F[19,x,1,k[1],k[2]])/(-1+k[0])
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1],k[2]]*k[0]-F[20,x,1,k[1],k[2]])/(-1+k[0])
F[20,x,k[0],k[1],k[2]] = (F[21,x,k[0],k[1]]*k[1]-F[21,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[21,x,k[0],k[1]] = F[1,x]+F[22,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[22,x,k[0],k[1]] = k[0]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[4,x]
F[24,x,k[0],k[1]] = F[25,x,k[1],k[0]]
F[25,x,k[0],k[1]] = 1/(-1+k[1])*(F[21,x,k[0],k[1]]*k[1]-F[21,x,k[0],1])
F[26,x,k[0],k[1]] = F[22,x,k[1],k[0]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]*F[4,x]
F[28,x,k[0],k[1]] = 1/(-1+k[1])*(F[13,x,k[0],k[1]]*k[1]-F[13,x,k[0],1])
F[29,x,k[0],k[1]] = F[27,x,k[1],k[0]]
F[30,x,k[0],k[1]] = F[14,x,k[1],k[0]]
F[31,x,k[0]] = k[0]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[34,x,1,k[0]]
F[34,x,k[0],k[1]] = (F[25,x,k[0],k[1]]*k[0]-F[25,x,1,k[1]])/(-1+k[0])
F[35,x] = F[6,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y_{0}\right) = -\frac{-F_{8}\! \left(x , y_{0}\right) y_{0}+F_{8}\! \left(x , 1\right)}{-1+y_{0}}
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , 1, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{15}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{1}, y_{0}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}, 1, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{19}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{20}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{21}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{21}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{1}, y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{21}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{21}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}, y_{0}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{13}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{13}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{1}, y_{0}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}, y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = y_{0} F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y_{0}\right) = F_{34}\! \left(x , 1, y_{0}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{35}\! \left(x \right) = F_{6}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_1(x) + F_35(x) + F_6(x))
Eq(F_6(x), F_4(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_31(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_12(x, k_0)*F_4(x))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_27(x, k_0, k_1) + F_29(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), k_0*F_15(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_4(x))
Eq(F_16(x, k_0, k_1), F_17(x, k_1, k_0))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, 1, k_1))
Eq(F_18(x, k_0, k_1, k_2), (-k_0*F_19(x, k_0, k_1, k_2) + F_19(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, k_1, k_2) + F_20(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_20(x, k_0, k_1, k_2), (-k_1*F_21(x, k_0, k_1) + k_2*F_21(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_21(x, k_0, k_1), F_1(x) + F_22(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), k_0*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_4(x))
Eq(F_24(x, k_0, k_1), F_25(x, k_1, k_0))
Eq(F_25(x, k_0, k_1), (k_1*F_21(x, k_0, k_1) - F_21(x, k_0, 1))/(k_1 - 1))
Eq(F_26(x, k_0, k_1), F_22(x, k_1, k_0))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1)*F_4(x))
Eq(F_28(x, k_0, k_1), (k_1*F_13(x, k_0, k_1) - F_13(x, k_0, 1))/(k_1 - 1))
Eq(F_29(x, k_0, k_1), F_27(x, k_1, k_0))
Eq(F_30(x, k_0, k_1), F_14(x, k_1, k_0))
Eq(F_31(x, k_0), k_0*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_34(x, 1, k_0))
Eq(F_34(x, k_0, k_1), (-k_0*F_25(x, k_0, k_1) + F_25(x, 1, k_1))/(1 - k_0))
Eq(F_35(x), F_6(x))
Pack JSON:
{"name": "point_and_row_and_col_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": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]], "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": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": 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"assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 5], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 4], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 5], [1, 3]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 4], [1, 1], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 0], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 5], [1, 1], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 4], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 5], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 4], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 3], [1, 3], [1, 5], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 4], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 5], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 4], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 3], [1, 5], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 0], [1, 3], [1, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 3], [1, 1], [1, 3], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 0], [1, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 3], [1, 3], [1, 1], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 4], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 5], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[1, 5]]}]}]}], "strategy": {"class_module": "tilings.strategies.symmetry", "strategy_class": "TilingComplement", "ignore_parent": false, "inferrable": false, "possibly_empty": false, "workable": false}}]}, {"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.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SkewComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionStrategy", "row_idx": 0, "col_idx": null, "tracked": true}}]}
Specification 5
Strategy pack name: col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24371/
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[33,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[29,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[27,x,k[0],k[1]]+F[28,x,k[0],k[1]]
F[13,x,k[0],k[1]] = k[0]*F[14,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[3,x]
F[15,x,k[0],k[1]] = (F[16,x,k[0],k[1]]*k[0]-F[16,x,1,k[1]])/(-1+k[0])
F[16,x,k[0],k[1]] = F[17,x,k[0],1,k[1]]
F[17,x,k[0],k[1],k[2]] = (F[18,x,k[0],k[1],k[2]]*k[1]-F[18,x,k[0],1,k[2]])/(-1+k[1])
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[19,x,k[0],k[1]] = F[1,x]+F[20,x,k[0],k[1]]+F[24,x,k[0],k[1]]
F[20,x,k[0],k[1]] = k[0]*F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[3,x]
F[22,x,k[0],k[1]] = F[23,x,k[1],k[0]]
F[23,x,k[0],k[1]] = 1/(-1+k[1])*(F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],1])
F[24,x,k[0],k[1]] = F[20,x,k[1],k[0]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]*F[3,x]
F[26,x,k[0],k[1]] = 1/(-1+k[1])*(F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],1])
F[27,x,k[0],k[1]] = F[25,x,k[1],k[0]]
F[28,x,k[0],k[1]] = F[13,x,k[1],k[0]]
F[29,x,k[0]] = k[0]*F[30,x,k[0]]
F[30,x,k[0]] = F[3,x]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,1,k[0]]
F[32,x,k[0],k[1]] = (F[23,x,k[0],k[1]]*k[0]-F[23,x,1,k[1]])/(-1+k[0])
F[33,x] = F[5,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{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_{33}\! \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_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , 1, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{14}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{16}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{16}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, 1, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{18}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{19}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{21}\! \left(x , y_{0}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{1}, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{19}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}, y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{26}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{12}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{1}, y_{0}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{1}, y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = y_{0} F_{30}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{32}\! \left(x , 1, y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{33}\! \left(x \right) = F_{5}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_33(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_29(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_25(x, k_0, k_1) + F_27(x, k_0, k_1) + F_28(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), k_0*F_14(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_3(x))
Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, k_0, k_1) + F_16(x, 1, k_1))/(1 - k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, 1, k_1))
Eq(F_17(x, k_0, k_1, k_2), (-k_1*F_18(x, k_0, k_1, k_2) + F_18(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_18(x, k_0, k_1, k_2), (-k_1*F_19(x, k_0, k_1) + k_2*F_19(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_19(x, k_0, k_1), F_1(x) + F_20(x, k_0, k_1) + F_24(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), k_0*F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_3(x))
Eq(F_22(x, k_0, k_1), F_23(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), (k_1*F_19(x, k_0, k_1) - F_19(x, k_0, 1))/(k_1 - 1))
Eq(F_24(x, k_0, k_1), F_20(x, k_1, k_0))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1)*F_3(x))
Eq(F_26(x, k_0, k_1), (k_1*F_12(x, k_0, k_1) - F_12(x, k_0, 1))/(k_1 - 1))
Eq(F_27(x, k_0, k_1), F_25(x, k_1, k_0))
Eq(F_28(x, k_0, k_1), F_13(x, k_1, k_0))
Eq(F_29(x, k_0), k_0*F_30(x, k_0))
Eq(F_30(x, k_0), F_3(x)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, 1, k_0))
Eq(F_32(x, k_0, k_1), (-k_0*F_23(x, k_0, k_1) + F_23(x, 1, k_1))/(1 - k_0))
Eq(F_33(x), F_5(x))
Pack JSON:
{"name": "col_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": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[1, 0, 3, 4, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [3, 1, 0, 4, 2], [3, 1, 4, 0, 2], [3, 4, 1, 0, 2]]}], "iterative": false}
Specification JSON:
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1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"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": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 3], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 3], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 3], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 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