01432_02431_10432_12430_20431_21430_30421_31420
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3030, 16726, 94656, 545968, 3196948, 18951262, 113495516, 685607382, 4172501820, 25557482080, 157433255292, 974650665616, 6060937958328, 37841668662028, 237121573101124, 1490722616840446, 9399868136641246, 59434160368600758, 376741719802602892, 2393644231307445230, 15240824893404305342, 97235132067916445826, 621503700754304502868, 3979385344887015641712, 25520625303284431041704, 163917584102292090313836, 1054334990015114627983860, 6790691803463743366854464, 43792363038502120838289396, 282749033255226467917533980, 1827654858305714437940460188, 11826376369544270528759028156, 76603710075173406234409758836, 496668305194139128997087110856, 3223154923448824770804178664620, 20935099426776645347522300378814, 136091291684356450200682835435842, 885381942097536382316071009786436, 5764486845049653464120350232535864, 37558303648202530283257583907201318, 244879923822208779013887948670086696, 1597679649516054784109943974022236624, 10430466170608774698238399371532525960, 68137174752791931452872239406810694414, 445369488293757975616465020175930466170, 2912747825579584879761333072207723936924, 19059965462533730514904350171631908479436, 124787003040741111188474427119037496211138, 817403188073622167965337698996882486402332, 5356920199319925050006038220636018328848932, 35123555008328558004717210659723501585977924, 230398232649503595007508162411959103944798144, 1511995555381800786204899572361024913558657436, 9926730265102874049188222055833757846900474052, 65198892303067450339449488964260668432056573516, 428397324618218711381743079582792803172559824476, 2815920177940593941448156801155012680395729132884, 18516366346539576448358132049271968841952257810040, 121800211797544382188112061586129142764858396150732, 801479505345115810032990997036956348637822455805600, 5275751814265116350190987159357873210623502041806484, 34739175656505084841726282961543181493667246781512832, 228819864457275004059472169083950264959114669753856556, 1507658666681536353136095744109808055816477052851156492, 9936732892240291885626962231880251947395409805325616328, 65510639319883484141798928586352729274452497302124669220, 432020342138855093960262590134232183030445548564014679676, 2849819382905439462374545400029926415574972809590237914444, 18803904388256920857236078108565928670151894878307696860512, 124106119581326318028739898211098778446612117363165177743260, 819313006704135360206606081536357046313953876398866675395452, 5410222578645297542408954501164691461155047596286805289814296, 35734383595776314037499534498425180262425892426327285361295524, 236080811465204811820019561463496992390226553429771278415133592, 1560040112465745201771174165464508014994598244709474686377999228, 10311196580435970906537439365192554918636818339654736923027911070, 68167634817367993267816970512473584100694360924816375439110650226, 450755422006024242803475204703440326255656895242553637755492607016, 2981227133173692690686702002504924623206234775527792311250208056168, 19721430685585906341792887171368685328816896435777466395716510158948, 130487516023159609175731205869009451861481004335913890994705669911462, 863544499278931185495169898846825542314732198750405405558644705188246, 5715888869743376337712404525251322147120394507213702248798226003745976, 37841145578346487160047526084335540654929249719262198307543164166067646, 250567320291023371596009509182593044859621669652121038448787743192149466, 1659443625254546785391940999443994723007403014860204127122643021609351842, 10992002619956561326002415795723799702163383472113156696458496065647452032, 72822530477912002758979079349053584832187858050655520543575879126503516272, 482533822260226852607170500250541668860466000502398832873418117025540299380, 3197873515164366902852469430529122732588530094058616432590080147016221664604, 21196534284344998154025634983560389855145932032118013717100111550425427455200, 140519649135052268888374350255390663052272116712729818096302752329751381112894, 931700850325237284044412839730978418839721278554439258003101228314244549227782, 6178482459492027393446076435778288375743505247528613810306609710507076157092948
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24568/
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[12,x]*F[4,x]
F[4,x] = F[1,x]+F[38,x]+F[5,x]
F[5,x] = F[12,x]*F[6,x]
F[6,x] = F[1,x]+F[36,x]+F[37,x]+F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[13,x,k[0]]+F[27,x,k[0]]+F[34,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[12,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x] = x
F[13,x,k[0]] = F[12,x]*F[14,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[17,x,k[0]]+F[27,x,k[0]]+F[32,x,k[0]]
F[16,x,k[0]] = F[12,x]*F[9,x,k[0]]
F[17,x,k[0]] = F[12,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[17,x,k[0]]+F[19,x,k[0]]+F[27,x,k[0]]+F[30,x,k[0]]
F[19,x,k[0]] = F[12,x]*F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,1,k[0]]
F[21,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[22,x,k[0],k[1]] = F[1,x]+F[16,x,k[1]]+F[23,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[27,x,k[1]]+F[28,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[12,x]*F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[25,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[15,x,k[0]]*F[26,x,k[0]]
F[28,x,k[0],k[1]] = F[12,x]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],1])/(-1+k[1])
F[30,x,k[0]] = F[12,x]*F[31,x,k[0]]
F[31,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[32,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[33,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[34,x,k[0]] = F[12,x]*F[35,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[36,x] = F[27,x,1]
F[37,x] = F[12,x]*F[8,x]
F[38,x] = F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x \right) = x
F_{13}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , 1, y\right)
F_{21}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) y +F_{22}\! \left(x , 1, z\right)}{-1+y}
F_{22}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)+F_{27}\! \left(x , z\right)+F_{28}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) y +F_{22}\! \left(x , 1, z\right)}{-1+y}
F_{25}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) z +F_{22}\! \left(x , y , 1\right)}{-1+z}
F_{30}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_38(x) + F_5(x))
Eq(F_5(x), F_12(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_36(x) + F_37(x) + F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_13(x, k_0) + F_27(x, k_0) + F_34(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_12(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x), x)
Eq(F_13(x, k_0), F_12(x)*F_14(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_17(x, k_0) + F_27(x, k_0) + F_32(x, k_0))
Eq(F_16(x, k_0), F_12(x)*F_9(x, k_0))
Eq(F_17(x, k_0), F_12(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_16(x, k_0) + F_17(x, k_0) + F_19(x, k_0) + F_27(x, k_0) + F_30(x, k_0))
Eq(F_19(x, k_0), F_12(x)*F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, 1, k_0))
Eq(F_21(x, k_0, k_1), (-k_0*F_22(x, k_0, k_1) + F_22(x, 1, k_1))/(1 - k_0))
Eq(F_22(x, k_0, k_1), F_1(x) + F_16(x, k_1) + F_23(x, k_0, k_1) + F_25(x, k_0, k_1) + F_27(x, k_1) + F_28(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_12(x)*F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), (k_0*F_22(x, k_0, k_1) - F_22(x, 1, k_1))/(k_0 - 1))
Eq(F_25(x, k_0, k_1), F_22(x, k_0, k_1)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_15(x, k_0)*F_26(x, k_0))
Eq(F_28(x, k_0, k_1), F_12(x)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_1*F_22(x, k_0, k_1) + F_22(x, k_0, 1))/(1 - k_1))
Eq(F_30(x, k_0), F_12(x)*F_31(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_32(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_33(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_12(x)*F_35(x, k_0))
Eq(F_35(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_36(x), F_27(x, 1))
Eq(F_37(x), F_12(x)*F_8(x))
Eq(F_38(x), F_12(x)*F_6(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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{"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24832/
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[12,x]*F[4,x]
F[4,x] = F[1,x]+F[38,x]+F[5,x]
F[5,x] = F[12,x]*F[6,x]
F[6,x] = F[1,x]+F[36,x]+F[37,x]+F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[13,x,k[0]]+F[27,x,k[0]]+F[34,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[12,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x] = x
F[13,x,k[0]] = F[12,x]*F[14,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[17,x,k[0]]+F[27,x,k[0]]+F[32,x,k[0]]
F[16,x,k[0]] = F[12,x]*F[9,x,k[0]]
F[17,x,k[0]] = F[12,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[17,x,k[0]]+F[19,x,k[0]]+F[27,x,k[0]]+F[30,x,k[0]]
F[19,x,k[0]] = F[12,x]*F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,1,k[0]]
F[21,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[22,x,k[0],k[1]] = F[1,x]+F[16,x,k[1]]+F[23,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[27,x,k[1]]+F[28,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[12,x]*F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[25,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[15,x,k[0]]*F[26,x,k[0]]
F[28,x,k[0],k[1]] = F[12,x]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],1])/(-1+k[1])
F[30,x,k[0]] = F[12,x]*F[31,x,k[0]]
F[31,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[32,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[33,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[34,x,k[0]] = F[12,x]*F[35,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[36,x] = F[27,x,1]
F[37,x] = F[12,x]*F[8,x]
F[38,x] = F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x \right) = x
F_{13}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , 1, y\right)
F_{21}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) y +F_{22}\! \left(x , 1, z\right)}{-1+y}
F_{22}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)+F_{27}\! \left(x , z\right)+F_{28}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) y +F_{22}\! \left(x , 1, z\right)}{-1+y}
F_{25}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) z +F_{22}\! \left(x , y , 1\right)}{-1+z}
F_{30}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_38(x) + F_5(x))
Eq(F_5(x), F_12(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_36(x) + F_37(x) + F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_13(x, k_0) + F_27(x, k_0) + F_34(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_12(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x), x)
Eq(F_13(x, k_0), F_12(x)*F_14(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_17(x, k_0) + F_27(x, k_0) + F_32(x, k_0))
Eq(F_16(x, k_0), F_12(x)*F_9(x, k_0))
Eq(F_17(x, k_0), F_12(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_16(x, k_0) + F_17(x, k_0) + F_19(x, k_0) + F_27(x, k_0) + F_30(x, k_0))
Eq(F_19(x, k_0), F_12(x)*F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, 1, k_0))
Eq(F_21(x, k_0, k_1), (-k_0*F_22(x, k_0, k_1) + F_22(x, 1, k_1))/(1 - k_0))
Eq(F_22(x, k_0, k_1), F_1(x) + F_16(x, k_1) + F_23(x, k_0, k_1) + F_25(x, k_0, k_1) + F_27(x, k_1) + F_28(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_12(x)*F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), (k_0*F_22(x, k_0, k_1) - F_22(x, 1, k_1))/(k_0 - 1))
Eq(F_25(x, k_0, k_1), F_22(x, k_0, k_1)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_15(x, k_0)*F_26(x, k_0))
Eq(F_28(x, k_0, k_1), F_12(x)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_1*F_22(x, k_0, k_1) + F_22(x, k_0, 1))/(1 - k_1))
Eq(F_30(x, k_0), F_12(x)*F_31(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_32(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_33(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_12(x)*F_35(x, k_0))
Eq(F_35(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_36(x), F_27(x, 1))
Eq(F_37(x), F_12(x)*F_8(x))
Eq(F_38(x), F_12(x)*F_6(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]]}], "iterative": false}
Specification JSON:
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{"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 3
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25397/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[37,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[35,x]+F[36,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[26,x,k[0]]+F[33,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[16,x,k[0]]+F[26,x,k[0]]+F[31,x,k[0]]
F[15,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[16,x,k[0]] = F[11,x]*F[17,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[16,x,k[0]]+F[18,x,k[0]]+F[26,x,k[0]]+F[29,x,k[0]]
F[18,x,k[0]] = F[11,x]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,1,k[0]]
F[20,x,k[0],k[1]] = 1/(-1+k[0])*(F[21,x,k[0],k[1]]*k[0]-F[21,x,1,k[1]])
F[21,x,k[0],k[1]] = F[1,x]+F[15,x,k[1]]+F[22,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[26,x,k[1]]+F[27,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[11,x]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = 1/(-1+k[0])*(F[21,x,k[0],k[1]]*k[0]-F[21,x,1,k[1]])
F[24,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[25,x,k[0]]
F[25,x,k[0]] = k[0]*x
F[26,x,k[0]] = F[14,x,k[0]]*F[25,x,k[0]]
F[27,x,k[0],k[1]] = F[11,x]*F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = (F[21,x,k[0],k[1]]*k[1]-F[21,x,k[0],1])/(-1+k[1])
F[29,x,k[0]] = F[11,x]*F[30,x,k[0]]
F[30,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[31,x,k[0]] = F[11,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[33,x,k[0]] = F[11,x]*F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[35,x] = F[26,x,1]
F[36,x] = F[11,x]*F[7,x]
F[37,x] = F[11,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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_{12}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , 1, y\right)
F_{20}\! \left(x , y , z\right) = -\frac{-F_{21}\! \left(x , y , z\right) y +F_{21}\! \left(x , 1, z\right)}{-1+y}
F_{21}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , z\right)+F_{22}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , z\right)+F_{27}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = -\frac{-F_{21}\! \left(x , y , z\right) y +F_{21}\! \left(x , 1, z\right)}{-1+y}
F_{24}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = y x
F_{26}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{27}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = -\frac{-F_{21}\! \left(x , y , z\right) z +F_{21}\! \left(x , y , 1\right)}{-1+z}
F_{29}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_37(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_35(x) + F_36(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_26(x, k_0) + F_33(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(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), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_16(x, k_0) + F_26(x, k_0) + F_31(x, k_0))
Eq(F_15(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_16(x, k_0), F_11(x)*F_17(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_15(x, k_0) + F_16(x, k_0) + F_18(x, k_0) + F_26(x, k_0) + F_29(x, k_0))
Eq(F_18(x, k_0), F_11(x)*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, 1, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, k_1) + F_21(x, 1, k_1))/(1 - k_0))
Eq(F_21(x, k_0, k_1), F_1(x) + F_15(x, k_1) + F_22(x, k_0, k_1) + F_24(x, k_0, k_1) + F_26(x, k_1) + F_27(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_11(x)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (k_0*F_21(x, k_0, k_1) - F_21(x, 1, k_1))/(k_0 - 1))
Eq(F_24(x, k_0, k_1), F_21(x, k_0, k_1)*F_25(x, k_0))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0), F_14(x, k_0)*F_25(x, k_0))
Eq(F_27(x, k_0, k_1), F_11(x)*F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), (-k_1*F_21(x, k_0, k_1) + F_21(x, k_0, 1))/(1 - k_1))
Eq(F_29(x, k_0), F_11(x)*F_30(x, k_0))
Eq(F_30(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_31(x, k_0), F_11(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_33(x, k_0), F_11(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_35(x), F_26(x, 1))
Eq(F_36(x), F_11(x)*F_7(x))
Eq(F_37(x), F_11(x)*F_5(x))
Pack JSON:
{"name": "row_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "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": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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"pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}, {"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], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], 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"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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25602/
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[12,x]*F[4,x]
F[4,x] = F[1,x]+F[38,x]+F[5,x]
F[5,x] = F[12,x]*F[6,x]
F[6,x] = F[1,x]+F[36,x]+F[37,x]+F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[13,x,k[0]]+F[27,x,k[0]]+F[34,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[12,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x] = x
F[13,x,k[0]] = F[12,x]*F[14,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[17,x,k[0]]+F[27,x,k[0]]+F[32,x,k[0]]
F[16,x,k[0]] = F[12,x]*F[9,x,k[0]]
F[17,x,k[0]] = F[12,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[17,x,k[0]]+F[19,x,k[0]]+F[27,x,k[0]]+F[30,x,k[0]]
F[19,x,k[0]] = F[12,x]*F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,1,k[0]]
F[21,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[22,x,k[0],k[1]] = F[1,x]+F[16,x,k[1]]+F[23,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[27,x,k[1]]+F[28,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[12,x]*F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = 1/(-1+k[0])*(F[22,x,k[0],k[1]]*k[0]-F[22,x,1,k[1]])
F[25,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[15,x,k[0]]*F[26,x,k[0]]
F[28,x,k[0],k[1]] = F[12,x]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],1])/(-1+k[1])
F[30,x,k[0]] = F[12,x]*F[31,x,k[0]]
F[31,x,k[0]] = (F[18,x,k[0]]*k[0]-F[18,x,1])/(-1+k[0])
F[32,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[33,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[34,x,k[0]] = F[12,x]*F[35,x,k[0]]
F[35,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[36,x] = F[27,x,1]
F[37,x] = F[12,x]*F[8,x]
F[38,x] = F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x \right) = x
F_{13}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , 1, y\right)
F_{21}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) y +F_{22}\! \left(x , 1, z\right)}{-1+y}
F_{22}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)+F_{27}\! \left(x , z\right)+F_{28}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) y +F_{22}\! \left(x , 1, z\right)}{-1+y}
F_{25}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = -\frac{-F_{22}\! \left(x , y , z\right) z +F_{22}\! \left(x , y , 1\right)}{-1+z}
F_{30}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{36}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_38(x) + F_5(x))
Eq(F_5(x), F_12(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_36(x) + F_37(x) + F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_13(x, k_0) + F_27(x, k_0) + F_34(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_12(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x), x)
Eq(F_13(x, k_0), F_12(x)*F_14(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_17(x, k_0) + F_27(x, k_0) + F_32(x, k_0))
Eq(F_16(x, k_0), F_12(x)*F_9(x, k_0))
Eq(F_17(x, k_0), F_12(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_16(x, k_0) + F_17(x, k_0) + F_19(x, k_0) + F_27(x, k_0) + F_30(x, k_0))
Eq(F_19(x, k_0), F_12(x)*F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, 1, k_0))
Eq(F_21(x, k_0, k_1), (-k_0*F_22(x, k_0, k_1) + F_22(x, 1, k_1))/(1 - k_0))
Eq(F_22(x, k_0, k_1), F_1(x) + F_16(x, k_1) + F_23(x, k_0, k_1) + F_25(x, k_0, k_1) + F_27(x, k_1) + F_28(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_12(x)*F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), (k_0*F_22(x, k_0, k_1) - F_22(x, 1, k_1))/(k_0 - 1))
Eq(F_25(x, k_0, k_1), F_22(x, k_0, k_1)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_15(x, k_0)*F_26(x, k_0))
Eq(F_28(x, k_0, k_1), F_12(x)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_1*F_22(x, k_0, k_1) + F_22(x, k_0, 1))/(1 - k_1))
Eq(F_30(x, k_0), F_12(x)*F_31(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_32(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_33(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_12(x)*F_35(x, k_0))
Eq(F_35(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_36(x), F_27(x, 1))
Eq(F_37(x), F_12(x)*F_8(x))
Eq(F_38(x), F_12(x)*F_6(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 4, 3, 2], [0, 2, 4, 3, 1], [1, 0, 4, 3, 2], [1, 2, 4, 3, 0], [2, 0, 4, 3, 1], [2, 1, 4, 3, 0], [3, 0, 4, 2, 1], [3, 1, 4, 2, 0]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, 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[0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 3, "tracked": true}}, {"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, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": 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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 0], "pos": [[5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 5
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25633/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[37,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[35,x]+F[36,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[26,x,k[0]]+F[33,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[16,x,k[0]]+F[26,x,k[0]]+F[31,x,k[0]]
F[15,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[16,x,k[0]] = F[11,x]*F[17,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[16,x,k[0]]+F[18,x,k[0]]+F[26,x,k[0]]+F[29,x,k[0]]
F[18,x,k[0]] = F[11,x]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,1,k[0]]
F[20,x,k[0],k[1]] = 1/(-1+k[0])*(F[21,x,k[0],k[1]]*k[0]-F[21,x,1,k[1]])
F[21,x,k[0],k[1]] = F[1,x]+F[15,x,k[1]]+F[22,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[26,x,k[1]]+F[27,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[11,x]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = 1/(-1+k[0])*(F[21,x,k[0],k[1]]*k[0]-F[21,x,1,k[1]])
F[24,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[25,x,k[0]]
F[25,x,k[0]] = k[0]*x
F[26,x,k[0]] = F[14,x,k[0]]*F[25,x,k[0]]
F[27,x,k[0],k[1]] = F[11,x]*F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = (F[21,x,k[0],k[1]]*k[1]-F[21,x,k[0],1])/(-1+k[1])
F[29,x,k[0]] = F[11,x]*F[30,x,k[0]]
F[30,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[31,x,k[0]] = F[11,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[33,x,k[0]] = F[11,x]*F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[35,x] = F[26,x,1]
F[36,x] = F[11,x]*F[7,x]
F[37,x] = F[11,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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_{12}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , 1, y\right)
F_{20}\! \left(x , y , z\right) = -\frac{-F_{21}\! \left(x , y , z\right) y +F_{21}\! \left(x , 1, z\right)}{-1+y}
F_{21}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , z\right)+F_{22}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , z\right)+F_{27}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = -\frac{-F_{21}\! \left(x , y , z\right) y +F_{21}\! \left(x , 1, z\right)}{-1+y}
F_{24}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = y x
F_{26}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{27}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = -\frac{-F_{21}\! \left(x , y , z\right) z +F_{21}\! \left(x , y , 1\right)}{-1+z}
F_{29}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{35}\! \left(x \right) = F_{26}\! \left(x , 1\right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_37(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_35(x) + F_36(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_26(x, k_0) + F_33(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(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), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_16(x, k_0) + F_26(x, k_0) + F_31(x, k_0))
Eq(F_15(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_16(x, k_0), F_11(x)*F_17(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_15(x, k_0) + F_16(x, k_0) + F_18(x, k_0) + F_26(x, k_0) + F_29(x, k_0))
Eq(F_18(x, k_0), F_11(x)*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, 1, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, k_1) + F_21(x, 1, k_1))/(1 - k_0))
Eq(F_21(x, k_0, k_1), F_1(x) + F_15(x, k_1) + F_22(x, k_0, k_1) + F_24(x, k_0, k_1) + F_26(x, k_1) + F_27(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_11(x)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (k_0*F_21(x, k_0, k_1) - F_21(x, 1, k_1))/(k_0 - 1))
Eq(F_24(x, k_0, k_1), F_21(x, k_0, k_1)*F_25(x, k_0))
Eq(F_25(x, k_0), k_0*x)
Eq(F_26(x, k_0), F_14(x, k_0)*F_25(x, k_0))
Eq(F_27(x, k_0, k_1), F_11(x)*F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), (-k_1*F_21(x, k_0, k_1) + F_21(x, k_0, 1))/(1 - k_1))
Eq(F_29(x, k_0), F_11(x)*F_30(x, k_0))
Eq(F_30(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_31(x, k_0), F_11(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_33(x, k_0), F_11(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_35(x), F_26(x, 1))
Eq(F_36(x), F_11(x)*F_7(x))
Eq(F_37(x), F_11(x)*F_5(x))
Pack JSON:
{"name": "row_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "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": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 4, 2, 0], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": 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