02413_03412_04312_12403_13402_14302_23401_24301_34201
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2760, 14154, 73265, 381921, 2002585, 10554288, 55880817, 297110895, 1585816885, 8494597060, 45654006627, 246129472048, 1330786232437, 7214928303663, 39215757976091, 213661316531238, 1166715777412377, 6384401224382053, 35005610565813473, 192294998820039959, 1058193994106052532, 5832933587515695643, 32202807078879303834, 178052760000200084663, 985865930670481721160, 5465997353874845210002, 30344066974601483023923, 168656608090618113821547, 938495849150000714999725, 5228013179669159328641641, 29153706038537690793528167, 162735587195462273033106887, 909249732878899831766988006, 5084838331672154594296219253, 28460793852252526821735482597, 159432327295285575023638394356, 893819602526142035480158791537, 5014792633932524855928010644967, 28156070264674295694265133337647, 158195520328300696996494379525400, 889420739574095648463990148569514, 5003798123535569203755834367668421, 28168318496892184747910724504029915, 158664740882835444542880816611333920, 894228667288337120153012066987341910, 5042619705270658000672831150108362605, 28450807700121587144796073541071451168, 160603674382333234535927399040355563733, 907049535015352069639705690104472241740, 5125234437221610300396780540823804169344, 28973208335818024407122169403445236879226, 163859955615504713503019397353633203665646, 927120231153372024219178978189305920197135, 5247834883853871200686719005600371626618328, 29716614390084382029231172238441515222406953, 168340267253532914084607243883147129565947551, 953983626495241576571188063031357791082883768, 5408203214312157991631666187666250078616335826, 30670399207184473255918038085028727775722149855, 173994526881153082239588247573168328966832645121, 987408962103231943258465750005985861777134331565, 5605310012660103287874108039923472104788997575434, 31830192148439788894402492311951272449872900398323, 180805675789429986731370525158970033241254339332151, 1027340289729104413907656919874982135736879488541514, 5839053844826700068834810183526312791934613172218330, 33196562879927220754328700899225298384742172660419923, 188783032067486652962670463479070160095537110465590543, 1073862899697452711737869930400465242072764637463825036, 6110091772940858707078272270740762621691838420239938767, 34774166377814972387519773856338858311188308776709493952, 197957982025484948120860335789977684220015043637370276577, 1127181639523121842541893543319547154254408943242107754598, 6419730452585066429479058457503673065748607631515053991877, 36571197205782538672816864726404058922565420797720800196773, 208381253568529904168586442683977893751751475461456627414008, 1187607340691751515506062294310617862105539433986798144953453, 6769858873546581136577082205265945664074010566089611466181428, 38599058124834339040786029753009309002212966040899744742848033, 220121295092772555925888252112485010668076738994563716544952780, 1255548960380118401459659783487562247795091387693140413472890103, 7162910711227847636350179364764063855886549610112286567931339490, 40872182485413331055502854364994137240891823138355611624874685655, 233263454985566016397012814817233947526808031279901031322884356306, 1331509901624300753157503703605767700951949238509807156852289517650, 7601848542149561214383786687851913549670773879128801509937185008586, 43407971329480316990517984436443885458745765423351495121117810169692, 247909764598688471503015109344835577109139248627498862385062644507017, 1416087517207641190900540377125105671107323512575663010895793031206291, 8090164904175118238857473706349493784415840506132812536736216590457441, 46226819879675169816341849547171499979101326401349663324890318732731911, 264179196989189311517519280607657997599801672145543515732482613079111949, 1509975153633356547969462813920151937064794886283774012766392579092824252, 8631896960363246751249407349107895135342062273732469020771248218156061863
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24199/
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[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[9,x,k[0]] = F[1,x]+F[23,x,k[0]]+F[8,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0]] = F[10,x,k[0]]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[12,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]
F[17,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[12,x,k[0]]*F[16,x,k[0]]*F[20,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[20,x,k[0]]^2*F[12,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]*F[3,x]
F[24,x,k[0]] = 1/(-1+k[0])*(F[25,x,k[0]]*k[0]-F[25,x,1])
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]^2*F[3,x]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[12,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[35,x,k[0]]+F[37,x,k[0]]
F[32,x,k[0]] = F[10,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[12,x,k[0]]*F[16,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[26,x]*F[3,x]*F[31,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[10,x,k[0]]*F[3,x]*F[31,x,k[0]]
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_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right)^{2} F_{12}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{25}\! \left(x , y\right)+F_{25}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26} \left(x \right)^{2} F_{3}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{3}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{3}\! \left(x \right) F_{31}\! \left(x , y\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_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_23(x, k_0) + F_8(x, k_0))
Eq(F_9(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0), F_10(x, k_0) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_12(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_18(x, k_0))
Eq(F_17(x, k_0), F_10(x, k_0)*F_13(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_12(x, k_0)*F_16(x, k_0)*F_20(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_12(x, k_0)*F_20(x, k_0)**2)
Eq(F_23(x, k_0), F_24(x, k_0)*F_3(x))
Eq(F_24(x, k_0), (k_0*F_25(x, k_0) - F_25(x, 1))/(k_0 - 1))
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)**2*F_3(x))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_12(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_35(x, k_0) + F_37(x, k_0))
Eq(F_32(x, k_0), F_10(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_12(x, k_0)*F_16(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_26(x)*F_3(x)*F_31(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_10(x, k_0)*F_3(x)*F_31(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "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": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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"pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [2, 1], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [2, 1], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[4, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [2, 1], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [2, 1], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24200/
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[6,x,1]
F[6,x,k[0]] = F[17,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[1,x]+F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0]]+F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]*F[14,x,k[0]]*F[7,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]^2*F[10,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[4,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[21,x,k[0]]
F[20,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[10,x,k[0]]*F[23,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = (F[26,x,1,k[0]]-F[26,x,1/k[0],k[0]])/(-1+k[0])
F[26,x,k[0],k[1]] = F[27,x,k[0]*k[1],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[10,x,k[0]]*F[14,x,k[0]]*F[29,x,k[0],k[1]]*F[7,x,k[1]]
F[29,x,k[0],k[1]] = F[27,x,k[0],k[1]]+F[7,x,k[1]]
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_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{8}\! \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 , y\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right)^{2} F_{10}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = \frac{F_{26}\! \left(x , 1, y\right)-F_{26}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y z , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{29}\! \left(x , y , z\right) F_{7}\! \left(x , z\right)
F_{29}\! \left(x , y , z\right) = F_{27}\! \left(x , y , z\right)+F_{7}\! \left(x , z\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_6(x, 1))
Eq(F_6(x, k_0), F_17(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_1(x) + F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0) + F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_10(x, k_0)*F_11(x, k_0)*F_14(x, k_0)*F_7(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_10(x, k_0)*F_14(x, k_0)**2)
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_4(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_21(x, k_0))
Eq(F_20(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_10(x, k_0)*F_23(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), -F_26(x, 1, k_0) + (k_0*F_26(x, 1, k_0) - F_26(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0*k_1, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_10(x, k_0)*F_14(x, k_0)*F_29(x, k_0, k_1)*F_7(x, k_1))
Eq(F_29(x, k_0, k_1), F_27(x, k_0, k_1) + F_7(x, k_1))
Pack JSON:
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Specification JSON:
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