0213_0321
Counting sequence:
1, 1, 2, 6, 22, 89, 380, 1677, 7566, 34676, 160808, 752608, 3548325, 16830544, 80234659, 384132724, 1845829988, 8897740300, 43010084460, 208409687323, 1012046126532, 4923952560917, 23997719075657, 117136530812812, 572552052378494, 2802078324448067, 13728966634684162, 67335389570300111, 330565613964005903, 1624224225165859149, 7986883361152504802, 39302853215554607117, 193535830662478346745, 953601497588456214420, 4701328219360979739133, 23190179296696194955854, 114446101859655286916888, 565062186907383324508694, 2791104792185547522903188, 13792030067033272760819915, 68177483653587349492859540, 337135104199734211125315537, 1667660297984940709970045828, 8251690882542041968265084582, 40841519795491518297159554082, 202198015009746305563837213072, 1001292505095055815391088142534, 4959611759370162017493407616315, 24571465499750977892098278287252, 121760256791195780389776816180479, 603484353821297595755057424910976, 2991628372740553886256592914092194, 14832896788310096875613626754682191, 73555786583290293857591589513002743, 364818088270984647916655453092258384, 1809676300281327814592566306364386412, 8978154034793188888130664799377152836, 44548351792072845116266428632284600790, 221070951924402717029745747602904577719, 1097196405770107904321652270049769643417, 5446118644078362705861296945711126088484, 27035685045881615283978539467130015843991, 134224840027933486255130129107355285192135, 666455969852222077705846642628381643999928, 3309413410578374636444063059295496636516241, 16434997189149054527160058945296266561234444, 81625427165132288728356581622763281240851035, 405430851095514824297315219382638012250845336, 2013918909807323722637613520198668854696516324, 10004594343754324649632566107112925536730928455, 49703600075576812397689649804503093957708990939, 246948097658333122969633112960369999540549898588, 1227020142352520380485952989823524990216293344290, 6097118386386092522877516603634318715317507189567, 30298652675770795585099197239179018181301128766663, 150572840732707077480917324771129483558028338586976, 748330680907167418228392107610582043855904051001268, 3719315617326260701920203654567571050098826487164408, 18486476217522649579299738269845460969178015765714425, 91889513406326716855726086313929562875032996242415434, 456770046546010035232319526034679344040670857560672130, 2270640132936757656308014062197579680219810686116789953, 11288006454705742861182101935691668668317300673628660055, 56118194570178774695901209871837268301797467630080621729, 279001748224903771301193080263182139271923442835999562592, 1387159100053694653247379664523542241388998602154444754075, 6897013849164770293524825790530142445631078899166430502636, 34293418388758084249791904614367792065455813750828878367417, 170519766173009039539797046703712683937847390827257065015442, 847915138764896645664051811254427038727476068078312765255354, 4216413795845869521403291416220305818270573812118559821825336, 20967503618303827195511719392061205623048274828824424553070279, 104270727581763453285113960688081134535573011427627862718091801, 518548987880517544423608258126605092268675303695575900819894079, 2578864009171761606483657316422138965931888205050394159309363297, 12825606985494904442396536654765418129386147204190890658704725647, 63787832048492581494915283323972835785635909864888290488162718904, 317254501647846327816031309119088734802092116565980103935593750320, 1577928813678084434160196925432943501464553051166718979143470918586, 7848313162722931808503555537543516403228341177517922087730580785500, 39036799260345856095495385564822461394634351744055849171212114769082
Specification 1
Strategy pack name: all_the_strategies_1_tracked_fusion
Tree: http://permpal.com/tree/99/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x]+F[9,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[5,x]^2*F[8,x]
F[8,x] = x
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[8,x]
F[12,x] = F[13,x]+F[14,x]+F[40,x]
F[13,x] = 0
F[14,x] = F[15,x,1]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x]+F[18,x,k[0]]+F[37,x,k[0]]+F[39,x,k[0]]
F[17,x] = F[3,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[8,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,1,k[0]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[29,x,k[0]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0]]+F[31,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[25,x,k[0]] = F[26,x,k[0]]+F[30,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[5,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[26,x,k[0]]*F[29,x,k[0]]*F[5,x]
F[29,x,k[0]] = k[0]*x
F[30,x,k[0]] = F[16,x,k[0]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]*F[8,x]
F[33,x,k[0],k[1]] = 1/(-1+k[0])*(F[23,x,k[0],k[1]]*k[0]-F[23,x,1,k[1]])
F[34,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[29,x,k[1]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[5,x]*F[8,x]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[39,x,k[0]] = F[16,x,k[0]]*F[29,x,k[0]]
F[40,x] = F[41,x]
F[41,x] = F[21,x,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{17}\! \left(x \right) = F_{3}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{19}\! \left(x , y\right) = \frac{F_{20}\! \left(x , y\right) y -F_{20}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , 1, y\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{29}\! \left(x , y\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{29}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{29}\! \left(x , y\right) = y x
F_{30}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{31}\! \left(x , y , z\right) = F_{32}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{33}\! \left(x , y , z\right) F_{8}\! \left(x \right)
F_{33}\! \left(x , y , z\right) = \frac{F_{23}\! \left(x , y , z\right) y -F_{23}\! \left(x , 1, z\right)}{-1+y}
F_{34}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right) F_{29}\! \left(x , z\right)
F_{35}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y\right) = \frac{F_{16}\! \left(x , y\right) y -F_{16}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{21}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x) + F_9(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)**2*F_8(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_8(x))
Eq(F_12(x), F_13(x) + F_14(x) + F_40(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x) + F_18(x, k_0) + F_37(x, k_0) + F_39(x, k_0))
Eq(F_17(x), F_3(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_8(x))
Eq(F_19(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, 1, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_29(x, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0) + F_31(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_25(x, k_0), F_26(x, k_0) + F_30(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_5(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_26(x, k_0)*F_29(x, k_0)*F_5(x))
Eq(F_29(x, k_0), k_0*x)
Eq(F_30(x, k_0), F_16(x, k_0))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1)*F_8(x))
Eq(F_33(x, k_0, k_1), (k_0*F_23(x, k_0, k_1) - F_23(x, 1, k_1))/(k_0 - 1))
Eq(F_34(x, k_0, k_1), F_24(x, k_0, k_1)*F_29(x, k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_23(x, k_0, k_1)*F_5(x)*F_8(x))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_16(x, k_0)*F_29(x, k_0))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_21(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 1, "strategy_class": "RequirementInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "ignore_parent": false, "strategy_class": "AllPlacementsFactory"}]], "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": "all_the_strategies_1_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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": false, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": 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[]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 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"ignore_parent": false, "include_empty": true, "indices": [0], "own_col": false, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": false, "strategy_class": "RequirementPlacementStrategy"}}, "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": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}]}], "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], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}]}], "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], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 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}}]}, {"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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"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": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "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": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/100/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[13,x]*F[6,x]
F[6,x] = F[36,x]+F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[17,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x]+F[15,x,k[0]]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]^2*F[13,x]
F[13,x] = F[14,x,1]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[10,x]*F[14,x,k[0]]*F[9,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[13,x]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[33,x,k[0]]+F[35,x,k[0]]+F[4,x]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[13,x]*F[22,x,k[0]]
F[22,x,k[0]] = 1/(-1+k[0])*(F[23,x,k[0]]*k[0]-F[23,x,1])
F[23,x,k[0]] = F[24,x,1,k[0]]
F[25,x,k[0],k[1],k[2]] = F[24,x,k[0]*k[1],k[1]*k[2]]
F[25,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[2]]+F[31,x,k[0],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]+F[30,x,k[0],k[1],k[2]]+F[8,x,k[0]*k[1]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[13,x]*F[29,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = 1/(k[0]*k[1]-1)*(F[25,x,k[0],k[1],k[2]]*k[0]*k[1]-F[25,x,1/k[1],k[1],k[2]])
F[30,x,k[0],k[1],k[2]] = F[14,x,k[2]]*F[26,x,k[0],k[1],k[2]]
F[31,x,k[0],k[1],k[2]] = F[32,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[10,x]*F[13,x]*F[25,x,k[0],k[1],k[2]]
F[33,x,k[0]] = F[13,x]*F[34,x,k[0]]
F[34,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[35,x,k[0]] = F[14,x,k[0]]*F[19,x,k[0]]
F[36,x] = F[37,x]
F[37,x] = F[38,x,1]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[13,x]*F[23,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_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{36}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{14}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{13}\! \left(x \right) F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{13}\! \left(x \right) F_{22}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{23}\! \left(x , y_{0}\right)+F_{23}\! \left(x , 1\right)}{-1+y_{0}}
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , 1, y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{8}\! \left(x , y_{0} y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x \right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{25}\! \left(x , \frac{1}{y_{1}}, y_{1}, y_{2}\right)}{y_{0} y_{1}-1}
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{2}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}\right) = F_{13}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{19}\! \left(x , y_{0}\right)+F_{19}\! \left(x , 1\right)}{-1+y_{0}}
F_{35}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x , 1\right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}\right) = F_{13}\! \left(x \right) F_{23}\! \left(x , y_{0}\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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_13(x)*F_6(x))
Eq(F_6(x), F_36(x) + F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_17(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x) + F_15(x, k_0))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)**2*F_13(x))
Eq(F_13(x), F_14(x, 1))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_10(x)*F_14(x, k_0)*F_9(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_13(x)*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_33(x, k_0) + F_35(x, k_0) + F_4(x))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_13(x)*F_22(x, k_0))
Eq(F_22(x, k_0), (k_0*F_23(x, k_0) - F_23(x, 1))/(k_0 - 1))
Eq(F_23(x, k_0), F_24(x, 1, k_0))
Eq(F_25(x, k_0, k_1, k_2), F_24(x, k_0*k_1, k_1*k_2))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, k_2) + F_8(x, k_0*k_1))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_13(x)*F_29(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), (k_0*k_1*F_25(x, k_0, k_1, k_2) - F_25(x, 1/k_1, k_1, k_2))/(k_0*k_1 - 1))
Eq(F_30(x, k_0, k_1, k_2), F_14(x, k_2)*F_26(x, k_0, k_1, k_2))
Eq(F_31(x, k_0, k_1, k_2), F_32(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_10(x)*F_13(x)*F_25(x, k_0, k_1, k_2))
Eq(F_33(x, k_0), F_13(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_35(x, k_0), F_14(x, k_0)*F_19(x, k_0))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x, 1))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_13(x)*F_23(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": 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": "point_and_row_and_col_placements_tracked_fusion_expand_verified", "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}}}, "rule_class": "ReverseRule"}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"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]]}]]}], "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": "Rule", "strategy": {"assumptions": [{"assumption": 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3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 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}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}]}], "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], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 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}}]}, {"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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"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": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "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": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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": [{"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"}}, {"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"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/101/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[46,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[46,x]*F[7,x]
F[7,x] = F[47,x]+F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[15,x,k[0]]
F[10,x,k[0]] = F[0,x]*F[11,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[11,x,k[0]]*F[17,x,k[0]]*F[46,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[19,x,k[0]]
F[18,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[46,x]
F[21,x,k[0]] = 1/(-1+k[0])*(F[22,x,k[0]]*k[0]-F[22,x,1])
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[24,x,1,k[0],k[1]]
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]+F[29,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[26,x,1,k[0],k[1],k[2]]
F[26,x,k[0],k[1],k[2],k[3]] = F[27,x,k[0],k[1],k[2],k[3]]
F[28,x,k[0],k[1],k[2],k[3]] = F[27,x,k[0],k[1],k[2]*k[3],k[3]]
F[28,x,k[0],k[1],k[2],k[3]] = F[11,x,k[1]]*F[11,x,k[3]]*F[9,x,k[3]]
F[29,x,k[0],k[1],k[2]] = F[30,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1],k[2]] = F[11,x,k[0]]*F[31,x,k[0],k[1],k[2]]*F[46,x]
F[31,x,k[0],k[1],k[2]] = F[32,x,k[0]*k[1],k[2]]+F[36,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1]] = F[32,x,k[0],k[0]*k[1]]
F[33,x,k[0],k[1]] = F[11,x,k[1]]*F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,1,k[0],k[1]]*k[0]-F[35,x,1/k[0],k[0],k[1]])
F[35,x,k[0],k[1],k[2]] = F[23,x,k[0]*k[1],k[1]*k[2]]
F[36,x,k[0],k[1],k[2]] = k[0]*(F[37,x,1,k[0],k[1],k[2]]-F[37,x,1/k[0],k[0],k[1],k[2]])/(-1+k[0])
F[37,x,k[0],k[1],k[2],k[3]] = F[38,x,k[0]*k[1],k[1]*k[2],k[3]]
F[38,x,k[0],k[1],k[2]] = F[39,x,k[0],k[1],k[2]]
F[40,x,k[0],k[1],k[2]] = F[39,x,k[0],k[1]*k[2],k[2]]
F[41,x,k[0],k[1],k[2]] = F[40,x,k[0],k[0]*k[1],k[2]]
F[41,x,k[0],k[1],k[2]] = F[14,x,k[0]]*F[42,x,k[0],k[1],k[2]]*F[43,x]
F[42,x,k[0],k[1],k[2]] = F[24,x,k[0],k[1]*k[2],k[2]]
F[43,x] = F[1,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[43,x]^2*F[46,x]
F[46,x] = x
F[47,x] = F[48,x]
F[48,x] = F[46,x]*F[49,x]
F[49,x] = F[22,x,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_{46}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{47}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{0}\! \left(x \right) F_{11}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}\right) F_{46}\! \left(x \right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{9}\! \left(x , y_{0}\right)+F_{9}\! \left(x , 1\right)}{-1+y_{0}}
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{46}\! \left(x \right)
F_{21}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{22}\! \left(x , y_{0}\right)+F_{22}\! \left(x , 1\right)}{-1+y_{0}}
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , 1, y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , 1, y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2} y_{3}, y_{3}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{11}\! \left(x , y_{1}\right) F_{11}\! \left(x , y_{3}\right) F_{9}\! \left(x , y_{3}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{46}\! \left(x \right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{32}\! \left(x , y_{0} y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{35}\! \left(x , 1, y_{0}, y_{1}\right)-F_{35}\! \left(x , \frac{1}{y_{0}}, y_{0}, y_{1}\right)}{-1+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} \left(F_{37}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)-F_{37}\! \left(x , \frac{1}{y_{0}}, y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{38}\! \left(x , y_{0} y_{1}, y_{1} y_{2}, y_{3}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{43}\! \left(x \right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{43} \left(x \right)^{2} F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = x
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_46(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_46(x)*F_7(x))
Eq(F_7(x), F_47(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_15(x, k_0))
Eq(F_10(x, k_0), F_0(x)*F_11(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_11(x, k_0)*F_17(x, k_0)*F_46(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_19(x, k_0))
Eq(F_18(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_46(x))
Eq(F_21(x, k_0), (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, 1, k_0, k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2) + F_29(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, 1, k_0, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2, k_3), F_27(x, k_0, k_1, k_2, k_3))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_27(x, k_0, k_1, k_2*k_3, k_3))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_11(x, k_1)*F_11(x, k_3)*F_9(x, k_3))
Eq(F_29(x, k_0, k_1, k_2), F_30(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1, k_2), F_11(x, k_0)*F_31(x, k_0, k_1, k_2)*F_46(x))
Eq(F_31(x, k_0, k_1, k_2), F_32(x, k_0*k_1, k_2) + F_36(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1), F_32(x, k_0, k_0*k_1))
Eq(F_33(x, k_0, k_1), F_11(x, k_1)*F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), (k_0*F_35(x, 1, k_0, k_1) - F_35(x, 1/k_0, k_0, k_1))/(k_0 - 1))
Eq(F_35(x, k_0, k_1, k_2), F_23(x, k_0*k_1, k_1*k_2))
Eq(F_36(x, k_0, k_1, k_2), -F_37(x, 1/k_0, k_0, k_1, k_2) + (k_0*F_37(x, 1, k_0, k_1, k_2) - F_37(x, 1/k_0, k_0, k_1, k_2))/(k_0 - 1))
Eq(F_37(x, k_0, k_1, k_2, k_3), F_38(x, k_0*k_1, k_1*k_2, k_3))
Eq(F_38(x, k_0, k_1, k_2), F_39(x, k_0, k_1, k_2))
Eq(F_40(x, k_0, k_1, k_2), F_39(x, k_0, k_1*k_2, k_2))
Eq(F_41(x, k_0, k_1, k_2), F_40(x, k_0, k_0*k_1, k_2))
Eq(F_41(x, k_0, k_1, k_2), F_14(x, k_0)*F_42(x, k_0, k_1, k_2)*F_43(x))
Eq(F_42(x, k_0, k_1, k_2), F_24(x, k_0, k_1*k_2, k_2))
Eq(F_43(x), F_1(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_43(x)**2*F_46(x))
Eq(F_46(x), x)
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_46(x)*F_49(x))
Eq(F_49(x), F_22(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion_expand_verified", "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 2]]}]}}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [5, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[5, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [5, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [1, 0], "pos": [[5, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}]}}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[5, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0], 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{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0], "pos": [[5, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 4]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [5, 2]]}, {"patt": [1, 0], "pos": [[4, 3], [4, 3]]}, {"patt": [1, 0], "pos": [[5, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 2]]}]}], "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], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "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}}]}, {"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": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"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": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "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": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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, 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"}}, {"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"}}]}
Specification 4
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/102/
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[0,x]+F[7,x,k[0]]
F[7,x,k[0]] = F[11,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+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[14,x,1,k[0]]
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]+F[6,x,k[1]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]
F[17,x,k[0],k[1]] = F[12,x,k[0]]*F[18,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[0]]+F[29,x,k[0],k[1]]
F[20,x,k[0]] = F[19,x,k[0]]+F[22,x,k[0]]
F[21,x,k[0]] = F[12,x,k[0]]*F[20,x,k[0]]
F[21,x,k[0]] = F[7,x,k[0]]
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[24,x,k[0]*k[1],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]+F[27,x,k[0],k[1]]+F[28,x,k[1],k[0]]+F[8,x]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]*F[4,x]
F[26,x,k[0],k[1]] = 1/(-1+k[0])*(F[24,x,k[0],k[1]]*k[0]-F[24,x,1,k[1]])
F[27,x,k[0],k[1]] = F[12,x,k[0]]*F[24,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[12,x,k[0]]*F[18,x,k[1],k[0]]
F[29,x,k[0],k[1]] = F[30,x,k[1],k[0]]
F[30,x,k[0],k[1]] = F[12,x,k[0]]*F[31,x,k[1],k[0]]
F[32,x,k[0],k[1]] = F[12,x,k[0]]*F[31,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[33,x,k[0],k[0]*k[1]]
F[35,x,k[0],k[1]] = F[34,x,k[0],k[1]]+F[91,x,k[0]*k[1]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]+F[80,x,k[0]*k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[0],k[0]*k[1]]
F[37,x,k[0],k[1]] = F[15,x,k[0],k[1]]+F[38,x,k[0],k[1]]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[1]]
F[39,x,k[0],k[1]] = F[4,x]*F[40,x,k[0],k[1]]
F[40,x,k[0],k[1]] = 1/(-1+k[0])*(F[41,x,k[0],k[1]]*k[0]-F[41,x,1,k[1]])
F[41,x,k[0],k[1]] = F[42,x,k[1]]+F[74,x,k[0],k[1]]
F[43,x,k[0]] = F[42,x,k[0]]+F[79,x,k[0]]
F[44,x,k[0]] = F[12,x,k[0]]*F[43,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[46,x,k[0]] = F[45,x,k[0]]+F[60,x,k[0]]
F[47,x,k[0]] = F[4,x]*F[46,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[7,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[12,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[53,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[49,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[57,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[12,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[1,x]+F[54,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[12,x,k[0]]*F[59,x,k[0]]
F[59,x,k[0]] = F[53,x,k[0]]
F[61,x,k[0]] = F[60,x,k[0]]+F[64,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[61,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[2,x]+F[48,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[66,x,k[0]] = F[12,x,k[0]]*F[65,x,k[0]]
F[66,x,k[0]] = F[7,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[70,x,k[0]]
F[68,x,k[0]] = F[69,x,1,k[0]]
F[69,x,k[0],k[1]] = F[16,x,k[0]*k[1],k[1]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[4,x]*F[72,x,k[0]]
F[72,x,k[0]] = k[0]*(F[73,x,1,k[0]]-F[73,x,1/k[0],k[0]])/(-1+k[0])
F[73,x,k[0],k[1]] = F[74,x,k[0]*k[1],k[1]]
F[74,x,k[0],k[1]] = F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = F[12,x,k[0]]*F[31,x,k[0],k[1]]*F[76,x]
F[76,x] = F[1,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[76,x]^2*F[4,x]
F[79,x,k[0]] = F[73,x,1,k[0]]
F[81,x,k[0]] = F[12,x,k[0]]*F[80,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[4,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[85,x,k[0]]
F[84,x,k[0]] = F[16,x,k[0],1]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[4,x]*F[87,x,k[0]]
F[87,x,k[0]] = -k[0]*(F[88,x,1]-F[88,x,k[0]])/(-1+k[0])
F[88,x,k[0]] = F[83,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[4,x]*F[76,x]*F[88,x,k[0]]
F[91,x,k[0]] = F[64,x,k[0]]+F[80,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_{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_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
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_{14}\! \left(x , 1, y\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right)+F_{6}\! \left(x , z\right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right)
F_{17}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{18}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right)+F_{29}\! \left(x , y , z\right)
F_{20}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , 1, y\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y z , z\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)+F_{28}\! \left(x , z , y\right)+F_{8}\! \left(x \right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y , z\right) = -\frac{-y F_{24}\! \left(x , y , z\right)+F_{24}\! \left(x , 1, z\right)}{-1+y}
F_{27}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{24}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{18}\! \left(x , z , y\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , z , y\right)
F_{30}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{31}\! \left(x , z , y\right)
F_{32}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{31}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{33}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = F_{33}\! \left(x , y , y z \right)
F_{35}\! \left(x , y , z\right) = F_{34}\! \left(x , y , z\right)+F_{91}\! \left(x , y z \right)
F_{35}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right)+F_{80}\! \left(x , y z \right)
F_{36}\! \left(x , y , z\right) = F_{37}\! \left(x , y , y z \right)
F_{37}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right)+F_{38}\! \left(x , y , z\right)
F_{38}\! \left(x , y , z\right) = F_{39}\! \left(x , y , z\right)
F_{39}\! \left(x , y , z\right) = F_{4}\! \left(x \right) F_{40}\! \left(x , y , z\right)
F_{40}\! \left(x , y , z\right) = -\frac{-y F_{41}\! \left(x , y , z\right)+F_{41}\! \left(x , 1, z\right)}{-1+y}
F_{41}\! \left(x , y , z\right) = F_{42}\! \left(x , z\right)+F_{74}\! \left(x , y , z\right)
F_{43}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , 1, y\right)
F_{69}\! \left(x , y , z\right) = F_{16}\! \left(x , y z , z\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = \frac{y \left(F_{73}\! \left(x , 1, y\right)-F_{73}\! \left(x , \frac{1}{y}, y\right)\right)}{-1+y}
F_{73}\! \left(x , y , z\right) = F_{74}\! \left(x , y z , z\right)
F_{74}\! \left(x , y , z\right) = F_{75}\! \left(x , y , z\right)
F_{75}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{31}\! \left(x , y , z\right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{1}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{76} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{73}\! \left(x , 1, y\right)
F_{81}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{16}\! \left(x , y , 1\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = -\frac{y \left(F_{88}\! \left(x , 1\right)-F_{88}\! \left(x , y\right)\right)}{-1+y}
F_{88}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{80}\! \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))
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_0(x) + F_7(x, k_0))
Eq(F_7(x, k_0), F_11(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
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_14(x, 1, k_0))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1) + F_6(x, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), F_12(x, k_0)*F_18(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0) + F_29(x, k_0, k_1))
Eq(F_20(x, k_0), F_19(x, k_0) + F_22(x, k_0))
Eq(F_21(x, k_0), F_12(x, k_0)*F_20(x, k_0))
Eq(F_21(x, k_0), F_7(x, k_0))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, k_0*k_1, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1) + F_27(x, k_0, k_1) + F_28(x, k_1, k_0) + F_8(x))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1)*F_4(x))
Eq(F_26(x, k_0, k_1), (k_0*F_24(x, k_0, k_1) - F_24(x, 1, k_1))/(k_0 - 1))
Eq(F_27(x, k_0, k_1), F_12(x, k_0)*F_24(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_12(x, k_0)*F_18(x, k_1, k_0))
Eq(F_29(x, k_0, k_1), F_30(x, k_1, k_0))
Eq(F_30(x, k_0, k_1), F_12(x, k_0)*F_31(x, k_1, k_0))
Eq(F_32(x, k_0, k_1), F_12(x, k_0)*F_31(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_33(x, k_0, k_0*k_1))
Eq(F_35(x, k_0, k_1), F_34(x, k_0, k_1) + F_91(x, k_0*k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1) + F_80(x, k_0*k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_0, k_0*k_1))
Eq(F_37(x, k_0, k_1), F_15(x, k_0, k_1) + F_38(x, k_0, k_1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), F_4(x)*F_40(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), (k_0*F_41(x, k_0, k_1) - F_41(x, 1, k_1))/(k_0 - 1))
Eq(F_41(x, k_0, k_1), F_42(x, k_1) + F_74(x, k_0, k_1))
Eq(F_43(x, k_0), F_42(x, k_0) + F_79(x, k_0))
Eq(F_44(x, k_0), F_12(x, k_0)*F_43(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_46(x, k_0), F_45(x, k_0) + F_60(x, k_0))
Eq(F_47(x, k_0), F_4(x)*F_46(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_7(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_12(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_53(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_49(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_57(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_12(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_1(x) + F_54(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_12(x, k_0)*F_59(x, k_0))
Eq(F_59(x, k_0), F_53(x, k_0))
Eq(F_61(x, k_0), F_60(x, k_0) + F_64(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_61(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_2(x) + F_48(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_66(x, k_0), F_12(x, k_0)*F_65(x, k_0))
Eq(F_66(x, k_0), F_7(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_70(x, k_0))
Eq(F_68(x, k_0), F_69(x, 1, k_0))
Eq(F_69(x, k_0, k_1), F_16(x, k_0*k_1, k_1))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_4(x)*F_72(x, k_0))
Eq(F_72(x, k_0), -F_73(x, 1/k_0, k_0) + (k_0*F_73(x, 1, k_0) - F_73(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_73(x, k_0, k_1), F_74(x, k_0*k_1, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), F_12(x, k_0)*F_31(x, k_0, k_1)*F_76(x))
Eq(F_76(x), F_1(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_76(x)**2)
Eq(F_79(x, k_0), F_73(x, 1, k_0))
Eq(F_81(x, k_0), F_12(x, k_0)*F_80(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_4(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_85(x, k_0))
Eq(F_84(x, k_0), F_16(x, k_0, 1))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_4(x)*F_87(x, k_0))
Eq(F_87(x, k_0), -F_88(x, 1) + (k_0*F_88(x, k_0) - F_88(x, 1))/(k_0 - 1))
Eq(F_88(x, k_0), F_83(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_4(x)*F_76(x)*F_88(x, k_0))
Eq(F_91(x, k_0), F_64(x, k_0) + F_80(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 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2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "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": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 5
Strategy pack name: insertion_point_row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/103/
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[18,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]*F[17,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x,k[0]]*F[15,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[13,x,k[0]]
F[17,x] = F[1,x]+F[11,x]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[2,x]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x]+F[22,x,k[0]]+F[30,x,k[0]]
F[21,x] = 0
F[22,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = -k[0]*(F[24,x,1]-F[24,x,k[0]])/(-1+k[0])
F[24,x,k[0]] = F[20,x,k[0]]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[14,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[29,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[30,x,k[0]] = F[14,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[19,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0],1]
F[33,x,k[0],k[1]] = F[34,x,1,k[0],k[1]]
F[34,x,k[0],k[1],k[2]] = F[138,x,k[0],k[1],k[2]]+F[35,x,k[0]*k[1]]
F[35,x,k[0]] = F[159,x,k[0]]+F[21,x]+F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[4,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[49,x,k[0]]
F[38,x,k[0]] = F[16,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[21,x]+F[40,x,k[0]]+F[44,x,k[0]]
F[40,x,k[0]] = F[4,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[38,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[46,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[14,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = F[11,x]+F[43,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[4,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[42,x,k[0]]
F[49,x,k[0]] = F[50,x,1,k[0]]
F[50,x,k[0],k[1]] = F[35,x,k[1]]+F[51,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[157,x,k[1],k[0]]+F[21,x]+F[52,x,k[0],k[1]]+F[66,x,k[0],k[1]]
F[52,x,k[0],k[1]] = -k[0]*(F[53,x,1,k[1]]-F[53,x,k[0],k[1]])/(-1+k[0])
F[53,x,k[0],k[1]] = F[4,x]*F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[51,x,k[0],k[1]]+F[55,x,k[0],k[1]]
F[56,x,k[0],k[1],k[2]] = F[55,x,k[0]*k[1],k[1]*k[2]]
F[56,x,k[0],k[1],k[2]] = F[57,x,k[1],k[0],k[2]]
F[57,x,k[0],k[1],k[2]] = F[14,x,k[2]]*F[15,x,k[2]]*F[58,x,k[1]]
F[58,x,k[0]] = F[16,x,k[0]]+F[59,x,k[0]]
F[59,x,k[0]] = F[16,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[21,x]+F[61,x,k[0]]+F[63,x,k[0]]
F[61,x,k[0]] = F[14,x,k[0]]*F[62,x,k[0]]
F[62,x,k[0]] = F[16,x,k[0]]+F[60,x,k[0]]
F[63,x,k[0]] = F[14,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[16,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[63,x,k[0]]
F[66,x,k[0],k[1]] = F[14,x,k[0]]*F[67,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[50,x,k[0],k[1]]+F[68,x,k[0],k[1]]
F[68,x,k[0],k[1]] = F[69,x,k[0],1,k[1]]
F[69,x,k[0],k[1],k[2]] = F[70,x,1,k[0],k[1],k[2]]
F[70,x,k[0],k[1],k[2],k[3]] = F[150,x,k[0],k[1],k[2],k[3]]+F[71,x,k[0]*k[1],k[3]]
F[71,x,k[0],k[1]] = F[72,x,k[1],k[0]]
F[73,x,k[0],k[1],k[2]] = F[72,x,k[0]*k[1],k[0]*k[2]]
F[73,x,k[0],k[1],k[2]] = F[14,x,k[1]]*F[74,x,k[2],k[0],k[1]]
F[74,x,k[0],k[1],k[2]] = F[34,x,k[0],k[1],k[2]]+F[75,x,k[0],k[1],k[2]]
F[75,x,k[0],k[1],k[2]] = F[76,x,k[0],k[1],k[2]]+F[83,x,k[0],k[1],k[2]]
F[76,x,k[0],k[1],k[2]] = F[77,x,k[2],k[1],k[0]]
F[77,x,k[0],k[1],k[2]] = F[78,x,k[0]*k[1],k[1]*k[2]]
F[79,x,k[0],k[1]] = F[78,x,k[0]*k[1],k[1]]
F[79,x,k[0],k[1]] = F[15,x,k[1]]*F[16,x,k[1]]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[82,x]^2*F[4,x]
F[82,x] = F[1,x]+F[80,x]
F[83,x,k[0],k[1],k[2]] = F[114,x,k[0],k[1],k[2]]+F[84,x,k[0]*k[1]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[4,x]*F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]+F[97,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[93,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[92,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[4,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[16,x,k[0]]+F[89,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[35,x,1]-F[35,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[94,x,k[0]]+F[96,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]
F[95,x,k[0]] = F[11,x]*F[16,x,k[0]]*F[80,x]
F[96,x,k[0]] = -k[0]*(F[84,x,1]-F[84,x,k[0]])/(-1+k[0])
F[97,x,k[0]] = F[103,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[94,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = -k[0]*(F[100,x,1]-F[100,x,k[0]])/(-1+k[0])
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[4,x]*F[82,x]
F[102,x,k[0]] = F[100,x,k[0]]+F[35,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[110,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,1,k[0]]
F[106,x,k[0],k[1]] = F[107,x,k[0]]*F[11,x]*F[16,x,k[1]]*F[80,x]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]^2*F[14,x,k[0]]
F[109,x,k[0]] = F[1,x]+F[107,x,k[0]]
F[110,x,k[0]] = -k[0]*(F[111,x,1]-F[111,x,k[0]])/(-1+k[0])
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[4,x]*F[82,x]
F[113,x,k[0]] = F[111,x,k[0]]+F[84,x,k[0]]
F[114,x,k[0],k[1],k[2]] = F[115,x,k[0]*k[1],k[1]*k[2]]
F[115,x,k[0],k[1]] = F[116,x,k[0],k[1]]
F[116,x,k[0],k[1]] = F[117,x,k[0],k[1]]
F[117,x,k[0],k[1]] = F[118,x,k[0],k[1]]*F[4,x]
F[118,x,k[0],k[1]] = F[119,x,k[0],k[1]]+F[130,x,k[0],k[1]]
F[119,x,k[0],k[1]] = F[120,x,k[0],k[1]]+F[125,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]+F[124,x,k[0],k[1]]
F[122,x,k[0],k[1],k[2]] = F[121,x,k[0]*k[1],k[1]*k[2]]
F[122,x,k[0],k[1],k[2]] = F[123,x,k[2],k[1],k[0]]
F[123,x,k[0],k[1],k[2]] = F[11,x]*F[16,x,k[1]]*F[16,x,k[2]]
F[124,x,k[0],k[1]] = -k[0]*(F[71,x,1,k[1]]-F[71,x,k[0],k[1]])/(-1+k[0])
F[125,x,k[0],k[1]] = F[126,x,k[0],k[1]]+F[129,x,k[0],k[1]]
F[127,x,k[0],k[1],k[2]] = F[126,x,k[0]*k[1],k[1]*k[2]]
F[127,x,k[0],k[1],k[2]] = F[128,x,k[2],k[1],k[0]]
F[128,x,k[0],k[1],k[2]] = F[11,x]*F[16,x,k[1]]*F[16,x,k[2]]*F[80,x]
F[129,x,k[0],k[1]] = -k[0]*(F[116,x,1,k[1]]-F[116,x,k[0],k[1]])/(-1+k[0])
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[139,x,k[0],k[1]]
F[131,x,k[0],k[1]] = F[126,x,k[0],k[1]]+F[132,x,k[0],k[1]]
F[132,x,k[0],k[1]] = -k[0]*(F[133,x,1,k[1]]-F[133,x,k[0],k[1]])/(-1+k[0])
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]
F[135,x,k[0],k[1],k[2]] = F[134,x,k[0]*k[1],k[1]*k[2]]
F[135,x,k[0],k[1],k[2]] = F[136,x,k[0],k[1],k[2]]
F[136,x,k[0],k[1],k[2]] = F[137,x,k[0],k[1],k[2]]*F[4,x]*F[82,x]
F[137,x,k[0],k[1],k[2]] = F[135,x,k[0],k[1],k[2]]+F[138,x,k[0],k[1],k[2]]
F[138,x,k[0],k[1],k[2]] = F[73,x,k[1],k[2],k[0]]
F[139,x,k[0],k[1]] = F[140,x,k[0],k[1]]+F[146,x,k[0],k[1]]
F[140,x,k[0],k[1]] = F[141,x,k[1],k[0]]
F[141,x,k[0],k[1]] = F[142,x,1,k[0],k[1]]
F[142,x,k[0],k[1],k[2]] = F[143,x,k[1],k[0],k[2]]
F[144,x,k[0],k[1],k[2]] = F[143,x,k[0],k[1],k[0]*k[2]]
F[145,x,k[0],k[1],k[2]] = F[144,x,k[0],k[1]*k[2],k[2]]
F[145,x,k[0],k[1],k[2]] = F[16,x,k[2]]^2*F[80,x]^2*F[16,x,k[0]]
F[146,x,k[0],k[1]] = -k[0]*(F[147,x,1,k[1]]-F[147,x,k[0],k[1]])/(-1+k[0])
F[147,x,k[0],k[1]] = F[148,x,k[0],k[1]]
F[148,x,k[0],k[1]] = F[149,x,k[0],k[1]]*F[4,x]*F[82,x]
F[149,x,k[0],k[1]] = F[116,x,k[0],k[1]]+F[147,x,k[0],k[1]]
F[150,x,k[0],k[1],k[2],k[3]] = F[151,x,k[1],k[2],k[0],k[3]]
F[151,x,k[0],k[1],k[2],k[3]] = F[14,x,k[1]]*F[152,x,k[2],k[0],k[1],k[3]]
F[152,x,k[0],k[1],k[2],k[3]] = k[3]*(F[153,x,k[0],k[1],k[2]]-F[153,x,k[0],k[1],k[3]/k[1]])/(k[1]*k[2]-k[3])
F[153,x,k[0],k[1],k[2]] = F[138,x,k[0],k[1],k[2]]+F[154,x,k[0],k[1],k[2]]
F[154,x,k[0],k[1],k[2]] = F[114,x,k[0],k[1],k[2]]+F[155,x,k[0],k[1],k[2]]
F[155,x,k[0],k[1],k[2]] = F[156,x,k[2],k[1],k[0]]
F[156,x,k[0],k[1],k[2]] = F[16,x,k[1]]*F[16,x,k[2]]*F[80,x]
F[157,x,k[0],k[1]] = F[14,x,k[0]]*F[158,x,k[1],k[0]]
F[158,x,k[0],k[1]] = F[35,x,k[0]]+F[71,x,k[0],k[1]]
F[159,x,k[0]] = F[14,x,k[0]]*F[160,x,k[0]]
F[160,x,k[0]] = F[2,x]+F[35,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_{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_{18}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right)+F_{22}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{24}\! \left(x , 1\right)-F_{24}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{24}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{28}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right) F_{16}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}, 1\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , 1, y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{35}\! \left(x , y_{0} y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right)+F_{21}\! \left(x \right)+F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{43}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{44}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{45}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right)+F_{43}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{50}\! \left(x , 1, y_{0}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{157}\! \left(x , y_{1}, y_{0}\right)+F_{21}\! \left(x \right)+F_{52}\! \left(x , y_{0}, y_{1}\right)+F_{66}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{53}\! \left(x , 1, y_{1}\right)-F_{53}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{4}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{55}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{57}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{2}\right) F_{15}\! \left(x , y_{2}\right) F_{58}\! \left(x , y_{1}\right)
F_{58}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{60}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right)+F_{61}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{60}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{64}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{67}\! \left(x , y_{0}, y_{1}\right)
F_{67}\! \left(x , y_{0}, y_{1}\right) = F_{50}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}, y_{1}\right)
F_{68}\! \left(x , y_{0}, y_{1}\right) = F_{69}\! \left(x , y_{0}, 1, y_{1}\right)
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{70}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{150}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{71}\! \left(x , y_{0} y_{1}, y_{3}\right)
F_{71}\! \left(x , y_{0}, y_{1}\right) = F_{72}\! \left(x , y_{1}, y_{0}\right)
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{72}\! \left(x , y_{0} y_{1}, y_{0} y_{2}\right)
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{1}\right) F_{74}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{77}\! \left(x , y_{2}, y_{1}, y_{0}\right)
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{78}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{79}\! \left(x , y_{0}, y_{1}\right) = F_{78}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{79}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{1}\right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{82}\! \left(x \right) = F_{1}\! \left(x \right)+F_{80}\! \left(x \right)
F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{84}\! \left(x , y_{0} y_{1}\right)
F_{84}\! \left(x , y_{0}\right) = F_{85}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{86}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{87}\! \left(x , y_{0}\right)+F_{97}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{88}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{89}\! \left(x , y_{0}\right)+F_{92}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{91}\! \left(x , y_{0}\right)
F_{91}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{89}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{35}\! \left(x , 1\right)-F_{35}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{93}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{95}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{16}\! \left(x , y_{0}\right) F_{80}\! \left(x \right)
F_{96}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{84}\! \left(x , 1\right)-F_{84}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{97}\! \left(x , y_{0}\right) = F_{103}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)+F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{100}\! \left(x , 1\right)-F_{100}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{100}\! \left(x , y_{0}\right) = F_{101}\! \left(x , y_{0}\right)
F_{101}\! \left(x , y_{0}\right) = F_{102}\! \left(x , y_{0}\right) F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{102}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{103}\! \left(x , y_{0}\right) = F_{104}\! \left(x , y_{0}\right)+F_{110}\! \left(x , y_{0}\right)
F_{104}\! \left(x , y_{0}\right) = F_{105}\! \left(x , y_{0}\right)
F_{105}\! \left(x , y_{0}\right) = F_{106}\! \left(x , 1, y_{0}\right)
F_{106}\! \left(x , y_{0}, y_{1}\right) = F_{107}\! \left(x , y_{0}\right) F_{11}\! \left(x \right) F_{16}\! \left(x , y_{1}\right) F_{80}\! \left(x \right)
F_{107}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x , y_{0}\right)^{2} F_{14}\! \left(x , y_{0}\right)
F_{109}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{107}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{111}\! \left(x , 1\right)-F_{111}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{113}\! \left(x , y_{0}\right) F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{113}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right)+F_{84}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{115}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{115}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)
F_{116}\! \left(x , y_{0}, y_{1}\right) = F_{117}\! \left(x , y_{0}, y_{1}\right)
F_{117}\! \left(x , y_{0}, y_{1}\right) = F_{118}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{118}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right)+F_{130}\! \left(x , y_{0}, y_{1}\right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{120}\! \left(x , y_{0}, y_{1}\right)+F_{125}\! \left(x , y_{0}, y_{1}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{0}, y_{1}\right)+F_{124}\! \left(x , y_{0}, y_{1}\right)
F_{122}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{121}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{122}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{123}\! \left(x , y_{2}, y_{1}, y_{0}\right)
F_{123}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{16}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{2}\right)
F_{124}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{71}\! \left(x , 1, y_{1}\right)-F_{71}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right)+F_{129}\! \left(x , y_{0}, y_{1}\right)
F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{126}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{128}\! \left(x , y_{2}, y_{1}, y_{0}\right)
F_{128}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{16}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{2}\right) F_{80}\! \left(x \right)
F_{129}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{116}\! \left(x , 1, y_{1}\right)-F_{116}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{130}\! \left(x , y_{0}, y_{1}\right) = F_{131}\! \left(x , y_{0}, y_{1}\right)+F_{139}\! \left(x , y_{0}, y_{1}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = F_{126}\! \left(x , y_{0}, y_{1}\right)+F_{132}\! \left(x , y_{0}, y_{1}\right)
F_{132}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{133}\! \left(x , 1, y_{1}\right)-F_{133}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{134}\! \left(x , y_{0}, y_{1}\right)
F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{134}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{136}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{136}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{73}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{139}\! \left(x , y_{0}, y_{1}\right) = F_{140}\! \left(x , y_{0}, y_{1}\right)+F_{146}\! \left(x , y_{0}, y_{1}\right)
F_{140}\! \left(x , y_{0}, y_{1}\right) = F_{141}\! \left(x , y_{1}, y_{0}\right)
F_{141}\! \left(x , y_{0}, y_{1}\right) = F_{142}\! \left(x , 1, y_{0}, y_{1}\right)
F_{142}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{143}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{143}\! \left(x , y_{0}, y_{1}, y_{0} y_{2}\right)
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{144}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{2}\right)^{2} F_{80} \left(x \right)^{2} F_{16}\! \left(x , y_{0}\right)
F_{146}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{147}\! \left(x , 1, y_{1}\right)-F_{147}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{147}\! \left(x , y_{0}, y_{1}\right) = F_{148}\! \left(x , y_{0}, y_{1}\right)
F_{148}\! \left(x , y_{0}, y_{1}\right) = F_{149}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{149}\! \left(x , y_{0}, y_{1}\right) = F_{116}\! \left(x , y_{0}, y_{1}\right)+F_{147}\! \left(x , y_{0}, y_{1}\right)
F_{150}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{151}\! \left(x , y_{1}, y_{2}, y_{0}, y_{3}\right)
F_{151}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{14}\! \left(x , y_{1}\right) F_{152}\! \left(x , y_{2}, y_{0}, y_{1}, y_{3}\right)
F_{152}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{y_{3} \left(F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{153}\! \left(x , y_{0}, y_{1}, \frac{y_{3}}{y_{1}}\right)\right)}{y_{1} y_{2}-y_{3}}
F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{138}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{154}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{154}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{156}\! \left(x , y_{2}, y_{1}, y_{0}\right)
F_{156}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{2}\right) F_{80}\! \left(x \right)
F_{157}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}\right) F_{158}\! \left(x , y_{1}, y_{0}\right)
F_{158}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)
F_{159}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{160}\! \left(x , y_{0}\right)
F_{160}\! \left(x , y_{0}\right) = F_{2}\! \left(x \right)+F_{35}\! \left(x , y_{0}\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_18(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x)*F_17(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x, k_0)*F_15(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_13(x, k_0))
Eq(F_17(x), F_1(x) + F_11(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_2(x) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x) + F_22(x, k_0) + F_30(x, k_0))
Eq(F_21(x), 0)
Eq(F_22(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), -F_24(x, 1) + (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_24(x, k_0), F_20(x, k_0) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_14(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_29(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_30(x, k_0), F_14(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_19(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0, 1))
Eq(F_33(x, k_0, k_1), F_34(x, 1, k_0, k_1))
Eq(F_34(x, k_0, k_1, k_2), F_138(x, k_0, k_1, k_2) + F_35(x, k_0*k_1))
Eq(F_35(x, k_0), F_159(x, k_0) + F_21(x) + F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_4(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_49(x, k_0))
Eq(F_38(x, k_0), F_16(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_21(x) + F_40(x, k_0) + F_44(x, k_0))
Eq(F_40(x, k_0), F_4(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_38(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_46(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_14(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), F_11(x) + F_43(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_4(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_42(x, k_0))
Eq(F_49(x, k_0), F_50(x, 1, k_0))
Eq(F_50(x, k_0, k_1), F_35(x, k_1) + F_51(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_157(x, k_1, k_0) + F_21(x) + F_52(x, k_0, k_1) + F_66(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), -F_53(x, 1, k_1) + (k_0*F_53(x, k_0, k_1) - F_53(x, 1, k_1))/(k_0 - 1))
Eq(F_53(x, k_0, k_1), F_4(x)*F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_51(x, k_0, k_1) + F_55(x, k_0, k_1))
Eq(F_56(x, k_0, k_1, k_2), F_55(x, k_0*k_1, k_1*k_2))
Eq(F_56(x, k_0, k_1, k_2), F_57(x, k_1, k_0, k_2))
Eq(F_57(x, k_0, k_1, k_2), F_14(x, k_2)*F_15(x, k_2)*F_58(x, k_1))
Eq(F_58(x, k_0), F_16(x, k_0) + F_59(x, k_0))
Eq(F_59(x, k_0), F_16(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_21(x) + F_61(x, k_0) + F_63(x, k_0))
Eq(F_61(x, k_0), F_14(x, k_0)*F_62(x, k_0))
Eq(F_62(x, k_0), F_16(x, k_0) + F_60(x, k_0))
Eq(F_63(x, k_0), F_14(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_16(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_63(x, k_0))
Eq(F_66(x, k_0, k_1), F_14(x, k_0)*F_67(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_50(x, k_0, k_1) + F_68(x, k_0, k_1))
Eq(F_68(x, k_0, k_1), F_69(x, k_0, 1, k_1))
Eq(F_69(x, k_0, k_1, k_2), F_70(x, 1, k_0, k_1, k_2))
Eq(F_70(x, k_0, k_1, k_2, k_3), F_150(x, k_0, k_1, k_2, k_3) + F_71(x, k_0*k_1, k_3))
Eq(F_71(x, k_0, k_1), F_72(x, k_1, k_0))
Eq(F_73(x, k_0, k_1, k_2), F_72(x, k_0*k_1, k_0*k_2))
Eq(F_73(x, k_0, k_1, k_2), F_14(x, k_1)*F_74(x, k_2, k_0, k_1))
Eq(F_74(x, k_0, k_1, k_2), F_34(x, k_0, k_1, k_2) + F_75(x, k_0, k_1, k_2))
Eq(F_75(x, k_0, k_1, k_2), F_76(x, k_0, k_1, k_2) + F_83(x, k_0, k_1, k_2))
Eq(F_76(x, k_0, k_1, k_2), F_77(x, k_2, k_1, k_0))
Eq(F_77(x, k_0, k_1, k_2), F_78(x, k_0*k_1, k_1*k_2))
Eq(F_79(x, k_0, k_1), F_78(x, k_0*k_1, k_1))
Eq(F_79(x, k_0, k_1), F_15(x, k_1)*F_16(x, k_1)*F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_82(x)**2)
Eq(F_82(x), F_1(x) + F_80(x))
Eq(F_83(x, k_0, k_1, k_2), F_114(x, k_0, k_1, k_2) + F_84(x, k_0*k_1))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_4(x)*F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0) + F_97(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_93(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_92(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_4(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_16(x, k_0) + F_89(x, k_0))
Eq(F_92(x, k_0), -F_35(x, 1) + (k_0*F_35(x, k_0) - F_35(x, 1))/(k_0 - 1))
Eq(F_93(x, k_0), F_94(x, k_0) + F_96(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0))
Eq(F_95(x, k_0), F_11(x)*F_16(x, k_0)*F_80(x))
Eq(F_96(x, k_0), -F_84(x, 1) + (k_0*F_84(x, k_0) - F_84(x, 1))/(k_0 - 1))
Eq(F_97(x, k_0), F_103(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_94(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), -F_100(x, 1) + (k_0*F_100(x, k_0) - F_100(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_4(x)*F_82(x))
Eq(F_102(x, k_0), F_100(x, k_0) + F_35(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_110(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, 1, k_0))
Eq(F_106(x, k_0, k_1), F_107(x, k_0)*F_11(x)*F_16(x, k_1)*F_80(x))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)**2*F_14(x, k_0))
Eq(F_109(x, k_0), F_1(x) + F_107(x, k_0))
Eq(F_110(x, k_0), -F_111(x, 1) + (k_0*F_111(x, k_0) - F_111(x, 1))/(k_0 - 1))
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_4(x)*F_82(x))
Eq(F_113(x, k_0), F_111(x, k_0) + F_84(x, k_0))
Eq(F_114(x, k_0, k_1, k_2), F_115(x, k_0*k_1, k_1*k_2))
Eq(F_115(x, k_0, k_1), F_116(x, k_0, k_1))
Eq(F_116(x, k_0, k_1), F_117(x, k_0, k_1))
Eq(F_117(x, k_0, k_1), F_118(x, k_0, k_1)*F_4(x))
Eq(F_118(x, k_0, k_1), F_119(x, k_0, k_1) + F_130(x, k_0, k_1))
Eq(F_119(x, k_0, k_1), F_120(x, k_0, k_1) + F_125(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1) + F_124(x, k_0, k_1))
Eq(F_122(x, k_0, k_1, k_2), F_121(x, k_0*k_1, k_1*k_2))
Eq(F_122(x, k_0, k_1, k_2), F_123(x, k_2, k_1, k_0))
Eq(F_123(x, k_0, k_1, k_2), F_11(x)*F_16(x, k_1)*F_16(x, k_2))
Eq(F_124(x, k_0, k_1), -F_71(x, 1, k_1) + (k_0*F_71(x, k_0, k_1) - F_71(x, 1, k_1))/(k_0 - 1))
Eq(F_125(x, k_0, k_1), F_126(x, k_0, k_1) + F_129(x, k_0, k_1))
Eq(F_127(x, k_0, k_1, k_2), F_126(x, k_0*k_1, k_1*k_2))
Eq(F_127(x, k_0, k_1, k_2), F_128(x, k_2, k_1, k_0))
Eq(F_128(x, k_0, k_1, k_2), F_11(x)*F_16(x, k_1)*F_16(x, k_2)*F_80(x))
Eq(F_129(x, k_0, k_1), -F_116(x, 1, k_1) + (k_0*F_116(x, k_0, k_1) - F_116(x, 1, k_1))/(k_0 - 1))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1) + F_139(x, k_0, k_1))
Eq(F_131(x, k_0, k_1), F_126(x, k_0, k_1) + F_132(x, k_0, k_1))
Eq(F_132(x, k_0, k_1), -F_133(x, 1, k_1) + (k_0*F_133(x, k_0, k_1) - F_133(x, 1, k_1))/(k_0 - 1))
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1))
Eq(F_135(x, k_0, k_1, k_2), F_134(x, k_0*k_1, k_1*k_2))
Eq(F_135(x, k_0, k_1, k_2), F_136(x, k_0, k_1, k_2))
Eq(F_136(x, k_0, k_1, k_2), F_137(x, k_0, k_1, k_2)*F_4(x)*F_82(x))
Eq(F_137(x, k_0, k_1, k_2), F_135(x, k_0, k_1, k_2) + F_138(x, k_0, k_1, k_2))
Eq(F_138(x, k_0, k_1, k_2), F_73(x, k_1, k_2, k_0))
Eq(F_139(x, k_0, k_1), F_140(x, k_0, k_1) + F_146(x, k_0, k_1))
Eq(F_140(x, k_0, k_1), F_141(x, k_1, k_0))
Eq(F_141(x, k_0, k_1), F_142(x, 1, k_0, k_1))
Eq(F_142(x, k_0, k_1, k_2), F_143(x, k_1, k_0, k_2))
Eq(F_144(x, k_0, k_1, k_2), F_143(x, k_0, k_1, k_0*k_2))
Eq(F_145(x, k_0, k_1, k_2), F_144(x, k_0, k_1*k_2, k_2))
Eq(F_145(x, k_0, k_1, k_2), F_16(x, k_0)*F_16(x, k_2)**2*F_80(x)**2)
Eq(F_146(x, k_0, k_1), -F_147(x, 1, k_1) + (k_0*F_147(x, k_0, k_1) - F_147(x, 1, k_1))/(k_0 - 1))
Eq(F_147(x, k_0, k_1), F_148(x, k_0, k_1))
Eq(F_148(x, k_0, k_1), F_149(x, k_0, k_1)*F_4(x)*F_82(x))
Eq(F_149(x, k_0, k_1), F_116(x, k_0, k_1) + F_147(x, k_0, k_1))
Eq(F_150(x, k_0, k_1, k_2, k_3), F_151(x, k_1, k_2, k_0, k_3))
Eq(F_151(x, k_0, k_1, k_2, k_3), F_14(x, k_1)*F_152(x, k_2, k_0, k_1, k_3))
Eq(F_152(x, k_0, k_1, k_2, k_3), -F_153(x, k_0, k_1, k_2) + (-k_1*k_2*F_153(x, k_0, k_1, k_2) + k_3*F_153(x, k_0, k_1, k_3/k_1))/(-k_1*k_2 + k_3))
Eq(F_153(x, k_0, k_1, k_2), F_138(x, k_0, k_1, k_2) + F_154(x, k_0, k_1, k_2))
Eq(F_154(x, k_0, k_1, k_2), F_114(x, k_0, k_1, k_2) + F_155(x, k_0, k_1, k_2))
Eq(F_155(x, k_0, k_1, k_2), F_156(x, k_2, k_1, k_0))
Eq(F_156(x, k_0, k_1, k_2), F_16(x, k_1)*F_16(x, k_2)*F_80(x))
Eq(F_157(x, k_0, k_1), F_14(x, k_0)*F_158(x, k_1, k_0))
Eq(F_158(x, k_0, k_1), F_35(x, k_0) + F_71(x, k_0, k_1))
Eq(F_159(x, k_0), F_14(x, k_0)*F_160(x, k_0))
Eq(F_160(x, k_0), F_2(x) + F_35(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"}], [{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_row_and_col_placements_tracked_fusion_expand_verified", "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 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