0132_0213_0321_23014
Counting sequence:
1, 1, 2, 6, 21, 78, 298, 1158, 4554, 18073, 72242, 290448, 1173306, 4758477, 19362607, 79009713, 323178078, 1324659890, 5439380174, 22370629854, 92131426357, 379898787427, 1568189955890, 6479607838062, 26796235072080, 110900994200024, 459304023164671, 1903438853582835, 7892702729516096, 32744471545587236, 135911289073530504, 564365553534354226, 2344428186353519088, 9742503403695967523, 40499399817203654732, 168406741602532601984, 700475302393982645261, 2914333500768046790958, 12128028676953927093917, 50482166687923358644679, 210172319404549318179092, 875177978812895702025660, 3644976304141180691572774, 15183263458369481728118792, 63256143602450305265131486, 263574224943341250078187598, 1098402842900053802166191790, 4577991819232577167851222834, 19082685740239662826809309072, 79552135986807233302192791404, 331672173944817174030049351794, 1382955749774205207573204020061, 5766960797481582724122360093875, 24050426498678763608066449461617, 100307499656846053209029665600156, 418385663955620419945905595782331, 1745223385798096213349146022206561, 7280384147297031105309909927708764, 30372807284107436529460547544718570, 126718895391852095016684160268186149, 528715652114775544224890627736038177, 2206103770298406207641536349754712317, 9205585376105614381108674411689274554, 38414695264509718779849097340967362392, 160310793517089848343730617276680619491, 669031359303496299029317902374349218220, 2792206543159245321878706518491774422116, 11653732263498528498510319425844404908331, 48640507051426418563651433676449508944987, 203023306239128611452060775813286320492218, 847437495100257802144059097811388971651931, 3537388092676361684593289492622844968274337, 14766253419263565774766257448975412698478165, 61641025914743213085792795884691605330497699, 257324256891251983445820991323247470893499929, 1074242560306452036981871578425306473549430765, 4484708321436496017234286192659775418339314296, 18723014036397152615760663282457467116815199856, 78167560119977219878324861641316383316021236838, 326351888063462055949062160241024719450487067164, 1362555039082089581720315364460190115762102797983, 5688921288945548033543810181760443882686724823649, 23752720506294067340435315803201605684464184013839, 99175407116532809345503428805560823766686321559515, 414096425439574857319223180476277704020157989604060, 1729041837588541376097437737303909372510523877514200, 7219643362120031360357902071275435668987831235568898, 30146154268433367863145125022638956548975227974442187, 125879132809529151910196313076264749017430868243190985, 525630983538424450913195451507514003493949773861227524, 2194892787798366870499714276224817160838350338125180584, 9165381965937623482940756494780130123870575790973287523, 38272999884698001735284744785843503067860191205212758851, 159822862015851827030707736294473180781663825763919343157, 667405166003454270677256498808524376113753071449739106679, 2787046999122274210942998276933608981980981557673204795543, 11638657967760710409352582568647579325289371571863027519061, 48603240818180331200192923555959571067359947961258696243716, 202969646658374569548123337516372348565835992122091042289307, 847618347510661429825996749530418712681263374547599878947410, 3539752016273827238040700417467375879355999939611401459020992
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24033/
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[0,x]+F[6,x]
F[6,x] = F[7,x,1]
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[1,x]+F[11,x,k[0]]+F[14,x,k[0]]+F[38,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[4,x]
F[15,x,k[0]] = F[16,x,1,k[0]]
F[16,x,k[0],k[1]] = F[1,x]+F[17,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[33,x,k[1],k[0]]+F[35,x,k[1],k[0]]
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[4,x]
F[18,x,k[0],k[1]] = 1/(-1+k[0])*(F[16,x,k[0],k[1]]*k[0]-F[16,x,1,k[1]])
F[19,x,k[0],k[1]] = F[12,x,k[0]]*F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[13,x,k[0]]+F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = k[1]*(F[22,x,k[0],1]-F[22,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[22,x,k[0],k[1]] = 2*F[8,x]+F[23,x,k[0],k[1]]+F[31,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[4,x]
F[24,x,k[0],k[1]] = F[25,x,k[1],k[0]]
F[25,x,k[0],k[1]] = F[12,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[27,x,k[0]*k[1],k[1]]
F[27,x,k[0],k[1]] = 1/(-1+k[1])*(F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])
F[29,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[30,x,k[0],k[1]] = F[12,x,k[1]]*F[29,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[22,x,k[1],k[0]]
F[31,x,k[0],k[1]] = F[12,x,k[1]]*F[32,x,k[0],k[1]]
F[20,x,k[0],k[1]] = (F[32,x,k[0],1]*k[0]-F[32,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[12,x,k[0]]*F[34,x,k[1],k[0]]
F[32,x,k[0],k[1]] = F[34,x,k[0],k[0]*k[1]]
F[35,x,k[0],k[1]] = F[12,x,k[0]]*F[36,x,k[1],k[0]]
F[36,x,k[0],k[1]] = (-F[37,x,1,k[1]]*k[1]+F[37,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[37,x,k[0],k[1]] = F[34,x,k[0]*k[1],k[1]]
F[38,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[13,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[40,x,k[0]] = F[7,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_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{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_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , 1, y\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , y , z\right)+F_{33}\! \left(x , z , y\right)+F_{35}\! \left(x , z , y\right)
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = \frac{F_{16}\! \left(x , y , z\right) y -F_{16}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right)+F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = \frac{z \left(F_{22}\! \left(x , y , 1\right)-F_{22}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{22}\! \left(x , y , z\right) = 2 F_{8}\! \left(x \right)+F_{23}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , z , y\right)
F_{25}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y z , z\right)
F_{27}\! \left(x , y , z\right) = \frac{F_{28}\! \left(x , y , z\right) z -F_{28}\! \left(x , y , 1\right)}{-1+z}
F_{29}\! \left(x , y , z\right) = F_{28}\! \left(x , y z , z\right)
F_{30}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = F_{22}\! \left(x , z , y\right)
F_{31}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right) F_{32}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = \frac{F_{32}\! \left(x , y , 1\right) y -F_{32}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{33}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{34}\! \left(x , z , y\right)
F_{32}\! \left(x , y , z\right) = F_{34}\! \left(x , y , y z \right)
F_{35}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x , z , y\right)
F_{36}\! \left(x , y , z\right) = \frac{-F_{37}\! \left(x , 1, z\right) z +F_{37}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{37}\! \left(x , y , z\right) = F_{34}\! \left(x , y z , z\right)
F_{38}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{7}\! \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_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
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_1(x) + F_11(x, k_0) + F_14(x, k_0) + F_38(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_4(x))
Eq(F_15(x, k_0), F_16(x, 1, k_0))
Eq(F_16(x, k_0, k_1), F_1(x) + F_17(x, k_0, k_1) + F_19(x, k_0, k_1) + F_33(x, k_1, k_0) + F_35(x, k_1, k_0))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_4(x))
Eq(F_18(x, k_0, k_1), (k_0*F_16(x, k_0, k_1) - F_16(x, 1, k_1))/(k_0 - 1))
Eq(F_19(x, k_0, k_1), F_12(x, k_0)*F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_13(x, k_0) + F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), -F_22(x, k_0, 1) + (-k_0*F_22(x, k_0, 1) + k_1*F_22(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1) + F_31(x, k_0, k_1) + 2*F_8(x))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_4(x))
Eq(F_24(x, k_0, k_1), F_25(x, k_1, k_0))
Eq(F_25(x, k_0, k_1), F_12(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0*k_1, k_1))
Eq(F_27(x, k_0, k_1), (k_1*F_28(x, k_0, k_1) - F_28(x, k_0, 1))/(k_1 - 1))
Eq(F_29(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_30(x, k_0, k_1), F_12(x, k_1)*F_29(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_22(x, k_1, k_0))
Eq(F_31(x, k_0, k_1), F_12(x, k_1)*F_32(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), (-k_0*F_32(x, k_0, 1) + k_1*F_32(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_12(x, k_0)*F_34(x, k_1, k_0))
Eq(F_32(x, k_0, k_1), F_34(x, k_0, k_0*k_1))
Eq(F_35(x, k_0, k_1), F_12(x, k_0)*F_36(x, k_1, k_0))
Eq(F_36(x, k_0, k_1), (-k_0*F_37(x, k_0/k_1, k_1) + k_1*F_37(x, 1, k_1))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1), F_34(x, k_0*k_1, k_1))
Eq(F_38(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_13(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_40(x, k_0), F_7(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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_col_placements_tracked_fusion_req_corrob", "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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [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, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 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[2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 4]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 0], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 0], [2, 0], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 1], [2, 0], [2, 0], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 0], [2, 0], [2, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 1], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 2], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [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, 0], [0, 0], [0, 2]]}, {"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], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"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]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 3]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "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_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24034/
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[10,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[11,x,k[0]]+F[7,x]+F[8,x,k[0]]
F[7,x] = 0
F[8,x,k[0]] = F[10,x]*F[9,x,k[0]]
F[9,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[10,x] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[22,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[26,x,k[0]]
F[15,x,k[0],k[1]] = F[10,x]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[17,x,1,k[0],k[1]]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[24,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[10,x]*F[19,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[22,x,k[0]]
F[21,x,k[0],k[1]] = (F[13,x,k[0],1]*k[0]-F[13,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[22,x,k[1]]
F[24,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[25,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = (F[14,x,k[0],k[2]]*k[0]-F[14,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0]] = F[22,x,k[0]]*F[27,x,k[0]]
F[12,x,k[0]] = F[27,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[6,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_{10}\! \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_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{7}\! \left(x \right)+F_{8}\! \left(x , y_{0}\right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , 1, y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{13}\! \left(x , y_{0}, 1\right)-y_{1} F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x , y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{14}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{6}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_11(x, k_0) + F_7(x) + F_8(x, k_0))
Eq(F_7(x), 0)
Eq(F_8(x, k_0), F_10(x)*F_9(x, k_0))
Eq(F_9(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_10(x), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_22(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_23(x, k_0, k_1) + F_26(x, k_0))
Eq(F_15(x, k_0, k_1), F_10(x)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, 1, k_0, k_1))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_0, k_1, k_2) + F_20(x, k_0, k_1) + F_23(x, k_0, k_1) + F_24(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_10(x)*F_19(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1)*F_22(x, k_0))
Eq(F_21(x, k_0, k_1), (-k_0*F_13(x, k_0, 1) + k_1*F_13(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1), F_14(x, k_0, k_1)*F_22(x, k_1))
Eq(F_24(x, k_0, k_1, k_2), F_22(x, k_2)*F_25(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_14(x, k_0, k_2) + k_1*F_14(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0), F_22(x, k_0)*F_27(x, k_0))
Eq(F_12(x, k_0), F_27(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_6(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": false, "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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_req_corrob", "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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [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]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"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], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "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": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 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]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": 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"EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 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, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"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]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 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, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"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], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, "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 3
Strategy pack name: point_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24035/
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[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[26,x]*F[7,x]
F[7,x] = F[125,x]+F[8,x]
F[8,x] = F[9,x,1]
F[10,x,k[0]] = F[117,x,k[0]]+F[9,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[38,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[16,x,k[0]]
F[12,x,k[0]] = F[0,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[9,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[26,x]
F[18,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[19,x,k[0]] = F[20,x]+F[37,x,k[0]]
F[20,x] = F[21,x]+F[32,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]+F[30,x]
F[23,x] = F[24,x]*F[27,x]
F[24,x] = F[1,x]+F[25,x]
F[25,x] = F[24,x]*F[26,x]
F[26,x] = x
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[22,x]*F[26,x]
F[30,x] = F[31,x]
F[31,x] = F[24,x]^2*F[26,x]*F[28,x]
F[32,x] = -F[36,x]+F[33,x]
F[33,x] = 1/F[26,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = -F[28,x]+F[5,x]
F[36,x] = F[37,x,1]
F[11,x,k[0]] = F[37,x,k[0]]+F[4,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[15,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,1,k[0]]
F[42,x,k[0],k[1]] = F[15,x,k[1]]*F[41,x,k[0],k[1]]
F[42,x,k[0],k[1]] = F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[116,x,k[0],k[1]]+F[44,x,k[1]]
F[45,x,k[0]] = F[4,x]+F[44,x,k[0]]
F[46,x,k[0]] = F[114,x,k[0]]+F[45,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[83,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[55,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[52,x,k[0]]
F[49,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[15,x,k[0]]*F[49,x,k[0]]
F[52,x,k[0]] = F[50,x,k[0]]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[15,x,k[0]]*F[52,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[26,x]*F[49,x,k[0]]*F[57,x,k[0]]
F[58,x,k[0]] = F[15,x,k[0]]*F[49,x,k[0]]*F[57,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[70,x,k[0]]
F[60,x,k[0]] = F[61,x]*F[64,x,k[0]]
F[61,x] = F[0,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[26,x]*F[7,x]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[15,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[49,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[50,x,k[0]]+F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[15,x,k[0]]*F[67,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[15,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[113,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[50,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = 1/(-1+k[0])*(F[75,x,1,k[0]]*k[0]-F[75,x,1/k[0],k[0]])
F[41,x,k[0],k[1]] = F[75,x,k[0],k[1]]+F[76,x,k[0],k[1]]
F[77,x,k[0],k[1]] = F[15,x,k[1]]*F[76,x,k[0],k[1]]
F[77,x,k[0],k[1]] = F[78,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[78,x,k[0],k[1]]+F[79,x,k[0],k[1]]
F[80,x,k[0],k[1]] = F[12,x,k[0]*k[1]]+F[79,x,k[0],k[1]]
F[80,x,k[0],k[1]] = F[112,x,k[0],k[1]]+F[81,x,k[1]]
F[45,x,k[0]] = F[81,x,k[0]]+F[82,x,k[0]]
F[83,x,k[0]] = F[82,x,k[0]]+F[91,x,k[0]]
F[84,x,k[0]] = F[55,x,k[0]]+F[83,x,k[0]]
F[85,x,k[0]] = F[15,x,k[0]]*F[84,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[26,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[59,x,k[0]]+F[89,x,k[0]]
F[89,x,k[0]] = -k[0]*(F[90,x,1]-F[90,x,k[0]])/(-1+k[0])
F[90,x,k[0]] = F[64,x,k[0]]+F[86,x,k[0]]
F[91,x,k[0]] = F[92,x,1,k[0]]
F[92,x,k[0],k[1]] = F[93,x,k[0],k[1]]
F[93,x,k[0],k[1]] = F[26,x]*F[94,x,k[0],k[1]]
F[94,x,k[0],k[1]] = k[0]*k[1]*(F[95,x,k[0],k[1]]-F[95,x,1/k[1],k[1]])/(k[0]*k[1]-1)
F[95,x,k[0],k[1]] = F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = F[15,x,k[1]]*F[97,x,k[0],k[1]]
F[98,x,k[0],k[1]] = F[15,x,k[1]]*F[97,x,k[0],k[1]]
F[98,x,k[0],k[1]] = F[99,x,k[0],k[1]]
F[99,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[102,x,k[0],k[1]]
F[100,x,k[0],k[1]] = F[101,x,k[0],k[1]]
F[101,x,k[0],k[1]] = F[0,x]*F[49,x,k[1]]*F[50,x,k[1]]
F[102,x,k[0],k[1]] = F[103,x,k[0],k[1]]
F[103,x,k[0],k[1]] = F[104,x,k[0],k[1]]*F[26,x]
F[104,x,k[0],k[1]] = F[105,x,k[0],k[1]]+F[106,x,k[0],k[1]]
F[105,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[99,x,k[0],k[1]]*k[0]*k[1]-F[99,x,1/k[1],k[1]])
F[106,x,k[0],k[1]] = F[107,x,k[0],k[1]]*F[50,x,k[1]]
F[107,x,k[0],k[1]] = F[105,x,k[0],k[1]]+F[108,x,k[0]*k[1]]
F[109,x,k[0]] = F[108,x,k[0]]*F[26,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[9,x,k[0]] = F[110,x,k[0]]+F[111,x,k[0]]
F[111,x,k[0]] = F[0,x]*F[49,x,k[0]]
F[95,x,k[0],k[1]] = F[112,x,k[0],k[1]]+F[92,x,k[0],k[1]]
F[113,x,k[0]] = F[108,x,k[0]]*F[50,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[91,x,k[0]]
F[115,x,k[0]] = F[112,x,1,k[0]]
F[95,x,k[0],k[1]] = F[116,x,k[0],k[1]]+F[37,x,k[0]*k[1]]
F[117,x,k[0]] = F[118,x,k[0]]+F[119,x,k[0]]
F[118,x,k[0]] = F[13,x,k[0]]*F[49,x,k[0]]
F[119,x,k[0]] = F[120,x,1,k[0]]
F[120,x,k[0],k[1]] = F[121,x,k[0],k[1]]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]*F[26,x]*F[49,x,k[1]]
F[122,x,k[0],k[1]] = k[0]*k[1]*(F[123,x,k[0],k[1]]-F[123,x,1/k[1],k[1]])/(k[0]*k[1]-1)
F[123,x,k[0],k[1]] = F[120,x,k[0],k[1]]+F[124,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[13,x,k[1]]*F[49,x,k[1]]
F[125,x] = F[117,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_{26}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{26}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{125}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{32}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{24}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{22}\! \left(x \right) F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{26}\! \left(x \right) F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{5}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x , 1\right)
F_{11}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , 1, y\right)
F_{42}\! \left(x , y , z\right) = F_{15}\! \left(x , z\right) F_{41}\! \left(x , y , z\right)
F_{42}\! \left(x , y , z\right) = F_{43}\! \left(x , y , z\right)
F_{43}\! \left(x , y , z\right) = F_{116}\! \left(x , y , z\right)+F_{44}\! \left(x , z\right)
F_{45}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{49}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{49}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x \right) F_{64}\! \left(x , y\right)
F_{61}\! \left(x \right) = F_{0}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{26}\! \left(x \right) F_{7}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{67}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{50}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = \frac{y F_{75}\! \left(x , 1, y\right)-F_{75}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{41}\! \left(x , y , z\right) = F_{75}\! \left(x , y , z\right)+F_{76}\! \left(x , y , z\right)
F_{77}\! \left(x , y , z\right) = F_{15}\! \left(x , z\right) F_{76}\! \left(x , y , z\right)
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , y , z\right)
F_{43}\! \left(x , y , z\right) = F_{78}\! \left(x , y , z\right)+F_{79}\! \left(x , y , z\right)
F_{80}\! \left(x , y , z\right) = F_{12}\! \left(x , y z \right)+F_{79}\! \left(x , y , z\right)
F_{80}\! \left(x , y , z\right) = F_{112}\! \left(x , y , z\right)+F_{81}\! \left(x , z\right)
F_{45}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = -\frac{y \left(F_{90}\! \left(x , 1\right)-F_{90}\! \left(x , y\right)\right)}{-1+y}
F_{90}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , 1, y\right)
F_{92}\! \left(x , y , z\right) = F_{93}\! \left(x , y , z\right)
F_{93}\! \left(x , y , z\right) = F_{26}\! \left(x \right) F_{94}\! \left(x , y , z\right)
F_{94}\! \left(x , y , z\right) = \frac{y z \left(F_{95}\! \left(x , y , z\right)-F_{95}\! \left(x , \frac{1}{z}, z\right)\right)}{y z -1}
F_{95}\! \left(x , y , z\right) = F_{96}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = F_{15}\! \left(x , z\right) F_{97}\! \left(x , y , z\right)
F_{98}\! \left(x , y , z\right) = F_{15}\! \left(x , z\right) F_{97}\! \left(x , y , z\right)
F_{98}\! \left(x , y , z\right) = F_{99}\! \left(x , y , z\right)
F_{99}\! \left(x , y , z\right) = F_{100}\! \left(x , y , z\right)+F_{102}\! \left(x , y , z\right)
F_{100}\! \left(x , y , z\right) = F_{101}\! \left(x , y , z\right)
F_{101}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{49}\! \left(x , z\right) F_{50}\! \left(x , z\right)
F_{102}\! \left(x , y , z\right) = F_{103}\! \left(x , y , z\right)
F_{103}\! \left(x , y , z\right) = F_{104}\! \left(x , y , z\right) F_{26}\! \left(x \right)
F_{104}\! \left(x , y , z\right) = F_{105}\! \left(x , y , z\right)+F_{106}\! \left(x , y , z\right)
F_{105}\! \left(x , y , z\right) = \frac{y z F_{99}\! \left(x , y , z\right)-F_{99}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{106}\! \left(x , y , z\right) = F_{107}\! \left(x , y , z\right) F_{50}\! \left(x , z\right)
F_{107}\! \left(x , y , z\right) = F_{105}\! \left(x , y , z\right)+F_{108}\! \left(x , y z \right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{95}\! \left(x , y , z\right) = F_{112}\! \left(x , y , z\right)+F_{92}\! \left(x , y , z\right)
F_{113}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{50}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{112}\! \left(x , 1, y\right)
F_{95}\! \left(x , y , z\right) = F_{116}\! \left(x , y , z\right)+F_{37}\! \left(x , y z \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , 1, y\right)
F_{120}\! \left(x , y , z\right) = F_{121}\! \left(x , y , z\right)
F_{121}\! \left(x , y , z\right) = F_{122}\! \left(x , y , z\right) F_{26}\! \left(x \right) F_{49}\! \left(x , z\right)
F_{122}\! \left(x , y , z\right) = \frac{y z \left(F_{123}\! \left(x , y , z\right)-F_{123}\! \left(x , \frac{1}{z}, z\right)\right)}{y z -1}
F_{123}\! \left(x , y , z\right) = F_{120}\! \left(x , y , z\right)+F_{124}\! \left(x , y , z\right)
F_{124}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{49}\! \left(x , z\right)
F_{125}\! \left(x \right) = F_{117}\! \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_26(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_26(x)*F_7(x))
Eq(F_7(x), F_125(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_10(x, k_0), F_117(x, k_0) + F_9(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_38(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_16(x, k_0))
Eq(F_12(x, k_0), F_0(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_9(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_26(x))
Eq(F_18(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_20(x) + F_37(x, k_0))
Eq(F_20(x), F_21(x) + F_32(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x) + F_30(x))
Eq(F_23(x), F_24(x)*F_27(x))
Eq(F_24(x), F_1(x) + F_25(x))
Eq(F_25(x), F_24(x)*F_26(x))
Eq(F_26(x), x)
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_22(x)*F_26(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_24(x)**2*F_26(x)*F_28(x))
Eq(F_32(x), F_33(x) - F_36(x))
Eq(F_33(x), F_34(x)/F_26(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), -F_28(x) + F_5(x))
Eq(F_36(x), F_37(x, 1))
Eq(F_11(x, k_0), F_37(x, k_0) + F_4(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_15(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, 1, k_0))
Eq(F_42(x, k_0, k_1), F_15(x, k_1)*F_41(x, k_0, k_1))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_116(x, k_0, k_1) + F_44(x, k_1))
Eq(F_45(x, k_0), F_4(x) + F_44(x, k_0))
Eq(F_46(x, k_0), F_114(x, k_0) + F_45(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_83(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_55(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_52(x, k_0))
Eq(F_49(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_15(x, k_0)*F_49(x, k_0))
Eq(F_52(x, k_0), F_50(x, k_0) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_15(x, k_0)*F_52(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_26(x)*F_49(x, k_0)*F_57(x, k_0))
Eq(F_58(x, k_0), F_15(x, k_0)*F_49(x, k_0)*F_57(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_70(x, k_0))
Eq(F_60(x, k_0), F_61(x)*F_64(x, k_0))
Eq(F_61(x), F_0(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_26(x)*F_7(x))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_15(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_49(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_50(x, k_0) + F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_15(x, k_0)*F_67(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_15(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_113(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_50(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), (k_0*F_75(x, 1, k_0) - F_75(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_41(x, k_0, k_1), F_75(x, k_0, k_1) + F_76(x, k_0, k_1))
Eq(F_77(x, k_0, k_1), F_15(x, k_1)*F_76(x, k_0, k_1))
Eq(F_77(x, k_0, k_1), F_78(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_78(x, k_0, k_1) + F_79(x, k_0, k_1))
Eq(F_80(x, k_0, k_1), F_12(x, k_0*k_1) + F_79(x, k_0, k_1))
Eq(F_80(x, k_0, k_1), F_112(x, k_0, k_1) + F_81(x, k_1))
Eq(F_45(x, k_0), F_81(x, k_0) + F_82(x, k_0))
Eq(F_83(x, k_0), F_82(x, k_0) + F_91(x, k_0))
Eq(F_84(x, k_0), F_55(x, k_0) + F_83(x, k_0))
Eq(F_85(x, k_0), F_15(x, k_0)*F_84(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_26(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_59(x, k_0) + F_89(x, k_0))
Eq(F_89(x, k_0), -F_90(x, 1) + (k_0*F_90(x, k_0) - F_90(x, 1))/(k_0 - 1))
Eq(F_90(x, k_0), F_64(x, k_0) + F_86(x, k_0))
Eq(F_91(x, k_0), F_92(x, 1, k_0))
Eq(F_92(x, k_0, k_1), F_93(x, k_0, k_1))
Eq(F_93(x, k_0, k_1), F_26(x)*F_94(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), -F_95(x, 1/k_1, k_1) + (k_0*k_1*F_95(x, k_0, k_1) - F_95(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_95(x, k_0, k_1), F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), F_15(x, k_1)*F_97(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), F_15(x, k_1)*F_97(x, k_0, k_1))
Eq(F_98(x, k_0, k_1), F_99(x, k_0, k_1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_1) + F_102(x, k_0, k_1))
Eq(F_100(x, k_0, k_1), F_101(x, k_0, k_1))
Eq(F_101(x, k_0, k_1), F_0(x)*F_49(x, k_1)*F_50(x, k_1))
Eq(F_102(x, k_0, k_1), F_103(x, k_0, k_1))
Eq(F_103(x, k_0, k_1), F_104(x, k_0, k_1)*F_26(x))
Eq(F_104(x, k_0, k_1), F_105(x, k_0, k_1) + F_106(x, k_0, k_1))
Eq(F_105(x, k_0, k_1), (k_0*k_1*F_99(x, k_0, k_1) - F_99(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_106(x, k_0, k_1), F_107(x, k_0, k_1)*F_50(x, k_1))
Eq(F_107(x, k_0, k_1), F_105(x, k_0, k_1) + F_108(x, k_0*k_1))
Eq(F_109(x, k_0), F_108(x, k_0)*F_26(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_9(x, k_0), F_110(x, k_0) + F_111(x, k_0))
Eq(F_111(x, k_0), F_0(x)*F_49(x, k_0))
Eq(F_95(x, k_0, k_1), F_112(x, k_0, k_1) + F_92(x, k_0, k_1))
Eq(F_113(x, k_0), F_108(x, k_0)*F_50(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_91(x, k_0))
Eq(F_115(x, k_0), F_112(x, 1, k_0))
Eq(F_95(x, k_0, k_1), F_116(x, k_0, k_1) + F_37(x, k_0*k_1))
Eq(F_117(x, k_0), F_118(x, k_0) + F_119(x, k_0))
Eq(F_118(x, k_0), F_13(x, k_0)*F_49(x, k_0))
Eq(F_119(x, k_0), F_120(x, 1, k_0))
Eq(F_120(x, k_0, k_1), F_121(x, k_0, k_1))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1)*F_26(x)*F_49(x, k_1))
Eq(F_122(x, k_0, k_1), -F_123(x, 1/k_1, k_1) + (k_0*k_1*F_123(x, k_0, k_1) - F_123(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_123(x, k_0, k_1), F_120(x, k_0, k_1) + F_124(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_13(x, k_1)*F_49(x, k_1))
Eq(F_125(x), F_117(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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_placements_tracked_fusion_req_corrob", "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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 2]]}, {"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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 1], [0, 2], [1, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 2]]}]]}, {"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], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 3], [0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 3], [0, 3], [0, 2], [0, 3], [0, 3]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 3], [0, 3], [0, 2], [0, 3], [2, 3]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [0, 3], [2, 3]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], 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{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion
Tree: http://permpal.com/tree/24036/
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[10,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[11,x,k[0]]+F[7,x]+F[8,x,k[0]]
F[7,x] = 0
F[8,x,k[0]] = F[10,x]*F[9,x,k[0]]
F[9,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[10,x] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[30,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[13,x,k[0]]+F[38,x,k[0]]
F[13,x,k[0]] = F[10,x]*F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,1,k[0]]
F[15,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[35,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[10,x]*F[17,x,k[0],k[1]]
F[17,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]*F[30,x,k[0]]
F[19,x,k[0],k[1]] = F[12,x,k[0]]+F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = k[1]*(F[21,x,k[0],1]-F[21,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = 2*F[7,x]+F[22,x,k[0],k[1]]+F[31,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[10,x]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]*F[30,x,k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[0]*k[1]]
F[26,x,k[0],k[1]] = 1/(-1+k[0])*(F[27,x,k[0],k[1]]*k[0]-F[27,x,1,k[1]])
F[28,x,k[0],k[1]] = F[27,x,k[0],k[0]*k[1]]
F[29,x,k[0],k[1]] = F[28,x,k[0],k[1]]*F[30,x,k[1]]
F[29,x,k[0],k[1]] = F[21,x,k[0],k[1]]
F[30,x,k[0]] = k[0]*x
F[31,x,k[0],k[1]] = F[30,x,k[1]]*F[32,x,k[0],k[1]]
F[19,x,k[0],k[1]] = (F[32,x,k[0],1]*k[0]-F[32,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[30,x,k[1]]*F[34,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[34,x,k[0],k[0]*k[1]]
F[35,x,k[0],k[1]] = F[30,x,k[1]]*F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = (-F[37,x,1,k[1]]*k[1]+F[37,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[37,x,k[0],k[1]] = F[34,x,k[0]*k[1],k[1]]
F[38,x,k[0]] = F[30,x,k[0]]*F[39,x,k[0]]
F[12,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[40,x,k[0]] = F[6,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_{10}\! \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_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{7}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x , y\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , 1, y\right)
F_{15}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = F_{10}\! \left(x \right) F_{17}\! \left(x , y , z\right)
F_{17}\! \left(x , y , z\right) = -\frac{-y F_{15}\! \left(x , y , z\right)+F_{15}\! \left(x , 1, z\right)}{-1+y}
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y , z\right) F_{30}\! \left(x , y\right)
F_{19}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right)+F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = \frac{z \left(F_{21}\! \left(x , y , 1\right)-F_{21}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{21}\! \left(x , y , z\right) = 2 F_{7}\! \left(x \right)+F_{22}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{10}\! \left(x \right) F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right) F_{30}\! \left(x , z\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , y z \right)
F_{26}\! \left(x , y , z\right) = -\frac{-y F_{27}\! \left(x , y , z\right)+F_{27}\! \left(x , 1, z\right)}{-1+y}
F_{28}\! \left(x , y , z\right) = F_{27}\! \left(x , y , y z \right)
F_{29}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right) F_{30}\! \left(x , z\right)
F_{29}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right)
F_{30}\! \left(x , y\right) = y x
F_{31}\! \left(x , y , z\right) = F_{30}\! \left(x , z\right) F_{32}\! \left(x , y , z\right)
F_{19}\! \left(x , y , z\right) = \frac{y F_{32}\! \left(x , y , 1\right)-z F_{32}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{33}\! \left(x , y , z\right) = F_{30}\! \left(x , z\right) F_{34}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{34}\! \left(x , y , y z \right)
F_{35}\! \left(x , y , z\right) = F_{30}\! \left(x , z\right) F_{36}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = -\frac{z F_{37}\! \left(x , 1, z\right)-y F_{37}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{37}\! \left(x , y , z\right) = F_{34}\! \left(x , y z , z\right)
F_{38}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{6}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_11(x, k_0) + F_7(x) + F_8(x, k_0))
Eq(F_7(x), 0)
Eq(F_8(x, k_0), F_10(x)*F_9(x, k_0))
Eq(F_9(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_10(x), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_30(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_11(x, k_0) + F_13(x, k_0) + F_38(x, k_0))
Eq(F_13(x, k_0), F_10(x)*F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, 1, k_0))
Eq(F_15(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_18(x, k_0, k_1) + F_33(x, k_0, k_1) + F_35(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_10(x)*F_17(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1)*F_30(x, k_0))
Eq(F_19(x, k_0, k_1), F_12(x, k_0) + F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), -F_21(x, k_0, 1) + (-k_0*F_21(x, k_0, 1) + k_1*F_21(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1) + F_31(x, k_0, k_1) + 2*F_7(x))
Eq(F_22(x, k_0, k_1), F_10(x)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1)*F_30(x, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_0*k_1))
Eq(F_26(x, k_0, k_1), (k_0*F_27(x, k_0, k_1) - F_27(x, 1, k_1))/(k_0 - 1))
Eq(F_28(x, k_0, k_1), F_27(x, k_0, k_0*k_1))
Eq(F_29(x, k_0, k_1), F_28(x, k_0, k_1)*F_30(x, k_1))
Eq(F_29(x, k_0, k_1), F_21(x, k_0, k_1))
Eq(F_30(x, k_0), k_0*x)
Eq(F_31(x, k_0, k_1), F_30(x, k_1)*F_32(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_32(x, k_0, 1) + k_1*F_32(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_30(x, k_1)*F_34(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_34(x, k_0, k_0*k_1))
Eq(F_35(x, k_0, k_1), F_30(x, k_1)*F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), (-k_0*F_37(x, k_0/k_1, k_1) + k_1*F_37(x, 1, k_1))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1), F_34(x, k_0*k_1, k_1))
Eq(F_38(x, k_0), F_30(x, k_0)*F_39(x, k_0))
Eq(F_12(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_40(x, k_0), F_6(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": false, "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_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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"tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [1, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [1, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [1, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 0], [0, 2], [2, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[4, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"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, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"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], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[3, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "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 5
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24037/
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[0,x]+F[6,x]
F[6,x] = F[7,x,1]
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,k[0],1]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[0]*k[1]]
F[15,x,k[0],k[1]] = F[1,x]+F[16,x,k[0],k[1]]+F[23,x,k[1],k[0]]+F[26,x,k[0]]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[4,x]
F[17,x,k[0],k[1]] = F[18,x,1,k[0],k[1]]
F[18,x,k[0],k[1],k[2]] = F[1,x]+F[19,x,k[0],k[1],k[2]]+F[21,x,k[0],k[1]]+F[23,x,k[1],k[0]]+F[24,x,k[2],k[0],k[1]]
F[19,x,k[0],k[1],k[2]] = F[20,x,k[0],k[1],k[2]]*F[4,x]
F[20,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[18,x,k[0],k[1],k[2]]*k[0]-F[18,x,1,k[1],k[2]])
F[21,x,k[0],k[1]] = F[12,x,k[0]]*F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = (F[14,x,k[0],1]*k[0]-F[14,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[12,x,k[0]]*F[15,x,k[1],k[0]]
F[24,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[25,x,k[1],k[2],k[0]]
F[25,x,k[0],k[1],k[2]] = (F[15,x,k[0],k[2]]*k[0]-F[15,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0]] = F[12,x,k[0]]*F[27,x,k[0]]
F[13,x,k[0]] = F[27,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[7,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_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = y_{0} x
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}, 1\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{1}, y_{0}\right)+F_{26}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , 1, y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{1}, y_{0}\right)+F_{24}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{14}\! \left(x , y_{0}, 1\right)-y_{1} F_{14}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{1}, y_{0}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{15}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{15}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{7}\! \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_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
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, k_0, 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_0*k_1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_16(x, k_0, k_1) + F_23(x, k_1, k_0) + F_26(x, k_0))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_4(x))
Eq(F_17(x, k_0, k_1), F_18(x, 1, k_0, k_1))
Eq(F_18(x, k_0, k_1, k_2), F_1(x) + F_19(x, k_0, k_1, k_2) + F_21(x, k_0, k_1) + F_23(x, k_1, k_0) + F_24(x, k_2, k_0, k_1))
Eq(F_19(x, k_0, k_1, k_2), F_20(x, k_0, k_1, k_2)*F_4(x))
Eq(F_20(x, k_0, k_1, k_2), (k_0*F_18(x, k_0, k_1, k_2) - F_18(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_21(x, k_0, k_1), F_12(x, k_0)*F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), (-k_0*F_14(x, k_0, 1) + k_1*F_14(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_12(x, k_0)*F_15(x, k_1, k_0))
Eq(F_24(x, k_0, k_1, k_2), F_12(x, k_0)*F_25(x, k_1, k_2, k_0))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_15(x, k_0, k_2) + k_1*F_15(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0), F_12(x, k_0)*F_27(x, k_0))
Eq(F_13(x, k_0), F_27(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_7(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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