01342_01423_01432_02341_02431_12340_12430
Counting sequence:
1, 1, 2, 6, 24, 113, 581, 3146, 17633, 101365, 594304, 3540230, 21367282, 130390278, 803164248, 4987221901, 31185297791, 196201973008, 1241107206783, 7888759271959, 50359685978648, 322735036684027, 2075574213202199, 13391257038736244, 86651310174081355, 562204535238936678, 3656674121426996925, 23837943992274024778, 155728804520510159917, 1019345712943715516123, 6684484837927070519352, 43909206974083518851028, 288892886613463449552126, 1903568658598427033435547, 12560630268632965812996589, 82990752688472498712975188, 549023094379845451490991675, 3636337067822323239631781340, 24111412912400703096610473735, 160044503797727080841495827300, 1063395853966214237627632079643, 7072346479760278538567095390487, 47078901480871466102491601830430, 313663966030583604912198323035261, 2091515310397323950966002331985655, 13957233759453703157766032295976664, 93210405216660873670853773970453279, 622933975137830477336150208917929751, 4165997056237419295456906161727581942, 27879358984392706441253287871127185843, 186690328309189987380566944922677813295, 1250907190172143712933170297205931297254, 8386529132543295107289612448171710684277, 56257910129029346713028588313233720257372, 377589497220973074708100138500634569873045, 2535610335560303476564666058918263861407176, 17035826600344392673637481430377543408614317, 114512851756061034684506876453484961456067594, 770101927939601833575946228638087565677340227, 5181293231491605160292241014839469533368609224, 34875262593989572140506236004234851395363103469, 234844210841443686267857000443468830672442908601, 1582046709937796741120682252966940990840094846358, 10661789832176092861093238075244335988787902228488, 71879802929448850860887537163701288809692826426848, 484779681991596595844063772077116789302605650104214, 3270677905176362278467229710776651660038092203624404, 22074062566533679118305233747758502812766278265609647, 149029891275531837388673449646317040677554182626246183, 1006483873011593757371993337190253330982939308355264118, 6799523212743569530970896624849376237634327459900873381, 45949878256835539356692232734943939063091678487893700948, 310613809126459979914680561309198557518988464757063289679, 2100313031092762434721494819690818602973984691020003040174, 14205963633060928870588093278355491018159700884961986694295, 96111962697365398812612540766818224901663707550740556210753, 650430763341764905353236806099957833955834474452110267628050, 4402896862876227564333720127002080306634692456842743603653119, 29811704732798357544684919538476101116945108548152905041615945, 201903167995693922043247168862101483078828416345253662981207178, 1367743783227631133724568191703957846122833477652399951281091431, 9267637370474609093699715933709782691309174826976794717486477439, 62810673630883533679219119025369637489648254653541588621713016454, 425790109068076634387618503792411781069299747640774814446970515657, 2887041555375125114501234241600579735311157588035485596733917825019, 19579589579695061488488003993311859383579758783590789518916511955322, 132814358654281247543435699111883636966823765277282275890970661316949, 901104713084791542536080385019969044501854889044714642074977097256585, 6114940587768744564856524778172892178464967621268181186530907076494118, 41504386930674715237665856455515522369407747403744225549626524768299643, 281759548970989919214456690686025935709779211155078349940797518001227073, 1913129303651021556581893616507675599914847976354673460910295127667623112, 12992396521326103833461003021502309212692794609660387743363850132840820577, 88249397928909464179677937216605231842273627417897642310612253745731012413, 599528886207574945049328870865555682895789131844605455847571293207601421694, 4073640878201091857383145826291114285385154404845788074054970249898655653067, 27683950986582772986223881571654338784788278685699383709130432078296010683041, 188167491594159977128591062741581527564119759247406837172702133974792034472014, 1279177600693430075707761767469787179213709359917601870403701315482654080296939, 8697319060658259839196810441523008408835941852440274213685499268303538065822366, 59143481665219728650672439284009011157286020612760226893834709184247362602638179
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24136/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]+F[5,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[43,x,k[0]]*F[9,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[16,x,k[0]]
F[15,x,k[0]] = F[14,x,k[0]]*F[9,x,k[0]]
F[5,x,k[0]] = F[0,x]+F[15,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[9,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[19,x,k[0]] = F[20,x,k[0]]
F[21,x,k[0]] = F[14,x,k[0]]+F[20,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[3,x]*F[36,x]
F[22,x,k[0]] = F[23,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]+F[5,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[27,x,k[0]]+F[33,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[3,x]
F[26,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[28,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[29,x,k[0]]+F[31,x,k[0]]
F[28,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[29,x,k[0]] = F[3,x]*F[30,x,k[0]]
F[30,x,k[0]] = 1/(-1+k[0])*(F[28,x,k[0]]*k[0]-F[28,x,1])
F[31,x,k[0]] = F[3,x]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[3,x]*F[35,x]*F[36,x]*F[5,x,k[0]]
F[35,x] = F[1,x]+F[3,x]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[3,x]*F[39,x]
F[39,x] = F[36,x]+F[40,x]
F[40,x] = F[3,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[3,x]*F[37,x]
F[43,x,k[0]] = F[1,x]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]*F[9,x,k[0]]
F[46,x,k[0]] = F[43,x,k[0]]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[9,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[44,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{5}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{43}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{15}\! \left(x , y\right)
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_{9}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{3}\! \left(x \right) F_{36}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{5}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right) F_{5}\! \left(x , y\right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{3}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{3}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{3}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{3}\! \left(x \right) F_{37}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{9}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0) + F_5(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_43(x, k_0)*F_9(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_16(x, k_0))
Eq(F_15(x, k_0), F_14(x, k_0)*F_9(x, k_0))
Eq(F_5(x, k_0), F_0(x) + F_15(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_9(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_21(x, k_0), F_14(x, k_0) + F_20(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_3(x)*F_36(x))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0) + F_5(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0) + F_27(x, k_0) + F_33(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_3(x))
Eq(F_26(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_28(x, k_0), F_1(x) + F_27(x, k_0) + F_29(x, k_0) + F_31(x, k_0))
Eq(F_28(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_3(x)*F_30(x, k_0))
Eq(F_30(x, k_0), (k_0*F_28(x, k_0) - F_28(x, 1))/(k_0 - 1))
Eq(F_31(x, k_0), F_3(x)*F_32(x, k_0))
Eq(F_32(x, k_0), (-k_0*F_24(x, k_0) + F_24(x, 1))/(1 - k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_3(x)*F_35(x)*F_36(x)*F_5(x, k_0))
Eq(F_35(x), F_1(x) + F_3(x))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_3(x)*F_39(x))
Eq(F_39(x), F_36(x) + F_40(x))
Eq(F_40(x), F_3(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_3(x)*F_37(x))
Eq(F_43(x, k_0), F_1(x) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0)*F_9(x, k_0))
Eq(F_46(x, k_0), F_43(x, k_0) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_9(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_44(x, k_0)*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], 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2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "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]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 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"}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24137/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[21,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[3,x]
F[13,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[11,x,k[0],k[1]]*k[0]*k[1]-F[11,x,1/k[1],k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[16,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[3,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[20,x,k[1],k[0]]*F[9,x,k[0]]
F[20,x,k[0],k[1]] = (-F[11,x,1,k[1]]*k[1]+F[11,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0]]*F[24,x,k[0]]*F[5,x,k[1]]*F[9,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[9,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[9,x,k[0]]
F[27,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[9,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[25,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{21}\! \left(x , z , y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{y z F_{11}\! \left(x , y , z\right)-F_{11}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = \frac{y F_{5}\! \left(x , y\right)-z F_{5}\! \left(x , z\right)}{-z +y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = -\frac{-y F_{16}\! \left(x , y , z\right)+F_{16}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , z , y\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = -\frac{z F_{11}\! \left(x , 1, z\right)-y F_{11}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y\right) F_{24}\! \left(x , y\right) F_{5}\! \left(x , z\right) F_{9}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{9}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_21(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_3(x))
Eq(F_13(x, k_0, k_1), (k_0*k_1*F_11(x, k_0, k_1) - F_11(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_3(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_20(x, k_1, k_0)*F_9(x, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_11(x, k_0/k_1, k_1) + k_1*F_11(x, 1, k_1))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0)*F_24(x, k_0)*F_5(x, k_1)*F_9(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_9(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_9(x, k_0))
Eq(F_27(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_9(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_25(x, k_0)*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": 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": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], 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