01243
Counting sequence:
1, 1, 2, 6, 24, 119, 694, 4582, 33324, 261808, 2190688, 19318688, 178108704, 1705985883, 16891621166, 172188608886, 1801013405436, 19274897768196, 210573149141896, 2343553478425816, 26525044132374656, 304856947930144656, 3553266124166899872, 41952101272633801376, 501228159413699278144, 6054582181256780696704, 73884542290182291304704, 910193895170720544149248, 11312196463176760501700224, 141756115346271817822954691, 1790158821899427408246810846, 22771425534677098061041394646, 291642099099498112188821162588, 3759242107953814033130572455916, 48751015815371292172234643194072, 635852547884023642520478819395592, 8338465173053718017144237028810592, 109913406624791838115057396950319036, 1455919003228078755280002195858923672, 19374979687575816540275835344651133144, 258979765348686847155069655246696267824, 3476328590102910965665689483937046945024, 46851370171582242155071537504570960602624, 633858018177741285037750807248408708401664, 8607098530902491974636809987706092837133824, 117286558208547537293433340721019086325451984, 1603623050878143932722397047915184802200125984, 21996763034860960417259405204172331608463797152, 302664297898124499421697046885532938663308311104, 4176922244743425434851827565214898395775758294208, 57808845869218440075832443346616034420583063507328, 802283220888975310339856786488603816420320224819328, 11163800163529547323754623817431192659251590878268416, 155741808084115897360585014916160126291788254860611968, 2178047449783852638357791655647435547947020212454442752, 30532382238075245259338398193146151040285528444895520512, 428992304950286649659085382315383342788062404084978970112, 6040874727342104396726698678329641023346831718342618510336, 85247065841778966494266703539191483914473291434364353226752, 1205473572352660080103797064048389676169509302028706218563584, 17080691329178796639203288554670322171239249809057073614580224, 242490618234260394252092752186168149866343533745706302824878099, 3449051981624944283634166260421462556836772680839011415343041342, 49146729874672701762343742496180797150361565596223012961791946134, 701545004462146571931529078848686432466537772696849687206721251868, 10031352489989751239375889390971997601358794041942918782490504935228, 143676099686863009951342537113515792745830857603081200700626957355128, 2061150250351970656999892659403413881472518135431862781844183696287848, 29615206122273812890085169569171618722487916233068581003415574000434208, 426167779622995865283628739158982711331849195508228917016661569107647988, 6141702429788647151614048924465683794039481288539951634700556550582875208, 88638329077516268256504732709195723293817371767346137874961745507175971208, 1281038038262029417796717108172094558123187360150836751350487829452144984464, 18539323868106760071083538228981183546048669741807961833166681519075442726848, 268659083392910925115389236368003573466025508349372868636275816090439444895616, 3898252089153013760606591506453077085164536792462028504205805189808904098454656, 56634964011625365908667601578408709687694459838514513263157997369977363075990656, 823818931232857530552332971921635579591067859072976250909883199022356035983086092, 11997699308963154964280843130275294061463096357792403917852111812701414812005490936, 174932450064168269018347363214442324212633030081364377896307113754412094815215503384, 2553504281624246561691067480152199264602819680340100525974352736312361730463065659504, 37315104646157204328336999941558617479257576710969616442036419601784424023613659634704, 545887416640237141109132957003042270457168239883345476947924676346529138573346476705312, 7994305508810343808146107618699014472009382643772204632273034605851049886931269089541984, 117194415752542808554075193101381376854622608233450349138684473195285936241197808865507328, 1719773557060102951512878337819967557540355689532574156318110647856857503784242426585956608, 25261770986755475764003269180603799708045891578990486022366488510538880900966733113482500608, 371428173496839552064039416273864941709920223507336778830440251860283101431737907899040971264, 5466320373191917897391429134978813557719743831463363413567518014350663852698349765602628400128, 80522172989847776031563704838745350633793312205518120600620492104226498338832824107187858630656, 1187209406159098387369096647625413273476968422796359061011962682923486783644754253513200498200576, 17519518380091590622797865397054913452571372762744217806224022352009530087220096395347383754469376, 258756824968960671989385416594602845076527743498347788611268415675063877237023213126670287401261056, 3824972913753427464348943615651025680974059937367212765968498770458313896579028219834569676969958736, 56587974148130931799463229388044887676974567583061353485385183696975926996507415151744128192253053216, 837860526911583684795540253616033044462350957776733238916756885331423352559785554642224159407468861856, 12415491425774912921818561551712152901860984373230486000363109734402277040758225591385499620730912929856, 184116925796590523778443139490136323786836501542973241873759790562903603761758069990775456442511819212096, 2732463436354077745057143354171418505402873070359457403918415905809591525436483678854886499535444035558016, 40582544781527006565651633083198385090545971207546357947430601121343380949971200970810483609084087015573376, 603173273162854339822566412441941235050530551864851734059039567852372982050992853961170036242075999045116416
Specification 1
Strategy pack name: all_the_strategies_1_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23953/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[4,x]*F[8,x,k[0]]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,k[0],1]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[18,x,k[1],k[0]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[4,x]
F[15,x,k[0],k[1]] = 1/(-1+k[0])*(F[13,x,k[0],k[1]]*k[0]-F[13,x,1,k[1]])
F[16,x,k[0],k[1]] = F[10,x,k[0]]*F[17,x,k[0],k[1]]
F[17,x,k[0],k[1]] = (F[12,x,k[0],1]*k[0]-F[12,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[18,x,k[0],k[1]] = F[10,x,k[0]]*F[19,x,k[1],k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1],1]
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[1]*k[2]]
F[21,x,k[0],k[1],k[2]] = F[1,x]+F[22,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]+F[27,x,k[1],k[0],k[2]]+F[29,x,k[2],k[0],k[1]]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[1],k[2]]*F[4,x]
F[23,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[21,x,k[0],k[1],k[2]]*k[0]-F[21,x,1,k[1],k[2]])
F[24,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[25,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = (F[26,x,k[0],1,k[2]]*k[0]-F[26,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[28,x,k[1],k[0],k[2]]
F[28,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1],1]*k[1]-F[20,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[29,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[21,x,k[1],k[2],k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = \frac{y_{0} F_{6}\! \left(x , y_{0}\right)-F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = y_{0} x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}, 1\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{13}\! \left(x , y_{0}, y_{1}\right)-F_{13}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{12}\! \left(x , y_{0}, 1\right)-y_{1} F_{12}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{1}, y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}, 1\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{29}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{21}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\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_{26}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{20}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{20}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{21}\! \left(x , y_{1}, y_{2}, 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_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_4(x)*F_8(x, k_0))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, k_0, 1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_16(x, k_0, k_1) + F_18(x, k_1, k_0))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_4(x))
Eq(F_15(x, k_0, k_1), (k_0*F_13(x, k_0, k_1) - F_13(x, 1, k_1))/(k_0 - 1))
Eq(F_16(x, k_0, k_1), F_10(x, k_0)*F_17(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), (-k_0*F_12(x, k_0, 1) + k_1*F_12(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1), F_10(x, k_0)*F_19(x, k_1, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1, 1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_1*k_2))
Eq(F_21(x, k_0, k_1, k_2), F_1(x) + F_22(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2) + F_27(x, k_1, k_0, k_2) + F_29(x, k_2, k_0, k_1))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_1, k_2)*F_4(x))
Eq(F_23(x, k_0, k_1, k_2), (k_0*F_21(x, k_0, k_1, k_2) - F_21(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_24(x, k_0, k_1, k_2), F_10(x, k_0)*F_25(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_26(x, k_0, 1, k_2) + k_1*F_26(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_10(x, k_0)*F_28(x, k_1, k_0, k_2))
Eq(F_28(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1, 1) + k_2*F_20(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_29(x, k_0, k_1, k_2), F_10(x, k_0)*F_21(x, k_1, k_2, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 1, "strategy_class": "RequirementInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "ignore_parent": false, "strategy_class": "AllPlacementsFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "all_the_strategies_1_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 4], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 4], [0, 2]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 3, "strategy_class": "FusionStrategy", "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "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": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], 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"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: row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23954/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[17,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
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[18,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[11,x,k[0],k[1]]*k[0]-F[11,x,1,k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[17,x,k[0]]
F[15,x,k[0],k[1]] = (F[16,x,k[0],1]*k[0]-F[16,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[16,x,k[0],k[1]] = F[11,x,k[0],k[0]*k[1]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[17,x,k[1]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],1,k[1]]
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1]*k[2],k[2]]
F[21,x,k[0],k[1],k[2]] = F[1,x]+F[22,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]+F[27,x,k[0],k[1],k[2]]+F[30,x,k[0],k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[1],k[2]]*F[7,x]
F[23,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[21,x,k[0],k[1],k[2]]*k[0]-F[21,x,1,k[1],k[2]])
F[24,x,k[0],k[1],k[2]] = F[17,x,k[0]]*F[25,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = (F[26,x,k[0],1,k[2]]*k[0]-F[26,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[17,x,k[1]]*F[28,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = (F[29,x,k[0],k[1],1]*k[1]-F[29,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[29,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[1]*k[2]]
F[30,x,k[0],k[1],k[2]] = F[17,x,k[2]]*F[21,x,k[0],k[1],k[2]]
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{11}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{17}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{16}\! \left(x , y_{0}, 1\right)-y_{1} F_{16}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{17}\! \left(x , y_{0}\right) = y_{0} x
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, 1, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}\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_{26}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{29}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{29}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{2}\right) F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\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_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_17(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
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_18(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), (k_0*F_11(x, k_0, k_1) - F_11(x, 1, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_17(x, k_0))
Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, k_0, 1) + k_1*F_16(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1), F_11(x, k_0, k_0*k_1))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_17(x, k_1)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, 1, k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1*k_2, k_2))
Eq(F_21(x, k_0, k_1, k_2), F_1(x) + F_22(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2) + F_27(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, k_2))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_1, k_2)*F_7(x))
Eq(F_23(x, k_0, k_1, k_2), (k_0*F_21(x, k_0, k_1, k_2) - F_21(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_24(x, k_0, k_1, k_2), F_17(x, k_0)*F_25(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_26(x, k_0, 1, k_2) + k_1*F_26(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_17(x, k_1)*F_28(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), (-k_1*F_29(x, k_0, k_1, 1) + k_2*F_29(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_29(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_1*k_2))
Eq(F_30(x, k_0, k_1, k_2), F_17(x, k_2)*F_21(x, k_0, k_1, k_2))
Pack JSON:
{"expansion_strats": [[{"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": "row_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "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, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, 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0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [3, 0]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[3, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 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[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [4, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 2, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"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 3
Strategy pack name: row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23955/
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[9,x]
F[3,x] = F[1,x]+F[33,x]+F[4,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[6,x,k[0]]*F[9,x]
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]*F[20,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0],1]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[21,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],1,k[1]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[9,x]
F[16,x,k[0],k[1],k[2]] = 1/(k[0]*k[1]-1)*(F[17,x,k[0],k[1],k[2]]*k[0]*k[1]-F[17,x,1/k[1],k[1],k[2]])
F[17,x,k[0],k[1],k[2]] = F[13,x,k[0]*k[1],k[1]*k[2]]
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]*F[20,x,k[0]]
F[19,x,k[0],k[1]] = (F[12,x,k[0],1]*k[0]-F[12,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0]] = k[0]*x
F[21,x,k[0],k[1]] = F[20,x,k[1]]*F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1],1]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[1],k[1]*k[2]]
F[24,x,k[0],k[1],k[2]] = F[1,x]+F[25,x,k[0],k[1],k[2]]+F[27,x,k[0],k[1],k[2]]+F[30,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[2]]*F[9,x]
F[26,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[24,x,k[0],k[1],k[2]]*k[0]-F[24,x,1,k[1],k[2]])
F[27,x,k[0],k[1],k[2]] = F[20,x,k[0]]*F[28,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = (F[29,x,k[0],1,k[2]]*k[0]-F[29,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[29,x,k[0],k[1],k[2]] = F[24,x,k[0],k[0]*k[1],k[2]]
F[30,x,k[0],k[1],k[2]] = F[20,x,k[1]]*F[31,x,k[0],k[1],k[2]]
F[31,x,k[0],k[1],k[2]] = (F[23,x,k[0],k[1],1]*k[1]-F[23,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[32,x,k[0],k[1],k[2]] = F[20,x,k[2]]*F[24,x,k[0],k[1],k[2]]
F[33,x] = F[34,x]*F[9,x]
F[34,x] = F[11,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}, 1\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, 1, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{17}\! \left(x , \frac{1}{y_{1}}, y_{1}, y_{2}\right)}{y_{0} y_{1}-1}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0}, y_{1}\right) F_{20}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{12}\! \left(x , y_{0}, 1\right)-y_{1} F_{12}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}\right) = y_{0} x
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{1}\right) F_{22}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}, 1\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{29}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{29}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{1}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{23}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{23}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{2}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{9}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \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)*F_9(x))
Eq(F_3(x), F_1(x) + F_33(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_6(x, k_0)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_20(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0, 1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_18(x, k_0, k_1) + F_21(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, 1, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_9(x))
Eq(F_16(x, k_0, k_1, k_2), (k_0*k_1*F_17(x, k_0, k_1, k_2) - F_17(x, 1/k_1, k_1, k_2))/(k_0*k_1 - 1))
Eq(F_17(x, k_0, k_1, k_2), F_13(x, k_0*k_1, k_1*k_2))
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1)*F_20(x, k_0))
Eq(F_19(x, k_0, k_1), (-k_0*F_12(x, k_0, 1) + k_1*F_12(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0, k_1), F_20(x, k_1)*F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1, 1))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_1, k_1*k_2))
Eq(F_24(x, k_0, k_1, k_2), F_1(x) + F_25(x, k_0, k_1, k_2) + F_27(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_2)*F_9(x))
Eq(F_26(x, k_0, k_1, k_2), (k_0*F_24(x, k_0, k_1, k_2) - F_24(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_27(x, k_0, k_1, k_2), F_20(x, k_0)*F_28(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), (-k_0*F_29(x, k_0, 1, k_2) + k_1*F_29(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_29(x, k_0, k_1, k_2), F_24(x, k_0, k_0*k_1, k_2))
Eq(F_30(x, k_0, k_1, k_2), F_20(x, k_1)*F_31(x, k_0, k_1, k_2))
Eq(F_31(x, k_0, k_1, k_2), (-k_1*F_23(x, k_0, k_1, 1) + k_2*F_23(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_32(x, k_0, k_1, k_2), F_20(x, k_2)*F_24(x, k_0, k_1, k_2))
Eq(F_33(x), F_34(x)*F_9(x))
Eq(F_34(x), F_11(x, 1))
Pack JSON:
{"expansion_strats": [[{"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": "row_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 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2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [4, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[4, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[5, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[5, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [4, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [5, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [3, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [3, 1], [5, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [4, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [3, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [3, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [4, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [3, 1], [5, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [1, 1], [4, 1], [5, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [1, 1], [3, 1], [4, 1], [5, 1]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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 4
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23956/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[4,x]*F[8,x,k[0]]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[4,x]
F[15,x,k[0],k[1]] = 1/(-1+k[0])*(F[13,x,k[0],k[1]]*k[0]-F[13,x,1,k[1]])
F[16,x,k[0],k[1]] = F[10,x,k[0]]*F[17,x,k[0],k[1]]
F[17,x,k[0],k[1]] = (F[18,x,k[0],1]*k[0]-F[18,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[18,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[19,x,k[0],k[1]] = F[10,x,k[0]]*F[20,x,k[1],k[0]]
F[20,x,k[0],k[1]] = F[21,x,k[0],1,k[1]]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0],k[1]*k[2],k[2]]
F[22,x,k[0],k[1],k[2]] = F[1,x]+F[23,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1],k[2]]+F[28,x,k[1],k[0],k[2]]+F[31,x,k[2],k[0],k[1]]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[1],k[2]]*F[4,x]
F[24,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[22,x,k[0],k[1],k[2]]*k[0]-F[22,x,1,k[1],k[2]])
F[25,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[26,x,k[0],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = (F[27,x,k[0],1,k[2]]*k[0]-F[27,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[27,x,k[0],k[1],k[2]] = F[22,x,k[0],k[0]*k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[29,x,k[1],k[0],k[2]]
F[29,x,k[0],k[1],k[2]] = (F[30,x,k[0],k[1],1]*k[1]-F[30,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[30,x,k[0],k[1],k[2]] = F[22,x,k[0],k[1],k[1]*k[2]]
F[31,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[22,x,k[1],k[2],k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{6}\! \left(x , y_{0}\right)+F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = y_{0} x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , 1, y_{0}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}, y_{0}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{13}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{18}\! \left(x , y_{0}, 1\right)-y_{1} F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{1}, y_{0}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, 1, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{31}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{27}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{27}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{30}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{30}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{2}, 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_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_4(x)*F_8(x, k_0))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x, k_0))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_16(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_4(x))
Eq(F_15(x, k_0, k_1), (k_0*F_13(x, k_0, k_1) - F_13(x, 1, k_1))/(k_0 - 1))
Eq(F_16(x, k_0, k_1), F_10(x, k_0)*F_17(x, k_0, k_1))
Eq(F_17(x, k_0, k_1), (-k_0*F_18(x, k_0, 1) + k_1*F_18(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_19(x, k_0, k_1), F_10(x, k_0)*F_20(x, k_1, k_0))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, 1, k_1))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0, k_1*k_2, k_2))
Eq(F_22(x, k_0, k_1, k_2), F_1(x) + F_23(x, k_0, k_1, k_2) + F_25(x, k_0, k_1, k_2) + F_28(x, k_1, k_0, k_2) + F_31(x, k_2, k_0, k_1))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_1, k_2)*F_4(x))
Eq(F_24(x, k_0, k_1, k_2), (k_0*F_22(x, k_0, k_1, k_2) - F_22(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_25(x, k_0, k_1, k_2), F_10(x, k_0)*F_26(x, k_0, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), (-k_0*F_27(x, k_0, 1, k_2) + k_1*F_27(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1, k_2), F_22(x, k_0, k_0*k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_10(x, k_0)*F_29(x, k_1, k_0, k_2))
Eq(F_29(x, k_0, k_1, k_2), (-k_1*F_30(x, k_0, k_1, 1) + k_2*F_30(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_30(x, k_0, k_1, k_2), F_22(x, k_0, k_1, k_1*k_2))
Eq(F_31(x, k_0, k_1, k_2), F_10(x, k_0)*F_22(x, k_1, k_2, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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, 2, 4, 3], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"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]]}]}], "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": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, 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{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [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": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [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": 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"}}]}
Specification 5
Strategy pack name: row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23957/
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[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[18,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[9,x,k[0]]
F[16,x,k[0],k[1]] = (F[17,x,k[0],1]*k[0]-F[17,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[1],k[0]]*F[9,x,k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],1,k[1]]
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1]*k[2],k[2]]
F[21,x,k[0],k[1],k[2]] = F[1,x]+F[22,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]+F[27,x,k[1],k[0],k[2]]+F[30,x,k[2],k[0],k[1]]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[1],k[2]]*F[3,x]
F[23,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[21,x,k[0],k[1],k[2]]*k[0]-F[21,x,1,k[1],k[2]])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]*F[9,x,k[0]]
F[25,x,k[0],k[1],k[2]] = (F[26,x,k[0],1,k[2]]*k[0]-F[26,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[1],k[0],k[2]]*F[9,x,k[0]]
F[28,x,k[0],k[1],k[2]] = (F[29,x,k[0],k[1],1]*k[1]-F[29,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[29,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[1]*k[2]]
F[30,x,k[0],k[1],k[2]] = F[21,x,k[1],k[2],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_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{17}\! \left(x , y_{0}, 1\right)-y_{1} F_{17}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, 1, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{30}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{26}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{29}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{29}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{9}\! \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)*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_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_18(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_12(x, k_0, k_1) - F_12(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_9(x, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0, 1) + k_1*F_17(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_1, k_0)*F_9(x, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, 1, k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1*k_2, k_2))
Eq(F_21(x, k_0, k_1, k_2), F_1(x) + F_22(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2) + F_27(x, k_1, k_0, k_2) + F_30(x, k_2, k_0, k_1))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_1, k_2)*F_3(x))
Eq(F_23(x, k_0, k_1, k_2), (k_0*F_21(x, k_0, k_1, k_2) - F_21(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2)*F_9(x, k_0))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_26(x, k_0, 1, k_2) + k_1*F_26(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_1, k_0, k_2)*F_9(x, k_0))
Eq(F_28(x, k_0, k_1, k_2), (-k_1*F_29(x, k_0, k_1, 1) + k_2*F_29(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_29(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_1*k_2))
Eq(F_30(x, k_0, k_1, k_2), F_21(x, k_1, k_2, 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_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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