0123_0213
Counting sequence:
1, 1, 2, 6, 22, 90, 396, 1837, 8864, 44074, 224352, 1163724, 6129840, 32703074, 176351644, 959658200, 5262988330, 29057961666, 161374413196, 900792925199, 5050924332096, 28434661250454, 160644331001476, 910455895039056, 5174722258676440, 29486753617569684, 168411404890025412, 963888354223500966, 5527261077912111036, 31750323052401948174, 182673854776113608008, 1052536026300221907395, 6072650552145496221972, 35079558927078987859060, 202872376907946923495224, 1174484310818072288097962, 6806019488518767818948516, 39475729733837249608891990, 229155518357781690343791436, 1331276658629929310437889345, 7739645350454324687539046258, 45026422630109088100085110386, 262112748036713663282450722804, 1526741252314158348497047261471, 8897808455759368179149740745540, 51883109560899856437474781599872, 302677727592954347348579233807632, 1766581616948274544027916235594418, 10315111766641212897343383403784232, 60254605539426917413587291151120914, 352105266966923254445287461322647216, 2058312783724831099535874233012887309, 12036440465554698818446754757564920484, 70408404828062119243228966300890177920, 411986615788986228289206066421574256648, 2411386502609993181180714628283227789423, 14117866641023300041395815352138059405720, 82676808150745934663613131396154875215602, 484289382995156291722144630193291538220636, 2837444811712657694016182912079749304824129, 16628231946589885018249936229264616849502264, 97466676920740203286057258171929113773444916, 571417093921443411468099005542842444740029444, 3350681109255865322430236826649928554383644209, 19651324702038870640024033233185860180516496466, 115272504144529527108005852846641064677093482506, 676287400371125898301380351454305304192990786240, 3968306861657807930695965265591322080879069019407, 23288658851606100745152136797043056898112166124348, 136692932188627836269870963883458981204257202371810, 802430118582351529177866548732962820794057267962220, 4711132800402850954321628806686078671450459326339820, 27662916102959071294972829433660458095500487262204064, 162451122381752260345688497780077949268704503968259078, 954107689794941802948432082211840203719042994595184568, 5604280895535891235164956566098860559742248295757354836, 32922152021527047386169666928056536350207495001049188448, 193419593389011041255570378157855701602700765445770708076, 1136461810430482532241221791071468559899301223758216082784, 6678049726183053124776201877998896146635325777591323196515, 39244901998415800014305893344200185186580229002604507074446, 230650342044691459907658329026523953975169365542569250541864, 1355691088917338101159033187835701980623856145612917440354872, 7968962173133099207271655120094016942039835304475535780914583, 46846359026716110214312870891812041068455979523012297972964608, 275411267103255850375382490939227925680221466375689898686739400, 1619265778286087649416685781165710058063825450667701502664604264, 9521031255651024804939940717859371611400775250956430562563291209, 55985835245362603296468559590969733854706093675884888087134362754, 329230149213279580832311681494851721447813216005361417182747559284, 1936186991097874645784862154329586127504146977484224067011831997832, 11387287862114040455815900458222975439923046573143050968473963027275, 66975765573338738523094458351725756983719931686165327262753054052044, 393947711907562925219106406320593445570092289733114228373145890515562, 2317299394617760824613529596306333636715421466576375186255796114128004, 13631623459757428955795624949262631369019367630287153899063167713971604, 80192566563765884182522797202716091599428653100025309103099332931606928, 471781610343897842846397548082201856974993379887690947284384470263488914, 2775668276195044665427765556795088985388896145898549551432614436949291940, 16331011992968450265892539628789706894341828888877647111998086151554159131, 96089729033417251072453394452515385696682327504811580193057012333068967056
Specification 1
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/22/
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,1]
F[4,x,k[0]] = F[23,x]*F[5,x,k[0]]
F[5,x,k[0]] = F[1,x]+F[24,x,k[0]]+F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0],1]
F[7,x,k[0],k[1]] = F[8,x,k[0],k[0]*k[1]]
F[8,x,k[0],k[1]] = F[12,x,k[0]]*F[9,x,k[0],k[1]]
F[10,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]
F[10,x,k[0],k[1]] = F[1,x]+F[11,x,k[1],k[0]]+F[13,x,k[0],k[1]]+F[6,x,k[1]]
F[11,x,k[0],k[1]] = F[10,x,k[1],k[0]]*F[12,x,k[1]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1],1]
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0],k[1],k[2]]*F[23,x]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[1],k[0],k[2]]+F[17,x,k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[22,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[15,x,k[1],k[0],k[2]]
F[17,x,k[0],k[1]] = (F[7,x,k[0],1]*k[0]-F[7,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0]*k[1],k[2]]*k[0]-F[19,x,k[1],k[2]])/(k[0]-1)
F[19,x,k[0],k[1]] = (-F[20,x,1,k[1]]*k[1]+F[20,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[21,x,k[0]*k[1],k[1]]
F[21,x,k[0],k[1]] = F[12,x,k[1]]*F[9,x,k[0],k[1]]
F[22,x,k[0],k[1],k[2]] = (F[14,x,k[0],k[1],k[2]]*k[2]-F[14,x,k[0],k[1],1])/(-1+k[2])
F[23,x] = x
F[24,x,k[0]] = (F[4,x,k[0]]*k[0]-F[4,x,1])/(k[0]-1)
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{23}\! \left(x \right) F_{5}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}\right)+F_{6}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}, 1\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{9}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{1}, y_{0}\right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{6}\! \left(x , y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{1}, y_{0}\right) F_{12}\! \left(x , y_{1}\right)
F_{12}\! \left(x , y_{0}\right) = y_{0} x
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}, 1\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{23}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{17}\! \left(x , y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{15}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{7}\! \left(x , y_{0}, 1\right)-y_{1} F_{7}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{19}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}-F_{19}\! \left(x , y_{1}, y_{2}\right)}{y_{0}-1}
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{-y_{1} F_{20}\! \left(x , 1, y_{1}\right)+y_{0} F_{20}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{14}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{23}\! \left(x \right) = x
F_{24}\! \left(x , y_{0}\right) = \frac{y_{0} F_{4}\! \left(x , y_{0}\right)-F_{4}\! \left(x , 1\right)}{y_{0}-1}
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, 1))
Eq(F_4(x, k_0), F_23(x)*F_5(x, k_0))
Eq(F_5(x, k_0), F_1(x) + F_24(x, k_0) + F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0, 1))
Eq(F_7(x, k_0, k_1), F_8(x, k_0, k_0*k_1))
Eq(F_8(x, k_0, k_1), F_12(x, k_0)*F_9(x, k_0, k_1))
Eq(F_10(x, k_0, k_1), F_9(x, k_0*k_1, k_1))
Eq(F_10(x, k_0, k_1), F_1(x) + F_11(x, k_1, k_0) + F_13(x, k_0, k_1) + F_6(x, k_1))
Eq(F_11(x, k_0, k_1), F_10(x, k_1, k_0)*F_12(x, k_1))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1, 1))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0, k_1, k_2)*F_23(x))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_1, k_0, k_2) + F_17(x, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_12(x, k_1)*F_15(x, k_1, k_0, k_2))
Eq(F_17(x, k_0, k_1), (-k_0*F_7(x, k_0, 1) + k_1*F_7(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1, k_2), (-k_0*k_1*F_19(x, k_0*k_1, k_2) + k_1*F_19(x, k_1, k_2))/(-k_0*k_1 + k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0/k_1, k_1) + k_1*F_20(x, 1, k_1))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0*k_1, k_1))
Eq(F_21(x, k_0, k_1), F_12(x, k_1)*F_9(x, k_0, k_1))
Eq(F_22(x, k_0, k_1, k_2), (-k_2*F_14(x, k_0, k_1, k_2) + F_14(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_23(x), x)
Eq(F_24(x, k_0), (-k_0*F_4(x, k_0) + F_4(x, 1))/(1 - 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.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], 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"pos": [[0, 2]]}]}}}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"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": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}, "rule_class": "ReverseRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}
Specification 2
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/23/
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[28,x]*F[4,x]
F[4,x] = F[5,x,1]
F[6,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[6,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[7,x,k[0],k[1]]
F[7,x,k[0],k[1]] = F[10,x,k[0]]*F[8,x,k[0],k[1]]
F[8,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[16,x,k[0],k[1]]+F[7,x,k[0],k[1]]+F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,k[0]]*F[8,x,k[0],k[1]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0],k[1]] = F[10,x,k[1]]*F[12,x,k[0],k[1]]
F[12,x,k[0],k[1]] = (-F[13,x,1,k[1]]*k[1]+F[13,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[15,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[8,x,k[0],k[1]] = (F[15,x,k[0],1]*k[0]-F[15,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]*F[28,x]
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[19,x,k[0],k[0]*k[1]]
F[20,x,k[0],k[1]] = F[19,x,k[0]*k[1],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1],1]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0]*k[1],k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = F[1,x]+F[23,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]+F[7,x,k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[22,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = F[10,x,k[2]]*F[25,x,k[0],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[2]]*k[0]-F[12,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]*F[28,x]
F[27,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],1])/(-1+k[2])
F[28,x] = x
F[29,x,k[0],k[1]] = F[28,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = (F[6,x,k[0],k[1]]*k[1]-F[6,x,k[0],1])/(-1+k[1])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{5}\! \left(x , y_{0}\right)-y_{1} F_{5}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{6}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{0}, y_{1}\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{0}, y_{1}\right)+F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}\right) = y_{0} x
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{1}\right) F_{12}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{13}\! \left(x , 1, y_{1}\right)-y_{0} F_{13}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{15}\! \left(x , y_{0}, 1\right)-y_{1} F_{15}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , y_{0}, y_{1}\right) F_{28}\! \left(x \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_{19}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, y_{1}, 1\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0} y_{1}, y_{1}, 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_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{7}\! \left(x , y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{2}\right) F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{12}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{12}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{28}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{28}\! \left(x \right) = x
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{6}\! \left(x , y_{0}, y_{1}\right)+F_{6}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
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_28(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_6(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_6(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_29(x, k_0, k_1) + F_7(x, k_0, k_1))
Eq(F_7(x, k_0, k_1), F_10(x, k_0)*F_8(x, k_0, k_1))
Eq(F_8(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_16(x, k_0, k_1) + F_7(x, k_0, k_1) + F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, k_0)*F_8(x, k_0, k_1))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0, k_1), F_10(x, k_1)*F_12(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), (-k_0*F_13(x, k_0/k_1, k_1) + k_1*F_13(x, 1, k_1))/(-k_0 + k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_15(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_8(x, k_0, k_1), (-k_0*F_15(x, k_0, 1) + k_1*F_15(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1)*F_28(x))
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_19(x, k_0, k_0*k_1))
Eq(F_20(x, k_0, k_1), F_19(x, k_0*k_1, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1, 1))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0*k_1, k_1, 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_24(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2) + F_7(x, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), F_10(x, k_0)*F_22(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_10(x, k_2)*F_25(x, k_0, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*F_12(x, k_0, k_2) + k_1*F_12(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2)*F_28(x))
Eq(F_27(x, k_0, k_1, k_2), (-k_2*F_22(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_28(x), x)
Eq(F_29(x, k_0, k_1), F_28(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (-k_1*F_6(x, k_0, k_1) + F_6(x, k_0, 1))/(1 - k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
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[1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, 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[0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 4], [0, 2], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 1], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 2], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 4], [0, 2], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 2, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 0], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 3], [0, 1], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 1, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 3
Strategy pack name: row_and_col_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/24/
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,1]
F[3,x,k[0]] = F[24,x]*F[4,x,k[0]]
F[4,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[5,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0],1]
F[6,x,k[0],k[1]] = F[7,x,k[0],k[0]*k[1]]
F[7,x,k[0],k[1]] = F[11,x,k[0]]*F[8,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[8,x,k[0]*k[1],k[1]]
F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[1],k[0]]+F[12,x,k[0],k[1]]+F[5,x,k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[1]]*F[9,x,k[1],k[0]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1],1]
F[13,x,k[0],k[1],k[2]] = F[14,x,k[0],k[1],k[2]]*F[24,x]
F[14,x,k[0],k[1],k[2]] = F[1,x]+F[15,x,k[1],k[0],k[2]]+F[16,x,k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = F[11,x,k[1]]*F[14,x,k[1],k[0],k[2]]
F[16,x,k[0],k[1]] = (F[6,x,k[0],1]*k[0]-F[6,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0]*k[1],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = F[18,x,k[0],k[0]*k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1]/k[2],k[2]]*k[0]*k[1]-F[20,x,k[0],1/k[0],k[2]]*k[2])/(k[0]*k[1]-k[2])
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[22,x,k[0]*k[1],k[2]]*k[1]-F[22,x,k[0],k[2]])/(k[1]-1)
F[22,x,k[0],k[1]] = F[11,x,k[1]]*F[8,x,k[0],k[1]]
F[23,x,k[0],k[1],k[2]] = (F[13,x,k[0],k[1],k[2]]*k[2]-F[13,x,k[0],k[1],1])/(-1+k[2])
F[24,x] = x
F[25,x,k[0]] = (F[3,x,k[0]]*k[0]-F[3,x,1])/(-1+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 , 1\right)
F_{3}\! \left(x , y_{0}\right) = F_{24}\! \left(x \right) F_{4}\! \left(x , y_{0}\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}, 1\right)
F_{6}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{1}, y_{0}\right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{5}\! \left(x , y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{1}, y_{0}\right)
F_{11}\! \left(x , y_{0}\right) = y_{0} x
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{16}\! \left(x , y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{1}\right) F_{14}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{6}\! \left(x , y_{0}, 1\right)-y_{1} F_{6}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right)+y_{2} F_{20}\! \left(x , y_{0}, \frac{1}{y_{0}}, y_{2}\right)}{y_{0} y_{1}-y_{2}}
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) = -\frac{-y_{1} F_{22}\! \left(x , y_{0} y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{2}\right)}{y_{1}-1}
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{1}\right) F_{8}\! \left(x , y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{13}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{24}\! \left(x \right) = x
F_{25}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{3}\! \left(x , y_{0}\right)+F_{3}\! \left(x , 1\right)}{-1+y_{0}}
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, 1))
Eq(F_3(x, k_0), F_24(x)*F_4(x, k_0))
Eq(F_4(x, k_0), F_1(x) + F_25(x, k_0) + F_5(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0, 1))
Eq(F_6(x, k_0, k_1), F_7(x, k_0, k_0*k_1))
Eq(F_7(x, k_0, k_1), F_11(x, k_0)*F_8(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_8(x, k_0*k_1, k_1))
Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_1, k_0) + F_12(x, k_0, k_1) + F_5(x, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_1)*F_9(x, k_1, k_0))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1, 1))
Eq(F_13(x, k_0, k_1, k_2), F_14(x, k_0, k_1, k_2)*F_24(x))
Eq(F_14(x, k_0, k_1, k_2), F_1(x) + F_15(x, k_1, k_0, k_2) + F_16(x, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_11(x, k_1)*F_14(x, k_1, k_0, k_2))
Eq(F_16(x, k_0, k_1), (-k_0*F_6(x, k_0, 1) + k_1*F_6(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0*k_1, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), F_18(x, k_0, k_0*k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*k_1*F_20(x, k_0, k_1/k_2, k_2) + k_2*F_20(x, k_0, 1/k_0, k_2))/(-k_0*k_1 + k_2))
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), (k_0*k_1*F_22(x, k_0*k_1, k_2) - k_0*F_22(x, k_0, k_2))/(k_0*k_1 - k_0))
Eq(F_22(x, k_0, k_1), F_11(x, k_1)*F_8(x, k_0, k_1))
Eq(F_23(x, k_0, k_1, k_2), (-k_2*F_13(x, k_0, k_1, k_2) + F_13(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_24(x), x)
Eq(F_25(x, k_0), (-k_0*F_3(x, k_0) + F_3(x, 1))/(1 - k_0))
Pack JSON:
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Specification JSON:
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"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]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}
Specification 4
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/25/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[26,x]*F[3,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[5,x,k[0]]
F[5,x,k[0]] = F[10,x,k[0]]*F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,1,k[0]]
F[7,x,k[0],k[1]] = F[8,x,k[0],k[1],1]
F[8,x,k[0],k[1],k[2]] = F[1,x]+F[11,x,k[0],k[1],k[2]]+F[5,x,k[1]*k[2]]+F[9,x,k[0],k[1],k[2]]
F[9,x,k[0],k[1],k[2]] = F[10,x,k[1]]*F[8,x,k[0],k[1],k[2]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1],k[2]]*F[26,x]
F[12,x,k[0],k[1],k[2]] = F[13,x,k[0]*k[1],k[1]*k[2]]
F[14,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1],1]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0]*k[1],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[1,x]+F[17,x,k[0],k[1],k[2]]+F[18,x,k[1],k[2]]+F[21,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]
F[17,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[16,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1]] = F[10,x,k[0]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[8,x,1,k[0],k[1]]
F[21,x,k[0],k[1],k[2]] = F[10,x,k[2]]*F[22,x,k[0],k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = (F[23,x,k[0],k[2]]*k[0]-F[23,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]*F[26,x]
F[25,x,k[0],k[1],k[2]] = (F[16,x,k[0],k[1],k[2]]*k[2]-F[16,x,k[0],k[1],1])/(-1+k[2])
F[26,x] = x
F[27,x,k[0]] = F[26,x]*F[28,x,k[0]]
F[28,x,k[0]] = (F[4,x,k[0]]*k[0]-F[4,x,1])/(-1+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_{26}\! \left(x \right) F_{3}\! \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_{27}\! \left(x , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{6}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , 1, y_{0}\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0}, y_{1}, 1\right)
F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{5}\! \left(x , y_{1} y_{2}\right)+F_{9}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{9}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{1}\right) F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{10}\! \left(x , y_{0}\right) = y_{0} x
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{26}\! \left(x \right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}, 1\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{20}\! \left(x , y_{0}, 1\right)-y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , 1, y_{0}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{2}\right) F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{23}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{23}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{7}\! \left(x , 1, y_{1}\right)-y_{0} F_{7}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{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_{26}\! \left(x \right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{26}\! \left(x \right) = x
F_{27}\! \left(x , y_{0}\right) = F_{26}\! \left(x \right) F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
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_26(x)*F_3(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_27(x, k_0) + F_5(x, k_0))
Eq(F_5(x, k_0), F_10(x, k_0)*F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, 1, k_0))
Eq(F_7(x, k_0, k_1), F_8(x, k_0, k_1, 1))
Eq(F_8(x, k_0, k_1, k_2), F_1(x) + F_11(x, k_0, k_1, k_2) + F_5(x, k_1*k_2) + F_9(x, k_0, k_1, k_2))
Eq(F_9(x, k_0, k_1, k_2), F_10(x, k_1)*F_8(x, k_0, k_1, k_2))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_0, k_1, k_2)*F_26(x))
Eq(F_12(x, k_0, k_1, k_2), F_13(x, k_0*k_1, k_1*k_2))
Eq(F_14(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1, 1))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0*k_1, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_1(x) + F_17(x, k_0, k_1, k_2) + F_18(x, k_1, k_2) + F_21(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2))
Eq(F_17(x, k_0, k_1, k_2), F_10(x, k_0)*F_16(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1), F_10(x, k_0)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_8(x, 1, k_0, k_1))
Eq(F_21(x, k_0, k_1, k_2), F_10(x, k_2)*F_22(x, k_0, k_1, k_2))
Eq(F_22(x, k_0, k_1, k_2), (-k_0*F_23(x, k_0, k_2) + k_1*F_23(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2)*F_26(x))
Eq(F_25(x, k_0, k_1, k_2), (-k_2*F_16(x, k_0, k_1, k_2) + F_16(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_26(x), x)
Eq(F_27(x, k_0), F_26(x)*F_28(x, k_0))
Eq(F_28(x, k_0), (-k_0*F_4(x, k_0) + F_4(x, 1))/(1 - k_0))
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", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], 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Specification 5
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/26/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[26,x]*F[3,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[5,x,k[0]]
F[5,x,k[0]] = F[10,x,k[0]]*F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,1,k[0]]
F[7,x,k[0],k[1]] = F[8,x,k[0],k[1],1]
F[8,x,k[0],k[1],k[2]] = F[1,x]+F[11,x,k[0],k[1],k[2]]+F[5,x,k[1]*k[2]]+F[9,x,k[1],k[0],k[2]]
F[9,x,k[0],k[1],k[2]] = F[10,x,k[1]]*F[8,x,k[1],k[0],k[2]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1],k[2]]*F[26,x]
F[12,x,k[0],k[1],k[2]] = F[13,x,k[0]*k[1],k[1]*k[2]]
F[14,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1],1]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0]*k[1],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[1,x]+F[17,x,k[0],k[1],k[2]]+F[18,x,k[1],k[2]]+F[21,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]
F[17,x,k[0],k[1],k[2]] = F[10,x,k[0]]*F[16,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1]] = F[10,x,k[0]]*F[19,x,k[0],k[1]]
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[8,x,1,k[0],k[1]]
F[21,x,k[0],k[1],k[2]] = F[10,x,k[2]]*F[22,x,k[0],k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = (F[23,x,k[0],k[2]]*k[0]-F[23,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]*F[26,x]
F[25,x,k[0],k[1],k[2]] = (F[16,x,k[0],k[1],k[2]]*k[2]-F[16,x,k[0],k[1],1])/(-1+k[2])
F[26,x] = x
F[27,x,k[0]] = F[26,x]*F[28,x,k[0]]
F[28,x,k[0]] = (F[4,x,k[0]]*k[0]-F[4,x,1])/(-1+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_{26}\! \left(x \right) F_{3}\! \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_{27}\! \left(x , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{6}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , 1, y_{0}\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0}, y_{1}, 1\right)
F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{5}\! \left(x , y_{1} y_{2}\right)+F_{9}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{9}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{1}\right) F_{8}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{10}\! \left(x , y_{0}\right) = y_{0} x
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{26}\! \left(x \right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{0}, y_{1}, 1\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}\right) F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{20}\! \left(x , y_{0}, 1\right)-y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , 1, y_{0}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{2}\right) F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{23}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{23}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{7}\! \left(x , 1, y_{1}\right)-y_{0} F_{7}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{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_{26}\! \left(x \right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{26}\! \left(x \right) = x
F_{27}\! \left(x , y_{0}\right) = F_{26}\! \left(x \right) F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
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_26(x)*F_3(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_27(x, k_0) + F_5(x, k_0))
Eq(F_5(x, k_0), F_10(x, k_0)*F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, 1, k_0))
Eq(F_7(x, k_0, k_1), F_8(x, k_0, k_1, 1))
Eq(F_8(x, k_0, k_1, k_2), F_1(x) + F_11(x, k_0, k_1, k_2) + F_5(x, k_1*k_2) + F_9(x, k_1, k_0, k_2))
Eq(F_9(x, k_0, k_1, k_2), F_10(x, k_1)*F_8(x, k_1, k_0, k_2))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_0, k_1, k_2)*F_26(x))
Eq(F_12(x, k_0, k_1, k_2), F_13(x, k_0*k_1, k_1*k_2))
Eq(F_14(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1, 1))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0*k_1, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_1(x) + F_17(x, k_0, k_1, k_2) + F_18(x, k_1, k_2) + F_21(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2))
Eq(F_17(x, k_0, k_1, k_2), F_10(x, k_0)*F_16(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1), F_10(x, k_0)*F_19(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_8(x, 1, k_0, k_1))
Eq(F_21(x, k_0, k_1, k_2), F_10(x, k_2)*F_22(x, k_0, k_1, k_2))
Eq(F_22(x, k_0, k_1, k_2), (-k_0*F_23(x, k_0, k_2) + k_1*F_23(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2)*F_26(x))
Eq(F_25(x, k_0, k_1, k_2), (-k_2*F_16(x, k_0, k_1, k_2) + F_16(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_26(x), x)
Eq(F_27(x, k_0), F_26(x)*F_28(x, k_0))
Eq(F_28(x, k_0), (-k_0*F_4(x, k_0) + F_4(x, 1))/(1 - 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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, 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