0132_0213_0321
Counting sequence:
1, 1, 2, 6, 21, 79, 310, 1251, 5150, 21517, 90921, 387595, 1663936, 7183750, 31158310, 135661904, 592558096, 2595232344, 11392504426, 50109205789, 220777103354, 974162444028, 4303957562319, 19036842605855, 84285643628790, 373502845338552, 1656428550764640, 7351106011540209, 32643855249507805, 145040974005303590, 644756480385363800, 2867442403207032074, 12757585143032068182, 56780610004782571243, 252798432449723547544, 1125843555685097572217, 5015325404095559202548, 22347395143382248367695, 99598284248651168753584, 443982013127877605506147, 1979519308346532905984901, 8827302227974854711515881, 39369858650227527845883378, 175615012892661627796131637, 783458875391672965505811358, 3495609284854653450577518243, 15598306151970705636710473030, 69610702701262572930242668697, 310681295389380234925043627878, 1386728712301161960573947374434, 6190166029373744732373971697006, 27634067043313137021192439931503, 123371996584352526991153923424297, 550827253340411737104334312407403, 2459457014511099806791429799028545, 10982119437623379765887688782143966, 49040452750976218070516617613158297, 218999223271877657741353100032153959, 978022876699353645477012485745401680, 4367897556652838639626552729913318200, 19507949775469229494935893182644904656, 87129541176056788381026188909976316233, 389164114678586336259516607579816690990, 1738251994459855933913907704023744449462, 7764337044905207069031902151127909529130, 34682219900748563032070821593895685351992, 154924282707720826777065139321457056145322, 692056401804988484028609491549160101806613, 3091521139767007058307640919370924191478726, 13810553258638990587368903973375527113952374, 61696069484627541434627538562216989191590087, 275620146278122693621351159475764365447788641, 1231320128199939879625283771254250636864728894, 5500942536106913026600246721347365010192370208, 24575871667115665540967499563089899407855904803, 109795883815781868698768547506704733138356623378, 490532892856913145753601607301275664831341284874, 2191567358023519366222677755179924713119987097460, 9791423051112751052815613506561543987618764367388, 43746249133024056879608996100335841127051041782843, 195451755308168291115330061325426988558142982570639, 873256496412272243684930788933118734379106841650060, 3901641301200802794721636911793272203523213367921764, 17432348637000873621918523080864233555904493341438982, 77887419082016879037512896757019437226036962371241661, 348001713714622809515637619253324899756840892299595233, 1554883793028262587834088602445723132671536947465893323, 6947312152922970713205705437363779252314513014257494107, 31041154022378378008427870792223939208953970204765953883, 138695040914998853438238787021631009834697947326539280358, 619706289097418536824498639185751770008282629351933198593, 2768934275912563561260702901094479029417811163332400548104, 12372032417567414152686208276677635912169369939536643882684, 55280377761718696904529374392071881138063236359854605040104, 247003101107662074240247331973465550920837058006978082332295, 1103659654794771255315055301483824402526495672688269582174676, 4931388270973249899374304451142956840201217483170764556885906, 22034561764327383591018301631077477281607719795055398133277809, 98455673944489752692961077404928072615967098616507177038305857, 439924472972739797865296396662809061939537640582153979928691624, 1965696526333772011050841054568470816439336445809085990770382408
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/248/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[9,x,1,k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0],k[0]*k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[1]]+F[18,x,k[0],k[1]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]+F[16,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[15,x]
F[14,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[15,x] = x
F[16,x,k[0]] = F[11,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[19,x,k[0]]+F[21,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[11,x,k[0]]*F[17,x,k[0]]
F[21,x,k[0],k[1]] = F[15,x]*F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = -k[0]*(F[18,x,1,k[1]]-F[18,x,k[0],k[1]])/(-1+k[0])
F[23,x,k[0],k[1]] = F[17,x,k[1]]*F[18,x,k[0],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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , 1, y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y , y z \right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x \right)
F_{14}\! \left(x , y\right) = \frac{y F_{8}\! \left(x , y\right)-F_{8}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x \right) = x
F_{16}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{21}\! \left(x , y , z\right) = F_{15}\! \left(x \right) F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = -\frac{y \left(F_{18}\! \left(x , 1, z\right)-F_{18}\! \left(x , y , z\right)\right)}{-1+y}
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , z\right) F_{18}\! \left(x , y , z\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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_15(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_9(x, 1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0, k_0*k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_1) + F_18(x, k_0, k_1))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0) + F_16(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_15(x))
Eq(F_14(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_15(x), x)
Eq(F_16(x, k_0), F_11(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_19(x, k_0) + F_21(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_11(x, k_0)*F_17(x, k_0))
Eq(F_21(x, k_0, k_1), F_15(x)*F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), -F_18(x, 1, k_1) + (k_0*F_18(x, k_0, k_1) - F_18(x, 1, k_1))/(k_0 - 1))
Eq(F_23(x, k_0, k_1), F_17(x, k_1)*F_18(x, k_0, 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": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 2]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, 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2]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}]}]}
Specification 2
Strategy pack name: point_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/249/
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[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = F[9,x,k[1],k[0]]
F[9,x,k[0],k[1]] = F[10,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[10,x,k[0],k[0]*k[1]]
F[11,x,k[0],k[1]] = F[12,x,k[0]]+F[30,x,k[0],k[1]]
F[12,x,k[0]] = F[13,x]+F[14,x,k[0]]+F[28,x,k[0]]
F[13,x] = 0
F[14,x,k[0]] = F[15,x,k[0]]*F[3,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,1,k[0]]
F[17,x,k[0],k[1]] = k[1]*(F[18,x,k[0],1]-F[18,x,k[0],k[1]/k[0]])/(-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[12,x,k[1]]+F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0]*k[1],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[1],k[0]]
F[23,x,k[0],k[1]] = F[24,x,k[1],k[0]]*F[27,x,k[0]]
F[24,x,k[0],k[1]] = F[10,x,k[0],k[1]]+F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]*F[3,x]
F[26,x,k[0],k[1]] = -k[0]*(F[24,x,1,k[1]]-F[24,x,k[0],k[1]])/(-1+k[0])
F[27,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[27,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[30,x,k[0],k[1]] = F[22,x,k[0],k[0]*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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , 1, y\right)
F_{8}\! \left(x , y , z\right) = F_{9}\! \left(x , z , y\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{10}\! \left(x , y , y z \right)
F_{11}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right)+F_{30}\! \left(x , y , z\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , 1, y\right)
F_{17}\! \left(x , y , z\right) = \frac{z \left(F_{18}\! \left(x , y , 1\right)-F_{18}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y , y z \right)
F_{20}\! \left(x , y , z\right) = F_{19}\! \left(x , y z , z\right)
F_{20}\! \left(x , y , z\right) = F_{12}\! \left(x , z\right)+F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y z , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , z , y\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , z , y\right) F_{27}\! \left(x , y\right)
F_{24}\! \left(x , y , z\right) = F_{10}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y , z\right) = -\frac{y \left(F_{24}\! \left(x , 1, z\right)-F_{24}\! \left(x , y , z\right)\right)}{-1+y}
F_{27}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{30}\! \left(x , y , z\right) = F_{22}\! \left(x , y , y z \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_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), F_9(x, k_1, k_0))
Eq(F_9(x, k_0, k_1), F_10(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_10(x, k_0, k_0*k_1))
Eq(F_11(x, k_0, k_1), F_12(x, k_0) + F_30(x, k_0, k_1))
Eq(F_12(x, k_0), F_13(x) + F_14(x, k_0) + F_28(x, k_0))
Eq(F_13(x), 0)
Eq(F_14(x, k_0), F_15(x, k_0)*F_3(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, 1, k_0))
Eq(F_17(x, k_0, k_1), -F_18(x, k_0, 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_12(x, k_1) + F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0*k_1, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, k_1, k_0)*F_27(x, k_0))
Eq(F_24(x, k_0, k_1), F_10(x, k_0, k_1) + F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1)*F_3(x))
Eq(F_26(x, k_0, k_1), -F_24(x, 1, k_1) + (k_0*F_24(x, k_0, k_1) - F_24(x, 1, k_1))/(k_0 - 1))
Eq(F_27(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_27(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_30(x, k_0, k_1), F_22(x, k_0, k_0*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}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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": [[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, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, 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{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "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, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"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, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}, "rule_class": "ReverseRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"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, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: insertion_row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/250/
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[9,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]^2*F[9,x]
F[8,x] = F[1,x]+F[6,x]
F[9,x] = x
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = F[13,x]+F[79,x]
F[13,x] = F[14,x]*F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[9,x]
F[17,x] = F[15,x]+F[18,x]
F[18,x] = F[19,x,1]
F[19,x,k[0]] = F[2,x]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[26,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[27,x,k[0]]
F[23,x,k[0]] = F[2,x]*F[24,x,k[0]]
F[24,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[28,x,k[0]]+F[5,x]
F[28,x,k[0]] = F[29,x,k[0]]+F[35,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[26,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = F[24,x,k[0]]*F[6,x]
F[33,x,k[0]] = F[34,x,k[0]]*F[8,x]
F[34,x,k[0]] = F[29,x,k[0]]+F[6,x]
F[35,x,k[0]] = F[36,x]+F[37,x,k[0]]+F[77,x,k[0]]
F[36,x] = 0
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = -k[0]*(F[39,x,1]-F[39,x,k[0]])/(-1+k[0])
F[39,x,k[0]] = F[40,x,k[0]]*F[9,x]
F[40,x,k[0]] = F[41,x,k[0]]+F[43,x,k[0]]
F[41,x,k[0]] = F[17,x]*F[42,x,k[0]]
F[42,x,k[0]] = F[25,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[53,x,k[0]]
F[44,x,k[0]] = F[15,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[36,x]+F[46,x,k[0]]+F[48,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[9,x]
F[47,x,k[0]] = F[42,x,k[0]]+F[45,x,k[0]]
F[48,x,k[0]] = F[26,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = F[45,x,k[0]]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[52,x]*F[9,x]
F[52,x] = F[1,x]+F[51,x]
F[53,x,k[0]] = F[54,x,k[0],1]
F[54,x,k[0],k[1]] = F[35,x,k[0]]+F[55,x,k[0],k[1]]
F[55,x,k[0],k[1]] = F[36,x]+F[56,x,k[0],k[1]]+F[68,x,k[0],k[1]]
F[56,x,k[0],k[1]] = F[57,x,k[0],k[1]]*F[9,x]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]+F[64,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[42,x,k[0]]*F[59,x,k[1]]
F[59,x,k[0]] = F[60,x,k[0]]+F[63,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]*F[9,x]
F[62,x,k[0]] = F[42,x,k[0]]+F[60,x,k[0]]
F[63,x,k[0]] = -k[0]*(F[20,x,1]-F[20,x,k[0]])/(-1+k[0])
F[64,x,k[0],k[1]] = F[65,x,k[0],k[1]]+F[67,x,k[0],k[1]]
F[65,x,k[0],k[1]] = F[66,x,k[0],k[1]]
F[66,x,k[0],k[1]] = F[15,x]*F[42,x,k[1]]*F[45,x,k[0]]
F[67,x,k[0],k[1]] = -k[1]*(F[55,x,k[0],1]-F[55,x,k[0],k[1]])/(-1+k[1])
F[68,x,k[0],k[1]] = F[26,x,k[0]]*F[69,x,k[0],k[1]]
F[69,x,k[0],k[1]] = F[55,x,k[0],k[1]]+F[70,x,k[1]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]*F[9,x]
F[72,x,k[0]] = F[59,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[76,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[15,x]*F[42,x,k[0]]*F[50,x]
F[76,x,k[0]] = -k[0]*(F[70,x,1]-F[70,x,k[0]])/(-1+k[0])
F[77,x,k[0]] = F[26,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[10,x]+F[35,x,k[0]]
F[79,x] = F[80,x]+F[84,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[15,x]*F[50,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[10,x]+F[70,x,k[0]]
F[84,x] = F[43,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{79}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x , 1\right)
F_{19}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{y \left(F_{39}\! \left(x , 1\right)-F_{39}\! \left(x , y\right)\right)}{-1+y}
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y , 1\right)
F_{54}\! \left(x , y , z\right) = F_{35}\! \left(x , y\right)+F_{55}\! \left(x , y , z\right)
F_{55}\! \left(x , y , z\right) = F_{36}\! \left(x \right)+F_{56}\! \left(x , y , z\right)+F_{68}\! \left(x , y , z\right)
F_{56}\! \left(x , y , z\right) = F_{57}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{57}\! \left(x , y , z\right) = F_{58}\! \left(x , y , z\right)+F_{64}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{42}\! \left(x , y\right) F_{59}\! \left(x , z\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{62}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = -\frac{y \left(F_{20}\! \left(x , 1\right)-F_{20}\! \left(x , y\right)\right)}{-1+y}
F_{64}\! \left(x , y , z\right) = F_{65}\! \left(x , y , z\right)+F_{67}\! \left(x , y , z\right)
F_{65}\! \left(x , y , z\right) = F_{66}\! \left(x , y , z\right)
F_{66}\! \left(x , y , z\right) = F_{15}\! \left(x \right) F_{42}\! \left(x , z\right) F_{45}\! \left(x , y\right)
F_{67}\! \left(x , y , z\right) = -\frac{z \left(F_{55}\! \left(x , y , 1\right)-F_{55}\! \left(x , y , z\right)\right)}{-1+z}
F_{68}\! \left(x , y , z\right) = F_{26}\! \left(x , y\right) F_{69}\! \left(x , y , z\right)
F_{69}\! \left(x , y , z\right) = F_{55}\! \left(x , y , z\right)+F_{70}\! \left(x , z\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{42}\! \left(x , y\right) F_{50}\! \left(x \right)
F_{76}\! \left(x , y\right) = -\frac{y \left(F_{70}\! \left(x , 1\right)-F_{70}\! \left(x , y\right)\right)}{-1+y}
F_{77}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{35}\! \left(x , y\right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{15}\! \left(x \right) F_{50}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{70}\! \left(x , y\right)
F_{84}\! \left(x \right) = F_{43}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_9(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_10(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)**2*F_9(x))
Eq(F_8(x), F_1(x) + F_6(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), F_13(x) + F_79(x))
Eq(F_13(x), F_14(x)*F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_9(x))
Eq(F_17(x), F_15(x) + F_18(x))
Eq(F_18(x), F_19(x, 1))
Eq(F_19(x, k_0), F_2(x) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_26(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_27(x, k_0))
Eq(F_23(x, k_0), F_2(x)*F_24(x, k_0))
Eq(F_24(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_28(x, k_0) + F_5(x))
Eq(F_28(x, k_0), F_29(x, k_0) + F_35(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_26(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), F_24(x, k_0)*F_6(x))
Eq(F_33(x, k_0), F_34(x, k_0)*F_8(x))
Eq(F_34(x, k_0), F_29(x, k_0) + F_6(x))
Eq(F_35(x, k_0), F_36(x) + F_37(x, k_0) + F_77(x, k_0))
Eq(F_36(x), 0)
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), -F_39(x, 1) + (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), F_40(x, k_0)*F_9(x))
Eq(F_40(x, k_0), F_41(x, k_0) + F_43(x, k_0))
Eq(F_41(x, k_0), F_17(x)*F_42(x, k_0))
Eq(F_42(x, k_0), F_25(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_53(x, k_0))
Eq(F_44(x, k_0), F_15(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_36(x) + F_46(x, k_0) + F_48(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_9(x))
Eq(F_47(x, k_0), F_42(x, k_0) + F_45(x, k_0))
Eq(F_48(x, k_0), F_26(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), F_45(x, k_0) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x)*F_9(x))
Eq(F_52(x), F_1(x) + F_51(x))
Eq(F_53(x, k_0), F_54(x, k_0, 1))
Eq(F_54(x, k_0, k_1), F_35(x, k_0) + F_55(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), F_36(x) + F_56(x, k_0, k_1) + F_68(x, k_0, k_1))
Eq(F_56(x, k_0, k_1), F_57(x, k_0, k_1)*F_9(x))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1) + F_64(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_42(x, k_0)*F_59(x, k_1))
Eq(F_59(x, k_0), F_60(x, k_0) + F_63(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0)*F_9(x))
Eq(F_62(x, k_0), F_42(x, k_0) + F_60(x, k_0))
Eq(F_63(x, k_0), -F_20(x, 1) + (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0, k_1), F_65(x, k_0, k_1) + F_67(x, k_0, k_1))
Eq(F_65(x, k_0, k_1), F_66(x, k_0, k_1))
Eq(F_66(x, k_0, k_1), F_15(x)*F_42(x, k_1)*F_45(x, k_0))
Eq(F_67(x, k_0, k_1), -F_55(x, k_0, 1) + (k_1*F_55(x, k_0, k_1) - F_55(x, k_0, 1))/(k_1 - 1))
Eq(F_68(x, k_0, k_1), F_26(x, k_0)*F_69(x, k_0, k_1))
Eq(F_69(x, k_0, k_1), F_55(x, k_0, k_1) + F_70(x, k_1))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0)*F_9(x))
Eq(F_72(x, k_0), F_59(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_76(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_15(x)*F_42(x, k_0)*F_50(x))
Eq(F_76(x, k_0), -F_70(x, 1) + (k_0*F_70(x, k_0) - F_70(x, 1))/(k_0 - 1))
Eq(F_77(x, k_0), F_26(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_10(x) + F_35(x, k_0))
Eq(F_79(x), F_80(x) + F_84(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_15(x)*F_50(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_10(x) + F_70(x, k_0))
Eq(F_84(x), F_43(x, 1))
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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 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, 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], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", 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"strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"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": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"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": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"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": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "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], "pos": [[0, 0], [0, 0]]}], "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": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "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", "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": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 4
Strategy pack name: insertion_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/251/
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[9,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]^2*F[9,x]
F[8,x] = F[1,x]+F[6,x]
F[9,x] = x
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = F[13,x]+F[81,x]
F[13,x] = F[14,x]*F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[9,x]
F[17,x] = F[15,x]+F[18,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x,1]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]*F[28,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[29,x,k[0]]
F[25,x,k[0]] = F[2,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[27,x,k[0]] = F[26,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = k[0]*x
F[29,x,k[0]] = F[30,x,k[0]]+F[5,x]
F[30,x,k[0]] = F[31,x,k[0]]+F[37,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[28,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[26,x,k[0]]*F[6,x]
F[35,x,k[0]] = F[36,x,k[0]]*F[8,x]
F[36,x,k[0]] = F[31,x,k[0]]+F[6,x]
F[37,x,k[0]] = F[38,x]+F[39,x,k[0]]+F[79,x,k[0]]
F[38,x] = 0
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = -k[0]*(F[41,x,1]-F[41,x,k[0]])/(-1+k[0])
F[41,x,k[0]] = F[42,x,k[0]]*F[9,x]
F[42,x,k[0]] = F[43,x,k[0]]+F[45,x,k[0]]
F[43,x,k[0]] = F[17,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[27,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]+F[55,x,k[0]]
F[46,x,k[0]] = F[15,x]*F[47,x,k[0]]
F[47,x,k[0]] = F[38,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]*F[9,x]
F[49,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[28,x,k[0]]*F[51,x,k[0]]
F[51,x,k[0]] = F[47,x,k[0]]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]*F[9,x]
F[54,x] = F[1,x]+F[53,x]
F[55,x,k[0]] = F[56,x,k[0],1]
F[56,x,k[0],k[1]] = F[37,x,k[0]]+F[57,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[38,x]+F[58,x,k[0],k[1]]+F[70,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[59,x,k[0],k[1]]*F[9,x]
F[59,x,k[0],k[1]] = F[60,x,k[0],k[1]]+F[66,x,k[0],k[1]]
F[60,x,k[0],k[1]] = F[44,x,k[0]]*F[61,x,k[1]]
F[61,x,k[0]] = F[62,x,k[0]]+F[65,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]*F[9,x]
F[64,x,k[0]] = F[44,x,k[0]]+F[62,x,k[0]]
F[65,x,k[0]] = -k[0]*(F[22,x,1]-F[22,x,k[0]])/(-1+k[0])
F[66,x,k[0],k[1]] = F[67,x,k[0],k[1]]+F[69,x,k[0],k[1]]
F[67,x,k[0],k[1]] = F[68,x,k[0],k[1]]
F[68,x,k[0],k[1]] = F[15,x]*F[44,x,k[1]]*F[47,x,k[0]]
F[69,x,k[0],k[1]] = -k[1]*(F[57,x,k[0],1]-F[57,x,k[0],k[1]])/(-1+k[1])
F[70,x,k[0],k[1]] = F[28,x,k[0]]*F[71,x,k[0],k[1]]
F[71,x,k[0],k[1]] = F[57,x,k[0],k[1]]+F[72,x,k[1]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]*F[9,x]
F[74,x,k[0]] = F[61,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[78,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[15,x]*F[44,x,k[0]]*F[52,x]
F[78,x,k[0]] = -k[0]*(F[72,x,1]-F[72,x,k[0]])/(-1+k[0])
F[79,x,k[0]] = F[28,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[10,x]+F[37,x,k[0]]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[15,x]*F[52,x]
F[84,x] = F[85,x,1]
F[85,x,k[0]] = F[10,x]+F[72,x,k[0]]
F[86,x] = F[45,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{81}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = y x
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{39}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = -\frac{y \left(F_{41}\! \left(x , 1\right)-F_{41}\! \left(x , y\right)\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{17}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{9}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y , 1\right)
F_{56}\! \left(x , y , z\right) = F_{37}\! \left(x , y\right)+F_{57}\! \left(x , y , z\right)
F_{57}\! \left(x , y , z\right) = F_{38}\! \left(x \right)+F_{58}\! \left(x , y , z\right)+F_{70}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{59}\! \left(x , y , z\right) F_{9}\! \left(x \right)
F_{59}\! \left(x , y , z\right) = F_{60}\! \left(x , y , z\right)+F_{66}\! \left(x , y , z\right)
F_{60}\! \left(x , y , z\right) = F_{44}\! \left(x , y\right) F_{61}\! \left(x , z\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{64}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = -\frac{y \left(F_{22}\! \left(x , 1\right)-F_{22}\! \left(x , y\right)\right)}{-1+y}
F_{66}\! \left(x , y , z\right) = F_{67}\! \left(x , y , z\right)+F_{69}\! \left(x , y , z\right)
F_{67}\! \left(x , y , z\right) = F_{68}\! \left(x , y , z\right)
F_{68}\! \left(x , y , z\right) = F_{15}\! \left(x \right) F_{44}\! \left(x , z\right) F_{47}\! \left(x , y\right)
F_{69}\! \left(x , y , z\right) = -\frac{z \left(F_{57}\! \left(x , y , 1\right)-F_{57}\! \left(x , y , z\right)\right)}{-1+z}
F_{70}\! \left(x , y , z\right) = F_{28}\! \left(x , y\right) F_{71}\! \left(x , y , z\right)
F_{71}\! \left(x , y , z\right) = F_{57}\! \left(x , y , z\right)+F_{72}\! \left(x , z\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{44}\! \left(x , y\right) F_{52}\! \left(x \right)
F_{78}\! \left(x , y\right) = -\frac{y \left(F_{72}\! \left(x , 1\right)-F_{72}\! \left(x , y\right)\right)}{-1+y}
F_{79}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{15}\! \left(x \right) F_{52}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{85}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{86}\! \left(x \right) = F_{45}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_9(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_10(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)**2*F_9(x))
Eq(F_8(x), F_1(x) + F_6(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), F_13(x) + F_81(x))
Eq(F_13(x), F_14(x)*F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_9(x))
Eq(F_17(x), F_15(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x, 1))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_28(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_29(x, k_0))
Eq(F_25(x, k_0), F_2(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_27(x, k_0), F_26(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), k_0*x)
Eq(F_29(x, k_0), F_30(x, k_0) + F_5(x))
Eq(F_30(x, k_0), F_31(x, k_0) + F_37(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_28(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_26(x, k_0)*F_6(x))
Eq(F_35(x, k_0), F_36(x, k_0)*F_8(x))
Eq(F_36(x, k_0), F_31(x, k_0) + F_6(x))
Eq(F_37(x, k_0), F_38(x) + F_39(x, k_0) + F_79(x, k_0))
Eq(F_38(x), 0)
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), -F_41(x, 1) + (k_0*F_41(x, k_0) - F_41(x, 1))/(k_0 - 1))
Eq(F_41(x, k_0), F_42(x, k_0)*F_9(x))
Eq(F_42(x, k_0), F_43(x, k_0) + F_45(x, k_0))
Eq(F_43(x, k_0), F_17(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_27(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0) + F_55(x, k_0))
Eq(F_46(x, k_0), F_15(x)*F_47(x, k_0))
Eq(F_47(x, k_0), F_38(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0)*F_9(x))
Eq(F_49(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_28(x, k_0)*F_51(x, k_0))
Eq(F_51(x, k_0), F_47(x, k_0) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)*F_9(x))
Eq(F_54(x), F_1(x) + F_53(x))
Eq(F_55(x, k_0), F_56(x, k_0, 1))
Eq(F_56(x, k_0, k_1), F_37(x, k_0) + F_57(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_38(x) + F_58(x, k_0, k_1) + F_70(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_59(x, k_0, k_1)*F_9(x))
Eq(F_59(x, k_0, k_1), F_60(x, k_0, k_1) + F_66(x, k_0, k_1))
Eq(F_60(x, k_0, k_1), F_44(x, k_0)*F_61(x, k_1))
Eq(F_61(x, k_0), F_62(x, k_0) + F_65(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0)*F_9(x))
Eq(F_64(x, k_0), F_44(x, k_0) + F_62(x, k_0))
Eq(F_65(x, k_0), -F_22(x, 1) + (k_0*F_22(x, k_0) - F_22(x, 1))/(k_0 - 1))
Eq(F_66(x, k_0, k_1), F_67(x, k_0, k_1) + F_69(x, k_0, k_1))
Eq(F_67(x, k_0, k_1), F_68(x, k_0, k_1))
Eq(F_68(x, k_0, k_1), F_15(x)*F_44(x, k_1)*F_47(x, k_0))
Eq(F_69(x, k_0, k_1), -F_57(x, k_0, 1) + (k_1*F_57(x, k_0, k_1) - F_57(x, k_0, 1))/(k_1 - 1))
Eq(F_70(x, k_0, k_1), F_28(x, k_0)*F_71(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), F_57(x, k_0, k_1) + F_72(x, k_1))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0)*F_9(x))
Eq(F_74(x, k_0), F_61(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_78(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_15(x)*F_44(x, k_0)*F_52(x))
Eq(F_78(x, k_0), -F_72(x, 1) + (k_0*F_72(x, k_0) - F_72(x, 1))/(k_0 - 1))
Eq(F_79(x, k_0), F_28(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_10(x) + F_37(x, k_0))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_15(x)*F_52(x))
Eq(F_84(x), F_85(x, 1))
Eq(F_85(x, k_0), F_10(x) + F_72(x, k_0))
Eq(F_86(x), F_45(x, 1))
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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 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, 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], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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"pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], 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"comb_class": {"assumptions": [{"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": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"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": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": 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{"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "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", "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": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 5
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/252/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0],1]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[12,x,k[0]]+F[18,x,k[0],k[1]]
F[12,x,k[0]] = F[0,x]+F[13,x,k[0]]+F[16,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[7,x]
F[15,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[16,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[19,x,k[1]]+F[21,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[7,x]
F[22,x,k[0],k[1]] = -k[1]*(F[18,x,k[0],1]-F[18,x,k[0],k[1]])/(-1+k[1])
F[23,x,k[0],k[1]] = F[17,x,k[0]]*F[18,x,k[0],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_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y , 1\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{12}\! \left(x , y\right)+F_{18}\! \left(x , y , z\right)
F_{12}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{15}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = -\frac{z \left(F_{18}\! \left(x , y , 1\right)-F_{18}\! \left(x , y , z\right)\right)}{-1+z}
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , y\right) F_{18}\! \left(x , y , z\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_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0, 1))
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_12(x, k_0) + F_18(x, k_0, k_1))
Eq(F_12(x, k_0), F_0(x) + F_13(x, k_0) + F_16(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_7(x))
Eq(F_15(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_16(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_19(x, k_1) + F_21(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_7(x))
Eq(F_22(x, k_0, k_1), -F_18(x, k_0, 1) + (k_1*F_18(x, k_0, k_1) - F_18(x, k_0, 1))/(k_1 - 1))
Eq(F_23(x, k_0, k_1), F_17(x, k_0)*F_18(x, k_0, 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}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [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]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 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]]}]]}], 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{"patt": [0, 2, 1], "pos": [[1, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 2], [2, 0], [2, 0]]}], "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], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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], "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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 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, 1], [1, 0]]}, {"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, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 3], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 2], [2, 0], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 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