02314_02341_03214_03241_03421_30214_30241_30421_34021
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2758, 14110, 72687, 375998, 1950212, 10134024, 52730484, 274647566, 1431611637, 7466906982, 38964752623, 203414137624, 1062281354847, 5549126721642, 28994684041417, 151532627312524, 792092520684134, 4141117956076628, 21653232078212560, 113235882230509216, 592236813901137134, 3097785561739209688, 16204933150179422865, 84777183595919660830, 443550401486916670097, 2320791075067221918148, 12143821660990598370241, 63547502234004267077968, 332554733974781436013550, 1740393059283216108655550, 9108551782599752906429442, 47672453817773750206694184, 249517169109863013796156908, 1306010969256820680596348938, 6836054450035525358717923087, 35782892957644502892892967946, 187307721846489504721307598964, 980494923099548007758655310556, 5132673876467823970606514325196, 26868903045712743286387718956158, 140657696516715928107636962160445, 736349128928809692551805144493994, 3854874383621455034214041233903678, 20180985580480561897365002014485084, 105652494717637259681233401584193895, 553123328477090108533065994512431864, 2895800623770843482472896271868169718, 15160707192702274047555935377719053690, 79373233141315846408600819678354413079, 415558531693566267301305630439189515518, 2175672854024371283734194949542650665581, 11390898941484286128875675277418348222478, 59638292138009525124883553830592520080112, 312244635657338627095684882239328818745276, 1634809580365865201658651231311742240902052, 8559365835277665275141830978112714401828466, 44814449955968315914375971426883840700506548, 234636985675625241261294024486353082593947372, 1228504223284874423010560718967430177388803681, 6432184508127564063723228640703071025079825370, 33677657364983249781163212412286309978001509883, 176330194884069164134075274180644962601190093260, 923236220286402970184784376943795928291488812913, 4833928501834120045415794131505997324315223751486, 25309803112189573084181791639817057481615196393078, 132519072622525177987707357778599735250256406571214, 693855464579885251221414175176397713360833475866966, 3632959645541605288010209481250220007081659458618478, 19021861155468377462652177511540390373766949190894734, 99596999548193401851030814373454180463659910578413774, 521483128985954303545631609338323887486577226920702585, 2730454724797522770880054374842545688564858853971266316, 14296520752049672895760491140751815644138350344602495978, 74855955294986204667404387373912998712878633843788887536, 391943018846944236456413587172397731132754527647089119601, 2052201732713991619558385515319029456271084516073083081914, 10745278390589920959743629901146182152210151404534297272817, 56262077675211392281186194629741637671943227808967471593148, 294587491383838511175519948473973995114810953389348532017147, 1542457660440001561788298166354342817923557799230827190102882, 8076302707229085402704047626971001797547601748296014583276146, 42287526911356370146867555826946999526863619116894861533630290, 221417694922811226216770908500975196071112070224805344956764778, 1159344966880362860011989400674785451632441432520360717860463950, 6070344439826239754589452497000220300074526952421801549413414740, 31784418210784421793643981681220947061920011083134065141261547902, 166423809873227736224588806962352689383239144707590778960727351429, 871398681345047449260983244690465727792731167723674545053140473808, 4562664825633288748709660797916585379548346273456563940809708713119, 23890236561423477256543236187710939717434434434423201585622891661214, 125089983661688483037912748793526898561831182546974196241072698790790, 654975131869908260513039100878281003338658449286813749185646509227166, 3429472020960198364336563456166809038767735190953472181474626625492654, 17956838803867865062307341882479989240601733649275870328145358453033854
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24711/
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[30,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x^2*k[0]^2+4*x*k[0]-1)*F[7,x,k[0]]^2+(4*x^2*k[0]^2-5*x*k[0]+2)*F[7,x,k[0]]+4*k[0]^2*x^2-k[0]*x
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[30,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[26,x,k[0]]*F[31,x]
F[15,x,k[0]] = F[14,x,k[0]]*F[30,x]*F[31,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[34,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[30,x]*F[31,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[27,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[22,x,k[0]]
F[21,x,k[0]] = -2+k[0]^2*x^2+F[21,x,k[0]]^2*(x^2*k[0]^2+4*x*k[0]-1)+(2*x^2*k[0]^2-13*x*k[0]+4)*F[21,x,k[0]]+8*k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]*F[7,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[23,x,k[0]]^2*F[26,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[17,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[7,x,k[0]]
F[29,x,k[0]] = (F[24,x,k[0]]-F[24,x,1])/(-1+k[0])
F[30,x] = x
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]^2*F[30,x]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[23,x,k[0]]*F[26,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[44,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = F[16,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]*F[7,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,1,k[0]]
F[42,x,k[0],k[1]] = (F[43,x,k[0]*k[1]]*k[0]-F[43,x,k[1]])/(-1+k[0])
F[43,x,k[0]] = (F[24,x,k[0]]-F[24,x,1])/(-1+k[0])
F[44,x,k[0]] = F[17,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = 1/(-1+k[0])*(F[23,x,k[0]]*k[0]-F[23,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_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+4 x^{2} F_{7}\! \left(x , y\right) y^{2}+4 y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -5 x F_{7}\! \left(x , y\right) y -y x -F_{7}\! \left(x , y\right)^{2}+2 F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{30}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
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_{26}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{30}\! \left(x \right) F_{31}\! \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 , y\right)+F_{34}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{30}\! \left(x \right) F_{31}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = x^{2} F_{21}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{21}\! \left(x , y\right) y^{2}+y^{2} x^{2}+4 x F_{21}\! \left(x , y\right)^{2} y -13 x F_{21}\! \left(x , y\right) y +8 y x -F_{21}\! \left(x , y\right)^{2}+4 F_{21}\! \left(x , y\right)-2
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{23}\! \left(x , y\right)^{2} F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x \right) = x
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31} \left(x \right)^{2} F_{30}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , 1, y\right)
F_{42}\! \left(x , y , z\right) = -\frac{-F_{43}\! \left(x , y z \right) y +F_{43}\! \left(x , z\right)}{-1+y}
F_{43}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{23}\! \left(x , y\right)+F_{23}\! \left(x , 1\right)}{-1+y}
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_30(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0**2*x**2 + 8*k_0*x + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 + 4*k_0*x - 1) + (F_7(x, k_0) + 1)*(2*k_0**2*x**2 - 13*k_0*x + 3) + F_7(x, k_0) - 2)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_30(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - 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_26(x, k_0)*F_31(x))
Eq(F_15(x, k_0), F_14(x, k_0)*F_30(x)*F_31(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_34(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_30(x)*F_31(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_27(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_22(x, k_0))
Eq(F_21(x, k_0), k_0**2*x**2 + 8*k_0*x + (k_0**2*x**2 + 4*k_0*x - 1)*F_21(x, k_0)**2 + (2*k_0**2*x**2 - 13*k_0*x + 4)*F_21(x, k_0) - 2)
Eq(F_22(x, k_0), F_23(x, k_0)*F_7(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_23(x, k_0)**2*F_26(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_17(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_7(x, k_0))
Eq(F_29(x, k_0), -F_24(x, k_0) + (-k_0*F_24(x, k_0) + F_24(x, 1))/(1 - k_0))
Eq(F_30(x), x)
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_30(x)*F_31(x)**2)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_23(x, k_0)*F_26(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_44(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), F_16(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0)*F_7(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, 1, k_0))
Eq(F_42(x, k_0, k_1), (-k_0*k_1*F_43(x, k_0*k_1) + k_1*F_43(x, k_1))/(-k_0*k_1 + k_1))
Eq(F_43(x, k_0), -F_24(x, k_0) + (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_17(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), (k_0*F_23(x, k_0) - F_23(x, 1))/(k_0 - 1))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0], "pos": [[6, 1]]}, {"patt": [0], "pos": [[6, 2]]}, {"patt": [0], "pos": [[6, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 2]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [4, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [4, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [5, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[6, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 1], [1, 1], 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"pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"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": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", 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0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"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": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 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"tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 4, 0, 2, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 4, 0, 2, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24909/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[26,x]*F[4,x]
F[4,x] = F[1,x]+F[27,x]+F[5,x]
F[5,x] = F[26,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[8,x,k[0]] = F[10,x,k[0]]+F[9,x]
F[9,x] = -2+x^2+8*x+F[9,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[9,x]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[18,x,k[0]]+F[24,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[9,x]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]^2*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[19,x,1,k[0]]
F[19,x,k[0],k[1]] = F[14,x,k[0]]*F[17,x,k[0]]*F[20,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[17,x,k[0]]*F[20,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,k[0]*x,k[1]]
F[8,x,k[0]] = F[14,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[12,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[26,x] = x
F[27,x] = F[26,x]*F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = (F[30,x,k[0]]*k[0]-F[30,x,1])/(-1+k[0])
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]+F[36,x,k[0]]
F[31,x,k[0]] = F[17,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[34,x,k[0]]
F[33,x,k[0]] = (F[14,x,k[0]]*k[0]-F[14,x,1])/(-1+k[0])
F[34,x,k[0]] = F[35,x,k[0],1]
F[35,x,k[0],k[1]] = (F[22,x,k[0],k[1]]*k[0]*k[1]-F[22,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[36,x,k[0]] = F[26,x]*F[29,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{26}\! \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) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x^{2} F_{9} \left(x \right)^{2}+2 x^{2} F_{9}\! \left(x \right)+4 x F_{9} \left(x \right)^{2}+x^{2}-13 x F_{9}\! \left(x \right)-F_{9} \left(x \right)^{2}+8 x +4 F_{9}\! \left(x \right)-2
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , 1, y\right)
F_{19}\! \left(x , y , z\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{20}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{17}\! \left(x , y\right) F_{20}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(y x , z\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{26}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y , 1\right)
F_{35}\! \left(x , y , z\right) = \frac{y z F_{22}\! \left(x , y , z\right)-F_{22}\! \left(x , y , \frac{1}{y}\right)}{y z -1}
F_{36}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{29}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_26(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_27(x) + F_5(x))
Eq(F_5(x), F_26(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_8(x, k_0), F_10(x, k_0) + F_9(x))
Eq(F_9(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_9(x)**2 + (2*x**2 - 13*x + 4)*F_9(x) - 2)
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_18(x, k_0) + F_24(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_9(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)**2*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_19(x, 1, k_0))
Eq(F_19(x, k_0, k_1), F_14(x, k_0)*F_17(x, k_0)*F_20(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_17(x, k_0)*F_20(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(k_0*x, k_1))
Eq(F_8(x, k_0), F_14(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_12(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_26(x), x)
Eq(F_27(x), F_26(x)*F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), (-k_0*F_30(x, k_0) + F_30(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0) + F_36(x, k_0))
Eq(F_31(x, k_0), F_17(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_34(x, k_0))
Eq(F_33(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_35(x, k_0, 1))
Eq(F_35(x, k_0, k_1), (-k_0*k_1*F_22(x, k_0, k_1) + F_22(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_36(x, k_0), F_26(x)*F_29(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false, "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "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]]}, {"patt": [3, 0, 2, 1], "pos": 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[[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25825/
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[31,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x^2*k[0]^2+4*x*k[0]-1)*F[7,x,k[0]]^2+(4*x^2*k[0]^2-5*x*k[0]+2)*F[7,x,k[0]]+4*k[0]^2*x^2-k[0]*x
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[31,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x,k[0]]*F[32,x]
F[15,x,k[0]] = F[14,x,k[0]]*F[31,x]*F[32,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[22,x,k[0]]
F[17,x,k[0]] = (F[18,x,k[0]]-F[18,x,1])/(-1+k[0])
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]^2*F[21,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0],1]
F[23,x,k[0],k[1]] = (F[24,x,k[0],k[1]]-F[24,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[20,x,k[1]]*F[21,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]+F[28,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[24,x,k[0],k[1]]+F[7,x,k[0]]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]*F[7,x,k[0]]
F[29,x,k[0],k[1]] = F[30,k[0]*x,k[1]]
F[30,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[31,x] = x
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[32,x]^2*F[31,x]
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_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+4 x^{2} F_{7}\! \left(x , y\right) y^{2}+4 y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -5 x F_{7}\! \left(x , y\right) y -y x -F_{7}\! \left(x , y\right)^{2}+2 F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
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_{21}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{31}\! \left(x \right) F_{32}\! \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 , y\right)+F_{22}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = -\frac{-F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)^{2} F_{21}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y , 1\right)
F_{23}\! \left(x , y , z\right) = \frac{F_{24}\! \left(x , y , z\right)-F_{24}\! \left(x , y , \frac{1}{y}\right)}{y z -1}
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{21}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right)+F_{7}\! \left(x , y\right)
F_{28}\! \left(x , y , z\right) = F_{29}\! \left(x , y , z\right) F_{7}\! \left(x , y\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(y x , z\right)
F_{30}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x \right) = x
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32} \left(x \right)^{2} F_{31}\! \left(x \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_31(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0**2*x**2 + 8*k_0*x + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 + 4*k_0*x - 1) + (F_7(x, k_0) + 1)*(2*k_0**2*x**2 - 13*k_0*x + 3) + F_7(x, k_0) - 2)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_31(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - 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_21(x, k_0)*F_32(x))
Eq(F_15(x, k_0), F_14(x, k_0)*F_31(x)*F_32(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_22(x, k_0))
Eq(F_17(x, k_0), -F_18(x, k_0) + (-k_0*F_18(x, k_0) + F_18(x, 1))/(1 - k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)**2*F_21(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0, 1))
Eq(F_23(x, k_0, k_1), -F_24(x, k_0, k_1) + (-k_0*k_1*F_24(x, k_0, k_1) + F_24(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_20(x, k_1)*F_21(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1) + F_28(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_24(x, k_0, k_1) + F_7(x, k_0))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1)*F_7(x, k_0))
Eq(F_29(x, k_0, k_1), F_30(k_0*x, k_1))
Eq(F_30(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_31(x), x)
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_31(x)*F_32(x)**2)
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", 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{"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.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25930/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[26,x]*F[4,x]
F[4,x] = F[1,x]+F[27,x]+F[5,x]
F[5,x] = F[26,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[8,x,k[0]] = F[10,x,k[0]]+F[9,x]
F[9,x] = -2+x^2+8*x+F[9,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[9,x]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[17,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[18,x,k[0]]+F[24,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[9,x]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]^2*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[19,x,1,k[0]]
F[19,x,k[0],k[1]] = F[14,x,k[0]]*F[17,x,k[0]]*F[20,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[17,x,k[0]]*F[20,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,k[0]*x,k[1]]
F[8,x,k[0]] = F[14,x,k[0]]+F[23,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[12,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[26,x] = x
F[27,x] = F[26,x]*F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = (F[30,x,k[0]]*k[0]-F[30,x,1])/(-1+k[0])
F[30,x,k[0]] = F[1,x]+F[31,x,k[0]]+F[36,x,k[0]]
F[31,x,k[0]] = F[17,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[34,x,k[0]]
F[33,x,k[0]] = (F[14,x,k[0]]*k[0]-F[14,x,1])/(-1+k[0])
F[34,x,k[0]] = F[35,x,k[0],1]
F[35,x,k[0],k[1]] = (F[22,x,k[0],k[1]]*k[0]*k[1]-F[22,x,k[0],1/k[0]])/(k[0]*k[1]-1)
F[36,x,k[0]] = F[26,x]*F[29,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{26}\! \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) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x^{2} F_{9} \left(x \right)^{2}+2 x^{2} F_{9}\! \left(x \right)+4 x F_{9} \left(x \right)^{2}+x^{2}-13 x F_{9}\! \left(x \right)-F_{9} \left(x \right)^{2}+8 x +4 F_{9}\! \left(x \right)-2
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , 1, y\right)
F_{19}\! \left(x , y , z\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{20}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{17}\! \left(x , y\right) F_{20}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(y x , z\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{26}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y , 1\right)
F_{35}\! \left(x , y , z\right) = \frac{y z F_{22}\! \left(x , y , z\right)-F_{22}\! \left(x , y , \frac{1}{y}\right)}{y z -1}
F_{36}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{29}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_26(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_27(x) + F_5(x))
Eq(F_5(x), F_26(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_8(x, k_0), F_10(x, k_0) + F_9(x))
Eq(F_9(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_9(x)**2 + (2*x**2 - 13*x + 4)*F_9(x) - 2)
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_17(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_18(x, k_0) + F_24(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_9(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)**2*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_19(x, 1, k_0))
Eq(F_19(x, k_0, k_1), F_14(x, k_0)*F_17(x, k_0)*F_20(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_17(x, k_0)*F_20(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(k_0*x, k_1))
Eq(F_8(x, k_0), F_14(x, k_0) + F_23(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_12(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_26(x), x)
Eq(F_27(x), F_26(x)*F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), (-k_0*F_30(x, k_0) + F_30(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_1(x) + F_31(x, k_0) + F_36(x, k_0))
Eq(F_31(x, k_0), F_17(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_34(x, k_0))
Eq(F_33(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_34(x, k_0), F_35(x, k_0, 1))
Eq(F_35(x, k_0, k_1), (-k_0*k_1*F_22(x, k_0, k_1) + F_22(x, k_0, 1/k_0))/(-k_0*k_1 + 1))
Eq(F_36(x, k_0), F_26(x)*F_29(x, k_0))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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