02314_02341_02431_04231_20314_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3122, 17287, 97469, 556360, 3203701, 18567896, 108147601, 632329025, 3708513267, 21803848887, 128454760828, 758056615388, 4479917273112, 26507056694241, 157000275633252, 930732336630252, 5521836792189067, 32781901459963781, 194733552135330690, 1157372792791379091, 6881860116411993540, 40937039867806701123, 243604909753643668717, 1450100718246341306573, 8634525624865016891921, 51427384399207984936750, 306376190133557087415962, 1825620450765629507113528, 10880585909006577274070121, 64859373354356774465396328, 386691913358740579836259058, 2305808475487582980331287451, 13751235734696736308723460181, 82019229664535165734394001608, 489261115669535455932078618685, 2918856836388495098852636883176, 17415195909139864358999690526957, 103916412650552137332946247313909, 620122045686707517261691004093839, 3700877734725304554703030309252679, 22088406205026522162404102032533560, 131842019391500314188196099991542840, 786993369424716521132991587807739608, 4698012525971980413804029863112819977, 28046676227524603344458209596697986960, 167444608497551021403124743755209307508, 999728336040634601623436064210593197583, 5969150722954891126690900962761897848597, 35641957329848608282256931511688969107730, 212827550432004931956379617419913339139507, 1270897060101201425818527100348410389227820, 7589412155074343495872641807333475522809559, 45323163500515482594049981601898141889731481, 270673507173735049296106358941070394658966121, 1616530664505768454392494206528624422741824609, 9654595136076465205901800532153234131570458250, 57662758967441764138183489653010979387119367614, 344403343807448677047511987057198818387922970648, 2057071041488737435509498510265371778603450323329, 12286852677778992360436366459441863571597404766636, 73390680976212094910064339563129832626556186710978, 438378856867326689398178158351115179916251888256767, 2618582369944045545556430357715891346964923831454301, 15641932485245871954675637289895111363731548950187704, 93437605272497302619893941677476540581879553613323589, 558161321857725487956431068394636659552210129800974920, 3334296140447747830303469600345313404685819172672900121, 19918409632770118814909174914415256028082878864418970169, 118990117898132093646159713250974437170159312410782086395, 710841182304866491553518886696384697478484552363029522375, 4246581263801561782415534854377307787518977700140293825092, 25369459215708449107945402000205056624815868570604357041460, 151561064073934068244007442600047739586197527923071714788696, 905458426875807146273149336189528530674087707770625540437793, 5409456073499801192554655380768172480708532173049143992019740, 32317867028919924433576982095710159977257736458060065520317020, 193079245622844054085780367289910124041665997432554514617481667, 1153538582350585567498878102129699032778482381996304315727173733, 6891791184508609457708754730794772230850626762476436079946359538, 41175168429185323661548768713833015825544656333958292843482110275, 246003786236051446247272311165159941559960841910383248624099986724, 1469776108804190508844171175578855247144971411766250031386446054571, 8781393152223599574779522361702292861712684252295328146284996434229, 52466050414726443612999752982658946050573388157611609002346698556677, 313469947096950827519760014953499701402226923941321172751512289920993, 1872905726578994084552548803969732965305430348194743966806157280742342, 11190211119679396871831362292589136986773242496550038231848363680113698, 66859464135981291085077546433675620768999389142770090992438905525602984, 399475040796765019508025786030234253339176773029506888921278941177875945, 2386813351358737906529115186231302967218077186618935933338090444325378048, 14260975248045316594946646897467813648574108583226068616477030006764698514, 85208293060494449388020201476295681949715663773430040515173308265406292387, 509115469773329503714979181398544314025944366848990996944548838260955588101, 3041952525171443482221245490295774424035815510351772850791072828321147296136
Generating function in Maple syntax:
((-3*x^3-7*x^2+x)*(x^2-6*x+1)^(1/2)+3*x^4-28*x^3+22*x^2+9*x-2)/(26*x^4-30*x^3+4*x^2+12*x-2)
Generating function in latex syntax:
\frac{\left(-3 x^{3}-7 x^{2}+x \right) \sqrt{x^{2}-6 x +1}+3 x^{4}-28 x^{3}+22 x^{2}+9 x -2}{26 x^{4}-30 x^{3}+4 x^{2}+12 x -2}
Generating function in sympy syntax:
(3*x**4 - 28*x**3 + 22*x**2 + 9*x + sqrt(x**2 - 6*x + 1)*(-3*x**3 - 7*x**2 + x) - 2)/(26*x**4 - 30*x**3 + 4*x**2 + 12*x - 2)
Implicit equation for the generating function in Maple syntax:
(13*x^4-15*x^3+2*x^2+6*x-1)*F(x)^2+(-3*x^4+28*x^3-22*x^2-9*x+2)*F(x)-3*x^3+18*x^2+3*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(13 x^{4}-15 x^{3}+2 x^{2}+6 x -1\right) F \! \left(x \right)^{2}+\left(-3 x^{4}+28 x^{3}-22 x^{2}-9 x +2\right) F \! \left(x \right)-3 x^{3}+18 x^{2}+3 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 580
a(7) = 3122
a(n+8) = -39*n/(7+n)*a(n)+(110+19*n)/(7+n)*a(7+n)+(169+188*n)/(7+n)*a(n+1)+(1651+349*n)/(7+n)*a(n+2)-9*(332+85*n)/(7+n)*a(n+3)+3*(491+119*n)/(7+n)*a(n+4)+2*(299+94*n)/(7+n)*a(n+5)-4*(134+29*n)/(7+n)*a(n+6), n >= 8
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 580
a(7) = 3122
a{\left(n + 8 \right)} = - \frac{39 n a{\left(n \right)}}{n + 7} + \frac{\left(19 n + 110\right) a{\left(n + 7 \right)}}{n + 7} - \frac{4 \left(29 n + 134\right) a{\left(n + 6 \right)}}{n + 7} - \frac{9 \left(85 n + 332\right) a{\left(n + 3 \right)}}{n + 7} + \frac{2 \left(94 n + 299\right) a{\left(n + 5 \right)}}{n + 7} + \frac{3 \left(119 n + 491\right) a{\left(n + 4 \right)}}{n + 7} + \frac{\left(188 n + 169\right) a{\left(n + 1 \right)}}{n + 7} + \frac{\left(349 n + 1651\right) a{\left(n + 2 \right)}}{n + 7}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24407/
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[22,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[22,x]*F[8,x]
F[8,x] = F[35,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[22,x]
F[12,x] = 1/F[22,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = -F[29,x]+F[15,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[0,x]*F[5,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[22,x]*F[23,x]
F[19,x] = 1/F[22,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[0,x]+F[4,x]
F[22,x] = x
F[23,x] = F[24,x,1]
F[24,x,k[0]] = F[25,x,k[0]]+F[26,x,k[0]]
F[25,x,k[0]] = x*F[25,x,k[0]]*k[0]+F[25,x,k[0]]^2-2*F[25,x,k[0]]+2
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[24,x,k[0]]^2*F[28,x,k[0]]
F[28,x,k[0]] = k[0]*x
F[29,x] = F[30,x]+F[5,x]
F[30,x] = F[31,x]
F[31,x] = F[22,x]*F[23,x]*F[32,x]
F[32,x] = 1/F[22,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = (1+F[34,x])*x+F[34,x]^2
F[35,x] = F[36,x]
F[36,x] = F[22,x]*F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[19,x]*F[39,x]
F[39,x] = F[40,x,1]
F[40,x,k[0]] = (F[25,x,k[0]]*k[0]-F[25,x,1])/(-1+k[0])
F[41,x] = F[42,x]
F[42,x] = F[22,x]*F[43,x]*F[49,x]*F[52,x]
F[43,x] = 1/F[22,x]/F[23,x]/F[49,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[22,x]*F[23,x]*F[4,x]*F[46,x]
F[46,x] = 1/F[22,x]/F[5,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[5,x]+F[32,x]
F[49,x] = F[1,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[22,x]*F[49,x]
F[52,x] = F[53,x,1]
F[53,x,k[0]] = (F[24,x,k[0]]*k[0]-F[24,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{35}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{23}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = x F_{25}\! \left(x , y\right) y +F_{25}\! \left(x , y\right)^{2}-2 F_{25}\! \left(x , y\right)+2
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{24}\! \left(x , y\right)^{2} F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = y x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{5}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right) F_{23}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{34}\! \left(x \right) x +F_{34} \left(x \right)^{2}+x
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{22}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{40}\! \left(x , y\right) = -\frac{-F_{25}\! \left(x , y\right) y +F_{25}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{22}\! \left(x \right) F_{43}\! \left(x \right) F_{49}\! \left(x \right) F_{52}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{22}\! \left(x \right) F_{23}\! \left(x \right) F_{49}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{22}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{22}\! \left(x \right) F_{5}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{32}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x , 1\right)
F_{53}\! \left(x , y\right) = -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_22(x)*F_8(x))
Eq(F_8(x), F_35(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_22(x))
Eq(F_12(x), F_13(x)/F_22(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) - F_29(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_0(x)*F_5(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_22(x)*F_23(x))
Eq(F_19(x), F_20(x)/F_22(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_0(x) + F_4(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x, 1))
Eq(F_24(x, k_0), F_25(x, k_0) + F_26(x, k_0))
Eq(F_25(x, k_0), (k_0*x - 2)*F_25(x, k_0) + F_25(x, k_0)**2 + 2)
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_24(x, k_0)**2*F_28(x, k_0))
Eq(F_28(x, k_0), k_0*x)
Eq(F_29(x), F_30(x) + F_5(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_22(x)*F_23(x)*F_32(x))
Eq(F_32(x), F_33(x)/F_22(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), (x - 3)*(F_34(x) + 1) + (F_34(x) + 1)**2 + F_34(x) + 2)
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_22(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_19(x)*F_39(x))
Eq(F_39(x), F_40(x, 1))
Eq(F_40(x, k_0), (-k_0*F_25(x, k_0) + F_25(x, 1))/(1 - k_0))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_22(x)*F_43(x)*F_49(x)*F_52(x))
Eq(F_43(x), F_44(x)/(F_22(x)*F_23(x)*F_49(x)))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_22(x)*F_23(x)*F_4(x)*F_46(x))
Eq(F_46(x), F_47(x)/(F_22(x)*F_5(x)))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_32(x) - F_5(x))
Eq(F_49(x), F_1(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_22(x)*F_49(x))
Eq(F_52(x), F_53(x, 1))
Eq(F_53(x, k_0), (-k_0*F_24(x, k_0) + F_24(x, 1))/(1 - k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "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}]], "symmetries": [], "iterative": false}
Specification JSON:
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0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 3], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 4], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 4], [0, 3], [0, 4], 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[0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[1, 7]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[2, 7]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[3, 7]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 5], [2, 5]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 5], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 4], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 5], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [3, 4], [3, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 6], [0, 7], [0, 7], [0, 7]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 6], [0, 7], [0, 7], [0, 7]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 6], [0, 7], [0, 7], [0, 7]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 7], [0, 6], [0, 7], [0, 7]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 7], [0, 6], [0, 7], [0, 7]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 7], [0, 6], [0, 7]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 7], [0, 7], [0, 7], [0, 7], [0, 7]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 7], [0, 7], [0, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 7], [0, 7], [0, 7], [0, 7], [0, 7]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 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{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": []}, "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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"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": [2, 0, 3, 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, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 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.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "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, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24490/
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[25,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (1+F[6,x])*x+F[6,x]^2
F[7,x] = F[8,x]
F[8,x] = F[25,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[4,x]*F[6,x]
F[11,x] = F[12,x]+F[56,x]
F[12,x] = F[13,x]+F[5,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[25,x]
F[15,x] = F[16,x]+F[52,x]
F[16,x] = F[17,x]*F[5,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = 2+F[18,x]^2+(-2+x)*F[18,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[25,x]*F[44,x]
F[21,x] = 1/F[43,x]*F[22,x]
F[22,x] = -F[26,x]+F[23,x]
F[23,x] = 1/F[25,x]*F[24,x]
F[24,x] = F[5,x]
F[25,x] = x
F[26,x] = -F[29,x]+F[27,x]
F[27,x] = 1/F[25,x]*F[28,x]
F[28,x] = F[7,x]
F[29,x] = F[21,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[25,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[1,x]+F[25,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[25,x]*F[37,x]
F[37,x] = F[1,x]+F[35,x]
F[38,x] = F[39,x]+F[40,x]+F[42,x]
F[39,x] = 0
F[40,x] = F[25,x]*F[41,x]
F[41,x] = F[25,x]+F[38,x]
F[42,x] = F[25,x]*F[35,x]
F[43,x] = F[1,x]+F[30,x]
F[44,x] = 1/F[0,x]*F[45,x]
F[45,x] = -F[48,x]+F[46,x]
F[46,x] = 1/F[25,x]*F[47,x]
F[47,x] = F[5,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[25,x]*F[50,x]
F[50,x] = F[7,x]
F[51,x] = F[2,x]*F[44,x]
F[52,x] = F[53,x]
F[53,x] = F[25,x]*F[44,x]*F[54,x]
F[54,x] = 1/F[25,x]*F[55,x]
F[55,x] = F[11,x]
F[56,x] = F[57,x]
F[57,x] = F[25,x]*F[58,x]
F[58,x] = F[59,x]+F[87,x]
F[59,x] = F[5,x]*F[60,x]
F[60,x] = 1/F[25,x]/F[4,x]/F[65,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[74,x]
F[63,x] = F[64,x]
F[64,x] = F[25,x]*F[4,x]*F[65,x]*F[71,x]
F[65,x] = 1/F[18,x]/F[25,x]/F[37,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[37,x]^2*F[25,x]*F[68,x]
F[68,x] = 1/F[25,x]/F[37,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[18,x]+F[21,x]
F[71,x] = F[18,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[25,x]*F[60,x]
F[74,x] = F[75,x]
F[75,x] = F[25,x]*F[76,x]
F[76,x] = F[77,x]+F[85,x]
F[77,x] = F[78,x]
F[78,x] = F[44,x]*F[79,x]
F[79,x] = 1/F[25,x]/F[44,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[25,x]*F[44,x]*F[82,x]
F[82,x] = 1/F[25,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[25,x]*F[62,x]
F[85,x] = F[86,x]
F[86,x] = F[44,x]*F[62,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[25,x]*F[60,x]*F[65,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_{25}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = F_{6}\! \left(x \right) x +F_{6} \left(x \right)^{2}+x
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{56}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{52}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{18}\! \left(x \right) x +F_{18} \left(x \right)^{2}-2 F_{18}\! \left(x \right)+2
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right) F_{44}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{43}\! \left(x \right)}
F_{22}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = x
F_{26}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{7}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{25}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right) F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{45}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{25}\! \left(x \right) F_{44}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{25}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{87}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{65}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{74}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{65}\! \left(x \right) F_{71}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{18}\! \left(x \right) F_{25}\! \left(x \right) F_{37}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{37} \left(x \right)^{2} F_{25}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{25}\! \left(x \right) F_{37}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{25}\! \left(x \right) F_{60}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{25}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{44}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{25}\! \left(x \right) F_{44}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{25}\! \left(x \right) F_{44}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{25}\! \left(x \right) F_{62}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{44}\! \left(x \right) F_{62}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{25}\! \left(x \right) F_{60}\! \left(x \right) F_{65}\! \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_25(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), (x - 3)*(F_6(x) + 1) + (F_6(x) + 1)**2 + F_6(x) + 2)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_25(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_4(x)*F_6(x))
Eq(F_11(x), F_12(x) + F_56(x))
Eq(F_12(x), F_13(x) + F_5(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_25(x))
Eq(F_15(x), F_16(x) + F_52(x))
Eq(F_16(x), F_17(x)*F_5(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), (x - 2)*F_18(x) + F_18(x)**2 + 2)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_25(x)*F_44(x))
Eq(F_21(x), F_22(x)/F_43(x))
Eq(F_22(x), F_23(x) - F_26(x))
Eq(F_23(x), F_24(x)/F_25(x))
Eq(F_24(x), F_5(x))
Eq(F_25(x), x)
Eq(F_26(x), F_27(x) - F_29(x))
Eq(F_27(x), F_28(x)/F_25(x))
Eq(F_28(x), F_7(x))
Eq(F_29(x), F_21(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_25(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_1(x) + F_25(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_25(x)*F_37(x))
Eq(F_37(x), F_1(x) + F_35(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_42(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_25(x)*F_41(x))
Eq(F_41(x), F_25(x) + F_38(x))
Eq(F_42(x), F_25(x)*F_35(x))
Eq(F_43(x), F_1(x) + F_30(x))
Eq(F_44(x), F_45(x)/F_0(x))
Eq(F_45(x), F_46(x) - F_48(x))
Eq(F_46(x), F_47(x)/F_25(x))
Eq(F_47(x), F_5(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_25(x))
Eq(F_50(x), F_7(x))
Eq(F_51(x), F_2(x)*F_44(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_25(x)*F_44(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_25(x))
Eq(F_55(x), F_11(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_25(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_87(x))
Eq(F_59(x), F_5(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_25(x)*F_4(x)*F_65(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_74(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_25(x)*F_4(x)*F_65(x)*F_71(x))
Eq(F_65(x), F_66(x)/(F_18(x)*F_25(x)*F_37(x)))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_25(x)*F_37(x)**2*F_68(x))
Eq(F_68(x), F_69(x)/(F_25(x)*F_37(x)))
Eq(F_69(x), F_70(x))
Eq(F_70(x), -F_18(x) + F_21(x))
Eq(F_71(x), F_18(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_25(x)*F_60(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_25(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_85(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_44(x)*F_79(x))
Eq(F_79(x), F_80(x)/(F_25(x)*F_44(x)))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_25(x)*F_44(x)*F_82(x))
Eq(F_82(x), F_83(x)/F_25(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_25(x)*F_62(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_44(x)*F_62(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_25(x)*F_60(x)*F_65(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": 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}]], "symmetries": [], "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, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 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], "pos": [[0, 1]]}, {"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, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 3], [2, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 3], [0, 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[2, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0], "pos": [[4, 5]]}, {"patt": [0], "pos": [[4, 6]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[3, 5], [3, 5]]}, {"patt": [1, 0], "pos": [[3, 5], [3, 5]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 4], [0, 6], [0, 6], [0, 6]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 6], [0, 4], [0, 6], [0, 6]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 6], [0, 4], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 6], [0, 4], [0, 6]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 6], [0, 4], [0, 6], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 4], [0, 4], [0, 6], [0, 4], [0, 6]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 6], [0, 6], [0, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}], "requirements": [[{"patt": [0], "pos": [[3, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": []}, "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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24938/
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[23,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[32,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = 1/F[23,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[2,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]*F[24,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[22,x]+F[21,x]
F[21,x] = -F[0,x]+F[4,x]
F[22,x] = (1+F[22,x])*x+F[22,x]^2
F[23,x] = x
F[24,x] = 1/F[0,x]*F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[23,x]*F[27,x]
F[27,x] = F[21,x]
F[28,x] = -F[31,x]+F[29,x]
F[29,x] = 1/F[23,x]*F[30,x]
F[30,x] = F[20,x]
F[31,x] = F[2,x]*F[24,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[21,x]*F[5,x]
F[34,x] = F[35,x]
F[35,x] = F[23,x]*F[36,x]
F[36,x] = F[37,x]+F[85,x]
F[37,x] = F[21,x]*F[38,x]
F[38,x] = 1/F[23,x]/F[4,x]/F[43,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]+F[72,x]
F[41,x] = F[42,x]
F[42,x] = F[23,x]*F[4,x]*F[43,x]*F[69,x]
F[43,x] = 1/F[23,x]/F[5,x]/F[62,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[62,x]^2*F[23,x]*F[46,x]
F[46,x] = 1/F[23,x]/F[62,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[5,x]+F[49,x]
F[49,x] = 1/F[68,x]*F[50,x]
F[50,x] = -F[53,x]+F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[21,x]
F[53,x] = -F[54,x]+F[18,x]
F[54,x] = F[49,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[23,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[1,x]+F[23,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[62,x]
F[62,x] = F[1,x]+F[60,x]
F[63,x] = F[64,x]+F[65,x]+F[67,x]
F[64,x] = 0
F[65,x] = F[23,x]*F[66,x]
F[66,x] = F[23,x]+F[63,x]
F[67,x] = F[23,x]*F[60,x]
F[68,x] = F[1,x]+F[55,x]
F[69,x] = F[5,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[23,x]*F[38,x]
F[72,x] = F[73,x]
F[73,x] = F[23,x]*F[74,x]
F[74,x] = F[75,x]+F[83,x]
F[75,x] = F[76,x]
F[76,x] = F[24,x]*F[77,x]
F[77,x] = 1/F[23,x]/F[24,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[23,x]*F[24,x]*F[80,x]
F[80,x] = 1/F[23,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[23,x]*F[40,x]
F[83,x] = F[84,x]
F[84,x] = F[24,x]*F[40,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[23,x]*F[38,x]*F[43,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{32}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{2}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{22}\! \left(x \right) x +F_{22} \left(x \right)^{2}+x
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{20}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{23}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{85}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{23}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{72}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right) F_{69}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{23}\! \left(x \right) F_{5}\! \left(x \right) F_{62}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{62} \left(x \right)^{2} F_{23}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{23}\! \left(x \right) F_{62}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{68}\! \left(x \right)}
F_{50}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{21}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{18}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{23}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = 0
F_{65}\! \left(x \right) = F_{23}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{23}\! \left(x \right)+F_{63}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{1}\! \left(x \right)+F_{55}\! \left(x \right)
F_{69}\! \left(x \right) = F_{5}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{23}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{83}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{24}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{23}\! \left(x \right) F_{24}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{23}\! \left(x \right) F_{40}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{24}\! \left(x \right) F_{40}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right) F_{43}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_32(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x)/F_23(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_2(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x)*F_24(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x) - F_22(x))
Eq(F_21(x), -F_0(x) + F_4(x))
Eq(F_22(x), (x - 3)*(F_22(x) + 1) + (F_22(x) + 1)**2 + F_22(x) + 2)
Eq(F_23(x), x)
Eq(F_24(x), F_25(x)/F_0(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_23(x))
Eq(F_27(x), F_21(x))
Eq(F_28(x), F_29(x) - F_31(x))
Eq(F_29(x), F_30(x)/F_23(x))
Eq(F_30(x), F_20(x))
Eq(F_31(x), F_2(x)*F_24(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_21(x)*F_5(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_23(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_85(x))
Eq(F_37(x), F_21(x)*F_38(x))
Eq(F_38(x), F_39(x)/(F_23(x)*F_4(x)*F_43(x)))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x) + F_72(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_23(x)*F_4(x)*F_43(x)*F_69(x))
Eq(F_43(x), F_44(x)/(F_23(x)*F_5(x)*F_62(x)))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_23(x)*F_46(x)*F_62(x)**2)
Eq(F_46(x), F_47(x)/(F_23(x)*F_62(x)))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) - F_5(x))
Eq(F_49(x), F_50(x)/F_68(x))
Eq(F_50(x), F_51(x) - F_53(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_21(x))
Eq(F_53(x), F_18(x) - F_54(x))
Eq(F_54(x), F_49(x)*F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_23(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_1(x) + F_23(x))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_62(x))
Eq(F_62(x), F_1(x) + F_60(x))
Eq(F_63(x), F_64(x) + F_65(x) + F_67(x))
Eq(F_64(x), 0)
Eq(F_65(x), F_23(x)*F_66(x))
Eq(F_66(x), F_23(x) + F_63(x))
Eq(F_67(x), F_23(x)*F_60(x))
Eq(F_68(x), F_1(x) + F_55(x))
Eq(F_69(x), F_5(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_23(x)*F_38(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_23(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_83(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_24(x)*F_77(x))
Eq(F_77(x), F_78(x)/(F_23(x)*F_24(x)))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_23(x)*F_24(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_23(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_23(x)*F_40(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_24(x)*F_40(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_23(x)*F_38(x)*F_43(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": 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}]], "symmetries": [], "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, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 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, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"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, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": 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0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [1, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 3], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [3, 2], [3, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 3], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [3, 3], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 2], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 3], [2, 0], [2, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 3], [2, 0], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 3], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 3], [2, 3], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 3], [2, 2], [2, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 3], [2, 2], [3, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 3], [2, 3], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 3], [2, 3], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 3], [2, 2], [2, 3], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": []}, "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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24946/
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[23,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[23,x]*F[8,x]
F[8,x] = F[32,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = 1/F[23,x]*F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[2,x]*F[5,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[23,x]*F[24,x]
F[18,x] = 1/F[23,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = -F[22,x]+F[21,x]
F[21,x] = -F[0,x]+F[4,x]
F[22,x] = (1+F[22,x])*x+F[22,x]^2
F[23,x] = x
F[24,x] = 1/F[0,x]*F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[23,x]*F[27,x]
F[27,x] = F[21,x]
F[28,x] = -F[31,x]+F[29,x]
F[29,x] = 1/F[23,x]*F[30,x]
F[30,x] = F[20,x]
F[31,x] = F[2,x]*F[24,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[21,x]*F[5,x]
F[34,x] = F[35,x]
F[35,x] = F[23,x]*F[36,x]
F[36,x] = F[37,x]+F[85,x]
F[37,x] = F[21,x]*F[38,x]
F[38,x] = 1/F[23,x]/F[4,x]/F[43,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[41,x]+F[72,x]
F[41,x] = F[42,x]
F[42,x] = F[23,x]*F[4,x]*F[43,x]*F[69,x]
F[43,x] = 1/F[23,x]/F[5,x]/F[62,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[62,x]^2*F[23,x]*F[46,x]
F[46,x] = 1/F[23,x]/F[62,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[5,x]+F[49,x]
F[49,x] = 1/F[68,x]*F[50,x]
F[50,x] = -F[53,x]+F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[21,x]
F[53,x] = -F[54,x]+F[18,x]
F[54,x] = F[49,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[23,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[1,x]+F[23,x]
F[59,x] = F[60,x]+F[63,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[62,x]
F[62,x] = F[1,x]+F[60,x]
F[63,x] = F[64,x]+F[65,x]+F[67,x]
F[64,x] = 0
F[65,x] = F[23,x]*F[66,x]
F[66,x] = F[23,x]+F[63,x]
F[67,x] = F[23,x]*F[60,x]
F[68,x] = F[1,x]+F[55,x]
F[69,x] = F[5,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[23,x]*F[38,x]
F[72,x] = F[73,x]
F[73,x] = F[23,x]*F[74,x]
F[74,x] = F[75,x]+F[83,x]
F[75,x] = F[76,x]
F[76,x] = F[24,x]*F[77,x]
F[77,x] = 1/F[23,x]/F[24,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[23,x]*F[24,x]*F[80,x]
F[80,x] = 1/F[23,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[23,x]*F[40,x]
F[83,x] = F[84,x]
F[84,x] = F[24,x]*F[40,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[23,x]*F[38,x]*F[43,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{32}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{2}\! \left(x \right) F_{5}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{22}\! \left(x \right) x +F_{22} \left(x \right)^{2}+x
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{20}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{23}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{85}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{23}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{72}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right) F_{43}\! \left(x \right) F_{69}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{23}\! \left(x \right) F_{5}\! \left(x \right) F_{62}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{62} \left(x \right)^{2} F_{23}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{23}\! \left(x \right) F_{62}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{68}\! \left(x \right)}
F_{50}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{21}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{18}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{23}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = 0
F_{65}\! \left(x \right) = F_{23}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{23}\! \left(x \right)+F_{63}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{1}\! \left(x \right)+F_{55}\! \left(x \right)
F_{69}\! \left(x \right) = F_{5}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{23}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{83}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{24}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{23}\! \left(x \right) F_{24}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{23}\! \left(x \right) F_{40}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{24}\! \left(x \right) F_{40}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right) F_{43}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_23(x)*F_8(x))
Eq(F_8(x), F_32(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x)/F_23(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_2(x)*F_5(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_23(x)*F_24(x))
Eq(F_18(x), F_19(x)/F_23(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x) - F_22(x))
Eq(F_21(x), -F_0(x) + F_4(x))
Eq(F_22(x), (x - 3)*(F_22(x) + 1) + (F_22(x) + 1)**2 + F_22(x) + 2)
Eq(F_23(x), x)
Eq(F_24(x), F_25(x)/F_0(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_23(x))
Eq(F_27(x), F_21(x))
Eq(F_28(x), F_29(x) - F_31(x))
Eq(F_29(x), F_30(x)/F_23(x))
Eq(F_30(x), F_20(x))
Eq(F_31(x), F_2(x)*F_24(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_21(x)*F_5(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_23(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_85(x))
Eq(F_37(x), F_21(x)*F_38(x))
Eq(F_38(x), F_39(x)/(F_23(x)*F_4(x)*F_43(x)))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x) + F_72(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_23(x)*F_4(x)*F_43(x)*F_69(x))
Eq(F_43(x), F_44(x)/(F_23(x)*F_5(x)*F_62(x)))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_23(x)*F_46(x)*F_62(x)**2)
Eq(F_46(x), F_47(x)/(F_23(x)*F_62(x)))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) - F_5(x))
Eq(F_49(x), F_50(x)/F_68(x))
Eq(F_50(x), F_51(x) - F_53(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_21(x))
Eq(F_53(x), F_18(x) - F_54(x))
Eq(F_54(x), F_49(x)*F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_23(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_1(x) + F_23(x))
Eq(F_59(x), F_60(x) + F_63(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_62(x))
Eq(F_62(x), F_1(x) + F_60(x))
Eq(F_63(x), F_64(x) + F_65(x) + F_67(x))
Eq(F_64(x), 0)
Eq(F_65(x), F_23(x)*F_66(x))
Eq(F_66(x), F_23(x) + F_63(x))
Eq(F_67(x), F_23(x)*F_60(x))
Eq(F_68(x), F_1(x) + F_55(x))
Eq(F_69(x), F_5(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_23(x)*F_38(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_23(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_83(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_24(x)*F_77(x))
Eq(F_77(x), F_78(x)/(F_23(x)*F_24(x)))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_23(x)*F_24(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_23(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_23(x)*F_40(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_24(x)*F_40(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_23(x)*F_38(x)*F_43(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": 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}]], "symmetries": [], "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, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 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, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, 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0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [1, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 3], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [3, 2], [3, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 3], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [3, 3], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 2], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 3], [2, 0], [2, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 3], [2, 0], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 3], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 3], [2, 3], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 3], [2, 2], [2, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 3], [2, 2], [3, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 3], [2, 3], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 3], [2, 3], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 3], [2, 2], [2, 3], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": []}, "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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25836/
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[25,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (1+F[6,x])*x+F[6,x]^2
F[7,x] = F[8,x]
F[8,x] = F[25,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[4,x]*F[6,x]
F[11,x] = F[12,x]+F[56,x]
F[12,x] = F[13,x]+F[5,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[25,x]
F[15,x] = F[16,x]+F[52,x]
F[16,x] = F[17,x]*F[5,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = 2+F[18,x]^2+(-2+x)*F[18,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[25,x]*F[44,x]
F[21,x] = 1/F[43,x]*F[22,x]
F[22,x] = -F[26,x]+F[23,x]
F[23,x] = 1/F[25,x]*F[24,x]
F[24,x] = F[5,x]
F[25,x] = x
F[26,x] = -F[29,x]+F[27,x]
F[27,x] = 1/F[25,x]*F[28,x]
F[28,x] = F[7,x]
F[29,x] = F[21,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[25,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[1,x]+F[25,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[25,x]*F[37,x]
F[37,x] = F[1,x]+F[35,x]
F[38,x] = F[39,x]+F[40,x]+F[42,x]
F[39,x] = 0
F[40,x] = F[25,x]*F[41,x]
F[41,x] = F[25,x]+F[38,x]
F[42,x] = F[25,x]*F[35,x]
F[43,x] = F[1,x]+F[30,x]
F[44,x] = 1/F[0,x]*F[45,x]
F[45,x] = -F[48,x]+F[46,x]
F[46,x] = 1/F[25,x]*F[47,x]
F[47,x] = F[5,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[25,x]*F[50,x]
F[50,x] = F[7,x]
F[51,x] = F[2,x]*F[44,x]
F[52,x] = F[53,x]
F[53,x] = F[25,x]*F[44,x]*F[54,x]
F[54,x] = 1/F[25,x]*F[55,x]
F[55,x] = F[11,x]
F[56,x] = F[57,x]
F[57,x] = F[25,x]*F[58,x]
F[58,x] = F[59,x]+F[87,x]
F[59,x] = F[5,x]*F[60,x]
F[60,x] = 1/F[25,x]/F[4,x]/F[65,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[74,x]
F[63,x] = F[64,x]
F[64,x] = F[25,x]*F[4,x]*F[65,x]*F[71,x]
F[65,x] = 1/F[18,x]/F[25,x]/F[37,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[37,x]^2*F[25,x]*F[68,x]
F[68,x] = 1/F[25,x]/F[37,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[18,x]+F[21,x]
F[71,x] = F[18,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[25,x]*F[60,x]
F[74,x] = F[75,x]
F[75,x] = F[25,x]*F[76,x]
F[76,x] = F[77,x]+F[85,x]
F[77,x] = F[78,x]
F[78,x] = F[44,x]*F[79,x]
F[79,x] = 1/F[25,x]/F[44,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[25,x]*F[44,x]*F[82,x]
F[82,x] = 1/F[25,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[25,x]*F[62,x]
F[85,x] = F[86,x]
F[86,x] = F[44,x]*F[62,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[25,x]*F[60,x]*F[65,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_{25}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = F_{6}\! \left(x \right) x +F_{6} \left(x \right)^{2}+x
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{56}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{25}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{52}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{18}\! \left(x \right) x +F_{18} \left(x \right)^{2}-2 F_{18}\! \left(x \right)+2
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right) F_{44}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{43}\! \left(x \right)}
F_{22}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = x
F_{26}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{7}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{25}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{25}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right) F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{45}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{5}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{25}\! \left(x \right) F_{44}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{25}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{87}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{65}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{74}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right) F_{65}\! \left(x \right) F_{71}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{18}\! \left(x \right) F_{25}\! \left(x \right) F_{37}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{37} \left(x \right)^{2} F_{25}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{25}\! \left(x \right) F_{37}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{25}\! \left(x \right) F_{60}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{25}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{44}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{25}\! \left(x \right) F_{44}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{25}\! \left(x \right) F_{44}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{25}\! \left(x \right) F_{62}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{44}\! \left(x \right) F_{62}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{25}\! \left(x \right) F_{60}\! \left(x \right) F_{65}\! \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_25(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), (x - 3)*(F_6(x) + 1) + (F_6(x) + 1)**2 + F_6(x) + 2)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_25(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_4(x)*F_6(x))
Eq(F_11(x), F_12(x) + F_56(x))
Eq(F_12(x), F_13(x) + F_5(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_25(x))
Eq(F_15(x), F_16(x) + F_52(x))
Eq(F_16(x), F_17(x)*F_5(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), (x - 2)*F_18(x) + F_18(x)**2 + 2)
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_25(x)*F_44(x))
Eq(F_21(x), F_22(x)/F_43(x))
Eq(F_22(x), F_23(x) - F_26(x))
Eq(F_23(x), F_24(x)/F_25(x))
Eq(F_24(x), F_5(x))
Eq(F_25(x), x)
Eq(F_26(x), F_27(x) - F_29(x))
Eq(F_27(x), F_28(x)/F_25(x))
Eq(F_28(x), F_7(x))
Eq(F_29(x), F_21(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_25(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_1(x) + F_25(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_25(x)*F_37(x))
Eq(F_37(x), F_1(x) + F_35(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_42(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_25(x)*F_41(x))
Eq(F_41(x), F_25(x) + F_38(x))
Eq(F_42(x), F_25(x)*F_35(x))
Eq(F_43(x), F_1(x) + F_30(x))
Eq(F_44(x), F_45(x)/F_0(x))
Eq(F_45(x), F_46(x) - F_48(x))
Eq(F_46(x), F_47(x)/F_25(x))
Eq(F_47(x), F_5(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_25(x))
Eq(F_50(x), F_7(x))
Eq(F_51(x), F_2(x)*F_44(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_25(x)*F_44(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_25(x))
Eq(F_55(x), F_11(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_25(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_87(x))
Eq(F_59(x), F_5(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_25(x)*F_4(x)*F_65(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_74(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_25(x)*F_4(x)*F_65(x)*F_71(x))
Eq(F_65(x), F_66(x)/(F_18(x)*F_25(x)*F_37(x)))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_25(x)*F_37(x)**2*F_68(x))
Eq(F_68(x), F_69(x)/(F_25(x)*F_37(x)))
Eq(F_69(x), F_70(x))
Eq(F_70(x), -F_18(x) + F_21(x))
Eq(F_71(x), F_18(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_25(x)*F_60(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_25(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_85(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_44(x)*F_79(x))
Eq(F_79(x), F_80(x)/(F_25(x)*F_44(x)))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_25(x)*F_44(x)*F_82(x))
Eq(F_82(x), F_83(x)/F_25(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_25(x)*F_62(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_44(x)*F_62(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_25(x)*F_60(x)*F_65(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": 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}]], "symmetries": [], "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, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, 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