01324_01342_01432_04132_10324_10342_10432_13024_13042_13204_13240_13402_13420_14032_14302_14320_40132_41032_41302_41320
Counting sequence:
1, 1, 2, 6, 24, 100, 420, 1764, 7392, 30888, 128700, 534820, 2217072, 9170616, 37858184, 156009000, 641865600, 2636997840, 10819447020, 44338518180, 181502706000, 742250539800, 3032623634040, 12379931112120, 50498375129280, 205835768190000, 838437695760600, 3413086373819304, 13885718922546912, 56461243343795248, 229460718022813200, 932085261485772240, 3784466610075565568, 15359135657423615904, 62309220792048078156, 252679995190569300900, 1024309493108660762640, 4150892279216525280984, 16815476530519797609752, 68099092009089422183448, 275704825947730454184000, 1115897609637160312639600, 4515302766800119411388040, 18265736976498044030040120, 73872061393323207970882080, 298689888826068996288186000, 1207431247557503154692242800, 4879888800515010334374542640, 19718181573218839167944497920, 79659355876913342276882160480, 321753350693314945421080155000, 1299358225208023702039251858600, 5246349916369338053410249857312, 21179269307937455957696129325936, 85485555798801255469307598919344, 344988878223673829724144922263600, 1392035931526096692058637289025920, 5616051456215349836207995764102624, 22654222603455151782899170883015472, 91370660675883543216327145963136208, 368473149423492956278584048594763200, 1485758682166931767774155002723629920, 5990124348102526001441374650325104672, 24147391806232446170802537789227008416, 97331422579959967361268600858573993984, 392270738324491435917811201376941320000, 1580775638767253469164948793241116415500, 6369530930473366775754150312346372577700, 25662497299256784820632279955848705075600, 103382237803019979938078328865155209165400, 416437402914978180057476644405676354055000, 1677302947475773398517215453471641364759000, 6755109818244482966744584409796453431995200, 27202795523939930820305949659638065405135600, 109535761885210178059542450265711570820831400, 441022365976179447018705718859538442308975000, 1775532206373288930483956861657212063955268000, 7147607369726576806821907745190594389389049040, 28771196035762003291438287567619555952913267120, 115803345482602508752452408201737453480806746480, 466069939624885137465241759721371120792600992000, 1875636526015716548463759322271100171873261650400, 7547700316726207518169905569065001247186291789480, 30370346080220509203644820270826742446898650160440, 122195350728880168091773399690907951096954545400160, 491620709688050590214320691527534140600914371554000, 1977774967097978312789376406643822220535107060016400, 7956012405264452840750260275481290864166259672618640, 32002693043148753367444511260476467501730520062433920, 128721385785099622674645543332694924274854967973170080, 517712417291960944107678066264030913516079097440610000, 2082095856509766523531178679978713089638822976897854000, 8373126877900570234312930525491928488442524245068097600, 33670531470544744088435155168563218405626615054283632800, 135390482084224097197115834317350276534265785919538815200, 544380627460589912660560692776808764605289679143421340000, 2188739311124862287140511882806107713817281146692653952000, 8799596006765811471523465865676397525748292820683426513600, 35376039101083002389170153366351118747198570665281868015800, 142211230613169140889937748868266531854139088933629423980200, 571659244889053442043658236019624277706805243085090448900000
Generating function in Maple syntax:
(-6*x^3*(-4*x+1)^(1/2)+2*x^2*(-4*x+1)^(1/2)+16*x^3+8*x^2-7*x+1)/(-1+4*x)^2
Generating function in latex syntax:
\frac{-6 x^{3} \sqrt{-4 x +1}+2 x^{2} \sqrt{-4 x +1}+16 x^{3}+8 x^{2}-7 x +1}{\left(-1+4 x \right)^{2}}
Generating function in sympy syntax:
(-6*x**3*sqrt(1 - 4*x) + 16*x**3 + 2*x**2*sqrt(1 - 4*x) + 8*x**2 - 7*x + 1)/(4*x - 1)**2
Implicit equation for the generating function in Maple syntax:
(-1+4*x)^3*F(x)^2-2*(x+1)*(-1+4*x)^3*F(x)+36*x^6+40*x^5+84*x^4-20*x^3-25*x^2+10*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(-1+4 x \right)^{3} F \! \left(x \right)^{2}-2 \left(x +1\right) \left(-1+4 x \right)^{3} F \! \left(x \right)+36 x^{6}+40 x^{5}+84 x^{4}-20 x^{3}-25 x^{2}+10 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+2) = -6*(-3+2*n)/n*a(n)+(-4+7*n)/n*a(n+1), n >= 4
Recurrence in latex format:
a{\left(0 \right)} = 1
a{\left(1 \right)} = 1
a{\left(2 \right)} = 2
a{\left(3 \right)} = 6
a{\left(n + 2 \right)} = - \frac{6 \left(2 n - 3\right) a{\left(n \right)}}{n} + \frac{\left(7 n - 4\right) a{\left(n + 1 \right)}}{n}, \quad n \geq 4
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24419/
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[17,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -1+x^2+4*x+F[5,x]^2*(-1+4*x)+(3-8*x)*F[5,x]
F[6,x] = F[7,x]+F[8,x]
F[7,x] = (-1+4*x)*F[7,x]^2+F[7,x]+x^2
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[17,x]
F[10,x] = F[11,x]+F[25,x]
F[11,x] = F[12,x]+F[19,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[17,x]*F[18,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[17,x]
F[17,x] = x
F[18,x] = F[12,x]+F[14,x]
F[19,x] = F[20,x]
F[20,x] = F[14,x]*F[17,x]*F[21,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[14,x]*F[23,x]
F[23,x] = F[11,x]
F[24,x] = F[12,x]*F[18,x]
F[25,x] = F[26,x]
F[26,x] = F[17,x]*F[27,x]
F[27,x] = 1/F[17,x]*F[28,x]
F[28,x] = F[23,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_{17}\! \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) = 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 4 x F_{7} \left(x \right)^{2}+x^{2}-F_{7} \left(x \right)^{2}+F_{7}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{23}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 4*x + (3 - 8*x)*F_5(x) + (4*x - 1)*F_5(x)**2 - 1)
Eq(F_6(x), F_7(x) + F_8(x))
Eq(F_7(x), x**2 + 4*x + (2 - 8*x)*(F_7(x) + 1) + (4*x - 1)*(F_7(x) + 1)**2 + F_7(x) - 1)
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_17(x))
Eq(F_10(x), F_11(x) + F_25(x))
Eq(F_11(x), F_12(x) + F_19(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_17(x)*F_18(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_17(x))
Eq(F_17(x), x)
Eq(F_18(x), F_12(x) + F_14(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_14(x)*F_17(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_14(x)*F_23(x))
Eq(F_23(x), F_11(x))
Eq(F_24(x), F_12(x)*F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_17(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_17(x))
Eq(F_28(x), F_23(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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "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, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [4, 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"workable": 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": 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"Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24649/
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[17,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -1+x^2+4*x+F[5,x]^2*(-1+4*x)+(3-8*x)*F[5,x]
F[6,x] = F[7,x]+F[8,x]
F[7,x] = (-1+4*x)*F[7,x]^2+F[7,x]+x^2
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[17,x]
F[10,x] = F[11,x]+F[26,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[17,x]*F[18,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[17,x]
F[17,x] = x
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[12,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[17,x]*F[22,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[11,x]
F[25,x] = F[12,x]*F[18,x]
F[26,x] = F[27,x]
F[27,x] = F[17,x]*F[28,x]
F[28,x] = 1/F[17,x]*F[29,x]
F[29,x] = F[24,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_{17}\! \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) = 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 4 x F_{7} \left(x \right)^{2}+x^{2}-F_{7} \left(x \right)^{2}+F_{7}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{24}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 4*x + (3 - 8*x)*F_5(x) + (4*x - 1)*F_5(x)**2 - 1)
Eq(F_6(x), F_7(x) + F_8(x))
Eq(F_7(x), x**2 + 4*x + (2 - 8*x)*(F_7(x) + 1) + (4*x - 1)*(F_7(x) + 1)**2 + F_7(x) - 1)
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_17(x))
Eq(F_10(x), F_11(x) + F_26(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_17(x)*F_18(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_17(x))
Eq(F_17(x), x)
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_12(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_17(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_11(x))
Eq(F_25(x), F_12(x)*F_18(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_17(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_17(x))
Eq(F_29(x), F_24(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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "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, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [4, 2], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 2], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 1], [3, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 2], [2, 2], [3, 0], [3, 2], [4, 0], [4, 2]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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{"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": 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2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25326/
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[17,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -1+x^2+4*x+F[5,x]^2*(-1+4*x)+(3-8*x)*F[5,x]
F[6,x] = F[7,x]+F[8,x]
F[7,x] = (-1+4*x)*F[7,x]^2+F[7,x]+x^2
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[17,x]
F[10,x] = F[11,x]+F[26,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[17,x]*F[18,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[17,x]
F[17,x] = x
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[12,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[17,x]*F[22,x]
F[22,x] = F[23,x]+F[25,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[11,x]
F[25,x] = F[12,x]*F[18,x]
F[26,x] = F[27,x]
F[27,x] = F[17,x]*F[28,x]
F[28,x] = 1/F[17,x]*F[29,x]
F[29,x] = F[24,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_{17}\! \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) = 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 4 x F_{7} \left(x \right)^{2}+x^{2}-F_{7} \left(x \right)^{2}+F_{7}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{24}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 4*x + (3 - 8*x)*F_5(x) + (4*x - 1)*F_5(x)**2 - 1)
Eq(F_6(x), F_7(x) + F_8(x))
Eq(F_7(x), x**2 + 4*x + (2 - 8*x)*(F_7(x) + 1) + (4*x - 1)*(F_7(x) + 1)**2 + F_7(x) - 1)
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_17(x))
Eq(F_10(x), F_11(x) + F_26(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_17(x)*F_18(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_17(x))
Eq(F_17(x), x)
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_12(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_17(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_25(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_11(x))
Eq(F_25(x), F_12(x)*F_18(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_17(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_17(x))
Eq(F_29(x), F_24(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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "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, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "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, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[2, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [4, 2], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 2], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 1], [3, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 2], [2, 2], [3, 0], [3, 2], [4, 0], [4, 2]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 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"pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0], "pos": [[6, 1]]}, {"patt": [0], "pos": [[6, 2]]}, {"patt": [0], "pos": [[6, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 3]]}, {"patt": [0, 1], "pos": [[5, 2], [5, 2]]}, {"patt": [1, 0], "pos": [[5, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": 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[[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[2, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_and_row_and_col_placements_req_corrob
Tree: http://permpal.com/tree/25405/
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[12,x]*F[4,x]
F[4,x] = F[1,x]+F[20,x]+F[5,x]
F[5,x] = F[12,x]*F[6,x]
F[6,x] = F[1,x]+F[13,x]+F[18,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[12,x]*F[6,x]*F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[9,x]^2*F[12,x]
F[12,x] = x
F[13,x] = F[14,x]
F[14,x] = F[15,x]^2*F[12,x]
F[15,x] = 1/F[12,x]*F[16,x]
F[16,x] = -F[1,x]+F[17,x]
F[17,x] = -1+x^2+4*x+F[17,x]^2*(-1+4*x)+(3-8*x)*F[17,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[6,x]*F[9,x]
F[20,x] = F[12,x]*F[6,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{18}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{9} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = 4 F_{17} \left(x \right)^{2} x +x^{2}-8 F_{17}\! \left(x \right) x -F_{17} \left(x \right)^{2}+4 x +3 F_{17}\! \left(x \right)-1
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_20(x) + F_5(x))
Eq(F_5(x), F_12(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_13(x) + F_18(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_12(x)*F_6(x)*F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x)**2)
Eq(F_12(x), x)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x)**2)
Eq(F_15(x), F_16(x)/F_12(x))
Eq(F_16(x), -F_1(x) + F_17(x))
Eq(F_17(x), x**2 + 4*x + (3 - 8*x)*F_17(x) + (4*x - 1)*F_17(x)**2 - 1)
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_6(x)*F_9(x))
Eq(F_20(x), F_12(x)*F_6(x))
Pack JSON:
{"name": "point_and_row_and_col_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": [], "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}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": true}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], 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0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 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[2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": 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"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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 2, 0, 4], [1, 3, 2, 4, 0], [1, 3, 4, 0, 2], [1, 3, 4, 2, 0], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2], [1, 4, 3, 2, 0], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2], [4, 1, 3, 0, 2], [4, 1, 3, 2, 0]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25682/
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[17,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -1+x^2+4*x+F[5,x]^2*(-1+4*x)+(3-8*x)*F[5,x]
F[6,x] = F[7,x]+F[8,x]
F[7,x] = (-1+4*x)*F[7,x]^2+F[7,x]+x^2
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[17,x]
F[10,x] = F[11,x]+F[25,x]
F[11,x] = F[12,x]+F[19,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[17,x]*F[18,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[17,x]
F[17,x] = x
F[18,x] = F[12,x]+F[14,x]
F[19,x] = F[20,x]
F[20,x] = F[14,x]*F[17,x]*F[21,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[14,x]*F[23,x]
F[23,x] = F[11,x]
F[24,x] = F[12,x]*F[18,x]
F[25,x] = F[26,x]
F[26,x] = F[17,x]*F[27,x]
F[27,x] = 1/F[17,x]*F[28,x]
F[28,x] = F[23,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_{17}\! \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) = 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 4 x F_{7} \left(x \right)^{2}+x^{2}-F_{7} \left(x \right)^{2}+F_{7}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{23}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 4*x + (3 - 8*x)*F_5(x) + (4*x - 1)*F_5(x)**2 - 1)
Eq(F_6(x), F_7(x) + F_8(x))
Eq(F_7(x), x**2 + 4*x + (2 - 8*x)*(F_7(x) + 1) + (4*x - 1)*(F_7(x) + 1)**2 + F_7(x) - 1)
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_17(x))
Eq(F_10(x), F_11(x) + F_25(x))
Eq(F_11(x), F_12(x) + F_19(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_17(x)*F_18(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_17(x))
Eq(F_17(x), x)
Eq(F_18(x), F_12(x) + F_14(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_14(x)*F_17(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_14(x)*F_23(x))
Eq(F_23(x), F_11(x))
Eq(F_24(x), F_12(x)*F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_17(x)*F_27(x))
Eq(F_27(x), F_28(x)/F_17(x))
Eq(F_28(x), F_23(x))
Pack JSON:
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Specification JSON:
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