0231
Counting sequence:
1, 1, 2, 6, 23, 103, 512, 2740, 15485, 91245, 555662, 3475090, 22214707, 144640291, 956560748, 6411521056, 43478151737, 297864793993, 2059159989914, 14350039389022, 100726680316559, 711630547589023, 5057282786190872, 36132861123763276, 259423620328055093, 1870954187618001253, 13549041867915516902, 98493788137663244010, 718525298103386363435, 5258953884555177635035, 38608510021625752571908, 284253038775757583692600, 2098389323692272548563313, 15529368446466119224539649, 115197409505476788103398002, 856432228884170647229448502, 6380429915080962685670505223, 47628110829955837445808343255, 356194421500881924802062824240, 2668570716214045155349403554020, 20026217049437558457939949234925, 150525961711080576138714470701405, 1133137277281599669470628551828030, 8542421566124039620220192697639490, 64487825918306182189971678353660195, 487467446035641544143557563510713235, 3689430487933824207830803477694484380, 27957298930232823111180001729323234640, 212095321864749159497629705511070827945, 1610816944969690113589326043674105118585, 12246754108169980488367206114149810535242, 93204562196170554303786309213422058768910, 710031210839545414098119359038847423836287, 5414090730290433628827054833475377652864271, 41320549226346663131415307525664095218918728, 315634598683099414161315500712933294929387644, 2413055810165083958393484496521074596447738277, 18462962790122764693250144938784052143313693781, 141375575587639314880501009049875350644800310678, 1083364688822786881266389192709359296698097121434, 8307898668853091543785689650101094449879460036891, 63754876561897228291248142255119231996771480683851, 489588633686731920895754740596110678258234586772532, 3762144060249036333348338213290952225215651304755816, 28927881180921082715959929485699529257766416029787873, 222569829021958947138744492082554269489602064833110001, 1713468704673705819457736054042885331916583492820867362, 13198920298937741211573434118583412160226583877345406438, 101729160532963759596492890573823929411438590682912983799, 784494946804553266056890789152413642354744322747944467527, 6052929262297982555003927664033938419639717135224823282784, 46726711966046616277224676697156085121365372355797630126868, 360896537578734931487285288775786747285167051067264675540317, 2788765750908334506000997516379592449216967177236370572778061, 21559932115497703441770520512492438678585053323470154504265198, 166756669888489495957162217833945783400821256791178194360281586, 1290369745274871787065554282695497138109002804879958584793681427, 9989301821803432278424348590492816101865676094534281081647086083, 77364402521736141306089773290890305935964051443096636017373789644, 599414927634613246890938740915091657771753872198124585373415852672, 4646112388390576408724976730316569330705958999505006092974343236889, 36026598334192037947566381076195670528885890721306426588290084854633, 279462775093959277628601551002761138238601182266322090845797544270842, 2168641520217951581202193717118465287041478900758268558205690159656126, 16834907550072921338289850951891616581057888661703370959873968927836783, 130734161104224931714503147625952692176308352236101424768880361689153151, 1015591746566283006858163763652865432601191164436557350029120982864525432, 7892188445040595146806647211740129562332236704271739659852404910693912748, 61350842715346722977316625890120940486888436561852312533780831874515363349, 477073324618113728913555038043535920929788471464018331595255984644438467397, 3710975386133348898124446302975515925710261235871215570934474603177462092614, 28875285159291471561318113449158926385329423224184031298897441910293545465418, 224748492953575072875727839773423150753204483370654318106937437801396603600907, 1749833474039509782733421668493126530633434335763846766133846832158018143111611, 13627723002323429535420219205448393513258097777734638012820380731148342537366628, 106163157861766679863385976110359165117724560304429898920428347528840483870727576, 827267010249202521627728457757250312194272405209048934792429133045246335567927377, 6448168903123813748081974951584646707036292069869742599228831182505069031096185313, 50274004282332554036694485356151639356975820514862931173735088050598550799906636754, 392070848172795040324349453897236884986619936530609939250187505593592141244860073622, 3058421424698917503531177400858233129490810700975844320259202588807319182007408127719
Generating function in Maple syntax:
1/2*(-8*(-8*x+1)^(1/2)*x-8*x^2+(-8*x+1)^(1/2)+20*x+1)/(x+1)^3
Generating function in latex syntax:
\frac{-8 \sqrt{-8 x +1}\, x -8 x^{2}+\sqrt{-8 x +1}+20 x +1}{2 \left(x +1\right)^{3}}
Generating function in sympy syntax:
(-4*x**2 - 4*x*sqrt(1 - 8*x) + 10*x + sqrt(1 - 8*x)/2 + 1/2)/(x + 1)**3
Implicit equation for the generating function in Maple syntax:
(x+1)^3*F(x)^2+(8*x^2-20*x-1)*F(x)+16*x = 0
Implicit equation for the generating function in latex syntax:
\left(x +1\right)^{3} F \! \left(x \right)^{2}+\left(8 x^{2}-20 x -1\right) F \! \left(x \right)+16 x = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(n+2) = 4*(3+2*n)/(n+2)*a(n)+(-8+7*n)/(n+2)*a(n+1), n >= 2
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(n +2\right) = \frac{4 \left(3+2 n \right) a \! \left(n \right)}{n +2}+\frac{\left(-8+7 n \right) a \! \left(n +1\right)}{n +2}, \quad n \geq 2
Specification 1
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/12/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[0,x]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[14,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[15,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[6,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]^2*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[4,x]*F[6,x,k[0]]
F[18,x,k[0]] = F[0,x]*F[17,x,k[0]]*F[4,x]
F[18,x,k[0]] = F[19,x,k[0]]
F[20,x,k[0]] = F[19,x,k[0]]+F[28,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[6,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[24,x,k[0]] = F[25,x,k[0]]+F[26,x,k[0]]
F[25,x,k[0]] = F[11,x,k[0]]*F[5,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[17,x,k[0]]*F[4,x]*F[5,x]
F[28,x,k[0]] = F[0,x]*F[11,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{4}\! \left(x \right) F_{6}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{17}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = \frac{y F_{24}\! \left(x , y\right)-F_{24}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{11}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_0(x) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_14(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_15(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_6(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)**2*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_4(x)*F_6(x, k_0))
Eq(F_18(x, k_0), F_0(x)*F_17(x, k_0)*F_4(x))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_20(x, k_0), F_19(x, k_0) + F_28(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_6(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_24(x, k_0), F_25(x, k_0) + F_26(x, k_0))
Eq(F_25(x, k_0), F_11(x, k_0)*F_5(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_17(x, k_0)*F_4(x)*F_5(x))
Eq(F_28(x, k_0), F_0(x)*F_11(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"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]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, 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[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 2]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "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": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "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": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/13/
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[27,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[27,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[14,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[10,x,k[0]]^2*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[27,x]*F[4,x]
F[17,x,k[0]] = F[0,x]*F[16,x,k[0]]*F[27,x]
F[17,x,k[0]] = F[18,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[31,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[28,x,k[0]]
F[20,x,k[0]] = F[0,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[13,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[25,x,k[0]]
F[24,x,k[0]] = F[10,x,k[0]]*F[20,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]*F[27,x]
F[27,x] = x
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[27,x]*F[30,x,k[0]]
F[30,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[31,x,k[0]] = F[0,x]*F[10,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{27}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{10}\! \left(x , y\right)^{2} F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x , y\right) F_{27}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = x
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{27}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{31}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{10}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_27(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_27(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_14(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_10(x, k_0)**2*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_27(x)*F_4(x))
Eq(F_17(x, k_0), F_0(x)*F_16(x, k_0)*F_27(x))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_31(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_28(x, k_0))
Eq(F_20(x, k_0), F_0(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_13(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_25(x, k_0))
Eq(F_24(x, k_0), F_10(x, k_0)*F_20(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_16(x, k_0)*F_20(x, k_0)*F_27(x))
Eq(F_27(x), x)
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_27(x)*F_30(x, k_0))
Eq(F_30(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_31(x, k_0), F_0(x)*F_10(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"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]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], 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Specification 3
Strategy pack name: point_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/14/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[14,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[13,x]*F[4,x]
F[11,x] = 1/F[0,x]/F[13,x]*F[12,x]
F[12,x] = F[5,x]
F[13,x] = x
F[14,x] = F[15,x,1]
F[16,x,k[0]] = F[15,x,k[0]]+F[45,x]
F[16,x,k[0]] = F[17,x,k[0]]+F[22,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[4,x]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]^2*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[13,x]*F[24,x,k[0]]*F[4,x]
F[25,x,k[0]] = F[13,x]*F[24,x,k[0]]*F[44,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[27,x,k[0]] = F[26,x,k[0]]+F[42,x,k[0]]
F[28,x,k[0]] = F[21,x,k[0]]*F[27,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[30,x,k[0]] = F[19,x,k[0]]+F[29,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[21,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]+F[38,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[4,x]
F[34,x,k[0]] = F[30,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[13,x]*F[37,x,k[0]]
F[37,x,k[0]] = -k[0]*(F[15,x,1]-F[15,x,k[0]])/(-1+k[0])
F[38,x,k[0]] = F[39,x,k[0]]+F[40,x,k[0]]
F[39,x,k[0]] = F[18,x,k[0]]*F[30,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[13,x]*F[24,x,k[0]]*F[30,x,k[0]]
F[42,x,k[0]] = F[18,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[2,x]+F[29,x,k[0]]
F[44,x,k[0]] = F[0,x]+F[30,x,k[0]]
F[45,x] = F[4,x]+F[9,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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right) F_{13}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{5}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{45}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right)^{2} F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{24}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{24}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = -\frac{y \left(F_{15}\! \left(x , 1\right)-F_{15}\! \left(x , y\right)\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{24}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_14(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_13(x)*F_4(x))
Eq(F_11(x), F_12(x)/(F_0(x)*F_13(x)))
Eq(F_12(x), F_5(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x, 1))
Eq(F_16(x, k_0), F_15(x, k_0) + F_45(x))
Eq(F_16(x, k_0), F_17(x, k_0) + F_22(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_4(x))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)**2*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_13(x)*F_24(x, k_0)*F_4(x))
Eq(F_25(x, k_0), F_13(x)*F_24(x, k_0)*F_44(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_27(x, k_0), F_26(x, k_0) + F_42(x, k_0))
Eq(F_28(x, k_0), F_21(x, k_0)*F_27(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_30(x, k_0), F_19(x, k_0) + F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_21(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0) + F_38(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_4(x))
Eq(F_34(x, k_0), F_30(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_13(x)*F_37(x, k_0))
Eq(F_37(x, k_0), -F_15(x, 1) + (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), F_39(x, k_0) + F_40(x, k_0))
Eq(F_39(x, k_0), F_18(x, k_0)*F_30(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_13(x)*F_24(x, k_0)*F_30(x, k_0))
Eq(F_42(x, k_0), F_18(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_2(x) + F_29(x, k_0))
Eq(F_44(x, k_0), F_0(x) + F_30(x, k_0))
Eq(F_45(x), F_4(x) + F_9(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 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]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 2]], [[1, 0], [2, 0], [4, 0]], [[3, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, 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"tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}]}
Specification 4
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/15/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[18,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[9,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[14,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[11,x,k[0]]*F[20,x,k[0]]*F[4,x]
F[20,x,k[0]] = F[21,x,k[0]]+F[28,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[2,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[14,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = F[18,x,k[0]]+F[27,x,k[0]]
F[27,x,k[0]] = F[15,x,k[0]]*F[23,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[4,x]
F[31,x,k[0]] = F[14,x,k[0]]*F[30,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]+F[36,x,k[0]]+F[8,x]
F[34,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = (F[12,x,k[0]]-F[12,x,1])/(-1+k[0])
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[14,x,k[0]]*F[38,x,k[0]]
F[39,x,k[0]] = F[14,x,k[0]]*F[38,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[41,x,k[0]] = F[40,x,k[0]]+F[44,x,k[0]]
F[42,x,k[0]] = F[14,x,k[0]]*F[41,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = -k[0]*(F[12,x,1]-F[12,x,k[0]])/(-1+k[0])
F[44,x,k[0]] = 1/(-1+k[0])*(F[45,x,k[0]]*k[0]-F[45,x,1])
F[45,x,k[0]] = F[46,x]+F[59,x,k[0]]
F[46,x] = F[47,x,1]
F[47,x,k[0]] = F[11,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[11,x,k[0]]*F[4,x]*F[50,x]
F[50,x] = 1/F[4,x]*F[51,x]
F[51,x] = -F[1,x]-F[55,x]+F[52,x]
F[52,x] = F[0,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[8,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[52,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[50,x]*F[52,x]
F[59,x,k[0]] = F[60,x,k[0]]+F[61,x,k[0]]
F[60,x,k[0]] = F[16,x,k[0]]*F[5,x]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[4,x]*F[5,x]*F[63,x,k[0]]
F[64,x,k[0]] = F[15,x,k[0]]*F[4,x]*F[63,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[66,x,k[0]] = F[65,x,k[0]]+F[67,x,k[0]]+F[68,x,k[0]]
F[9,x,k[0]] = F[47,x,k[0]]+F[66,x,k[0]]
F[67,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[69,x,k[0]]
F[70,x,k[0]] = F[69,x,k[0]]+F[75,x,k[0]]
F[71,x,k[0]] = F[14,x,k[0]]*F[70,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[21,x,k[0]] = F[52,x]+F[72,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[14,x,k[0]]*F[15,x,k[0]]*F[20,x,k[0]]
F[76,x,k[0]] = F[4,x]*F[75,x,k[0]]
F[47,x,k[0]] = F[15,x,k[0]]+F[76,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[15,x,k[0]]*F[4,x]*F[50,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{F_{12}\! \left(x , 1\right)-F_{12}\! \left(x , y\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = -\frac{y \left(F_{12}\! \left(x , 1\right)-F_{12}\! \left(x , y\right)\right)}{-1+y}
F_{44}\! \left(x , y\right) = -\frac{-y F_{45}\! \left(x , y\right)+F_{45}\! \left(x , 1\right)}{-1+y}
F_{45}\! \left(x , y\right) = F_{46}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{46}\! \left(x \right) = F_{47}\! \left(x , 1\right)
F_{47}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{51}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{55}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{0}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right) F_{52}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{4}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{52}\! \left(x \right)+F_{72}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{4}\! \left(x \right) F_{50}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_18(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_15(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_9(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0)*F_15(x, k_0)**2)
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_11(x, k_0)*F_20(x, k_0)*F_4(x))
Eq(F_20(x, k_0), F_21(x, k_0) + F_28(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_2(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_14(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), F_18(x, k_0) + F_27(x, k_0))
Eq(F_27(x, k_0), F_15(x, k_0)*F_23(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_4(x))
Eq(F_31(x, k_0), F_14(x, k_0)*F_30(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0) + F_36(x, k_0) + F_8(x))
Eq(F_34(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), -F_12(x, k_0) + (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_14(x, k_0)*F_38(x, k_0))
Eq(F_39(x, k_0), F_14(x, k_0)*F_38(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_41(x, k_0), F_40(x, k_0) + F_44(x, k_0))
Eq(F_42(x, k_0), F_14(x, k_0)*F_41(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), -F_12(x, 1) + (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), (k_0*F_45(x, k_0) - F_45(x, 1))/(k_0 - 1))
Eq(F_45(x, k_0), F_46(x) + F_59(x, k_0))
Eq(F_46(x), F_47(x, 1))
Eq(F_47(x, k_0), F_11(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_11(x, k_0)*F_4(x)*F_50(x))
Eq(F_50(x), F_51(x)/F_4(x))
Eq(F_51(x), -F_1(x) + F_52(x) - F_55(x))
Eq(F_52(x), F_0(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_8(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_52(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_50(x)*F_52(x))
Eq(F_59(x, k_0), F_60(x, k_0) + F_61(x, k_0))
Eq(F_60(x, k_0), F_16(x, k_0)*F_5(x))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_4(x)*F_5(x)*F_63(x, k_0))
Eq(F_64(x, k_0), F_15(x, k_0)*F_4(x)*F_63(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_66(x, k_0), F_65(x, k_0) + F_67(x, k_0) + F_68(x, k_0))
Eq(F_9(x, k_0), F_47(x, k_0) + F_66(x, k_0))
Eq(F_67(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_69(x, k_0))
Eq(F_70(x, k_0), F_69(x, k_0) + F_75(x, k_0))
Eq(F_71(x, k_0), F_14(x, k_0)*F_70(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_21(x, k_0), F_52(x) + F_72(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_14(x, k_0)*F_15(x, k_0)*F_20(x, k_0))
Eq(F_76(x, k_0), F_4(x)*F_75(x, k_0))
Eq(F_47(x, k_0), F_15(x, k_0) + F_76(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_15(x, k_0)*F_4(x)*F_50(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"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], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [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]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "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": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [1, 0], [3, 0]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 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, 1], [0, 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": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[2, 2]]}]}], "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": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"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, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"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, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [2, 0], [2, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"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, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 3], [1, 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"tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 4], [1, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 4], [1, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [3, 4], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [3, 4], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [1, 4], [3, 4]]}, {"patt": [1, 2, 0], "pos": [[1, 4], [3, 4], [3, 4]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [3, 4], [3, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 4], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 4], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[3, 4]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]], [[2, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}]}
Specification 5
Strategy pack name: insertion_point_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/16/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[80,x]
F[10,x] = F[11,x]*F[14,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]^2*F[8,x]
F[14,x] = F[12,x]+F[15,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x,1]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[26,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[25,x,k[0]]
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[21,x,k[0]]^2*F[24,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[17,x,k[0]]+F[2,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[62,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[2,x]*F[21,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[6,x]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[8,x]
F[32,x,k[0]] = F[33,x,k[0]]+F[41,x,k[0]]
F[33,x,k[0]] = F[11,x]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[40,x,k[0]]
F[35,x,k[0]] = (-F[36,x,1]*k[0]+F[36,x,k[0]])/(-1+k[0])
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[24,x,k[0]]*F[38,x,k[0]]
F[38,x,k[0]] = F[22,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[40,x,k[0]] = -k[0]*(F[17,x,1]-F[17,x,k[0]])/(-1+k[0])
F[41,x,k[0]] = F[42,x,k[0]]+F[46,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[45,x,k[0]]
F[43,x,k[0]] = (-F[44,x,1]*k[0]+F[44,x,k[0]])/(-1+k[0])
F[44,x,k[0]] = F[2,x]*F[36,x,k[0]]
F[45,x,k[0]] = -k[0]*(F[30,x,1]-F[30,x,k[0]])/(-1+k[0])
F[46,x,k[0]] = F[47,x,k[0]]+F[49,x,k[0]]
F[47,x,k[0]] = (-F[48,x,1]*k[0]+F[48,x,k[0]])/(-1+k[0])
F[48,x,k[0]] = F[16,x]*F[36,x,k[0]]
F[49,x,k[0]] = -k[0]*(F[50,x,1]-F[50,x,k[0]])/(-1+k[0])
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]*F[8,x]
F[52,x,k[0]] = F[53,x,k[0]]+F[61,x,k[0]]
F[53,x,k[0]] = F[12,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[54,x,k[0]]+F[57,x,k[0]]
F[56,x,k[0]] = F[55,x,k[0]]*F[8,x]
F[56,x,k[0]] = F[30,x,k[0]]
F[57,x,k[0]] = F[2,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[54,x,k[0]]+F[59,x,k[0]]
F[60,x,k[0]] = F[59,x,k[0]]*F[8,x]
F[60,x,k[0]] = F[17,x,k[0]]
F[61,x,k[0]] = F[16,x]*F[58,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[64,x,k[0]]
F[63,x,k[0]] = F[17,x,k[0]]*F[21,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[75,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]*F[8,x]
F[67,x,k[0]] = F[68,x,k[0]]+F[74,x,k[0]]
F[68,x,k[0]] = F[22,x,k[0]]*F[69,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[8,x]*F[71,x]
F[71,x] = F[6,x]
F[72,x] = F[2,x]*F[73,x]
F[73,x] = F[4,x]+F[69,x]
F[74,x,k[0]] = F[17,x,k[0]]*F[73,x]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[8,x]
F[77,x,k[0]] = F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[22,x,k[0]]*F[54,x,k[0]]
F[79,x,k[0]] = F[17,x,k[0]]*F[58,x,k[0]]
F[80,x] = F[81,x]+F[85,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[12,x]*F[2,x]
F[83,x] = F[6,x]+F[84,x]
F[84,x] = F[30,x,1]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[12,x]*F[16,x]
F[87,x] = F[88,x]+F[93,x]
F[88,x] = F[89,x]
F[89,x] = F[8,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[12,x]*F[69,x]
F[92,x] = F[16,x]*F[73,x]
F[93,x] = F[50,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{80}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x , 1\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{21}\! \left(x , y\right)^{2} F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = -\frac{F_{36}\! \left(x , 1\right) y -F_{36}\! \left(x , y\right)}{-1+y}
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = -\frac{y \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y\right)\right)}{-1+y}
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = -\frac{F_{44}\! \left(x , 1\right) y -F_{44}\! \left(x , y\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{y \left(F_{30}\! \left(x , 1\right)-F_{30}\! \left(x , y\right)\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = -\frac{F_{48}\! \left(x , 1\right) y -F_{48}\! \left(x , y\right)}{-1+y}
F_{48}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = -\frac{y \left(F_{50}\! \left(x , 1\right)-F_{50}\! \left(x , y\right)\right)}{-1+y}
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{6}\! \left(x \right)
F_{72}\! \left(x \right) = F_{2}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right)+F_{69}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{73}\! \left(x \right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{58}\! \left(x , y\right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{85}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{83}\! \left(x \right) = F_{6}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{93}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{8}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{92}\! \left(x \right) = F_{16}\! \left(x \right) F_{73}\! \left(x \right)
F_{93}\! \left(x \right) = F_{50}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_80(x))
Eq(F_10(x), F_11(x)*F_14(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)**2*F_8(x))
Eq(F_14(x), F_12(x) + F_15(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x, 1))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_26(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_25(x, k_0))
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_21(x, k_0)**2*F_24(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_17(x, k_0) + F_2(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_62(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_2(x)*F_21(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_6(x))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_8(x))
Eq(F_32(x, k_0), F_33(x, k_0) + F_41(x, k_0))
Eq(F_33(x, k_0), F_11(x)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_40(x, k_0))
Eq(F_35(x, k_0), -F_36(x, 1) - F_36(x, k_0) + (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_24(x, k_0)*F_38(x, k_0))
Eq(F_38(x, k_0), F_22(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_40(x, k_0), -F_17(x, 1) + (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_41(x, k_0), F_42(x, k_0) + F_46(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_45(x, k_0))
Eq(F_43(x, k_0), -F_44(x, 1) - F_44(x, k_0) + (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_2(x)*F_36(x, k_0))
Eq(F_45(x, k_0), -F_30(x, 1) + (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_46(x, k_0), F_47(x, k_0) + F_49(x, k_0))
Eq(F_47(x, k_0), -F_48(x, 1) - F_48(x, k_0) + (k_0*F_48(x, k_0) - F_48(x, 1))/(k_0 - 1))
Eq(F_48(x, k_0), F_16(x)*F_36(x, k_0))
Eq(F_49(x, k_0), -F_50(x, 1) + (k_0*F_50(x, k_0) - F_50(x, 1))/(k_0 - 1))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0)*F_8(x))
Eq(F_52(x, k_0), F_53(x, k_0) + F_61(x, k_0))
Eq(F_53(x, k_0), F_12(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_54(x, k_0) + F_57(x, k_0))
Eq(F_56(x, k_0), F_55(x, k_0)*F_8(x))
Eq(F_56(x, k_0), F_30(x, k_0))
Eq(F_57(x, k_0), F_2(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_54(x, k_0) + F_59(x, k_0))
Eq(F_60(x, k_0), F_59(x, k_0)*F_8(x))
Eq(F_60(x, k_0), F_17(x, k_0))
Eq(F_61(x, k_0), F_16(x)*F_58(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_64(x, k_0))
Eq(F_63(x, k_0), F_17(x, k_0)*F_21(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_75(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0)*F_8(x))
Eq(F_67(x, k_0), F_68(x, k_0) + F_74(x, k_0))
Eq(F_68(x, k_0), F_22(x, k_0)*F_69(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_8(x))
Eq(F_71(x), F_6(x))
Eq(F_72(x), F_2(x)*F_73(x))
Eq(F_73(x), F_4(x) + F_69(x))
Eq(F_74(x, k_0), F_17(x, k_0)*F_73(x))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_8(x))
Eq(F_77(x, k_0), F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_22(x, k_0)*F_54(x, k_0))
Eq(F_79(x, k_0), F_17(x, k_0)*F_58(x, k_0))
Eq(F_80(x), F_81(x) + F_85(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_12(x)*F_2(x))
Eq(F_83(x), F_6(x) + F_84(x))
Eq(F_84(x), F_30(x, 1))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_12(x)*F_16(x))
Eq(F_87(x), F_88(x) + F_93(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_8(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_12(x)*F_69(x))
Eq(F_92(x), F_16(x)*F_73(x))
Eq(F_93(x), F_50(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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