0132_1203
Counting sequence:
1, 1, 2, 6, 22, 88, 367, 1571, 6861, 30468, 137229, 625573, 2881230, 13388094, 62688448, 295504025, 1401195334, 6678877732, 31984089193, 153809536017, 742462191363, 3596290278723, 17473993136316, 85147347832182, 415997039428899, 2037323575386383, 10000024336253853, 49186129273614768, 242393790200039756, 1196687427997471342, 5917920133042928976, 29311647094192569773, 145395847225338512156, 722214350189996750669, 3592092964531698384956, 17888105053182117621447, 89184016409400781954866, 445131777749672743679758, 2224047840902970074468182, 11123221105950673370055621, 55683510895085770647184702, 279005306838782028444915720, 1399167629029194980283567881, 7022331901072054017419544160, 35272099901515510541036838389, 177298367533271087792641061813, 891841493493430452609604471377, 4489180517035073947756404567448, 22611567631448657389933912923876, 113963814557234943455717755679787, 574731714264456555947298072309055, 2900113787928322772721183376093511, 14642222328779027860335147885528241, 73965972531089821418284831531984447, 373836236205859738906337127676778527, 1890371514450389632381963777778560032, 9563604459427228245715265656256129802, 48405805151674593846556695514980226050, 245113817337268164644581622238306901422, 1241726907076908381565698316403048707194, 6293121533212758472158899327184219789210, 31906704790191028340647048944837316578858, 161833326715749326500500841538841784429656, 821142957917306711108104180620397930117773, 4168014950493669223048428184376450675201244, 21163844582855892705168888060770499103122861, 107500379110058453002241368070850329014392798, 546224415730091799359895302000677632730981698, 2776346340509618455520804567158313474349192870, 14116060766494757853940241982634335440878026888, 71793782959444326815601359215613432434213990905, 365249692598955660886202589246019309296704657580, 1858741516917147219765751100307158273942087276877, 9461735900427428997751644688201847216191342402695, 48177252297904431866050526400885984930550106574831, 245374511821225480246405189914499822132220100586026, 1250057652055244875869100922631813644322151883139318, 6370021310245661555749636994871987838693639237751160, 32468271016063132792021049136629159085215116047429660, 165532078277962843518938434828890966152783982985786727, 844126035285348750817311629256279113441051999904539622, 4305583694027324405296665370827944209077638110560832125, 21966151282660205307606549097966660691061890343197563802, 112091006257302512675829625935132931572058551474287238457, 572110844574920379956446687535848307028085134876396262230, 2920653506873855495133892248769870185953891746328105860934, 14913110832811621022540521477581253163707109736668007290228, 76162779073045139127166585890288207333502522879427855737448, 389046663016774298243443096656564579975860886998139417480718, 1987664557718800561019832284763843089075183334080002874660835, 10156993040262053807263244415297322850994412906550834672029017, 51911802903910699088140717388168302012692696508409136969469383, 265365376583110675826668318628328706491974350114775994636036587, 1356744090089048946450641525503623160416025930784480756727333957, 6937860343843168026952301842380294981538272039960032042619483261, 35483426581087108711351107326552758219033435909021532320810359380, 181508276568819184885159441665583765334455154733301126416567704230, 928617235387622245312138186221953346345512428153757587384780180952, 4751656760873060615622186658494881545169196244765026525606044010086, 24317561836488799964507703704888360531063401818475330596080516703449, 124468746012804503243350906727031552840332908915189017409217528293056
Implicit equation for the generating function in Maple syntax:
x^3*F(x)^3+(x^2-5*x+2)*x*F(x)^2+(x+1)*(2*x-1)*F(x)-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{3} F \! \left(x \right)^{3}+\left(x^{2}-5 x +2\right) x F \! \left(x \right)^{2}+\left(x +1\right) \left(2 x -1\right) F \! \left(x \right)-2 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 88
a(6) = 367
a(7) = 1571
a(8) = 6861
a(9) = 30468
a(10) = 137229
a(11) = 625573
a(12) = 2881230
a(13) = 13388094
a(n+14) = 18*n*(n+1)/(n+16)/(n+15)*a(n)-18*(23*n+36)*(n+1)/(n+16)/(n+15)*a(n+1)+9/2*(391*n^2+1620*n+1544)/(n+16)/(n+15)*a(n+2)-3*(433*n^2+286*n-4863)/(n+16)/(n+15)*a(n+3)-1/2*(18571*n^2+223276*n+638988)/(n+16)/(n+15)*a(n+4)+1/8*(266425*n^2+3417769*n+10815822)/(n+16)/(n+15)*a(n+5)-1/8*(455705*n^2+6632129*n+23950446)/(n+16)/(n+15)*a(n+6)+1/4*(245047*n^2+4033768*n+16509135)/(n+16)/(n+15)*a(n+7)-1/8*(358243*n^2+6605005*n+30306696)/(n+16)/(n+15)*a(n+8)+1/4*(91297*n^2+1867024*n+9507849)/(n+16)/(n+15)*a(n+9)-3/8*(21593*n^2+485627*n+2721148)/(n+16)/(n+15)*a(n+10)+1/8*(15593*n^2+382907*n+2343864)/(n+16)/(n+15)*a(n+11)-3/4*(401*n^2+10688*n+71049)/(n+16)/(n+15)*a(n+12)+1/2*(53*n+731)/(n+16)*a(n+13), n >= 14
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 88
a \! \left(6\right) = 367
a \! \left(7\right) = 1571
a \! \left(8\right) = 6861
a \! \left(9\right) = 30468
a \! \left(10\right) = 137229
a \! \left(11\right) = 625573
a \! \left(12\right) = 2881230
a \! \left(13\right) = 13388094
a \! \left(n +14\right) = \frac{18 n \left(n +1\right) a \! \left(n \right)}{\left(n +16\right) \left(n +15\right)}-\frac{18 \left(23 n +36\right) \left(n +1\right) a \! \left(n +1\right)}{\left(n +16\right) \left(n +15\right)}+\frac{9 \left(391 n^{2}+1620 n +1544\right) a \! \left(n +2\right)}{2 \left(n +16\right) \left(n +15\right)}-\frac{3 \left(433 n^{2}+286 n -4863\right) a \! \left(n +3\right)}{\left(n +16\right) \left(n +15\right)}-\frac{\left(18571 n^{2}+223276 n +638988\right) a \! \left(n +4\right)}{2 \left(n +16\right) \left(n +15\right)}+\frac{\left(266425 n^{2}+3417769 n +10815822\right) a \! \left(n +5\right)}{8 \left(n +16\right) \left(n +15\right)}-\frac{\left(455705 n^{2}+6632129 n +23950446\right) a \! \left(n +6\right)}{8 \left(n +16\right) \left(n +15\right)}+\frac{\left(245047 n^{2}+4033768 n +16509135\right) a \! \left(n +7\right)}{4 \left(n +16\right) \left(n +15\right)}-\frac{\left(358243 n^{2}+6605005 n +30306696\right) a \! \left(n +8\right)}{8 \left(n +16\right) \left(n +15\right)}+\frac{\left(91297 n^{2}+1867024 n +9507849\right) a \! \left(n +9\right)}{4 \left(n +16\right) \left(n +15\right)}-\frac{3 \left(21593 n^{2}+485627 n +2721148\right) a \! \left(n +10\right)}{8 \left(n +16\right) \left(n +15\right)}+\frac{\left(15593 n^{2}+382907 n +2343864\right) a \! \left(n +11\right)}{8 \left(n +16\right) \left(n +15\right)}-\frac{3 \left(401 n^{2}+10688 n +71049\right) a \! \left(n +12\right)}{4 \left(n +16\right) \left(n +15\right)}+\frac{\left(53 n +731\right) a \! \left(n +13\right)}{2 n +32}, \quad n \geq 14
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/67/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[32,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[26,x]*F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]*F[26,x]
F[13,x,k[0]] = F[12,x,k[0]]+F[14,x,k[0]]+F[30,x,k[0]]+F[31,x,k[0]]+F[6,x]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[0,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[14,x,k[0]]+F[18,x,k[0]]+F[6,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[26,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[22,x,k[0]]+F[28,x,k[0]]+F[6,x]
F[20,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = F[19,x,k[0]]+F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]*F[26,x]
F[23,x,k[0]] = F[20,x,k[0]]+F[22,x,k[0]]+F[24,x,k[0]]+F[27,x,k[0]]+F[6,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[26,x]
F[25,x,k[0]] = -k[0]*(F[13,x,1]-F[13,x,k[0]])/(-1+k[0])
F[26,x] = x
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[26,x]*F[29,x,k[0]]
F[29,x,k[0]] = -k[0]*(F[19,x,1]-F[19,x,k[0]])/(-1+k[0])
F[30,x,k[0]] = F[12,x,k[0]]
F[31,x,k[0]] = F[18,x,k[0]]
F[32,x] = F[18,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_{26}\! \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_{32}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{y \left(F_{13}\! \left(x , 1\right)-F_{13}\! \left(x , y\right)\right)}{-1+y}
F_{26}\! \left(x \right) = x
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{y \left(F_{19}\! \left(x , 1\right)-F_{19}\! \left(x , y\right)\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{18}\! \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_26(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_32(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_26(x)*F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_26(x))
Eq(F_13(x, k_0), F_12(x, k_0) + F_14(x, k_0) + F_30(x, k_0) + F_31(x, k_0) + F_6(x))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_0(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0) + F_18(x, k_0) + F_6(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_26(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_22(x, k_0) + F_28(x, k_0) + F_6(x))
Eq(F_20(x, k_0), F_15(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), F_19(x, k_0) + F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0)*F_26(x))
Eq(F_23(x, k_0), F_20(x, k_0) + F_22(x, k_0) + F_24(x, k_0) + F_27(x, k_0) + F_6(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_26(x))
Eq(F_25(x, k_0), -F_13(x, 1) + (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_26(x), x)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_26(x)*F_29(x, k_0))
Eq(F_29(x, k_0), -F_19(x, 1) + (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_12(x, k_0))
Eq(F_31(x, k_0), F_18(x, k_0))
Eq(F_32(x), F_18(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_isolated", "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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[2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[1, 0]]}], "strategy_class": "ObstructionInferralStrategy"}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [5, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}], "strategy_class": "ObstructionInferralStrategy"}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: row_and_col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/68/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[21,x]*F[6,x]
F[6,x] = F[38,x]+F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[12,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]+F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[8,x,k[0]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x]
F[14,x,k[0]] = F[15,x,k[0]]+F[16,x,k[0]]
F[15,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[21,x]*F[22,x]
F[18,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[19,x,k[0]] = F[15,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]*F[21,x]
F[21,x] = x
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[21,x]*F[26,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]
F[31,x] = F[21,x]*F[32,x]
F[32,x] = F[1,x]+F[30,x]
F[33,x] = F[34,x]+F[35,x]+F[37,x]
F[34,x] = 0
F[35,x] = F[21,x]*F[36,x]
F[36,x] = F[27,x]+F[33,x]
F[37,x] = F[21,x]*F[29,x]
F[38,x] = F[39,x]
F[39,x] = F[21,x]*F[22,x]*F[40,x]
F[40,x] = F[19,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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{21}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{38}\! \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_{12}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x \right) F_{22}\! \left(x \right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{21}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{21}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \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_21(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_21(x)*F_6(x))
Eq(F_6(x), F_38(x) + F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_12(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x) + F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_8(x, k_0))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_21(x))
Eq(F_14(x, k_0), F_15(x, k_0) + F_16(x, k_0))
Eq(F_15(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_21(x)*F_22(x))
Eq(F_18(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), F_15(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)*F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_21(x)*F_26(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_21(x)*F_32(x))
Eq(F_32(x), F_1(x) + F_30(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_37(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_21(x)*F_36(x))
Eq(F_36(x), F_27(x) + F_33(x))
Eq(F_37(x), F_21(x)*F_29(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_21(x)*F_22(x)*F_40(x))
Eq(F_40(x), F_19(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.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": "row_and_col_placements_tracked_fusion_isolated", "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}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy"}]}
Specification JSON:
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{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "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": [1, 0], "pos": [[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": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_isolated_req_corrob
Tree: http://permpal.com/tree/69/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[32,x]+F[6,x]+F[7,x]
F[6,x] = 0
F[7,x] = F[26,x]*F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x,k[0]]*F[26,x]
F[13,x,k[0]] = F[12,x,k[0]]+F[14,x,k[0]]+F[30,x,k[0]]+F[31,x,k[0]]+F[6,x]
F[14,x,k[0]] = F[15,x,k[0]]*F[16,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[0,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[14,x,k[0]]+F[18,x,k[0]]+F[6,x]
F[18,x,k[0]] = F[19,x,k[0]]*F[26,x]
F[19,x,k[0]] = F[20,x,k[0]]+F[22,x,k[0]]+F[28,x,k[0]]+F[6,x]
F[20,x,k[0]] = F[15,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = F[19,x,k[0]]+F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]*F[26,x]
F[23,x,k[0]] = F[20,x,k[0]]+F[22,x,k[0]]+F[24,x,k[0]]+F[27,x,k[0]]+F[6,x]
F[24,x,k[0]] = F[25,x,k[0]]*F[26,x]
F[25,x,k[0]] = -k[0]*(F[13,x,1]-F[13,x,k[0]])/(-1+k[0])
F[26,x] = x
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[26,x]*F[29,x,k[0]]
F[29,x,k[0]] = -k[0]*(F[19,x,1]-F[19,x,k[0]])/(-1+k[0])
F[30,x,k[0]] = F[12,x,k[0]]
F[31,x,k[0]] = F[18,x,k[0]]
F[32,x] = F[18,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_{26}\! \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_{32}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{13}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{26}\! \left(x \right)
F_{25}\! \left(x , y\right) = -\frac{y \left(F_{13}\! \left(x , 1\right)-F_{13}\! \left(x , y\right)\right)}{-1+y}
F_{26}\! \left(x \right) = x
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{26}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = -\frac{y \left(F_{19}\! \left(x , 1\right)-F_{19}\! \left(x , y\right)\right)}{-1+y}
F_{30}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{18}\! \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_26(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_32(x) + F_6(x) + F_7(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_26(x)*F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_26(x))
Eq(F_13(x, k_0), F_12(x, k_0) + F_14(x, k_0) + F_30(x, k_0) + F_31(x, k_0) + F_6(x))
Eq(F_14(x, k_0), F_15(x, k_0)*F_16(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_0(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0) + F_18(x, k_0) + F_6(x))
Eq(F_18(x, k_0), F_19(x, k_0)*F_26(x))
Eq(F_19(x, k_0), F_20(x, k_0) + F_22(x, k_0) + F_28(x, k_0) + F_6(x))
Eq(F_20(x, k_0), F_15(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), F_19(x, k_0) + F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0)*F_26(x))
Eq(F_23(x, k_0), F_20(x, k_0) + F_22(x, k_0) + F_24(x, k_0) + F_27(x, k_0) + F_6(x))
Eq(F_24(x, k_0), F_25(x, k_0)*F_26(x))
Eq(F_25(x, k_0), -F_13(x, 1) + (-k_0*F_13(x, k_0) + F_13(x, 1))/(1 - k_0))
Eq(F_26(x), x)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_26(x)*F_29(x, k_0))
Eq(F_29(x, k_0), -F_19(x, 1) + (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), F_12(x, k_0))
Eq(F_31(x, k_0), F_18(x, k_0))
Eq(F_32(x), F_18(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_placements_tracked_fusion_isolated_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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[2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], 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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": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 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{"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"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, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": 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[5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[1, 0]]}], "strategy_class": "ObstructionInferralStrategy"}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [5, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}], "strategy_class": "ObstructionInferralStrategy"}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[3, 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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 0], [5, 0]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [5, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[4, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [0], "pos": [[2, 0]]}], "strategy_class": "ObstructionInferralStrategy"}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/70/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[40,x]+F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[14,x,k[0]]
F[10,x,k[0]] = F[0,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[9,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[23,x]
F[16,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]
F[17,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[23,x]*F[24,x]
F[20,x,k[0]] = (F[21,x,k[0]]*k[0]-F[21,x,1])/(-1+k[0])
F[21,x,k[0]] = F[17,x,k[0]]+F[22,x,k[0]]
F[22,x,k[0]] = F[20,x,k[0]]*F[23,x]
F[23,x] = x
F[24,x] = F[1,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[23,x]*F[28,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[23,x]*F[34,x]
F[34,x] = F[1,x]+F[32,x]
F[35,x] = F[36,x]+F[37,x]+F[39,x]
F[36,x] = 0
F[37,x] = F[23,x]*F[38,x]
F[38,x] = F[29,x]+F[35,x]
F[39,x] = F[23,x]*F[31,x]
F[40,x] = F[41,x]
F[41,x] = F[23,x]*F[24,x]*F[42,x]
F[42,x] = F[21,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_{23}\! \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_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{40}\! \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_{14}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{0}\! \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_{13}\! \left(x , y\right) F_{9}\! \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_{23}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right) F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{23}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{23}\! \left(x \right) F_{31}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \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_23(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_23(x)*F_7(x))
Eq(F_7(x), F_40(x) + F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_14(x, k_0))
Eq(F_10(x, k_0), F_0(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_9(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_23(x))
Eq(F_16(x, k_0), F_17(x, k_0) + F_18(x, k_0))
Eq(F_17(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_23(x)*F_24(x))
Eq(F_20(x, k_0), (-k_0*F_21(x, k_0) + F_21(x, 1))/(1 - k_0))
Eq(F_21(x, k_0), F_17(x, k_0) + F_22(x, k_0))
Eq(F_22(x, k_0), F_20(x, k_0)*F_23(x))
Eq(F_23(x), x)
Eq(F_24(x), F_1(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_23(x)*F_28(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_23(x)*F_34(x))
Eq(F_34(x), F_1(x) + F_32(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_39(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_23(x)*F_38(x))
Eq(F_38(x), F_29(x) + F_35(x))
Eq(F_39(x), F_23(x)*F_31(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_23(x)*F_24(x)*F_42(x))
Eq(F_42(x), F_21(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_col_placements_tracked_fusion_isolated", "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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[1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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[2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": 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"pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2], [1, 2], [2, 0]], [[3, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 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[[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"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": [[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, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"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": [[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, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 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": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "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, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "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, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[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": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[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": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_isolated
Tree: http://permpal.com/tree/71/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[21,x]*F[6,x]
F[6,x] = F[38,x]+F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[12,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]+F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[8,x,k[0]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x]
F[14,x,k[0]] = F[15,x,k[0]]+F[16,x,k[0]]
F[15,x,k[0]] = (F[8,x,k[0]]*k[0]-F[8,x,1])/(-1+k[0])
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[21,x]*F[22,x]
F[18,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[19,x,k[0]] = F[15,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]*F[21,x]
F[21,x] = x
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[21,x]*F[26,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]
F[31,x] = F[21,x]*F[32,x]
F[32,x] = F[1,x]+F[30,x]
F[33,x] = F[34,x]+F[35,x]+F[37,x]
F[34,x] = 0
F[35,x] = F[21,x]*F[36,x]
F[36,x] = F[27,x]+F[33,x]
F[37,x] = F[21,x]*F[29,x]
F[38,x] = F[39,x]
F[39,x] = F[21,x]*F[22,x]*F[40,x]
F[40,x] = F[19,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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{21}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{38}\! \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_{12}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x \right) F_{22}\! \left(x \right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{21}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{21}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \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_21(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_21(x)*F_6(x))
Eq(F_6(x), F_38(x) + F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_12(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x) + F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_8(x, k_0))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_21(x))
Eq(F_14(x, k_0), F_15(x, k_0) + F_16(x, k_0))
Eq(F_15(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_21(x)*F_22(x))
Eq(F_18(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_19(x, k_0), F_15(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)*F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_21(x)*F_26(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_21(x)*F_32(x))
Eq(F_32(x), F_1(x) + F_30(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_37(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_21(x)*F_36(x))
Eq(F_36(x), F_27(x) + F_33(x))
Eq(F_37(x), F_21(x)*F_29(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_21(x)*F_22(x)*F_40(x))
Eq(F_40(x), F_19(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": 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}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_isolated", "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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[2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 0, 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