0231_2301
Counting sequence:
1, 1, 2, 6, 22, 88, 366, 1556, 6720, 29396, 129996, 580276, 2611290, 11834116, 53963190, 247414100, 1139860150, 5274189156, 24498929370, 114199276476, 534028437710, 2504543749532, 11777411979050, 55518128412708, 262301674637860, 1241868060613788, 5891050888101112, 27995910970158108, 133268783605730774, 635399515622237548, 3033940330121284634, 14506743281153923212, 69454444046385293664, 332939197257047868276, 1597845794233980977164, 7676840935023550353268, 36921796493911298451190, 177751188852863578409076, 856544956249907535913666, 4131196889076943498666676, 19942116904306903316781280, 96342762522551614852123212, 465804219276910803929434836, 2253768515422270152955481148, 10912463875792096630313860766, 52872628213043911189376705420, 256342910452907457880286924402, 1243605309934588012681770284988, 6036759472048963930151445998438, 29320749145631902427338436913148, 142490713898965285881839365271666, 692834233577266493803694213680980, 3370504089628000473022468976117778, 16404955449457471236552755658305652, 79884458175374914537064947615578198, 389178948554873513712090226632234108, 1896834040353128745668395753192481388, 9249021000849977543621202741508560612, 45117231871650273646997084495911389528, 220172712807124723035557022183583273572, 1074863485012621649246345234445265776506, 5249362460796393805965859881576919483988, 25645913074581657880790354014369875384758, 125338148396821570296829613742324334478004, 612769666225331321640062084201867319472838, 2996785750470397170408358610830205622864100, 14660688183664415487721459350403097684050666, 71744596909204738138021933877440145781086204, 351201492344624099800476112403329483680587054, 1719697686656683282047028540541287568200891164, 8423118468553490168823592647521673889997628810, 41268183211448904974010080175227011930748801828, 202244238968340835798162491703611857732043414304, 991407493109974344045250313870815648146246721612, 4861165939024689991885559547718244370925369545044, 23841743297666710705135818296651049944843289218300, 116961274736037221494065988318797615429297551957838, 573918229207691739935413790879363493315979901809932, 2816820705722834316018600862661314789555433125962402, 13828248046283006482932635159204396756015571407198332, 67900268719131424674329565049653911780317804179650290, 333480074590905863965256922664264906570584713850042604, 1638174359418926004671887266689982390164015590773091422, 8048965130232461991324864269405315137647006760414543156, 39555563949750582169020701934625582168159438901665967562, 194428857810637402223770230838907495639385134614894034900, 955867164242146976392607885546563251392174019389184880414, 4700198124217615711657391292614066851269781733689152024876, 23116111568891573167698930352771664753005981582885892645596, 113708163516908511933936186257325195928647616626984654487636, 559429112494886025028114589406041967259545500391127225748760, 2752792000590113543368041267831650038874483742170463948584852, 13547996102869391854383525155814369497055960456062564386296066, 66688127582884290154451475082661869285007157822425683647720068, 328316184467535880428694487475627461527366702394364007912532046, 1616608751230767510011454353801603268797818234195987038680898340, 7961319005007176701634659649566035984230668936076735847505566692, 39213105540565953816327572075510773229293183640655025727182041708, 193171141581689431725565156227345207511914906582403006268824418888, 951736606961195685585464697046814846055472266402599099753430684668, 4689792008691649172382476340196531764334849209205348821949397427930
Generating function in Maple syntax:
(2*(5*x^2-6*x+1)^(1/2)*x-4*x^2-(5*x^2-6*x+1)^(1/2)+3*x)*(x-1)/(4*x^4-20*x^3+24*x^2-10*x+1)
Generating function in latex syntax:
\frac{\left(2 \sqrt{5 x^{2}-6 x +1}\, x -4 x^{2}-\sqrt{5 x^{2}-6 x +1}+3 x \right) \left(x -1\right)}{4 x^{4}-20 x^{3}+24 x^{2}-10 x +1}
Generating function in sympy syntax:
(x - 1)*(-4*x**2 + 2*x*sqrt(5*x**2 - 6*x + 1) + 3*x - sqrt(5*x**2 - 6*x + 1))/(4*x**4 - 20*x**3 + 24*x**2 - 10*x + 1)
Implicit equation for the generating function in Maple syntax:
(4*x^4-20*x^3+24*x^2-10*x+1)*F(x)^2+2*x*(4*x-3)*(x-1)*F(x)-(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{4}-20 x^{3}+24 x^{2}-10 x +1\right) F \! \left(x \right)^{2}+2 x \left(4 x -3\right) \left(x -1\right) F \! \left(x \right)-\left(x -1\right)^{2} = 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) = 366
a(n+7) = 40*(n+1)/(n+7)*a(n)-4*(105+67*n)/(n+7)*a(n+1)+4*(377+153*n)/(n+7)*a(n+2)-16*(143+42*n)/(n+7)*a(n+3)+28*(61+14*n)/(n+7)*a(n+4)-(643+121*n)/(n+7)*a(n+5)+2*(56+9*n)/(n+7)*a(n+6), n >= 7
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) = 366
a \! \left(n +7\right) = \frac{40 \left(n +1\right) a \! \left(n \right)}{n +7}-\frac{4 \left(105+67 n \right) a \! \left(n +1\right)}{n +7}+\frac{4 \left(377+153 n \right) a \! \left(n +2\right)}{n +7}-\frac{16 \left(143+42 n \right) a \! \left(n +3\right)}{n +7}+\frac{28 \left(61+14 n \right) a \! \left(n +4\right)}{n +7}-\frac{\left(643+121 n \right) a \! \left(n +5\right)}{n +7}+\frac{2 \left(56+9 n \right) a \! \left(n +6\right)}{n +7}, \quad n \geq 7
Specification 1
Strategy pack name: point_and_col_placements
Tree: http://permpal.com/tree/183/
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[4,x]
F[3,x] = x
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[3,x]*F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[0,x]+F[6,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[3,x]
F[11,x] = F[12,x]+F[21,x]
F[12,x] = F[0,x]+F[13,x]+F[9,x]
F[13,x] = F[14,x]
F[14,x] = F[0,x]*F[15,x]*F[3,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]+F[18,x]
F[17,x] = F[16,x]*F[3,x]
F[18,x] = F[15,x]*F[3,x]
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[16,x]*F[3,x]
F[21,x] = F[22,x]*F[3,x]
F[22,x] = F[11,x]+F[23,x]
F[23,x] = F[16,x]*F[5,x]
F[24,x] = F[25,x]
F[25,x] = F[16,x]*F[3,x]*F[7,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
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_{3}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{24}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \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_{3}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right)+F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{3}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right) F_{3}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{3}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{5}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right) F_{3}\! \left(x \right) F_{7}\! \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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_3(x)*F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_0(x) + F_6(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_3(x))
Eq(F_11(x), F_12(x) + F_21(x))
Eq(F_12(x), F_0(x) + F_13(x) + F_9(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_0(x)*F_15(x)*F_3(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x) + F_18(x))
Eq(F_17(x), F_16(x)*F_3(x))
Eq(F_18(x), F_15(x)*F_3(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_16(x)*F_3(x))
Eq(F_21(x), F_22(x)*F_3(x))
Eq(F_22(x), F_11(x) + F_23(x))
Eq(F_23(x), F_16(x)*F_5(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_16(x)*F_3(x)*F_7(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": 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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_and_col_placements", "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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"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, 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, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [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, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [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, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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"pos": [[2, 5], [2, 5]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 3], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [3, 4], [3, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 2], [1, 2], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}, {"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, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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[3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [3, 3], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [3, 3], [3, 3]]}, {"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": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "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}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}], "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": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "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}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "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, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 0], "pos": [[2, 5], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 5], [2, 5], [2, 5]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "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}}]}, {"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"}}]}
Specification 2
Strategy pack name: row_and_col_placements
Tree: http://permpal.com/tree/184/
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[8,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[5,x]*F[8,x]
F[5,x] = F[6,x]+F[9,x]
F[6,x] = F[1,x]+F[4,x]+F[7,x]
F[7,x] = F[6,x]*F[8,x]
F[8,x] = x
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[23,x]*F[8,x]
F[11,x] = F[12,x]+F[36,x]+F[38,x]
F[12,x] = F[1,x]+F[13,x]+F[32,x]
F[13,x] = F[14,x]*F[8,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = 1/F[8,x]*F[16,x]
F[16,x] = -F[1,x]+F[0,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[8,x]
F[19,x] = F[11,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]*F[23,x]*F[8,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[23,x]*F[8,x]
F[26,x] = F[24,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[31,x]
F[28,x] = 0
F[29,x] = F[30,x]*F[8,x]
F[30,x] = F[24,x]+F[27,x]
F[31,x] = F[26,x]*F[8,x]
F[32,x] = F[33,x]*F[8,x]
F[33,x] = 1/F[8,x]*F[34,x]
F[34,x] = -F[1,x]-F[35,x]+F[15,x]
F[35,x] = F[14,x]*F[8,x]
F[36,x] = F[37,x]
F[37,x] = F[19,x]*F[8,x]
F[38,x] = F[39,x]*F[8,x]
F[39,x] = 1/F[8,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = -F[12,x]+F[33,x]
F[42,x] = F[43,x]*F[8,x]
F[43,x] = F[3,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[8,x]
F[46,x] = F[11,x]+F[47,x]+F[52,x]
F[47,x] = F[48,x]
F[48,x] = F[19,x]*F[49,x]*F[8,x]
F[49,x] = F[23,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[49,x]^2*F[8,x]
F[52,x] = F[53,x]
F[53,x] = F[39,x]*F[49,x]*F[8,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_{8}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{6}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{32}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{1}\! \left(x \right)+F_{0}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right) F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{23}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{34}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{35}\! \left(x \right)+F_{15}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{33}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{3}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{8}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right)+F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{19}\! \left(x \right) F_{49}\! \left(x \right) F_{8}\! \left(x \right)
F_{49}\! \left(x \right) = F_{23}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{39}\! \left(x \right) F_{49}\! \left(x \right) F_{8}\! \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)*F_8(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_5(x)*F_8(x))
Eq(F_5(x), F_6(x) + F_9(x))
Eq(F_6(x), F_1(x) + F_4(x) + F_7(x))
Eq(F_7(x), F_6(x)*F_8(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_23(x)*F_8(x))
Eq(F_11(x), F_12(x) + F_36(x) + F_38(x))
Eq(F_12(x), F_1(x) + F_13(x) + F_32(x))
Eq(F_13(x), F_14(x)*F_8(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x)/F_8(x))
Eq(F_16(x), F_0(x) - F_1(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_8(x))
Eq(F_19(x), F_11(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x)*F_23(x)*F_8(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_23(x)*F_8(x))
Eq(F_26(x), F_24(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_31(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_30(x)*F_8(x))
Eq(F_30(x), F_24(x) + F_27(x))
Eq(F_31(x), F_26(x)*F_8(x))
Eq(F_32(x), F_33(x)*F_8(x))
Eq(F_33(x), F_34(x)/F_8(x))
Eq(F_34(x), -F_1(x) + F_15(x) - F_35(x))
Eq(F_35(x), F_14(x)*F_8(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_19(x)*F_8(x))
Eq(F_38(x), F_39(x)*F_8(x))
Eq(F_39(x), F_40(x)/F_8(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), -F_12(x) + F_33(x))
Eq(F_42(x), F_43(x)*F_8(x))
Eq(F_43(x), F_3(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_8(x))
Eq(F_46(x), F_11(x) + F_47(x) + F_52(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_19(x)*F_49(x)*F_8(x))
Eq(F_49(x), F_23(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_49(x)**2*F_8(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_39(x)*F_49(x)*F_8(x))
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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_and_col_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "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]]}, {"patt": [2, 3, 0, 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], "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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "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"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"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, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [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, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 3], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 1], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 1], [1, 1]]}, {"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, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "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, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "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": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], 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"rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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.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": [], "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
Tree: http://permpal.com/tree/185/
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[6,x]
F[6,x] = F[13,x]*F[7,x]
F[7,x] = F[23,x]+F[8,x]
F[8,x] = F[0,x]+F[22,x]+F[9,x]
F[9,x] = F[10,x]*F[13,x]*F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[1,x]+F[16,x]+F[17,x]
F[16,x] = F[13,x]*F[14,x]
F[17,x] = F[13,x]*F[15,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = -F[0,x]+F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[13,x]*F[18,x]
F[22,x] = F[5,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]*F[25,x]
F[25,x] = F[26,x]+F[56,x]
F[26,x] = -F[50,x]+F[27,x]
F[27,x] = F[28,x]+F[30,x]+F[48,x]
F[28,x] = 1/F[13,x]*F[29,x]
F[29,x] = F[19,x]
F[30,x] = F[31,x]
F[31,x] = F[13,x]*F[32,x]*F[45,x]
F[32,x] = 1/F[13,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[4,x]-F[43,x]+F[35,x]
F[35,x] = 1/F[13,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[40,x]+F[38,x]
F[38,x] = 1/F[13,x]*F[39,x]
F[39,x] = F[2,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[40,x]^2*F[13,x]
F[43,x] = F[44,x]
F[44,x] = F[13,x]*F[27,x]
F[45,x] = F[10,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[45,x]^2*F[13,x]
F[48,x] = F[49,x]
F[49,x] = F[13,x]*F[27,x]*F[45,x]
F[50,x] = F[51,x]
F[51,x] = F[45,x]*F[52,x]
F[52,x] = -F[53,x]+F[35,x]
F[53,x] = F[4,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[13,x]*F[26,x]
F[56,x] = F[57,x]
F[57,x] = F[45,x]*F[58,x]
F[58,x] = -F[53,x]+F[7,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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right)+F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{22}\! \left(x \right) = F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{56}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{19}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right) F_{45}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{4}\! \left(x \right)-F_{43}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{40} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right)
F_{45}\! \left(x \right) = F_{10}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{45} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right) F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{45}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{35}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{45}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{7}\! \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_6(x))
Eq(F_6(x), F_13(x)*F_7(x))
Eq(F_7(x), F_23(x) + F_8(x))
Eq(F_8(x), F_0(x) + F_22(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_13(x)*F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_1(x) + F_16(x) + F_17(x))
Eq(F_16(x), F_13(x)*F_14(x))
Eq(F_17(x), F_13(x)*F_15(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), -F_0(x) + F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_13(x)*F_18(x))
Eq(F_22(x), F_5(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_56(x))
Eq(F_26(x), F_27(x) - F_50(x))
Eq(F_27(x), F_28(x) + F_30(x) + F_48(x))
Eq(F_28(x), F_29(x)/F_13(x))
Eq(F_29(x), F_19(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_13(x)*F_32(x)*F_45(x))
Eq(F_32(x), F_33(x)/F_13(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) - F_4(x) - F_43(x))
Eq(F_35(x), F_36(x)/F_13(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x) - F_40(x))
Eq(F_38(x), F_39(x)/F_13(x))
Eq(F_39(x), F_2(x))
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_13(x)*F_40(x)**2)
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_13(x)*F_27(x))
Eq(F_45(x), F_10(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)*F_45(x)**2)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_13(x)*F_27(x)*F_45(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_45(x)*F_52(x))
Eq(F_52(x), F_35(x) - F_53(x))
Eq(F_53(x), F_4(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_13(x)*F_26(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_45(x)*F_58(x))
Eq(F_58(x), -F_53(x) + F_7(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": 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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_and_row_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "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]]}, {"patt": [2, 3, 0, 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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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]]}, 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"comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 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": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[2, 0]]}], "ignore_parent": false, "include_empty": false, "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": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [3, 4], [3, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "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, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 2], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}], "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}}, "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": [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": [], "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}}, "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": [[0, 1], [0, 1]]}], "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], "pos": [[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"}]}, {"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": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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.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"}}]}
Specification 4
Strategy pack name: insertion_row_and_col_placements_req_corrob
Tree: http://permpal.com/tree/186/
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]+F[9,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]^2*F[4,x]
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[25,x]
F[13,x] = F[14,x]*F[6,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[20,x]+F[22,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[4,x]*F[6,x]
F[22,x] = F[23,x]
F[23,x] = F[16,x]*F[24,x]*F[4,x]
F[24,x] = F[15,x]+F[6,x]
F[25,x] = F[26,x]+F[69,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[2,x]*F[6,x]
F[28,x] = F[29,x]+F[42,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[17,x]*F[2,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[2,x]+F[29,x]
F[35,x] = F[2,x]*F[36,x]
F[36,x] = F[18,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[41,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[18,x]+F[37,x]
F[41,x] = F[36,x]*F[4,x]
F[42,x] = F[38,x]+F[43,x]+F[60,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[54,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[2,x]*F[7,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[14,x]*F[2,x]*F[6,x]
F[52,x] = F[24,x]*F[53,x]
F[53,x] = F[29,x]+F[48,x]
F[54,x] = F[55,x]+F[59,x]
F[55,x] = F[2,x]*F[56,x]
F[56,x] = F[57,x]+F[7,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[20,x]+F[22,x]+F[38,x]
F[59,x] = F[18,x]*F[46,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[53,x]+F[62,x]
F[62,x] = F[42,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[2,x]*F[6,x]*F[7,x]
F[68,x] = F[24,x]*F[62,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[10,x]*F[6,x]
F[71,x] = F[72,x]+F[74,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[18,x]*F[4,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[4,x]*F[76,x]
F[76,x] = F[57,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_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{25}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{69}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right) F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{42}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right) F_{2}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right)+F_{43}\! \left(x \right)+F_{60}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{2}\! \left(x \right) F_{7}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right) F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{29}\! \left(x \right)+F_{48}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{59}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)+F_{38}\! \left(x \right)
F_{59}\! \left(x \right) = F_{18}\! \left(x \right) F_{46}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{42}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right) F_{6}\! \left(x \right) F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{24}\! \left(x \right) F_{62}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{10}\! \left(x \right) F_{6}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{57}\! \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_6(x) + F_9(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_6(x)**2)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_25(x))
Eq(F_13(x), F_14(x)*F_6(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_20(x) + F_22(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_4(x)*F_6(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_16(x)*F_24(x)*F_4(x))
Eq(F_24(x), F_15(x) + F_6(x))
Eq(F_25(x), F_26(x) + F_69(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_2(x)*F_6(x))
Eq(F_28(x), F_29(x) + F_42(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_17(x)*F_2(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_2(x) + F_29(x))
Eq(F_35(x), F_2(x)*F_36(x))
Eq(F_36(x), F_18(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_41(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_18(x) + F_37(x))
Eq(F_41(x), F_36(x)*F_4(x))
Eq(F_42(x), F_38(x) + F_43(x) + F_60(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_54(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_2(x)*F_7(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_14(x)*F_2(x)*F_6(x))
Eq(F_52(x), F_24(x)*F_53(x))
Eq(F_53(x), F_29(x) + F_48(x))
Eq(F_54(x), F_55(x) + F_59(x))
Eq(F_55(x), F_2(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_7(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_20(x) + F_22(x) + F_38(x))
Eq(F_59(x), F_18(x)*F_46(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_53(x) + F_62(x))
Eq(F_62(x), F_42(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_2(x)*F_6(x)*F_7(x))
Eq(F_68(x), F_24(x)*F_62(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_10(x)*F_6(x))
Eq(F_71(x), F_72(x) + F_74(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_18(x)*F_4(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_4(x)*F_76(x))
Eq(F_76(x), F_57(x))
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.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_row_and_col_placements_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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [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": 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": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [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, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [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": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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{"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "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", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 4], [2, 4]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [3, 3], [3, 3]]}], "requirements": [[{"patt": [0], "pos": [[2, 4]]}]]}], "class_module": 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{"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", "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": [[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": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"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]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "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"}]}, {"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": [], "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: insertion_point_placements_req_corrob
Tree: http://permpal.com/tree/187/
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]+F[9,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]^2*F[4,x]
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[27,x]
F[13,x] = F[14,x]*F[6,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[20,x]+F[22,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[4,x]*F[6,x]
F[22,x] = F[23,x]
F[23,x] = F[16,x]*F[24,x]*F[4,x]
F[24,x] = F[17,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[24,x]^2*F[4,x]
F[27,x] = F[28,x]+F[85,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[2,x]*F[6,x]
F[30,x] = F[31,x]+F[38,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[2,x]+F[31,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[17,x]*F[2,x]
F[37,x] = F[18,x]*F[34,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[63,x]
F[41,x] = F[42,x]*F[6,x]
F[42,x] = F[43,x]+F[48,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[18,x]+F[43,x]
F[47,x] = F[46,x]*F[6,x]
F[48,x] = F[49,x]+F[53,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[20,x]+F[22,x]+F[52,x]
F[52,x] = 0
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[62,x]
F[56,x] = F[57,x]+F[61,x]
F[57,x] = F[53,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[18,x]+F[58,x]
F[61,x] = F[14,x]*F[46,x]
F[62,x] = F[24,x]*F[57,x]
F[63,x] = F[64,x]+F[78,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[2,x]*F[43,x]
F[66,x] = F[38,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[76,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[67,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[18,x]*F[31,x]
F[74,x] = F[75,x]
F[75,x] = F[14,x]*F[2,x]*F[46,x]
F[76,x] = F[77,x]
F[77,x] = F[24,x]*F[71,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[10,x]*F[43,x]
F[80,x] = F[81,x]+F[83,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[4,x]*F[49,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[4,x]*F[53,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[10,x]*F[6,x]
F[87,x] = F[81,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[10,x]*F[17,x]*F[4,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_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{85}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right) F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right) F_{2}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right) F_{34}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{63}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{6}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)
F_{47}\! \left(x \right) = F_{46}\! \left(x \right) F_{6}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 0
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right) F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{78}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{2}\! \left(x \right) F_{43}\! \left(x \right)
F_{66}\! \left(x \right) = F_{38}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{76}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{18}\! \left(x \right) F_{31}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right) F_{2}\! \left(x \right) F_{46}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{24}\! \left(x \right) F_{71}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{10}\! \left(x \right) F_{43}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{10}\! \left(x \right) F_{6}\! \left(x \right)
F_{87}\! \left(x \right) = F_{81}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right) F_{4}\! \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_6(x) + F_9(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_6(x)**2)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_27(x))
Eq(F_13(x), F_14(x)*F_6(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_20(x) + F_22(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_4(x)*F_6(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_16(x)*F_24(x)*F_4(x))
Eq(F_24(x), F_17(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_24(x)**2*F_4(x))
Eq(F_27(x), F_28(x) + F_85(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_2(x)*F_6(x))
Eq(F_30(x), F_31(x) + F_38(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_2(x) + F_31(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_17(x)*F_2(x))
Eq(F_37(x), F_18(x)*F_34(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_63(x))
Eq(F_41(x), F_42(x)*F_6(x))
Eq(F_42(x), F_43(x) + F_48(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_18(x) + F_43(x))
Eq(F_47(x), F_46(x)*F_6(x))
Eq(F_48(x), F_49(x) + F_53(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_20(x) + F_22(x) + F_52(x))
Eq(F_52(x), 0)
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_62(x))
Eq(F_56(x), F_57(x) + F_61(x))
Eq(F_57(x), F_53(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_18(x) + F_58(x))
Eq(F_61(x), F_14(x)*F_46(x))
Eq(F_62(x), F_24(x)*F_57(x))
Eq(F_63(x), F_64(x) + F_78(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_2(x)*F_43(x))
Eq(F_66(x), F_38(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_76(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_67(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_18(x)*F_31(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_14(x)*F_2(x)*F_46(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_24(x)*F_71(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_10(x)*F_43(x))
Eq(F_80(x), F_81(x) + F_83(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_4(x)*F_49(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_4(x)*F_53(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_10(x)*F_6(x))
Eq(F_87(x), F_81(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_10(x)*F_17(x)*F_4(x))
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.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_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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [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": 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": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": 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