01243_02143_02413_20143_20413_24013
Counting sequence:
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Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25414/
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[31,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[6,x,k[0]]+F[7,x,k[0]]
F[6,x,k[0]] = 1+F[6,x,k[0]]^2*(x^2*k[0]^2-2*x*k[0]+3)+F[6,x,k[0]]^3*(-x*k[0]-1)+(2*x*k[0]-2)*F[6,x,k[0]]+k[0]*x*F[6,x,k[0]]^4
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[31,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[11,x,k[0]]
F[10,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[26,x,k[0]]
F[13,x,k[0]] = F[14,x,1,k[0]]
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[31,x]
F[16,x,k[0],k[1]] = F[17,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[17,x,k[0],k[1]]+F[23,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]+F[5,x,k[0]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]*F[26,x,k[1]]*F[27,x,k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[5,x,k[0]]
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]+F[6,x,k[0]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[23,x,k[0],k[1]]*F[26,x,k[1]]*F[27,x,k[1]]*F[6,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[27,x,k[0]]^2*F[26,x,k[0]]
F[30,x,k[0],k[1]] = F[0,x]*F[17,x,k[0],k[1]]
F[31,x] = 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_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = x^{2} F_{6}\! \left(x , y\right)^{2} y^{2}+y x F_{6}\! \left(x , y\right)^{4}-x F_{6}\! \left(x , y\right)^{3} y -2 x F_{6}\! \left(x , y\right)^{2} y +2 x F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , y\right)^{3}+3 F_{6}\! \left(x , y\right)^{2}-2 F_{6}\! \left(x , y\right)+1
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , 1, y\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{31}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = F_{17}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y , z\right)+F_{5}\! \left(x , y\right)
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right)
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right) F_{26}\! \left(x , z\right) F_{27}\! \left(x , z\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{5}\! \left(x , y\right)
F_{23}\! \left(x , y , z\right) = F_{24}\! \left(x , y , z\right)+F_{6}\! \left(x , y\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{23}\! \left(x , y , z\right) F_{26}\! \left(x , z\right) F_{27}\! \left(x , z\right) F_{6}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{27}\! \left(x , y\right)^{2} F_{26}\! \left(x , y\right)
F_{30}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{17}\! \left(x , y , z\right)
F_{31}\! \left(x \right) = x
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_31(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_6(x, k_0) + F_7(x, k_0))
Eq(F_6(x, k_0), k_0*x*F_6(x, k_0)**4 + (-k_0*x - 1)*F_6(x, k_0)**3 + (2*k_0*x - 2)*F_6(x, k_0) + (k_0**2*x**2 - 2*k_0*x + 3)*F_6(x, k_0)**2 + 1)
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_31(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_11(x, k_0))
Eq(F_10(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_26(x, k_0))
Eq(F_13(x, k_0), F_14(x, 1, k_0))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_15(x, k_0, k_1)*F_31(x))
Eq(F_16(x, k_0, k_1), F_17(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_17(x, k_0, k_1) + F_23(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1) + F_5(x, k_0))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1)*F_26(x, k_1)*F_27(x, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, k_1)*F_5(x, k_0))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1) + F_6(x, k_0))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_23(x, k_0, k_1)*F_26(x, k_1)*F_27(x, k_1)*F_6(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_26(x, k_0)*F_27(x, k_0)**2)
Eq(F_30(x, k_0, k_1), F_0(x)*F_17(x, k_0, k_1))
Eq(F_31(x), x)
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 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{"patt": [0, 1, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [2, 3], 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[[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 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"tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25565/
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[34,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x*F[7,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[7,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[7,x,k[0]]+x^2*k[0]^2)*(1+F[7,x,k[0]])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[34,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[26,x,k[0]]
F[15,x,k[0]] = F[14,x,k[0]]*F[34,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]
F[17,x,k[0]] = F[2,x]+F[8,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[26,x,k[0]]*F[31,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[30,x,k[0]]
F[21,x,k[0]] = F[17,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]+F[22,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]+F[27,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]*F[26,x,k[0]]
F[25,x,k[0]] = F[6,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[16,x,k[0]]+F[27,x,k[0]]
F[29,x,k[0]] = F[26,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0]] = F[8,x,k[0]]
F[30,x,k[0]] = F[0,x]*F[16,x,k[0]]
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[31,x,k[0]]^2*F[26,x,k[0]]
F[34,x] = 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_{34}\! \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 , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+x F_{7}\! \left(x , y\right)^{4} y +2 x^{2} F_{7}\! \left(x , y\right) y^{2}+3 x F_{7}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{7}\! \left(x , y\right)^{2} y -x F_{7}\! \left(x , y\right) y -F_{7}\! \left(x , y\right)^{3}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{31}\! \left(x , y\right)^{2} F_{26}\! \left(x , y\right)
F_{34}\! \left(x \right) = x
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_34(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(F_7(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_7(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_7(x, k_0) + 1) + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_7(x, k_0) + 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_34(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_26(x, k_0))
Eq(F_15(x, k_0), F_14(x, k_0)*F_34(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_18(x, k_0))
Eq(F_17(x, k_0), F_2(x) + F_8(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_26(x, k_0)*F_31(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_30(x, k_0))
Eq(F_21(x, k_0), F_17(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0) + F_22(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0) + F_27(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0)*F_26(x, k_0))
Eq(F_25(x, k_0), F_6(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_16(x, k_0) + F_27(x, k_0))
Eq(F_29(x, k_0), F_26(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0), F_8(x, k_0))
Eq(F_30(x, k_0), F_0(x)*F_16(x, k_0))
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_26(x, k_0)*F_31(x, k_0)**2)
Eq(F_34(x), x)
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [1, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 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3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[5, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[6, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 4, 0, 1, 3]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25621/
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[34,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x*F[7,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[7,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[7,x,k[0]]+x^2*k[0]^2)*(1+F[7,x,k[0]])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[34,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[26,x,k[0]]
F[15,x,k[0]] = F[14,x,k[0]]*F[34,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]
F[17,x,k[0]] = F[2,x]+F[8,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[26,x,k[0]]*F[31,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[30,x,k[0]]
F[21,x,k[0]] = F[17,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]+F[22,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]+F[27,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]*F[26,x,k[0]]
F[25,x,k[0]] = F[6,x,k[0]]
F[26,x,k[0]] = k[0]*x
F[28,x,k[0]] = F[16,x,k[0]]+F[27,x,k[0]]
F[29,x,k[0]] = F[26,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0]] = F[8,x,k[0]]
F[30,x,k[0]] = F[0,x]*F[16,x,k[0]]
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[31,x,k[0]]^2*F[26,x,k[0]]
F[34,x] = 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_{34}\! \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 , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+x F_{7}\! \left(x , y\right)^{4} y +2 x^{2} F_{7}\! \left(x , y\right) y^{2}+3 x F_{7}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{7}\! \left(x , y\right)^{2} y -x F_{7}\! \left(x , y\right) y -F_{7}\! \left(x , y\right)^{3}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = y x
F_{28}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{31}\! \left(x , y\right)^{2} F_{26}\! \left(x , y\right)
F_{34}\! \left(x \right) = x
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_34(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(F_7(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_7(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_7(x, k_0) + 1) + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_7(x, k_0) + 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_34(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_26(x, k_0))
Eq(F_15(x, k_0), F_14(x, k_0)*F_34(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_18(x, k_0))
Eq(F_17(x, k_0), F_2(x) + F_8(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_26(x, k_0)*F_31(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_30(x, k_0))
Eq(F_21(x, k_0), F_17(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0) + F_22(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0) + F_27(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0)*F_26(x, k_0))
Eq(F_25(x, k_0), F_6(x, k_0))
Eq(F_26(x, k_0), k_0*x)
Eq(F_28(x, k_0), F_16(x, k_0) + F_27(x, k_0))
Eq(F_29(x, k_0), F_26(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0), F_8(x, k_0))
Eq(F_30(x, k_0), F_0(x)*F_16(x, k_0))
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_26(x, k_0)*F_31(x, k_0)**2)
Eq(F_34(x), x)
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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