01243_02143_10243_12043_12403_12430_20143_21043_21403_21430
Counting sequence:
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Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24457/
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[7,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[6,x,k[0]] = x*F[6,x,k[0]]*k[0]+F[6,x,k[0]]^2-2*F[6,x,k[0]]+2
F[7,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_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{6}\! \left(x , y\right) = x F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , y\right)^{2}-2 F_{6}\! \left(x , y\right)+2
F_{7}\! \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_4(x)*F_7(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_6(x, k_0), (k_0*x - 2)*F_6(x, k_0) + F_6(x, k_0)**2 + 2)
Eq(F_7(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:
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{"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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": 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1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false, "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}}, {"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, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}}]}, {"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]]}], "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], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"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]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24494/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[139,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[19,x]
F[11,x] = F[12,x]+F[135,x]
F[12,x] = F[13,x]+F[131,x]
F[13,x] = F[14,x]*F[28,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = 2+F[15,x]^2+(-2+x)*F[15,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[20,x]
F[19,x] = x
F[20,x] = 1/F[19,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = -F[27,x]+F[24,x]
F[24,x] = -F[0,x]+F[25,x]
F[25,x] = 1/F[19,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = (1+F[27,x])*x+F[27,x]^2
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = -F[32,x]+F[30,x]
F[30,x] = 1/F[19,x]*F[31,x]
F[31,x] = F[16,x]
F[32,x] = -F[130,x]+F[33,x]
F[33,x] = 1/F[19,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[19,x]*F[36,x]
F[36,x] = F[104,x]+F[37,x]
F[37,x] = F[17,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[107,x]*F[19,x]*F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[19,x]*F[42,x]
F[42,x] = F[35,x]
F[43,x] = F[44,x]
F[44,x] = 1/F[19,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[19,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[119,x]*F[19,x]*F[49,x]
F[49,x] = 1/F[19,x]/F[77,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[67,x]+F[52,x]
F[52,x] = 1/F[19,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[55,x]+F[30,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[15,x]^2
F[57,x] = F[58,x]
F[58,x] = F[19,x]*F[20,x]*F[59,x]
F[59,x] = 1/F[15,x]*F[60,x]
F[60,x] = -F[63,x]+F[61,x]
F[61,x] = 1/F[19,x]*F[62,x]
F[62,x] = F[17,x]
F[63,x] = -F[66,x]+F[64,x]
F[64,x] = 1/F[19,x]*F[65,x]
F[65,x] = F[35,x]
F[66,x] = F[27,x]*F[59,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[28,x]*F[55,x]
F[69,x] = F[70,x]
F[70,x] = F[19,x]*F[71,x]*F[77,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[15,x]*F[59,x]
F[73,x] = F[74,x]
F[74,x] = F[19,x]*F[59,x]*F[75,x]
F[75,x] = 1/F[19,x]*F[76,x]
F[76,x] = F[40,x]
F[77,x] = F[129,x]+F[78,x]
F[78,x] = 1/F[119,x]/F[19,x]^2*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = -F[124,x]+F[82,x]
F[82,x] = -F[85,x]+F[83,x]
F[83,x] = 1/F[19,x]*F[84,x]
F[84,x] = F[23,x]
F[85,x] = -F[88,x]+F[86,x]
F[86,x] = 1/F[19,x]*F[87,x]
F[87,x] = F[22,x]
F[88,x] = -F[108,x]+F[89,x]
F[89,x] = 1/F[19,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = -F[0,x]+F[92,x]
F[92,x] = F[15,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[19,x]*F[95,x]
F[95,x] = F[104,x]+F[96,x]
F[96,x] = F[37,x]+F[97,x]
F[97,x] = F[15,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[19,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[15,x]*F[97,x]
F[102,x] = F[103,x]
F[103,x] = F[19,x]*F[59,x]*F[77,x]
F[104,x] = F[105,x]+F[57,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[19,x]*F[47,x]
F[107,x] = F[15,x]+F[81,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[19,x]
F[110,x] = 1/F[19,x]*F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]+F[98,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[19,x]
F[115,x] = F[116,x]+F[120,x]
F[116,x] = F[117,x]*F[20,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]^2*F[19,x]
F[119,x] = F[1,x]+F[117,x]
F[120,x] = F[107,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[119,x]^2*F[123,x]*F[19,x]
F[123,x] = F[119,x]+F[121,x]
F[124,x] = -F[93,x]+F[125,x]
F[125,x] = -F[108,x]+F[126,x]
F[126,x] = 1/F[19,x]*F[127,x]
F[127,x] = F[128,x]
F[128,x] = -F[27,x]+F[91,x]
F[129,x] = F[119,x]*F[81,x]
F[130,x] = F[27,x]*F[28,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[19,x]*F[77,x]
F[133,x] = F[134,x]+F[59,x]
F[134,x] = F[47,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[19,x]*F[77,x]
F[137,x] = F[138,x]+F[59,x]
F[138,x] = F[40,x]
F[139,x] = F[140,x]
F[140,x] = F[19,x]*F[59,x]*F[86,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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{139}\! \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_{19}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{135}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{131}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{15}\! \left(x \right) x +F_{15} \left(x \right)^{2}-2 F_{15}\! \left(x \right)+2
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = F_{27}\! \left(x \right) x +F_{27} \left(x \right)^{2}+x
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{16}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{104}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{17}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{107}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{119}\! \left(x \right) F_{19}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{19}\! \left(x \right) F_{77}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{30}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15} \left(x \right)^{2}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{60}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{17}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{35}\! \left(x \right)
F_{66}\! \left(x \right) = F_{27}\! \left(x \right) F_{59}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{28}\! \left(x \right) F_{55}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right) F_{71}\! \left(x \right) F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{40}\! \left(x \right)
F_{77}\! \left(x \right) = F_{129}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{119}\! \left(x \right) F_{19} \left(x \right)^{2}}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{84}\! \left(x \right) = F_{23}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{22}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{104}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{37}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{15}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{19}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{15}\! \left(x \right) F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{77}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{57}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{107}\! \left(x \right) = F_{15}\! \left(x \right)+F_{81}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{19}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{98}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{19}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{120}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{20}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119} \left(x \right)^{2} F_{19}\! \left(x \right)
F_{119}\! \left(x \right) = F_{1}\! \left(x \right)+F_{117}\! \left(x \right)
F_{120}\! \left(x \right) = F_{107}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119} \left(x \right)^{2} F_{123}\! \left(x \right) F_{19}\! \left(x \right)
F_{123}\! \left(x \right) = F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{124}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{91}\! \left(x \right)
F_{129}\! \left(x \right) = F_{119}\! \left(x \right) F_{81}\! \left(x \right)
F_{130}\! \left(x \right) = F_{27}\! \left(x \right) F_{28}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{59}\! \left(x \right)
F_{134}\! \left(x \right) = F_{47}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{59}\! \left(x \right)
F_{138}\! \left(x \right) = F_{40}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{86}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_139(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_135(x))
Eq(F_12(x), F_13(x) + F_131(x))
Eq(F_13(x), F_14(x)*F_28(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), (x - 2)*F_15(x) + F_15(x)**2 + 2)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_20(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x)/F_19(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_24(x) - F_27(x))
Eq(F_24(x), -F_0(x) + F_25(x))
Eq(F_25(x), F_26(x)/F_19(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), (x - 3)*(F_27(x) + 1) + (F_27(x) + 1)**2 + F_27(x) + 2)
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x) - F_32(x))
Eq(F_30(x), F_31(x)/F_19(x))
Eq(F_31(x), F_16(x))
Eq(F_32(x), -F_130(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_19(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_19(x)*F_36(x))
Eq(F_36(x), F_104(x) + F_37(x))
Eq(F_37(x), F_17(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_107(x)*F_19(x)*F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_19(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x)/F_19(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_19(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_119(x)*F_19(x)*F_49(x))
Eq(F_49(x), F_50(x)/(F_19(x)*F_77(x)))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) - F_67(x))
Eq(F_52(x), F_53(x)/F_19(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_30(x) - F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_15(x)**2)
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_19(x)*F_20(x)*F_59(x))
Eq(F_59(x), F_60(x)/F_15(x))
Eq(F_60(x), F_61(x) - F_63(x))
Eq(F_61(x), F_62(x)/F_19(x))
Eq(F_62(x), F_17(x))
Eq(F_63(x), F_64(x) - F_66(x))
Eq(F_64(x), F_65(x)/F_19(x))
Eq(F_65(x), F_35(x))
Eq(F_66(x), F_27(x)*F_59(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_28(x)*F_55(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_19(x)*F_71(x)*F_77(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_15(x)*F_59(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_19(x)*F_59(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_19(x))
Eq(F_76(x), F_40(x))
Eq(F_77(x), F_129(x) + F_78(x))
Eq(F_78(x), F_79(x)/(F_119(x)*F_19(x)**2))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), -F_124(x) + F_82(x))
Eq(F_82(x), F_83(x) - F_85(x))
Eq(F_83(x), F_84(x)/F_19(x))
Eq(F_84(x), F_23(x))
Eq(F_85(x), F_86(x) - F_88(x))
Eq(F_86(x), F_87(x)/F_19(x))
Eq(F_87(x), F_22(x))
Eq(F_88(x), -F_108(x) + F_89(x))
Eq(F_89(x), F_90(x)/F_19(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), -F_0(x) + F_92(x))
Eq(F_92(x), F_15(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_19(x)*F_95(x))
Eq(F_95(x), F_104(x) + F_96(x))
Eq(F_96(x), F_37(x) + F_97(x))
Eq(F_97(x), F_15(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_19(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_15(x)*F_97(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_19(x)*F_59(x)*F_77(x))
Eq(F_104(x), F_105(x) + F_57(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_19(x)*F_47(x))
Eq(F_107(x), F_15(x) + F_81(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_19(x))
Eq(F_110(x), F_111(x)/F_19(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x) + F_98(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_19(x))
Eq(F_115(x), F_116(x) + F_120(x))
Eq(F_116(x), F_117(x)*F_20(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)**2*F_19(x))
Eq(F_119(x), F_1(x) + F_117(x))
Eq(F_120(x), F_107(x)*F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_119(x)**2*F_123(x)*F_19(x))
Eq(F_123(x), F_119(x) + F_121(x))
Eq(F_124(x), F_125(x) - F_93(x))
Eq(F_125(x), -F_108(x) + F_126(x))
Eq(F_126(x), F_127(x)/F_19(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), -F_27(x) + F_91(x))
Eq(F_129(x), F_119(x)*F_81(x))
Eq(F_130(x), F_27(x)*F_28(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_19(x)*F_77(x))
Eq(F_133(x), F_134(x) + F_59(x))
Eq(F_134(x), F_47(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_19(x)*F_77(x))
Eq(F_137(x), F_138(x) + F_59(x))
Eq(F_138(x), F_40(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_19(x)*F_59(x)*F_86(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, 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[[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24985/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[139,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[19,x]
F[11,x] = F[12,x]+F[135,x]
F[12,x] = F[13,x]+F[131,x]
F[13,x] = F[14,x]*F[28,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = 2+F[15,x]^2+(-2+x)*F[15,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[20,x]
F[19,x] = x
F[20,x] = 1/F[19,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = -F[27,x]+F[24,x]
F[24,x] = -F[0,x]+F[25,x]
F[25,x] = 1/F[19,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = (1+F[27,x])*x+F[27,x]^2
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = -F[32,x]+F[30,x]
F[30,x] = 1/F[19,x]*F[31,x]
F[31,x] = F[16,x]
F[32,x] = -F[130,x]+F[33,x]
F[33,x] = 1/F[19,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[19,x]*F[36,x]
F[36,x] = F[104,x]+F[37,x]
F[37,x] = F[17,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[107,x]*F[19,x]*F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[19,x]*F[42,x]
F[42,x] = F[35,x]
F[43,x] = F[44,x]
F[44,x] = 1/F[19,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[19,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[119,x]*F[19,x]*F[49,x]
F[49,x] = 1/F[19,x]/F[77,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[67,x]+F[52,x]
F[52,x] = 1/F[19,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[55,x]+F[30,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[15,x]^2
F[57,x] = F[58,x]
F[58,x] = F[19,x]*F[20,x]*F[59,x]
F[59,x] = 1/F[15,x]*F[60,x]
F[60,x] = -F[63,x]+F[61,x]
F[61,x] = 1/F[19,x]*F[62,x]
F[62,x] = F[17,x]
F[63,x] = -F[66,x]+F[64,x]
F[64,x] = 1/F[19,x]*F[65,x]
F[65,x] = F[35,x]
F[66,x] = F[27,x]*F[59,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[28,x]*F[55,x]
F[69,x] = F[70,x]
F[70,x] = F[19,x]*F[71,x]*F[77,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[15,x]*F[59,x]
F[73,x] = F[74,x]
F[74,x] = F[19,x]*F[59,x]*F[75,x]
F[75,x] = 1/F[19,x]*F[76,x]
F[76,x] = F[40,x]
F[77,x] = F[129,x]+F[78,x]
F[78,x] = 1/F[119,x]/F[19,x]^2*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = -F[124,x]+F[82,x]
F[82,x] = -F[85,x]+F[83,x]
F[83,x] = 1/F[19,x]*F[84,x]
F[84,x] = F[23,x]
F[85,x] = -F[88,x]+F[86,x]
F[86,x] = 1/F[19,x]*F[87,x]
F[87,x] = F[22,x]
F[88,x] = -F[108,x]+F[89,x]
F[89,x] = 1/F[19,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = -F[0,x]+F[92,x]
F[92,x] = F[15,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[19,x]*F[95,x]
F[95,x] = F[104,x]+F[96,x]
F[96,x] = F[37,x]+F[97,x]
F[97,x] = F[15,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[19,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[15,x]*F[97,x]
F[102,x] = F[103,x]
F[103,x] = F[19,x]*F[59,x]*F[77,x]
F[104,x] = F[105,x]+F[57,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[19,x]*F[47,x]
F[107,x] = F[15,x]+F[81,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[19,x]
F[110,x] = 1/F[19,x]*F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]+F[98,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[19,x]
F[115,x] = F[116,x]+F[120,x]
F[116,x] = F[117,x]*F[20,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]^2*F[19,x]
F[119,x] = F[1,x]+F[117,x]
F[120,x] = F[107,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[119,x]^2*F[123,x]*F[19,x]
F[123,x] = F[119,x]+F[121,x]
F[124,x] = -F[93,x]+F[125,x]
F[125,x] = -F[108,x]+F[126,x]
F[126,x] = 1/F[19,x]*F[127,x]
F[127,x] = F[128,x]
F[128,x] = -F[27,x]+F[91,x]
F[129,x] = F[119,x]*F[81,x]
F[130,x] = F[27,x]*F[28,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[19,x]*F[77,x]
F[133,x] = F[134,x]+F[59,x]
F[134,x] = F[47,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[19,x]*F[77,x]
F[137,x] = F[138,x]+F[59,x]
F[138,x] = F[40,x]
F[139,x] = F[140,x]
F[140,x] = F[19,x]*F[59,x]*F[86,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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{139}\! \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_{19}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{135}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{131}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{15}\! \left(x \right) x +F_{15} \left(x \right)^{2}-2 F_{15}\! \left(x \right)+2
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = F_{27}\! \left(x \right) x +F_{27} \left(x \right)^{2}+x
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{16}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{104}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{17}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{107}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{119}\! \left(x \right) F_{19}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{19}\! \left(x \right) F_{77}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{30}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15} \left(x \right)^{2}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{60}\! \left(x \right) = -F_{63}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{17}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{35}\! \left(x \right)
F_{66}\! \left(x \right) = F_{27}\! \left(x \right) F_{59}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{28}\! \left(x \right) F_{55}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right) F_{71}\! \left(x \right) F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{40}\! \left(x \right)
F_{77}\! \left(x \right) = F_{129}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{119}\! \left(x \right) F_{19} \left(x \right)^{2}}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{84}\! \left(x \right) = F_{23}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{22}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{104}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{37}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{15}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{19}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{15}\! \left(x \right) F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{77}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{57}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{107}\! \left(x \right) = F_{15}\! \left(x \right)+F_{81}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{19}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{98}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{19}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{120}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{20}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119} \left(x \right)^{2} F_{19}\! \left(x \right)
F_{119}\! \left(x \right) = F_{1}\! \left(x \right)+F_{117}\! \left(x \right)
F_{120}\! \left(x \right) = F_{107}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119} \left(x \right)^{2} F_{123}\! \left(x \right) F_{19}\! \left(x \right)
F_{123}\! \left(x \right) = F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{124}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{91}\! \left(x \right)
F_{129}\! \left(x \right) = F_{119}\! \left(x \right) F_{81}\! \left(x \right)
F_{130}\! \left(x \right) = F_{27}\! \left(x \right) F_{28}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{59}\! \left(x \right)
F_{134}\! \left(x \right) = F_{47}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{59}\! \left(x \right)
F_{138}\! \left(x \right) = F_{40}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{86}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_139(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_135(x))
Eq(F_12(x), F_13(x) + F_131(x))
Eq(F_13(x), F_14(x)*F_28(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), (x - 2)*F_15(x) + F_15(x)**2 + 2)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_20(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x)/F_19(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_24(x) - F_27(x))
Eq(F_24(x), -F_0(x) + F_25(x))
Eq(F_25(x), F_26(x)/F_19(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), (x - 3)*(F_27(x) + 1) + (F_27(x) + 1)**2 + F_27(x) + 2)
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x) - F_32(x))
Eq(F_30(x), F_31(x)/F_19(x))
Eq(F_31(x), F_16(x))
Eq(F_32(x), -F_130(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_19(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_19(x)*F_36(x))
Eq(F_36(x), F_104(x) + F_37(x))
Eq(F_37(x), F_17(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_107(x)*F_19(x)*F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_19(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x)/F_19(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_19(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_119(x)*F_19(x)*F_49(x))
Eq(F_49(x), F_50(x)/(F_19(x)*F_77(x)))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) - F_67(x))
Eq(F_52(x), F_53(x)/F_19(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_30(x) - F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_15(x)**2)
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_19(x)*F_20(x)*F_59(x))
Eq(F_59(x), F_60(x)/F_15(x))
Eq(F_60(x), F_61(x) - F_63(x))
Eq(F_61(x), F_62(x)/F_19(x))
Eq(F_62(x), F_17(x))
Eq(F_63(x), F_64(x) - F_66(x))
Eq(F_64(x), F_65(x)/F_19(x))
Eq(F_65(x), F_35(x))
Eq(F_66(x), F_27(x)*F_59(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_28(x)*F_55(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_19(x)*F_71(x)*F_77(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_15(x)*F_59(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_19(x)*F_59(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_19(x))
Eq(F_76(x), F_40(x))
Eq(F_77(x), F_129(x) + F_78(x))
Eq(F_78(x), F_79(x)/(F_119(x)*F_19(x)**2))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), -F_124(x) + F_82(x))
Eq(F_82(x), F_83(x) - F_85(x))
Eq(F_83(x), F_84(x)/F_19(x))
Eq(F_84(x), F_23(x))
Eq(F_85(x), F_86(x) - F_88(x))
Eq(F_86(x), F_87(x)/F_19(x))
Eq(F_87(x), F_22(x))
Eq(F_88(x), -F_108(x) + F_89(x))
Eq(F_89(x), F_90(x)/F_19(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), -F_0(x) + F_92(x))
Eq(F_92(x), F_15(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_19(x)*F_95(x))
Eq(F_95(x), F_104(x) + F_96(x))
Eq(F_96(x), F_37(x) + F_97(x))
Eq(F_97(x), F_15(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_19(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_15(x)*F_97(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_19(x)*F_59(x)*F_77(x))
Eq(F_104(x), F_105(x) + F_57(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_19(x)*F_47(x))
Eq(F_107(x), F_15(x) + F_81(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_19(x))
Eq(F_110(x), F_111(x)/F_19(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x) + F_98(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_19(x))
Eq(F_115(x), F_116(x) + F_120(x))
Eq(F_116(x), F_117(x)*F_20(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)**2*F_19(x))
Eq(F_119(x), F_1(x) + F_117(x))
Eq(F_120(x), F_107(x)*F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_119(x)**2*F_123(x)*F_19(x))
Eq(F_123(x), F_119(x) + F_121(x))
Eq(F_124(x), F_125(x) - F_93(x))
Eq(F_125(x), -F_108(x) + F_126(x))
Eq(F_126(x), F_127(x)/F_19(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), -F_27(x) + F_91(x))
Eq(F_129(x), F_119(x)*F_81(x))
Eq(F_130(x), F_27(x)*F_28(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_19(x)*F_77(x))
Eq(F_133(x), F_134(x) + F_59(x))
Eq(F_134(x), F_47(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_19(x)*F_77(x))
Eq(F_137(x), F_138(x) + F_59(x))
Eq(F_138(x), F_40(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_19(x)*F_59(x)*F_86(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, 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[[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25086/
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[7,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[6,x,k[0]] = x*F[6,x,k[0]]*k[0]+F[6,x,k[0]]^2-2*F[6,x,k[0]]+2
F[7,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_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{6}\! \left(x , y\right) = x F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , y\right)^{2}-2 F_{6}\! \left(x , y\right)+2
F_{7}\! \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_4(x)*F_7(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_6(x, k_0), (k_0*x - 2)*F_6(x, k_0) + F_6(x, k_0)**2 + 2)
Eq(F_7(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:
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{"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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false, "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}}, {"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, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}}]}, {"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]]}], "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], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"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]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25783/
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[7,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[6,x,k[0]] = x*F[6,x,k[0]]*k[0]+F[6,x,k[0]]^2-2*F[6,x,k[0]]+2
F[7,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_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{6}\! \left(x , y\right) = x F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , y\right)^{2}-2 F_{6}\! \left(x , y\right)+2
F_{7}\! \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_4(x)*F_7(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_6(x, k_0), (k_0*x - 2)*F_6(x, k_0) + F_6(x, k_0)**2 + 2)
Eq(F_7(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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "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, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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