01234
Counting sequence:
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117286558208547537293433340721019086325451984, 1603623050878143932722397047915184802200125984, 21996763034860960417259405204172331608463797152, 302664297898124499421697046885532938663308311104, 4176922244743425434851827565214898395775758294208, 57808845869218440075832443346616034420583063507328, 802283220888975310339856786488603816420320224819328, 11163800163529547323754623817431192659251590878268416, 155741808084115897360585014916160126291788254860611968, 2178047449783852638357791655647435547947020212454442752, 30532382238075245259338398193146151040285528444895520512, 428992304950286649659085382315383342788062404084978970112, 6040874727342104396726698678329641023346831718342618510336, 85247065841778966494266703539191483914473291434364353226752, 1205473572352660080103797064048389676169509302028706218563584, 17080691329178796639203288554670322171239249809057073614580224, 242490618234260394252092752186168149866343533745706302824878099, 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Specification 1
Strategy pack name: row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23948/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[23,x]*F[3,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[28,x,k[0]]+F[5,x,k[0]]
F[5,x,k[0]] = F[14,x,k[0]]*F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,1,k[0]]
F[7,x,k[0],k[1]] = F[8,x,k[0]*k[1],k[1]]
F[8,x,k[0],k[1]] = F[1,x]+F[24,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[14,x,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0],1,k[1]]
F[11,x,k[0],k[1],k[2]] = F[12,x,k[0],k[0]*k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[1],k[2]]+F[15,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[21,x,k[0],k[1],k[2]]
F[13,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1],k[2]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0],k[1],k[2]] = F[14,x,k[1]]*F[16,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = (-F[17,x,1,k[1],k[2]]*k[1]+F[17,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[17,x,k[0],k[1],k[2]] = F[12,x,k[0]*k[1],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[14,x,k[2]]*F[19,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = (-F[20,x,k[0],1,k[2]]*k[2]+F[20,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[20,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1]*k[2],k[2]]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0],k[1],k[2]]*F[23,x]
F[22,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1],k[2]]*k[2]-F[12,x,k[0],k[1],1])/(-1+k[2])
F[23,x] = x
F[24,x,k[0],k[1]] = F[14,x,k[1]]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[26,x,k[0],k[1]] = F[23,x]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = (F[8,x,k[0],k[1]]*k[1]-F[8,x,k[0],1])/(-1+k[1])
F[28,x,k[0]] = F[23,x]*F[29,x,k[0]]
F[29,x,k[0]] = (F[4,x,k[0]]*k[0]-F[4,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{23}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{6}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , 1, y_{0}\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, 1, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{14}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} F_{17}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{17}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{2}\right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{2} F_{20}\! \left(x , y_{0}, 1, y_{2}\right)+y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right)}{-y_{2}+y_{1}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{23}\! \left(x \right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{2} F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{12}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{23}\! \left(x \right) = x
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{25}\! \left(x , y_{0}, y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = \frac{-y_{1} F_{7}\! \left(x , 1, y_{1}\right)+y_{0} F_{7}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{1} F_{8}\! \left(x , y_{0}, y_{1}\right)-F_{8}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{28}\! \left(x , y_{0}\right) = F_{23}\! \left(x \right) F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = \frac{y_{0} F_{4}\! \left(x , y_{0}\right)-F_{4}\! \left(x , 1\right)}{-1+y_{0}}
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_23(x)*F_3(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_28(x, k_0) + F_5(x, k_0))
Eq(F_5(x, k_0), F_14(x, k_0)*F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, 1, k_0))
Eq(F_7(x, k_0, k_1), F_8(x, k_0*k_1, k_1))
Eq(F_8(x, k_0, k_1), F_1(x) + F_24(x, k_0, k_1) + F_26(x, k_0, k_1) + F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, k_0, k_1)*F_14(x, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, 1, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_0, k_0*k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_1, k_2) + F_15(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_21(x, k_0, k_1, k_2))
Eq(F_13(x, k_0, k_1, k_2), F_12(x, k_0, k_1, k_2)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0, k_1, k_2), F_14(x, k_1)*F_16(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), (-k_0*F_17(x, k_0/k_1, k_1, k_2) + k_1*F_17(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1, k_2), F_12(x, k_0*k_1, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_14(x, k_2)*F_19(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1/k_2, k_2) + k_2*F_20(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_20(x, k_0, k_1, k_2), F_12(x, k_0, k_1*k_2, k_2))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0, k_1, k_2)*F_23(x))
Eq(F_22(x, k_0, k_1, k_2), (-k_2*F_12(x, k_0, k_1, k_2) + F_12(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_23(x), x)
Eq(F_24(x, k_0, k_1), F_14(x, k_1)*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1), F_23(x)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), (-k_1*F_8(x, k_0, k_1) + F_8(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0), F_23(x)*F_29(x, k_0))
Eq(F_29(x, k_0), (-k_0*F_4(x, k_0) + F_4(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 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[2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 2, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: row_placements_tracked_fusion_req_corrob_expand_verified
Tree: http://permpal.com/tree/23949/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[27,x]*F[3,x]
F[3,x] = F[1,x]+F[32,x]+F[4,x]
F[4,x] = F[27,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,1,k[0]]
F[7,x,k[0],k[1]] = F[8,x,k[0]*k[1],k[1]]
F[8,x,k[0],k[1]] = F[1,x]+F[28,x,k[0],k[1]]+F[30,x,k[0],k[1]]+F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,k[0],k[1]]*F[14,x,k[0]]
F[10,x,k[0],k[1]] = F[11,x,1,k[0],k[1]]
F[11,x,k[0],k[1],k[2]] = F[12,x,k[0]*k[1],k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[1],k[2]]+F[15,x,k[0],k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1],k[2]]
F[13,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1],k[2]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0],k[1],k[2]] = F[14,x,k[1]]*F[16,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = (-F[11,x,1,k[1],k[2]]*k[1]+F[11,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[17,x,k[0],k[1],k[2]] = F[14,x,k[2]]*F[18,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],1,k[2]]
F[19,x,k[0],k[1],k[2],k[3]] = F[20,x,k[0],1,k[1],k[2],k[3]]
F[20,x,k[0],k[1],k[2],k[3],k[4]] = (F[21,x,k[0],k[1],k[2]/k[4],k[3]*k[4]]*k[1]*k[2]-F[21,x,k[0],k[1],1/k[1],k[3]*k[4]]*k[4])/(k[1]*k[2]-k[4])
F[21,x,k[0],k[1],k[2],k[3]] = F[22,x,k[0],k[1],1,k[2],k[3]]
F[22,x,k[0],k[1],k[2],k[3],k[4]] = F[23,x,k[0]*k[1],k[2],k[1]*k[3],k[4]]
F[23,x,k[0],k[1],k[2],k[3]] = F[24,x,k[0]*k[1],k[2],k[1]*k[3]]
F[24,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1]*k[2],k[2]]
F[25,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[2]]*F[27,x]
F[26,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1],k[2]]*k[2]-F[12,x,k[0],k[1],1])/(-1+k[2])
F[27,x] = x
F[28,x,k[0],k[1]] = F[14,x,k[1]]*F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[30,x,k[0],k[1]] = F[27,x]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = (F[8,x,k[0],k[1]]*k[1]-F[8,x,k[0],1])/(-1+k[1])
F[32,x] = F[27,x]*F[33,x]
F[33,x] = F[34,x,1]
F[34,x,k[0]] = (F[35,x,k[0]]*k[0]-F[35,x,1])/(-1+k[0])
F[35,x,k[0]] = F[1,x]+F[36,x,k[0]]+F[37,x,k[0]]
F[36,x,k[0]] = F[14,x,k[0]]*F[6,x,k[0]]
F[37,x,k[0]] = F[27,x]*F[34,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{27}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , 1, y_{0}\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}, y_{1}\right) F_{14}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , 1, y_{0}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{14}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{1}\right) F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{11}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{11}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{14}\! \left(x , y_{2}\right) F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{20}\! \left(x , y_{0}, 1, y_{1}, y_{2}, y_{3}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}, y_{4}\right) = -\frac{-y_{1} y_{2} F_{21}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{4}}, y_{3} y_{4}\right)+y_{4} F_{21}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}, y_{3} y_{4}\right)}{y_{1} y_{2}-y_{4}}
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{22}\! \left(x , y_{0}, y_{1}, 1, y_{2}, y_{3}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}, y_{4}\right) = F_{23}\! \left(x , y_{0} y_{1}, y_{2}, y_{1} y_{3}, y_{4}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{24}\! \left(x , y_{0} y_{1}, y_{2}, y_{1} y_{3}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{27}\! \left(x \right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{12}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{27}\! \left(x \right) = x
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{29}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{7}\! \left(x , 1, y_{1}\right)-y_{0} F_{7}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{8}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{32}\! \left(x \right) = F_{27}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x , 1\right)
F_{34}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{35}\! \left(x , y_{0}\right)+F_{35}\! \left(x , 1\right)}{-1+y_{0}}
F_{35}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{6}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{34}\! \left(x , y_{0}\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_27(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_32(x) + F_4(x))
Eq(F_4(x), F_27(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, 1, k_0))
Eq(F_7(x, k_0, k_1), F_8(x, k_0*k_1, k_1))
Eq(F_8(x, k_0, k_1), F_1(x) + F_28(x, k_0, k_1) + F_30(x, k_0, k_1) + F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, k_0, k_1)*F_14(x, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, 1, k_0, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_0*k_1, k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_1, k_2) + F_15(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_25(x, k_0, k_1, k_2))
Eq(F_13(x, k_0, k_1, k_2), F_12(x, k_0, k_1, k_2)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0, k_1, k_2), F_14(x, k_1)*F_16(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), (-k_0*F_11(x, k_0/k_1, k_1, k_2) + k_1*F_11(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1, k_2), F_14(x, k_2)*F_18(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, 1, k_2))
Eq(F_19(x, k_0, k_1, k_2, k_3), F_20(x, k_0, 1, k_1, k_2, k_3))
Eq(F_20(x, k_0, k_1, k_2, k_3, k_4), (-k_1*k_2*F_21(x, k_0, k_1, k_2/k_4, k_3*k_4) + k_4*F_21(x, k_0, k_1, 1/k_1, k_3*k_4))/(-k_1*k_2 + k_4))
Eq(F_21(x, k_0, k_1, k_2, k_3), F_22(x, k_0, k_1, 1, k_2, k_3))
Eq(F_22(x, k_0, k_1, k_2, k_3, k_4), F_23(x, k_0*k_1, k_2, k_1*k_3, k_4))
Eq(F_23(x, k_0, k_1, k_2, k_3), F_24(x, k_0*k_1, k_2, k_1*k_3))
Eq(F_24(x, k_0, k_1, k_2), F_12(x, k_0, k_1*k_2, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_2)*F_27(x))
Eq(F_26(x, k_0, k_1, k_2), (-k_2*F_12(x, k_0, k_1, k_2) + F_12(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_27(x), x)
Eq(F_28(x, k_0, k_1), F_14(x, k_1)*F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))
Eq(F_30(x, k_0, k_1), F_27(x)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), (-k_1*F_8(x, k_0, k_1) + F_8(x, k_0, 1))/(1 - k_1))
Eq(F_32(x), F_27(x)*F_33(x))
Eq(F_33(x), F_34(x, 1))
Eq(F_34(x, k_0), (-k_0*F_35(x, k_0) + F_35(x, 1))/(1 - k_0))
Eq(F_35(x, k_0), F_1(x) + F_36(x, k_0) + F_37(x, k_0))
Eq(F_36(x, k_0), F_14(x, k_0)*F_6(x, k_0))
Eq(F_37(x, k_0), F_27(x)*F_34(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "row_placements_tracked_fusion_req_corrob_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": 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2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/23950/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[23,x]*F[4,x]
F[4,x] = F[1,x]+F[28,x]+F[5,x]
F[5,x] = F[23,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]
F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[15,x,k[0]]
F[11,x,k[0],k[1]] = F[12,x,1,k[0],k[1]]
F[12,x,k[0],k[1],k[2]] = F[13,x,k[0]*k[1],k[1],k[2]]
F[13,x,k[0],k[1],k[2]] = F[1,x]+F[14,x,k[0],k[1],k[2]]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[21,x,k[0],k[1],k[2]]
F[14,x,k[0],k[1],k[2]] = F[13,x,k[0],k[1],k[2]]*F[15,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0],k[1],k[2]] = F[15,x,k[1]]*F[17,x,k[0],k[1],k[2]]
F[17,x,k[0],k[1],k[2]] = (-F[12,x,1,k[1],k[2]]*k[1]+F[12,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[18,x,k[0],k[1],k[2]] = F[15,x,k[2]]*F[19,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = (-F[20,x,k[0],1,k[2]]*k[2]+F[20,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[20,x,k[0],k[1],k[2]] = F[13,x,k[0],k[1]*k[2],k[2]]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0],k[1],k[2]]*F[23,x]
F[22,x,k[0],k[1],k[2]] = (F[13,x,k[0],k[1],k[2]]*k[2]-F[13,x,k[0],k[1],1])/(-1+k[2])
F[23,x] = x
F[24,x,k[0],k[1]] = F[15,x,k[1]]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = (-F[8,x,1,k[1]]*k[1]+F[8,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[26,x,k[0],k[1]] = F[23,x]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = (F[9,x,k[0],k[1]]*k[1]-F[9,x,k[0],1])/(-1+k[1])
F[28,x] = F[23,x]*F[29,x]
F[29,x] = F[30,x,1]
F[30,x,k[0]] = (F[31,x,k[0]]*k[0]-F[31,x,1])/(-1+k[0])
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = F[15,x,k[0]]*F[7,x,k[0]]
F[33,x,k[0]] = F[23,x]*F[30,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{23}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{8}\! \left(x , 1, y_{0}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{9}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{1}\right) F_{15}\! \left(x , y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , 1, y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{15}\! \left(x , y_{0}\right)
F_{15}\! \left(x , y_{0}\right) = y_{0} x
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{1}\right) F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{12}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{12}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{2}\right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} F_{20}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right)}{-y_{2}+y_{1}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{23}\! \left(x \right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{13}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{23}\! \left(x \right) = x
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , y_{1}\right) F_{25}\! \left(x , y_{0}, y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{8}\! \left(x , 1, y_{1}\right)-y_{0} F_{8}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{9}\! \left(x , y_{0}, y_{1}\right)+F_{9}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{28}\! \left(x \right) = F_{23}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{30}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{31}\! \left(x , y_{0}\right)+F_{31}\! \left(x , 1\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right) F_{7}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{23}\! \left(x \right) F_{30}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_23(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_28(x) + F_5(x))
Eq(F_5(x), F_23(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), F_9(x, k_0*k_1, k_1))
Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_0, k_1) + F_24(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, k_1)*F_15(x, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, 1, k_0, k_1))
Eq(F_12(x, k_0, k_1, k_2), F_13(x, k_0*k_1, k_1, k_2))
Eq(F_13(x, k_0, k_1, k_2), F_1(x) + F_14(x, k_0, k_1, k_2) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_21(x, k_0, k_1, k_2))
Eq(F_14(x, k_0, k_1, k_2), F_13(x, k_0, k_1, k_2)*F_15(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0, k_1, k_2), F_15(x, k_1)*F_17(x, k_0, k_1, k_2))
Eq(F_17(x, k_0, k_1, k_2), (-k_0*F_12(x, k_0/k_1, k_1, k_2) + k_1*F_12(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1, k_2), F_15(x, k_2)*F_19(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1/k_2, k_2) + k_2*F_20(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_20(x, k_0, k_1, k_2), F_13(x, k_0, k_1*k_2, k_2))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0, k_1, k_2)*F_23(x))
Eq(F_22(x, k_0, k_1, k_2), (-k_2*F_13(x, k_0, k_1, k_2) + F_13(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_23(x), x)
Eq(F_24(x, k_0, k_1), F_15(x, k_1)*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), (-k_0*F_8(x, k_0/k_1, k_1) + k_1*F_8(x, 1, k_1))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1), F_23(x)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), (-k_1*F_9(x, k_0, k_1) + F_9(x, k_0, 1))/(1 - k_1))
Eq(F_28(x), F_23(x)*F_29(x))
Eq(F_29(x), F_30(x, 1))
Eq(F_30(x, k_0), (-k_0*F_31(x, k_0) + F_31(x, 1))/(1 - k_0))
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), F_15(x, k_0)*F_7(x, k_0))
Eq(F_33(x, k_0), F_23(x)*F_30(x, k_0))
Pack JSON:
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Specification JSON:
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3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/23951/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[27,x]+F[4,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0],1]
F[7,x,k[0],k[1]] = F[1,x]+F[22,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[8,x,k[0],k[1]]
F[8,x,k[0],k[1]] = F[13,x,k[0]]*F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,1,k[0],k[1]]
F[10,x,k[0],k[1],k[2]] = F[11,x,k[0]*k[1],k[1],k[2]]
F[11,x,k[0],k[1],k[2]] = F[1,x]+F[12,x,k[0],k[1],k[2]]+F[14,x,k[0],k[1],k[2]]+F[16,x,k[0],k[1],k[2]]+F[19,x,k[0],k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1],k[2]]*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0],k[1],k[2]] = F[13,x,k[1]]*F[15,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = (-F[10,x,1,k[1],k[2]]*k[1]+F[10,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[16,x,k[0],k[1],k[2]] = F[13,x,k[2]]*F[17,x,k[0],k[1],k[2]]
F[17,x,k[0],k[1],k[2]] = (-F[18,x,k[0],1,k[2]]*k[2]+F[18,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[18,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1]*k[2],k[2]]
F[19,x,k[0],k[1],k[2]] = F[20,x,k[0],k[1],k[2]]*F[21,x]
F[20,x,k[0],k[1],k[2]] = (F[11,x,k[0],k[1],k[2]]*k[2]-F[11,x,k[0],k[1],1])/(-1+k[2])
F[21,x] = x
F[22,x,k[0],k[1]] = F[13,x,k[1]]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = (-F[24,x,1,k[1]]*k[1]+F[24,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1]] = F[7,x,k[0]*k[1],k[1]]
F[25,x,k[0],k[1]] = F[21,x]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (F[7,x,k[0],k[1]]*k[1]-F[7,x,k[0],1])/(-1+k[1])
F[27,x] = F[21,x]*F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[1,x]+F[30,x,k[0]]+F[33,x,k[0]]+F[35,x,k[0]]
F[30,x,k[0]] = F[13,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = (F[32,x,k[0],1]*k[0]-F[32,x,k[0],1/k[0]])/(-1+k[0])
F[32,x,k[0],k[1]] = F[7,x,k[0],k[0]*k[1]]
F[33,x,k[0]] = F[21,x]*F[34,x,k[0]]
F[34,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[35,x,k[0]] = F[21,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[29,x,k[0]]*k[0]-F[29,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}, 1\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x , y_{0}, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , 1, y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{13}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = y_{0} x
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{1}\right) F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{10}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{10}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{2}\right) F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} F_{18}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right)}{-y_{2}+y_{1}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{11}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{24}\! \left(x , 1, y_{1}\right)-y_{0} F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{7}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{27}\! \left(x \right) = F_{21}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = \frac{y_{0} F_{32}\! \left(x , y_{0}, 1\right)-F_{32}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{-1+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{33}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{6}\! \left(x , y_{0}\right)+F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{35}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{29}\! \left(x , y_{0}\right)+F_{29}\! \left(x , 1\right)}{-1+y_{0}}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_27(x) + F_4(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0, 1))
Eq(F_7(x, k_0, k_1), F_1(x) + F_22(x, k_0, k_1) + F_25(x, k_0, k_1) + F_8(x, k_0, k_1))
Eq(F_8(x, k_0, k_1), F_13(x, k_0)*F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, 1, k_0, k_1))
Eq(F_10(x, k_0, k_1, k_2), F_11(x, k_0*k_1, k_1, k_2))
Eq(F_11(x, k_0, k_1, k_2), F_1(x) + F_12(x, k_0, k_1, k_2) + F_14(x, k_0, k_1, k_2) + F_16(x, k_0, k_1, k_2) + F_19(x, k_0, k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_11(x, k_0, k_1, k_2)*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0, k_1, k_2), F_13(x, k_1)*F_15(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), (-k_0*F_10(x, k_0/k_1, k_1, k_2) + k_1*F_10(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1, k_2), F_13(x, k_2)*F_17(x, k_0, k_1, k_2))
Eq(F_17(x, k_0, k_1, k_2), (-k_1*F_18(x, k_0, k_1/k_2, k_2) + k_2*F_18(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_18(x, k_0, k_1, k_2), F_11(x, k_0, k_1*k_2, k_2))
Eq(F_19(x, k_0, k_1, k_2), F_20(x, k_0, k_1, k_2)*F_21(x))
Eq(F_20(x, k_0, k_1, k_2), (-k_2*F_11(x, k_0, k_1, k_2) + F_11(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_21(x), x)
Eq(F_22(x, k_0, k_1), F_13(x, k_1)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0/k_1, k_1) + k_1*F_24(x, 1, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1), F_7(x, k_0*k_1, k_1))
Eq(F_25(x, k_0, k_1), F_21(x)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_1*F_7(x, k_0, k_1) + F_7(x, k_0, 1))/(1 - k_1))
Eq(F_27(x), F_21(x)*F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_1(x) + F_30(x, k_0) + F_33(x, k_0) + F_35(x, k_0))
Eq(F_30(x, k_0), F_13(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_32(x, k_0, 1) + F_32(x, k_0, 1/k_0))/(1 - k_0))
Eq(F_32(x, k_0, k_1), F_7(x, k_0, k_0*k_1))
Eq(F_33(x, k_0), F_21(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_35(x, k_0), F_21(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_29(x, k_0) + F_29(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 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[2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [1, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [2, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 2, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/23952/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[27,x]+F[4,x]
F[4,x] = F[21,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0],1]
F[7,x,k[0],k[1]] = F[1,x]+F[22,x,k[0],k[1]]+F[25,x,k[0],k[1]]+F[8,x,k[0],k[1]]
F[8,x,k[0],k[1]] = F[13,x,k[0]]*F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,1,k[0],k[1]]
F[10,x,k[0],k[1],k[2]] = F[11,x,k[0]*k[1],k[1],k[2]]
F[11,x,k[0],k[1],k[2]] = F[1,x]+F[12,x,k[0],k[1],k[2]]+F[14,x,k[0],k[1],k[2]]+F[16,x,k[0],k[1],k[2]]+F[19,x,k[0],k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1],k[2]]*F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0],k[1],k[2]] = F[13,x,k[1]]*F[15,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = (-F[10,x,1,k[1],k[2]]*k[1]+F[10,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[16,x,k[0],k[1],k[2]] = F[13,x,k[2]]*F[17,x,k[0],k[1],k[2]]
F[17,x,k[0],k[1],k[2]] = (-F[18,x,k[0],1,k[2]]*k[2]+F[18,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[18,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1]*k[2],k[2]]
F[19,x,k[0],k[1],k[2]] = F[20,x,k[0],k[1],k[2]]*F[21,x]
F[20,x,k[0],k[1],k[2]] = (F[11,x,k[0],k[1],k[2]]*k[2]-F[11,x,k[0],k[1],1])/(-1+k[2])
F[21,x] = x
F[22,x,k[0],k[1]] = F[13,x,k[1]]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = (-F[24,x,1,k[1]]*k[1]+F[24,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1]] = F[7,x,k[0]*k[1],k[1]]
F[25,x,k[0],k[1]] = F[21,x]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (F[7,x,k[0],k[1]]*k[1]-F[7,x,k[0],1])/(-1+k[1])
F[27,x] = F[21,x]*F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[1,x]+F[30,x,k[0]]+F[33,x,k[0]]+F[35,x,k[0]]
F[30,x,k[0]] = F[13,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = (F[32,x,k[0],1]*k[0]-F[32,x,k[0],1/k[0]])/(-1+k[0])
F[32,x,k[0],k[1]] = F[7,x,k[0],k[0]*k[1]]
F[33,x,k[0]] = F[21,x]*F[34,x,k[0]]
F[34,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[35,x,k[0]] = F[21,x]*F[36,x,k[0]]
F[36,x,k[0]] = (F[29,x,k[0]]*k[0]-F[29,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}, 1\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x , y_{0}, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}, y_{1}\right)
F_{9}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , 1, y_{0}, y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{13}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = y_{0} x
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{1}\right) F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{10}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{10}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{2}\right) F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} F_{18}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right)}{-y_{2}+y_{1}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{2} F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{11}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{21}\! \left(x \right) = x
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} F_{24}\! \left(x , 1, y_{1}\right)-y_{0} F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x \right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{7}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{27}\! \left(x \right) = F_{21}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = \frac{y_{0} F_{32}\! \left(x , y_{0}, 1\right)-F_{32}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{-1+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{33}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{6}\! \left(x , y_{0}\right)+F_{6}\! \left(x , 1\right)}{-1+y_{0}}
F_{35}\! \left(x , y_{0}\right) = F_{21}\! \left(x \right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{29}\! \left(x , y_{0}\right)+F_{29}\! \left(x , 1\right)}{-1+y_{0}}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_27(x) + F_4(x))
Eq(F_4(x), F_21(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0, 1))
Eq(F_7(x, k_0, k_1), F_1(x) + F_22(x, k_0, k_1) + F_25(x, k_0, k_1) + F_8(x, k_0, k_1))
Eq(F_8(x, k_0, k_1), F_13(x, k_0)*F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, 1, k_0, k_1))
Eq(F_10(x, k_0, k_1, k_2), F_11(x, k_0*k_1, k_1, k_2))
Eq(F_11(x, k_0, k_1, k_2), F_1(x) + F_12(x, k_0, k_1, k_2) + F_14(x, k_0, k_1, k_2) + F_16(x, k_0, k_1, k_2) + F_19(x, k_0, k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_11(x, k_0, k_1, k_2)*F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0, k_1, k_2), F_13(x, k_1)*F_15(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), (-k_0*F_10(x, k_0/k_1, k_1, k_2) + k_1*F_10(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1, k_2), F_13(x, k_2)*F_17(x, k_0, k_1, k_2))
Eq(F_17(x, k_0, k_1, k_2), (-k_1*F_18(x, k_0, k_1/k_2, k_2) + k_2*F_18(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_18(x, k_0, k_1, k_2), F_11(x, k_0, k_1*k_2, k_2))
Eq(F_19(x, k_0, k_1, k_2), F_20(x, k_0, k_1, k_2)*F_21(x))
Eq(F_20(x, k_0, k_1, k_2), (-k_2*F_11(x, k_0, k_1, k_2) + F_11(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_21(x), x)
Eq(F_22(x, k_0, k_1), F_13(x, k_1)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_24(x, k_0/k_1, k_1) + k_1*F_24(x, 1, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1), F_7(x, k_0*k_1, k_1))
Eq(F_25(x, k_0, k_1), F_21(x)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_1*F_7(x, k_0, k_1) + F_7(x, k_0, 1))/(1 - k_1))
Eq(F_27(x), F_21(x)*F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_1(x) + F_30(x, k_0) + F_33(x, k_0) + F_35(x, k_0))
Eq(F_30(x, k_0), F_13(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), (-k_0*F_32(x, k_0, 1) + F_32(x, k_0, 1/k_0))/(1 - k_0))
Eq(F_32(x, k_0, k_1), F_7(x, k_0, k_0*k_1))
Eq(F_33(x, k_0), F_21(x)*F_34(x, k_0))
Eq(F_34(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_35(x, k_0), F_21(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (-k_0*F_29(x, k_0) + F_29(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3, 4], "pos": 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