0123_0231_2301
Counting sequence:
1, 1, 2, 6, 21, 74, 248, 780, 2309, 6483, 17407, 45028, 112921, 275964, 660030, 1550320, 3586449, 8190493, 18500893, 41399992, 91896773, 202564062, 443789172, 967093220, 2097536909, 4530328551, 9748157339, 20905142940, 44695397953, 95295673696, 202670082154, 430035177864, 910534952121, 1924147591153, 4058746749753, 8546988048592, 17970146839885, 37726997022658, 79096122724832, 165613944737820, 346346169461205, 723478658812283, 1509629473823927, 3146802288874644, 6553089313170857, 13633944197662788, 28341011732592790, 58863454521652960, 122160139911677857, 253327479061296069, 524950831589787861, 1087056360083953960, 2249548013902248981, 4652218415108017702, 9615185204474261836, 19860874356746472724, 41000771007628316381, 84595615400579885583, 174451435165881653331, 359567394249324648908, 740752066709970089297, 1525315150594936682664, 3139405257044530280642, 6458666268807651201528, 13281655733070980769865, 27301181229090249893785, 56096548728150870639601, 115218363484389995067840, 236561046001251437973021, 485518304020035559886602, 996124179980315962905528, 2043013799651480451546316, 4188739070305375511950501, 8585262265857015223496611, 17590815148689428664839279, 36031656264295393244443716, 73782253928355337104218937, 151040169588102732823216268, 309107220502715497440497390, 632419319385902887377026256, 1293550626987653217322192049, 2645129693316808634673188205, 5407525191136236298908146317, 11051999842916939915644574872, 22582734310401272984027416933, 46132609276494249307341202542, 94218842677485739360493780772, 192383619230193628346677344580, 392736477463286892212427014445, 801566175437283727997909898295, 1635628276905808688211244646155, 3336867375893742530991418727932, 6806194335991020751396269923681, 13879783720467683642169924368880, 28299309298063793084194985165082, 57688005830698720810300259422568, 117574593171168276988820361550553, 239585963443135356882878117371713, 488124709250382583913825565668009, 994313439554017436798977944402864, 2025071833864596468890984822420461
Generating function in Maple syntax:
-(17*x^9-95*x^8+269*x^7-463*x^6+521*x^5-393*x^4+198*x^3-64*x^2+12*x-1)/(2*x-1)^3/(-1+x)^7
Generating function in latex syntax:
-\frac{17 x^{9}-95 x^{8}+269 x^{7}-463 x^{6}+521 x^{5}-393 x^{4}+198 x^{3}-64 x^{2}+12 x -1}{\left(2 x -1\right)^{3} \left(-1+x \right)^{7}}
Generating function in sympy syntax:
(-17*x**9 + 95*x**8 - 269*x**7 + 463*x**6 - 521*x**5 + 393*x**4 - 198*x**3 + 64*x**2 - 12*x + 1)/((x - 1)**7*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(-1+x)^7*F(x)+17*x^9-95*x^8+269*x^7-463*x^6+521*x^5-393*x^4+198*x^3-64*x^2+12*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(-1+x \right)^{7} F \! \left(x \right)+17 x^{9}-95 x^{8}+269 x^{7}-463 x^{6}+521 x^{5}-393 x^{4}+198 x^{3}-64 x^{2}+12 x -1 = 0
Explicit closed form in Maple syntax:
1/720*(90*n^2+2790*n-28800)*2^n+1/720*n^6+1/240*n^5+29/144*n^4+17/16*n^3+2627/360*n^2+703/30*n+41
Explicit closed form in latex syntax:
\frac{\left(90 n^{2}+2790 n -28800\right) 2^{n}}{720}+\frac{n^{6}}{720}+\frac{n^{5}}{240}+\frac{29 n^{4}}{144}+\frac{17 n^{3}}{16}+\frac{2627 n^{2}}{360}+\frac{703 n}{30}+41
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(6) = 248
a(7) = 780
a(8) = 2309
a(9) = 6483
a(n+3) = -1/720*n^6+1/48*n^5-29/144*n^4+47/48*n^3-647/360*n^2+8*a(n)-12*a(n+1)+6*a(n+2)+4*n-2, n >= 10
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 74
a \! \left(6\right) = 248
a \! \left(7\right) = 780
a \! \left(8\right) = 2309
a \! \left(9\right) = 6483
a \! \left(n +3\right) = -\frac{n^{6}}{720}+\frac{n^{5}}{48}-\frac{29 n^{4}}{144}+\frac{47 n^{3}}{48}-\frac{647 n^{2}}{360}+8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)+4 n -2, \quad n \geq 10
Specification 1
Strategy pack name: point_and_row_and_col_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/21102/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[31,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[7,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[10,x]+F[12,x]+F[16,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[12,x]*F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[26,x]
F[19,x] = F[12,x]+F[20,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[13,x]+F[21,x]
F[25,x] = F[15,x]*F[20,x]
F[26,x] = F[13,x]+F[27,x]
F[27,x] = F[22,x]+F[28,x]+F[30,x]
F[28,x] = F[15,x]*F[29,x]
F[29,x] = F[13,x]+F[27,x]
F[30,x] = F[15,x]*F[26,x]
F[31,x] = F[22,x]+F[32,x]+F[52,x]
F[32,x] = F[15,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[15,x]*F[35,x]
F[35,x] = F[34,x]+F[36,x]+F[42,x]+F[8,x]
F[36,x] = F[15,x]*F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = 1/F[15,x]*F[39,x]
F[39,x] = -F[40,x]+F[11,x]
F[40,x] = F[12,x]+F[26,x]
F[41,x] = F[26,x]*F[40,x]
F[42,x] = -F[22,x]-F[47,x]+F[43,x]
F[43,x] = -F[46,x]+F[44,x]
F[44,x] = 1/F[15,x]*F[45,x]
F[45,x] = F[31,x]
F[46,x] = F[19,x]*F[6,x]
F[47,x] = F[15,x]*F[48,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[15,x]*F[50,x]
F[50,x] = F[31,x]
F[51,x] = F[12,x]*F[6,x]
F[52,x] = F[15,x]*F[53,x]
F[53,x] = F[5,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[12,x]*F[15,x]*F[19,x]*F[6,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_{15}\! \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_{31}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{10}\! \left(x \right)+F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right)+F_{32}\! \left(x \right)+F_{52}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)+F_{42}\! \left(x \right)+F_{8}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{11}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right)+F_{26}\! \left(x \right)
F_{41}\! \left(x \right) = F_{26}\! \left(x \right) F_{40}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{22}\! \left(x \right)-F_{47}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{31}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{6}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{31}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{5}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{19}\! \left(x \right) F_{6}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_31(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_7(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_10(x) + F_12(x) + F_16(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_12(x)*F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_26(x))
Eq(F_19(x), F_12(x) + F_20(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_13(x) + F_21(x))
Eq(F_25(x), F_15(x)*F_20(x))
Eq(F_26(x), F_13(x) + F_27(x))
Eq(F_27(x), F_22(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_15(x)*F_29(x))
Eq(F_29(x), F_13(x) + F_27(x))
Eq(F_30(x), F_15(x)*F_26(x))
Eq(F_31(x), F_22(x) + F_32(x) + F_52(x))
Eq(F_32(x), F_15(x)*F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_15(x)*F_35(x))
Eq(F_35(x), F_34(x) + F_36(x) + F_42(x) + F_8(x))
Eq(F_36(x), F_15(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x)/F_15(x))
Eq(F_39(x), F_11(x) - F_40(x))
Eq(F_40(x), F_12(x) + F_26(x))
Eq(F_41(x), F_26(x)*F_40(x))
Eq(F_42(x), -F_22(x) + F_43(x) - F_47(x))
Eq(F_43(x), F_44(x) - F_46(x))
Eq(F_44(x), F_45(x)/F_15(x))
Eq(F_45(x), F_31(x))
Eq(F_46(x), F_19(x)*F_6(x))
Eq(F_47(x), F_15(x)*F_48(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_15(x))
Eq(F_50(x), F_31(x))
Eq(F_51(x), F_12(x)*F_6(x))
Eq(F_52(x), F_15(x)*F_53(x))
Eq(F_53(x), F_5(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_12(x)*F_15(x)*F_19(x)*F_6(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_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:
{"root": {"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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, 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{"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 3], [0, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [1, 0], "pos": [[2, 3], [2, 1]]}], "strategy_class": "ObstructionInferralStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[4, 3], [4, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[3, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: insertion_row_and_col_placements_expand_verified
Tree: http://permpal.com/tree/21103/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[31,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[7,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[10,x]+F[12,x]+F[16,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[12,x]*F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[26,x]
F[19,x] = F[12,x]+F[20,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[13,x]+F[21,x]
F[25,x] = F[15,x]*F[20,x]
F[26,x] = F[13,x]+F[27,x]
F[27,x] = F[22,x]+F[28,x]+F[30,x]
F[28,x] = F[15,x]*F[29,x]
F[29,x] = F[13,x]+F[27,x]
F[30,x] = F[15,x]*F[26,x]
F[31,x] = F[113,x]+F[22,x]+F[32,x]
F[32,x] = F[15,x]*F[33,x]
F[33,x] = F[34,x]+F[41,x]
F[34,x] = F[13,x]+F[35,x]
F[35,x] = F[22,x]+F[36,x]+F[39,x]
F[36,x] = F[15,x]*F[37,x]
F[37,x] = F[13,x]+F[38,x]
F[38,x] = F[36,x]
F[39,x] = F[15,x]*F[40,x]
F[40,x] = F[13,x]+F[35,x]
F[41,x] = F[42,x]+F[68,x]
F[42,x] = F[43,x]
F[43,x] = F[15,x]*F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[34,x]+F[46,x]
F[46,x] = F[12,x]*F[13,x]
F[47,x] = F[48,x]+F[67,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[13,x]*F[6,x]
F[50,x] = F[22,x]+F[51,x]+F[56,x]
F[51,x] = F[52,x]
F[52,x] = F[13,x]*F[15,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[12,x]*F[13,x]
F[55,x] = F[12,x]*F[20,x]
F[56,x] = F[15,x]*F[57,x]
F[57,x] = F[50,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[15,x]*F[60,x]
F[60,x] = F[61,x]+F[63,x]
F[61,x] = 2*F[62,x]
F[62,x] = F[12,x]*F[13,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[58,x]+F[65,x]
F[65,x] = F[13,x]*F[20,x]
F[66,x] = F[13,x]*F[27,x]
F[67,x] = F[12,x]*F[42,x]
F[68,x] = F[69,x]
F[69,x] = F[15,x]*F[70,x]
F[70,x] = F[100,x]+F[71,x]
F[71,x] = F[72,x]+F[86,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[35,x]+F[68,x]
F[74,x] = F[13,x]*F[75,x]
F[75,x] = F[40,x]+F[76,x]
F[76,x] = F[27,x]+F[77,x]
F[77,x] = F[22,x]+F[78,x]+F[80,x]+F[85,x]
F[78,x] = F[15,x]*F[79,x]
F[79,x] = F[35,x]+F[77,x]
F[80,x] = F[15,x]*F[81,x]
F[81,x] = F[27,x]+F[82,x]
F[82,x] = 2*F[22,x]+F[80,x]+F[83,x]
F[83,x] = F[15,x]*F[84,x]
F[84,x] = F[38,x]+F[82,x]
F[85,x] = F[15,x]*F[76,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[13,x]*F[88,x]
F[88,x] = F[37,x]+F[81,x]
F[89,x] = F[90,x]+F[95,x]
F[90,x] = F[91,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[35,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[13,x]^3
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[26,x]*F[35,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]^2*F[99,x]
F[99,x] = F[27,x]+F[82,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[13,x]
F[102,x] = F[103,x]+F[110,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[13,x]^2
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[15,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[12,x]*F[27,x]
F[109,x] = F[24,x]*F[29,x]
F[110,x] = F[111,x]*F[13,x]
F[111,x] = F[112,x]+F[54,x]
F[112,x] = F[105,x]+F[21,x]
F[113,x] = F[114,x]*F[15,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[116,x]
F[116,x] = F[12,x]*F[6,x]
F[117,x] = F[118,x]+F[31,x]
F[118,x] = F[119,x]
F[119,x] = F[12,x]*F[120,x]*F[15,x]*F[6,x]
F[120,x] = F[13,x]+F[20,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_{15}\! \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_{31}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{10}\! \left(x \right)+F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{31}\! \left(x \right) = F_{113}\! \left(x \right)+F_{22}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{13}\! \left(x \right)+F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{68}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{34}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{67}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{50}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{66}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{100}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{86}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{35}\! \left(x \right)+F_{68}\! \left(x \right)
F_{74}\! \left(x \right) = F_{13}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{40}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{27}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{22}\! \left(x \right)+F_{78}\! \left(x \right)+F_{80}\! \left(x \right)+F_{85}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{35}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{27}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{15}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{38}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \left(x \right) F_{76}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{13}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{37}\! \left(x \right)+F_{81}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{35}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{13} \left(x \right)^{3}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{27}\! \left(x \right)+F_{82}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{13}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{110}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{13} \left(x \right)^{2}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{15}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{109}\! \left(x \right) = F_{24}\! \left(x \right) F_{29}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{13}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{54}\! \left(x \right)
F_{112}\! \left(x \right) = F_{105}\! \left(x \right)+F_{21}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{15}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{31}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{120}\! \left(x \right) = F_{13}\! \left(x \right)+F_{20}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_31(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_7(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_10(x) + F_12(x) + F_16(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_12(x)*F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_26(x))
Eq(F_19(x), F_12(x) + F_20(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_13(x) + F_21(x))
Eq(F_25(x), F_15(x)*F_20(x))
Eq(F_26(x), F_13(x) + F_27(x))
Eq(F_27(x), F_22(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_15(x)*F_29(x))
Eq(F_29(x), F_13(x) + F_27(x))
Eq(F_30(x), F_15(x)*F_26(x))
Eq(F_31(x), F_113(x) + F_22(x) + F_32(x))
Eq(F_32(x), F_15(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_41(x))
Eq(F_34(x), F_13(x) + F_35(x))
Eq(F_35(x), F_22(x) + F_36(x) + F_39(x))
Eq(F_36(x), F_15(x)*F_37(x))
Eq(F_37(x), F_13(x) + F_38(x))
Eq(F_38(x), F_36(x))
Eq(F_39(x), F_15(x)*F_40(x))
Eq(F_40(x), F_13(x) + F_35(x))
Eq(F_41(x), F_42(x) + F_68(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_15(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_34(x) + F_46(x))
Eq(F_46(x), F_12(x)*F_13(x))
Eq(F_47(x), F_48(x) + F_67(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_13(x)*F_6(x))
Eq(F_50(x), F_22(x) + F_51(x) + F_56(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_13(x)*F_15(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_12(x)*F_13(x))
Eq(F_55(x), F_12(x)*F_20(x))
Eq(F_56(x), F_15(x)*F_57(x))
Eq(F_57(x), F_50(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_15(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_63(x))
Eq(F_61(x), 2*F_62(x))
Eq(F_62(x), F_12(x)*F_13(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_58(x) + F_65(x))
Eq(F_65(x), F_13(x)*F_20(x))
Eq(F_66(x), F_13(x)*F_27(x))
Eq(F_67(x), F_12(x)*F_42(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_15(x)*F_70(x))
Eq(F_70(x), F_100(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_86(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_35(x) + F_68(x))
Eq(F_74(x), F_13(x)*F_75(x))
Eq(F_75(x), F_40(x) + F_76(x))
Eq(F_76(x), F_27(x) + F_77(x))
Eq(F_77(x), F_22(x) + F_78(x) + F_80(x) + F_85(x))
Eq(F_78(x), F_15(x)*F_79(x))
Eq(F_79(x), F_35(x) + F_77(x))
Eq(F_80(x), F_15(x)*F_81(x))
Eq(F_81(x), F_27(x) + F_82(x))
Eq(F_82(x), 2*F_22(x) + F_80(x) + F_83(x))
Eq(F_83(x), F_15(x)*F_84(x))
Eq(F_84(x), F_38(x) + F_82(x))
Eq(F_85(x), F_15(x)*F_76(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_13(x)*F_88(x))
Eq(F_88(x), F_37(x) + F_81(x))
Eq(F_89(x), F_90(x) + F_95(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_35(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_13(x)**3)
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_26(x)*F_35(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)**2*F_99(x))
Eq(F_99(x), F_27(x) + F_82(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_13(x))
Eq(F_102(x), F_103(x) + F_110(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_13(x)**2)
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_15(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_12(x)*F_27(x))
Eq(F_109(x), F_24(x)*F_29(x))
Eq(F_110(x), F_111(x)*F_13(x))
Eq(F_111(x), F_112(x) + F_54(x))
Eq(F_112(x), F_105(x) + F_21(x))
Eq(F_113(x), F_114(x)*F_15(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_12(x)*F_6(x))
Eq(F_117(x), F_118(x) + F_31(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_12(x)*F_120(x)*F_15(x)*F_6(x))
Eq(F_120(x), F_13(x) + F_20(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_and_col_placements_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], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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Specification 3
Strategy pack name: row_and_col_placements_expand_verified
Tree: http://permpal.com/tree/21104/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[8,x]
F[3,x] = F[1,x]+F[31,x]+F[4,x]
F[4,x] = F[5,x]*F[8,x]
F[5,x] = F[6,x]+F[9,x]
F[6,x] = F[1,x]+F[4,x]+F[7,x]
F[7,x] = F[6,x]*F[8,x]
F[8,x] = x
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]*F[8,x]
F[11,x] = F[12,x]+F[15,x]+F[16,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[8,x]
F[15,x] = F[11,x]*F[8,x]
F[16,x] = F[17,x]
F[17,x] = F[12,x]*F[18,x]*F[8,x]
F[18,x] = F[19,x]+F[26,x]
F[19,x] = F[12,x]+F[20,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[8,x]
F[24,x] = F[13,x]+F[21,x]
F[25,x] = F[20,x]*F[8,x]
F[26,x] = F[13,x]+F[27,x]
F[27,x] = F[22,x]+F[28,x]+F[30,x]
F[28,x] = F[29,x]*F[8,x]
F[29,x] = F[13,x]+F[27,x]
F[30,x] = F[26,x]*F[8,x]
F[31,x] = F[32,x]*F[8,x]
F[32,x] = F[3,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[8,x]
F[35,x] = F[36,x]+F[86,x]
F[36,x] = 1/F[8,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[83,x]+F[39,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = 1/F[8,x]*F[41,x]
F[41,x] = -F[1,x]+F[0,x]
F[42,x] = F[43,x]*F[8,x]
F[43,x] = F[44,x]+F[81,x]
F[44,x] = F[45,x]+F[71,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[57,x]
F[47,x] = F[1,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[8,x]
F[50,x] = F[12,x]+F[51,x]
F[51,x] = F[48,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]*F[8,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[13,x]
F[56,x] = F[52,x]
F[57,x] = F[13,x]+F[58,x]
F[58,x] = F[22,x]+F[59,x]+F[61,x]
F[59,x] = F[60,x]*F[8,x]
F[60,x] = F[48,x]+F[58,x]
F[61,x] = F[62,x]*F[8,x]
F[62,x] = F[20,x]+F[63,x]
F[63,x] = F[58,x]+F[64,x]
F[64,x] = 2*F[22,x]+F[65,x]+F[67,x]
F[65,x] = F[66,x]*F[8,x]
F[66,x] = F[52,x]+F[64,x]
F[67,x] = F[68,x]*F[8,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[21,x]
F[70,x] = F[64,x]
F[71,x] = F[19,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]*F[8,x]
F[74,x] = F[72,x]+F[75,x]
F[75,x] = -F[78,x]+F[76,x]
F[76,x] = 1/F[8,x]*F[77,x]
F[77,x] = -F[1,x]+F[78,x]
F[78,x] = F[1,x]+F[79,x]
F[79,x] = F[8,x]*F[80,x]
F[80,x] = F[15,x]+F[78,x]
F[81,x] = F[19,x]*F[8,x]*F[82,x]
F[82,x] = 1/F[8,x]*F[75,x]
F[83,x] = F[0,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[77,x]
F[86,x] = F[87,x]
F[87,x] = F[19,x]*F[8,x]*F[88,x]
F[88,x] = 1/F[8,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[12,x]-F[91,x]+F[11,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]*F[19,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{8}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{6}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{8}\! \left(x \right)
F_{32}\! \left(x \right) = F_{3}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{86}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{41}\! \left(x \right) = -F_{1}\! \left(x \right)+F_{0}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{81}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{71}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{13}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{22}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{8}\! \left(x \right)
F_{60}\! \left(x \right) = F_{48}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{8}\! \left(x \right)
F_{62}\! \left(x \right) = F_{20}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right) F_{8}\! \left(x \right)
F_{66}\! \left(x \right) = F_{52}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right) F_{8}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{21}\! \left(x \right)
F_{70}\! \left(x \right) = F_{64}\! \left(x \right)
F_{71}\! \left(x \right) = F_{19}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right) F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{77}\! \left(x \right) = -F_{1}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{1}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{8}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{0}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{77}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{12}\! \left(x \right)-F_{91}\! \left(x \right)+F_{11}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_8(x))
Eq(F_3(x), F_1(x) + F_31(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_8(x))
Eq(F_5(x), F_6(x) + F_9(x))
Eq(F_6(x), F_1(x) + F_4(x) + F_7(x))
Eq(F_7(x), F_6(x)*F_8(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x)*F_8(x))
Eq(F_11(x), F_12(x) + F_15(x) + F_16(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_8(x))
Eq(F_15(x), F_11(x)*F_8(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_12(x)*F_18(x)*F_8(x))
Eq(F_18(x), F_19(x) + F_26(x))
Eq(F_19(x), F_12(x) + F_20(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), F_13(x) + F_21(x))
Eq(F_25(x), F_20(x)*F_8(x))
Eq(F_26(x), F_13(x) + F_27(x))
Eq(F_27(x), F_22(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_29(x)*F_8(x))
Eq(F_29(x), F_13(x) + F_27(x))
Eq(F_30(x), F_26(x)*F_8(x))
Eq(F_31(x), F_32(x)*F_8(x))
Eq(F_32(x), F_3(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_8(x))
Eq(F_35(x), F_36(x) + F_86(x))
Eq(F_36(x), F_37(x)/F_8(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x) - F_83(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_41(x)/F_8(x))
Eq(F_41(x), F_0(x) - F_1(x))
Eq(F_42(x), F_43(x)*F_8(x))
Eq(F_43(x), F_44(x) + F_81(x))
Eq(F_44(x), F_45(x) + F_71(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_57(x))
Eq(F_47(x), F_1(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_8(x))
Eq(F_50(x), F_12(x) + F_51(x))
Eq(F_51(x), F_48(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)*F_8(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_13(x))
Eq(F_56(x), F_52(x))
Eq(F_57(x), F_13(x) + F_58(x))
Eq(F_58(x), F_22(x) + F_59(x) + F_61(x))
Eq(F_59(x), F_60(x)*F_8(x))
Eq(F_60(x), F_48(x) + F_58(x))
Eq(F_61(x), F_62(x)*F_8(x))
Eq(F_62(x), F_20(x) + F_63(x))
Eq(F_63(x), F_58(x) + F_64(x))
Eq(F_64(x), 2*F_22(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_66(x)*F_8(x))
Eq(F_66(x), F_52(x) + F_64(x))
Eq(F_67(x), F_68(x)*F_8(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_21(x))
Eq(F_70(x), F_64(x))
Eq(F_71(x), F_19(x)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x)*F_8(x))
Eq(F_74(x), F_72(x) + F_75(x))
Eq(F_75(x), F_76(x) - F_78(x))
Eq(F_76(x), F_77(x)/F_8(x))
Eq(F_77(x), -F_1(x) + F_78(x))
Eq(F_78(x), F_1(x) + F_79(x))
Eq(F_79(x), F_8(x)*F_80(x))
Eq(F_80(x), F_15(x) + F_78(x))
Eq(F_81(x), F_19(x)*F_8(x)*F_82(x))
Eq(F_82(x), F_75(x)/F_8(x))
Eq(F_83(x), F_0(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_77(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_19(x)*F_8(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_8(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_11(x) - F_12(x) - F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x)*F_19(x)*F_8(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_and_col_placements_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, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}], "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": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}], [{"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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_placements_expand_verified
Tree: http://permpal.com/tree/21105/
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[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[78,x]+F[9,x]
F[9,x] = F[10,x]+F[23,x]+F[24,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[7,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[7,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[7,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[15,x]
F[22,x] = F[18,x]
F[23,x] = F[5,x]
F[24,x] = F[25,x]*F[7,x]
F[25,x] = F[26,x]+F[51,x]+F[56,x]
F[26,x] = F[1,x]+F[27,x]+F[50,x]
F[27,x] = F[28,x]*F[7,x]
F[28,x] = F[26,x]+F[29,x]
F[29,x] = F[30,x]+F[48,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[7,x]
F[32,x] = F[14,x]+F[31,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[14,x]*F[35,x]*F[7,x]
F[35,x] = F[36,x]+F[43,x]
F[36,x] = F[14,x]+F[37,x]
F[37,x] = F[15,x]+F[38,x]
F[38,x] = F[39,x]+F[40,x]+F[42,x]
F[39,x] = 0
F[40,x] = F[41,x]*F[7,x]
F[41,x] = F[15,x]+F[38,x]
F[42,x] = F[37,x]*F[7,x]
F[43,x] = F[15,x]+F[44,x]
F[44,x] = F[39,x]+F[45,x]+F[47,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[15,x]+F[44,x]
F[47,x] = F[43,x]*F[7,x]
F[48,x] = F[49,x]
F[49,x] = F[29,x]*F[7,x]
F[50,x] = F[26,x]*F[7,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[7,x]
F[53,x] = F[25,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[15,x]*F[36,x]
F[56,x] = F[57,x]
F[57,x] = F[58,x]*F[7,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[14,x]*F[35,x]*F[36,x]
F[60,x] = F[14,x]*F[61,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]*F[7,x]
F[64,x] = F[15,x]+F[65,x]
F[65,x] = F[18,x]+F[62,x]
F[66,x] = F[39,x]+F[67,x]+F[68,x]
F[67,x] = F[61,x]*F[7,x]
F[68,x] = F[69,x]*F[7,x]
F[69,x] = F[38,x]+F[70,x]
F[70,x] = F[66,x]+F[71,x]
F[71,x] = 2*F[39,x]+F[72,x]+F[74,x]
F[72,x] = F[7,x]*F[73,x]
F[73,x] = F[18,x]+F[71,x]
F[74,x] = F[7,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[38,x]
F[77,x] = F[71,x]
F[78,x] = F[79,x]
F[79,x] = F[32,x]*F[36,x]*F[7,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{78}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{5}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{50}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{7}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right) F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{43}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{37}\! \left(x \right) F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{39}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right) F_{7}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{29}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right) F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{7}\! \left(x \right)
F_{53}\! \left(x \right) = F_{25}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{15}\! \left(x \right) F_{36}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right) F_{7}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{7}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right)+F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{39}\! \left(x \right)+F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right) F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right) F_{7}\! \left(x \right)
F_{69}\! \left(x \right) = F_{38}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{18}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{38}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{32}\! \left(x \right) F_{36}\! \left(x \right) F_{7}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_78(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_23(x) + F_24(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_7(x))
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_7(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_7(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_15(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_5(x))
Eq(F_24(x), F_25(x)*F_7(x))
Eq(F_25(x), F_26(x) + F_51(x) + F_56(x))
Eq(F_26(x), F_1(x) + F_27(x) + F_50(x))
Eq(F_27(x), F_28(x)*F_7(x))
Eq(F_28(x), F_26(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_48(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_7(x))
Eq(F_32(x), F_14(x) + F_31(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_14(x)*F_35(x)*F_7(x))
Eq(F_35(x), F_36(x) + F_43(x))
Eq(F_36(x), F_14(x) + F_37(x))
Eq(F_37(x), F_15(x) + F_38(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_42(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_41(x)*F_7(x))
Eq(F_41(x), F_15(x) + F_38(x))
Eq(F_42(x), F_37(x)*F_7(x))
Eq(F_43(x), F_15(x) + F_44(x))
Eq(F_44(x), F_39(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_15(x) + F_44(x))
Eq(F_47(x), F_43(x)*F_7(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_29(x)*F_7(x))
Eq(F_50(x), F_26(x)*F_7(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_7(x))
Eq(F_53(x), F_25(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_15(x)*F_36(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x)*F_7(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_14(x)*F_35(x)*F_36(x))
Eq(F_60(x), F_14(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)*F_7(x))
Eq(F_64(x), F_15(x) + F_65(x))
Eq(F_65(x), F_18(x) + F_62(x))
Eq(F_66(x), F_39(x) + F_67(x) + F_68(x))
Eq(F_67(x), F_61(x)*F_7(x))
Eq(F_68(x), F_69(x)*F_7(x))
Eq(F_69(x), F_38(x) + F_70(x))
Eq(F_70(x), F_66(x) + F_71(x))
Eq(F_71(x), 2*F_39(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_7(x)*F_73(x))
Eq(F_73(x), F_18(x) + F_71(x))
Eq(F_74(x), F_7(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_38(x))
Eq(F_77(x), F_71(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_32(x)*F_36(x)*F_7(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_and_row_placements_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], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 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0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": 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"RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": 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"pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, 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1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]]}], "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": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 2]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: insertion_point_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/21106/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[31,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[7,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[10,x]+F[12,x]+F[16,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[12,x]*F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[26,x]
F[19,x] = F[12,x]+F[20,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[25,x]
F[22,x] = 0
F[23,x] = F[15,x]*F[24,x]
F[24,x] = F[13,x]+F[21,x]
F[25,x] = F[15,x]*F[20,x]
F[26,x] = F[13,x]+F[27,x]
F[27,x] = F[22,x]+F[28,x]+F[30,x]
F[28,x] = F[15,x]*F[29,x]
F[29,x] = F[13,x]+F[27,x]
F[30,x] = F[15,x]*F[26,x]
F[31,x] = F[32,x]
F[32,x] = F[15,x]*F[33,x]
F[33,x] = F[34,x]+F[80,x]
F[34,x] = F[35,x]+F[5,x]
F[35,x] = -F[79,x]+F[36,x]
F[36,x] = 1/F[15,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[15,x]*F[40,x]
F[40,x] = F[41,x]+F[47,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[13,x]+F[43,x]
F[43,x] = F[12,x]*F[13,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[13,x]*F[6,x]
F[46,x] = F[12,x]*F[38,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[13,x]^2
F[50,x] = F[12,x]*F[27,x]
F[51,x] = F[52,x]+F[61,x]
F[52,x] = F[13,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[15,x]*F[55,x]
F[55,x] = F[56,x]+F[60,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[13,x]+F[53,x]
F[58,x] = F[13,x]*F[59,x]
F[59,x] = F[12,x]+F[26,x]
F[60,x] = F[13,x]*F[20,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[64,x]
F[64,x] = F[65,x]+F[77,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[53,x]+F[62,x]
F[67,x] = F[13,x]*F[68,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[13,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[15,x]*F[69,x]
F[72,x] = F[27,x]+F[73,x]
F[73,x] = 2*F[22,x]+F[74,x]+F[76,x]
F[74,x] = F[15,x]*F[75,x]
F[75,x] = F[70,x]+F[73,x]
F[76,x] = F[15,x]*F[72,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[13,x]*F[20,x]
F[79,x] = F[38,x]+F[6,x]
F[80,x] = F[20,x]*F[6,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_{15}\! \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_{31}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{10}\! \left(x \right)+F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{80}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13} \left(x \right)^{2}
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{61}\! \left(x \right)
F_{52}\! \left(x \right) = F_{13}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{13}\! \left(x \right)+F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right)+F_{26}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{77}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{13}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{13}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{15}\! \left(x \right) F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{27}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{15}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{79}\! \left(x \right) = F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right) F_{6}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_31(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_15(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_7(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_10(x) + F_12(x) + F_16(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_12(x)*F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_26(x))
Eq(F_19(x), F_12(x) + F_20(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_25(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_15(x)*F_24(x))
Eq(F_24(x), F_13(x) + F_21(x))
Eq(F_25(x), F_15(x)*F_20(x))
Eq(F_26(x), F_13(x) + F_27(x))
Eq(F_27(x), F_22(x) + F_28(x) + F_30(x))
Eq(F_28(x), F_15(x)*F_29(x))
Eq(F_29(x), F_13(x) + F_27(x))
Eq(F_30(x), F_15(x)*F_26(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_15(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_80(x))
Eq(F_34(x), F_35(x) + F_5(x))
Eq(F_35(x), F_36(x) - F_79(x))
Eq(F_36(x), F_37(x)/F_15(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_15(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_47(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_13(x) + F_43(x))
Eq(F_43(x), F_12(x)*F_13(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_13(x)*F_6(x))
Eq(F_46(x), F_12(x)*F_38(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_13(x)**2)
Eq(F_50(x), F_12(x)*F_27(x))
Eq(F_51(x), F_52(x) + F_61(x))
Eq(F_52(x), F_13(x)*F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_15(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_60(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_13(x) + F_53(x))
Eq(F_58(x), F_13(x)*F_59(x))
Eq(F_59(x), F_12(x) + F_26(x))
Eq(F_60(x), F_13(x)*F_20(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_77(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_53(x) + F_62(x))
Eq(F_67(x), F_13(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_13(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_15(x)*F_69(x))
Eq(F_72(x), F_27(x) + F_73(x))
Eq(F_73(x), 2*F_22(x) + F_74(x) + F_76(x))
Eq(F_74(x), F_15(x)*F_75(x))
Eq(F_75(x), F_70(x) + F_73(x))
Eq(F_76(x), F_15(x)*F_72(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_13(x)*F_20(x))
Eq(F_79(x), F_38(x) + F_6(x))
Eq(F_80(x), F_20(x)*F_6(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_placements_req_corrob_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], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0], [2, 1]], [[1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 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