0213_13042_20413_315042
Counting sequence:
1, 1, 2, 6, 23, 101, 477, 2343, 11762, 59786, 306132, 1574536, 8120782, 41957030, 217021682, 1123371986, 5817788471, 30139492189, 156174965473, 809382185187, 4195096032623, 21745137658765, 112720985668763, 584336632836945, 3029232133574325, 15703985220888071, 81412823495242113, 422065421214079867, 2188112323584573261, 11343877474909034719, 58810509351743729037, 304894394309770828415, 1580682794218637926834, 8194842012081625064122, 42485121255169592612524, 220258888842744316480688, 1141905721721967770239218, 5920075123621590433967618, 30691937607732086523404750, 159118795975416830228629878, 824933093162776056189434652, 4276771196062958584686781592, 22172432536898175343574024944, 114950454844308232524737051812, 595947586569102815056634908980, 3089622726284532172851467160656, 16017799283149209594018481118404, 83042468701888209921019728144704, 430524292353615831618115621609278, 2232004552248222811627453279157574, 11571575511704017005746437371267962, 59991526646242086676550052713004810, 311019297302298217651356783541046078, 1612444440118110218237098903907112086, 8359536212224603953762681445969587374, 43339072073398292359492069585001593126, 224686528407039458818574051149114707322, 1164861952075608115673906884445598693402, 6039095347631883553721386003779993835466, 31309008395920200728791375322221325695210, 162318021277765007035252711206871787248922, 841519466423465641162435440611802994938522, 4362762723186632760062616054517274401454994, 22618251082174924403633638456774627335146882, 117261770704043151112512626588912534503941303, 607930419554851257293023538355580368842833085, 3151746667547022508464405062917591960661249873, 16339874988017681747825444263756748206971823475, 84712238259579862926655848872018845210219517575, 439181041252363794574722565104404744250821056117, 2276884556030677612277859435320499717190155225027, 11804251082422122900371449003142701891315238343977, 61197807877282292896662549358526993460077738907145, 317273130067462049876867796401584863416549715977843, 1644866745315777223946617995037170385167256487030541, 8527626052940107916588316817854843073981654805475951, 44210515110836593863448989568008208760869063184500193, 229204427379642569395128028508833228751292566566758507, 1188284492927831185486009097879289609792434001326499281, 6160526881082319353510966830764580923084037302214240283, 31938556531256468048880250447231780768745303103601193471, 165581842753380154952518651778825771779369287077708938125, 858440381386529458882655635083750559745249170522737423107, 4450487300670244266338642055275857290926005454967847354601, 23073049268074635859383368432920979900797342128098237489791, 119619620630533943735481883452301327111215016195274090639549, 620154426645084317746788764626720540564535704683358522396863, 3215120653788456927897723009549092755045703703668145522873437, 16668430272020863960655360023422708728400225159306954514828803, 86415596069737332921696022882213792278456965192063419644850745, 448011907673371692664196084585442913012350065138004731901385923, 2322667186779226694507426658165847990367086506770943472402672825, 12041605966585877226323337846779451496693119532597679484974726915, 62428347496306427183512649284605420940971573434237797325988356057, 323652723892001737210444626065743645345448600203234512430575405467, 1677941029736726010497594252506149919659397983970691210214104928577, 8699095948945196170984709344197108076853207093228947775598684848405, 45099481440554070509785545966250836453839904635562679443495113784263, 233813173017539507011518251033637570330809835203383593583781214653361, 1212178014698224485029000755319185647593364315614609992331081958839371, 6284400148863775133337289424021806227003158496719755215956142093388613
Generating function in Maple syntax:
((-2*x^2-5*x+1)*(1-4*x)^(1/2)-8*x^2+17*x-3)/(8*x^3-10*x^2+12*x-2)
Generating function in latex syntax:
\frac{\left(-2 x^{2}-5 x +1\right) \sqrt{1-4 x}-8 x^{2}+17 x -3}{8 x^{3}-10 x^{2}+12 x -2}
Generating function in sympy syntax:
(-8*x**2 + 17*x + sqrt(1 - 4*x)*(-2*x**2 - 5*x + 1) - 3)/(8*x**3 - 10*x**2 + 12*x - 2)
Implicit equation for the generating function in Maple syntax:
(4*x^3-5*x^2+6*x-1)*F(x)^2+(8*x^2-17*x+3)*F(x)+x^2+10*x-2 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{3}-5 x^{2}+6 x -1\right) F \! \left(x \right)^{2}+\left(8 x^{2}-17 x +3\right) F \! \left(x \right)+x^{2}+10 x -2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 23
a(5) = 101
a(n+6) = 16*(1+2*n)/(n+6)*a(n)+4*(41+8*n)/(n+6)*a(n+1)-2*(179+39*n)/(n+6)*a(n+2)+(486+149*n)/(n+6)*a(n+3)-(304+77*n)/(n+6)*a(n+4)+(74+15*n)/(n+6)*a(n+5), n >= 6
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) = 23
a \! \left(5\right) = 101
a \! \left(n +6\right) = \frac{16 \left(1+2 n \right) a \! \left(n \right)}{n +6}+\frac{4 \left(41+8 n \right) a \! \left(n +1\right)}{n +6}-\frac{2 \left(179+39 n \right) a \! \left(n +2\right)}{n +6}+\frac{\left(486+149 n \right) a \! \left(n +3\right)}{n +6}-\frac{\left(304+77 n \right) a \! \left(n +4\right)}{n +6}+\frac{\left(74+15 n \right) a \! \left(n +5\right)}{n +6}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements_expand_verified
Tree: http://permpal.com/tree/24048/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[15,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[12,x]*F[7,x]
F[11,x] = x
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]^2*F[11,x]
F[15,x] = F[16,x]
F[16,x] = F[11,x]*F[17,x]
F[17,x] = F[18,x]+F[24,x]
F[18,x] = F[19,x]*F[8,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[11,x]*F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[19,x]*F[20,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]^2*F[11,x]*F[19,x]*F[26,x]
F[26,x] = F[27,x]+F[31,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[19,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]*F[12,x]*F[19,x]*F[26,x]
F[31,x] = F[32,x]
F[32,x] = F[15,x]*F[19,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_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{11}\! \left(x \right) = x
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)^{2} F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{19}\! \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_{19}\! \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_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_15(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_12(x)*F_7(x))
Eq(F_11(x), x)
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_11(x)*F_12(x)**2)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_11(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_24(x))
Eq(F_18(x), F_19(x)*F_8(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_11(x)*F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_19(x)*F_20(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_12(x)**2*F_19(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_31(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_19(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x)*F_12(x)*F_19(x)*F_26(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_15(x)*F_19(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"}]], "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_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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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[2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 1], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 1], [0, 4], [2, 4]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 4], [0, 3], [0, 4], [2, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 4], [0, 1], [0, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 4], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 1], [0, 4], [0, 1], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 1], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 4], [0, 1], [0, 4], [0, 1], [0, 4]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 3], [0, 4]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 1], [0, 4], [0, 4]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 3], [0, 4], [0, 4]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_row_and_col_placements_expand_verified
Tree: http://permpal.com/tree/24049/
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[8,x]
F[4,x] = F[5,x]+F[9,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[5,x]^2*F[8,x]
F[8,x] = x
F[9,x] = F[10,x]+F[2,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[8,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = F[10,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[5,x]*F[8,x]
F[17,x] = F[18,x]+F[23,x]
F[18,x] = F[19,x]
F[19,x] = F[5,x]^2*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]^2*F[8,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[24,x]+F[55,x]
F[24,x] = F[25,x]+F[42,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[8,x]
F[27,x] = F[28,x]+F[32,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[6,x]+F[9,x]
F[30,x] = F[24,x]+F[31,x]
F[31,x] = F[20,x]*F[6,x]
F[32,x] = F[30,x]+F[33,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[35,x]
F[35,x] = F[20,x]^2*F[6,x]
F[36,x] = F[37,x]+F[39,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[27,x]*F[8,x]
F[39,x] = F[40,x]
F[40,x] = F[22,x]*F[41,x]*F[8,x]
F[41,x] = F[39,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]*F[8,x]
F[44,x] = F[23,x]+F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]^2*F[5,x]^2
F[48,x] = F[36,x]+F[49,x]
F[49,x] = F[39,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[22,x]*F[52,x]*F[8,x]
F[52,x] = F[50,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[5,x]*F[55,x]*F[8,x]
F[55,x] = F[42,x]+F[53,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_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{10}\! \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_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{5} \left(x \right)^{2} F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{55}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{20}\! \left(x \right) F_{6}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{6}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right) F_{41}\! \left(x \right) F_{8}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20} \left(x \right)^{2} F_{5} \left(x \right)^{2}
F_{48}\! \left(x \right) = F_{36}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{39}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{52}\! \left(x \right) F_{8}\! \left(x \right)
F_{52}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{5}\! \left(x \right) F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{42}\! \left(x \right)+F_{53}\! \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_8(x))
Eq(F_4(x), F_5(x) + F_9(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_5(x)**2*F_8(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_2(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_8(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_10(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_5(x)*F_8(x))
Eq(F_17(x), F_18(x) + F_23(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_5(x)**2)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)**2*F_8(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_24(x) + F_55(x))
Eq(F_24(x), F_25(x) + F_42(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_8(x))
Eq(F_27(x), F_28(x) + F_32(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_6(x) + F_9(x))
Eq(F_30(x), F_24(x) + F_31(x))
Eq(F_31(x), F_20(x)*F_6(x))
Eq(F_32(x), F_30(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_20(x)**2*F_6(x))
Eq(F_36(x), F_37(x) + F_39(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_27(x)*F_8(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_22(x)*F_41(x)*F_8(x))
Eq(F_41(x), F_39(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x)*F_8(x))
Eq(F_44(x), F_23(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x)**2*F_5(x)**2)
Eq(F_48(x), F_36(x) + F_49(x))
Eq(F_49(x), F_39(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_22(x)*F_52(x)*F_8(x))
Eq(F_52(x), F_50(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_5(x)*F_55(x)*F_8(x))
Eq(F_55(x), F_42(x) + F_53(x))
Pack JSON:
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Specification JSON:
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2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [3, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[2, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "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": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24050/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[32,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]+F[17,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]^2*F[16,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[16,x]*F[19,x]*F[22,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[19,x]^2*F[16,x]
F[22,x] = F[23,x]+F[30,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[19,x]*F[8,x]
F[25,x] = F[26,x]
F[26,x] = F[13,x]*F[16,x]*F[19,x]*F[27,x]
F[27,x] = F[11,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[13,x]*F[16,x]*F[19,x]*F[27,x]
F[30,x] = F[31,x]
F[31,x] = F[13,x]*F[16,x]*F[19,x]*F[22,x]
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[19,x]*F[23,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{32}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{17}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{23}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_16(x)*F_7(x))
Eq(F_7(x), F_32(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x) + F_17(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)**2*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_16(x)*F_19(x)*F_22(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_19(x)**2)
Eq(F_22(x), F_23(x) + F_30(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_19(x)*F_8(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_13(x)*F_16(x)*F_19(x)*F_27(x))
Eq(F_27(x), F_11(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_13(x)*F_16(x)*F_19(x)*F_27(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_13(x)*F_16(x)*F_19(x)*F_22(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_19(x)*F_23(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"}]], "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_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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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"comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0], "pos": [[5, 4]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [4, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[3, 0], [4, 0]]}, {"patt": [0, 1], "pos": [[4, 0], [4, 4]]}, {"patt": [0, 1], "pos": [[4, 2], [4, 4]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [5, 0], [5, 1]]}, {"patt": [0, 1, 2], "pos": [[4, 0], [5, 0], [5, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [4, 0], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [4, 2], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [4, 0], [5, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 0], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[4, 4], [4, 4], [4, 4]]}, {"patt": [1, 0, 2], "pos": [[5, 1], [5, 1], [5, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[5, 0], [5, 1], [5, 0], [5, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [5, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [5, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[3, 0], [3, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[5, 1], [5, 0], [5, 1], [5, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 1], [5, 0], [5, 1], [5, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[5, 0], [5, 0], [5, 1], [5, 0], [5, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[3, 0], [3, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[4, 0], [4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 1], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 0], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_and_col_placements_req_corrob_expand_verified
Tree: http://permpal.com/tree/24051/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[19,x]*F[6,x]
F[6,x] = F[34,x]+F[4,x]+F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[6,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[19,x]
F[11,x] = F[12,x]+F[20,x]+F[8,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[19,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]*F[19,x]
F[16,x] = F[14,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[14,x]*F[16,x]*F[19,x]
F[19,x] = x
F[20,x] = F[21,x]
F[21,x] = F[19,x]*F[22,x]*F[28,x]
F[22,x] = F[23,x]+F[8,x]
F[23,x] = F[24,x]
F[24,x] = F[19,x]*F[25,x]
F[25,x] = F[11,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[11,x]*F[16,x]*F[19,x]
F[28,x] = F[1,x]+F[29,x]+F[30,x]
F[29,x] = F[19,x]*F[28,x]
F[30,x] = F[31,x]
F[31,x] = F[19,x]*F[28,x]*F[32,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[19,x]*F[28,x]
F[34,x] = F[35,x]
F[35,x] = F[19,x]*F[36,x]
F[36,x] = F[37,x]+F[51,x]
F[37,x] = F[38,x]+F[44,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[4,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[19,x]*F[37,x]
F[42,x] = F[43,x]
F[43,x] = F[19,x]*F[32,x]*F[37,x]
F[44,x] = F[45,x]
F[45,x] = F[19,x]*F[46,x]
F[46,x] = F[37,x]+F[47,x]+F[49,x]
F[47,x] = F[48,x]
F[48,x] = F[14,x]*F[19,x]*F[46,x]
F[49,x] = F[50,x]
F[50,x] = F[32,x]^2*F[19,x]*F[22,x]
F[51,x] = F[52,x]
F[52,x] = F[19,x]*F[28,x]*F[37,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{19}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{34}\! \left(x \right)+F_{4}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)+F_{8}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \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_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{28}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{8}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right) F_{28}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right) F_{28}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{28}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{51}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right) F_{32}\! \left(x \right) F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{37}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right) F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{32} \left(x \right)^{2} F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{19}\! \left(x \right) F_{28}\! \left(x \right) F_{37}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_19(x)*F_6(x))
Eq(F_6(x), F_34(x) + F_4(x) + F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_6(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_20(x) + F_8(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_19(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x)*F_19(x))
Eq(F_16(x), F_14(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_14(x)*F_16(x)*F_19(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_19(x)*F_22(x)*F_28(x))
Eq(F_22(x), F_23(x) + F_8(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_19(x)*F_25(x))
Eq(F_25(x), F_11(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_11(x)*F_16(x)*F_19(x))
Eq(F_28(x), F_1(x) + F_29(x) + F_30(x))
Eq(F_29(x), F_19(x)*F_28(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_19(x)*F_28(x)*F_32(x))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_19(x)*F_28(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_19(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_51(x))
Eq(F_37(x), F_38(x) + F_44(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_4(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_19(x)*F_37(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_19(x)*F_32(x)*F_37(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_19(x)*F_46(x))
Eq(F_46(x), F_37(x) + F_47(x) + F_49(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_14(x)*F_19(x)*F_46(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_19(x)*F_22(x)*F_32(x)**2)
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_19(x)*F_28(x)*F_37(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 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0, 4, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 2], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 1], [0, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 2], [2, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], 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3], [1, 5], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [1, 5], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 5], [0, 1], [0, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 5], [0, 3], [0, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [1, 5]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 5], [0, 5], [1, 5], [1, 5]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 5], [0, 5], [1, 5], [1, 5]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 5], [0, 1], [0, 5], [1, 5]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 5], [0, 3], [0, 5], [1, 5]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 5], [0, 1], [0, 5]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 3], [0, 5], [0, 3], [0, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 5], [1, 5], [1, 0], [1, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 5], [1, 5], [1, 3], [1, 5]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 5], [1, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 5], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 5], [0, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 3], [0, 5], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 1], [0, 5], [0, 5]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 3], [0, 5], [0, 5]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [1, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 1], [0, 5], [0, 1], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 1], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 3], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [1, 5]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 5], [0, 5], [0, 5], [1, 5], [1, 5]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 5], [0, 5], [0, 5], [1, 5], [1, 5]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 5], [0, 1], [0, 5], [0, 1], [0, 5]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 3], [0, 5]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 1], [0, 5], [0, 5]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 3], [0, 5], [0, 5]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [3, 1, 5, 0, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5], [1, 5]]}], "requirements": [[{"patt": [0], "pos": [[2, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: insertion_point_col_placements_expand_verified
Tree: http://permpal.com/tree/24052/
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[9,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]^2*F[9,x]
F[8,x] = F[1,x]+F[6,x]
F[9,x] = x
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = F[13,x]+F[52,x]
F[13,x] = F[14,x]+F[50,x]
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]^2*F[9,x]
F[17,x] = F[1,x]+F[15,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[9,x]
F[21,x] = F[22,x]+F[26,x]
F[22,x] = F[18,x]+F[23,x]
F[23,x] = F[19,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[17,x]*F[23,x]*F[9,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = F[28,x]
F[28,x] = F[17,x]^2*F[6,x]
F[29,x] = F[30,x]+F[47,x]
F[30,x] = F[10,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[9,x]
F[33,x] = F[29,x]+F[34,x]
F[34,x] = F[35,x]+F[37,x]
F[35,x] = F[36,x]
F[36,x] = F[17,x]^2*F[6,x]^2
F[37,x] = F[38,x]+F[44,x]
F[38,x] = F[39,x]+F[41,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[6,x]*F[9,x]
F[41,x] = F[42,x]
F[42,x] = F[43,x]*F[8,x]*F[9,x]
F[43,x] = F[31,x]+F[41,x]
F[44,x] = F[41,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[17,x]*F[44,x]*F[9,x]
F[47,x] = F[31,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[17,x]*F[47,x]*F[9,x]
F[50,x] = F[30,x]+F[51,x]
F[51,x] = F[15,x]*F[6,x]
F[52,x] = F[50,x]+F[53,x]
F[53,x] = F[38,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[6,x]^2*F[15,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_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{52}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{50}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{17}\! \left(x \right) F_{23}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{47}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{9}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{6} \left(x \right)^{2}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{43}\! \left(x \right) = F_{31}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{17}\! \left(x \right) F_{44}\! \left(x \right) F_{9}\! \left(x \right)
F_{47}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{17}\! \left(x \right) F_{47}\! \left(x \right) F_{9}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{38}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{6} \left(x \right)^{2} F_{15}\! \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_9(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_10(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)**2*F_9(x))
Eq(F_8(x), F_1(x) + F_6(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), F_13(x) + F_52(x))
Eq(F_13(x), F_14(x) + F_50(x))
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)**2*F_9(x))
Eq(F_17(x), F_1(x) + F_15(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_9(x))
Eq(F_21(x), F_22(x) + F_26(x))
Eq(F_22(x), F_18(x) + F_23(x))
Eq(F_23(x), F_19(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_17(x)*F_23(x)*F_9(x))
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_17(x)**2*F_6(x))
Eq(F_29(x), F_30(x) + F_47(x))
Eq(F_30(x), F_10(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_9(x))
Eq(F_33(x), F_29(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_37(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_17(x)**2*F_6(x)**2)
Eq(F_37(x), F_38(x) + F_44(x))
Eq(F_38(x), F_39(x) + F_41(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_6(x)*F_9(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_43(x)*F_8(x)*F_9(x))
Eq(F_43(x), F_31(x) + F_41(x))
Eq(F_44(x), F_41(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_17(x)*F_44(x)*F_9(x))
Eq(F_47(x), F_31(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_17(x)*F_47(x)*F_9(x))
Eq(F_50(x), F_30(x) + F_51(x))
Eq(F_51(x), F_15(x)*F_6(x))
Eq(F_52(x), F_50(x) + F_53(x))
Eq(F_53(x), F_38(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_15(x)*F_6(x)**2)
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}], [{"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"}], "iterative": false, "name": "insertion_point_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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