01342_02341_10342_12340_20341_21340_30241_31240
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3024, 16600, 93008, 528632, 3036016, 17572504, 102318256, 598547640, 3514448784, 20697555288, 122193434256, 722870024568, 4283626417712, 25420652476696, 151040171643632, 898365403478840, 5348177958053200, 31863910803613144, 189971863888481232, 1133286919217296888, 6764252546801191664, 40392674250900726680, 241304556987475797808, 1442078674261088894392, 8620965459242992376080, 51552719499645670469208, 308363556187027745995536, 1844925997351610277865080, 11040514128223244647741872, 66082315332681015545971224, 395602452858134015816904048, 2368664245230016163201287224, 14184453998834111909135410896, 84953401919612475669843221208, 508865463553505098270332359760, 3048419639120795432530261060344, 18263838744751984221148237695600, 109433748233891951807135352386712, 655766290852357203038419393631664, 3929909229677349335413404998102712, 23553142323911958397797050606771856, 141171045908466019691883604775291736, 846195281443214390393745178475284368, 5072495907584836676143846757313307512, 30408645418131385101355569033294974256, 182303492723355215113858607886127061784, 1092984177330474244850809376310892613616, 6553182839997611945350372280107409661240, 39292430290819285187942984218969756913744, 235603896792641746644069869433142840696792, 1412771389199118808824608205966302545134800, 8471808233740453634181739799956122632974328, 50803564462877744243798187420413990218961392, 304666851830522603623852289945652898768639384, 1827125404106187418035816394588331595629349936, 10957787518356363319009818885466190907713155000, 65718562305105932645369180322825950790201379856, 394151548346267801568845770011979849599700695128, 2364001857242062353838178497044297008731942861840, 14178856783954684034569254135758517129834057920632, 85043850633735642443151606677631618893361776814256, 510096591765192347793484568597225600571930119881752, 3059632562116368706716604461020498509571804507044464, 18352407564040475912906823623647881111086915398551096, 110083780391274563376581340049873379220439265792451024, 660328087321539134260921645196844856377175732773860568, 3960974093435121164326047252963805973149229441701010768, 23760178697855615355864045370589433286625605870322681080, 142528779633083221046919586896356297085073741887412494704, 854988566971519191593963917794935079161142083928533239448, 5128881393158126721665195991626252332221304651025552345776, 30767298187348313536912183601243677376962558664287067111608, 184569605758701753519752665609402847304260420197559135117712, 1107222508145840127243819847625598462938048095345415949858136, 6642220909326942954586042383586679320820573035421290767472784, 39846962158559701663172848892630157707110245472892474900663672, 239045419902874890968339318370587686683834765146280496807693360, 1434064783090131127747700904982965619996062821823843650940632344, 8603201306347830684277691957517485245410459945055045462625791216, 51612419190060572162710999121785450492248208835185467642356645688, 309635693212729945019710652548791500309304339557489660160848534352, 1857592097896450889533454144717424557032837434379133365921767152088, 11144282105031524926952848647532006962419563654180591316911601868240, 66858422176483784611114768334722176920167916867559057510090560760312, 401108918109734422215396370061714106610716252739036482009807355214064, 2406415260265587071910807396569854189159776102871956042054240785303448, 14437127288849578616927488240499986270398055885671481768057999043072304, 86614949956928542305349145083707964597519928355209313523747328841589176, 519644937969720693789264729678148512784351680031994282646887295985655568, 3117613156870598473446554221570652262800110930416843865366027456851542616, 18704209162970334779934534260061686559529733518529960322809373469278543120, 112216830434241572631500237399408730259886268911255906348948021517720844920, 673252685609707100454254897800555228839407623744519745517649516080253417392, 4039239182814913386304312081265634400956794326536522830221403536049067689496
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24713/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[39,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[36,x]+F[38,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[34,x,k[0]]+F[35,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[15,x,k[0]]+F[17,x,k[0]]+F[6,x]
F[15,x,k[0]] = F[14,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[11,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[17,x,k[0]]+F[19,x]+F[22,x,k[0]]+F[25,x,k[0]]
F[19,x] = F[11,x]*F[20,x]
F[20,x] = F[21,x,1]
F[21,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[22,x,k[0]] = F[11,x]*F[23,x,k[0]]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[24,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[25,x,k[0]] = F[11,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0],1]
F[27,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[28,x,k[0],k[1]] = F[1,x]+F[15,x,k[0]]+F[29,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[9,x,k[1]]
F[29,x,k[0],k[1]] = F[11,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[31,x,k[0],k[1]]*k[0]-F[31,x,1,k[1]])
F[31,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[32,x,k[0],k[1]] = F[16,x,k[1]]*F[28,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[11,x]*F[27,x,k[0],k[1]]
F[34,x,k[0]] = F[16,x,k[0]]*F[8,x,k[0]]
F[35,x,k[0]] = F[11,x]*F[21,x,k[0]]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[14,x,1]
F[38,x] = F[11,x]*F[7,x]
F[39,x] = F[11,x]*F[5,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \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_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{21}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y , 1\right)
F_{27}\! \left(x , y , z\right) = -\frac{-F_{28}\! \left(x , y , z\right) z +F_{28}\! \left(x , y , 1\right)}{-1+z}
F_{28}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{29}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)+F_{9}\! \left(x , z\right)
F_{29}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{30}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = -\frac{-F_{31}\! \left(x , y , z\right) y +F_{31}\! \left(x , 1, z\right)}{-1+y}
F_{31}\! \left(x , y , z\right) = \frac{y F_{14}\! \left(x , y\right)-z F_{14}\! \left(x , z\right)}{-z +y}
F_{32}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{28}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{27}\! \left(x , y , z\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_39(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_36(x) + F_38(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_34(x, k_0) + F_35(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_12(x, k_0) + F_15(x, k_0) + F_17(x, k_0) + F_6(x))
Eq(F_15(x, k_0), F_14(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_11(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_15(x, k_0) + F_17(x, k_0) + F_19(x) + F_22(x, k_0) + F_25(x, k_0))
Eq(F_19(x), F_11(x)*F_20(x))
Eq(F_20(x), F_21(x, 1))
Eq(F_21(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_11(x)*F_23(x, k_0))
Eq(F_23(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_24(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_11(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0, 1))
Eq(F_27(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_15(x, k_0) + F_29(x, k_0, k_1) + F_32(x, k_0, k_1) + F_33(x, k_0, k_1) + F_9(x, k_1))
Eq(F_29(x, k_0, k_1), F_11(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (k_0*F_31(x, k_0, k_1) - F_31(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1), F_16(x, k_1)*F_28(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_11(x)*F_27(x, k_0, k_1))
Eq(F_34(x, k_0), F_16(x, k_0)*F_8(x, k_0))
Eq(F_35(x, k_0), F_11(x)*F_21(x, k_0))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_14(x, 1))
Eq(F_38(x), F_11(x)*F_7(x))
Eq(F_39(x), F_11(x)*F_5(x))
Pack JSON:
{"name": "row_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 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[0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [5, 0], [5, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 0], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [2, 1, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 3, "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25130/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[39,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[36,x]+F[38,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[34,x,k[0]]+F[35,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[15,x,k[0]]+F[17,x,k[0]]+F[6,x]
F[15,x,k[0]] = F[14,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[11,x]*F[18,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[17,x,k[0]]+F[19,x]+F[22,x,k[0]]+F[25,x,k[0]]
F[19,x] = F[11,x]*F[20,x]
F[20,x] = F[21,x,1]
F[21,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[22,x,k[0]] = F[11,x]*F[23,x,k[0]]
F[23,x,k[0]] = 1/(-1+k[0])*(F[24,x,k[0]]*k[0]-F[24,x,1])
F[24,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[25,x,k[0]] = F[11,x]*F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0],1]
F[27,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[28,x,k[0],k[1]] = F[1,x]+F[15,x,k[0]]+F[29,x,k[0],k[1]]+F[32,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[9,x,k[1]]
F[29,x,k[0],k[1]] = F[11,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = 1/(-1+k[0])*(F[31,x,k[0],k[1]]*k[0]-F[31,x,1,k[1]])
F[31,x,k[0],k[1]] = (F[14,x,k[0]]*k[0]-F[14,x,k[1]]*k[1])/(-k[1]+k[0])
F[32,x,k[0],k[1]] = F[16,x,k[1]]*F[28,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[11,x]*F[27,x,k[0],k[1]]
F[34,x,k[0]] = F[16,x,k[0]]*F[8,x,k[0]]
F[35,x,k[0]] = F[11,x]*F[21,x,k[0]]
F[36,x] = F[11,x]*F[37,x]
F[37,x] = F[14,x,1]
F[38,x] = F[11,x]*F[7,x]
F[39,x] = F[11,x]*F[5,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \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_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{21}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}
F_{24}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y , 1\right)
F_{27}\! \left(x , y , z\right) = -\frac{-F_{28}\! \left(x , y , z\right) z +F_{28}\! \left(x , y , 1\right)}{-1+z}
F_{28}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{29}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)+F_{9}\! \left(x , z\right)
F_{29}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{30}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = -\frac{-F_{31}\! \left(x , y , z\right) y +F_{31}\! \left(x , 1, z\right)}{-1+y}
F_{31}\! \left(x , y , z\right) = \frac{y F_{14}\! \left(x , y\right)-z F_{14}\! \left(x , z\right)}{-z +y}
F_{32}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{28}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{11}\! \left(x \right) F_{27}\! \left(x , y , z\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_39(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_36(x) + F_38(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_1(x) + F_12(x, k_0) + F_34(x, k_0) + F_35(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_12(x, k_0) + F_15(x, k_0) + F_17(x, k_0) + F_6(x))
Eq(F_15(x, k_0), F_14(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_11(x)*F_18(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_15(x, k_0) + F_17(x, k_0) + F_19(x) + F_22(x, k_0) + F_25(x, k_0))
Eq(F_19(x), F_11(x)*F_20(x))
Eq(F_20(x), F_21(x, 1))
Eq(F_21(x, k_0), (-k_0*F_8(x, k_0) + F_8(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_11(x)*F_23(x, k_0))
Eq(F_23(x, k_0), (k_0*F_24(x, k_0) - F_24(x, 1))/(k_0 - 1))
Eq(F_24(x, k_0), (-k_0*F_14(x, k_0) + F_14(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_11(x)*F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0, 1))
Eq(F_27(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_15(x, k_0) + F_29(x, k_0, k_1) + F_32(x, k_0, k_1) + F_33(x, k_0, k_1) + F_9(x, k_1))
Eq(F_29(x, k_0, k_1), F_11(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (k_0*F_31(x, k_0, k_1) - F_31(x, 1, k_1))/(k_0 - 1))
Eq(F_31(x, k_0, k_1), (-k_0*F_14(x, k_0) + k_1*F_14(x, k_1))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1), F_16(x, k_1)*F_28(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_11(x)*F_27(x, k_0, k_1))
Eq(F_34(x, k_0), F_16(x, k_0)*F_8(x, k_0))
Eq(F_35(x, k_0), F_11(x)*F_21(x, k_0))
Eq(F_36(x), F_11(x)*F_37(x))
Eq(F_37(x), F_14(x, 1))
Eq(F_38(x), F_11(x)*F_7(x))
Eq(F_39(x), F_11(x)*F_5(x))
Pack JSON:
{"name": "row_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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