0132_0321
Counting sequence:
1, 1, 2, 6, 22, 89, 382, 1711, 7922, 37663, 182936, 904302, 4535994, 23034564, 118209806, 612165222, 3195359360, 16795435994, 88825567814, 472356139660, 2524292893556, 13549955878141, 73026827854516, 395017112175542, 2143881709415478, 11671226062503926, 63717160152793490, 348759626655606356, 1913558711839152932, 10522719736133406089, 57985227476697094630, 320146747899076836656, 1770794859325334219916, 9811265439769351164312, 54447019760249260909322, 302603678792692983237298, 1684176194146380834580354, 9385976275521450217366597, 52374293281464619479531148, 292600054428865115793578589, 1636519187135314291073036018, 9162906997847474763761289371, 51355596606207607707148637826, 288113170772598589967614256426, 1617853891416162073024084753804, 9092801895774294684758000892611, 51147104196895215527068007771718, 287934064106301967793088606114655, 1622178166445760683476587981463230, 9145834815291166263679770140482869, 51600525038786015478060497999157408, 291325386886214044405190949970050988, 1645827104598242495466937544236218698, 9303806448920677115697958627934938792, 52625622821923480624839387891905552908, 297840732022832021616958769147812889858, 1686599134279771885243290349356961312590, 9555904101402869415445808497727329298334, 54169581028496423205240956462671024049526, 307223936406104002273937333692225209945688, 1743263366366260574302267822557097080178618, 9896285661784661249436948909472637671354186, 56205128523727937178763412937106007853598558, 319350603609332891235690827352203458208015992, 1815271097399589152186938978497800167054550696, 10322654051210302366378003492454710448354319992, 58723485820870747348625369795020815239856786812, 334193161812660841056752497187446936406693052090, 1902582563247313621725821342599365900806078108924, 10835397718580454815393272447546897687827786853784, 61730099562564088470185223481992667608653372023112, 351799695218724145419672218000002533341714583092076, 2005561925388124463965946477261149100776384240768110, 11437070106308282797977555637952069279209176631279636, 65242065683145293624405539995572310466310849891385724, 372281211751982930337818514458406126831709560611328916, 2124914521856936177737449561041962873677573717383412296, 12132081458292166976256035884300782940543069691981101729, 69286622470664894817899124455458779874694631002156648814, 395804317271656735062237853051782824021706685176734495932, 2261651520266427307910803582275109684146414496941315364994, 12926529934102368842037806810963637112864460372703617613982, 73900354042790072551712899046094026410588934837432591530078, 422587524272694651571010364993875988294286955869760688669754, 2417073226294900983251774248783779281203497631217495539650386, 13828128805369086346964143196017492737188480926860721571921746, 79128890413403593817235701907999613543135358070939416653713002, 452900136426648901891301714180965400053096229401598520003216236, 2592765802819520757881403650516113044063472277994728176954782364, 14846203738894100171844812947623776766310417896188201652600345170, 85026975281116686754123566270357831170690893581631158520396301668, 487063070167676031928535390332258631099763533896701588086286382664, 2790608234483417511133393314761923936193484080454063935970380313912, 15991744494828356325822695659286672541502002772602423588039518046548, 91658824037357252930141535083088790600311722256163676797522931360596, 525451230687501775973178554143434816253541576170135782005269596602670, 3012787652877623261766988779549855606003592917182083667552100660108748, 17277501783317170740399842355329749085340405888219659944735641101308408, 99098726710176004801873739602679986832768497264873393744371796839895656, 568497221915734615803597484841175604236621172776120583778888679480538570, 3261821956307616298668185797071131143097134213343258792191267916935211572
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/52/
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,1]
F[3,x,k[0]] = F[17,x]*F[4,x,k[0]]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[6,x,k[0]]
F[5,x,k[0]] = 1/(-1+k[0])*(F[3,x,k[0]]*k[0]-F[3,x,1])
F[6,x,k[0]] = F[7,x,k[0],1]
F[7,x,k[0],k[1]] = F[8,x,1,k[0],k[1]]
F[8,x,k[0],k[1],k[2]] = F[18,x,k[2]]*F[9,x,k[0],k[1],k[2]]
F[9,x,k[0],k[1],k[2]] = F[1,x]+F[10,x,k[0],k[1],k[2]]+F[30,x,k[0],k[1],k[2]]+F[8,x,k[0],k[1],k[2]]
F[10,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1],k[2]]*F[17,x]
F[11,x,k[0],k[1],k[2]] = F[12,x,k[0]*k[1],k[1]*k[2]]
F[13,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[1,x]+F[15,x,k[0],k[1],k[2]]+F[19,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]+F[28,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[17,x]
F[16,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[14,x,k[0],k[1],k[2]]*k[0]-F[14,x,1,k[1],k[2]])
F[17,x] = F[18,x,1]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1]*k[2]]*k[1]-F[20,x,k[0],k[2]])/(k[1]-1)
F[20,x,k[0],k[1]] = F[21,x,k[0],1,k[1]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1],1]*k[0]*k[1]-F[22,x,k[0],k[1],k[2]/k[0]/k[1]]*k[2])/(k[0]*k[1]-k[2])
F[22,x,k[0],k[1],k[2]] = F[23,x,k[0],k[1],k[1]*k[2]]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[0]*k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = F[18,x,k[1]]*F[25,x,k[0],k[2]]
F[25,x,k[0],k[1]] = F[9,x,1,k[0],k[1]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1]*k[2],k[2]]
F[21,x,k[0],k[1],k[2]] = F[27,x,k[0],k[0]*k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = (-F[29,x,k[1],k[2]]*k[1]*k[2]+F[29,x,k[0]/k[2],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[29,x,k[0],k[1]] = F[8,x,k[0],k[1],1]
F[30,x,k[0],k[1],k[2]] = (F[31,x,k[0]*k[1],1]*k[0]-F[31,x,k[0]*k[1],k[2]/k[0]]*k[2])/(-k[2]+k[0])
F[31,x,k[0],k[1]] = F[32,x,k[0],k[0]*k[1]]
F[32,x,k[0],k[1]] = F[18,x,k[0]]*F[33,x,k[1]]
F[33,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[39,x,k[0]]
F[34,x,k[0]] = F[35,x,1,k[0]]
F[35,x,k[0],k[1]] = F[17,x]*F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[1,x]+F[20,x,k[0],k[1]]+F[37,x,k[0],k[1]]+F[38,x,k[0],k[1]]
F[37,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,k[0],k[1]]*k[0]-F[35,x,1,k[1]])
F[8,x,k[0],k[1],k[2]] = F[38,x,k[0]*k[1],k[1]*k[2]]
F[39,x,k[0]] = F[31,x,k[0],1]
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 , 1\right)
F_{3}\! \left(x , y_{0}\right) = F_{17}\! \left(x \right) F_{4}\! \left(x , y_{0}\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{6}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = \frac{F_{3}\! \left(x , y_{0}\right) y_{0}-F_{3}\! \left(x , 1\right)}{-1+y_{0}}
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}, 1\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , 1, y_{0}, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{2}\right) F_{9}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{9}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{17}\! \left(x \right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{17}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}-F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{17}\! \left(x \right) = F_{18}\! \left(x , 1\right)
F_{18}\! \left(x , y_{0}\right) = y_{0} x
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}-F_{20}\! \left(x , y_{0}, y_{2}\right)}{y_{1}-1}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, 1, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}, 1\right) y_{0} y_{1}-F_{22}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{0} y_{1}}\right) y_{2}}{y_{0} y_{1}-y_{2}}
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{1}\right) F_{25}\! \left(x , y_{0}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{9}\! \left(x , 1, y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-F_{29}\! \left(x , y_{1}, y_{2}\right) y_{1} y_{2}+F_{29}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right) y_{0}}{-y_{1} y_{2}+y_{0}}
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0}, y_{1}, 1\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{31}\! \left(x , y_{0} y_{1}, 1\right) y_{0}-F_{31}\! \left(x , y_{0} y_{1}, \frac{y_{2}}{y_{0}}\right) y_{2}}{-y_{2}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{1}\right)
F_{33}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y_{0}\right)+F_{39}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , 1, y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x \right) F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{35}\! \left(x , y_{0}, y_{1}\right) y_{0}-F_{35}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{38}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{39}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}, 1\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, 1))
Eq(F_3(x, k_0), F_17(x)*F_4(x, k_0))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_6(x, k_0))
Eq(F_5(x, k_0), (k_0*F_3(x, k_0) - F_3(x, 1))/(k_0 - 1))
Eq(F_6(x, k_0), F_7(x, k_0, 1))
Eq(F_7(x, k_0, k_1), F_8(x, 1, k_0, k_1))
Eq(F_8(x, k_0, k_1, k_2), F_18(x, k_2)*F_9(x, k_0, k_1, k_2))
Eq(F_9(x, k_0, k_1, k_2), F_1(x) + F_10(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, k_2) + F_8(x, k_0, k_1, k_2))
Eq(F_10(x, k_0, k_1, k_2), F_11(x, k_0, k_1, k_2)*F_17(x))
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_0*k_1, k_1*k_2))
Eq(F_13(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_1(x) + F_15(x, k_0, k_1, k_2) + F_19(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2) + F_28(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_17(x))
Eq(F_16(x, k_0, k_1, k_2), (k_0*F_14(x, k_0, k_1, k_2) - F_14(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_17(x), F_18(x, 1))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0, k_1, k_2), (-k_1*k_2*F_20(x, k_0, k_1*k_2) + k_2*F_20(x, k_0, k_2))/(-k_1*k_2 + k_2))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, 1, k_1))
Eq(F_21(x, k_0, k_1, k_2), (-k_0*k_1*F_22(x, k_0, k_1, 1) + k_2*F_22(x, k_0, k_1, k_2/(k_0*k_1)))/(-k_0*k_1 + k_2))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_0, k_1, k_1*k_2))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_0*k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_18(x, k_1)*F_25(x, k_0, k_2))
Eq(F_25(x, k_0, k_1), F_9(x, 1, k_0, k_1))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1*k_2, k_2))
Eq(F_21(x, k_0, k_1, k_2), F_27(x, k_0, k_0*k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), (-k_0*F_29(x, k_0/k_2, k_2) + k_1*k_2*F_29(x, k_1, k_2))/(-k_0 + k_1*k_2))
Eq(F_29(x, k_0, k_1), F_8(x, k_0, k_1, 1))
Eq(F_30(x, k_0, k_1, k_2), (-k_0*F_31(x, k_0*k_1, 1) + k_2*F_31(x, k_0*k_1, k_2/k_0))/(-k_0 + k_2))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_0*k_1))
Eq(F_32(x, k_0, k_1), F_18(x, k_0)*F_33(x, k_1))
Eq(F_33(x, k_0), F_1(x) + F_34(x, k_0) + F_39(x, k_0))
Eq(F_34(x, k_0), F_35(x, 1, k_0))
Eq(F_35(x, k_0, k_1), F_17(x)*F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_20(x, k_0, k_1) + F_37(x, k_0, k_1) + F_38(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), (k_0*F_35(x, k_0, k_1) - F_35(x, 1, k_1))/(k_0 - 1))
Eq(F_8(x, k_0, k_1, k_2), F_38(x, k_0*k_1, k_1*k_2))
Eq(F_39(x, k_0), F_31(x, k_0, 1))
Pack JSON:
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Specification JSON:
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"pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], 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"tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], 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"workable": false}}]}
Specification 2
Strategy pack name: row_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/53/
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,1]
F[3,x,k[0]] = F[19,x]*F[4,x,k[0]]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[6,x,k[0]]
F[5,x,k[0]] = 1/(-1+k[0])*(F[3,x,k[0]]*k[0]-F[3,x,1])
F[6,x,k[0]] = F[7,x,k[0],1]
F[7,x,k[0],k[1]] = F[8,x,k[0],1,k[1]]
F[8,x,k[0],k[1],k[2]] = F[9,x,k[0],k[0]*k[1],k[2]]
F[9,x,k[0],k[1],k[2]] = F[10,x,k[0],k[2]]*F[39,x,k[1]]
F[10,x,k[0],k[1]] = F[11,x,1,k[0],k[1]]
F[11,x,k[0],k[1],k[2]] = F[1,x]+F[12,x,k[0],k[1],k[2]]+F[30,x,k[0],k[1],k[2]]+F[40,x,k[0],k[1],k[2]]
F[12,x,k[0],k[1],k[2]] = F[13,x,k[0]*k[1],k[1]*k[2]]
F[14,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[19,x]
F[16,x,k[0],k[1],k[2]] = F[1,x]+F[17,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1],k[2]]+F[24,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]*F[19,x]
F[18,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[16,x,k[0],k[1],k[2]]*k[0]-F[16,x,1,k[1],k[2]])
F[19,x] = x
F[20,x,k[0],k[1],k[2]] = (F[21,x,k[0],k[1]*k[2]]*k[1]-F[21,x,k[0],k[2]])/(k[1]-1)
F[21,x,k[0],k[1]] = F[22,x,k[0],1,k[1]]
F[22,x,k[0],k[1],k[2]] = (F[23,x,k[0],k[1],1]*k[0]*k[1]-F[23,x,k[0],k[1],k[2]/k[0]/k[1]]*k[2])/(k[0]*k[1]-k[2])
F[23,x,k[0],k[1],k[2]] = F[8,x,k[0],k[1],k[1]*k[2]]
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1]*k[2],k[2]]
F[22,x,k[0],k[1],k[2]] = F[25,x,k[0],k[0]*k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = (-F[27,x,k[1],k[2]]*k[1]*k[2]+F[27,x,k[0]/k[2],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[27,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[29,x,k[0],k[1]] = F[28,x,k[0],k[0]*k[1]]
F[29,x,k[0],k[1]] = F[23,x,k[0],k[1],1]
F[30,x,k[0],k[1],k[2]] = (F[31,x,k[0]*k[1],1]*k[0]-F[31,x,k[0]*k[1],k[2]/k[0]]*k[2])/(-k[2]+k[0])
F[31,x,k[0],k[1]] = F[32,x,k[0],k[0]*k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[1]]*F[39,x,k[0]]
F[33,x,k[0]] = F[1,x]+F[34,x,k[0]]+F[38,x,k[0]]
F[34,x,k[0]] = F[35,x,1,k[0]]
F[35,x,k[0],k[1]] = F[19,x]*F[36,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[37,x,k[0],k[1]] = 1/(-1+k[0])*(F[35,x,k[0],k[1]]*k[0]-F[35,x,1,k[1]])
F[38,x,k[0]] = F[31,x,k[0],1]
F[39,x,k[0]] = k[0]*x
F[40,x,k[0],k[1],k[2]] = F[28,x,k[0]*k[1],k[1]*k[2]]
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 , 1\right)
F_{3}\! \left(x , y_{0}\right) = F_{19}\! \left(x \right) F_{4}\! \left(x , y_{0}\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{6}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{3}\! \left(x , y_{0}\right)+F_{3}\! \left(x , 1\right)}{-1+y_{0}}
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}, 1\right)
F_{7}\! \left(x , y_{0}, y_{1}\right) = F_{8}\! \left(x , y_{0}, 1, y_{1}\right)
F_{8}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{9}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{9}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x , y_{0}, y_{2}\right) F_{39}\! \left(x , y_{1}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , 1, y_{0}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{19}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{19}\! \left(x \right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{19}\! \left(x \right) = x
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{21}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{1}+F_{21}\! \left(x , y_{0}, y_{2}\right)}{y_{1}-1}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, 1, y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} y_{1} F_{23}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{23}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{0} y_{1}}\right)}{y_{0} y_{1}-y_{2}}
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{8}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} y_{2} F_{27}\! \left(x , y_{1}, y_{2}\right)-y_{0} F_{27}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, y_{1}, 1\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{31}\! \left(x , y_{0} y_{1}, 1\right)-y_{2} F_{31}\! \left(x , y_{0} y_{1}, \frac{y_{2}}{y_{0}}\right)}{-y_{2}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{1}\right) F_{39}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y_{0}\right)+F_{38}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , 1, y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x \right) F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{35}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{38}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}, 1\right)
F_{39}\! \left(x , y_{0}\right) = y_{0} x
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\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, 1))
Eq(F_3(x, k_0), F_19(x)*F_4(x, k_0))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_6(x, k_0))
Eq(F_5(x, k_0), (k_0*F_3(x, k_0) - F_3(x, 1))/(k_0 - 1))
Eq(F_6(x, k_0), F_7(x, k_0, 1))
Eq(F_7(x, k_0, k_1), F_8(x, k_0, 1, k_1))
Eq(F_8(x, k_0, k_1, k_2), F_9(x, k_0, k_0*k_1, k_2))
Eq(F_9(x, k_0, k_1, k_2), F_10(x, k_0, k_2)*F_39(x, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, 1, k_0, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_1(x) + F_12(x, k_0, k_1, k_2) + F_30(x, k_0, k_1, k_2) + F_40(x, k_0, k_1, k_2))
Eq(F_12(x, k_0, k_1, k_2), F_13(x, k_0*k_1, k_1*k_2))
Eq(F_14(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_19(x))
Eq(F_16(x, k_0, k_1, k_2), F_1(x) + F_17(x, k_0, k_1, k_2) + F_20(x, k_0, k_1, k_2) + F_24(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2)*F_19(x))
Eq(F_18(x, k_0, k_1, k_2), (k_0*F_16(x, k_0, k_1, k_2) - F_16(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_19(x), x)
Eq(F_20(x, k_0, k_1, k_2), (-k_1*k_2*F_21(x, k_0, k_1*k_2) + k_2*F_21(x, k_0, k_2))/(-k_1*k_2 + k_2))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, 1, k_1))
Eq(F_22(x, k_0, k_1, k_2), (-k_0*k_1*F_23(x, k_0, k_1, 1) + k_2*F_23(x, k_0, k_1, k_2/(k_0*k_1)))/(-k_0*k_1 + k_2))
Eq(F_23(x, k_0, k_1, k_2), F_8(x, k_0, k_1, k_1*k_2))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1*k_2, k_2))
Eq(F_22(x, k_0, k_1, k_2), F_25(x, k_0, k_0*k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), (-k_0*F_27(x, k_0/k_2, k_2) + k_1*k_2*F_27(x, k_1, k_2))/(-k_0 + k_1*k_2))
Eq(F_27(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_29(x, k_0, k_1), F_28(x, k_0, k_0*k_1))
Eq(F_29(x, k_0, k_1), F_23(x, k_0, k_1, 1))
Eq(F_30(x, k_0, k_1, k_2), (-k_0*F_31(x, k_0*k_1, 1) + k_2*F_31(x, k_0*k_1, k_2/k_0))/(-k_0 + k_2))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_0*k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_1)*F_39(x, k_0))
Eq(F_33(x, k_0), F_1(x) + F_34(x, k_0) + F_38(x, k_0))
Eq(F_34(x, k_0), F_35(x, 1, k_0))
Eq(F_35(x, k_0, k_1), F_19(x)*F_36(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_28(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), (k_0*F_35(x, k_0, k_1) - F_35(x, 1, k_1))/(k_0 - 1))
Eq(F_38(x, k_0), F_31(x, k_0, 1))
Eq(F_39(x, k_0), k_0*x)
Eq(F_40(x, k_0, k_1, k_2), F_28(x, k_0*k_1, k_1*k_2))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[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"}}, {"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"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 1]]}]}], "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, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 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], "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, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 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{"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [4, 1]]}], "requirements": 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[{"patt": [0], "pos": [[4, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[3, 1], [4, 1]]}, {"patt": [1, 0], "pos": [[4, 1], [4, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}}}, "rule_class": "ReverseRule"}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion
Tree: http://permpal.com/tree/54/
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[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]
F[7,x,k[0]] = F[12,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0],1]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0],k[1],k[2]]*F[22,x,k[2]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0]*k[1],k[1]*k[2]]
F[17,x,k[0],k[1]] = F[16,x,k[0],k[0]*k[1]]
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]+F[29,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[0]*k[1]]+F[23,x,k[0],k[1]]
F[19,x,k[0]] = F[1,x]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[19,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1]] = F[20,x,k[0]]+F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[8,x]
F[25,x,k[0],k[1]] = F[22,x,k[0]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[20,x,k[0]*k[1]]+F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[25,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[22,x,k[1]]*F[23,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[30,x,k[0],k[1]]+F[48,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[8,x]
F[30,x,k[0],k[1]] = F[31,x,1,k[0],k[1]]
F[31,x,k[0],k[1],k[2]] = F[11,x]*F[32,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[33,x,k[0]*k[1],k[1]*k[2]]
F[34,x,k[0],k[1]] = F[33,x,k[0],k[0]*k[1]]
F[34,x,k[0],k[1]] = F[35,x,1,k[0],k[1]]
F[35,x,k[0],k[1],k[2]] = F[36,x,k[0],k[1],k[1]*k[2]]
F[36,x,k[0],k[1],k[2]] = F[1,x]+F[37,x,k[0],k[1],k[2]]+F[39,x,k[0],k[1],k[2]]+F[43,x,k[0],k[1],k[2]]+F[45,x,k[0],k[1],k[2]]
F[37,x,k[0],k[1],k[2]] = F[11,x]*F[38,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[36,x,k[0],k[1],k[2]]*k[0]-F[36,x,1,k[1],k[2]])
F[39,x,k[0],k[1],k[2]] = F[22,x,k[0]]*F[40,x,k[0],k[1],k[2]]
F[40,x,k[0],k[1],k[2]] = (F[41,x,k[0],1,k[2]]*k[0]-F[41,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[42,x,k[0],k[1],k[2]] = F[41,x,k[0],k[1]*k[2],k[2]]
F[42,x,k[0],k[1],k[2]] = (F[17,x,k[0],k[1]*k[2]]*k[0]*k[1]-F[17,x,k[0],k[2]/k[0]])/(k[0]*k[1]-1)
F[43,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[44,x,k[0],k[1],k[2]]
F[41,x,k[0],k[1],k[2]] = F[44,x,k[0],k[0]*k[1],k[2]]
F[45,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[46,x,k[0],k[1],k[2]]
F[47,x,k[0],k[1],k[2]] = F[46,x,k[0],k[1],k[1]*k[2]]
F[47,x,k[0],k[1],k[2]] = (-F[15,x,1,k[1],k[2]]*k[1]+F[15,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[48,x,k[0],k[1]] = F[22,x,k[0]]*F[49,x,k[0],k[1]]
F[49,x,k[0],k[1]] = (F[50,x,k[0]*k[1]]*k[1]-F[50,x,k[0]])/(k[1]-1)
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[11,x]*F[19,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,1,k[0]]
F[53,x,k[0],k[1]] = F[1,x]+F[54,x,k[0],k[1]]+F[56,x,k[0],k[1]]+F[58,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[11,x]*F[55,x,k[0],k[1]]
F[55,x,k[0],k[1]] = 1/(-1+k[0])*(F[53,x,k[0],k[1]]*k[0]-F[53,x,1,k[1]])
F[56,x,k[0],k[1]] = F[22,x,k[0]]*F[57,x,k[0],k[1]]
F[57,x,k[0],k[1]] = (F[17,x,k[0],1]*k[0]-F[17,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[58,x,k[0],k[1]] = F[14,x,k[0],1,k[1]]
F[59,x,k[0],k[1]] = F[22,x,k[1]]*F[29,x,k[0],k[1]]
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_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}, 1\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{22}\! \left(x , y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{19}\! \left(x , y_{0} y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x \right)
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0} y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{25}\! \left(x , y_{0}, y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x \right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , 1, y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{33}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , 1, y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x \right) F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{41}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{41}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{41}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{17}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{0} y_{1}-F_{17}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)}{y_{0} y_{1}-1}
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{44}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{46}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{15}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{15}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}, y_{1}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{50}\! \left(x , y_{0} y_{1}\right)+F_{50}\! \left(x , y_{0}\right)}{y_{1}-1}
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{19}\! \left(x , y_{0}\right) F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{53}\! \left(x , 1, y_{0}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{54}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x \right) F_{55}\! \left(x , y_{0}, y_{1}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{53}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{17}\! \left(x , y_{0}, 1\right)-y_{1} F_{17}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, 1, y_{1}\right)
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{29}\! \left(x , y_{0}, y_{1}\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_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0))
Eq(F_7(x, k_0), F_12(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0, 1))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0, k_1, k_2)*F_22(x, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0*k_1, k_1*k_2))
Eq(F_17(x, k_0, k_1), F_16(x, k_0, k_0*k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1) + F_29(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0*k_1) + F_23(x, k_0, k_1))
Eq(F_19(x, k_0), F_1(x) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_19(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1), F_20(x, k_0) + F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1) + F_28(x, k_0, k_1) + F_8(x))
Eq(F_25(x, k_0, k_1), F_22(x, k_0)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_20(x, k_0*k_1) + F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_25(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_22(x, k_1)*F_23(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_1) + F_48(x, k_0, k_1) + F_59(x, k_0, k_1) + F_8(x))
Eq(F_30(x, k_0, k_1), F_31(x, 1, k_0, k_1))
Eq(F_31(x, k_0, k_1, k_2), F_11(x)*F_32(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_33(x, k_0*k_1, k_1*k_2))
Eq(F_34(x, k_0, k_1), F_33(x, k_0, k_0*k_1))
Eq(F_34(x, k_0, k_1), F_35(x, 1, k_0, k_1))
Eq(F_35(x, k_0, k_1, k_2), F_36(x, k_0, k_1, k_1*k_2))
Eq(F_36(x, k_0, k_1, k_2), F_1(x) + F_37(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, k_2) + F_43(x, k_0, k_1, k_2) + F_45(x, k_0, k_1, k_2))
Eq(F_37(x, k_0, k_1, k_2), F_11(x)*F_38(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1, k_2), (k_0*F_36(x, k_0, k_1, k_2) - F_36(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_39(x, k_0, k_1, k_2), F_22(x, k_0)*F_40(x, k_0, k_1, k_2))
Eq(F_40(x, k_0, k_1, k_2), (-k_0*F_41(x, k_0, 1, k_2) + k_1*F_41(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_42(x, k_0, k_1, k_2), F_41(x, k_0, k_1*k_2, k_2))
Eq(F_42(x, k_0, k_1, k_2), (-k_0*k_1*k_2*F_17(x, k_0, k_1*k_2) + k_2*F_17(x, k_0, k_2/k_0))/(-k_0*k_1*k_2 + k_2))
Eq(F_43(x, k_0, k_1, k_2), F_22(x, k_1)*F_44(x, k_0, k_1, k_2))
Eq(F_41(x, k_0, k_1, k_2), F_44(x, k_0, k_0*k_1, k_2))
Eq(F_45(x, k_0, k_1, k_2), F_22(x, k_2)*F_46(x, k_0, k_1, k_2))
Eq(F_47(x, k_0, k_1, k_2), F_46(x, k_0, k_1, k_1*k_2))
Eq(F_47(x, k_0, k_1, k_2), (-k_0*F_15(x, k_0/k_1, k_1, k_2) + k_1*F_15(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_48(x, k_0, k_1), F_22(x, k_0)*F_49(x, k_0, k_1))
Eq(F_49(x, k_0, k_1), (k_0*k_1*F_50(x, k_0*k_1) - k_0*F_50(x, k_0))/(k_0*k_1 - k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_11(x)*F_19(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, 1, k_0))
Eq(F_53(x, k_0, k_1), F_1(x) + F_54(x, k_0, k_1) + F_56(x, k_0, k_1) + F_58(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_11(x)*F_55(x, k_0, k_1))
Eq(F_55(x, k_0, k_1), (k_0*F_53(x, k_0, k_1) - F_53(x, 1, k_1))/(k_0 - 1))
Eq(F_56(x, k_0, k_1), F_22(x, k_0)*F_57(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), (-k_0*F_17(x, k_0, 1) + k_1*F_17(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_58(x, k_0, k_1), F_14(x, k_0, 1, k_1))
Eq(F_59(x, k_0, k_1), F_22(x, k_1)*F_29(x, k_0, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 4
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/55/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[9,x,k[0]] = F[10,x,k[0],1]
F[10,x,k[0],k[1]] = F[11,x,k[0],k[1],1]
F[11,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[13,x,k[2],k[0],k[1]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1],k[2]] = F[1,x]+F[11,x,k[1],k[2],k[0]]+F[14,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0],k[1],k[2]]*F[3,x]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0]*k[1],k[1]*k[2]]
F[17,x,k[0],k[1]] = F[16,x,k[0],k[0]*k[1]]
F[17,x,k[0],k[1]] = F[18,x,1,k[0],k[1]]
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[1]*k[2]]
F[19,x,k[0],k[1],k[2]] = F[1,x]+F[20,x,k[0],k[1],k[2]]+F[22,x,k[0],k[1],k[2]]+F[27,x,k[1],k[0],k[2]]+F[29,x,k[2],k[0],k[1]]
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[3,x]
F[21,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[19,x,k[0],k[1],k[2]]*k[0]-F[19,x,1,k[1],k[2]])
F[22,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[23,x,k[0],k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = (F[24,x,k[0],1,k[2]]*k[0]-F[24,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[24,x,k[0],k[1]*k[2],k[2]]
F[25,x,k[0],k[1],k[2]] = (F[26,x,k[0],k[1]*k[2]]*k[0]*k[1]-F[26,x,k[0],k[2]/k[0]])/(k[0]*k[1]-1)
F[26,x,k[0],k[1]] = F[13,x,1,k[0],k[1]]
F[27,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[28,x,k[1],k[0],k[2]]
F[24,x,k[0],k[1],k[2]] = F[28,x,k[0],k[0]*k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[30,x,k[1],k[2],k[0]]
F[31,x,k[0],k[1],k[2]] = F[30,x,k[0],k[1],k[1]*k[2]]
F[31,x,k[0],k[1],k[2]] = (-F[13,x,1,k[1],k[2]]*k[1]+F[13,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[32,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[34,x,k[0]*k[1],k[1]*k[2]]
F[35,x,k[0],k[1]] = F[34,x,k[0],k[0]*k[1]]
F[35,x,k[0],k[1]] = F[36,x,k[0],k[1]]+F[44,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[0]*k[1]]+F[40,x,k[0],k[1]]
F[37,x,k[0]] = F[1,x]+F[38,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[12,x,k[0]]*F[37,x,k[0]]
F[40,x,k[0],k[1]] = F[38,x,k[0]]+F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,k[0],k[1]]
F[42,x,k[0],k[1]] = F[12,x,k[0]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[38,x,k[0]*k[1]]+F[41,x,k[0],k[1]]
F[44,x,k[0],k[1]] = (F[45,x,k[0]*k[1]]*k[1]-F[45,x,k[0]])/(k[1]-1)
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[3,x]*F[37,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,1,k[0]]
F[48,x,k[0],k[1]] = F[1,x]+F[49,x,k[0],k[1]]+F[51,x,k[0],k[1]]+F[53,x,k[1],k[0]]
F[49,x,k[0],k[1]] = F[3,x]*F[50,x,k[0],k[1]]
F[50,x,k[0],k[1]] = 1/(-1+k[0])*(F[48,x,k[0],k[1]]*k[0]-F[48,x,1,k[1]])
F[51,x,k[0],k[1]] = F[12,x,k[0]]*F[52,x,k[0],k[1]]
F[52,x,k[0],k[1]] = (F[26,x,k[0],1]*k[0]-F[26,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[53,x,k[0],k[1]] = F[11,x,1,k[0],k[1]]
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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{8}\! \left(x , 1, y_{0}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{5}\! \left(x , y_{0}\right)-y_{1} F_{5}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}, 1\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{1}, 1\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{13}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}\right) = y_{0} x
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{1}, y_{2}, y_{0}\right)+F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , 1, y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{29}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{24}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{24}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{26}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{0} y_{1}-F_{26}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)}{y_{0} y_{1}-1}
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , 1, y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} F_{13}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{13}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{37}\! \left(x , y_{0} y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y_{0}\right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , y_{0}\right)
F_{39}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{37}\! \left(x , y_{0}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0} y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{45}\! \left(x , y_{0} y_{1}\right)+F_{45}\! \left(x , y_{0}\right)}{y_{1}-1}
F_{45}\! \left(x , y_{0}\right) = F_{46}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{37}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , 1, y_{0}\right)
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{1}, y_{0}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{48}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}\right) F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{26}\! \left(x , y_{0}, 1\right) y_{0}-F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , 1, y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_9(x, k_0), F_10(x, k_0, 1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, k_1, 1))
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_1)*F_13(x, k_2, k_0, k_1))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1, k_2), F_1(x) + F_11(x, k_1, k_2, k_0) + F_14(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0, k_1, k_2)*F_3(x))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0*k_1, k_1*k_2))
Eq(F_17(x, k_0, k_1), F_16(x, k_0, k_0*k_1))
Eq(F_17(x, k_0, k_1), F_18(x, 1, k_0, k_1))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_1*k_2))
Eq(F_19(x, k_0, k_1, k_2), F_1(x) + F_20(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, k_2) + F_27(x, k_1, k_0, k_2) + F_29(x, k_2, k_0, k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_3(x))
Eq(F_21(x, k_0, k_1, k_2), (k_0*F_19(x, k_0, k_1, k_2) - F_19(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_22(x, k_0, k_1, k_2), F_12(x, k_0)*F_23(x, k_0, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*F_24(x, k_0, 1, k_2) + k_1*F_24(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_24(x, k_0, k_1*k_2, k_2))
Eq(F_25(x, k_0, k_1, k_2), (-k_0*k_1*k_2*F_26(x, k_0, k_1*k_2) + k_2*F_26(x, k_0, k_2/k_0))/(-k_0*k_1*k_2 + k_2))
Eq(F_26(x, k_0, k_1), F_13(x, 1, k_0, k_1))
Eq(F_27(x, k_0, k_1, k_2), F_12(x, k_0)*F_28(x, k_1, k_0, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_28(x, k_0, k_0*k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_12(x, k_0)*F_30(x, k_1, k_2, k_0))
Eq(F_31(x, k_0, k_1, k_2), F_30(x, k_0, k_1, k_1*k_2))
Eq(F_31(x, k_0, k_1, k_2), (-k_0*F_13(x, k_0/k_1, k_1, k_2) + k_1*F_13(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1, k_2), F_12(x, k_1)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_34(x, k_0*k_1, k_1*k_2))
Eq(F_35(x, k_0, k_1), F_34(x, k_0, k_0*k_1))
Eq(F_35(x, k_0, k_1), F_36(x, k_0, k_1) + F_44(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_0*k_1) + F_40(x, k_0, k_1))
Eq(F_37(x, k_0), F_1(x) + F_38(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_12(x, k_0)*F_37(x, k_0))
Eq(F_40(x, k_0, k_1), F_38(x, k_0) + F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0, k_1))
Eq(F_42(x, k_0, k_1), F_12(x, k_0)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_38(x, k_0*k_1) + F_41(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), (k_0*k_1*F_45(x, k_0*k_1) - k_0*F_45(x, k_0))/(k_0*k_1 - k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_3(x)*F_37(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, 1, k_0))
Eq(F_48(x, k_0, k_1), F_1(x) + F_49(x, k_0, k_1) + F_51(x, k_0, k_1) + F_53(x, k_1, k_0))
Eq(F_49(x, k_0, k_1), F_3(x)*F_50(x, k_0, k_1))
Eq(F_50(x, k_0, k_1), (k_0*F_48(x, k_0, k_1) - F_48(x, 1, k_1))/(k_0 - 1))
Eq(F_51(x, k_0, k_1), F_12(x, k_0)*F_52(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), (-k_0*F_26(x, k_0, 1) + k_1*F_26(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_53(x, k_0, k_1), F_11(x, 1, k_0, k_1))
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": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 5
Strategy pack name: col_placements_tracked_fusion_expand_verified
Tree: http://permpal.com/tree/56/
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[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[9,x,k[0]] = F[10,x,k[0],1]
F[10,x,k[0],k[1]] = F[11,x,k[0],1,k[1]]
F[11,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[13,x,k[2],k[0],k[1]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0],k[1],k[2]] = F[1,x]+F[11,x,k[1],k[2],k[0]]+F[14,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0],k[1],k[2]]*F[3,x]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0]*k[1],k[1]*k[2]]
F[17,x,k[0],k[1]] = F[16,x,k[0]*k[1],k[1]]
F[17,x,k[0],k[1]] = F[18,x,1,k[0],k[1]]
F[18,x,k[0],k[1],k[2]] = F[1,x]+F[19,x,k[0],k[1],k[2]]+F[21,x,k[0],k[1],k[2]]+F[27,x,k[1],k[2],k[0]]+F[30,x,k[2],k[0],k[1]]
F[19,x,k[0],k[1],k[2]] = F[20,x,k[0],k[1],k[2]]*F[3,x]
F[20,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[18,x,k[0],k[1],k[2]]*k[0]-F[18,x,1,k[1],k[2]])
F[21,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[22,x,k[0],k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = (-F[23,x,k[0],k[1]/k[0],k[2]]*k[1]*k[2]+F[23,x,k[0],1/k[2],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[0]*k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1]*k[2],k[2]]
F[26,x,k[0],k[1],k[2]] = F[25,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = (F[13,x,k[0],k[1],1]*k[1]-F[13,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0]*k[1],k[2],k[1]]
F[29,x,k[0],k[1],k[2]] = F[28,x,k[0],k[0]*k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[26,x,k[1],k[0],k[2]]
F[30,x,k[0],k[1],k[2]] = F[12,x,k[0]]*F[31,x,k[1],k[2],k[0]]
F[31,x,k[0],k[1],k[2]] = (-F[32,x,k[1],k[2]]*k[1]*k[2]+F[32,x,k[0]/k[2],k[2]]*k[0])/(-k[1]*k[2]+k[0])
F[32,x,k[0],k[1]] = F[13,x,k[0],k[1],1]
F[33,x,k[0],k[1],k[2]] = F[12,x,k[1]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (F[35,x,k[0]*k[1]]*k[0]-F[35,x,k[1]*k[2]]*k[2])/(k[0]-k[2])
F[35,x,k[0]] = F[1,x]+F[36,x,k[0]]+F[43,x,k[0]]
F[36,x,k[0]] = F[3,x]*F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,1,k[0]]
F[38,x,k[0],k[1]] = F[1,x]+F[39,x,k[0],k[1]]+F[41,x,k[0],k[1]]+F[42,x,k[1],k[0]]
F[39,x,k[0],k[1]] = F[3,x]*F[40,x,k[0],k[1]]
F[40,x,k[0],k[1]] = 1/(-1+k[0])*(F[38,x,k[0],k[1]]*k[0]-F[38,x,1,k[1]])
F[41,x,k[0],k[1]] = F[29,x,k[0],1,k[1]]
F[11,x,k[0],k[1],k[2]] = F[42,x,k[0]*k[1],k[0]*k[2]]
F[43,x,k[0]] = F[12,x,k[0]]*F[35,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = F_{8}\! \left(x , 1, y_{0}\right)
F_{8}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{5}\! \left(x , y_{0}\right)-y_{1} F_{5}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}, 1\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, 1, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{13}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}\right) = y_{0} x
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{1}, y_{2}, y_{0}\right)+F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{16}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , 1, y_{0}, y_{1}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{2}, y_{0}\right)+F_{30}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-y_{0} F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-y_{1} y_{2} F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)+y_{0} F_{23}\! \left(x , y_{0}, \frac{1}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{13}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{13}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{1} y_{2} F_{32}\! \left(x , y_{1}, y_{2}\right)-y_{0} F_{32}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}, 1\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{35}\! \left(x , y_{0} y_{1}\right) y_{0}-y_{2} F_{35}\! \left(x , y_{1} y_{2}\right)}{y_{0}-y_{2}}
F_{35}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{37}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , 1, y_{0}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{1}, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{40}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}, 1, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0} y_{1}, y_{0} y_{2}\right)
F_{43}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_9(x, k_0), F_10(x, k_0, 1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0, 1, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_12(x, k_1)*F_13(x, k_2, k_0, k_1))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0, k_1, k_2), F_1(x) + F_11(x, k_1, k_2, k_0) + F_14(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0, k_1, k_2)*F_3(x))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0*k_1, k_1*k_2))
Eq(F_17(x, k_0, k_1), F_16(x, k_0*k_1, k_1))
Eq(F_17(x, k_0, k_1), F_18(x, 1, k_0, k_1))
Eq(F_18(x, k_0, k_1, k_2), F_1(x) + F_19(x, k_0, k_1, k_2) + F_21(x, k_0, k_1, k_2) + F_27(x, k_1, k_2, k_0) + F_30(x, k_2, k_0, k_1))
Eq(F_19(x, k_0, k_1, k_2), F_20(x, k_0, k_1, k_2)*F_3(x))
Eq(F_20(x, k_0, k_1, k_2), (k_0*F_18(x, k_0, k_1, k_2) - F_18(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_21(x, k_0, k_1, k_2), F_12(x, k_0)*F_22(x, k_0, k_1, k_2))
Eq(F_22(x, k_0, k_1, k_2), (-k_0*F_23(x, k_0, 1/k_2, k_2) + k_1*k_2*F_23(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1*k_2))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_0*k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1*k_2, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_25(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), (-k_1*F_13(x, k_0, k_1, 1) + k_2*F_13(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0*k_1, k_2, k_1))
Eq(F_29(x, k_0, k_1, k_2), F_28(x, k_0, k_0*k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_12(x, k_0)*F_26(x, k_1, k_0, k_2))
Eq(F_30(x, k_0, k_1, k_2), F_12(x, k_0)*F_31(x, k_1, k_2, k_0))
Eq(F_31(x, k_0, k_1, k_2), (-k_0*F_32(x, k_0/k_2, k_2) + k_1*k_2*F_32(x, k_1, k_2))/(-k_0 + k_1*k_2))
Eq(F_32(x, k_0, k_1), F_13(x, k_0, k_1, 1))
Eq(F_33(x, k_0, k_1, k_2), F_12(x, k_1)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_0*k_1*F_35(x, k_0*k_1) + k_1*k_2*F_35(x, k_1*k_2))/(-k_0*k_1 + k_1*k_2))
Eq(F_35(x, k_0), F_1(x) + F_36(x, k_0) + F_43(x, k_0))
Eq(F_36(x, k_0), F_3(x)*F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, 1, k_0))
Eq(F_38(x, k_0, k_1), F_1(x) + F_39(x, k_0, k_1) + F_41(x, k_0, k_1) + F_42(x, k_1, k_0))
Eq(F_39(x, k_0, k_1), F_3(x)*F_40(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), (k_0*F_38(x, k_0, k_1) - F_38(x, 1, k_1))/(k_0 - 1))
Eq(F_41(x, k_0, k_1), F_29(x, k_0, 1, k_1))
Eq(F_11(x, k_0, k_1, k_2), F_42(x, k_0*k_1, k_0*k_2))
Eq(F_43(x, k_0), F_12(x, k_0)*F_35(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion_expand_verified", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "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"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 3], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 3], [1, 3], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 3], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 3], [1, 1], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}]}], "class_module": 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