02341_03241_04231_12340_13240_14230_23140_24130
Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2920, 15448, 82559, 443914, 2396111, 12966510, 70291127, 381520224, 2072657955, 11267580694, 61285333693, 333468586348, 1815051190597, 9881680555786, 53809598032774, 293061993185492, 1596310596093854, 8696077648238156, 47377212774419420, 258136372636759298, 1406556581474889834, 7664594381198088112, 41767792172647461788, 227620434351913890894, 1240497412431664051010, 6760724884054246936608, 36846961140647338908432, 200825842714960516566218, 1094575566922505122752710, 5965942171800263467232064, 32517603625088679803128727, 177240688261895437529661012, 966079871705418589191522955, 5265829034681522024890428242, 28702787530478031008068473027, 156453236511999310754709721998, 852801183088178742689539939881, 4648506760097950581970914631938, 25338521869385150418633106072701, 138118218352355671336379234422080, 752874029566541811522359503702965, 4103884482762888050386760501846490, 22370167201017191669000321313382623, 121939517942331048815806403410976280, 664692420971084122377504561579627771, 3623246433617406026717344061947092682, 19750396173333095436795366419043896017, 107660018862994553107940507743349658196, 586858925704621188356353038264846678601, 3198994768421355626189185307698560472906, 17437886098868842501606105237061937765370, 95054915481592406680201481228475871724018, 518150249827336356202752432984247834965974, 2824471451788644048071348014572021776256572, 15396392534037870819290725128157951618339841, 83926871580480067417711728459273626707509386, 457491826407005856918192864431333846683075907, 2493824354906816995375742009571443797733235930, 13594041122649615324795687190587946711951331157, 74102262918420935759310898448557087709648088864, 403937819783316433528520488879411285935969096945, 2201900562339843960884112192259868979044358942246, 12002756944517504014541034170577465097943510850378, 65428118574221179196847400895548184431246542482942, 356654700140850571614682244825480580308095910444276, 1944158015501481592369898766356949931827336380376680, 10597788506431033996776727324361087874686756593014725, 57769553075992273214443792404280337378937815126153894, 314907374450610473172386408992862065345787103101939801, 1716590527019430195035943865205069339469859767081304582, 9357301940092810496769312692362140498667448616302262412, 51007568495423820668799693044472671675942461132035505084, 278047273466335246797515689410167291491343067509853307360, 1515663168564411597964245921131639663088834177609269315032, 8262030366649334272062250480574343338631783368312927935943, 45037150666063222831696890664263713410370664689986808049448, 245502010477634617032230041911481930613374141298475012400961, 1338256075458776221806736018331746182955326864906620412996642, 7294968418127962553073537982300512300342032849732328642392408, 39765608084254983290071859109825632314963291217641527359949720, 216766346279278304770008945732222347666072759023836206312388864, 1181615291484676135714455584359831275500243471305923402970251872, 6441104750383957172908457365392653307291478200674582066126866478, 35111116050875057080010810189191070581773845789248612387356322782, 191394263994064253954524145896349562986903076805384169777909183576, 1043309620543980375836606591465515738185050460871651773339781168980, 5687187092212845140825690721537860990997328477937162482168349456668, 31001437167865717260884513254344068139071571210064426881744054788702, 168992000377624976007209114186465501460836336122364199229573409280234, 921192668773142196446456983736419223641794213075131092687504206578400, 5021515474852864536857566079115622983230778181495827276315567803149734, 27372794900545654679169512852686934134939640518990580793333317382258978, 149211908844607223409023744567495617337454866588075225970934166216757564, 813369407587598978213115029081491041262973536731153700133472600661155348
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24499/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[32,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[32,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[17,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]
F[13,x,k[0]] = F[10,x,k[0]]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,k[0]]+F[34,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[33,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[29,x,k[0]]
F[20,x,k[0]] = F[10,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[2,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[26,x,k[0]]
F[25,x,k[0]] = F[10,x,k[0]]*F[21,x,k[0]]
F[26,x,k[0]] = F[21,x,k[0]]+F[27,x,k[0]]
F[27,x,k[0]] = F[2,x]*F[28,x,k[0]]
F[28,x,k[0]] = (F[11,x,k[0]]-F[11,x,1])/(-1+k[0])
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[32,x]
F[31,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[32,x] = x
F[33,x,k[0]] = F[0,x]*F[10,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[32,x]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[38,x,k[0]]
F[37,x,k[0]] = F[28,x,k[0]]*F[7,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[32,x]*F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[63,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[32,x]*F[44,x,k[0]]
F[45,x,k[0]] = F[26,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[5,x]
F[48,x,k[0]] = F[2,x]*F[47,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[50,x,k[0]] = F[49,x,k[0]]+F[53,x,k[0]]
F[50,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[52,x,k[0]] = F[16,x,k[0]]*F[51,x,k[0]]
F[52,x,k[0]] = F[22,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]*F[62,x]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = (F[56,x,k[0]]*k[0]-F[56,x,1])/(-1+k[0])
F[51,x,k[0]] = F[56,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[13,x,k[0]]*F[2,x]
F[59,x,k[0]] = F[56,x,k[0]]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]^2*F[32,x]
F[62,x] = F[1,x]+F[60,x]
F[63,x,k[0]] = F[64,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[66,x,k[0]] = F[32,x]*F[65,x,k[0]]
F[66,x,k[0]] = F[17,x,k[0]]
F[67,x,k[0]] = F[46,x,k[0]]+F[68,x,k[0]]
F[69,x,k[0]] = F[32,x]*F[68,x,k[0]]
F[69,x,k[0]] = F[18,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{32}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{31}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x \right) = x
F_{33}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{10}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = -\frac{-F_{51}\! \left(x , y\right) y +F_{51}\! \left(x , 1\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{62}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = -\frac{-y F_{56}\! \left(x , y\right)+F_{56}\! \left(x , 1\right)}{-1+y}
F_{51}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62} \left(x \right)^{2} F_{32}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_32(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_32(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_17(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_16(x, k_0))
Eq(F_13(x, k_0), F_10(x, k_0) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_10(x, k_0)*F_13(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, k_0) + F_34(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_33(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_29(x, k_0))
Eq(F_20(x, k_0), F_10(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_2(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_26(x, k_0))
Eq(F_25(x, k_0), F_10(x, k_0)*F_21(x, k_0))
Eq(F_26(x, k_0), F_21(x, k_0) + F_27(x, k_0))
Eq(F_27(x, k_0), F_2(x)*F_28(x, k_0))
Eq(F_28(x, k_0), -F_11(x, k_0) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_32(x))
Eq(F_31(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_32(x), x)
Eq(F_33(x, k_0), F_0(x)*F_10(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_32(x)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_38(x, k_0))
Eq(F_37(x, k_0), F_28(x, k_0)*F_7(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_32(x)*F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_63(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_32(x)*F_44(x, k_0))
Eq(F_45(x, k_0), F_26(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_5(x))
Eq(F_48(x, k_0), F_2(x)*F_47(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_50(x, k_0), F_49(x, k_0) + F_53(x, k_0))
Eq(F_50(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_16(x, k_0)*F_51(x, k_0))
Eq(F_52(x, k_0), F_22(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0)*F_62(x))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), (-k_0*F_56(x, k_0) + F_56(x, 1))/(1 - k_0))
Eq(F_51(x, k_0), F_56(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_13(x, k_0)*F_2(x))
Eq(F_59(x, k_0), F_56(x, k_0)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_32(x)*F_62(x)**2)
Eq(F_62(x), F_1(x) + F_60(x))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_66(x, k_0), F_32(x)*F_65(x, k_0))
Eq(F_66(x, k_0), F_17(x, k_0))
Eq(F_67(x, k_0), F_46(x, k_0) + F_68(x, k_0))
Eq(F_69(x, k_0), F_32(x)*F_68(x, k_0))
Eq(F_69(x, k_0), F_18(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0], "pos": [[5, 3]]}, {"patt": [0], "pos": [[6, 0]]}, {"patt": [0], "pos": [[6, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 1], "pos": [[5, 1], [5, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [2, 2]]}, {"patt": [1, 0], "pos": [[5, 1], [5, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [4, 2], [4, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [4, 2], [4, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [4, 2], [4, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [4, 2], [4, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [4, 2], [4, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [6, 3], [6, 2]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [6, 3], [6, 3]]}, {"patt": [1, 2, 0], "pos": [[4, 2], [6, 3], [6, 2]]}, {"patt": [1, 2, 0], "pos": [[6, 2], [6, 3], [6, 2]]}, {"patt": [1, 2, 0], "pos": [[6, 3], [6, 3], [6, 2]]}, {"patt": [1, 2, 0], "pos": [[6, 3], [6, 3], [6, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [4, 2], [6, 2], [6, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [6, 2], [6, 2], [6, 2]]}, 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"pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25364/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[32,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[32,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[17,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[16,x,k[0]]
F[13,x,k[0]] = F[10,x,k[0]]+F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,k[0]]+F[34,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[33,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[29,x,k[0]]
F[20,x,k[0]] = F[10,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[2,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[16,x,k[0]]*F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[26,x,k[0]]
F[25,x,k[0]] = F[10,x,k[0]]*F[21,x,k[0]]
F[26,x,k[0]] = F[21,x,k[0]]+F[27,x,k[0]]
F[27,x,k[0]] = F[2,x]*F[28,x,k[0]]
F[28,x,k[0]] = (F[11,x,k[0]]-F[11,x,1])/(-1+k[0])
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]*F[32,x]
F[31,x,k[0]] = 1/(-1+k[0])*(F[8,x,k[0]]*k[0]-F[8,x,1])
F[32,x] = x
F[33,x,k[0]] = F[0,x]*F[10,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[32,x]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[38,x,k[0]]
F[37,x,k[0]] = F[28,x,k[0]]*F[7,x]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[32,x]*F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[63,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[32,x]*F[44,x,k[0]]
F[45,x,k[0]] = F[26,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]*F[5,x]
F[48,x,k[0]] = F[2,x]*F[47,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[50,x,k[0]] = F[49,x,k[0]]+F[53,x,k[0]]
F[50,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[52,x,k[0]] = F[16,x,k[0]]*F[51,x,k[0]]
F[52,x,k[0]] = F[22,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]*F[62,x]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = (F[56,x,k[0]]*k[0]-F[56,x,1])/(-1+k[0])
F[51,x,k[0]] = F[56,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[59,x,k[0]]
F[58,x,k[0]] = F[13,x,k[0]]*F[2,x]
F[59,x,k[0]] = F[56,x,k[0]]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]^2*F[32,x]
F[62,x] = F[1,x]+F[60,x]
F[63,x,k[0]] = F[64,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[66,x,k[0]] = F[32,x]*F[65,x,k[0]]
F[66,x,k[0]] = F[17,x,k[0]]
F[67,x,k[0]] = F[46,x,k[0]]+F[68,x,k[0]]
F[69,x,k[0]] = F[32,x]*F[68,x,k[0]]
F[69,x,k[0]] = F[18,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{32}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{31}\! \left(x , y\right) = -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}
F_{32}\! \left(x \right) = x
F_{33}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{10}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = -\frac{-F_{51}\! \left(x , y\right) y +F_{51}\! \left(x , 1\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{51}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{62}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = -\frac{-y F_{56}\! \left(x , y\right)+F_{56}\! \left(x , 1\right)}{-1+y}
F_{51}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62} \left(x \right)^{2} F_{32}\! \left(x \right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{65}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_32(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_32(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_17(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_16(x, k_0))
Eq(F_13(x, k_0), F_10(x, k_0) + F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_10(x, k_0)*F_13(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, k_0) + F_34(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_33(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_29(x, k_0))
Eq(F_20(x, k_0), F_10(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_2(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_16(x, k_0)*F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_26(x, k_0))
Eq(F_25(x, k_0), F_10(x, k_0)*F_21(x, k_0))
Eq(F_26(x, k_0), F_21(x, k_0) + F_27(x, k_0))
Eq(F_27(x, k_0), F_2(x)*F_28(x, k_0))
Eq(F_28(x, k_0), -F_11(x, k_0) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0)*F_32(x))
Eq(F_31(x, k_0), (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_32(x), x)
Eq(F_33(x, k_0), F_0(x)*F_10(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_32(x)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_38(x, k_0))
Eq(F_37(x, k_0), F_28(x, k_0)*F_7(x))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_32(x)*F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_63(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_32(x)*F_44(x, k_0))
Eq(F_45(x, k_0), F_26(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0)*F_5(x))
Eq(F_48(x, k_0), F_2(x)*F_47(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_50(x, k_0), F_49(x, k_0) + F_53(x, k_0))
Eq(F_50(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_16(x, k_0)*F_51(x, k_0))
Eq(F_52(x, k_0), F_22(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0)*F_62(x))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), (-k_0*F_56(x, k_0) + F_56(x, 1))/(1 - k_0))
Eq(F_51(x, k_0), F_56(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_59(x, k_0))
Eq(F_58(x, k_0), F_13(x, k_0)*F_2(x))
Eq(F_59(x, k_0), F_56(x, k_0)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_32(x)*F_62(x)**2)
Eq(F_62(x), F_1(x) + F_60(x))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_66(x, k_0), F_32(x)*F_65(x, k_0))
Eq(F_66(x, k_0), F_17(x, k_0))
Eq(F_67(x, k_0), F_46(x, k_0) + F_68(x, k_0))
Eq(F_69(x, k_0), F_32(x)*F_68(x, k_0))
Eq(F_69(x, k_0), F_18(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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