02341_02413_02431_04123_04213_04231_20341_20413_20431_23041
Counting sequence:
1, 1, 2, 6, 24, 110, 530, 2607, 12997, 65567, 334424, 1722836, 8954716, 46910874, 247465716, 1313525562, 7010603100, 37602603286, 202587359614, 1095855413831, 5949482476092, 32407760133857, 177067529335585, 970152239342940, 5329120044416953, 29342708464432138, 161918969707778151, 895323346999229535, 4960043906588548260, 27527034801622139682, 153021276218725492479, 851956694984214276297, 4750239106769057081421, 26522119858005055821150, 148272832234405205892143, 829935141499288790265471, 4650794281449416211600681, 26090594643068022425586613, 146517740605854027813232195, 823613006899979853186710912, 4634063203400888237432753019, 26096785236866060468741487837, 147089024682568693952406522630, 829707200647470547296563632393, 4683872351759451423973967868428, 26460993236608387286570496483945, 149594068569090206535838350360665, 846285411483423330975951716592114, 4790727668666079333844725747403748, 27136691239449749694107373554957935, 153805684326927716647535444494095249, 872243792632572746963454761533211175, 4949301315543813365022730870655184532, 28098390055506171194089149319020409774, 159603362118832143912745536899393403219, 907021682392219076372337762494486643049, 5157042846253558122331085767725028816586, 29334861748272461650659213391240386712324, 166940132456819534432897794457292662899807, 950439273481068898281256650035577834313553, 5413382773701993014381767596645800197707295, 30845227226754146796697712554972304622515925, 175823328699752263013158649605716342776899023, 1002602964402806980115452210340314313749430049, 5719266795173693254522030600171882881373022699, 32636664602620576517726363641785544858858082945, 186303319892215169568166707923607595296043830037, 1063850033222098146987405085801059828700628189898, 6076884645761444150952074007758220501995215437837, 34723083987795207033769033044609819689842422145784, 198467058168874520739508955641509267682170979258984, 1134717375244081752776962945368076020310224854595345, 6489519628300372966816685542165811567496842403831501, 37124409522747740829026126670409197328508461187293771, 212434692295658576724046051736983051813771098612224382, 1215925777937058594468142485998187592274722119861403125, 6961477164512717930894649470100574505074369201835652417, 39866264815554250379135792831364519642543639845925826311, 228358248663117403509634541096343266992247833184926020012, 1308374833854160423471228868254312932844565563687908017868, 7498068309627201682020182928754168135905433842899139335341, 42979943568803779450418184827850080052536173830268382873399, 246421798493549772075454717183947049088628989986105218025602, 1413145633421607730018551354161332618394384506593515749874752, 8105634178501179354828922137090678810027214094458936864642519, 46502596346881701368540874022640306600474261905137481408814287, 266842772328972381461732354540941394921291665668321664536778922, 1531509576483119170209189403353096030607613219252705732125404835, 8791603160218622167035295911072541624958810939057244165549601197, 50477593880859361728972873774735623813042236991567184580183925184, 289874229494361361418482516550233410309472308718713527363617929644, 1664942373691813184142196966625642698428661879563645313700220681360, 9564576464963206778222884138316679765443751698925409779368260212801, 54955045725933295788892835851344514519500774153995409615727873908574, 315807983023594260766862860001835910748876796946973438190677008244307, 1815142777851970884568181229531427491795781921170822786618478780723703, 10434439925444121070924043976372823266019538744195660148127397573496202, 59992465190352032669288789607982148209858028106412320945487044731344758, 344978542357241203402475824247498393592034833396283078796864231319338509, 1984055902276419787141788105864792445387986444555670512995356285170357467, 11412501606729562858155747823181585045616153655266719083434869967620623034
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24231/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[88,x]+F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]^2*F[4,x]
F[13,x] = F[0,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[0,x]*F[13,x]*F[4,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[48,x]
F[19,x] = F[10,x]*F[20,x]
F[20,x] = F[0,x]+F[21,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[32,x]
F[25,x] = -F[30,x]+F[26,x]
F[26,x] = -F[32,x]+F[27,x]
F[27,x] = 1/F[4,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[0,x]+F[30,x]
F[30,x] = 1/F[4,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[37,x]*F[4,x]
F[34,x] = F[1,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[34,x]*F[4,x]
F[37,x] = 1/F[4,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = -F[5,x]+F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[4,x]*F[42,x]
F[42,x] = F[6,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[20,x]*F[40,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]*F[80,x]
F[50,x] = F[51,x]+F[62,x]
F[51,x] = F[1,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[1,x]+F[4,x]
F[56,x] = F[35,x]+F[57,x]
F[57,x] = F[58,x]+F[59,x]+F[61,x]
F[58,x] = 0
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[4,x]+F[57,x]
F[61,x] = F[35,x]*F[4,x]
F[62,x] = F[35,x]+F[63,x]
F[63,x] = F[58,x]+F[64,x]+F[66,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[52,x]+F[63,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[56,x]+F[68,x]
F[68,x] = F[69,x]+F[74,x]
F[69,x] = F[58,x]+F[70,x]+F[72,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[35,x]+F[69,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[35,x]+F[69,x]
F[74,x] = F[58,x]+F[75,x]+F[77,x]+F[79,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[57,x]+F[74,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[57,x]+F[74,x]
F[79,x] = F[4,x]*F[69,x]
F[80,x] = 1/F[4,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = -F[85,x]+F[83,x]
F[83,x] = 1/F[4,x]*F[84,x]
F[84,x] = F[21,x]
F[85,x] = F[20,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[0,x]*F[4,x]*F[41,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[186,x]+F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[0,x]*F[8,x]
F[93,x] = F[94,x]
F[94,x] = F[0,x]*F[4,x]*F[95,x]
F[95,x] = 1/F[4,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[177,x]+F[98,x]
F[98,x] = F[13,x]*F[99,x]
F[99,x] = -F[13,x]+F[100,x]
F[100,x] = 1/F[34,x]^2/F[4,x]*F[101,x]
F[101,x] = F[102,x]
F[102,x] = -F[170,x]+F[103,x]
F[103,x] = F[104,x,1]
F[104,x,k[0]] = F[105,x,k[0]]+F[111,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[2,x]*F[34,x]
F[107,x,k[0]] = F[1,x]+F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[107,x,k[0]]*F[110,x,k[0]]
F[110,x,k[0]] = k[0]*x
F[111,x,k[0]] = F[112,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]*F[4,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[115,x,k[0]]
F[114,x,k[0]] = F[104,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[34,x]
F[117,x,k[0]] = F[118,x]+F[168,x,k[0]]
F[118,x] = -F[30,x]+F[119,x]
F[119,x] = F[120,x]+F[122,x]
F[120,x] = F[0,x]+F[121,x]
F[121,x] = F[2,x]*F[34,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[125,x]+F[166,x]
F[125,x] = -F[152,x]+F[126,x]
F[126,x] = -F[163,x]+F[127,x]
F[127,x] = F[128,x]+F[152,x]
F[128,x] = F[129,x]+F[146,x]
F[129,x] = F[130,x]+F[143,x]
F[130,x] = F[131,x]+F[141,x]
F[131,x] = F[132,x]+F[20,x]
F[132,x] = F[133,x]
F[133,x] = F[13,x]*F[134,x]*F[4,x]
F[134,x] = 1/F[34,x]/F[35,x]*F[135,x]
F[135,x] = F[136,x]
F[136,x] = -F[139,x]+F[137,x]
F[137,x] = 1/F[34,x]/F[4,x]*F[138,x]
F[138,x] = F[103,x]
F[139,x] = 1/F[34,x]/F[4,x]*F[140,x]
F[140,x] = F[102,x]
F[141,x] = F[142,x]
F[142,x] = F[127,x]*F[4,x]
F[143,x] = 1/F[4,x]*F[144,x]
F[144,x] = F[145,x]
F[145,x] = -F[21,x]+F[25,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[34,x]*F[4,x]
F[148,x] = 1/F[4,x]*F[149,x]
F[149,x] = F[150,x]
F[150,x] = -F[151,x]+F[37,x]
F[151,x] = F[100,x]*F[13,x]
F[152,x] = F[153,x]
F[153,x] = F[13,x]*F[154,x]*F[4,x]
F[154,x] = F[139,x]+F[155,x]
F[155,x] = 1/F[4,x]*F[156,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[161,x]
F[159,x] = F[160,x]
F[160,x] = F[154,x]*F[4,x]
F[161,x] = F[162,x]
F[162,x] = F[13,x]^2*F[21,x]*F[4,x]
F[163,x] = F[143,x]+F[164,x]
F[164,x] = -F[165,x]+F[146,x]
F[165,x] = F[155,x]
F[166,x] = F[167,x]
F[167,x] = F[134,x]*F[2,x]*F[34,x]
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[108,x,k[0]]*F[13,x]*F[2,x]
F[170,x] = F[171,x]+F[175,x]
F[171,x] = F[172,x]
F[172,x] = F[173,x]*F[34,x]*F[4,x]
F[173,x] = F[174,x]
F[174,x] = -F[34,x]+F[13,x]
F[175,x] = F[176,x]
F[176,x] = F[35,x]^2*F[134,x]*F[34,x]*F[4,x]
F[177,x] = F[178,x]*F[183,x]
F[178,x] = -F[13,x]+F[179,x]
F[179,x] = 1/F[35,x]*F[180,x]
F[180,x] = -F[100,x]+F[181,x]
F[181,x] = 1/F[34,x]^2/F[4,x]*F[182,x]
F[182,x] = F[103,x]
F[183,x] = -F[13,x]+F[184,x]
F[184,x] = 1/F[0,x]/F[21,x]/F[4,x]*F[185,x]
F[185,x] = F[161,x]
F[186,x] = F[187,x]
F[187,x] = F[13,x]*F[188,x]
F[188,x] = -F[20,x]+F[9,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{88}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{6}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right) F_{40}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right) F_{80}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{62}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{56}\! \left(x \right) = F_{35}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = 0
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right)+F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{35}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{52}\! \left(x \right)+F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{56}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{69}\! \left(x \right) = F_{58}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{35}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{35}\! \left(x \right)+F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{58}\! \left(x \right)+F_{75}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{57}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{57}\! \left(x \right)+F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{84}\! \left(x \right) = F_{21}\! \left(x \right)
F_{85}\! \left(x \right) = F_{20}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{186}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{0}\! \left(x \right) F_{8}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{177}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{34} \left(x \right)^{2} F_{4}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{170}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = y x
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{104}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x \right)+F_{168}\! \left(x , y\right)
F_{118}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{122}\! \left(x \right)
F_{120}\! \left(x \right) = F_{0}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{166}\! \left(x \right)
F_{125}\! \left(x \right) = -F_{152}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{152}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{146}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{143}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{141}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{20}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{13}\! \left(x \right) F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = \frac{F_{135}\! \left(x \right)}{F_{34}\! \left(x \right) F_{35}\! \left(x \right)}
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = -F_{139}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{34}\! \left(x \right) F_{4}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{103}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{34}\! \left(x \right) F_{4}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{102}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = \frac{F_{149}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = -F_{151}\! \left(x \right)+F_{37}\! \left(x \right)
F_{151}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{13}\! \left(x \right) F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{139}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = \frac{F_{156}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{161}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{163}\! \left(x \right) = F_{143}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{146}\! \left(x \right)
F_{165}\! \left(x \right) = F_{155}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{134}\! \left(x \right) F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{175}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{13}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{35} \left(x \right)^{2} F_{134}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{183}\! \left(x \right)
F_{178}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = \frac{F_{180}\! \left(x \right)}{F_{35}\! \left(x \right)}
F_{180}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = \frac{F_{182}\! \left(x \right)}{F_{34} \left(x \right)^{2} F_{4}\! \left(x \right)}
F_{182}\! \left(x \right) = F_{103}\! \left(x \right)
F_{183}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = \frac{F_{185}\! \left(x \right)}{F_{0}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)}
F_{185}\! \left(x \right) = F_{161}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{13}\! \left(x \right) F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{9}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_88(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)**2*F_4(x))
Eq(F_13(x), F_0(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_0(x)*F_13(x)*F_4(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_48(x))
Eq(F_19(x), F_10(x)*F_20(x))
Eq(F_20(x), F_0(x) + F_21(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_32(x))
Eq(F_25(x), F_26(x) - F_30(x))
Eq(F_26(x), F_27(x) - F_32(x))
Eq(F_27(x), F_28(x)/F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), -F_0(x) + F_30(x))
Eq(F_30(x), F_31(x)/F_4(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_37(x)*F_4(x))
Eq(F_34(x), F_1(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_34(x)*F_4(x))
Eq(F_37(x), F_38(x)/F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x) - F_5(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_4(x))
Eq(F_42(x), F_6(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_20(x)*F_40(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x)*F_80(x))
Eq(F_50(x), F_51(x) + F_62(x))
Eq(F_51(x), F_1(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_1(x) + F_4(x))
Eq(F_56(x), F_35(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_59(x) + F_61(x))
Eq(F_58(x), 0)
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_4(x) + F_57(x))
Eq(F_61(x), F_35(x)*F_4(x))
Eq(F_62(x), F_35(x) + F_63(x))
Eq(F_63(x), F_58(x) + F_64(x) + F_66(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_52(x) + F_63(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_56(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_74(x))
Eq(F_69(x), F_58(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_35(x) + F_69(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_35(x) + F_69(x))
Eq(F_74(x), F_58(x) + F_75(x) + F_77(x) + F_79(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_57(x) + F_74(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_57(x) + F_74(x))
Eq(F_79(x), F_4(x)*F_69(x))
Eq(F_80(x), F_81(x)/F_4(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x) - F_85(x))
Eq(F_83(x), F_84(x)/F_4(x))
Eq(F_84(x), F_21(x))
Eq(F_85(x), F_20(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_0(x)*F_4(x)*F_41(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_186(x) + F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_0(x)*F_8(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_0(x)*F_4(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_4(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_177(x) + F_98(x))
Eq(F_98(x), F_13(x)*F_99(x))
Eq(F_99(x), F_100(x) - F_13(x))
Eq(F_100(x), F_101(x)/(F_34(x)**2*F_4(x)))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x) - F_170(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_104(x, k_0), F_105(x, k_0) + F_111(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_2(x)*F_34(x))
Eq(F_107(x, k_0), F_1(x) + F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_107(x, k_0)*F_110(x, k_0))
Eq(F_110(x, k_0), k_0*x)
Eq(F_111(x, k_0), F_112(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0)*F_4(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_115(x, k_0))
Eq(F_114(x, k_0), F_104(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0)*F_34(x))
Eq(F_117(x, k_0), F_118(x) + F_168(x, k_0))
Eq(F_118(x), F_119(x) - F_30(x))
Eq(F_119(x), F_120(x) + F_122(x))
Eq(F_120(x), F_0(x) + F_121(x))
Eq(F_121(x), F_2(x)*F_34(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_125(x) + F_166(x))
Eq(F_125(x), F_126(x) - F_152(x))
Eq(F_126(x), F_127(x) - F_163(x))
Eq(F_127(x), F_128(x) + F_152(x))
Eq(F_128(x), F_129(x) + F_146(x))
Eq(F_129(x), F_130(x) + F_143(x))
Eq(F_130(x), F_131(x) + F_141(x))
Eq(F_131(x), F_132(x) + F_20(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_13(x)*F_134(x)*F_4(x))
Eq(F_134(x), F_135(x)/(F_34(x)*F_35(x)))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x) - F_139(x))
Eq(F_137(x), F_138(x)/(F_34(x)*F_4(x)))
Eq(F_138(x), F_103(x))
Eq(F_139(x), F_140(x)/(F_34(x)*F_4(x)))
Eq(F_140(x), F_102(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_127(x)*F_4(x))
Eq(F_143(x), F_144(x)/F_4(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), -F_21(x) + F_25(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_34(x)*F_4(x))
Eq(F_148(x), F_149(x)/F_4(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), -F_151(x) + F_37(x))
Eq(F_151(x), F_100(x)*F_13(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_13(x)*F_154(x)*F_4(x))
Eq(F_154(x), F_139(x) + F_155(x))
Eq(F_155(x), F_156(x)/F_4(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_161(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_154(x)*F_4(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_13(x)**2*F_21(x)*F_4(x))
Eq(F_163(x), F_143(x) + F_164(x))
Eq(F_164(x), F_146(x) - F_165(x))
Eq(F_165(x), F_155(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_134(x)*F_2(x)*F_34(x))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_108(x, k_0)*F_13(x)*F_2(x))
Eq(F_170(x), F_171(x) + F_175(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_173(x)*F_34(x)*F_4(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_13(x) - F_34(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_134(x)*F_34(x)*F_35(x)**2*F_4(x))
Eq(F_177(x), F_178(x)*F_183(x))
Eq(F_178(x), -F_13(x) + F_179(x))
Eq(F_179(x), F_180(x)/F_35(x))
Eq(F_180(x), -F_100(x) + F_181(x))
Eq(F_181(x), F_182(x)/(F_34(x)**2*F_4(x)))
Eq(F_182(x), F_103(x))
Eq(F_183(x), -F_13(x) + F_184(x))
Eq(F_184(x), F_185(x)/(F_0(x)*F_21(x)*F_4(x)))
Eq(F_185(x), F_161(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_13(x)*F_188(x))
Eq(F_188(x), -F_20(x) + F_9(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.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_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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