02314_02341_02431_03214_03241_30214_30241
Counting sequence:
1, 1, 2, 6, 24, 113, 581, 3140, 17501, 99591, 575344, 3362532, 19835154, 117905606, 705420571, 4244074958, 25658374379, 155788750261, 949506585826, 5806878680779, 35622536908044, 219139063338236, 1351513061977690, 8354737809775790, 51757799199644352, 321275183041895871, 1997897439814942793, 12445348564266913116, 77647599374076776414, 485166157326275374468, 3035661551383821015768, 19018636678898380012556, 119298453407598925602560, 749184654862349418382670, 4709919121068895101286826, 29640313119106735679726851, 186712429569572588580827129, 1177234539709386072394379399, 7429027733166983200788954448, 46920387088227520923128720256, 296575027817305570119687774514, 1876009151384720075491770205077, 11875388066974487481318049986508, 75224493224519114068809095817965, 476822094078880906523507791559230, 3024314756798860412452910077016162, 19193747193682003310353684158467071, 121883261191925677096350528466255756, 774408073576638575554321446372152666, 4922976689683346041186938150961641541, 31311864339590544173617374550953961709, 199253041023555727470260046777545006497, 1268551158360313332821900940939983015132, 8079985008454586553125856138954785312807, 51487951211446585071694345609354187118171, 328236197618889640495888426116898663878074, 2093373909717380709912159924272790110463491, 13356128909569731792144541590607231120796772, 85247597401062574803086943874009819695363004, 544309626628955721249597936824344431109974572, 3476698566668491671758686917421293884857557425, 22214692058418724278891856666283479762218526554, 141991092984321431054837540587901896106484852969, 907872747058954192587853955456592015289771207862, 5806676862663196709571434132744592536031401308587, 37150533912616996428401577256754660653691735330303, 237756983674138084551950778698710800707249985930326, 1522048864325690195367580601165044425526696730309149, 9746471708214380492787478547411171375626166288949948, 62428996466678684690213392256419629490605069433243714, 399983519380671467190274334422419758924183668414545596, 2563371262646001698502796022942450428043426916948208431, 16432043513783960463949427573559914699200717163444823919, 105360881016687321201090297527817036712248469686106063732, 675728408128715291098409589826915673547695826891226710134, 4334781890349113035630687673468628904876521989237200673626, 27813909482724508375719438188970878555252688162604495281128, 178506509921802606512864441636741058567019616051496771348716, 1145884724955513515441531016096809673190837924110476750139695, 7357331967987297349419542345852976017206504138374360656425079, 47248726761674213030965620883841747399307508238080687428409711, 303492572895293771466520733224144359432353494492728053189368547, 1949809422793346229092900860860552770885024951679474988761520083, 12529115534199978986248994394328569728635111509297631351935627283, 80525030025739421904632287645407340369740095506381259730486349535, 517632761289222061969725819137171422219336940965349433487709887648, 3328060420720310355415925660744723201883781751540701465280043484821, 21401169409681997496897349152364551690663570982032721910215512092372, 137644539958466900992366315072982863948592639910518717930693251582659, 885429594567242822339806705894152447851901019133467979805715073178500, 5696670138172073107777802359872185234592516627305950898292086579256502, 36657140816434171163929951736809981471104551314550956361293102222392257, 235920190183860150983964838273089342754672301975945614087989082187704295, 1518585379410333759503715606810510695878189997573121995303390132827832499, 9776412596885792359097569238517036193027514651533168032228581044686444093, 62948399883895588656168956399951851211625678984833153188856130062914987587, 405371709483642051074996330093062321239786825386949182958932015379854877866, 2610865429131775442782061272072453362907924306512330047853375937204303673635, 16818088285924036372381679691018708428723516973311320866051166924875165473826, 108349939193793036403918041475609786687793661284846186884159566943567127761627, 698135092528300915238199853509932734175854561416951943426095298558436286885071
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24926/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[173,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[7,x]
F[21,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[23,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[145,x,k[0]]+F[26,x]+F[27,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]+F[30,x]
F[30,x] = F[31,x]+F[48,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[7,x]
F[34,x] = F[31,x]+F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[26,x]+F[37,x]+F[40,x]
F[37,x] = F[38,x]*F[7,x]
F[38,x] = F[39,x]
F[39,x] = F[32,x]+F[36,x]
F[40,x] = F[41,x]*F[7,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[32,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[47,x]
F[47,x] = F[32,x]+F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[7,x]
F[50,x] = F[143,x]+F[4,x]+F[51,x]
F[51,x] = F[52,x]*F[7,x]
F[52,x] = 1/F[7,x]*F[53,x]
F[53,x] = -F[54,x]-F[71,x]+F[8,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[31,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]*F[63,x]
F[58,x,k[0]] = F[1,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[1,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[18,x,k[0]]*F[61,x,k[0]]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[31,x]*F[65,x]
F[65,x] = F[1,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[65,x]*F[7,x]
F[68,x] = F[69,x]
F[69,x] = F[7,x]*F[70,x]
F[70,x] = F[35,x]+F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[7,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[1,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[75,x]^2*F[7,x]
F[78,x] = F[26,x]+F[79,x]+F[97,x]+F[99,x]
F[79,x] = F[80,x]
F[80,x] = F[7,x]*F[81,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[73,x]+F[84,x,k[0]]
F[84,x,k[0]] = F[8,x]*F[85,x,k[0]]
F[85,x,k[0]] = -k[0]*(F[16,x,1]-F[16,x,k[0]])/(-1+k[0])
F[86,x] = F[134,x]+F[26,x]+F[87,x]+F[88,x]+F[90,x]
F[87,x] = F[7,x]*F[73,x]
F[88,x] = F[89,x]
F[89,x] = F[7,x]*F[86,x]
F[90,x] = F[91,x]
F[91,x] = F[75,x]^2*F[7,x]*F[92,x]
F[92,x] = -F[128,x]+F[93,x]
F[93,x] = F[26,x]+F[94,x]+F[97,x]+F[99,x]
F[94,x] = F[7,x]*F[8,x]*F[95,x]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = (F[15,x,k[0]]*k[0]-F[15,x,1])/(-1+k[0])
F[97,x] = F[98,x]
F[98,x] = F[7,x]*F[75,x]*F[93,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[7,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[7,x]*F[95,x]
F[103,x] = F[104,x,1]
F[105,x,k[0]] = (F[104,x,k[0]]*k[0]-F[104,x,1])/(-1+k[0])
F[106,x,k[0]] = F[105,x,k[0]]*F[7,x]
F[107,x,k[0]] = F[106,x,k[0]]+F[110,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[7,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[22,x,k[0]] = F[109,x,k[0]]+F[29,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[111,x,k[0]]*F[7,x]
F[112,x,k[0]] = F[19,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x]*F[7,x]*F[96,x,k[0]]
F[115,x] = 1/F[117,x]/F[125,x]/F[7,x]*F[116,x]
F[116,x] = F[78,x]
F[117,x] = F[1,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[7,x]
F[120,x] = F[117,x]+F[121,x]
F[121,x] = F[122,x]+F[66,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[7,x]
F[124,x] = F[118,x]+F[122,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[65,x]*F[75,x]
F[127,x] = F[85,x,1]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[7,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[75,x]*F[93,x]
F[132,x] = F[133,x]
F[133,x] = F[75,x]*F[93,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[7,x]*F[75,x]
F[136,x] = -F[137,x]+F[101,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[7,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[101,x]*F[75,x]
F[141,x] = F[142,x]
F[142,x] = F[101,x]*F[75,x]
F[143,x] = F[144,x]
F[144,x] = F[7,x]*F[73,x]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[7,x]
F[147,x,k[0]] = F[148,x,k[0]]
F[149,x,k[0]] = F[148,x,k[0]]+F[50,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[154,x,k[0]]+F[171,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[1,x]+F[151,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[7,x]
F[155,x,k[0]] = F[156,x,k[0]]+F[52,x]
F[157,x,k[0]] = F[156,x,k[0]]+F[170,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[167,x]
F[158,x,k[0]] = (F[159,x,k[0]]*k[0]-F[159,x,1])/(-1+k[0])
F[160,x,k[0]] = F[159,x,k[0]]+F[162,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]*F[7,x]
F[10,x,k[0]] = F[13,x,k[0]]+F[161,x,k[0]]+F[31,x]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[7,x]
F[164,x,k[0]] = (F[165,x,k[0]]*k[0]-F[165,x,1])/(-1+k[0])
F[166,x,k[0]] = F[165,x,k[0]]*F[7,x]
F[22,x,k[0]] = F[166,x,k[0]]+F[24,x,k[0]]+F[34,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[7,x]
F[169,x] = F[164,x,1]
F[170,x] = F[160,x,1]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[7,x]*F[83,x,k[0]]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[7,x]
F[175,x] = -F[193,x]+F[176,x]
F[176,x] = 1/F[75,x]*F[177,x]
F[177,x] = -F[187,x]+F[178,x]
F[178,x] = 1/F[7,x]*F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[181,x]+F[188,x]+F[190,x]+F[26,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[7,x]
F[183,x] = F[184,x]+F[187,x]
F[184,x] = F[185,x]*F[75,x]
F[185,x] = F[180,x]+F[186,x]
F[186,x] = F[8,x]+F[92,x]
F[187,x] = F[132,x]
F[188,x] = F[189,x]
F[189,x] = F[127,x]*F[7,x]*F[8,x]
F[190,x] = F[191,x]
F[191,x] = F[192,x]*F[7,x]
F[192,x] = F[156,x,1]
F[193,x] = F[93,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_{7}\! \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_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{173}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{143}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)-F_{71}\! \left(x \right)+F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{31}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right) F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{7}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{35}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{78}\! \left(x \right) = F_{26}\! \left(x \right)+F_{79}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{7}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{73}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{y \left(F_{16}\! \left(x , 1\right)-F_{16}\! \left(x , y\right)\right)}{-1+y}
F_{86}\! \left(x \right) = F_{134}\! \left(x \right)+F_{26}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{94}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{7}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{7}\! \left(x \right) F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{105}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x \right) F_{7}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{115}\! \left(x \right) = \frac{F_{116}\! \left(x \right)}{F_{117}\! \left(x \right) F_{125}\! \left(x \right) F_{7}\! \left(x \right)}
F_{116}\! \left(x \right) = F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{7}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{66}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{7}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{65}\! \left(x \right) F_{75}\! \left(x \right)
F_{127}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{7}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{136}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{101}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{7}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{170}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{167}\! \left(x \right)
F_{158}\! \left(x , y\right) = -\frac{-F_{159}\! \left(x , y\right) y +F_{159}\! \left(x , 1\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{164}\! \left(x , y\right) = -\frac{-y F_{165}\! \left(x , y\right)+F_{165}\! \left(x , 1\right)}{-1+y}
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{7}\! \left(x \right)
F_{169}\! \left(x \right) = F_{164}\! \left(x , 1\right)
F_{170}\! \left(x \right) = F_{160}\! \left(x , 1\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{7}\! \left(x \right)
F_{175}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{75}\! \left(x \right)}
F_{177}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = \frac{F_{179}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{26}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{7}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{75}\! \left(x \right)
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{8}\! \left(x \right)+F_{92}\! \left(x \right)
F_{187}\! \left(x \right) = F_{132}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{127}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{7}\! \left(x \right)
F_{192}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{93}\! \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_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_173(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)**2*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_7(x))
Eq(F_21(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_145(x, k_0) + F_26(x) + F_27(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0) + F_30(x))
Eq(F_30(x), F_31(x) + F_48(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_7(x))
Eq(F_34(x), F_31(x) + F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_26(x) + F_37(x) + F_40(x))
Eq(F_37(x), F_38(x)*F_7(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_32(x) + F_36(x))
Eq(F_40(x), F_41(x)*F_7(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_32(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_32(x) + F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_7(x))
Eq(F_50(x), F_143(x) + F_4(x) + F_51(x))
Eq(F_51(x), F_52(x)*F_7(x))
Eq(F_52(x), F_53(x)/F_7(x))
Eq(F_53(x), -F_54(x) - F_71(x) + F_8(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_31(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0)*F_63(x))
Eq(F_58(x, k_0), F_1(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_1(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_18(x, k_0)*F_61(x, k_0))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_31(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_65(x)*F_7(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_7(x)*F_70(x))
Eq(F_70(x), F_35(x) + F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_7(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_1(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_7(x)*F_75(x)**2)
Eq(F_78(x), F_26(x) + F_79(x) + F_97(x) + F_99(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_7(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_73(x) + F_84(x, k_0))
Eq(F_84(x, k_0), F_8(x)*F_85(x, k_0))
Eq(F_85(x, k_0), -F_16(x, 1) + (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_86(x), F_134(x) + F_26(x) + F_87(x) + F_88(x) + F_90(x))
Eq(F_87(x), F_7(x)*F_73(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_7(x)*F_86(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_7(x)*F_75(x)**2*F_92(x))
Eq(F_92(x), -F_128(x) + F_93(x))
Eq(F_93(x), F_26(x) + F_94(x) + F_97(x) + F_99(x))
Eq(F_94(x), F_7(x)*F_8(x)*F_95(x))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_7(x)*F_75(x)*F_93(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_7(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_7(x)*F_95(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_105(x, k_0), (-k_0*F_104(x, k_0) + F_104(x, 1))/(1 - k_0))
Eq(F_106(x, k_0), F_105(x, k_0)*F_7(x))
Eq(F_107(x, k_0), F_106(x, k_0) + F_110(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_7(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_22(x, k_0), F_109(x, k_0) + F_29(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_111(x, k_0)*F_7(x))
Eq(F_112(x, k_0), F_19(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x)*F_7(x)*F_96(x, k_0))
Eq(F_115(x), F_116(x)/(F_117(x)*F_125(x)*F_7(x)))
Eq(F_116(x), F_78(x))
Eq(F_117(x), F_1(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_7(x))
Eq(F_120(x), F_117(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_66(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_7(x))
Eq(F_124(x), F_118(x) + F_122(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_65(x)*F_75(x))
Eq(F_127(x), F_85(x, 1))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_7(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_75(x)*F_93(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_75(x)*F_93(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_7(x)*F_75(x))
Eq(F_136(x), F_101(x) - F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_7(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_101(x)*F_75(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_101(x)*F_75(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_7(x)*F_73(x))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_7(x))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_149(x, k_0), F_148(x, k_0) + F_50(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_154(x, k_0) + F_171(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_1(x) + F_151(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_11(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_7(x))
Eq(F_155(x, k_0), F_156(x, k_0) + F_52(x))
Eq(F_157(x, k_0), F_156(x, k_0) + F_170(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_167(x))
Eq(F_158(x, k_0), (-k_0*F_159(x, k_0) + F_159(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_159(x, k_0) + F_162(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0)*F_7(x))
Eq(F_10(x, k_0), F_13(x, k_0) + F_161(x, k_0) + F_31(x))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_7(x))
Eq(F_164(x, k_0), (-k_0*F_165(x, k_0) + F_165(x, 1))/(1 - k_0))
Eq(F_166(x, k_0), F_165(x, k_0)*F_7(x))
Eq(F_22(x, k_0), F_166(x, k_0) + F_24(x, k_0) + F_34(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_7(x))
Eq(F_169(x), F_164(x, 1))
Eq(F_170(x), F_160(x, 1))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_7(x)*F_83(x, k_0))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_7(x))
Eq(F_175(x), F_176(x) - F_193(x))
Eq(F_176(x), F_177(x)/F_75(x))
Eq(F_177(x), F_178(x) - F_187(x))
Eq(F_178(x), F_179(x)/F_7(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_181(x) + F_188(x) + F_190(x) + F_26(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_7(x))
Eq(F_183(x), F_184(x) + F_187(x))
Eq(F_184(x), F_185(x)*F_75(x))
Eq(F_185(x), F_180(x) + F_186(x))
Eq(F_186(x), F_8(x) + F_92(x))
Eq(F_187(x), F_132(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_127(x)*F_7(x)*F_8(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_192(x)*F_7(x))
Eq(F_192(x), F_156(x, 1))
Eq(F_193(x), F_93(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[1, 1], [1, 0], [1, 1], [1, 0], [1, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [1, 1], [1, 1], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [1, 0], [1, 1], [1, 1], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 1], [1, 0], [1, 1], [1, 1], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [3, 2], [3, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 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[[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}]}, "children": [{"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], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25074/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[173,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[7,x]
F[21,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[23,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[145,x,k[0]]+F[26,x]+F[27,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]+F[30,x]
F[30,x] = F[31,x]+F[48,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[7,x]
F[34,x] = F[31,x]+F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[26,x]+F[37,x]+F[40,x]
F[37,x] = F[38,x]*F[7,x]
F[38,x] = F[39,x]
F[39,x] = F[32,x]+F[36,x]
F[40,x] = F[41,x]*F[7,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[32,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[47,x]
F[47,x] = F[32,x]+F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[7,x]
F[50,x] = F[143,x]+F[4,x]+F[51,x]
F[51,x] = F[52,x]*F[7,x]
F[52,x] = 1/F[7,x]*F[53,x]
F[53,x] = -F[54,x]-F[71,x]+F[8,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[31,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]*F[63,x]
F[58,x,k[0]] = F[1,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[1,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[18,x,k[0]]*F[61,x,k[0]]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[31,x]*F[65,x]
F[65,x] = F[1,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[65,x]*F[7,x]
F[68,x] = F[69,x]
F[69,x] = F[7,x]*F[70,x]
F[70,x] = F[35,x]+F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[7,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[1,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[75,x]^2*F[7,x]
F[78,x] = F[26,x]+F[79,x]+F[97,x]+F[99,x]
F[79,x] = F[80,x]
F[80,x] = F[7,x]*F[81,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[73,x]+F[84,x,k[0]]
F[84,x,k[0]] = F[8,x]*F[85,x,k[0]]
F[85,x,k[0]] = -k[0]*(F[16,x,1]-F[16,x,k[0]])/(-1+k[0])
F[86,x] = F[134,x]+F[26,x]+F[87,x]+F[88,x]+F[90,x]
F[87,x] = F[7,x]*F[73,x]
F[88,x] = F[89,x]
F[89,x] = F[7,x]*F[86,x]
F[90,x] = F[91,x]
F[91,x] = F[75,x]^2*F[7,x]*F[92,x]
F[92,x] = -F[128,x]+F[93,x]
F[93,x] = F[26,x]+F[94,x]+F[97,x]+F[99,x]
F[94,x] = F[7,x]*F[8,x]*F[95,x]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = (F[15,x,k[0]]*k[0]-F[15,x,1])/(-1+k[0])
F[97,x] = F[98,x]
F[98,x] = F[7,x]*F[75,x]*F[93,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[7,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[7,x]*F[95,x]
F[103,x] = F[104,x,1]
F[105,x,k[0]] = (F[104,x,k[0]]*k[0]-F[104,x,1])/(-1+k[0])
F[106,x,k[0]] = F[105,x,k[0]]*F[7,x]
F[107,x,k[0]] = F[106,x,k[0]]+F[110,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[7,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[22,x,k[0]] = F[109,x,k[0]]+F[29,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[111,x,k[0]]*F[7,x]
F[112,x,k[0]] = F[19,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x]*F[7,x]*F[96,x,k[0]]
F[115,x] = 1/F[117,x]/F[125,x]/F[7,x]*F[116,x]
F[116,x] = F[78,x]
F[117,x] = F[1,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[7,x]
F[120,x] = F[117,x]+F[121,x]
F[121,x] = F[122,x]+F[66,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[7,x]
F[124,x] = F[118,x]+F[122,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[65,x]*F[75,x]
F[127,x] = F[85,x,1]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[7,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[75,x]*F[93,x]
F[132,x] = F[133,x]
F[133,x] = F[75,x]*F[93,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[7,x]*F[75,x]
F[136,x] = -F[137,x]+F[101,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[7,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[101,x]*F[75,x]
F[141,x] = F[142,x]
F[142,x] = F[101,x]*F[75,x]
F[143,x] = F[144,x]
F[144,x] = F[7,x]*F[73,x]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[7,x]
F[147,x,k[0]] = F[148,x,k[0]]
F[149,x,k[0]] = F[148,x,k[0]]+F[50,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[154,x,k[0]]+F[171,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[1,x]+F[151,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[7,x]
F[155,x,k[0]] = F[156,x,k[0]]+F[52,x]
F[157,x,k[0]] = F[156,x,k[0]]+F[170,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[167,x]
F[158,x,k[0]] = (F[159,x,k[0]]*k[0]-F[159,x,1])/(-1+k[0])
F[160,x,k[0]] = F[159,x,k[0]]+F[162,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]*F[7,x]
F[10,x,k[0]] = F[13,x,k[0]]+F[161,x,k[0]]+F[31,x]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[7,x]
F[164,x,k[0]] = (F[165,x,k[0]]*k[0]-F[165,x,1])/(-1+k[0])
F[166,x,k[0]] = F[165,x,k[0]]*F[7,x]
F[22,x,k[0]] = F[166,x,k[0]]+F[24,x,k[0]]+F[34,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[7,x]
F[169,x] = F[164,x,1]
F[170,x] = F[160,x,1]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[7,x]*F[83,x,k[0]]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[7,x]
F[175,x] = -F[193,x]+F[176,x]
F[176,x] = 1/F[75,x]*F[177,x]
F[177,x] = -F[187,x]+F[178,x]
F[178,x] = 1/F[7,x]*F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[181,x]+F[188,x]+F[190,x]+F[26,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[7,x]
F[183,x] = F[184,x]+F[187,x]
F[184,x] = F[185,x]*F[75,x]
F[185,x] = F[180,x]+F[186,x]
F[186,x] = F[8,x]+F[92,x]
F[187,x] = F[132,x]
F[188,x] = F[189,x]
F[189,x] = F[127,x]*F[7,x]*F[8,x]
F[190,x] = F[191,x]
F[191,x] = F[192,x]*F[7,x]
F[192,x] = F[156,x,1]
F[193,x] = F[93,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_{7}\! \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_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{173}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{143}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)-F_{71}\! \left(x \right)+F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{31}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right) F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{7}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{35}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{78}\! \left(x \right) = F_{26}\! \left(x \right)+F_{79}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{7}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{73}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{y \left(F_{16}\! \left(x , 1\right)-F_{16}\! \left(x , y\right)\right)}{-1+y}
F_{86}\! \left(x \right) = F_{134}\! \left(x \right)+F_{26}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{94}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{7}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{7}\! \left(x \right) F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{105}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x \right) F_{7}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{115}\! \left(x \right) = \frac{F_{116}\! \left(x \right)}{F_{117}\! \left(x \right) F_{125}\! \left(x \right) F_{7}\! \left(x \right)}
F_{116}\! \left(x \right) = F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{7}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{66}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{7}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{65}\! \left(x \right) F_{75}\! \left(x \right)
F_{127}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{7}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{136}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{101}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{7}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{170}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{167}\! \left(x \right)
F_{158}\! \left(x , y\right) = -\frac{-F_{159}\! \left(x , y\right) y +F_{159}\! \left(x , 1\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{164}\! \left(x , y\right) = -\frac{-y F_{165}\! \left(x , y\right)+F_{165}\! \left(x , 1\right)}{-1+y}
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{7}\! \left(x \right)
F_{169}\! \left(x \right) = F_{164}\! \left(x , 1\right)
F_{170}\! \left(x \right) = F_{160}\! \left(x , 1\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{7}\! \left(x \right)
F_{175}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{75}\! \left(x \right)}
F_{177}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = \frac{F_{179}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{26}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{7}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{75}\! \left(x \right)
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{8}\! \left(x \right)+F_{92}\! \left(x \right)
F_{187}\! \left(x \right) = F_{132}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{127}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{7}\! \left(x \right)
F_{192}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{93}\! \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_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_173(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)**2*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_7(x))
Eq(F_21(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_145(x, k_0) + F_26(x) + F_27(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0) + F_30(x))
Eq(F_30(x), F_31(x) + F_48(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_7(x))
Eq(F_34(x), F_31(x) + F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_26(x) + F_37(x) + F_40(x))
Eq(F_37(x), F_38(x)*F_7(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_32(x) + F_36(x))
Eq(F_40(x), F_41(x)*F_7(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_32(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_32(x) + F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_7(x))
Eq(F_50(x), F_143(x) + F_4(x) + F_51(x))
Eq(F_51(x), F_52(x)*F_7(x))
Eq(F_52(x), F_53(x)/F_7(x))
Eq(F_53(x), -F_54(x) - F_71(x) + F_8(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_31(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0)*F_63(x))
Eq(F_58(x, k_0), F_1(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_1(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_18(x, k_0)*F_61(x, k_0))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_31(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_65(x)*F_7(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_7(x)*F_70(x))
Eq(F_70(x), F_35(x) + F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_7(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_1(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_7(x)*F_75(x)**2)
Eq(F_78(x), F_26(x) + F_79(x) + F_97(x) + F_99(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_7(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_73(x) + F_84(x, k_0))
Eq(F_84(x, k_0), F_8(x)*F_85(x, k_0))
Eq(F_85(x, k_0), -F_16(x, 1) + (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_86(x), F_134(x) + F_26(x) + F_87(x) + F_88(x) + F_90(x))
Eq(F_87(x), F_7(x)*F_73(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_7(x)*F_86(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_7(x)*F_75(x)**2*F_92(x))
Eq(F_92(x), -F_128(x) + F_93(x))
Eq(F_93(x), F_26(x) + F_94(x) + F_97(x) + F_99(x))
Eq(F_94(x), F_7(x)*F_8(x)*F_95(x))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_7(x)*F_75(x)*F_93(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_7(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_7(x)*F_95(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_105(x, k_0), (-k_0*F_104(x, k_0) + F_104(x, 1))/(1 - k_0))
Eq(F_106(x, k_0), F_105(x, k_0)*F_7(x))
Eq(F_107(x, k_0), F_106(x, k_0) + F_110(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_7(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_22(x, k_0), F_109(x, k_0) + F_29(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_111(x, k_0)*F_7(x))
Eq(F_112(x, k_0), F_19(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x)*F_7(x)*F_96(x, k_0))
Eq(F_115(x), F_116(x)/(F_117(x)*F_125(x)*F_7(x)))
Eq(F_116(x), F_78(x))
Eq(F_117(x), F_1(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_7(x))
Eq(F_120(x), F_117(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_66(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_7(x))
Eq(F_124(x), F_118(x) + F_122(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_65(x)*F_75(x))
Eq(F_127(x), F_85(x, 1))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_7(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_75(x)*F_93(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_75(x)*F_93(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_7(x)*F_75(x))
Eq(F_136(x), F_101(x) - F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_7(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_101(x)*F_75(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_101(x)*F_75(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_7(x)*F_73(x))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_7(x))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_149(x, k_0), F_148(x, k_0) + F_50(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_154(x, k_0) + F_171(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_1(x) + F_151(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_11(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_7(x))
Eq(F_155(x, k_0), F_156(x, k_0) + F_52(x))
Eq(F_157(x, k_0), F_156(x, k_0) + F_170(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_167(x))
Eq(F_158(x, k_0), (-k_0*F_159(x, k_0) + F_159(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_159(x, k_0) + F_162(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0)*F_7(x))
Eq(F_10(x, k_0), F_13(x, k_0) + F_161(x, k_0) + F_31(x))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_7(x))
Eq(F_164(x, k_0), (-k_0*F_165(x, k_0) + F_165(x, 1))/(1 - k_0))
Eq(F_166(x, k_0), F_165(x, k_0)*F_7(x))
Eq(F_22(x, k_0), F_166(x, k_0) + F_24(x, k_0) + F_34(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_7(x))
Eq(F_169(x), F_164(x, 1))
Eq(F_170(x), F_160(x, 1))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_7(x)*F_83(x, k_0))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_7(x))
Eq(F_175(x), F_176(x) - F_193(x))
Eq(F_176(x), F_177(x)/F_75(x))
Eq(F_177(x), F_178(x) - F_187(x))
Eq(F_178(x), F_179(x)/F_7(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_181(x) + F_188(x) + F_190(x) + F_26(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_7(x))
Eq(F_183(x), F_184(x) + F_187(x))
Eq(F_184(x), F_185(x)*F_75(x))
Eq(F_185(x), F_180(x) + F_186(x))
Eq(F_186(x), F_8(x) + F_92(x))
Eq(F_187(x), F_132(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_127(x)*F_7(x)*F_8(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_192(x)*F_7(x))
Eq(F_192(x), F_156(x, 1))
Eq(F_193(x), F_93(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[1, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 1], [1, 1], 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"TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"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, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [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": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}]}, "children": [{"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], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25859/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[173,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[7,x]
F[21,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[23,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[145,x,k[0]]+F[26,x]+F[27,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]+F[30,x]
F[30,x] = F[31,x]+F[48,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[7,x]
F[34,x] = F[31,x]+F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[26,x]+F[37,x]+F[40,x]
F[37,x] = F[38,x]*F[7,x]
F[38,x] = F[39,x]
F[39,x] = F[32,x]+F[36,x]
F[40,x] = F[41,x]*F[7,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[32,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[47,x]
F[47,x] = F[32,x]+F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[7,x]
F[50,x] = F[143,x]+F[4,x]+F[51,x]
F[51,x] = F[52,x]*F[7,x]
F[52,x] = 1/F[7,x]*F[53,x]
F[53,x] = -F[54,x]-F[71,x]+F[8,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[31,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]*F[63,x]
F[58,x,k[0]] = F[1,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[1,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[18,x,k[0]]*F[61,x,k[0]]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[31,x]*F[65,x]
F[65,x] = F[1,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[65,x]*F[7,x]
F[68,x] = F[69,x]
F[69,x] = F[7,x]*F[70,x]
F[70,x] = F[35,x]+F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[7,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[1,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[75,x]^2*F[7,x]
F[78,x] = F[26,x]+F[79,x]+F[97,x]+F[99,x]
F[79,x] = F[80,x]
F[80,x] = F[7,x]*F[81,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[73,x]+F[84,x,k[0]]
F[84,x,k[0]] = F[8,x]*F[85,x,k[0]]
F[85,x,k[0]] = -k[0]*(F[16,x,1]-F[16,x,k[0]])/(-1+k[0])
F[86,x] = F[134,x]+F[26,x]+F[87,x]+F[88,x]+F[90,x]
F[87,x] = F[7,x]*F[73,x]
F[88,x] = F[89,x]
F[89,x] = F[7,x]*F[86,x]
F[90,x] = F[91,x]
F[91,x] = F[75,x]^2*F[7,x]*F[92,x]
F[92,x] = -F[128,x]+F[93,x]
F[93,x] = F[26,x]+F[94,x]+F[97,x]+F[99,x]
F[94,x] = F[7,x]*F[8,x]*F[95,x]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = (F[15,x,k[0]]*k[0]-F[15,x,1])/(-1+k[0])
F[97,x] = F[98,x]
F[98,x] = F[7,x]*F[75,x]*F[93,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[7,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[7,x]*F[95,x]
F[103,x] = F[104,x,1]
F[105,x,k[0]] = (F[104,x,k[0]]*k[0]-F[104,x,1])/(-1+k[0])
F[106,x,k[0]] = F[105,x,k[0]]*F[7,x]
F[107,x,k[0]] = F[106,x,k[0]]+F[110,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[7,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[22,x,k[0]] = F[109,x,k[0]]+F[29,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[111,x,k[0]]*F[7,x]
F[112,x,k[0]] = F[19,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x]*F[7,x]*F[96,x,k[0]]
F[115,x] = 1/F[117,x]/F[125,x]/F[7,x]*F[116,x]
F[116,x] = F[78,x]
F[117,x] = F[1,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[7,x]
F[120,x] = F[117,x]+F[121,x]
F[121,x] = F[122,x]+F[66,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[7,x]
F[124,x] = F[118,x]+F[122,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[65,x]*F[75,x]
F[127,x] = F[85,x,1]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[7,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[75,x]*F[93,x]
F[132,x] = F[133,x]
F[133,x] = F[75,x]*F[93,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[7,x]*F[75,x]
F[136,x] = -F[137,x]+F[101,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[7,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[101,x]*F[75,x]
F[141,x] = F[142,x]
F[142,x] = F[101,x]*F[75,x]
F[143,x] = F[144,x]
F[144,x] = F[7,x]*F[73,x]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[7,x]
F[147,x,k[0]] = F[148,x,k[0]]
F[149,x,k[0]] = F[148,x,k[0]]+F[50,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[154,x,k[0]]+F[171,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[1,x]+F[151,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[7,x]
F[155,x,k[0]] = F[156,x,k[0]]+F[52,x]
F[157,x,k[0]] = F[156,x,k[0]]+F[170,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[167,x]
F[158,x,k[0]] = (F[159,x,k[0]]*k[0]-F[159,x,1])/(-1+k[0])
F[160,x,k[0]] = F[159,x,k[0]]+F[162,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]*F[7,x]
F[10,x,k[0]] = F[13,x,k[0]]+F[161,x,k[0]]+F[31,x]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[7,x]
F[164,x,k[0]] = (F[165,x,k[0]]*k[0]-F[165,x,1])/(-1+k[0])
F[166,x,k[0]] = F[165,x,k[0]]*F[7,x]
F[22,x,k[0]] = F[166,x,k[0]]+F[24,x,k[0]]+F[34,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[7,x]
F[169,x] = F[164,x,1]
F[170,x] = F[160,x,1]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[7,x]*F[83,x,k[0]]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[7,x]
F[175,x] = -F[193,x]+F[176,x]
F[176,x] = 1/F[75,x]*F[177,x]
F[177,x] = -F[187,x]+F[178,x]
F[178,x] = 1/F[7,x]*F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[181,x]+F[188,x]+F[190,x]+F[26,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[7,x]
F[183,x] = F[184,x]+F[187,x]
F[184,x] = F[185,x]*F[75,x]
F[185,x] = F[180,x]+F[186,x]
F[186,x] = F[8,x]+F[92,x]
F[187,x] = F[132,x]
F[188,x] = F[189,x]
F[189,x] = F[127,x]*F[7,x]*F[8,x]
F[190,x] = F[191,x]
F[191,x] = F[192,x]*F[7,x]
F[192,x] = F[156,x,1]
F[193,x] = F[93,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_{7}\! \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_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{173}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{143}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)-F_{71}\! \left(x \right)+F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{31}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right) F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{7}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{35}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{78}\! \left(x \right) = F_{26}\! \left(x \right)+F_{79}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{7}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{73}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{y \left(F_{16}\! \left(x , 1\right)-F_{16}\! \left(x , y\right)\right)}{-1+y}
F_{86}\! \left(x \right) = F_{134}\! \left(x \right)+F_{26}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{94}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{7}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{7}\! \left(x \right) F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{105}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x \right) F_{7}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{115}\! \left(x \right) = \frac{F_{116}\! \left(x \right)}{F_{117}\! \left(x \right) F_{125}\! \left(x \right) F_{7}\! \left(x \right)}
F_{116}\! \left(x \right) = F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{7}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{66}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{7}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{65}\! \left(x \right) F_{75}\! \left(x \right)
F_{127}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{7}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{136}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{101}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{7}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{170}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{167}\! \left(x \right)
F_{158}\! \left(x , y\right) = -\frac{-F_{159}\! \left(x , y\right) y +F_{159}\! \left(x , 1\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{164}\! \left(x , y\right) = -\frac{-y F_{165}\! \left(x , y\right)+F_{165}\! \left(x , 1\right)}{-1+y}
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{7}\! \left(x \right)
F_{169}\! \left(x \right) = F_{164}\! \left(x , 1\right)
F_{170}\! \left(x \right) = F_{160}\! \left(x , 1\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{7}\! \left(x \right)
F_{175}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{75}\! \left(x \right)}
F_{177}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = \frac{F_{179}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{26}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{7}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{75}\! \left(x \right)
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{8}\! \left(x \right)+F_{92}\! \left(x \right)
F_{187}\! \left(x \right) = F_{132}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{127}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{7}\! \left(x \right)
F_{192}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{93}\! \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_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_173(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)**2*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_7(x))
Eq(F_21(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_145(x, k_0) + F_26(x) + F_27(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0) + F_30(x))
Eq(F_30(x), F_31(x) + F_48(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_7(x))
Eq(F_34(x), F_31(x) + F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_26(x) + F_37(x) + F_40(x))
Eq(F_37(x), F_38(x)*F_7(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_32(x) + F_36(x))
Eq(F_40(x), F_41(x)*F_7(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_32(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_32(x) + F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_7(x))
Eq(F_50(x), F_143(x) + F_4(x) + F_51(x))
Eq(F_51(x), F_52(x)*F_7(x))
Eq(F_52(x), F_53(x)/F_7(x))
Eq(F_53(x), -F_54(x) - F_71(x) + F_8(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_31(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0)*F_63(x))
Eq(F_58(x, k_0), F_1(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_1(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_18(x, k_0)*F_61(x, k_0))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_31(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_65(x)*F_7(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_7(x)*F_70(x))
Eq(F_70(x), F_35(x) + F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_7(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_1(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_7(x)*F_75(x)**2)
Eq(F_78(x), F_26(x) + F_79(x) + F_97(x) + F_99(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_7(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_73(x) + F_84(x, k_0))
Eq(F_84(x, k_0), F_8(x)*F_85(x, k_0))
Eq(F_85(x, k_0), -F_16(x, 1) + (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_86(x), F_134(x) + F_26(x) + F_87(x) + F_88(x) + F_90(x))
Eq(F_87(x), F_7(x)*F_73(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_7(x)*F_86(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_7(x)*F_75(x)**2*F_92(x))
Eq(F_92(x), -F_128(x) + F_93(x))
Eq(F_93(x), F_26(x) + F_94(x) + F_97(x) + F_99(x))
Eq(F_94(x), F_7(x)*F_8(x)*F_95(x))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_7(x)*F_75(x)*F_93(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_7(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_7(x)*F_95(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_105(x, k_0), (-k_0*F_104(x, k_0) + F_104(x, 1))/(1 - k_0))
Eq(F_106(x, k_0), F_105(x, k_0)*F_7(x))
Eq(F_107(x, k_0), F_106(x, k_0) + F_110(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_7(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_22(x, k_0), F_109(x, k_0) + F_29(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_111(x, k_0)*F_7(x))
Eq(F_112(x, k_0), F_19(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x)*F_7(x)*F_96(x, k_0))
Eq(F_115(x), F_116(x)/(F_117(x)*F_125(x)*F_7(x)))
Eq(F_116(x), F_78(x))
Eq(F_117(x), F_1(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_7(x))
Eq(F_120(x), F_117(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_66(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_7(x))
Eq(F_124(x), F_118(x) + F_122(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_65(x)*F_75(x))
Eq(F_127(x), F_85(x, 1))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_7(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_75(x)*F_93(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_75(x)*F_93(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_7(x)*F_75(x))
Eq(F_136(x), F_101(x) - F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_7(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_101(x)*F_75(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_101(x)*F_75(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_7(x)*F_73(x))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_7(x))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_149(x, k_0), F_148(x, k_0) + F_50(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_154(x, k_0) + F_171(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_1(x) + F_151(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_11(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_7(x))
Eq(F_155(x, k_0), F_156(x, k_0) + F_52(x))
Eq(F_157(x, k_0), F_156(x, k_0) + F_170(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_167(x))
Eq(F_158(x, k_0), (-k_0*F_159(x, k_0) + F_159(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_159(x, k_0) + F_162(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0)*F_7(x))
Eq(F_10(x, k_0), F_13(x, k_0) + F_161(x, k_0) + F_31(x))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_7(x))
Eq(F_164(x, k_0), (-k_0*F_165(x, k_0) + F_165(x, 1))/(1 - k_0))
Eq(F_166(x, k_0), F_165(x, k_0)*F_7(x))
Eq(F_22(x, k_0), F_166(x, k_0) + F_24(x, k_0) + F_34(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_7(x))
Eq(F_169(x), F_164(x, 1))
Eq(F_170(x), F_160(x, 1))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_7(x)*F_83(x, k_0))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_7(x))
Eq(F_175(x), F_176(x) - F_193(x))
Eq(F_176(x), F_177(x)/F_75(x))
Eq(F_177(x), F_178(x) - F_187(x))
Eq(F_178(x), F_179(x)/F_7(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_181(x) + F_188(x) + F_190(x) + F_26(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_7(x))
Eq(F_183(x), F_184(x) + F_187(x))
Eq(F_184(x), F_185(x)*F_75(x))
Eq(F_185(x), F_180(x) + F_186(x))
Eq(F_186(x), F_8(x) + F_92(x))
Eq(F_187(x), F_132(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_127(x)*F_7(x)*F_8(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_192(x)*F_7(x))
Eq(F_192(x), F_156(x, 1))
Eq(F_193(x), F_93(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": 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2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}]}, "children": [{"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], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25878/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[173,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[7,x]
F[21,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[23,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[145,x,k[0]]+F[26,x]+F[27,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]+F[30,x]
F[30,x] = F[31,x]+F[48,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[7,x]
F[34,x] = F[31,x]+F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[26,x]+F[37,x]+F[40,x]
F[37,x] = F[38,x]*F[7,x]
F[38,x] = F[39,x]
F[39,x] = F[32,x]+F[36,x]
F[40,x] = F[41,x]*F[7,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[32,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[47,x]
F[47,x] = F[32,x]+F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[7,x]
F[50,x] = F[143,x]+F[4,x]+F[51,x]
F[51,x] = F[52,x]*F[7,x]
F[52,x] = 1/F[7,x]*F[53,x]
F[53,x] = -F[54,x]-F[71,x]+F[8,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[31,x]+F[56,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]*F[63,x]
F[58,x,k[0]] = F[1,x]+F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[18,x,k[0]]*F[58,x,k[0]]*F[61,x,k[0]]
F[61,x,k[0]] = F[1,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[18,x,k[0]]*F[61,x,k[0]]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[31,x]*F[65,x]
F[65,x] = F[1,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[65,x]*F[7,x]
F[68,x] = F[69,x]
F[69,x] = F[7,x]*F[70,x]
F[70,x] = F[35,x]+F[68,x]
F[71,x] = F[72,x]
F[72,x] = F[7,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[75,x]*F[8,x]
F[75,x] = F[1,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[75,x]^2*F[7,x]
F[78,x] = F[26,x]+F[79,x]+F[97,x]+F[99,x]
F[79,x] = F[80,x]
F[80,x] = F[7,x]*F[81,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[73,x]+F[84,x,k[0]]
F[84,x,k[0]] = F[8,x]*F[85,x,k[0]]
F[85,x,k[0]] = -k[0]*(F[16,x,1]-F[16,x,k[0]])/(-1+k[0])
F[86,x] = F[134,x]+F[26,x]+F[87,x]+F[88,x]+F[90,x]
F[87,x] = F[7,x]*F[73,x]
F[88,x] = F[89,x]
F[89,x] = F[7,x]*F[86,x]
F[90,x] = F[91,x]
F[91,x] = F[75,x]^2*F[7,x]*F[92,x]
F[92,x] = -F[128,x]+F[93,x]
F[93,x] = F[26,x]+F[94,x]+F[97,x]+F[99,x]
F[94,x] = F[7,x]*F[8,x]*F[95,x]
F[95,x] = F[96,x,1]
F[96,x,k[0]] = (F[15,x,k[0]]*k[0]-F[15,x,1])/(-1+k[0])
F[97,x] = F[98,x]
F[98,x] = F[7,x]*F[75,x]*F[93,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[7,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[7,x]*F[95,x]
F[103,x] = F[104,x,1]
F[105,x,k[0]] = (F[104,x,k[0]]*k[0]-F[104,x,1])/(-1+k[0])
F[106,x,k[0]] = F[105,x,k[0]]*F[7,x]
F[107,x,k[0]] = F[106,x,k[0]]+F[110,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[7,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[22,x,k[0]] = F[109,x,k[0]]+F[29,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[113,x,k[0]]
F[112,x,k[0]] = F[111,x,k[0]]*F[7,x]
F[112,x,k[0]] = F[19,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x]*F[7,x]*F[96,x,k[0]]
F[115,x] = 1/F[117,x]/F[125,x]/F[7,x]*F[116,x]
F[116,x] = F[78,x]
F[117,x] = F[1,x]+F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[7,x]
F[120,x] = F[117,x]+F[121,x]
F[121,x] = F[122,x]+F[66,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[7,x]
F[124,x] = F[118,x]+F[122,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[65,x]*F[75,x]
F[127,x] = F[85,x,1]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[7,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[75,x]*F[93,x]
F[132,x] = F[133,x]
F[133,x] = F[75,x]*F[93,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[7,x]*F[75,x]
F[136,x] = -F[137,x]+F[101,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[7,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[101,x]*F[75,x]
F[141,x] = F[142,x]
F[142,x] = F[101,x]*F[75,x]
F[143,x] = F[144,x]
F[144,x] = F[7,x]*F[73,x]
F[145,x,k[0]] = F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]*F[7,x]
F[147,x,k[0]] = F[148,x,k[0]]
F[149,x,k[0]] = F[148,x,k[0]]+F[50,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[154,x,k[0]]+F[171,x,k[0]]
F[151,x,k[0]] = F[150,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[1,x]+F[151,x,k[0]]+F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[7,x]
F[155,x,k[0]] = F[156,x,k[0]]+F[52,x]
F[157,x,k[0]] = F[156,x,k[0]]+F[170,x]
F[157,x,k[0]] = F[158,x,k[0]]+F[167,x]
F[158,x,k[0]] = (F[159,x,k[0]]*k[0]-F[159,x,1])/(-1+k[0])
F[160,x,k[0]] = F[159,x,k[0]]+F[162,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]*F[7,x]
F[10,x,k[0]] = F[13,x,k[0]]+F[161,x,k[0]]+F[31,x]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[7,x]
F[164,x,k[0]] = (F[165,x,k[0]]*k[0]-F[165,x,1])/(-1+k[0])
F[166,x,k[0]] = F[165,x,k[0]]*F[7,x]
F[22,x,k[0]] = F[166,x,k[0]]+F[24,x,k[0]]+F[34,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[7,x]
F[169,x] = F[164,x,1]
F[170,x] = F[160,x,1]
F[171,x,k[0]] = F[172,x,k[0]]
F[172,x,k[0]] = F[7,x]*F[83,x,k[0]]
F[173,x] = F[174,x]
F[174,x] = F[175,x]*F[7,x]
F[175,x] = -F[193,x]+F[176,x]
F[176,x] = 1/F[75,x]*F[177,x]
F[177,x] = -F[187,x]+F[178,x]
F[178,x] = 1/F[7,x]*F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[181,x]+F[188,x]+F[190,x]+F[26,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[7,x]
F[183,x] = F[184,x]+F[187,x]
F[184,x] = F[185,x]*F[75,x]
F[185,x] = F[180,x]+F[186,x]
F[186,x] = F[8,x]+F[92,x]
F[187,x] = F[132,x]
F[188,x] = F[189,x]
F[189,x] = F[127,x]*F[7,x]*F[8,x]
F[190,x] = F[191,x]
F[191,x] = F[192,x]*F[7,x]
F[192,x] = F[156,x,1]
F[193,x] = F[93,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_{7}\! \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_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{173}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{22}\! \left(x , y\right) y +F_{22}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{145}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{143}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)-F_{71}\! \left(x \right)+F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{58}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{31}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right) F_{7}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{7}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{35}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right) F_{8}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{78}\! \left(x \right) = F_{26}\! \left(x \right)+F_{79}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{7}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{73}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = -\frac{y \left(F_{16}\! \left(x , 1\right)-F_{16}\! \left(x , y\right)\right)}{-1+y}
F_{86}\! \left(x \right) = F_{134}\! \left(x \right)+F_{26}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{7}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{128}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{94}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{94}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x , 1\right)
F_{96}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{7}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{7}\! \left(x \right) F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{105}\! \left(x , y\right) = -\frac{-F_{104}\! \left(x , y\right) y +F_{104}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x \right) F_{7}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{115}\! \left(x \right) = \frac{F_{116}\! \left(x \right)}{F_{117}\! \left(x \right) F_{125}\! \left(x \right) F_{7}\! \left(x \right)}
F_{116}\! \left(x \right) = F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{7}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{66}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{7}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{65}\! \left(x \right) F_{75}\! \left(x \right)
F_{127}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{7}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{75}\! \left(x \right) F_{93}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{136}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{101}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{7}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{101}\! \left(x \right) F_{75}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{7}\! \left(x \right) F_{73}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{148}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{170}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{167}\! \left(x \right)
F_{158}\! \left(x , y\right) = -\frac{-F_{159}\! \left(x , y\right) y +F_{159}\! \left(x , 1\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{164}\! \left(x , y\right) = -\frac{-y F_{165}\! \left(x , y\right)+F_{165}\! \left(x , 1\right)}{-1+y}
F_{166}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{7}\! \left(x \right)
F_{169}\! \left(x \right) = F_{164}\! \left(x , 1\right)
F_{170}\! \left(x \right) = F_{160}\! \left(x , 1\right)
F_{171}\! \left(x , y\right) = F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{7}\! \left(x \right)
F_{175}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{75}\! \left(x \right)}
F_{177}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = \frac{F_{179}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{188}\! \left(x \right)+F_{190}\! \left(x \right)+F_{26}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{7}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right) F_{75}\! \left(x \right)
F_{185}\! \left(x \right) = F_{180}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{8}\! \left(x \right)+F_{92}\! \left(x \right)
F_{187}\! \left(x \right) = F_{132}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{127}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right) F_{7}\! \left(x \right)
F_{192}\! \left(x \right) = F_{156}\! \left(x , 1\right)
F_{193}\! \left(x \right) = F_{93}\! \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_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_173(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)**2*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_7(x))
Eq(F_21(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_145(x, k_0) + F_26(x) + F_27(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0) + F_30(x))
Eq(F_30(x), F_31(x) + F_48(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_7(x))
Eq(F_34(x), F_31(x) + F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_26(x) + F_37(x) + F_40(x))
Eq(F_37(x), F_38(x)*F_7(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_32(x) + F_36(x))
Eq(F_40(x), F_41(x)*F_7(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_32(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_32(x) + F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_7(x))
Eq(F_50(x), F_143(x) + F_4(x) + F_51(x))
Eq(F_51(x), F_52(x)*F_7(x))
Eq(F_52(x), F_53(x)/F_7(x))
Eq(F_53(x), -F_54(x) - F_71(x) + F_8(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_31(x) + F_56(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0)*F_63(x))
Eq(F_58(x, k_0), F_1(x) + F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_18(x, k_0)*F_58(x, k_0)*F_61(x, k_0))
Eq(F_61(x, k_0), F_1(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_18(x, k_0)*F_61(x, k_0))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_31(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_65(x)*F_7(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_7(x)*F_70(x))
Eq(F_70(x), F_35(x) + F_68(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_7(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_75(x)*F_8(x))
Eq(F_75(x), F_1(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_7(x)*F_75(x)**2)
Eq(F_78(x), F_26(x) + F_79(x) + F_97(x) + F_99(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_7(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_73(x) + F_84(x, k_0))
Eq(F_84(x, k_0), F_8(x)*F_85(x, k_0))
Eq(F_85(x, k_0), -F_16(x, 1) + (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_86(x), F_134(x) + F_26(x) + F_87(x) + F_88(x) + F_90(x))
Eq(F_87(x), F_7(x)*F_73(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_7(x)*F_86(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_7(x)*F_75(x)**2*F_92(x))
Eq(F_92(x), -F_128(x) + F_93(x))
Eq(F_93(x), F_26(x) + F_94(x) + F_97(x) + F_99(x))
Eq(F_94(x), F_7(x)*F_8(x)*F_95(x))
Eq(F_95(x), F_96(x, 1))
Eq(F_96(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_7(x)*F_75(x)*F_93(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_7(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_7(x)*F_95(x))
Eq(F_103(x), F_104(x, 1))
Eq(F_105(x, k_0), (-k_0*F_104(x, k_0) + F_104(x, 1))/(1 - k_0))
Eq(F_106(x, k_0), F_105(x, k_0)*F_7(x))
Eq(F_107(x, k_0), F_106(x, k_0) + F_110(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_7(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_22(x, k_0), F_109(x, k_0) + F_29(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_113(x, k_0))
Eq(F_112(x, k_0), F_111(x, k_0)*F_7(x))
Eq(F_112(x, k_0), F_19(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x)*F_7(x)*F_96(x, k_0))
Eq(F_115(x), F_116(x)/(F_117(x)*F_125(x)*F_7(x)))
Eq(F_116(x), F_78(x))
Eq(F_117(x), F_1(x) + F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_7(x))
Eq(F_120(x), F_117(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_66(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_7(x))
Eq(F_124(x), F_118(x) + F_122(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_65(x)*F_75(x))
Eq(F_127(x), F_85(x, 1))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_7(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_75(x)*F_93(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_75(x)*F_93(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_7(x)*F_75(x))
Eq(F_136(x), F_101(x) - F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_7(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_101(x)*F_75(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_101(x)*F_75(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_7(x)*F_73(x))
Eq(F_145(x, k_0), F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0)*F_7(x))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_149(x, k_0), F_148(x, k_0) + F_50(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_154(x, k_0) + F_171(x, k_0))
Eq(F_151(x, k_0), F_150(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_1(x) + F_151(x, k_0) + F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_11(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_7(x))
Eq(F_155(x, k_0), F_156(x, k_0) + F_52(x))
Eq(F_157(x, k_0), F_156(x, k_0) + F_170(x))
Eq(F_157(x, k_0), F_158(x, k_0) + F_167(x))
Eq(F_158(x, k_0), (-k_0*F_159(x, k_0) + F_159(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_159(x, k_0) + F_162(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0)*F_7(x))
Eq(F_10(x, k_0), F_13(x, k_0) + F_161(x, k_0) + F_31(x))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_7(x))
Eq(F_164(x, k_0), (-k_0*F_165(x, k_0) + F_165(x, 1))/(1 - k_0))
Eq(F_166(x, k_0), F_165(x, k_0)*F_7(x))
Eq(F_22(x, k_0), F_166(x, k_0) + F_24(x, k_0) + F_34(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_7(x))
Eq(F_169(x), F_164(x, 1))
Eq(F_170(x), F_160(x, 1))
Eq(F_171(x, k_0), F_172(x, k_0))
Eq(F_172(x, k_0), F_7(x)*F_83(x, k_0))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x)*F_7(x))
Eq(F_175(x), F_176(x) - F_193(x))
Eq(F_176(x), F_177(x)/F_75(x))
Eq(F_177(x), F_178(x) - F_187(x))
Eq(F_178(x), F_179(x)/F_7(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_181(x) + F_188(x) + F_190(x) + F_26(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_7(x))
Eq(F_183(x), F_184(x) + F_187(x))
Eq(F_184(x), F_185(x)*F_75(x))
Eq(F_185(x), F_180(x) + F_186(x))
Eq(F_186(x), F_8(x) + F_92(x))
Eq(F_187(x), F_132(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_127(x)*F_7(x)*F_8(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_192(x)*F_7(x))
Eq(F_192(x), F_156(x, 1))
Eq(F_193(x), F_93(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.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": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 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2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"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, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}]}, "children": [{"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], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "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": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25924/
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[7,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[8,x]
F[7,x] = x
F[8,x] = F[167,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[10,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[7,x]
F[21,x,k[0]] = (F[22,x,k[0]]*k[0]-F[22,x,1])/(-1+k[0])
F[23,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[139,x,k[0]]+F[26,x]+F[27,x,k[0]]
F[26,x] = 0
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]+F[30,x]
F[30,x] = F[31,x]+F[48,x]
F[31,x] = F[1,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[7,x]
F[34,x] = F[31,x]+F[35,x]
F[35,x] = F[32,x]+F[36,x]
F[36,x] = F[26,x]+F[37,x]+F[40,x]
F[37,x] = F[38,x]*F[7,x]
F[38,x] = F[39,x]
F[39,x] = F[32,x]+F[36,x]
F[40,x] = F[41,x]*F[7,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[32,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[7,x]
F[46,x] = F[47,x]
F[47,x] = F[32,x]+F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]*F[7,x]
F[50,x] = F[137,x]+F[4,x]+F[51,x]
F[51,x] = F[52,x]*F[7,x]
F[52,x] = 1/F[7,x]*F[53,x]
F[53,x] = -F[54,x]-F[73,x]+F[8,x]
F[54,x] = F[31,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[57,x]*F[64,x]*F[68,x]*F[7,x]
F[57,x] = F[1,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[60,x]*F[7,x]
F[60,x] = F[57,x]+F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]*F[7,x]
F[64,x] = F[1,x]+F[62,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]*F[7,x]
F[67,x] = F[58,x]+F[65,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[31,x]*F[64,x]
F[70,x] = F[71,x]
F[71,x] = F[7,x]*F[72,x]
F[72,x] = F[35,x]+F[70,x]
F[73,x] = F[74,x]
F[74,x] = F[7,x]*F[75,x]
F[75,x] = F[76,x]+F[80,x]
F[76,x] = F[77,x]*F[8,x]
F[77,x] = F[1,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[77,x]^2*F[7,x]
F[80,x] = F[101,x]+F[26,x]+F[81,x]+F[99,x]
F[81,x] = F[82,x]
F[82,x] = F[7,x]*F[83,x]
F[83,x] = F[84,x]+F[88,x]
F[84,x] = F[85,x,1]
F[85,x,k[0]] = F[75,x]+F[86,x,k[0]]
F[86,x,k[0]] = F[8,x]*F[87,x,k[0]]
F[87,x,k[0]] = -k[0]*(F[16,x,1]-F[16,x,k[0]])/(-1+k[0])
F[88,x] = F[128,x]+F[26,x]+F[89,x]+F[90,x]+F[92,x]
F[89,x] = F[7,x]*F[75,x]
F[90,x] = F[91,x]
F[91,x] = F[7,x]*F[88,x]
F[92,x] = F[93,x]
F[93,x] = F[77,x]^2*F[7,x]*F[94,x]
F[94,x] = -F[122,x]+F[95,x]
F[95,x] = F[101,x]+F[26,x]+F[96,x]+F[99,x]
F[96,x] = F[7,x]*F[8,x]*F[97,x]
F[97,x] = F[98,x,1]
F[98,x,k[0]] = (F[15,x,k[0]]*k[0]-F[15,x,1])/(-1+k[0])
F[99,x] = F[100,x]
F[100,x] = F[7,x]*F[77,x]*F[95,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[7,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[7,x]*F[97,x]
F[105,x] = F[106,x,1]
F[107,x,k[0]] = (F[106,x,k[0]]*k[0]-F[106,x,1])/(-1+k[0])
F[108,x,k[0]] = F[107,x,k[0]]*F[7,x]
F[109,x,k[0]] = F[108,x,k[0]]+F[112,x,k[0]]
F[110,x,k[0]] = F[109,x,k[0]]*F[7,x]
F[110,x,k[0]] = F[111,x,k[0]]
F[22,x,k[0]] = F[111,x,k[0]]+F[29,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[115,x,k[0]]
F[114,x,k[0]] = F[113,x,k[0]]*F[7,x]
F[114,x,k[0]] = F[19,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[117,x]*F[7,x]*F[98,x,k[0]]
F[117,x] = 1/F[119,x]/F[57,x]/F[7,x]*F[118,x]
F[118,x] = F[80,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[64,x]*F[77,x]
F[121,x] = F[87,x,1]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[7,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[77,x]*F[95,x]
F[126,x] = F[127,x]
F[127,x] = F[77,x]*F[95,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[7,x]*F[77,x]
F[130,x] = -F[131,x]+F[103,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[7,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[103,x]*F[77,x]
F[135,x] = F[136,x]
F[136,x] = F[103,x]*F[77,x]
F[137,x] = F[138,x]
F[138,x] = F[7,x]*F[75,x]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[7,x]
F[141,x,k[0]] = F[142,x,k[0]]
F[143,x,k[0]] = F[142,x,k[0]]+F[50,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[148,x,k[0]]+F[165,x,k[0]]
F[145,x,k[0]] = F[144,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[1,x]+F[145,x,k[0]]+F[146,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[11,x,k[0]]*F[15,x,k[0]]*F[18,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[7,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[52,x]
F[151,x,k[0]] = F[150,x,k[0]]+F[164,x]
F[151,x,k[0]] = F[152,x,k[0]]+F[161,x]
F[152,x,k[0]] = (F[153,x,k[0]]*k[0]-F[153,x,1])/(-1+k[0])
F[154,x,k[0]] = F[153,x,k[0]]+F[156,x,k[0]]
F[155,x,k[0]] = F[154,x,k[0]]*F[7,x]
F[10,x,k[0]] = F[13,x,k[0]]+F[155,x,k[0]]+F[31,x]
F[156,x,k[0]] = F[157,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]*F[7,x]
F[158,x,k[0]] = (F[159,x,k[0]]*k[0]-F[159,x,1])/(-1+k[0])
F[160,x,k[0]] = F[159,x,k[0]]*F[7,x]
F[22,x,k[0]] = F[160,x,k[0]]+F[24,x,k[0]]+F[34,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[7,x]
F[163,x] = F[158,x,1]
F[164,x] = F[154,x,1]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[7,x]*F[85,x,k[0]]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[7,x]
F[169,x] = -F[187,x]+F[170,x]
F[170,x] = 1/F[77,x]*F[171,x]
F[171,x] = -F[181,x]+F[172,x]
F[172,x] = 1/F[7,x]*F[173,x]
F[173,x] = F[174,x]
F[174,x] = F[175,x]+F[182,x]+F[184,x]+F[26,x]
F[175,x] = F[176,x]
F[176,x] = F[177,x]*F[7,x]
F[177,x] = F[178,x]+F[181,x]
F[178,x] = F[179,x]*F[77,x]
F[179,x] = F[174,x]+F[180,x]
F[180,x] = F[8,x]+F[94,x]
F[181,x] = F[126,x]
F[182,x] = F[183,x]
F[183,x] = F[121,x]*F[7,x]*F[8,x]
F[184,x] = F[185,x]
F[185,x] = F[186,x]*F[7,x]
F[186,x] = F[150,x,1]
F[187,x] = F[95,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_{7}\! \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_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = x
F_{8}\! \left(x \right) = F_{167}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}
F_{23}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{31}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{137}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)-F_{73}\! \left(x \right)+F_{8}\! \left(x \right)
F_{54}\! \left(x \right) = F_{31}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right) F_{64}\! \left(x \right) F_{68}\! \left(x \right) F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{1}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{7}\! \left(x \right)
F_{60}\! \left(x \right) = F_{57}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{7}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right) F_{7}\! \left(x \right)
F_{67}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{31}\! \left(x \right) F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{7}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{35}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right) F_{8}\! \left(x \right)
F_{77}\! \left(x \right) = F_{1}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{77} \left(x \right)^{2} F_{7}\! \left(x \right)
F_{80}\! \left(x \right) = F_{101}\! \left(x \right)+F_{26}\! \left(x \right)+F_{81}\! \left(x \right)+F_{99}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{7}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{88}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x , 1\right)
F_{85}\! \left(x , y\right) = F_{75}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = -\frac{y \left(F_{16}\! \left(x , 1\right)-F_{16}\! \left(x , y\right)\right)}{-1+y}
F_{88}\! \left(x \right) = F_{128}\! \left(x \right)+F_{26}\! \left(x \right)+F_{89}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{7}\! \left(x \right) F_{88}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{77} \left(x \right)^{2} F_{7}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{26}\! \left(x \right)+F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{96}\! \left(x \right) = F_{7}\! \left(x \right) F_{8}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x , 1\right)
F_{98}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{7}\! \left(x \right) F_{77}\! \left(x \right) F_{95}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{7}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{7}\! \left(x \right) F_{97}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x , 1\right)
F_{107}\! \left(x , y\right) = -\frac{-F_{106}\! \left(x , y\right) y +F_{106}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{19}\! \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 \right) F_{7}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{119}\! \left(x \right) F_{57}\! \left(x \right) F_{7}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{80}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{64}\! \left(x \right) F_{77}\! \left(x \right)
F_{121}\! \left(x \right) = F_{87}\! \left(x , 1\right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{7}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{77}\! \left(x \right) F_{95}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{77}\! \left(x \right) F_{95}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{7}\! \left(x \right) F_{77}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{131}\! \left(x \right)+F_{103}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{7}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{103}\! \left(x \right) F_{77}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{103}\! \left(x \right) F_{77}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{7}\! \left(x \right) F_{75}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{148}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{164}\! \left(x \right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{161}\! \left(x \right)
F_{152}\! \left(x , y\right) = -\frac{-F_{153}\! \left(x , y\right) y +F_{153}\! \left(x , 1\right)}{-1+y}
F_{154}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{156}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{155}\! \left(x , y\right)+F_{31}\! \left(x \right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{158}\! \left(x , y\right) = -\frac{-y F_{159}\! \left(x , y\right)+F_{159}\! \left(x , 1\right)}{-1+y}
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{34}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{7}\! \left(x \right)
F_{163}\! \left(x \right) = F_{158}\! \left(x , 1\right)
F_{164}\! \left(x \right) = F_{154}\! \left(x , 1\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{7}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{7}\! \left(x \right)
F_{169}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = \frac{F_{171}\! \left(x \right)}{F_{77}\! \left(x \right)}
F_{171}\! \left(x \right) = -F_{181}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = \frac{F_{173}\! \left(x \right)}{F_{7}\! \left(x \right)}
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{182}\! \left(x \right)+F_{184}\! \left(x \right)+F_{26}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right) F_{7}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{181}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{77}\! \left(x \right)
F_{179}\! \left(x \right) = F_{174}\! \left(x \right)+F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{8}\! \left(x \right)+F_{94}\! \left(x \right)
F_{181}\! \left(x \right) = F_{126}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{121}\! \left(x \right) F_{7}\! \left(x \right) F_{8}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right) F_{7}\! \left(x \right)
F_{186}\! \left(x \right) = F_{150}\! \left(x , 1\right)
F_{187}\! \left(x \right) = F_{95}\! \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_7(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_7(x)*F_8(x))
Eq(F_7(x), x)
Eq(F_8(x), F_167(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_10(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)**2*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_7(x))
Eq(F_21(x, k_0), (-k_0*F_22(x, k_0) + F_22(x, 1))/(1 - k_0))
Eq(F_23(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_139(x, k_0) + F_26(x) + F_27(x, k_0))
Eq(F_26(x), 0)
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_15(x, k_0)*F_18(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0) + F_30(x))
Eq(F_30(x), F_31(x) + F_48(x))
Eq(F_31(x), F_1(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_7(x))
Eq(F_34(x), F_31(x) + F_35(x))
Eq(F_35(x), F_32(x) + F_36(x))
Eq(F_36(x), F_26(x) + F_37(x) + F_40(x))
Eq(F_37(x), F_38(x)*F_7(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_32(x) + F_36(x))
Eq(F_40(x), F_41(x)*F_7(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_32(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_7(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_32(x) + F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x)*F_7(x))
Eq(F_50(x), F_137(x) + F_4(x) + F_51(x))
Eq(F_51(x), F_52(x)*F_7(x))
Eq(F_52(x), F_53(x)/F_7(x))
Eq(F_53(x), -F_54(x) - F_73(x) + F_8(x))
Eq(F_54(x), F_31(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x)*F_64(x)*F_68(x)*F_7(x))
Eq(F_57(x), F_1(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_60(x)*F_7(x))
Eq(F_60(x), F_57(x) + F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)*F_7(x))
Eq(F_64(x), F_1(x) + F_62(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x)*F_7(x))
Eq(F_67(x), F_58(x) + F_65(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_31(x)*F_64(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_7(x)*F_72(x))
Eq(F_72(x), F_35(x) + F_70(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_7(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_80(x))
Eq(F_76(x), F_77(x)*F_8(x))
Eq(F_77(x), F_1(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_7(x)*F_77(x)**2)
Eq(F_80(x), F_101(x) + F_26(x) + F_81(x) + F_99(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_7(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_88(x))
Eq(F_84(x), F_85(x, 1))
Eq(F_85(x, k_0), F_75(x) + F_86(x, k_0))
Eq(F_86(x, k_0), F_8(x)*F_87(x, k_0))
Eq(F_87(x, k_0), -F_16(x, 1) + (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_88(x), F_128(x) + F_26(x) + F_89(x) + F_90(x) + F_92(x))
Eq(F_89(x), F_7(x)*F_75(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_7(x)*F_88(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_7(x)*F_77(x)**2*F_94(x))
Eq(F_94(x), -F_122(x) + F_95(x))
Eq(F_95(x), F_101(x) + F_26(x) + F_96(x) + F_99(x))
Eq(F_96(x), F_7(x)*F_8(x)*F_97(x))
Eq(F_97(x), F_98(x, 1))
Eq(F_98(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_7(x)*F_77(x)*F_95(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_7(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_7(x)*F_97(x))
Eq(F_105(x), F_106(x, 1))
Eq(F_107(x, k_0), (-k_0*F_106(x, k_0) + F_106(x, 1))/(1 - k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_7(x))
Eq(F_109(x, k_0), F_108(x, k_0) + F_112(x, k_0))
Eq(F_110(x, k_0), F_109(x, k_0)*F_7(x))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_22(x, k_0), F_111(x, k_0) + F_29(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_115(x, k_0))
Eq(F_114(x, k_0), F_113(x, k_0)*F_7(x))
Eq(F_114(x, k_0), F_19(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x)*F_7(x)*F_98(x, k_0))
Eq(F_117(x), F_118(x)/(F_119(x)*F_57(x)*F_7(x)))
Eq(F_118(x), F_80(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_64(x)*F_77(x))
Eq(F_121(x), F_87(x, 1))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_7(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_77(x)*F_95(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_77(x)*F_95(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_7(x)*F_77(x))
Eq(F_130(x), F_103(x) - F_131(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_7(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_103(x)*F_77(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_103(x)*F_77(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_7(x)*F_75(x))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_7(x))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_143(x, k_0), F_142(x, k_0) + F_50(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_148(x, k_0) + F_165(x, k_0))
Eq(F_145(x, k_0), F_144(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_1(x) + F_145(x, k_0) + F_146(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_11(x, k_0)*F_15(x, k_0)*F_18(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_7(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_52(x))
Eq(F_151(x, k_0), F_150(x, k_0) + F_164(x))
Eq(F_151(x, k_0), F_152(x, k_0) + F_161(x))
Eq(F_152(x, k_0), (-k_0*F_153(x, k_0) + F_153(x, 1))/(1 - k_0))
Eq(F_154(x, k_0), F_153(x, k_0) + F_156(x, k_0))
Eq(F_155(x, k_0), F_154(x, k_0)*F_7(x))
Eq(F_10(x, k_0), F_13(x, k_0) + F_155(x, k_0) + F_31(x))
Eq(F_156(x, k_0), F_157(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0)*F_7(x))
Eq(F_158(x, k_0), (-k_0*F_159(x, k_0) + F_159(x, 1))/(1 - k_0))
Eq(F_160(x, k_0), F_159(x, k_0)*F_7(x))
Eq(F_22(x, k_0), F_160(x, k_0) + F_24(x, k_0) + F_34(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_7(x))
Eq(F_163(x), F_158(x, 1))
Eq(F_164(x), F_154(x, 1))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_7(x)*F_85(x, k_0))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_7(x))
Eq(F_169(x), F_170(x) - F_187(x))
Eq(F_170(x), F_171(x)/F_77(x))
Eq(F_171(x), F_172(x) - F_181(x))
Eq(F_172(x), F_173(x)/F_7(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_175(x) + F_182(x) + F_184(x) + F_26(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_177(x)*F_7(x))
Eq(F_177(x), F_178(x) + F_181(x))
Eq(F_178(x), F_179(x)*F_77(x))
Eq(F_179(x), F_174(x) + F_180(x))
Eq(F_180(x), F_8(x) + F_94(x))
Eq(F_181(x), F_126(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_121(x)*F_7(x)*F_8(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_186(x)*F_7(x))
Eq(F_186(x), F_150(x, 1))
Eq(F_187(x), F_95(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": 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": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "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, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "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": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 1], [1, 1], [1, 0], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 1], [1, 1], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 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