01342_01432_03142_03412_04132_04312_30142_30412
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3028, 16696, 94374, 543828, 3182646, 18864084, 113006524, 683119088, 4161653752, 25525347772, 157490549854, 976827148808, 6087139664582, 38091807447792, 239273172136908, 1508158465014088, 9535808024275760, 60465777556236488, 384416234806559832, 2449875728029138204, 15647939146230519056, 100154438764619325696, 642273327683308612514, 4126191056525436210644, 26552613676176015455650, 171138352465928415027136, 1104657035007804549335610, 7140182638134568554406480, 46212339439451282176454386, 299461750955504614280826892, 1942809267056345725468789200, 12618198647052786180695008112, 82038561271631256512632765360, 533911385079982453688398392500, 3477999351504046925326693708042, 22676666880314577386717342578844, 147978966694155550315899281331398, 966439591899570174020223258934832, 6316659251529708994120503669920500, 41316479927691159711095167090471992, 270438413923573174765045816052008440, 1771371310878091399558933181584481644, 11610067840560546679714153513547527622, 76143413178169836650354308329257929304, 499679516980199107349274544296413443446, 3280969547190753102163826409234421784532, 21555331297994939691270178120057809937192, 141690260555686994061776388957195870764628, 931857559080882328150319612389028276080372, 6131619673884765529538333819658366734838452, 40365409722542650227784537447519102053097882, 265854941861911942166567130824226524670557212, 1751759319696589044774793566542251267608534026, 11547605007767993860009830552930545032312827128, 76153693345298638917266490312448019066654816696, 502418560872629294886873832392063579759771593252, 3315968558194162288252513132455316782437562086944, 21893731827096488841582906941809013325613651269724, 144606805656503272400049958972247552803933683533650, 955459627629884564184392486382630458828607018269448, 6315183299075116696072898812957151355628128637065310, 41754678163174239098798602737273760583670834884237948, 276163084844912940683701197135349418629956034499276900, 1827104313260560762340321304491381386193766076236157792, 12091895768273660686863251185121355991460200263735547760, 80048840746828666644103180271991208732515665461174191720, 530080366774648715277263487366658340641305740643932282014, 3511162889786656656869679466123111395769890058409074342236, 23263739592735177096751005211515461895695988271271157597766, 154178638206924689028208461640587248467725740085373118930788, 1022073129232405676901468610463546248448137434089656445035728, 6777193747947381645564203855997366519672044607902769788251272, 44949533401401887287757651135693659132096652101129115068142776, 298198274243465179438792825702647936085732202178697193921807376, 1978732613703588754053858484749454968185889578005982702450830706, 13133141976325281199894622898172859296531744902362685240699687920, 87186108130932073672351410197048626169624330829662450778358025718, 578922915395537774570243530362397149711921948198495784675064126148, 3844914963811432125118401699565252115298321214634944303340098917564, 25541307186587921116310653311088779428286629172570452348216638150368, 169702324887748215945510416054901604825163098380421329765291108134552, 1127765316294624062283792133273624920566229339616183453783578065375936, 7496076229555641927792324146515624628026535721345173549851624496202348, 49834681492177295096469168047463139011533124985638404991431019982550140, 331367558552626928019593523765677247886174220789499802051167046223125036, 2203774400121045656538612258693636379978345803419376627908447648016573320, 14658901204257118531384074452901342921418869642029951972185135474020019242, 97523928717999702223824670168895838683830433950757943270942908869528131068, 648925508501360612642377137956455183428002234787514472607957241456818213566, 4318678176914034753448055155794232872470043139007097360588916962864574558044, 28746016839114050069297965605134630641638270426097204000786098244163059146456, 191370015556836347664884232780392883729732238903425949066770935633416567020720, 1274201410534420303501083293343489751565565068977340299746359343335908919286172, 8485332716614470869937130987966497353671193485053144133640107876802368266340916
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24695/
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[86,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[86,x]
F[7,x] = F[8,x,1]
F[9,x,k[0]] = F[13,x,k[0]]*F[8,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[54,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[15,x,k[0]]+F[29,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[13,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[26,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[13,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[13,x,k[0]]*F[23,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[13,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[16,x,k[0]]+F[26,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[39,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[13,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[22,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[24,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[35,x]+F[36,x,k[0]]+F[38,x,k[0]]
F[35,x] = 0
F[36,x,k[0]] = F[13,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[20,x,k[0]]+F[34,x,k[0]]
F[38,x,k[0]] = F[13,x,k[0]]*F[33,x,k[0]]
F[39,x,k[0]] = F[35,x]+F[40,x,k[0]]+F[46,x,k[0]]
F[40,x,k[0]] = F[13,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[28,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[50,x,k[0]]
F[43,x,k[0]] = F[35,x]+F[44,x,k[0]]+F[46,x,k[0]]
F[44,x,k[0]] = F[13,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = F[16,x,k[0]]+F[43,x,k[0]]
F[46,x,k[0]] = F[13,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[24,x,k[0]]+F[43,x,k[0]]
F[49,x,k[0]] = F[34,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = 2*F[35,x]+F[51,x,k[0]]+F[53,x,k[0]]
F[51,x,k[0]] = F[13,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[26,x,k[0]]+F[50,x,k[0]]
F[53,x,k[0]] = F[13,x,k[0]]*F[42,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]*F[86,x]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = -k[0]*(F[10,x,1]-F[10,x,k[0]])/(-1+k[0])
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[13,x,k[0]]*F[60,x,k[0]]
F[61,x,k[0]] = F[60,x,k[0]]*F[86,x]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,1,k[0]]
F[63,x,k[0],k[1]] = F[64,x,k[0]*k[1],k[1]]
F[64,x,k[0],k[1]] = F[374,x,k[0],k[1]]+F[65,x,k[1]]
F[65,x,k[0]] = F[2,x]+F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[13,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[70,x,k[0]]
F[69,x,k[0]] = F[15,x,k[0]]*F[2,x]*F[22,x,k[0]]
F[70,x,k[0]] = F[245,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[65,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]*F[86,x]
F[74,x,k[0]] = F[117,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[111,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,1,k[0]]
F[77,x,k[0],k[1]] = F[78,x,k[0]]+F[95,x,k[0],k[1]]
F[78,x,k[0]] = F[79,x,k[0]]+F[89,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[81,x,k[0]]
F[80,x,k[0]] = F[0,x]*F[13,x,k[0]]
F[81,x,k[0]] = F[82,x]*F[87,x,k[0]]
F[82,x] = F[83,x]
F[83,x] = F[1,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[83,x]*F[86,x]
F[86,x] = x
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[13,x,k[0]]*F[24,x,k[0]]
F[89,x,k[0]] = F[82,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[13,x,k[0]]*F[92,x,k[0]]
F[92,x,k[0]] = F[16,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[39,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[36,x,k[0]]
F[95,x,k[0],k[1]] = F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = F[109,x,k[1]]*F[13,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[103,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[100,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[13,x,k[0]]*F[32,x,k[0]]
F[102,x,k[0]] = F[11,x,k[0]]+F[99,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[108,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[2,x]
F[105,x,k[0]] = F[106,x]*F[11,x,k[0]]
F[106,x] = F[107,x]
F[107,x] = F[82,x]*F[86,x]
F[108,x,k[0]] = F[100,x,k[0]]*F[106,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[16,x,k[0]]
F[110,x,k[0]] = F[15,x,k[0]]*F[20,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[5,x]
F[112,x,k[0]] = F[113,x,k[0]]+F[86,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[115,x,k[0]]+F[35,x]
F[114,x,k[0]] = F[16,x,k[0]]*F[86,x]
F[115,x,k[0]] = F[116,x,k[0]]*F[13,x,k[0]]
F[116,x,k[0]] = F[112,x,k[0]]
F[117,x,k[0]] = F[118,x,1,k[0]]
F[119,x,k[0],k[1]] = F[118,x,k[0],k[1]]+F[372,x,k[0],k[1]]
F[119,x,k[0],k[1]] = F[120,x,k[1]]+F[234,x,k[0],k[1]]
F[121,x,k[0]] = F[120,x,k[0]]+F[371,x,k[0]]
F[122,x,k[0]] = F[121,x,k[0]]*F[86,x]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[5,x]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[16,x,k[0]]*F[2,x]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[86,x]
F[129,x,k[0]] = F[130,x,k[0]]+F[207,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[109,x,k[0]]*F[132,x]*F[86,x]
F[132,x] = F[133,x]+F[176,x]
F[133,x] = F[134,x,1]
F[134,x,k[0]] = F[135,x,k[0]]+F[173,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]+F[138,x]
F[136,x,k[0]] = F[137,x]+F[173,x,k[0]]
F[137,x] = F[1,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[86,x]
F[140,x] = F[141,x]+F[149,x]
F[141,x] = F[1,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[86,x]
F[144,x] = F[141,x]+F[145,x]
F[145,x] = F[146,x]+F[84,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[86,x]
F[148,x] = F[142,x]+F[146,x]
F[149,x] = F[150,x]+F[158,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[86,x]
F[152,x] = F[153,x]+F[83,x]
F[153,x] = F[106,x]+F[154,x]
F[154,x] = F[155,x]+F[157,x]+F[35,x]
F[155,x] = F[156,x]*F[86,x]
F[156,x] = F[154,x]+F[84,x]
F[157,x] = F[153,x]*F[86,x]
F[158,x] = F[159,x]+F[165,x]+F[35,x]
F[159,x] = F[160,x]*F[86,x]
F[160,x] = F[148,x]+F[161,x]
F[161,x] = F[162,x]+F[169,x]
F[162,x] = F[163,x]+F[165,x]+F[35,x]
F[163,x] = F[164,x]*F[86,x]
F[164,x] = F[142,x]+F[162,x]
F[165,x] = F[166,x]*F[86,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[106,x]+F[162,x]
F[168,x] = F[154,x]+F[169,x]
F[169,x] = 2*F[35,x]+F[170,x]+F[172,x]
F[170,x] = F[171,x]*F[86,x]
F[171,x] = F[146,x]+F[169,x]
F[172,x] = F[161,x]*F[86,x]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[13,x,k[0]]*F[175,x]*F[32,x,k[0]]
F[175,x] = F[137,x]+F[138,x]
F[176,x] = F[177,x,1]
F[177,x,k[0]] = F[178,x,k[0]]+F[179,x,k[0]]
F[178,x,k[0]] = F[103,x,k[0]]+F[54,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]+F[200,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[86,x]
F[182,x,k[0]] = F[183,x,k[0]]+F[194,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]+F[185,x,k[0]]
F[184,x,k[0]] = F[180,x,k[0]]+F[30,x,k[0]]
F[185,x,k[0]] = F[186,x,1,k[0]]
F[186,x,k[0],k[1]] = F[187,x,k[0],k[1]]
F[187,x,k[0],k[1]] = F[13,x,k[1]]*F[188,x,k[0],k[1]]
F[188,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[190,x,k[0],k[1]]
F[189,x,k[0],k[1]] = F[10,x,k[0]]+F[186,x,k[0],k[1]]
F[190,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[191,x,k[0],k[1]]
F[191,x,k[0],k[1]] = F[192,x,k[0],k[1]]
F[192,x,k[0],k[1]] = F[193,x,k[0],k[1]]*F[86,x]
F[193,x,k[0],k[1]] = -k[0]*(F[190,x,1,k[1]]-F[190,x,k[0],k[1]])/(-1+k[0])
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[13,x,k[0]]*F[196,x,k[0]]*F[22,x,k[0]]
F[196,x,k[0]] = F[194,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,1,k[0]]
F[198,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[199,x,k[1]]
F[199,x,k[0]] = F[0,x]+F[184,x,k[0]]
F[200,x,k[0]] = F[201,x,1,k[0]]
F[201,x,k[0],k[1]] = F[202,x,k[0]*k[1],k[1]]
F[202,x,k[0],k[1]] = F[203,x,k[0],k[1]]
F[203,x,k[0],k[1]] = F[13,x,k[1]]*F[204,x,k[0],k[1]]
F[204,x,k[0],k[1]] = F[205,x,k[0],k[1]]+F[206,x,k[0],k[1]]
F[205,x,k[0],k[1]] = F[202,x,k[0],k[1]]+F[54,x,k[0]]
F[206,x,k[0],k[1]] = F[191,x,k[0],k[1]]+F[205,x,k[0],k[1]]
F[208,x,k[0]] = F[207,x,k[0]]+F[349,x,k[0]]
F[208,x,k[0]] = F[209,x,1,k[0]]
F[210,x,k[0],k[1]] = F[209,x,k[0],k[1]]+F[360,x,k[0],k[1]]
F[211,x,k[0],k[1]] = F[13,x,k[0]]*F[210,x,k[0],k[1]]
F[211,x,k[0],k[1]] = F[212,x,k[0],k[1]]
F[212,x,k[0],k[1]] = F[213,x,k[0],k[1]]
F[213,x,k[0],k[1]] = F[13,x,k[0]]*F[214,x,k[0],k[1]]
F[214,x,k[0],k[1]] = F[215,x,k[0],k[1]]+F[341,x,k[1]]
F[215,x,k[0],k[1]] = F[216,x,k[0],k[1]]+F[226,x,k[0],k[1]]
F[216,x,k[0],k[1]] = k[1]*(F[217,x,k[0],1]-F[217,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[217,x,k[0],k[1]] = F[218,x,k[0],k[0]*k[1]]
F[218,x,k[0],k[1]] = F[219,x,k[0],k[1]]
F[219,x,k[0],k[1]] = F[220,x,k[0],k[1]]*F[86,x]
F[220,x,k[0],k[1]] = F[221,x,k[0],k[1]]+F[223,x,k[0],k[1]]
F[221,x,k[0],k[1]] = F[222,x,k[1]]+F[95,x,k[0],k[1]]
F[222,x,k[0]] = F[0,x]*F[16,x,k[0]]
F[223,x,k[0],k[1]] = F[224,x,k[0],k[1]]*F[5,x]
F[224,x,k[0],k[1]] = F[16,x,k[1]]+F[225,x,k[0],k[1]]
F[225,x,k[0],k[1]] = k[0]*F[113,x,k[1]]
F[226,x,k[0],k[1]] = k[1]*(F[227,x,k[0],1]-F[227,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[227,x,k[0],k[1]] = F[228,x,k[0],k[0]*k[1]]
F[229,x,k[0],k[1]] = F[228,x,k[0],k[1]]+F[273,x,k[0]]
F[229,x,k[0],k[1]] = F[230,x,k[0],k[1]]+F[64,x,k[0],k[1]]
F[230,x,k[0],k[1]] = F[231,x,k[0],k[1]]
F[231,x,k[0],k[1]] = F[232,x,k[0],k[1]]*F[86,x]
F[232,x,k[0],k[1]] = F[118,x,k[0],k[1]]+F[233,x,k[0],k[1]]
F[233,x,k[0],k[1]] = (F[234,x,k[0],k[1]]-F[234,x,1,k[1]])/(-1+k[0])
F[234,x,k[0],k[1]] = F[235,x,k[0],k[1]]+F[252,x,k[0],k[1]]
F[235,x,k[0],k[1]] = F[236,x,k[0],k[1]]+F[249,x,k[0],k[1]]
F[236,x,k[0],k[1]] = F[10,x,k[0]]+F[237,x,k[0],k[1]]
F[237,x,k[0],k[1]] = F[238,x,k[0],k[1]]
F[238,x,k[0],k[1]] = F[13,x,k[0]]*F[239,x,k[0],k[1]]
F[239,x,k[0],k[1]] = F[240,x,k[0],k[1]]+F[243,x,k[1]]
F[240,x,k[0],k[1]] = k[1]*(F[241,x,k[0],1]-F[241,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[241,x,k[0],k[1]] = F[242,x,k[0],k[0]*k[1]]
F[242,x,k[0],k[1]] = F[221,x,k[0],k[1]]+F[228,x,k[0],k[1]]
F[243,x,k[0]] = F[244,x,k[0]]+F[245,x,k[0]]
F[244,x,k[0]] = F[0,x]*F[15,x,k[0]]*F[20,x,k[0]]
F[246,x,k[0],k[1]] = F[226,x,k[0],k[1]]+F[245,x,k[1]]
F[214,x,k[0],k[1]] = F[246,x,k[0],k[1]]+F[247,x,k[0],k[1]]
F[247,x,k[0],k[1]] = F[216,x,k[0],k[1]]+F[248,x,k[1]]
F[248,x,k[0]] = F[15,x,k[0]]*F[2,x]*F[20,x,k[0]]
F[249,x,k[0],k[1]] = F[250,x,k[0],k[1]]
F[250,x,k[0],k[1]] = F[251,x,k[0],k[1]]*F[86,x]
F[251,x,k[0],k[1]] = -k[0]*(-F[234,x,k[0],k[1]]+F[234,x,1,k[1]])/(-1+k[0])
F[252,x,k[0],k[1]] = k[0]*F[253,x,k[1]]
F[253,x,k[0]] = F[254,x,k[0]]
F[255,x,k[0]] = F[254,x,k[0]]+F[271,x,k[0]]
F[256,x,k[0]] = F[255,x,k[0]]+F[265,x,k[0]]
F[257,x,k[0]] = F[256,x,k[0]]*F[86,x]
F[257,x,k[0]] = F[258,x,k[0]]
F[259,x,k[0]] = F[258,x,k[0]]+F[261,x,k[0]]
F[260,x,k[0]] = F[13,x,k[0]]*F[259,x,k[0]]
F[260,x,k[0]] = F[10,x,k[0]]
F[261,x,k[0]] = F[262,x,1,k[0]]
F[262,x,k[0],k[1]] = F[263,x,k[0]*k[1],k[1]]
F[263,x,k[0],k[1]] = F[236,x,k[0],k[1]]+F[264,x,k[1]]
F[264,x,k[0]] = F[15,x,k[0]]+F[65,x,k[0]]
F[265,x,k[0]] = F[266,x,1,k[0]]
F[266,x,k[0],k[1]] = (-F[267,x,1,k[1]]*k[1]+F[267,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[267,x,k[0],k[1]] = F[268,x,k[0]*k[1],k[1]]
F[268,x,k[0],k[1]] = F[235,x,k[0],k[1]]+F[269,x,k[1]]
F[269,x,k[0]] = F[270,x,k[0]]+F[71,x,k[0]]
F[270,x,k[0]] = F[0,x]*F[15,x,k[0]]
F[272,x,k[0]] = F[13,x,k[0]]*F[271,x,k[0]]
F[272,x,k[0]] = F[125,x,k[0]]
F[273,x,k[0]] = F[274,x,k[0]]+F[275,x,k[0]]
F[274,x,k[0]] = F[2,x]+F[54,x,k[0]]
F[275,x,k[0]] = F[276,x,k[0]]
F[276,x,k[0]] = F[277,x,k[0]]*F[86,x]
F[277,x,k[0]] = F[278,x,k[0]]+F[281,x,k[0]]
F[278,x,k[0]] = (F[279,x,k[0]]-F[279,x,1])/(-1+k[0])
F[279,x,k[0]] = F[280,x,k[0]]+F[78,x,k[0]]
F[280,x,k[0]] = F[13,x,k[0]]*F[5,x]
F[281,x,k[0]] = 1/(-1+k[0])*(F[282,x,k[0]]*k[0]-F[282,x,1])
F[282,x,k[0]] = F[273,x,k[0]]+F[283,x,k[0]]
F[283,x,k[0]] = F[284,x]+F[338,x,k[0]]
F[284,x] = -F[320,x]+F[285,x]
F[285,x] = -F[289,x]+F[286,x]
F[286,x] = 1/F[86,x]*F[287,x]
F[287,x] = F[288,x]
F[288,x] = -F[2,x]+F[5,x]
F[289,x] = F[290,x]
F[290,x] = F[291,x]*F[86,x]
F[291,x] = F[292,x,1]
F[292,x,k[0]] = F[293,x,k[0]]+F[297,x]
F[293,x,k[0]] = F[294,x,k[0]]+F[8,x,k[0]]
F[294,x,k[0]] = F[295,x,k[0]]
F[295,x,k[0]] = F[296,x,k[0]]*F[86,x]
F[296,x,k[0]] = 1/(-1+k[0])*(F[292,x,k[0]]*k[0]-F[292,x,1])
F[297,x] = F[298,x]
F[298,x] = F[299,x]*F[86,x]
F[299,x] = F[300,x]+F[302,x]
F[300,x] = F[289,x]+F[301,x]
F[301,x] = F[285,x]+F[4,x]
F[302,x] = F[303,x]
F[303,x] = F[300,x]*F[304,x]*F[86,x]
F[304,x] = F[305,x]+F[308,x]
F[305,x] = F[306,x]+F[82,x]
F[306,x] = F[307,x]
F[307,x] = F[304,x]*F[82,x]*F[86,x]
F[308,x] = F[309,x]
F[309,x] = F[310,x]+F[5,x]
F[310,x] = -F[313,x]+F[311,x]
F[311,x] = F[312,x]
F[312,x] = F[291,x]*F[86,x]
F[313,x] = -F[328,x]+F[314,x]
F[314,x] = -F[317,x]+F[315,x]
F[315,x] = 1/F[86,x]*F[316,x]
F[316,x] = F[288,x]
F[317,x] = -F[321,x]+F[318,x]
F[318,x] = 1/F[86,x]*F[319,x]
F[319,x] = F[320,x]
F[320,x] = F[2,x]+F[288,x]
F[321,x] = F[322,x]+F[325,x]
F[322,x] = F[0,x]+F[323,x]
F[323,x] = F[324,x]
F[324,x] = F[0,x]*F[304,x]*F[86,x]
F[325,x] = F[326,x]+F[328,x]
F[326,x] = F[327,x]
F[327,x] = F[7,x]*F[86,x]
F[328,x] = F[329,x]
F[329,x] = F[330,x]*F[86,x]
F[330,x] = F[331,x,1]
F[331,x,k[0]] = F[332,x,k[0]]+F[335,x,k[0]]
F[332,x,k[0]] = F[333,x,k[0],1]
F[333,x,k[0],k[1]] = F[237,x,k[0],k[1]]+F[334,x,k[1]]
F[334,x,k[0]] = F[16,x,k[0]]+F[66,x,k[0]]
F[335,x,k[0]] = F[336,x,k[0]]
F[336,x,k[0]] = F[337,x,k[0]]*F[86,x]
F[337,x,k[0]] = 1/(-1+k[0])*(F[331,x,k[0]]*k[0]-F[331,x,1])
F[338,x,k[0]] = k[0]*F[339,x]
F[339,x] = F[340,x]
F[340,x] = F[86,x]^2*F[302,x]
F[341,x,k[0]] = F[342,x,k[0]]+F[343,x,k[0]]
F[342,x,k[0]] = F[20,x,k[0]]*F[65,x,k[0]]
F[343,x,k[0]] = F[344,x,k[0]]
F[344,x,k[0]] = F[345,x,k[0]]*F[86,x]
F[345,x,k[0]] = F[346,x,k[0]]+F[353,x,k[0]]
F[346,x,k[0]] = F[347,x,k[0]]+F[349,x,k[0]]
F[347,x,k[0]] = F[15,x,k[0]]*F[20,x,k[0]]*F[348,x]
F[348,x] = F[0,x]+F[326,x]
F[349,x,k[0]] = F[350,x,k[0]]
F[350,x,k[0]] = F[348,x]*F[351,x,k[0]]*F[86,x]
F[352,x,k[0]] = F[0,x]*F[351,x,k[0]]*F[86,x]
F[352,x,k[0]] = F[245,x,k[0]]
F[353,x,k[0]] = F[13,x,k[0]]*F[354,x,k[0]]
F[354,x,k[0]] = F[355,x,1,k[0]]
F[355,x,k[0],k[1]] = F[356,x,k[0],k[0]*k[1]]
F[356,x,k[0],k[1]] = F[236,x,k[0],k[1]]+F[357,x,k[0],k[1]]
F[357,x,k[0],k[1]] = F[358,x,k[0],k[1]]
F[358,x,k[0],k[1]] = F[359,x,k[0],k[1]]*F[86,x]
F[359,x,k[0],k[1]] = -k[0]*(F[356,x,1,k[1]]-F[356,x,k[0],k[1]])/(-1+k[0])
F[360,x,k[0],k[1]] = F[361,x,k[0],k[1]]+F[362,x,k[0],k[1]]
F[361,x,k[0],k[1]] = F[20,x,k[1]]*F[274,x,k[0]]
F[363,x,k[0],k[1]] = F[362,x,k[0],k[1]]+F[367,x,k[0],k[1]]
F[363,x,k[0],k[1]] = F[364,x,k[0],k[1]]+F[365,x,k[0],k[1]]
F[364,x,k[0],k[1]] = F[15,x,k[1]]*F[22,x,k[1]]*F[274,x,k[0]]
F[365,x,k[0],k[1]] = F[366,x,k[0],k[1]]
F[366,x,k[0],k[1]] = F[13,x,k[0]]*F[15,x,k[1]]*F[177,x,k[0]]*F[22,x,k[1]]
F[367,x,k[0],k[1]] = F[368,x,k[0],k[1]]+F[369,x,k[0]]
F[368,x,k[0],k[1]] = F[22,x,k[1]]*F[274,x,k[0]]
F[369,x,k[0]] = F[370,x,k[0]]
F[370,x,k[0]] = F[13,x,k[0]]*F[177,x,k[0]]
F[371,x,k[0]] = F[234,x,1,k[0]]
F[372,x,k[0],k[1]] = F[220,x,k[0],k[1]]+F[373,x,k[0]]
F[373,x,k[0]] = F[279,x,k[0]]+F[4,x]
F[374,x,k[0],k[1]] = F[212,x,k[0],k[1]]+F[54,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \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_{86}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{29}\! \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_{13}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \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_{13}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = 2 F_{35}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -\frac{y \left(F_{10}\! \left(x , 1\right)-F_{10}\! \left(x , y\right)\right)}{-1+y}
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , 1, y\right)
F_{63}\! \left(x , y , z\right) = F_{64}\! \left(x , y z , z\right)
F_{64}\! \left(x , y , z\right) = F_{374}\! \left(x , y , z\right)+F_{65}\! \left(x , z\right)
F_{65}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{2}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{245}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , 1, y\right)
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , y\right)+F_{95}\! \left(x , y , z\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{1}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = x
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{82}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{95}\! \left(x , y , z\right) = F_{96}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = F_{109}\! \left(x , z\right) F_{13}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x \right) F_{11}\! \left(x , y\right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{82}\! \left(x \right) F_{86}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{106}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , 1, y\right)
F_{119}\! \left(x , y , z\right) = F_{118}\! \left(x , y , z\right)+F_{372}\! \left(x , y , z\right)
F_{119}\! \left(x , y , z\right) = F_{120}\! \left(x , z\right)+F_{234}\! \left(x , y , z\right)
F_{121}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{371}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{132}\! \left(x \right) F_{86}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{176}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x , 1\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{138}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x \right)+F_{173}\! \left(x , y\right)
F_{137}\! \left(x \right) = F_{1}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{86}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{149}\! \left(x \right)
F_{141}\! \left(x \right) = F_{1}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{86}\! \left(x \right)
F_{144}\! \left(x \right) = F_{141}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{84}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{86}\! \left(x \right)
F_{148}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{158}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{86}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{83}\! \left(x \right)
F_{153}\! \left(x \right) = F_{106}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{157}\! \left(x \right)+F_{35}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{86}\! \left(x \right)
F_{156}\! \left(x \right) = F_{154}\! \left(x \right)+F_{84}\! \left(x \right)
F_{157}\! \left(x \right) = F_{153}\! \left(x \right) F_{86}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{165}\! \left(x \right)+F_{35}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{86}\! \left(x \right)
F_{160}\! \left(x \right) = F_{148}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{169}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{165}\! \left(x \right)+F_{35}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{86}\! \left(x \right)
F_{164}\! \left(x \right) = F_{142}\! \left(x \right)+F_{162}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{86}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{106}\! \left(x \right)+F_{162}\! \left(x \right)
F_{168}\! \left(x \right) = F_{154}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{170}\! \left(x \right)+F_{172}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{86}\! \left(x \right)
F_{171}\! \left(x \right) = F_{146}\! \left(x \right)+F_{169}\! \left(x \right)
F_{172}\! \left(x \right) = F_{161}\! \left(x \right) F_{86}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{175}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{175}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x , 1\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , 1, y\right)
F_{186}\! \left(x , y , z\right) = F_{187}\! \left(x , y , z\right)
F_{187}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{188}\! \left(x , y , z\right)
F_{188}\! \left(x , y , z\right) = F_{189}\! \left(x , y , z\right)+F_{190}\! \left(x , y , z\right)
F_{189}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right)+F_{186}\! \left(x , y , z\right)
F_{190}\! \left(x , y , z\right) = F_{189}\! \left(x , y , z\right)+F_{191}\! \left(x , y , z\right)
F_{191}\! \left(x , y , z\right) = F_{192}\! \left(x , y , z\right)
F_{192}\! \left(x , y , z\right) = F_{193}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{193}\! \left(x , y , z\right) = -\frac{y \left(F_{190}\! \left(x , 1, z\right)-F_{190}\! \left(x , y , z\right)\right)}{-1+y}
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{196}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , 1, y\right)
F_{198}\! \left(x , y , z\right) = F_{189}\! \left(x , y , z\right)+F_{199}\! \left(x , z\right)
F_{199}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{184}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , 1, y\right)
F_{201}\! \left(x , y , z\right) = F_{202}\! \left(x , y z , z\right)
F_{202}\! \left(x , y , z\right) = F_{203}\! \left(x , y , z\right)
F_{203}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{204}\! \left(x , y , z\right)
F_{204}\! \left(x , y , z\right) = F_{205}\! \left(x , y , z\right)+F_{206}\! \left(x , y , z\right)
F_{205}\! \left(x , y , z\right) = F_{202}\! \left(x , y , z\right)+F_{54}\! \left(x , y\right)
F_{206}\! \left(x , y , z\right) = F_{191}\! \left(x , y , z\right)+F_{205}\! \left(x , y , z\right)
F_{208}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{349}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , 1, y\right)
F_{210}\! \left(x , y , z\right) = F_{209}\! \left(x , y , z\right)+F_{360}\! \left(x , y , z\right)
F_{211}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{210}\! \left(x , y , z\right)
F_{211}\! \left(x , y , z\right) = F_{212}\! \left(x , y , z\right)
F_{212}\! \left(x , y , z\right) = F_{213}\! \left(x , y , z\right)
F_{213}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{214}\! \left(x , y , z\right)
F_{214}\! \left(x , y , z\right) = F_{215}\! \left(x , y , z\right)+F_{341}\! \left(x , z\right)
F_{215}\! \left(x , y , z\right) = F_{216}\! \left(x , y , z\right)+F_{226}\! \left(x , y , z\right)
F_{216}\! \left(x , y , z\right) = \frac{z \left(F_{217}\! \left(x , y , 1\right)-F_{217}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{217}\! \left(x , y , z\right) = F_{218}\! \left(x , y , y z \right)
F_{218}\! \left(x , y , z\right) = F_{219}\! \left(x , y , z\right)
F_{219}\! \left(x , y , z\right) = F_{220}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{220}\! \left(x , y , z\right) = F_{221}\! \left(x , y , z\right)+F_{223}\! \left(x , y , z\right)
F_{221}\! \left(x , y , z\right) = F_{222}\! \left(x , z\right)+F_{95}\! \left(x , y , z\right)
F_{222}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{223}\! \left(x , y , z\right) = F_{224}\! \left(x , y , z\right) F_{5}\! \left(x \right)
F_{224}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right)+F_{225}\! \left(x , y , z\right)
F_{225}\! \left(x , y , z\right) = y F_{113}\! \left(x , z\right)
F_{226}\! \left(x , y , z\right) = \frac{z \left(F_{227}\! \left(x , y , 1\right)-F_{227}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{227}\! \left(x , y , z\right) = F_{228}\! \left(x , y , y z \right)
F_{229}\! \left(x , y , z\right) = F_{228}\! \left(x , y , z\right)+F_{273}\! \left(x , y\right)
F_{229}\! \left(x , y , z\right) = F_{230}\! \left(x , y , z\right)+F_{64}\! \left(x , y , z\right)
F_{230}\! \left(x , y , z\right) = F_{231}\! \left(x , y , z\right)
F_{231}\! \left(x , y , z\right) = F_{232}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{232}\! \left(x , y , z\right) = F_{118}\! \left(x , y , z\right)+F_{233}\! \left(x , y , z\right)
F_{233}\! \left(x , y , z\right) = -\frac{-F_{234}\! \left(x , y , z\right)+F_{234}\! \left(x , 1, z\right)}{-1+y}
F_{234}\! \left(x , y , z\right) = F_{235}\! \left(x , y , z\right)+F_{252}\! \left(x , y , z\right)
F_{235}\! \left(x , y , z\right) = F_{236}\! \left(x , y , z\right)+F_{249}\! \left(x , y , z\right)
F_{236}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right)+F_{237}\! \left(x , y , z\right)
F_{237}\! \left(x , y , z\right) = F_{238}\! \left(x , y , z\right)
F_{238}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{239}\! \left(x , y , z\right)
F_{239}\! \left(x , y , z\right) = F_{240}\! \left(x , y , z\right)+F_{243}\! \left(x , z\right)
F_{240}\! \left(x , y , z\right) = \frac{z \left(F_{241}\! \left(x , y , 1\right)-F_{241}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{241}\! \left(x , y , z\right) = F_{242}\! \left(x , y , y z \right)
F_{242}\! \left(x , y , z\right) = F_{221}\! \left(x , y , z\right)+F_{228}\! \left(x , y , z\right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)+F_{245}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{246}\! \left(x , y , z\right) = F_{226}\! \left(x , y , z\right)+F_{245}\! \left(x , z\right)
F_{214}\! \left(x , y , z\right) = F_{246}\! \left(x , y , z\right)+F_{247}\! \left(x , y , z\right)
F_{247}\! \left(x , y , z\right) = F_{216}\! \left(x , y , z\right)+F_{248}\! \left(x , z\right)
F_{248}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{2}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{249}\! \left(x , y , z\right) = F_{250}\! \left(x , y , z\right)
F_{250}\! \left(x , y , z\right) = F_{251}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{251}\! \left(x , y , z\right) = -\frac{y \left(-F_{234}\! \left(x , y , z\right)+F_{234}\! \left(x , 1, z\right)\right)}{-1+y}
F_{252}\! \left(x , y , z\right) = y F_{253}\! \left(x , z\right)
F_{253}\! \left(x , y\right) = F_{254}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{254}\! \left(x , y\right)+F_{271}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{265}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{256}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{258}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{259}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , 1, y\right)
F_{262}\! \left(x , y , z\right) = F_{263}\! \left(x , y z , z\right)
F_{263}\! \left(x , y , z\right) = F_{236}\! \left(x , y , z\right)+F_{264}\! \left(x , z\right)
F_{264}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , 1, y\right)
F_{266}\! \left(x , y , z\right) = -\frac{F_{267}\! \left(x , 1, z\right) z -y F_{267}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{267}\! \left(x , y , z\right) = F_{268}\! \left(x , y z , z\right)
F_{268}\! \left(x , y , z\right) = F_{235}\! \left(x , y , z\right)+F_{269}\! \left(x , z\right)
F_{269}\! \left(x , y\right) = F_{270}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{270}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{271}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{277}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{277}\! \left(x , y\right) = F_{278}\! \left(x , y\right)+F_{281}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = -\frac{-F_{279}\! \left(x , y\right)+F_{279}\! \left(x , 1\right)}{-1+y}
F_{279}\! \left(x , y\right) = F_{280}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{281}\! \left(x , y\right) = -\frac{-F_{282}\! \left(x , y\right) y +F_{282}\! \left(x , 1\right)}{-1+y}
F_{282}\! \left(x , y\right) = F_{273}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{284}\! \left(x \right)+F_{338}\! \left(x , y\right)
F_{284}\! \left(x \right) = -F_{320}\! \left(x \right)+F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = -F_{289}\! \left(x \right)+F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = \frac{F_{287}\! \left(x \right)}{F_{86}\! \left(x \right)}
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{289}\! \left(x \right) = F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = F_{291}\! \left(x \right) F_{86}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x , 1\right)
F_{292}\! \left(x , y\right) = F_{293}\! \left(x , y\right)+F_{297}\! \left(x \right)
F_{293}\! \left(x , y\right) = F_{294}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{295}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{296}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{296}\! \left(x , y\right) = -\frac{-F_{292}\! \left(x , y\right) y +F_{292}\! \left(x , 1\right)}{-1+y}
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{299}\! \left(x \right) F_{86}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)+F_{302}\! \left(x \right)
F_{300}\! \left(x \right) = F_{289}\! \left(x \right)+F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = F_{285}\! \left(x \right)+F_{4}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right)
F_{303}\! \left(x \right) = F_{300}\! \left(x \right) F_{304}\! \left(x \right) F_{86}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)+F_{308}\! \left(x \right)
F_{305}\! \left(x \right) = F_{306}\! \left(x \right)+F_{82}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{304}\! \left(x \right) F_{82}\! \left(x \right) F_{86}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right)+F_{5}\! \left(x \right)
F_{310}\! \left(x \right) = -F_{313}\! \left(x \right)+F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = F_{291}\! \left(x \right) F_{86}\! \left(x \right)
F_{313}\! \left(x \right) = -F_{328}\! \left(x \right)+F_{314}\! \left(x \right)
F_{314}\! \left(x \right) = -F_{317}\! \left(x \right)+F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = \frac{F_{316}\! \left(x \right)}{F_{86}\! \left(x \right)}
F_{316}\! \left(x \right) = F_{288}\! \left(x \right)
F_{317}\! \left(x \right) = -F_{321}\! \left(x \right)+F_{318}\! \left(x \right)
F_{318}\! \left(x \right) = \frac{F_{319}\! \left(x \right)}{F_{86}\! \left(x \right)}
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{2}\! \left(x \right)+F_{288}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right)+F_{325}\! \left(x \right)
F_{322}\! \left(x \right) = F_{0}\! \left(x \right)+F_{323}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = F_{0}\! \left(x \right) F_{304}\! \left(x \right) F_{86}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right)+F_{328}\! \left(x \right)
F_{326}\! \left(x \right) = F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{328}\! \left(x \right) = F_{329}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right) F_{86}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x , 1\right)
F_{331}\! \left(x , y\right) = F_{332}\! \left(x , y\right)+F_{335}\! \left(x , y\right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y , 1\right)
F_{333}\! \left(x , y , z\right) = F_{237}\! \left(x , y , z\right)+F_{334}\! \left(x , z\right)
F_{334}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{336}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{337}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{337}\! \left(x , y\right) = -\frac{-y F_{331}\! \left(x , y\right)+F_{331}\! \left(x , 1\right)}{-1+y}
F_{338}\! \left(x , y\right) = y F_{339}\! \left(x \right)
F_{339}\! \left(x \right) = F_{340}\! \left(x \right)
F_{340}\! \left(x \right) = F_{86} \left(x \right)^{2} F_{302}\! \left(x \right)
F_{341}\! \left(x , y\right) = F_{342}\! \left(x , y\right)+F_{343}\! \left(x , y\right)
F_{342}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{343}\! \left(x , y\right) = F_{344}\! \left(x , y\right)
F_{344}\! \left(x , y\right) = F_{345}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{345}\! \left(x , y\right) = F_{346}\! \left(x , y\right)+F_{353}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{347}\! \left(x , y\right)+F_{349}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{348}\! \left(x \right)
F_{348}\! \left(x \right) = F_{0}\! \left(x \right)+F_{326}\! \left(x \right)
F_{349}\! \left(x , y\right) = F_{350}\! \left(x , y\right)
F_{350}\! \left(x , y\right) = F_{348}\! \left(x \right) F_{351}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{352}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{351}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{352}\! \left(x , y\right) = F_{245}\! \left(x , y\right)
F_{353}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{354}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{355}\! \left(x , 1, y\right)
F_{355}\! \left(x , y , z\right) = F_{356}\! \left(x , y , y z \right)
F_{356}\! \left(x , y , z\right) = F_{236}\! \left(x , y , z\right)+F_{357}\! \left(x , y , z\right)
F_{357}\! \left(x , y , z\right) = F_{358}\! \left(x , y , z\right)
F_{358}\! \left(x , y , z\right) = F_{359}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{359}\! \left(x , y , z\right) = -\frac{y \left(F_{356}\! \left(x , 1, z\right)-F_{356}\! \left(x , y , z\right)\right)}{-1+y}
F_{360}\! \left(x , y , z\right) = F_{361}\! \left(x , y , z\right)+F_{362}\! \left(x , y , z\right)
F_{361}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{274}\! \left(x , y\right)
F_{363}\! \left(x , y , z\right) = F_{362}\! \left(x , y , z\right)+F_{367}\! \left(x , y , z\right)
F_{363}\! \left(x , y , z\right) = F_{364}\! \left(x , y , z\right)+F_{365}\! \left(x , y , z\right)
F_{364}\! \left(x , y , z\right) = F_{15}\! \left(x , z\right) F_{22}\! \left(x , z\right) F_{274}\! \left(x , y\right)
F_{365}\! \left(x , y , z\right) = F_{366}\! \left(x , y , z\right)
F_{366}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , z\right) F_{177}\! \left(x , y\right) F_{22}\! \left(x , z\right)
F_{367}\! \left(x , y , z\right) = F_{368}\! \left(x , y , z\right)+F_{369}\! \left(x , y\right)
F_{368}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{274}\! \left(x , y\right)
F_{369}\! \left(x , y\right) = F_{370}\! \left(x , y\right)
F_{370}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{177}\! \left(x , y\right)
F_{371}\! \left(x , y\right) = F_{234}\! \left(x , 1, y\right)
F_{372}\! \left(x , y , z\right) = F_{220}\! \left(x , y , z\right)+F_{373}\! \left(x , y\right)
F_{373}\! \left(x , y\right) = F_{279}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{374}\! \left(x , y , z\right) = F_{212}\! \left(x , y , z\right)+F_{54}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_86(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_86(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_9(x, k_0), F_13(x, k_0)*F_8(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_54(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_15(x, k_0) + F_29(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_13(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_26(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_13(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_13(x, k_0)*F_23(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_13(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_16(x, k_0) + F_26(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_39(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_13(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_22(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_24(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x) + F_36(x, k_0) + F_38(x, k_0))
Eq(F_35(x), 0)
Eq(F_36(x, k_0), F_13(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_20(x, k_0) + F_34(x, k_0))
Eq(F_38(x, k_0), F_13(x, k_0)*F_33(x, k_0))
Eq(F_39(x, k_0), F_35(x) + F_40(x, k_0) + F_46(x, k_0))
Eq(F_40(x, k_0), F_13(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_28(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_50(x, k_0))
Eq(F_43(x, k_0), F_35(x) + F_44(x, k_0) + F_46(x, k_0))
Eq(F_44(x, k_0), F_13(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), F_16(x, k_0) + F_43(x, k_0))
Eq(F_46(x, k_0), F_13(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_24(x, k_0) + F_43(x, k_0))
Eq(F_49(x, k_0), F_34(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), 2*F_35(x) + F_51(x, k_0) + F_53(x, k_0))
Eq(F_51(x, k_0), F_13(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_26(x, k_0) + F_50(x, k_0))
Eq(F_53(x, k_0), F_13(x, k_0)*F_42(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0)*F_86(x))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), -F_10(x, 1) + (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_13(x, k_0)*F_60(x, k_0))
Eq(F_61(x, k_0), F_60(x, k_0)*F_86(x))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, 1, k_0))
Eq(F_63(x, k_0, k_1), F_64(x, k_0*k_1, k_1))
Eq(F_64(x, k_0, k_1), F_374(x, k_0, k_1) + F_65(x, k_1))
Eq(F_65(x, k_0), F_2(x) + F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_13(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_70(x, k_0))
Eq(F_69(x, k_0), F_15(x, k_0)*F_2(x)*F_22(x, k_0))
Eq(F_70(x, k_0), F_245(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_65(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0)*F_86(x))
Eq(F_74(x, k_0), F_117(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_111(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, 1, k_0))
Eq(F_77(x, k_0, k_1), F_78(x, k_0) + F_95(x, k_0, k_1))
Eq(F_78(x, k_0), F_79(x, k_0) + F_89(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_81(x, k_0))
Eq(F_80(x, k_0), F_0(x)*F_13(x, k_0))
Eq(F_81(x, k_0), F_82(x)*F_87(x, k_0))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_1(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_83(x)*F_86(x))
Eq(F_86(x), x)
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_13(x, k_0)*F_24(x, k_0))
Eq(F_89(x, k_0), F_82(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_13(x, k_0)*F_92(x, k_0))
Eq(F_92(x, k_0), F_16(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_39(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_36(x, k_0))
Eq(F_95(x, k_0, k_1), F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), F_109(x, k_1)*F_13(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_103(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_100(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_13(x, k_0)*F_32(x, k_0))
Eq(F_102(x, k_0), F_11(x, k_0) + F_99(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_108(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_2(x))
Eq(F_105(x, k_0), F_106(x)*F_11(x, k_0))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_82(x)*F_86(x))
Eq(F_108(x, k_0), F_100(x, k_0)*F_106(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_16(x, k_0))
Eq(F_110(x, k_0), F_15(x, k_0)*F_20(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_5(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_86(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_115(x, k_0) + F_35(x))
Eq(F_114(x, k_0), F_16(x, k_0)*F_86(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_13(x, k_0))
Eq(F_116(x, k_0), F_112(x, k_0))
Eq(F_117(x, k_0), F_118(x, 1, k_0))
Eq(F_119(x, k_0, k_1), F_118(x, k_0, k_1) + F_372(x, k_0, k_1))
Eq(F_119(x, k_0, k_1), F_120(x, k_1) + F_234(x, k_0, k_1))
Eq(F_121(x, k_0), F_120(x, k_0) + F_371(x, k_0))
Eq(F_122(x, k_0), F_121(x, k_0)*F_86(x))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_5(x))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_16(x, k_0)*F_2(x))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_86(x))
Eq(F_129(x, k_0), F_130(x, k_0) + F_207(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_109(x, k_0)*F_132(x)*F_86(x))
Eq(F_132(x), F_133(x) + F_176(x))
Eq(F_133(x), F_134(x, 1))
Eq(F_134(x, k_0), F_135(x, k_0) + F_173(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0) + F_138(x))
Eq(F_136(x, k_0), F_137(x) + F_173(x, k_0))
Eq(F_137(x), F_1(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_86(x))
Eq(F_140(x), F_141(x) + F_149(x))
Eq(F_141(x), F_1(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_86(x))
Eq(F_144(x), F_141(x) + F_145(x))
Eq(F_145(x), F_146(x) + F_84(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_86(x))
Eq(F_148(x), F_142(x) + F_146(x))
Eq(F_149(x), F_150(x) + F_158(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_86(x))
Eq(F_152(x), F_153(x) + F_83(x))
Eq(F_153(x), F_106(x) + F_154(x))
Eq(F_154(x), F_155(x) + F_157(x) + F_35(x))
Eq(F_155(x), F_156(x)*F_86(x))
Eq(F_156(x), F_154(x) + F_84(x))
Eq(F_157(x), F_153(x)*F_86(x))
Eq(F_158(x), F_159(x) + F_165(x) + F_35(x))
Eq(F_159(x), F_160(x)*F_86(x))
Eq(F_160(x), F_148(x) + F_161(x))
Eq(F_161(x), F_162(x) + F_169(x))
Eq(F_162(x), F_163(x) + F_165(x) + F_35(x))
Eq(F_163(x), F_164(x)*F_86(x))
Eq(F_164(x), F_142(x) + F_162(x))
Eq(F_165(x), F_166(x)*F_86(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_106(x) + F_162(x))
Eq(F_168(x), F_154(x) + F_169(x))
Eq(F_169(x), F_170(x) + F_172(x) + 2*F_35(x))
Eq(F_170(x), F_171(x)*F_86(x))
Eq(F_171(x), F_146(x) + F_169(x))
Eq(F_172(x), F_161(x)*F_86(x))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_13(x, k_0)*F_175(x)*F_32(x, k_0))
Eq(F_175(x), F_137(x) + F_138(x))
Eq(F_176(x), F_177(x, 1))
Eq(F_177(x, k_0), F_178(x, k_0) + F_179(x, k_0))
Eq(F_178(x, k_0), F_103(x, k_0) + F_54(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0) + F_200(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0)*F_86(x))
Eq(F_182(x, k_0), F_183(x, k_0) + F_194(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0) + F_185(x, k_0))
Eq(F_184(x, k_0), F_180(x, k_0) + F_30(x, k_0))
Eq(F_185(x, k_0), F_186(x, 1, k_0))
Eq(F_186(x, k_0, k_1), F_187(x, k_0, k_1))
Eq(F_187(x, k_0, k_1), F_13(x, k_1)*F_188(x, k_0, k_1))
Eq(F_188(x, k_0, k_1), F_189(x, k_0, k_1) + F_190(x, k_0, k_1))
Eq(F_189(x, k_0, k_1), F_10(x, k_0) + F_186(x, k_0, k_1))
Eq(F_190(x, k_0, k_1), F_189(x, k_0, k_1) + F_191(x, k_0, k_1))
Eq(F_191(x, k_0, k_1), F_192(x, k_0, k_1))
Eq(F_192(x, k_0, k_1), F_193(x, k_0, k_1)*F_86(x))
Eq(F_193(x, k_0, k_1), -F_190(x, 1, k_1) + (k_0*F_190(x, k_0, k_1) - F_190(x, 1, k_1))/(k_0 - 1))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_13(x, k_0)*F_196(x, k_0)*F_22(x, k_0))
Eq(F_196(x, k_0), F_194(x, k_0) + F_197(x, k_0))
Eq(F_197(x, k_0), F_198(x, 1, k_0))
Eq(F_198(x, k_0, k_1), F_189(x, k_0, k_1) + F_199(x, k_1))
Eq(F_199(x, k_0), F_0(x) + F_184(x, k_0))
Eq(F_200(x, k_0), F_201(x, 1, k_0))
Eq(F_201(x, k_0, k_1), F_202(x, k_0*k_1, k_1))
Eq(F_202(x, k_0, k_1), F_203(x, k_0, k_1))
Eq(F_203(x, k_0, k_1), F_13(x, k_1)*F_204(x, k_0, k_1))
Eq(F_204(x, k_0, k_1), F_205(x, k_0, k_1) + F_206(x, k_0, k_1))
Eq(F_205(x, k_0, k_1), F_202(x, k_0, k_1) + F_54(x, k_0))
Eq(F_206(x, k_0, k_1), F_191(x, k_0, k_1) + F_205(x, k_0, k_1))
Eq(F_208(x, k_0), F_207(x, k_0) + F_349(x, k_0))
Eq(F_208(x, k_0), F_209(x, 1, k_0))
Eq(F_210(x, k_0, k_1), F_209(x, k_0, k_1) + F_360(x, k_0, k_1))
Eq(F_211(x, k_0, k_1), F_13(x, k_0)*F_210(x, k_0, k_1))
Eq(F_211(x, k_0, k_1), F_212(x, k_0, k_1))
Eq(F_212(x, k_0, k_1), F_213(x, k_0, k_1))
Eq(F_213(x, k_0, k_1), F_13(x, k_0)*F_214(x, k_0, k_1))
Eq(F_214(x, k_0, k_1), F_215(x, k_0, k_1) + F_341(x, k_1))
Eq(F_215(x, k_0, k_1), F_216(x, k_0, k_1) + F_226(x, k_0, k_1))
Eq(F_216(x, k_0, k_1), -F_217(x, k_0, 1) + (-k_0*F_217(x, k_0, 1) + k_1*F_217(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_217(x, k_0, k_1), F_218(x, k_0, k_0*k_1))
Eq(F_218(x, k_0, k_1), F_219(x, k_0, k_1))
Eq(F_219(x, k_0, k_1), F_220(x, k_0, k_1)*F_86(x))
Eq(F_220(x, k_0, k_1), F_221(x, k_0, k_1) + F_223(x, k_0, k_1))
Eq(F_221(x, k_0, k_1), F_222(x, k_1) + F_95(x, k_0, k_1))
Eq(F_222(x, k_0), F_0(x)*F_16(x, k_0))
Eq(F_223(x, k_0, k_1), F_224(x, k_0, k_1)*F_5(x))
Eq(F_224(x, k_0, k_1), F_16(x, k_1) + F_225(x, k_0, k_1))
Eq(F_225(x, k_0, k_1), k_0*F_113(x, k_1))
Eq(F_226(x, k_0, k_1), -F_227(x, k_0, 1) + (-k_0*F_227(x, k_0, 1) + k_1*F_227(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_227(x, k_0, k_1), F_228(x, k_0, k_0*k_1))
Eq(F_229(x, k_0, k_1), F_228(x, k_0, k_1) + F_273(x, k_0))
Eq(F_229(x, k_0, k_1), F_230(x, k_0, k_1) + F_64(x, k_0, k_1))
Eq(F_230(x, k_0, k_1), F_231(x, k_0, k_1))
Eq(F_231(x, k_0, k_1), F_232(x, k_0, k_1)*F_86(x))
Eq(F_232(x, k_0, k_1), F_118(x, k_0, k_1) + F_233(x, k_0, k_1))
Eq(F_233(x, k_0, k_1), -F_234(x, k_0, k_1) + (k_0*F_234(x, k_0, k_1) - F_234(x, 1, k_1))/(k_0 - 1))
Eq(F_234(x, k_0, k_1), F_235(x, k_0, k_1) + F_252(x, k_0, k_1))
Eq(F_235(x, k_0, k_1), F_236(x, k_0, k_1) + F_249(x, k_0, k_1))
Eq(F_236(x, k_0, k_1), F_10(x, k_0) + F_237(x, k_0, k_1))
Eq(F_237(x, k_0, k_1), F_238(x, k_0, k_1))
Eq(F_238(x, k_0, k_1), F_13(x, k_0)*F_239(x, k_0, k_1))
Eq(F_239(x, k_0, k_1), F_240(x, k_0, k_1) + F_243(x, k_1))
Eq(F_240(x, k_0, k_1), -F_241(x, k_0, 1) + (-k_0*F_241(x, k_0, 1) + k_1*F_241(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_241(x, k_0, k_1), F_242(x, k_0, k_0*k_1))
Eq(F_242(x, k_0, k_1), F_221(x, k_0, k_1) + F_228(x, k_0, k_1))
Eq(F_243(x, k_0), F_244(x, k_0) + F_245(x, k_0))
Eq(F_244(x, k_0), F_0(x)*F_15(x, k_0)*F_20(x, k_0))
Eq(F_246(x, k_0, k_1), F_226(x, k_0, k_1) + F_245(x, k_1))
Eq(F_214(x, k_0, k_1), F_246(x, k_0, k_1) + F_247(x, k_0, k_1))
Eq(F_247(x, k_0, k_1), F_216(x, k_0, k_1) + F_248(x, k_1))
Eq(F_248(x, k_0), F_15(x, k_0)*F_2(x)*F_20(x, k_0))
Eq(F_249(x, k_0, k_1), F_250(x, k_0, k_1))
Eq(F_250(x, k_0, k_1), F_251(x, k_0, k_1)*F_86(x))
Eq(F_251(x, k_0, k_1), -F_234(x, 1, k_1) + (k_0*F_234(x, k_0, k_1) - F_234(x, 1, k_1))/(k_0 - 1))
Eq(F_252(x, k_0, k_1), k_0*F_253(x, k_1))
Eq(F_253(x, k_0), F_254(x, k_0))
Eq(F_255(x, k_0), F_254(x, k_0) + F_271(x, k_0))
Eq(F_256(x, k_0), F_255(x, k_0) + F_265(x, k_0))
Eq(F_257(x, k_0), F_256(x, k_0)*F_86(x))
Eq(F_257(x, k_0), F_258(x, k_0))
Eq(F_259(x, k_0), F_258(x, k_0) + F_261(x, k_0))
Eq(F_260(x, k_0), F_13(x, k_0)*F_259(x, k_0))
Eq(F_260(x, k_0), F_10(x, k_0))
Eq(F_261(x, k_0), F_262(x, 1, k_0))
Eq(F_262(x, k_0, k_1), F_263(x, k_0*k_1, k_1))
Eq(F_263(x, k_0, k_1), F_236(x, k_0, k_1) + F_264(x, k_1))
Eq(F_264(x, k_0), F_15(x, k_0) + F_65(x, k_0))
Eq(F_265(x, k_0), F_266(x, 1, k_0))
Eq(F_266(x, k_0, k_1), (-k_0*F_267(x, k_0/k_1, k_1) + k_1*F_267(x, 1, k_1))/(-k_0 + k_1))
Eq(F_267(x, k_0, k_1), F_268(x, k_0*k_1, k_1))
Eq(F_268(x, k_0, k_1), F_235(x, k_0, k_1) + F_269(x, k_1))
Eq(F_269(x, k_0), F_270(x, k_0) + F_71(x, k_0))
Eq(F_270(x, k_0), F_0(x)*F_15(x, k_0))
Eq(F_272(x, k_0), F_13(x, k_0)*F_271(x, k_0))
Eq(F_272(x, k_0), F_125(x, k_0))
Eq(F_273(x, k_0), F_274(x, k_0) + F_275(x, k_0))
Eq(F_274(x, k_0), F_2(x) + F_54(x, k_0))
Eq(F_275(x, k_0), F_276(x, k_0))
Eq(F_276(x, k_0), F_277(x, k_0)*F_86(x))
Eq(F_277(x, k_0), F_278(x, k_0) + F_281(x, k_0))
Eq(F_278(x, k_0), -F_279(x, k_0) + (k_0*F_279(x, k_0) - F_279(x, 1))/(k_0 - 1))
Eq(F_279(x, k_0), F_280(x, k_0) + F_78(x, k_0))
Eq(F_280(x, k_0), F_13(x, k_0)*F_5(x))
Eq(F_281(x, k_0), (k_0*F_282(x, k_0) - F_282(x, 1))/(k_0 - 1))
Eq(F_282(x, k_0), F_273(x, k_0) + F_283(x, k_0))
Eq(F_283(x, k_0), F_284(x) + F_338(x, k_0))
Eq(F_284(x), F_285(x) - F_320(x))
Eq(F_285(x), F_286(x) - F_289(x))
Eq(F_286(x), F_287(x)/F_86(x))
Eq(F_287(x), F_288(x))
Eq(F_288(x), -F_2(x) + F_5(x))
Eq(F_289(x), F_290(x))
Eq(F_290(x), F_291(x)*F_86(x))
Eq(F_291(x), F_292(x, 1))
Eq(F_292(x, k_0), F_293(x, k_0) + F_297(x))
Eq(F_293(x, k_0), F_294(x, k_0) + F_8(x, k_0))
Eq(F_294(x, k_0), F_295(x, k_0))
Eq(F_295(x, k_0), F_296(x, k_0)*F_86(x))
Eq(F_296(x, k_0), (k_0*F_292(x, k_0) - F_292(x, 1))/(k_0 - 1))
Eq(F_297(x), F_298(x))
Eq(F_298(x), F_299(x)*F_86(x))
Eq(F_299(x), F_300(x) + F_302(x))
Eq(F_300(x), F_289(x) + F_301(x))
Eq(F_301(x), F_285(x) + F_4(x))
Eq(F_302(x), F_303(x))
Eq(F_303(x), F_300(x)*F_304(x)*F_86(x))
Eq(F_304(x), F_305(x) + F_308(x))
Eq(F_305(x), F_306(x) + F_82(x))
Eq(F_306(x), F_307(x))
Eq(F_307(x), F_304(x)*F_82(x)*F_86(x))
Eq(F_308(x), F_309(x))
Eq(F_309(x), F_310(x) + F_5(x))
Eq(F_310(x), F_311(x) - F_313(x))
Eq(F_311(x), F_312(x))
Eq(F_312(x), F_291(x)*F_86(x))
Eq(F_313(x), F_314(x) - F_328(x))
Eq(F_314(x), F_315(x) - F_317(x))
Eq(F_315(x), F_316(x)/F_86(x))
Eq(F_316(x), F_288(x))
Eq(F_317(x), F_318(x) - F_321(x))
Eq(F_318(x), F_319(x)/F_86(x))
Eq(F_319(x), F_320(x))
Eq(F_320(x), F_2(x) + F_288(x))
Eq(F_321(x), F_322(x) + F_325(x))
Eq(F_322(x), F_0(x) + F_323(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_0(x)*F_304(x)*F_86(x))
Eq(F_325(x), F_326(x) + F_328(x))
Eq(F_326(x), F_327(x))
Eq(F_327(x), F_7(x)*F_86(x))
Eq(F_328(x), F_329(x))
Eq(F_329(x), F_330(x)*F_86(x))
Eq(F_330(x), F_331(x, 1))
Eq(F_331(x, k_0), F_332(x, k_0) + F_335(x, k_0))
Eq(F_332(x, k_0), F_333(x, k_0, 1))
Eq(F_333(x, k_0, k_1), F_237(x, k_0, k_1) + F_334(x, k_1))
Eq(F_334(x, k_0), F_16(x, k_0) + F_66(x, k_0))
Eq(F_335(x, k_0), F_336(x, k_0))
Eq(F_336(x, k_0), F_337(x, k_0)*F_86(x))
Eq(F_337(x, k_0), (k_0*F_331(x, k_0) - F_331(x, 1))/(k_0 - 1))
Eq(F_338(x, k_0), k_0*F_339(x))
Eq(F_339(x), F_340(x))
Eq(F_340(x), F_302(x)*F_86(x)**2)
Eq(F_341(x, k_0), F_342(x, k_0) + F_343(x, k_0))
Eq(F_342(x, k_0), F_20(x, k_0)*F_65(x, k_0))
Eq(F_343(x, k_0), F_344(x, k_0))
Eq(F_344(x, k_0), F_345(x, k_0)*F_86(x))
Eq(F_345(x, k_0), F_346(x, k_0) + F_353(x, k_0))
Eq(F_346(x, k_0), F_347(x, k_0) + F_349(x, k_0))
Eq(F_347(x, k_0), F_15(x, k_0)*F_20(x, k_0)*F_348(x))
Eq(F_348(x), F_0(x) + F_326(x))
Eq(F_349(x, k_0), F_350(x, k_0))
Eq(F_350(x, k_0), F_348(x)*F_351(x, k_0)*F_86(x))
Eq(F_352(x, k_0), F_0(x)*F_351(x, k_0)*F_86(x))
Eq(F_352(x, k_0), F_245(x, k_0))
Eq(F_353(x, k_0), F_13(x, k_0)*F_354(x, k_0))
Eq(F_354(x, k_0), F_355(x, 1, k_0))
Eq(F_355(x, k_0, k_1), F_356(x, k_0, k_0*k_1))
Eq(F_356(x, k_0, k_1), F_236(x, k_0, k_1) + F_357(x, k_0, k_1))
Eq(F_357(x, k_0, k_1), F_358(x, k_0, k_1))
Eq(F_358(x, k_0, k_1), F_359(x, k_0, k_1)*F_86(x))
Eq(F_359(x, k_0, k_1), -F_356(x, 1, k_1) + (k_0*F_356(x, k_0, k_1) - F_356(x, 1, k_1))/(k_0 - 1))
Eq(F_360(x, k_0, k_1), F_361(x, k_0, k_1) + F_362(x, k_0, k_1))
Eq(F_361(x, k_0, k_1), F_20(x, k_1)*F_274(x, k_0))
Eq(F_363(x, k_0, k_1), F_362(x, k_0, k_1) + F_367(x, k_0, k_1))
Eq(F_363(x, k_0, k_1), F_364(x, k_0, k_1) + F_365(x, k_0, k_1))
Eq(F_364(x, k_0, k_1), F_15(x, k_1)*F_22(x, k_1)*F_274(x, k_0))
Eq(F_365(x, k_0, k_1), F_366(x, k_0, k_1))
Eq(F_366(x, k_0, k_1), F_13(x, k_0)*F_15(x, k_1)*F_177(x, k_0)*F_22(x, k_1))
Eq(F_367(x, k_0, k_1), F_368(x, k_0, k_1) + F_369(x, k_0))
Eq(F_368(x, k_0, k_1), F_22(x, k_1)*F_274(x, k_0))
Eq(F_369(x, k_0), F_370(x, k_0))
Eq(F_370(x, k_0), F_13(x, k_0)*F_177(x, k_0))
Eq(F_371(x, k_0), F_234(x, 1, k_0))
Eq(F_372(x, k_0, k_1), F_220(x, k_0, k_1) + F_373(x, k_0))
Eq(F_373(x, k_0), F_279(x, k_0) + F_4(x))
Eq(F_374(x, k_0, k_1), F_212(x, k_0, k_1) + F_54(x, k_0))
Pack JSON:
{"name": "point_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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
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0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24890/
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[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0],1]
F[11,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[8,x]
F[17,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[15,x,k[0],k[1],k[2]]*k[0]-F[15,x,1,k[1],k[2]])
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[22,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],1,k[2]]*k[0]-F[20,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[21,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2]]+F[55,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[2]]+F[29,x,k[0],k[2]]+F[31,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1]] = F[22,x,k[0]]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = (F[11,x,k[0],1]*k[0]-F[11,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[31,x,k[0],k[1],k[2]] = F[12,x,k[0],k[2]]*F[22,x,k[1]]
F[32,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[34,x,k[1],k[2]]+F[54,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1]] = F[35,x,k[1]]+F[52,x,k[0],k[1]]
F[35,x,k[0]] = F[36,x,k[0]]+F[46,x,k[0]]
F[36,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[45,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,1,k[0]]
F[39,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]*F[8,x]
F[41,x,k[0],k[1]] = 1/(-1+k[0])*(F[39,x,k[0],k[1]]*k[0]-F[39,x,1,k[1]])
F[42,x,k[0],k[1]] = F[22,x,k[1]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[44,x,k[0],1,k[1]]
F[44,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1]*k[2],k[2]]
F[45,x,k[0]] = F[22,x,k[0]]*F[35,x,k[0]]
F[46,x,k[0]] = k[0]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[36,x,k[0]]*F[49,x,k[0]]*F[8,x]
F[49,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]*F[49,x,k[0]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*F[47,x,k[1]]
F[54,x,k[0],k[1],k[2]] = F[53,x,k[0],k[2]]
F[55,x,k[0],k[1],k[2]] = F[56,x,k[0],k[2]]
F[43,x,k[0],k[1]] = F[12,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[22,x,k[1]]*F[34,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}, 1\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{12}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{11}\! \left(x , y_{0}, 1\right)-F_{11}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{2}\right) F_{22}\! \left(x , y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{1}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0}, 1, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{45}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = y_{0} F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{49}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{47}\! \left(x , y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{56}\! \left(x , y_{0}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_22(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0, 1))
Eq(F_11(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_29(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_8(x))
Eq(F_17(x, k_0, k_1, k_2), (k_0*F_15(x, k_0, k_1, k_2) - F_15(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_22(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, 1, k_2) + k_1*F_20(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_12(x, k_0, k_1) + k_2*F_12(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1, k_2), F_22(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_21(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_22(x, k_2)*F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2) + F_55(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_2) + F_29(x, k_0, k_2) + F_31(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1), F_22(x, k_0)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (-k_0*F_11(x, k_0, 1) + k_1*F_11(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_31(x, k_0, k_1, k_2), F_12(x, k_0, k_2)*F_22(x, k_1))
Eq(F_32(x, k_0, k_1, k_2), F_22(x, k_2)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_34(x, k_1, k_2) + F_54(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1), F_35(x, k_1) + F_52(x, k_0, k_1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_46(x, k_0))
Eq(F_36(x, k_0), F_1(x) + F_37(x, k_0) + F_45(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_40(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1)*F_8(x))
Eq(F_41(x, k_0, k_1), (k_0*F_39(x, k_0, k_1) - F_39(x, 1, k_1))/(k_0 - 1))
Eq(F_42(x, k_0, k_1), F_22(x, k_1)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_44(x, k_0, 1, k_1))
Eq(F_44(x, k_0, k_1, k_2), F_28(x, k_0, k_1*k_2, k_2))
Eq(F_45(x, k_0), F_22(x, k_0)*F_35(x, k_0))
Eq(F_46(x, k_0), k_0*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_36(x, k_0)*F_49(x, k_0)*F_8(x))
Eq(F_49(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0)*F_49(x, k_0))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), k_0*F_47(x, k_1))
Eq(F_54(x, k_0, k_1, k_2), F_53(x, k_0, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_56(x, k_0, k_2))
Eq(F_43(x, k_0, k_1), F_12(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_22(x, k_1)*F_34(x, k_0, k_1))
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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], 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0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[2, 0]]}]}}]}, {"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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "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"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25382/
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[86,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[7,x]*F[86,x]
F[7,x] = F[8,x,1]
F[9,x,k[0]] = F[13,x,k[0]]*F[8,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[54,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x,k[0]] = F[15,x,k[0]]+F[29,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[13,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = F[15,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[26,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[13,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[13,x,k[0]]*F[23,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[13,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[16,x,k[0]]+F[26,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[39,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[13,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[22,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[24,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[35,x]+F[36,x,k[0]]+F[38,x,k[0]]
F[35,x] = 0
F[36,x,k[0]] = F[13,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[20,x,k[0]]+F[34,x,k[0]]
F[38,x,k[0]] = F[13,x,k[0]]*F[33,x,k[0]]
F[39,x,k[0]] = F[35,x]+F[40,x,k[0]]+F[46,x,k[0]]
F[40,x,k[0]] = F[13,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[28,x,k[0]]+F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[50,x,k[0]]
F[43,x,k[0]] = F[35,x]+F[44,x,k[0]]+F[46,x,k[0]]
F[44,x,k[0]] = F[13,x,k[0]]*F[45,x,k[0]]
F[45,x,k[0]] = F[16,x,k[0]]+F[43,x,k[0]]
F[46,x,k[0]] = F[13,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[49,x,k[0]]
F[48,x,k[0]] = F[24,x,k[0]]+F[43,x,k[0]]
F[49,x,k[0]] = F[34,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = 2*F[35,x]+F[51,x,k[0]]+F[53,x,k[0]]
F[51,x,k[0]] = F[13,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = F[26,x,k[0]]+F[50,x,k[0]]
F[53,x,k[0]] = F[13,x,k[0]]*F[42,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]*F[86,x]
F[56,x,k[0]] = F[57,x,k[0]]+F[58,x,k[0]]
F[57,x,k[0]] = -k[0]*(F[10,x,1]-F[10,x,k[0]])/(-1+k[0])
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[13,x,k[0]]*F[60,x,k[0]]
F[61,x,k[0]] = F[60,x,k[0]]*F[86,x]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,1,k[0]]
F[63,x,k[0],k[1]] = F[64,x,k[0]*k[1],k[1]]
F[64,x,k[0],k[1]] = F[378,x,k[0],k[1]]+F[65,x,k[1]]
F[65,x,k[0]] = F[2,x]+F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[13,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[70,x,k[0]]
F[69,x,k[0]] = F[15,x,k[0]]*F[2,x]*F[22,x,k[0]]
F[70,x,k[0]] = F[249,x,k[0]]+F[71,x,k[0]]
F[71,x,k[0]] = F[65,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]*F[86,x]
F[74,x,k[0]] = F[117,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[111,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,1,k[0]]
F[77,x,k[0],k[1]] = F[78,x,k[0]]+F[95,x,k[0],k[1]]
F[78,x,k[0]] = F[79,x,k[0]]+F[89,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[81,x,k[0]]
F[80,x,k[0]] = F[0,x]*F[13,x,k[0]]
F[81,x,k[0]] = F[82,x]*F[87,x,k[0]]
F[82,x] = F[83,x]
F[83,x] = F[1,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[83,x]*F[86,x]
F[86,x] = x
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[13,x,k[0]]*F[24,x,k[0]]
F[89,x,k[0]] = F[82,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[13,x,k[0]]*F[92,x,k[0]]
F[92,x,k[0]] = F[16,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[39,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[36,x,k[0]]
F[95,x,k[0],k[1]] = F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = F[109,x,k[1]]*F[13,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[103,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[100,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[13,x,k[0]]*F[32,x,k[0]]
F[102,x,k[0]] = F[11,x,k[0]]+F[99,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[108,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]+F[2,x]
F[105,x,k[0]] = F[106,x]*F[11,x,k[0]]
F[106,x] = F[107,x]
F[107,x] = F[82,x]*F[86,x]
F[108,x,k[0]] = F[100,x,k[0]]*F[106,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[16,x,k[0]]
F[110,x,k[0]] = F[15,x,k[0]]*F[20,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[5,x]
F[112,x,k[0]] = F[113,x,k[0]]+F[86,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[115,x,k[0]]+F[35,x]
F[114,x,k[0]] = F[16,x,k[0]]*F[86,x]
F[115,x,k[0]] = F[116,x,k[0]]*F[13,x,k[0]]
F[116,x,k[0]] = F[112,x,k[0]]
F[117,x,k[0]] = F[118,x,1,k[0]]
F[119,x,k[0],k[1]] = F[118,x,k[0],k[1]]+F[376,x,k[0],k[1]]
F[119,x,k[0],k[1]] = F[120,x,k[1]]+F[238,x,k[0],k[1]]
F[121,x,k[0]] = F[120,x,k[0]]+F[375,x,k[0]]
F[122,x,k[0]] = F[121,x,k[0]]*F[86,x]
F[122,x,k[0]] = F[123,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[5,x]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]+F[127,x,k[0]]
F[126,x,k[0]] = F[16,x,k[0]]*F[2,x]
F[127,x,k[0]] = F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]*F[86,x]
F[129,x,k[0]] = F[130,x,k[0]]+F[207,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[109,x,k[0]]*F[132,x]*F[86,x]
F[132,x] = F[133,x]+F[176,x]
F[133,x] = F[134,x,1]
F[134,x,k[0]] = F[135,x,k[0]]+F[173,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]+F[138,x]
F[136,x,k[0]] = F[137,x]+F[173,x,k[0]]
F[137,x] = F[1,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[86,x]
F[140,x] = F[141,x]+F[149,x]
F[141,x] = F[1,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[86,x]
F[144,x] = F[141,x]+F[145,x]
F[145,x] = F[146,x]+F[84,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[86,x]
F[148,x] = F[142,x]+F[146,x]
F[149,x] = F[150,x]+F[158,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[86,x]
F[152,x] = F[153,x]+F[83,x]
F[153,x] = F[106,x]+F[154,x]
F[154,x] = F[155,x]+F[157,x]+F[35,x]
F[155,x] = F[156,x]*F[86,x]
F[156,x] = F[154,x]+F[84,x]
F[157,x] = F[153,x]*F[86,x]
F[158,x] = F[159,x]+F[165,x]+F[35,x]
F[159,x] = F[160,x]*F[86,x]
F[160,x] = F[148,x]+F[161,x]
F[161,x] = F[162,x]+F[169,x]
F[162,x] = F[163,x]+F[165,x]+F[35,x]
F[163,x] = F[164,x]*F[86,x]
F[164,x] = F[142,x]+F[162,x]
F[165,x] = F[166,x]*F[86,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[106,x]+F[162,x]
F[168,x] = F[154,x]+F[169,x]
F[169,x] = 2*F[35,x]+F[170,x]+F[172,x]
F[170,x] = F[171,x]*F[86,x]
F[171,x] = F[146,x]+F[169,x]
F[172,x] = F[161,x]*F[86,x]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[13,x,k[0]]*F[175,x]*F[32,x,k[0]]
F[175,x] = F[137,x]+F[138,x]
F[176,x] = F[177,x,1]
F[177,x,k[0]] = F[178,x,k[0]]+F[179,x,k[0]]
F[178,x,k[0]] = F[103,x,k[0]]+F[54,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]+F[200,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[86,x]
F[182,x,k[0]] = F[183,x,k[0]]+F[194,x,k[0]]
F[183,x,k[0]] = F[184,x,k[0]]+F[185,x,k[0]]
F[184,x,k[0]] = F[180,x,k[0]]+F[30,x,k[0]]
F[185,x,k[0]] = F[186,x,1,k[0]]
F[186,x,k[0],k[1]] = F[187,x,k[0],k[1]]
F[187,x,k[0],k[1]] = F[13,x,k[1]]*F[188,x,k[0],k[1]]
F[188,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[190,x,k[0],k[1]]
F[189,x,k[0],k[1]] = F[10,x,k[0]]+F[186,x,k[0],k[1]]
F[190,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[191,x,k[0],k[1]]
F[191,x,k[0],k[1]] = F[192,x,k[0],k[1]]
F[192,x,k[0],k[1]] = F[193,x,k[0],k[1]]*F[86,x]
F[193,x,k[0],k[1]] = -k[0]*(F[190,x,1,k[1]]-F[190,x,k[0],k[1]])/(-1+k[0])
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[13,x,k[0]]*F[196,x,k[0]]*F[22,x,k[0]]
F[196,x,k[0]] = F[194,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,1,k[0]]
F[198,x,k[0],k[1]] = F[189,x,k[0],k[1]]+F[199,x,k[1]]
F[199,x,k[0]] = F[0,x]+F[184,x,k[0]]
F[200,x,k[0]] = F[201,x,1,k[0]]
F[201,x,k[0],k[1]] = F[202,x,k[0]*k[1],k[1]]
F[202,x,k[0],k[1]] = F[203,x,k[0],k[1]]
F[203,x,k[0],k[1]] = F[13,x,k[1]]*F[204,x,k[0],k[1]]
F[204,x,k[0],k[1]] = F[205,x,k[0],k[1]]+F[206,x,k[0],k[1]]
F[205,x,k[0],k[1]] = F[202,x,k[0],k[1]]+F[54,x,k[0]]
F[206,x,k[0],k[1]] = F[191,x,k[0],k[1]]+F[205,x,k[0],k[1]]
F[208,x,k[0]] = F[207,x,k[0]]+F[353,x,k[0]]
F[208,x,k[0]] = F[209,x,1,k[0]]
F[210,x,k[0],k[1]] = F[209,x,k[0],k[1]]+F[364,x,k[0],k[1]]
F[211,x,k[0],k[1]] = F[13,x,k[0]]*F[210,x,k[0],k[1]]
F[211,x,k[0],k[1]] = F[212,x,k[0],k[1]]
F[212,x,k[0],k[1]] = F[213,x,k[0],k[1]]
F[213,x,k[0],k[1]] = F[13,x,k[0]]*F[214,x,k[0],k[1]]
F[214,x,k[0],k[1]] = F[215,x,k[0],k[1]]+F[345,x,k[1]]
F[215,x,k[0],k[1]] = F[216,x,k[0],k[1]]+F[230,x,k[0],k[1]]
F[216,x,k[0],k[1]] = k[1]*(F[217,x,k[0],1]-F[217,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[217,x,k[0],k[1]] = F[218,x,k[0],k[0]*k[1]]
F[218,x,k[0],k[1]] = F[219,x,k[0],k[1]]
F[219,x,k[0],k[1]] = F[220,x,k[0],k[1]]*F[86,x]
F[220,x,k[0],k[1]] = F[221,x,k[0],k[1]]+F[223,x,k[0],k[1]]
F[221,x,k[0],k[1]] = F[222,x,k[1]]+F[95,x,k[0],k[1]]
F[222,x,k[0]] = F[0,x]*F[16,x,k[0]]
F[223,x,k[0],k[1]] = F[224,x,k[0],k[1]]*F[5,x]
F[224,x,k[0],k[1]] = F[16,x,k[1]]+F[225,x,k[0],k[1]]
F[225,x,k[0],k[1]] = F[226,x,k[0],k[1]]+F[227,x,k[0],k[1]]+F[35,x]
F[226,x,k[0],k[1]] = F[13,x,k[0]]*F[16,x,k[1]]
F[227,x,k[0],k[1]] = F[13,x,k[1]]*F[228,x,k[0],k[1]]
F[228,x,k[0],k[1]] = F[229,x,k[0],k[1]]
F[229,x,k[0],k[1]] = F[13,x,k[0]]+F[225,x,k[0],k[1]]
F[230,x,k[0],k[1]] = k[1]*(F[231,x,k[0],1]-F[231,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[231,x,k[0],k[1]] = F[232,x,k[0],k[0]*k[1]]
F[233,x,k[0],k[1]] = F[232,x,k[0],k[1]]+F[277,x,k[0]]
F[233,x,k[0],k[1]] = F[234,x,k[0],k[1]]+F[64,x,k[0],k[1]]
F[234,x,k[0],k[1]] = F[235,x,k[0],k[1]]
F[235,x,k[0],k[1]] = F[236,x,k[0],k[1]]*F[86,x]
F[236,x,k[0],k[1]] = F[118,x,k[0],k[1]]+F[237,x,k[0],k[1]]
F[237,x,k[0],k[1]] = (F[238,x,k[0],k[1]]-F[238,x,1,k[1]])/(-1+k[0])
F[238,x,k[0],k[1]] = F[239,x,k[0],k[1]]+F[256,x,k[0],k[1]]
F[239,x,k[0],k[1]] = F[240,x,k[0],k[1]]+F[253,x,k[0],k[1]]
F[240,x,k[0],k[1]] = F[10,x,k[0]]+F[241,x,k[0],k[1]]
F[241,x,k[0],k[1]] = F[242,x,k[0],k[1]]
F[242,x,k[0],k[1]] = F[13,x,k[0]]*F[243,x,k[0],k[1]]
F[243,x,k[0],k[1]] = F[244,x,k[0],k[1]]+F[247,x,k[1]]
F[244,x,k[0],k[1]] = k[1]*(F[245,x,k[0],1]-F[245,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[245,x,k[0],k[1]] = F[246,x,k[0],k[0]*k[1]]
F[246,x,k[0],k[1]] = F[221,x,k[0],k[1]]+F[232,x,k[0],k[1]]
F[247,x,k[0]] = F[248,x,k[0]]+F[249,x,k[0]]
F[248,x,k[0]] = F[0,x]*F[15,x,k[0]]*F[20,x,k[0]]
F[250,x,k[0],k[1]] = F[230,x,k[0],k[1]]+F[249,x,k[1]]
F[214,x,k[0],k[1]] = F[250,x,k[0],k[1]]+F[251,x,k[0],k[1]]
F[251,x,k[0],k[1]] = F[216,x,k[0],k[1]]+F[252,x,k[1]]
F[252,x,k[0]] = F[15,x,k[0]]*F[2,x]*F[20,x,k[0]]
F[253,x,k[0],k[1]] = F[254,x,k[0],k[1]]
F[254,x,k[0],k[1]] = F[255,x,k[0],k[1]]*F[86,x]
F[255,x,k[0],k[1]] = -k[0]*(-F[238,x,k[0],k[1]]+F[238,x,1,k[1]])/(-1+k[0])
F[256,x,k[0],k[1]] = k[0]*F[257,x,k[1]]
F[257,x,k[0]] = F[258,x,k[0]]
F[259,x,k[0]] = F[258,x,k[0]]+F[275,x,k[0]]
F[260,x,k[0]] = F[259,x,k[0]]+F[269,x,k[0]]
F[261,x,k[0]] = F[260,x,k[0]]*F[86,x]
F[261,x,k[0]] = F[262,x,k[0]]
F[263,x,k[0]] = F[262,x,k[0]]+F[265,x,k[0]]
F[264,x,k[0]] = F[13,x,k[0]]*F[263,x,k[0]]
F[264,x,k[0]] = F[10,x,k[0]]
F[265,x,k[0]] = F[266,x,1,k[0]]
F[266,x,k[0],k[1]] = F[267,x,k[0]*k[1],k[1]]
F[267,x,k[0],k[1]] = F[240,x,k[0],k[1]]+F[268,x,k[1]]
F[268,x,k[0]] = F[15,x,k[0]]+F[65,x,k[0]]
F[269,x,k[0]] = F[270,x,1,k[0]]
F[270,x,k[0],k[1]] = (-F[271,x,1,k[1]]*k[1]+F[271,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[271,x,k[0],k[1]] = F[272,x,k[0]*k[1],k[1]]
F[272,x,k[0],k[1]] = F[239,x,k[0],k[1]]+F[273,x,k[1]]
F[273,x,k[0]] = F[274,x,k[0]]+F[71,x,k[0]]
F[274,x,k[0]] = F[0,x]*F[15,x,k[0]]
F[276,x,k[0]] = F[13,x,k[0]]*F[275,x,k[0]]
F[276,x,k[0]] = F[125,x,k[0]]
F[277,x,k[0]] = F[278,x,k[0]]+F[279,x,k[0]]
F[278,x,k[0]] = F[2,x]+F[54,x,k[0]]
F[279,x,k[0]] = F[280,x,k[0]]
F[280,x,k[0]] = F[281,x,k[0]]*F[86,x]
F[281,x,k[0]] = F[282,x,k[0]]+F[285,x,k[0]]
F[282,x,k[0]] = (F[283,x,k[0]]-F[283,x,1])/(-1+k[0])
F[283,x,k[0]] = F[284,x,k[0]]+F[78,x,k[0]]
F[284,x,k[0]] = F[13,x,k[0]]*F[5,x]
F[285,x,k[0]] = 1/(-1+k[0])*(F[286,x,k[0]]*k[0]-F[286,x,1])
F[286,x,k[0]] = F[277,x,k[0]]+F[287,x,k[0]]
F[287,x,k[0]] = F[288,x]+F[342,x,k[0]]
F[288,x] = -F[324,x]+F[289,x]
F[289,x] = -F[293,x]+F[290,x]
F[290,x] = 1/F[86,x]*F[291,x]
F[291,x] = F[292,x]
F[292,x] = -F[2,x]+F[5,x]
F[293,x] = F[294,x]
F[294,x] = F[295,x]*F[86,x]
F[295,x] = F[296,x,1]
F[296,x,k[0]] = F[297,x,k[0]]+F[301,x]
F[297,x,k[0]] = F[298,x,k[0]]+F[8,x,k[0]]
F[298,x,k[0]] = F[299,x,k[0]]
F[299,x,k[0]] = F[300,x,k[0]]*F[86,x]
F[300,x,k[0]] = 1/(-1+k[0])*(F[296,x,k[0]]*k[0]-F[296,x,1])
F[301,x] = F[302,x]
F[302,x] = F[303,x]*F[86,x]
F[303,x] = F[304,x]+F[306,x]
F[304,x] = F[293,x]+F[305,x]
F[305,x] = F[289,x]+F[4,x]
F[306,x] = F[307,x]
F[307,x] = F[304,x]*F[308,x]*F[86,x]
F[308,x] = F[309,x]+F[312,x]
F[309,x] = F[310,x]+F[82,x]
F[310,x] = F[311,x]
F[311,x] = F[308,x]*F[82,x]*F[86,x]
F[312,x] = F[313,x]
F[313,x] = F[314,x]+F[5,x]
F[314,x] = -F[317,x]+F[315,x]
F[315,x] = F[316,x]
F[316,x] = F[295,x]*F[86,x]
F[317,x] = -F[332,x]+F[318,x]
F[318,x] = -F[321,x]+F[319,x]
F[319,x] = 1/F[86,x]*F[320,x]
F[320,x] = F[292,x]
F[321,x] = -F[325,x]+F[322,x]
F[322,x] = 1/F[86,x]*F[323,x]
F[323,x] = F[324,x]
F[324,x] = F[2,x]+F[292,x]
F[325,x] = F[326,x]+F[329,x]
F[326,x] = F[0,x]+F[327,x]
F[327,x] = F[328,x]
F[328,x] = F[0,x]*F[308,x]*F[86,x]
F[329,x] = F[330,x]+F[332,x]
F[330,x] = F[331,x]
F[331,x] = F[7,x]*F[86,x]
F[332,x] = F[333,x]
F[333,x] = F[334,x]*F[86,x]
F[334,x] = F[335,x,1]
F[335,x,k[0]] = F[336,x,k[0]]+F[339,x,k[0]]
F[336,x,k[0]] = F[337,x,k[0],1]
F[337,x,k[0],k[1]] = F[241,x,k[0],k[1]]+F[338,x,k[1]]
F[338,x,k[0]] = F[16,x,k[0]]+F[66,x,k[0]]
F[339,x,k[0]] = F[340,x,k[0]]
F[340,x,k[0]] = F[341,x,k[0]]*F[86,x]
F[341,x,k[0]] = 1/(-1+k[0])*(F[335,x,k[0]]*k[0]-F[335,x,1])
F[342,x,k[0]] = k[0]*F[343,x]
F[343,x] = F[344,x]
F[344,x] = F[86,x]^2*F[306,x]
F[345,x,k[0]] = F[346,x,k[0]]+F[347,x,k[0]]
F[346,x,k[0]] = F[20,x,k[0]]*F[65,x,k[0]]
F[347,x,k[0]] = F[348,x,k[0]]
F[348,x,k[0]] = F[349,x,k[0]]*F[86,x]
F[349,x,k[0]] = F[350,x,k[0]]+F[357,x,k[0]]
F[350,x,k[0]] = F[351,x,k[0]]+F[353,x,k[0]]
F[351,x,k[0]] = F[15,x,k[0]]*F[20,x,k[0]]*F[352,x]
F[352,x] = F[0,x]+F[330,x]
F[353,x,k[0]] = F[354,x,k[0]]
F[354,x,k[0]] = F[352,x]*F[355,x,k[0]]*F[86,x]
F[356,x,k[0]] = F[0,x]*F[355,x,k[0]]*F[86,x]
F[356,x,k[0]] = F[249,x,k[0]]
F[357,x,k[0]] = F[13,x,k[0]]*F[358,x,k[0]]
F[358,x,k[0]] = F[359,x,1,k[0]]
F[359,x,k[0],k[1]] = F[360,x,k[0],k[0]*k[1]]
F[360,x,k[0],k[1]] = F[240,x,k[0],k[1]]+F[361,x,k[0],k[1]]
F[361,x,k[0],k[1]] = F[362,x,k[0],k[1]]
F[362,x,k[0],k[1]] = F[363,x,k[0],k[1]]*F[86,x]
F[363,x,k[0],k[1]] = -k[0]*(F[360,x,1,k[1]]-F[360,x,k[0],k[1]])/(-1+k[0])
F[364,x,k[0],k[1]] = F[365,x,k[0],k[1]]+F[366,x,k[0],k[1]]
F[365,x,k[0],k[1]] = F[20,x,k[1]]*F[278,x,k[0]]
F[367,x,k[0],k[1]] = F[366,x,k[0],k[1]]+F[371,x,k[0],k[1]]
F[367,x,k[0],k[1]] = F[368,x,k[0],k[1]]+F[369,x,k[0],k[1]]
F[368,x,k[0],k[1]] = F[15,x,k[1]]*F[22,x,k[1]]*F[278,x,k[0]]
F[369,x,k[0],k[1]] = F[370,x,k[0],k[1]]
F[370,x,k[0],k[1]] = F[13,x,k[0]]*F[15,x,k[1]]*F[177,x,k[0]]*F[22,x,k[1]]
F[371,x,k[0],k[1]] = F[372,x,k[0],k[1]]+F[373,x,k[0]]
F[372,x,k[0],k[1]] = F[22,x,k[1]]*F[278,x,k[0]]
F[373,x,k[0]] = F[374,x,k[0]]
F[374,x,k[0]] = F[13,x,k[0]]*F[177,x,k[0]]
F[375,x,k[0]] = F[238,x,1,k[0]]
F[376,x,k[0],k[1]] = F[220,x,k[0],k[1]]+F[377,x,k[0]]
F[377,x,k[0]] = F[283,x,k[0]]+F[4,x]
F[378,x,k[0],k[1]] = F[212,x,k[0],k[1]]+F[54,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \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_{86}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{29}\! \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_{13}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \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_{13}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = 2 F_{35}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -\frac{y \left(F_{10}\! \left(x , 1\right)-F_{10}\! \left(x , y\right)\right)}{-1+y}
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , 1, y\right)
F_{63}\! \left(x , y , z\right) = F_{64}\! \left(x , y z , z\right)
F_{64}\! \left(x , y , z\right) = F_{378}\! \left(x , y , z\right)+F_{65}\! \left(x , z\right)
F_{65}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{2}\! \left(x \right) F_{22}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{249}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , 1, y\right)
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , y\right)+F_{95}\! \left(x , y , z\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{1}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = x
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{82}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{95}\! \left(x , y , z\right) = F_{96}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = F_{109}\! \left(x , z\right) F_{13}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{108}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{2}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x \right) F_{11}\! \left(x , y\right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{82}\! \left(x \right) F_{86}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{106}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{35}\! \left(x \right)
F_{114}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{112}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , 1, y\right)
F_{119}\! \left(x , y , z\right) = F_{118}\! \left(x , y , z\right)+F_{376}\! \left(x , y , z\right)
F_{119}\! \left(x , y , z\right) = F_{120}\! \left(x , z\right)+F_{238}\! \left(x , y , z\right)
F_{121}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{375}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{132}\! \left(x \right) F_{86}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{176}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x , 1\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{138}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x \right)+F_{173}\! \left(x , y\right)
F_{137}\! \left(x \right) = F_{1}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{86}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{149}\! \left(x \right)
F_{141}\! \left(x \right) = F_{1}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{86}\! \left(x \right)
F_{144}\! \left(x \right) = F_{141}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{84}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{86}\! \left(x \right)
F_{148}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{158}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{86}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{83}\! \left(x \right)
F_{153}\! \left(x \right) = F_{106}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{157}\! \left(x \right)+F_{35}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{86}\! \left(x \right)
F_{156}\! \left(x \right) = F_{154}\! \left(x \right)+F_{84}\! \left(x \right)
F_{157}\! \left(x \right) = F_{153}\! \left(x \right) F_{86}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{165}\! \left(x \right)+F_{35}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{86}\! \left(x \right)
F_{160}\! \left(x \right) = F_{148}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{169}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{165}\! \left(x \right)+F_{35}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right) F_{86}\! \left(x \right)
F_{164}\! \left(x \right) = F_{142}\! \left(x \right)+F_{162}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{86}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{106}\! \left(x \right)+F_{162}\! \left(x \right)
F_{168}\! \left(x \right) = F_{154}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{170}\! \left(x \right)+F_{172}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{86}\! \left(x \right)
F_{171}\! \left(x \right) = F_{146}\! \left(x \right)+F_{169}\! \left(x \right)
F_{172}\! \left(x \right) = F_{161}\! \left(x \right) F_{86}\! \left(x \right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{175}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{175}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x , 1\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , 1, y\right)
F_{186}\! \left(x , y , z\right) = F_{187}\! \left(x , y , z\right)
F_{187}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{188}\! \left(x , y , z\right)
F_{188}\! \left(x , y , z\right) = F_{189}\! \left(x , y , z\right)+F_{190}\! \left(x , y , z\right)
F_{189}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right)+F_{186}\! \left(x , y , z\right)
F_{190}\! \left(x , y , z\right) = F_{189}\! \left(x , y , z\right)+F_{191}\! \left(x , y , z\right)
F_{191}\! \left(x , y , z\right) = F_{192}\! \left(x , y , z\right)
F_{192}\! \left(x , y , z\right) = F_{193}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{193}\! \left(x , y , z\right) = -\frac{y \left(F_{190}\! \left(x , 1, z\right)-F_{190}\! \left(x , y , z\right)\right)}{-1+y}
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{196}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{194}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , 1, y\right)
F_{198}\! \left(x , y , z\right) = F_{189}\! \left(x , y , z\right)+F_{199}\! \left(x , z\right)
F_{199}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{184}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , 1, y\right)
F_{201}\! \left(x , y , z\right) = F_{202}\! \left(x , y z , z\right)
F_{202}\! \left(x , y , z\right) = F_{203}\! \left(x , y , z\right)
F_{203}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{204}\! \left(x , y , z\right)
F_{204}\! \left(x , y , z\right) = F_{205}\! \left(x , y , z\right)+F_{206}\! \left(x , y , z\right)
F_{205}\! \left(x , y , z\right) = F_{202}\! \left(x , y , z\right)+F_{54}\! \left(x , y\right)
F_{206}\! \left(x , y , z\right) = F_{191}\! \left(x , y , z\right)+F_{205}\! \left(x , y , z\right)
F_{208}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{353}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , 1, y\right)
F_{210}\! \left(x , y , z\right) = F_{209}\! \left(x , y , z\right)+F_{364}\! \left(x , y , z\right)
F_{211}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{210}\! \left(x , y , z\right)
F_{211}\! \left(x , y , z\right) = F_{212}\! \left(x , y , z\right)
F_{212}\! \left(x , y , z\right) = F_{213}\! \left(x , y , z\right)
F_{213}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{214}\! \left(x , y , z\right)
F_{214}\! \left(x , y , z\right) = F_{215}\! \left(x , y , z\right)+F_{345}\! \left(x , z\right)
F_{215}\! \left(x , y , z\right) = F_{216}\! \left(x , y , z\right)+F_{230}\! \left(x , y , z\right)
F_{216}\! \left(x , y , z\right) = \frac{z \left(F_{217}\! \left(x , y , 1\right)-F_{217}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{217}\! \left(x , y , z\right) = F_{218}\! \left(x , y , y z \right)
F_{218}\! \left(x , y , z\right) = F_{219}\! \left(x , y , z\right)
F_{219}\! \left(x , y , z\right) = F_{220}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{220}\! \left(x , y , z\right) = F_{221}\! \left(x , y , z\right)+F_{223}\! \left(x , y , z\right)
F_{221}\! \left(x , y , z\right) = F_{222}\! \left(x , z\right)+F_{95}\! \left(x , y , z\right)
F_{222}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{223}\! \left(x , y , z\right) = F_{224}\! \left(x , y , z\right) F_{5}\! \left(x \right)
F_{224}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right)+F_{225}\! \left(x , y , z\right)
F_{225}\! \left(x , y , z\right) = F_{226}\! \left(x , y , z\right)+F_{227}\! \left(x , y , z\right)+F_{35}\! \left(x \right)
F_{226}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{16}\! \left(x , z\right)
F_{227}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{228}\! \left(x , y , z\right)
F_{228}\! \left(x , y , z\right) = F_{229}\! \left(x , y , z\right)
F_{229}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right)+F_{225}\! \left(x , y , z\right)
F_{230}\! \left(x , y , z\right) = \frac{z \left(F_{231}\! \left(x , y , 1\right)-F_{231}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{231}\! \left(x , y , z\right) = F_{232}\! \left(x , y , y z \right)
F_{233}\! \left(x , y , z\right) = F_{232}\! \left(x , y , z\right)+F_{277}\! \left(x , y\right)
F_{233}\! \left(x , y , z\right) = F_{234}\! \left(x , y , z\right)+F_{64}\! \left(x , y , z\right)
F_{234}\! \left(x , y , z\right) = F_{235}\! \left(x , y , z\right)
F_{235}\! \left(x , y , z\right) = F_{236}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{236}\! \left(x , y , z\right) = F_{118}\! \left(x , y , z\right)+F_{237}\! \left(x , y , z\right)
F_{237}\! \left(x , y , z\right) = -\frac{-F_{238}\! \left(x , y , z\right)+F_{238}\! \left(x , 1, z\right)}{-1+y}
F_{238}\! \left(x , y , z\right) = F_{239}\! \left(x , y , z\right)+F_{256}\! \left(x , y , z\right)
F_{239}\! \left(x , y , z\right) = F_{240}\! \left(x , y , z\right)+F_{253}\! \left(x , y , z\right)
F_{240}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right)+F_{241}\! \left(x , y , z\right)
F_{241}\! \left(x , y , z\right) = F_{242}\! \left(x , y , z\right)
F_{242}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{243}\! \left(x , y , z\right)
F_{243}\! \left(x , y , z\right) = F_{244}\! \left(x , y , z\right)+F_{247}\! \left(x , z\right)
F_{244}\! \left(x , y , z\right) = \frac{z \left(F_{245}\! \left(x , y , 1\right)-F_{245}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{245}\! \left(x , y , z\right) = F_{246}\! \left(x , y , y z \right)
F_{246}\! \left(x , y , z\right) = F_{221}\! \left(x , y , z\right)+F_{232}\! \left(x , y , z\right)
F_{247}\! \left(x , y\right) = F_{248}\! \left(x , y\right)+F_{249}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{250}\! \left(x , y , z\right) = F_{230}\! \left(x , y , z\right)+F_{249}\! \left(x , z\right)
F_{214}\! \left(x , y , z\right) = F_{250}\! \left(x , y , z\right)+F_{251}\! \left(x , y , z\right)
F_{251}\! \left(x , y , z\right) = F_{216}\! \left(x , y , z\right)+F_{252}\! \left(x , z\right)
F_{252}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{2}\! \left(x \right) F_{20}\! \left(x , y\right)
F_{253}\! \left(x , y , z\right) = F_{254}\! \left(x , y , z\right)
F_{254}\! \left(x , y , z\right) = F_{255}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{255}\! \left(x , y , z\right) = -\frac{y \left(-F_{238}\! \left(x , y , z\right)+F_{238}\! \left(x , 1, z\right)\right)}{-1+y}
F_{256}\! \left(x , y , z\right) = y F_{257}\! \left(x , z\right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{258}\! \left(x , y\right)+F_{275}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{269}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{260}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{261}\! \left(x , y\right) = F_{262}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{262}\! \left(x , y\right)+F_{265}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{263}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , 1, y\right)
F_{266}\! \left(x , y , z\right) = F_{267}\! \left(x , y z , z\right)
F_{267}\! \left(x , y , z\right) = F_{240}\! \left(x , y , z\right)+F_{268}\! \left(x , z\right)
F_{268}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{270}\! \left(x , 1, y\right)
F_{270}\! \left(x , y , z\right) = -\frac{F_{271}\! \left(x , 1, z\right) z -y F_{271}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{271}\! \left(x , y , z\right) = F_{272}\! \left(x , y z , z\right)
F_{272}\! \left(x , y , z\right) = F_{239}\! \left(x , y , z\right)+F_{273}\! \left(x , z\right)
F_{273}\! \left(x , y\right) = F_{274}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{275}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = F_{278}\! \left(x , y\right)+F_{279}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{280}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{281}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{281}\! \left(x , y\right) = F_{282}\! \left(x , y\right)+F_{285}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = -\frac{-F_{283}\! \left(x , y\right)+F_{283}\! \left(x , 1\right)}{-1+y}
F_{283}\! \left(x , y\right) = F_{284}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{5}\! \left(x \right)
F_{285}\! \left(x , y\right) = -\frac{-F_{286}\! \left(x , y\right) y +F_{286}\! \left(x , 1\right)}{-1+y}
F_{286}\! \left(x , y\right) = F_{277}\! \left(x , y\right)+F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = F_{288}\! \left(x \right)+F_{342}\! \left(x , y\right)
F_{288}\! \left(x \right) = -F_{324}\! \left(x \right)+F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = -F_{293}\! \left(x \right)+F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = \frac{F_{291}\! \left(x \right)}{F_{86}\! \left(x \right)}
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{295}\! \left(x \right) F_{86}\! \left(x \right)
F_{295}\! \left(x \right) = F_{296}\! \left(x , 1\right)
F_{296}\! \left(x , y\right) = F_{297}\! \left(x , y\right)+F_{301}\! \left(x \right)
F_{297}\! \left(x , y\right) = F_{298}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{299}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{300}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{300}\! \left(x , y\right) = -\frac{-F_{296}\! \left(x , y\right) y +F_{296}\! \left(x , 1\right)}{-1+y}
F_{301}\! \left(x \right) = F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = F_{303}\! \left(x \right) F_{86}\! \left(x \right)
F_{303}\! \left(x \right) = F_{304}\! \left(x \right)+F_{306}\! \left(x \right)
F_{304}\! \left(x \right) = F_{293}\! \left(x \right)+F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = F_{289}\! \left(x \right)+F_{4}\! \left(x \right)
F_{306}\! \left(x \right) = F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{304}\! \left(x \right) F_{308}\! \left(x \right) F_{86}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)+F_{312}\! \left(x \right)
F_{309}\! \left(x \right) = F_{310}\! \left(x \right)+F_{82}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right)
F_{311}\! \left(x \right) = F_{308}\! \left(x \right) F_{82}\! \left(x \right) F_{86}\! \left(x \right)
F_{312}\! \left(x \right) = F_{313}\! \left(x \right)
F_{313}\! \left(x \right) = F_{314}\! \left(x \right)+F_{5}\! \left(x \right)
F_{314}\! \left(x \right) = -F_{317}\! \left(x \right)+F_{315}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{295}\! \left(x \right) F_{86}\! \left(x \right)
F_{317}\! \left(x \right) = -F_{332}\! \left(x \right)+F_{318}\! \left(x \right)
F_{318}\! \left(x \right) = -F_{321}\! \left(x \right)+F_{319}\! \left(x \right)
F_{319}\! \left(x \right) = \frac{F_{320}\! \left(x \right)}{F_{86}\! \left(x \right)}
F_{320}\! \left(x \right) = F_{292}\! \left(x \right)
F_{321}\! \left(x \right) = -F_{325}\! \left(x \right)+F_{322}\! \left(x \right)
F_{322}\! \left(x \right) = \frac{F_{323}\! \left(x \right)}{F_{86}\! \left(x \right)}
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = F_{2}\! \left(x \right)+F_{292}\! \left(x \right)
F_{325}\! \left(x \right) = F_{326}\! \left(x \right)+F_{329}\! \left(x \right)
F_{326}\! \left(x \right) = F_{0}\! \left(x \right)+F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = F_{0}\! \left(x \right) F_{308}\! \left(x \right) F_{86}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)+F_{332}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x \right)
F_{331}\! \left(x \right) = F_{7}\! \left(x \right) F_{86}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{334}\! \left(x \right) F_{86}\! \left(x \right)
F_{334}\! \left(x \right) = F_{335}\! \left(x , 1\right)
F_{335}\! \left(x , y\right) = F_{336}\! \left(x , y\right)+F_{339}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{337}\! \left(x , y , 1\right)
F_{337}\! \left(x , y , z\right) = F_{241}\! \left(x , y , z\right)+F_{338}\! \left(x , z\right)
F_{338}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{339}\! \left(x , y\right) = F_{340}\! \left(x , y\right)
F_{340}\! \left(x , y\right) = F_{341}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{341}\! \left(x , y\right) = -\frac{-y F_{335}\! \left(x , y\right)+F_{335}\! \left(x , 1\right)}{-1+y}
F_{342}\! \left(x , y\right) = y F_{343}\! \left(x \right)
F_{343}\! \left(x \right) = F_{344}\! \left(x \right)
F_{344}\! \left(x \right) = F_{86} \left(x \right)^{2} F_{306}\! \left(x \right)
F_{345}\! \left(x , y\right) = F_{346}\! \left(x , y\right)+F_{347}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{348}\! \left(x , y\right)
F_{348}\! \left(x , y\right) = F_{349}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{349}\! \left(x , y\right) = F_{350}\! \left(x , y\right)+F_{357}\! \left(x , y\right)
F_{350}\! \left(x , y\right) = F_{351}\! \left(x , y\right)+F_{353}\! \left(x , y\right)
F_{351}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{352}\! \left(x \right)
F_{352}\! \left(x \right) = F_{0}\! \left(x \right)+F_{330}\! \left(x \right)
F_{353}\! \left(x , y\right) = F_{354}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{352}\! \left(x \right) F_{355}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{356}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{355}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{356}\! \left(x , y\right) = F_{249}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{358}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{359}\! \left(x , 1, y\right)
F_{359}\! \left(x , y , z\right) = F_{360}\! \left(x , y , y z \right)
F_{360}\! \left(x , y , z\right) = F_{240}\! \left(x , y , z\right)+F_{361}\! \left(x , y , z\right)
F_{361}\! \left(x , y , z\right) = F_{362}\! \left(x , y , z\right)
F_{362}\! \left(x , y , z\right) = F_{363}\! \left(x , y , z\right) F_{86}\! \left(x \right)
F_{363}\! \left(x , y , z\right) = -\frac{y \left(F_{360}\! \left(x , 1, z\right)-F_{360}\! \left(x , y , z\right)\right)}{-1+y}
F_{364}\! \left(x , y , z\right) = F_{365}\! \left(x , y , z\right)+F_{366}\! \left(x , y , z\right)
F_{365}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{278}\! \left(x , y\right)
F_{367}\! \left(x , y , z\right) = F_{366}\! \left(x , y , z\right)+F_{371}\! \left(x , y , z\right)
F_{367}\! \left(x , y , z\right) = F_{368}\! \left(x , y , z\right)+F_{369}\! \left(x , y , z\right)
F_{368}\! \left(x , y , z\right) = F_{15}\! \left(x , z\right) F_{22}\! \left(x , z\right) F_{278}\! \left(x , y\right)
F_{369}\! \left(x , y , z\right) = F_{370}\! \left(x , y , z\right)
F_{370}\! \left(x , y , z\right) = F_{13}\! \left(x , y\right) F_{15}\! \left(x , z\right) F_{177}\! \left(x , y\right) F_{22}\! \left(x , z\right)
F_{371}\! \left(x , y , z\right) = F_{372}\! \left(x , y , z\right)+F_{373}\! \left(x , y\right)
F_{372}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{278}\! \left(x , y\right)
F_{373}\! \left(x , y\right) = F_{374}\! \left(x , y\right)
F_{374}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{177}\! \left(x , y\right)
F_{375}\! \left(x , y\right) = F_{238}\! \left(x , 1, y\right)
F_{376}\! \left(x , y , z\right) = F_{220}\! \left(x , y , z\right)+F_{377}\! \left(x , y\right)
F_{377}\! \left(x , y\right) = F_{283}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{378}\! \left(x , y , z\right) = F_{212}\! \left(x , y , z\right)+F_{54}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_86(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_86(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_9(x, k_0), F_13(x, k_0)*F_8(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_54(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x, k_0), F_15(x, k_0) + F_29(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_13(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), F_15(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_26(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_13(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_13(x, k_0)*F_23(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_13(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_16(x, k_0) + F_26(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_39(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_13(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_22(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_24(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x) + F_36(x, k_0) + F_38(x, k_0))
Eq(F_35(x), 0)
Eq(F_36(x, k_0), F_13(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_20(x, k_0) + F_34(x, k_0))
Eq(F_38(x, k_0), F_13(x, k_0)*F_33(x, k_0))
Eq(F_39(x, k_0), F_35(x) + F_40(x, k_0) + F_46(x, k_0))
Eq(F_40(x, k_0), F_13(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_28(x, k_0) + F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_50(x, k_0))
Eq(F_43(x, k_0), F_35(x) + F_44(x, k_0) + F_46(x, k_0))
Eq(F_44(x, k_0), F_13(x, k_0)*F_45(x, k_0))
Eq(F_45(x, k_0), F_16(x, k_0) + F_43(x, k_0))
Eq(F_46(x, k_0), F_13(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_49(x, k_0))
Eq(F_48(x, k_0), F_24(x, k_0) + F_43(x, k_0))
Eq(F_49(x, k_0), F_34(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), 2*F_35(x) + F_51(x, k_0) + F_53(x, k_0))
Eq(F_51(x, k_0), F_13(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), F_26(x, k_0) + F_50(x, k_0))
Eq(F_53(x, k_0), F_13(x, k_0)*F_42(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0)*F_86(x))
Eq(F_56(x, k_0), F_57(x, k_0) + F_58(x, k_0))
Eq(F_57(x, k_0), -F_10(x, 1) + (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_13(x, k_0)*F_60(x, k_0))
Eq(F_61(x, k_0), F_60(x, k_0)*F_86(x))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, 1, k_0))
Eq(F_63(x, k_0, k_1), F_64(x, k_0*k_1, k_1))
Eq(F_64(x, k_0, k_1), F_378(x, k_0, k_1) + F_65(x, k_1))
Eq(F_65(x, k_0), F_2(x) + F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_13(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_70(x, k_0))
Eq(F_69(x, k_0), F_15(x, k_0)*F_2(x)*F_22(x, k_0))
Eq(F_70(x, k_0), F_249(x, k_0) + F_71(x, k_0))
Eq(F_71(x, k_0), F_65(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0)*F_86(x))
Eq(F_74(x, k_0), F_117(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_111(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, 1, k_0))
Eq(F_77(x, k_0, k_1), F_78(x, k_0) + F_95(x, k_0, k_1))
Eq(F_78(x, k_0), F_79(x, k_0) + F_89(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_81(x, k_0))
Eq(F_80(x, k_0), F_0(x)*F_13(x, k_0))
Eq(F_81(x, k_0), F_82(x)*F_87(x, k_0))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_1(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_83(x)*F_86(x))
Eq(F_86(x), x)
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_13(x, k_0)*F_24(x, k_0))
Eq(F_89(x, k_0), F_82(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_13(x, k_0)*F_92(x, k_0))
Eq(F_92(x, k_0), F_16(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_39(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_36(x, k_0))
Eq(F_95(x, k_0, k_1), F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), F_109(x, k_1)*F_13(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_103(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_100(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_13(x, k_0)*F_32(x, k_0))
Eq(F_102(x, k_0), F_11(x, k_0) + F_99(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_108(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0) + F_2(x))
Eq(F_105(x, k_0), F_106(x)*F_11(x, k_0))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_82(x)*F_86(x))
Eq(F_108(x, k_0), F_100(x, k_0)*F_106(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_16(x, k_0))
Eq(F_110(x, k_0), F_15(x, k_0)*F_20(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_5(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_86(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_115(x, k_0) + F_35(x))
Eq(F_114(x, k_0), F_16(x, k_0)*F_86(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_13(x, k_0))
Eq(F_116(x, k_0), F_112(x, k_0))
Eq(F_117(x, k_0), F_118(x, 1, k_0))
Eq(F_119(x, k_0, k_1), F_118(x, k_0, k_1) + F_376(x, k_0, k_1))
Eq(F_119(x, k_0, k_1), F_120(x, k_1) + F_238(x, k_0, k_1))
Eq(F_121(x, k_0), F_120(x, k_0) + F_375(x, k_0))
Eq(F_122(x, k_0), F_121(x, k_0)*F_86(x))
Eq(F_122(x, k_0), F_123(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_5(x))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_127(x, k_0))
Eq(F_126(x, k_0), F_16(x, k_0)*F_2(x))
Eq(F_127(x, k_0), F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0)*F_86(x))
Eq(F_129(x, k_0), F_130(x, k_0) + F_207(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_109(x, k_0)*F_132(x)*F_86(x))
Eq(F_132(x), F_133(x) + F_176(x))
Eq(F_133(x), F_134(x, 1))
Eq(F_134(x, k_0), F_135(x, k_0) + F_173(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0) + F_138(x))
Eq(F_136(x, k_0), F_137(x) + F_173(x, k_0))
Eq(F_137(x), F_1(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_86(x))
Eq(F_140(x), F_141(x) + F_149(x))
Eq(F_141(x), F_1(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_86(x))
Eq(F_144(x), F_141(x) + F_145(x))
Eq(F_145(x), F_146(x) + F_84(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_86(x))
Eq(F_148(x), F_142(x) + F_146(x))
Eq(F_149(x), F_150(x) + F_158(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_86(x))
Eq(F_152(x), F_153(x) + F_83(x))
Eq(F_153(x), F_106(x) + F_154(x))
Eq(F_154(x), F_155(x) + F_157(x) + F_35(x))
Eq(F_155(x), F_156(x)*F_86(x))
Eq(F_156(x), F_154(x) + F_84(x))
Eq(F_157(x), F_153(x)*F_86(x))
Eq(F_158(x), F_159(x) + F_165(x) + F_35(x))
Eq(F_159(x), F_160(x)*F_86(x))
Eq(F_160(x), F_148(x) + F_161(x))
Eq(F_161(x), F_162(x) + F_169(x))
Eq(F_162(x), F_163(x) + F_165(x) + F_35(x))
Eq(F_163(x), F_164(x)*F_86(x))
Eq(F_164(x), F_142(x) + F_162(x))
Eq(F_165(x), F_166(x)*F_86(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_106(x) + F_162(x))
Eq(F_168(x), F_154(x) + F_169(x))
Eq(F_169(x), F_170(x) + F_172(x) + 2*F_35(x))
Eq(F_170(x), F_171(x)*F_86(x))
Eq(F_171(x), F_146(x) + F_169(x))
Eq(F_172(x), F_161(x)*F_86(x))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_13(x, k_0)*F_175(x)*F_32(x, k_0))
Eq(F_175(x), F_137(x) + F_138(x))
Eq(F_176(x), F_177(x, 1))
Eq(F_177(x, k_0), F_178(x, k_0) + F_179(x, k_0))
Eq(F_178(x, k_0), F_103(x, k_0) + F_54(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0) + F_200(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0)*F_86(x))
Eq(F_182(x, k_0), F_183(x, k_0) + F_194(x, k_0))
Eq(F_183(x, k_0), F_184(x, k_0) + F_185(x, k_0))
Eq(F_184(x, k_0), F_180(x, k_0) + F_30(x, k_0))
Eq(F_185(x, k_0), F_186(x, 1, k_0))
Eq(F_186(x, k_0, k_1), F_187(x, k_0, k_1))
Eq(F_187(x, k_0, k_1), F_13(x, k_1)*F_188(x, k_0, k_1))
Eq(F_188(x, k_0, k_1), F_189(x, k_0, k_1) + F_190(x, k_0, k_1))
Eq(F_189(x, k_0, k_1), F_10(x, k_0) + F_186(x, k_0, k_1))
Eq(F_190(x, k_0, k_1), F_189(x, k_0, k_1) + F_191(x, k_0, k_1))
Eq(F_191(x, k_0, k_1), F_192(x, k_0, k_1))
Eq(F_192(x, k_0, k_1), F_193(x, k_0, k_1)*F_86(x))
Eq(F_193(x, k_0, k_1), -F_190(x, 1, k_1) + (k_0*F_190(x, k_0, k_1) - F_190(x, 1, k_1))/(k_0 - 1))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_13(x, k_0)*F_196(x, k_0)*F_22(x, k_0))
Eq(F_196(x, k_0), F_194(x, k_0) + F_197(x, k_0))
Eq(F_197(x, k_0), F_198(x, 1, k_0))
Eq(F_198(x, k_0, k_1), F_189(x, k_0, k_1) + F_199(x, k_1))
Eq(F_199(x, k_0), F_0(x) + F_184(x, k_0))
Eq(F_200(x, k_0), F_201(x, 1, k_0))
Eq(F_201(x, k_0, k_1), F_202(x, k_0*k_1, k_1))
Eq(F_202(x, k_0, k_1), F_203(x, k_0, k_1))
Eq(F_203(x, k_0, k_1), F_13(x, k_1)*F_204(x, k_0, k_1))
Eq(F_204(x, k_0, k_1), F_205(x, k_0, k_1) + F_206(x, k_0, k_1))
Eq(F_205(x, k_0, k_1), F_202(x, k_0, k_1) + F_54(x, k_0))
Eq(F_206(x, k_0, k_1), F_191(x, k_0, k_1) + F_205(x, k_0, k_1))
Eq(F_208(x, k_0), F_207(x, k_0) + F_353(x, k_0))
Eq(F_208(x, k_0), F_209(x, 1, k_0))
Eq(F_210(x, k_0, k_1), F_209(x, k_0, k_1) + F_364(x, k_0, k_1))
Eq(F_211(x, k_0, k_1), F_13(x, k_0)*F_210(x, k_0, k_1))
Eq(F_211(x, k_0, k_1), F_212(x, k_0, k_1))
Eq(F_212(x, k_0, k_1), F_213(x, k_0, k_1))
Eq(F_213(x, k_0, k_1), F_13(x, k_0)*F_214(x, k_0, k_1))
Eq(F_214(x, k_0, k_1), F_215(x, k_0, k_1) + F_345(x, k_1))
Eq(F_215(x, k_0, k_1), F_216(x, k_0, k_1) + F_230(x, k_0, k_1))
Eq(F_216(x, k_0, k_1), -F_217(x, k_0, 1) + (-k_0*F_217(x, k_0, 1) + k_1*F_217(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_217(x, k_0, k_1), F_218(x, k_0, k_0*k_1))
Eq(F_218(x, k_0, k_1), F_219(x, k_0, k_1))
Eq(F_219(x, k_0, k_1), F_220(x, k_0, k_1)*F_86(x))
Eq(F_220(x, k_0, k_1), F_221(x, k_0, k_1) + F_223(x, k_0, k_1))
Eq(F_221(x, k_0, k_1), F_222(x, k_1) + F_95(x, k_0, k_1))
Eq(F_222(x, k_0), F_0(x)*F_16(x, k_0))
Eq(F_223(x, k_0, k_1), F_224(x, k_0, k_1)*F_5(x))
Eq(F_224(x, k_0, k_1), F_16(x, k_1) + F_225(x, k_0, k_1))
Eq(F_225(x, k_0, k_1), F_226(x, k_0, k_1) + F_227(x, k_0, k_1) + F_35(x))
Eq(F_226(x, k_0, k_1), F_13(x, k_0)*F_16(x, k_1))
Eq(F_227(x, k_0, k_1), F_13(x, k_1)*F_228(x, k_0, k_1))
Eq(F_228(x, k_0, k_1), F_229(x, k_0, k_1))
Eq(F_229(x, k_0, k_1), F_13(x, k_0) + F_225(x, k_0, k_1))
Eq(F_230(x, k_0, k_1), -F_231(x, k_0, 1) + (-k_0*F_231(x, k_0, 1) + k_1*F_231(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_231(x, k_0, k_1), F_232(x, k_0, k_0*k_1))
Eq(F_233(x, k_0, k_1), F_232(x, k_0, k_1) + F_277(x, k_0))
Eq(F_233(x, k_0, k_1), F_234(x, k_0, k_1) + F_64(x, k_0, k_1))
Eq(F_234(x, k_0, k_1), F_235(x, k_0, k_1))
Eq(F_235(x, k_0, k_1), F_236(x, k_0, k_1)*F_86(x))
Eq(F_236(x, k_0, k_1), F_118(x, k_0, k_1) + F_237(x, k_0, k_1))
Eq(F_237(x, k_0, k_1), -F_238(x, k_0, k_1) + (k_0*F_238(x, k_0, k_1) - F_238(x, 1, k_1))/(k_0 - 1))
Eq(F_238(x, k_0, k_1), F_239(x, k_0, k_1) + F_256(x, k_0, k_1))
Eq(F_239(x, k_0, k_1), F_240(x, k_0, k_1) + F_253(x, k_0, k_1))
Eq(F_240(x, k_0, k_1), F_10(x, k_0) + F_241(x, k_0, k_1))
Eq(F_241(x, k_0, k_1), F_242(x, k_0, k_1))
Eq(F_242(x, k_0, k_1), F_13(x, k_0)*F_243(x, k_0, k_1))
Eq(F_243(x, k_0, k_1), F_244(x, k_0, k_1) + F_247(x, k_1))
Eq(F_244(x, k_0, k_1), -F_245(x, k_0, 1) + (-k_0*F_245(x, k_0, 1) + k_1*F_245(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_245(x, k_0, k_1), F_246(x, k_0, k_0*k_1))
Eq(F_246(x, k_0, k_1), F_221(x, k_0, k_1) + F_232(x, k_0, k_1))
Eq(F_247(x, k_0), F_248(x, k_0) + F_249(x, k_0))
Eq(F_248(x, k_0), F_0(x)*F_15(x, k_0)*F_20(x, k_0))
Eq(F_250(x, k_0, k_1), F_230(x, k_0, k_1) + F_249(x, k_1))
Eq(F_214(x, k_0, k_1), F_250(x, k_0, k_1) + F_251(x, k_0, k_1))
Eq(F_251(x, k_0, k_1), F_216(x, k_0, k_1) + F_252(x, k_1))
Eq(F_252(x, k_0), F_15(x, k_0)*F_2(x)*F_20(x, k_0))
Eq(F_253(x, k_0, k_1), F_254(x, k_0, k_1))
Eq(F_254(x, k_0, k_1), F_255(x, k_0, k_1)*F_86(x))
Eq(F_255(x, k_0, k_1), -F_238(x, 1, k_1) + (k_0*F_238(x, k_0, k_1) - F_238(x, 1, k_1))/(k_0 - 1))
Eq(F_256(x, k_0, k_1), k_0*F_257(x, k_1))
Eq(F_257(x, k_0), F_258(x, k_0))
Eq(F_259(x, k_0), F_258(x, k_0) + F_275(x, k_0))
Eq(F_260(x, k_0), F_259(x, k_0) + F_269(x, k_0))
Eq(F_261(x, k_0), F_260(x, k_0)*F_86(x))
Eq(F_261(x, k_0), F_262(x, k_0))
Eq(F_263(x, k_0), F_262(x, k_0) + F_265(x, k_0))
Eq(F_264(x, k_0), F_13(x, k_0)*F_263(x, k_0))
Eq(F_264(x, k_0), F_10(x, k_0))
Eq(F_265(x, k_0), F_266(x, 1, k_0))
Eq(F_266(x, k_0, k_1), F_267(x, k_0*k_1, k_1))
Eq(F_267(x, k_0, k_1), F_240(x, k_0, k_1) + F_268(x, k_1))
Eq(F_268(x, k_0), F_15(x, k_0) + F_65(x, k_0))
Eq(F_269(x, k_0), F_270(x, 1, k_0))
Eq(F_270(x, k_0, k_1), (-k_0*F_271(x, k_0/k_1, k_1) + k_1*F_271(x, 1, k_1))/(-k_0 + k_1))
Eq(F_271(x, k_0, k_1), F_272(x, k_0*k_1, k_1))
Eq(F_272(x, k_0, k_1), F_239(x, k_0, k_1) + F_273(x, k_1))
Eq(F_273(x, k_0), F_274(x, k_0) + F_71(x, k_0))
Eq(F_274(x, k_0), F_0(x)*F_15(x, k_0))
Eq(F_276(x, k_0), F_13(x, k_0)*F_275(x, k_0))
Eq(F_276(x, k_0), F_125(x, k_0))
Eq(F_277(x, k_0), F_278(x, k_0) + F_279(x, k_0))
Eq(F_278(x, k_0), F_2(x) + F_54(x, k_0))
Eq(F_279(x, k_0), F_280(x, k_0))
Eq(F_280(x, k_0), F_281(x, k_0)*F_86(x))
Eq(F_281(x, k_0), F_282(x, k_0) + F_285(x, k_0))
Eq(F_282(x, k_0), -F_283(x, k_0) + (k_0*F_283(x, k_0) - F_283(x, 1))/(k_0 - 1))
Eq(F_283(x, k_0), F_284(x, k_0) + F_78(x, k_0))
Eq(F_284(x, k_0), F_13(x, k_0)*F_5(x))
Eq(F_285(x, k_0), (k_0*F_286(x, k_0) - F_286(x, 1))/(k_0 - 1))
Eq(F_286(x, k_0), F_277(x, k_0) + F_287(x, k_0))
Eq(F_287(x, k_0), F_288(x) + F_342(x, k_0))
Eq(F_288(x), F_289(x) - F_324(x))
Eq(F_289(x), F_290(x) - F_293(x))
Eq(F_290(x), F_291(x)/F_86(x))
Eq(F_291(x), F_292(x))
Eq(F_292(x), -F_2(x) + F_5(x))
Eq(F_293(x), F_294(x))
Eq(F_294(x), F_295(x)*F_86(x))
Eq(F_295(x), F_296(x, 1))
Eq(F_296(x, k_0), F_297(x, k_0) + F_301(x))
Eq(F_297(x, k_0), F_298(x, k_0) + F_8(x, k_0))
Eq(F_298(x, k_0), F_299(x, k_0))
Eq(F_299(x, k_0), F_300(x, k_0)*F_86(x))
Eq(F_300(x, k_0), (k_0*F_296(x, k_0) - F_296(x, 1))/(k_0 - 1))
Eq(F_301(x), F_302(x))
Eq(F_302(x), F_303(x)*F_86(x))
Eq(F_303(x), F_304(x) + F_306(x))
Eq(F_304(x), F_293(x) + F_305(x))
Eq(F_305(x), F_289(x) + F_4(x))
Eq(F_306(x), F_307(x))
Eq(F_307(x), F_304(x)*F_308(x)*F_86(x))
Eq(F_308(x), F_309(x) + F_312(x))
Eq(F_309(x), F_310(x) + F_82(x))
Eq(F_310(x), F_311(x))
Eq(F_311(x), F_308(x)*F_82(x)*F_86(x))
Eq(F_312(x), F_313(x))
Eq(F_313(x), F_314(x) + F_5(x))
Eq(F_314(x), F_315(x) - F_317(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_295(x)*F_86(x))
Eq(F_317(x), F_318(x) - F_332(x))
Eq(F_318(x), F_319(x) - F_321(x))
Eq(F_319(x), F_320(x)/F_86(x))
Eq(F_320(x), F_292(x))
Eq(F_321(x), F_322(x) - F_325(x))
Eq(F_322(x), F_323(x)/F_86(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_2(x) + F_292(x))
Eq(F_325(x), F_326(x) + F_329(x))
Eq(F_326(x), F_0(x) + F_327(x))
Eq(F_327(x), F_328(x))
Eq(F_328(x), F_0(x)*F_308(x)*F_86(x))
Eq(F_329(x), F_330(x) + F_332(x))
Eq(F_330(x), F_331(x))
Eq(F_331(x), F_7(x)*F_86(x))
Eq(F_332(x), F_333(x))
Eq(F_333(x), F_334(x)*F_86(x))
Eq(F_334(x), F_335(x, 1))
Eq(F_335(x, k_0), F_336(x, k_0) + F_339(x, k_0))
Eq(F_336(x, k_0), F_337(x, k_0, 1))
Eq(F_337(x, k_0, k_1), F_241(x, k_0, k_1) + F_338(x, k_1))
Eq(F_338(x, k_0), F_16(x, k_0) + F_66(x, k_0))
Eq(F_339(x, k_0), F_340(x, k_0))
Eq(F_340(x, k_0), F_341(x, k_0)*F_86(x))
Eq(F_341(x, k_0), (k_0*F_335(x, k_0) - F_335(x, 1))/(k_0 - 1))
Eq(F_342(x, k_0), k_0*F_343(x))
Eq(F_343(x), F_344(x))
Eq(F_344(x), F_306(x)*F_86(x)**2)
Eq(F_345(x, k_0), F_346(x, k_0) + F_347(x, k_0))
Eq(F_346(x, k_0), F_20(x, k_0)*F_65(x, k_0))
Eq(F_347(x, k_0), F_348(x, k_0))
Eq(F_348(x, k_0), F_349(x, k_0)*F_86(x))
Eq(F_349(x, k_0), F_350(x, k_0) + F_357(x, k_0))
Eq(F_350(x, k_0), F_351(x, k_0) + F_353(x, k_0))
Eq(F_351(x, k_0), F_15(x, k_0)*F_20(x, k_0)*F_352(x))
Eq(F_352(x), F_0(x) + F_330(x))
Eq(F_353(x, k_0), F_354(x, k_0))
Eq(F_354(x, k_0), F_352(x)*F_355(x, k_0)*F_86(x))
Eq(F_356(x, k_0), F_0(x)*F_355(x, k_0)*F_86(x))
Eq(F_356(x, k_0), F_249(x, k_0))
Eq(F_357(x, k_0), F_13(x, k_0)*F_358(x, k_0))
Eq(F_358(x, k_0), F_359(x, 1, k_0))
Eq(F_359(x, k_0, k_1), F_360(x, k_0, k_0*k_1))
Eq(F_360(x, k_0, k_1), F_240(x, k_0, k_1) + F_361(x, k_0, k_1))
Eq(F_361(x, k_0, k_1), F_362(x, k_0, k_1))
Eq(F_362(x, k_0, k_1), F_363(x, k_0, k_1)*F_86(x))
Eq(F_363(x, k_0, k_1), -F_360(x, 1, k_1) + (k_0*F_360(x, k_0, k_1) - F_360(x, 1, k_1))/(k_0 - 1))
Eq(F_364(x, k_0, k_1), F_365(x, k_0, k_1) + F_366(x, k_0, k_1))
Eq(F_365(x, k_0, k_1), F_20(x, k_1)*F_278(x, k_0))
Eq(F_367(x, k_0, k_1), F_366(x, k_0, k_1) + F_371(x, k_0, k_1))
Eq(F_367(x, k_0, k_1), F_368(x, k_0, k_1) + F_369(x, k_0, k_1))
Eq(F_368(x, k_0, k_1), F_15(x, k_1)*F_22(x, k_1)*F_278(x, k_0))
Eq(F_369(x, k_0, k_1), F_370(x, k_0, k_1))
Eq(F_370(x, k_0, k_1), F_13(x, k_0)*F_15(x, k_1)*F_177(x, k_0)*F_22(x, k_1))
Eq(F_371(x, k_0, k_1), F_372(x, k_0, k_1) + F_373(x, k_0))
Eq(F_372(x, k_0, k_1), F_22(x, k_1)*F_278(x, k_0))
Eq(F_373(x, k_0), F_374(x, k_0))
Eq(F_374(x, k_0), F_13(x, k_0)*F_177(x, k_0))
Eq(F_375(x, k_0), F_238(x, 1, k_0))
Eq(F_376(x, k_0, k_1), F_220(x, k_0, k_1) + F_377(x, k_0))
Eq(F_377(x, k_0), F_283(x, k_0) + F_4(x))
Eq(F_378(x, k_0, k_1), F_212(x, k_0, k_1) + F_54(x, k_0))
Pack JSON:
{"name": "point_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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": 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{"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25396/
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[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0],1]
F[11,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[8,x]
F[17,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[15,x,k[0],k[1],k[2]]*k[0]-F[15,x,1,k[1],k[2]])
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[22,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],1,k[2]]*k[0]-F[20,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[21,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2]]+F[55,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[2]]+F[29,x,k[0],k[2]]+F[31,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1]] = F[22,x,k[0]]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = (F[11,x,k[0],1]*k[0]-F[11,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[31,x,k[0],k[1],k[2]] = F[12,x,k[0],k[2]]*F[22,x,k[1]]
F[32,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[34,x,k[1],k[2]]+F[54,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1]] = F[35,x,k[1]]+F[52,x,k[0],k[1]]
F[35,x,k[0]] = F[36,x,k[0]]+F[46,x,k[0]]
F[36,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[45,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,1,k[0]]
F[39,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]*F[8,x]
F[41,x,k[0],k[1]] = 1/(-1+k[0])*(F[39,x,k[0],k[1]]*k[0]-F[39,x,1,k[1]])
F[42,x,k[0],k[1]] = F[22,x,k[1]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[44,x,k[0],1,k[1]]
F[44,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1]*k[2],k[2]]
F[45,x,k[0]] = F[22,x,k[0]]*F[35,x,k[0]]
F[46,x,k[0]] = k[0]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[36,x,k[0]]*F[49,x,k[0]]*F[8,x]
F[49,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]*F[49,x,k[0]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*F[47,x,k[1]]
F[54,x,k[0],k[1],k[2]] = F[53,x,k[0],k[2]]
F[55,x,k[0],k[1],k[2]] = F[56,x,k[0],k[2]]
F[43,x,k[0],k[1]] = F[12,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[22,x,k[1]]*F[34,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}, 1\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{12}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{11}\! \left(x , y_{0}, 1\right)-F_{11}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{2}\right) F_{22}\! \left(x , y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{1}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0}, 1, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{45}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = y_{0} F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{49}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{47}\! \left(x , y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{56}\! \left(x , y_{0}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_22(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0, 1))
Eq(F_11(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_29(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_8(x))
Eq(F_17(x, k_0, k_1, k_2), (k_0*F_15(x, k_0, k_1, k_2) - F_15(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_22(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, 1, k_2) + k_1*F_20(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_12(x, k_0, k_1) + k_2*F_12(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1, k_2), F_22(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_21(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_22(x, k_2)*F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2) + F_55(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_2) + F_29(x, k_0, k_2) + F_31(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1), F_22(x, k_0)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (-k_0*F_11(x, k_0, 1) + k_1*F_11(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_31(x, k_0, k_1, k_2), F_12(x, k_0, k_2)*F_22(x, k_1))
Eq(F_32(x, k_0, k_1, k_2), F_22(x, k_2)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_34(x, k_1, k_2) + F_54(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1), F_35(x, k_1) + F_52(x, k_0, k_1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_46(x, k_0))
Eq(F_36(x, k_0), F_1(x) + F_37(x, k_0) + F_45(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_40(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1)*F_8(x))
Eq(F_41(x, k_0, k_1), (k_0*F_39(x, k_0, k_1) - F_39(x, 1, k_1))/(k_0 - 1))
Eq(F_42(x, k_0, k_1), F_22(x, k_1)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_44(x, k_0, 1, k_1))
Eq(F_44(x, k_0, k_1, k_2), F_28(x, k_0, k_1*k_2, k_2))
Eq(F_45(x, k_0), F_22(x, k_0)*F_35(x, k_0))
Eq(F_46(x, k_0), k_0*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_36(x, k_0)*F_49(x, k_0)*F_8(x))
Eq(F_49(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0)*F_49(x, k_0))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), k_0*F_47(x, k_1))
Eq(F_54(x, k_0, k_1, k_2), F_53(x, k_0, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_56(x, k_0, k_2))
Eq(F_43(x, k_0, k_1), F_12(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_22(x, k_1)*F_34(x, k_0, k_1))
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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], 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0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [4, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [4, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[4, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[2, 0]]}]}}]}, {"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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "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"}}]}
Specification 5
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25673/
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[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0],1]
F[11,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[57,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[8,x]
F[17,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[15,x,k[0],k[1],k[2]]*k[0]-F[15,x,1,k[1],k[2]])
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[22,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],1,k[2]]*k[0]-F[20,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[21,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2]]+F[55,x,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[2]]+F[29,x,k[0],k[2]]+F[31,x,k[0],k[1],k[2]]+F[32,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1]] = F[22,x,k[0]]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = (F[11,x,k[0],1]*k[0]-F[11,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[31,x,k[0],k[1],k[2]] = F[12,x,k[0],k[2]]*F[22,x,k[1]]
F[32,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[34,x,k[1],k[2]]+F[54,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1]] = F[35,x,k[1]]+F[52,x,k[0],k[1]]
F[35,x,k[0]] = F[36,x,k[0]]+F[46,x,k[0]]
F[36,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[45,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,1,k[0]]
F[39,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]*F[8,x]
F[41,x,k[0],k[1]] = 1/(-1+k[0])*(F[39,x,k[0],k[1]]*k[0]-F[39,x,1,k[1]])
F[42,x,k[0],k[1]] = F[22,x,k[1]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[44,x,k[0],1,k[1]]
F[44,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1]*k[2],k[2]]
F[45,x,k[0]] = F[22,x,k[0]]*F[35,x,k[0]]
F[46,x,k[0]] = k[0]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[36,x,k[0]]*F[49,x,k[0]]*F[8,x]
F[49,x,k[0]] = F[1,x]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]*F[49,x,k[0]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = k[0]*F[47,x,k[1]]
F[54,x,k[0],k[1],k[2]] = F[53,x,k[0],k[2]]
F[55,x,k[0],k[1],k[2]] = F[56,x,k[0],k[2]]
F[43,x,k[0],k[1]] = F[12,x,k[0],k[1]]+F[56,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[22,x,k[1]]*F[34,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}, 1\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{12}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{11}\! \left(x , y_{0}, 1\right)-F_{11}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{2}\right) F_{22}\! \left(x , y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{1}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{44}\! \left(x , y_{0}, 1, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{45}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = y_{0} F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{49}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{22}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{47}\! \left(x , y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{56}\! \left(x , y_{0}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_22(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0, 1))
Eq(F_11(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_29(x, k_0, k_1) + F_57(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_8(x))
Eq(F_17(x, k_0, k_1, k_2), (k_0*F_15(x, k_0, k_1, k_2) - F_15(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_22(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, 1, k_2) + k_1*F_20(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_12(x, k_0, k_1) + k_2*F_12(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1, k_2), F_22(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_21(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_22(x, k_2)*F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2) + F_55(x, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_2) + F_29(x, k_0, k_2) + F_31(x, k_0, k_1, k_2) + F_32(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1), F_22(x, k_0)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), (-k_0*F_11(x, k_0, 1) + k_1*F_11(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_31(x, k_0, k_1, k_2), F_12(x, k_0, k_2)*F_22(x, k_1))
Eq(F_32(x, k_0, k_1, k_2), F_22(x, k_2)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_34(x, k_1, k_2) + F_54(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1), F_35(x, k_1) + F_52(x, k_0, k_1))
Eq(F_35(x, k_0), F_36(x, k_0) + F_46(x, k_0))
Eq(F_36(x, k_0), F_1(x) + F_37(x, k_0) + F_45(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_40(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1)*F_8(x))
Eq(F_41(x, k_0, k_1), (k_0*F_39(x, k_0, k_1) - F_39(x, 1, k_1))/(k_0 - 1))
Eq(F_42(x, k_0, k_1), F_22(x, k_1)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_44(x, k_0, 1, k_1))
Eq(F_44(x, k_0, k_1, k_2), F_28(x, k_0, k_1*k_2, k_2))
Eq(F_45(x, k_0), F_22(x, k_0)*F_35(x, k_0))
Eq(F_46(x, k_0), k_0*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_36(x, k_0)*F_49(x, k_0)*F_8(x))
Eq(F_49(x, k_0), F_1(x) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0)*F_49(x, k_0))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), k_0*F_47(x, k_1))
Eq(F_54(x, k_0, k_1, k_2), F_53(x, k_0, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_56(x, k_0, k_2))
Eq(F_43(x, k_0, k_1), F_12(x, k_0, k_1) + F_56(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_22(x, k_1)*F_34(x, k_0, k_1))
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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"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": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [0, 4, 1, 3, 2], [0, 4, 3, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
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