01342_01423_01432_02341_02413_02431_03412_03421
Counting sequence:
1, 1, 2, 6, 24, 112, 570, 3064, 17106, 98204, 576030, 3437076, 20796660, 127303696, 786958924, 4905865372, 30806558534, 194687435962, 1237294497628, 7902715882558, 50701233702936, 326591391118864, 2111387984943844, 13695072856551438, 89098084789131018, 581260154044071876, 3801671031251193482, 24922700950706288566, 163740672711446920468, 1077932006293460760428, 7109498329166468066740, 46972629855973675746258, 310856501537532892831260, 2060343600913271241190806, 13675508838913798550971804, 90893868914825092739583698, 604893926019807590415889674, 4030384708975068271125116642, 26884876582630376633817417094, 179530288104776990456323389158, 1200083411141882683155283615060, 8029839496243312718787771545046, 53777841260225675634756453077538, 360480482584802405564626563499000, 2418378105614424184135989581164998, 16237310299435139116624623596334526, 109102805077414466779131938369457618, 733626808909522952668254325594653768, 4936491123002275180659674535951902532, 33239364198280275869899140446143188896, 223957859181756490055097442089097451208, 1509899175145831235789342313167086008952, 10185610867617027390238378526653882680306, 68750168404367031008606998116774953592622, 464299944529780105457917244573947632588358, 3137276707299056499200764066536996559786424, 21209380278441997791044548932382674643627902, 143455160511810982902906829695534527364250654, 970755625149053234364928186328322921194264376, 6572068608651489128909977387214366291033613018, 44512905824897065044554037916723680018525029410, 301616488220649123510119755966271446226069828542, 2044576637025579456208173273307026912189521970698, 13865166620855602458906234320396018421362028680082, 94062096758124929153064363425091991453411807445468, 638361696332306586599719504908849369854342689985992, 4333876877234620997423696015891504251523935522730386, 29433310598231031171193379739774656486701559844685244, 199963108262730358759140023596255354435546054620932042, 1358953178799561128323411218501741719637583079724747858, 9238442863347834532375468974898254042891469149049609954, 62824454651663386931471717806171572221539952709918276624, 427356695436292216339459973162747935860180820871362928868, 2907906649707381406698445209779948999939019060031323540646, 19792244673365939291723108287431152202780707803263769479460, 134750661702880409215535861369288564454454053616679196205708, 917666303264543059085879596948318279505212415763560733907494, 6251058624534261602315235621960178526142024824809123999838030, 42592612177284773302167926461246516622798532670195510850359670, 290284615620384108942796340589816485107198978291280212543723096, 1978882630635715130629300104910153518656090778492593064278368338, 13493346180483932410619945660468003223969471959551353696266475574, 92028074119643782201664597045972809513111191539812924090492106626, 627797495967788933832698275298201237909372682173028258400732785292, 4283660250134083119047457470346797536545747162852086669477684993228, 29235084638955277705538192285327289091166737382002104929547030266560, 199565459404095636324622204822899105777973409825274641243559159684948, 1362560966022766116134617590221126841901937405442651793710760196797144, 9304948927150216877519085329399011938499733041807870290725836844471186, 63556143168646525382365522775365494376357311540477696515710037904019876, 434194822819319509684040875153608536066329670472190311378146426437957900, 2966835390656491402651397875003471315600218382293792548804984483662940326, 20275994541241282410221941997200850385296730787951156860847924450973428368, 138595472685922266208122851975613816942694909145792365455513475596884616052, 947528761509087129404001482285906102829230601146691222507196775093746968756, 6479039200180795848900991611019570804808930995442371294262867055853940800930, 44310033981518887077405276771998583999451702209767591604738835174352731615918, 303085596885127444947048957521328653693681671788541369338652531581256615527384, 2073474847800826186971856977828517783945288122496570961795003745654249106159602, 14187342900188163144940111613758622129693118560393088574321500712256178437163822, 97089169756332761529476957291993592706384245722514331700379861272018171515609104
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24992/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[49,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[16,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[16,x,k[0]]
F[14,x,k[0]] = F[11,x,k[0]]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[17,x,k[0]]
F[16,x,k[0]] = k[0]*x
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[12,x,k[0]]*F[16,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[33,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[16,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[24,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[28,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[16,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]+F[32,x,k[0]]
F[29,x] = 0
F[30,x,k[0]] = F[16,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[16,x,k[0]]+F[28,x,k[0]]
F[32,x,k[0]] = F[16,x,k[0]]*F[25,x,k[0]]
F[33,x,k[0]] = F[29,x]+F[34,x,k[0]]+F[41,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[37,x,k[0]]
F[36,x,k[0]] = F[12,x,k[0]]+F[17,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[45,x,k[0]]
F[38,x,k[0]] = F[29,x]+F[39,x,k[0]]+F[41,x,k[0]]
F[39,x,k[0]] = F[16,x,k[0]]*F[40,x,k[0]]
F[40,x,k[0]] = F[12,x,k[0]]+F[38,x,k[0]]
F[41,x,k[0]] = F[16,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[44,x,k[0]]
F[43,x,k[0]] = F[25,x,k[0]]+F[38,x,k[0]]
F[44,x,k[0]] = F[28,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = 2*F[29,x]+F[46,x,k[0]]+F[48,x,k[0]]
F[46,x,k[0]] = F[16,x,k[0]]*F[47,x,k[0]]
F[47,x,k[0]] = F[17,x,k[0]]+F[45,x,k[0]]
F[48,x,k[0]] = F[16,x,k[0]]*F[38,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[4,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[53,x,k[0]]
F[52,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[16,x,k[0]]*F[55,x,k[0]]
F[56,x,k[0]] = F[4,x]*F[55,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0],1]
F[58,x,k[0],k[1]] = F[59,x,k[0],k[0]*k[1]]
F[59,x,k[0],k[1]] = F[160,x,k[0],k[1]]+F[60,x,k[1]]
F[60,x,k[0]] = F[2,x]+F[61,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[16,x,k[0]]*F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[65,x,k[0]]
F[64,x,k[0]] = F[23,x,k[0]]*F[60,x,k[0]]
F[65,x,k[0]] = F[159,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[4,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,1,k[0]]
F[70,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[69,x,k[0],k[1]]
F[71,x,k[0],k[1]] = F[16,x,k[0]]*F[70,x,k[0],k[1]]
F[71,x,k[0],k[1]] = F[72,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[73,x,k[1],k[0]]
F[73,x,k[0],k[1]] = F[16,x,k[1]]*F[74,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[112,x,k[0]]+F[75,x,k[1],k[0]]
F[75,x,k[0],k[1]] = (F[76,x,k[0],1]*k[0]-F[76,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[76,x,k[0],k[1]] = F[77,x,k[0],k[0]*k[1]]
F[77,x,k[0],k[1]] = F[78,x,k[1]]+F[80,x,k[0],k[1]]
F[78,x,k[0]] = F[66,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[11,x,k[0]]+F[60,x,k[0]]
F[80,x,k[0],k[1]] = F[72,x,k[0],k[1]]+F[81,x,k[0],k[1]]
F[81,x,k[0],k[1]] = F[82,x,k[0],k[1]]
F[82,x,k[0],k[1]] = F[4,x]*F[83,x,k[0],k[1]]
F[83,x,k[0],k[1]] = -k[0]*(F[84,x,1,k[1]]-F[84,x,k[0],k[1]])/(-1+k[0])
F[84,x,k[0],k[1]] = F[80,x,k[0],k[1]]+F[85,x,k[0],k[1]]
F[85,x,k[0],k[1]] = k[0]*F[86,x,k[1]]
F[86,x,k[0]] = F[87,x,k[0]]
F[88,x,k[0]] = F[100,x,k[0]]+F[87,x,k[0]]
F[89,x,k[0]] = F[88,x,k[0]]+F[97,x,k[0]]
F[90,x,k[0]] = F[4,x]*F[89,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[92,x,k[0]] = F[91,x,k[0]]+F[94,x,k[0]]
F[93,x,k[0]] = F[16,x,k[0]]*F[92,x,k[0]]
F[93,x,k[0]] = F[7,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0],1]
F[95,x,k[0],k[1]] = F[96,x,k[0],k[0]*k[1]]
F[96,x,k[0],k[1]] = F[72,x,k[0],k[1]]+F[79,x,k[1]]
F[97,x,k[0]] = F[98,x,k[0],1]
F[98,x,k[0],k[1]] = F[99,x,k[0],k[0]*k[1]]
F[99,x,k[0],k[1]] = 1/(-1+k[0])*(F[77,x,k[0],k[1]]*k[0]-F[77,x,1,k[1]])
F[101,x,k[0]] = F[100,x,k[0]]*F[16,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]+F[7,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]+F[106,x,k[0]]
F[105,x,k[0]] = F[104,x,k[0]]*F[4,x]
F[105,x,k[0]] = F[49,x,k[0]]
F[107,x,k[0]] = F[106,x,k[0]]+F[110,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[4,x]
F[108,x,k[0]] = F[109,x,k[0]]
F[109,x,k[0]] = F[2,x]+F[49,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[66,x,k[0]]
F[111,x,k[0]] = F[0,x]+F[7,x,k[0]]
F[112,x,k[0]] = k[0]*F[113,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]+F[115,x,k[0]]
F[114,x,k[0]] = F[4,x]*F[79,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]*F[4,x]
F[117,x,k[0]] = F[118,x,k[0]]+F[66,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]*F[4,x]
F[120,x,k[0]] = F[121,x,1,k[0]]
F[122,x,k[0],k[1]] = F[121,x,k[0],k[1]]+F[124,x,k[0],k[1]]
F[123,x,k[0],k[1]] = F[122,x,k[0],k[1]]*F[16,x,k[0]]
F[123,x,k[0],k[1]] = F[84,x,k[0],k[1]]
F[125,x,k[0],k[1]] = F[124,x,k[0],k[1]]+F[127,x,k[0],k[1]]
F[126,x,k[0],k[1]] = F[125,x,k[0],k[1]]*F[16,x,k[0]]
F[126,x,k[0],k[1]] = F[80,x,k[0],k[1]]
F[127,x,k[0],k[1]] = F[128,x,k[0],k[1]]+F[69,x,k[0],k[1]]
F[128,x,k[0],k[1]] = F[129,x,k[0],k[1]]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]*F[4,x]
F[130,x,k[0],k[1]] = 1/(-1+k[0])*(F[121,x,k[0],k[1]]*k[0]-F[121,x,1,k[1]])
F[132,x,k[0],k[1]] = F[131,x,k[0],k[1]]+F[135,x,k[0],k[1]]
F[133,x,k[0],k[1]] = F[132,x,k[0],k[1]]*F[16,x,k[1]]
F[133,x,k[0],k[1]] = F[134,x,k[0],k[1]]
F[96,x,k[0],k[1]] = F[111,x,k[0]]+F[134,x,k[0],k[1]]
F[136,x,k[0],k[1]] = F[135,x,k[0],k[1]]+F[138,x,k[0],k[1]]
F[137,x,k[0],k[1]] = F[136,x,k[0],k[1]]*F[16,x,k[1]]
F[137,x,k[0],k[1]] = F[134,x,k[0],k[1]]
F[138,x,k[0],k[1]] = F[139,x,k[0],k[1]]
F[139,x,k[0],k[1]] = k[1]*F[140,x,k[0],k[1]]
F[140,x,k[0],k[1]] = F[141,x,k[0],k[1]]+F[143,x,k[0],k[1]]
F[141,x,k[0],k[1]] = F[142,x,k[0],k[1]]
F[142,x,k[0],k[1]] = F[11,x,k[1]]*F[111,x,k[0]]*F[4,x]
F[143,x,k[0],k[1]] = F[144,x,k[0],k[1]]
F[144,x,k[0],k[1]] = F[111,x,k[0]]*F[145,x,k[1]]*F[4,x]
F[146,x,k[0]] = F[0,x]*F[145,x,k[0]]*F[4,x]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,1,k[0]]
F[149,x,k[0],k[1]] = F[148,x,k[0],k[1]]+F[157,x,k[0],k[1]]
F[149,x,k[0],k[1]] = F[150,x,k[0],k[1]]+F[154,x,k[0],k[1]]
F[150,x,k[0],k[1]] = k[0]*F[151,x,k[1]]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]*F[4,x]
F[153,x,k[0]] = F[60,x,k[0]]+F[66,x,k[0]]
F[154,x,k[0],k[1]] = k[0]*F[155,x,k[1]]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[118,x,k[0]]*F[4,x]
F[157,x,k[0],k[1]] = F[158,x,k[0],k[1]]
F[158,x,k[0],k[1]] = F[11,x,k[1]]*F[16,x,k[0]]*F[2,x]
F[159,x,k[0]] = k[0]*F[115,x,k[0]]
F[160,x,k[0],k[1]] = F[161,x,k[1],k[0]]
F[161,x,k[0],k[1]] = F[16,x,k[1]]*F[162,x,k[0],k[1]]
F[162,x,k[0],k[1]] = F[163,x,k[1],k[0]]+F[167,x,k[0]]
F[163,x,k[0],k[1]] = (F[164,x,k[0],1]*k[0]-F[164,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[164,x,k[0],k[1]] = F[165,x,k[0],k[1]]+F[58,x,k[0],k[1]]
F[165,x,k[0],k[1]] = F[166,x,k[0],k[0]*k[1]]
F[166,x,k[0],k[1]] = F[66,x,k[1]]+F[81,x,k[0],k[1]]
F[167,x,k[0]] = F[159,x,k[0]]+F[168,x,k[0]]
F[168,x,k[0]] = F[16,x,k[0]]*F[60,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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y x
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{39}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y , 1\right)
F_{58}\! \left(x , y , z\right) = F_{59}\! \left(x , y , y z \right)
F_{59}\! \left(x , y , z\right) = F_{160}\! \left(x , y , z\right)+F_{60}\! \left(x , z\right)
F_{60}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{159}\! \left(x , y\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_{4}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , 1, y\right)
F_{70}\! \left(x , y , z\right) = F_{131}\! \left(x , y , z\right)+F_{69}\! \left(x , y , z\right)
F_{71}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right) F_{70}\! \left(x , y , z\right)
F_{71}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right)
F_{72}\! \left(x , y , z\right) = F_{73}\! \left(x , z , y\right)
F_{73}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{74}\! \left(x , y , z\right)
F_{74}\! \left(x , y , z\right) = F_{112}\! \left(x , y\right)+F_{75}\! \left(x , z , y\right)
F_{75}\! \left(x , y , z\right) = \frac{F_{76}\! \left(x , y , 1\right) y -F_{76}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{76}\! \left(x , y , z\right) = F_{77}\! \left(x , y , y z \right)
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , z\right)+F_{80}\! \left(x , y , z\right)
F_{78}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{80}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right)+F_{81}\! \left(x , y , z\right)
F_{81}\! \left(x , y , z\right) = F_{82}\! \left(x , y , z\right)
F_{82}\! \left(x , y , z\right) = F_{4}\! \left(x \right) F_{83}\! \left(x , y , z\right)
F_{83}\! \left(x , y , z\right) = -\frac{y \left(F_{84}\! \left(x , 1, z\right)-F_{84}\! \left(x , y , z\right)\right)}{-1+y}
F_{84}\! \left(x , y , z\right) = F_{80}\! \left(x , y , z\right)+F_{85}\! \left(x , y , z\right)
F_{85}\! \left(x , y , z\right) = y F_{86}\! \left(x , z\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y , 1\right)
F_{95}\! \left(x , y , z\right) = F_{96}\! \left(x , y , y z \right)
F_{96}\! \left(x , y , z\right) = F_{72}\! \left(x , y , z\right)+F_{79}\! \left(x , z\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y , 1\right)
F_{98}\! \left(x , y , z\right) = F_{99}\! \left(x , y , y z \right)
F_{99}\! \left(x , y , z\right) = -\frac{-F_{77}\! \left(x , y , z\right) y +F_{77}\! \left(x , 1, z\right)}{-1+y}
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = y F_{113}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , 1, y\right)
F_{122}\! \left(x , y , z\right) = F_{121}\! \left(x , y , z\right)+F_{124}\! \left(x , y , z\right)
F_{123}\! \left(x , y , z\right) = F_{122}\! \left(x , y , z\right) F_{16}\! \left(x , y\right)
F_{123}\! \left(x , y , z\right) = F_{84}\! \left(x , y , z\right)
F_{125}\! \left(x , y , z\right) = F_{124}\! \left(x , y , z\right)+F_{127}\! \left(x , y , z\right)
F_{126}\! \left(x , y , z\right) = F_{125}\! \left(x , y , z\right) F_{16}\! \left(x , y\right)
F_{126}\! \left(x , y , z\right) = F_{80}\! \left(x , y , z\right)
F_{127}\! \left(x , y , z\right) = F_{128}\! \left(x , y , z\right)+F_{69}\! \left(x , y , z\right)
F_{128}\! \left(x , y , z\right) = F_{129}\! \left(x , y , z\right)
F_{129}\! \left(x , y , z\right) = F_{130}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{130}\! \left(x , y , z\right) = -\frac{-F_{121}\! \left(x , y , z\right) y +F_{121}\! \left(x , 1, z\right)}{-1+y}
F_{132}\! \left(x , y , z\right) = F_{131}\! \left(x , y , z\right)+F_{135}\! \left(x , y , z\right)
F_{133}\! \left(x , y , z\right) = F_{132}\! \left(x , y , z\right) F_{16}\! \left(x , z\right)
F_{133}\! \left(x , y , z\right) = F_{134}\! \left(x , y , z\right)
F_{96}\! \left(x , y , z\right) = F_{111}\! \left(x , y\right)+F_{134}\! \left(x , y , z\right)
F_{136}\! \left(x , y , z\right) = F_{135}\! \left(x , y , z\right)+F_{138}\! \left(x , y , z\right)
F_{137}\! \left(x , y , z\right) = F_{136}\! \left(x , y , z\right) F_{16}\! \left(x , z\right)
F_{137}\! \left(x , y , z\right) = F_{134}\! \left(x , y , z\right)
F_{138}\! \left(x , y , z\right) = F_{139}\! \left(x , y , z\right)
F_{139}\! \left(x , y , z\right) = z F_{140}\! \left(x , y , z\right)
F_{140}\! \left(x , y , z\right) = F_{141}\! \left(x , y , z\right)+F_{143}\! \left(x , y , z\right)
F_{141}\! \left(x , y , z\right) = F_{142}\! \left(x , y , z\right)
F_{142}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{111}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{143}\! \left(x , y , z\right) = F_{144}\! \left(x , y , z\right)
F_{144}\! \left(x , y , z\right) = F_{111}\! \left(x , y\right) F_{145}\! \left(x , z\right) F_{4}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{145}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , 1, y\right)
F_{149}\! \left(x , y , z\right) = F_{148}\! \left(x , y , z\right)+F_{157}\! \left(x , y , z\right)
F_{149}\! \left(x , y , z\right) = F_{150}\! \left(x , y , z\right)+F_{154}\! \left(x , y , z\right)
F_{150}\! \left(x , y , z\right) = y F_{151}\! \left(x , z\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{154}\! \left(x , y , z\right) = y F_{155}\! \left(x , z\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{157}\! \left(x , y , z\right) = F_{158}\! \left(x , y , z\right)
F_{158}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{16}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{159}\! \left(x , y\right) = y F_{115}\! \left(x , y\right)
F_{160}\! \left(x , y , z\right) = F_{161}\! \left(x , z , y\right)
F_{161}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right) F_{162}\! \left(x , y , z\right)
F_{162}\! \left(x , y , z\right) = F_{163}\! \left(x , z , y\right)+F_{167}\! \left(x , y\right)
F_{163}\! \left(x , y , z\right) = \frac{y F_{164}\! \left(x , y , 1\right)-z F_{164}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{164}\! \left(x , y , z\right) = F_{165}\! \left(x , y , z\right)+F_{58}\! \left(x , y , z\right)
F_{165}\! \left(x , y , z\right) = F_{166}\! \left(x , y , y z \right)
F_{166}\! \left(x , y , z\right) = F_{66}\! \left(x , z\right)+F_{81}\! \left(x , y , z\right)
F_{167}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{60}\! \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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_49(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_16(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_16(x, k_0))
Eq(F_14(x, k_0), F_11(x, k_0) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_17(x, k_0))
Eq(F_16(x, k_0), k_0*x)
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_12(x, k_0)*F_16(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_33(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_16(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_24(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_28(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_16(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0) + F_32(x, k_0))
Eq(F_29(x), 0)
Eq(F_30(x, k_0), F_16(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_16(x, k_0) + F_28(x, k_0))
Eq(F_32(x, k_0), F_16(x, k_0)*F_25(x, k_0))
Eq(F_33(x, k_0), F_29(x) + F_34(x, k_0) + F_41(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_37(x, k_0))
Eq(F_36(x, k_0), F_12(x, k_0) + F_17(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_45(x, k_0))
Eq(F_38(x, k_0), F_29(x) + F_39(x, k_0) + F_41(x, k_0))
Eq(F_39(x, k_0), F_16(x, k_0)*F_40(x, k_0))
Eq(F_40(x, k_0), F_12(x, k_0) + F_38(x, k_0))
Eq(F_41(x, k_0), F_16(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_44(x, k_0))
Eq(F_43(x, k_0), F_25(x, k_0) + F_38(x, k_0))
Eq(F_44(x, k_0), F_28(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), 2*F_29(x) + F_46(x, k_0) + F_48(x, k_0))
Eq(F_46(x, k_0), F_16(x, k_0)*F_47(x, k_0))
Eq(F_47(x, k_0), F_17(x, k_0) + F_45(x, k_0))
Eq(F_48(x, k_0), F_16(x, k_0)*F_38(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_4(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_53(x, k_0))
Eq(F_52(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_16(x, k_0)*F_55(x, k_0))
Eq(F_56(x, k_0), F_4(x)*F_55(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0, 1))
Eq(F_58(x, k_0, k_1), F_59(x, k_0, k_0*k_1))
Eq(F_59(x, k_0, k_1), F_160(x, k_0, k_1) + F_60(x, k_1))
Eq(F_60(x, k_0), F_2(x) + F_61(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_16(x, k_0)*F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_65(x, k_0))
Eq(F_64(x, k_0), F_23(x, k_0)*F_60(x, k_0))
Eq(F_65(x, k_0), F_159(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_4(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, 1, k_0))
Eq(F_70(x, k_0, k_1), F_131(x, k_0, k_1) + F_69(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), F_16(x, k_0)*F_70(x, k_0, k_1))
Eq(F_71(x, k_0, k_1), F_72(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_73(x, k_1, k_0))
Eq(F_73(x, k_0, k_1), F_16(x, k_1)*F_74(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_112(x, k_0) + F_75(x, k_1, k_0))
Eq(F_75(x, k_0, k_1), (-k_0*F_76(x, k_0, 1) + k_1*F_76(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_76(x, k_0, k_1), F_77(x, k_0, k_0*k_1))
Eq(F_77(x, k_0, k_1), F_78(x, k_1) + F_80(x, k_0, k_1))
Eq(F_78(x, k_0), F_66(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_11(x, k_0) + F_60(x, k_0))
Eq(F_80(x, k_0, k_1), F_72(x, k_0, k_1) + F_81(x, k_0, k_1))
Eq(F_81(x, k_0, k_1), F_82(x, k_0, k_1))
Eq(F_82(x, k_0, k_1), F_4(x)*F_83(x, k_0, k_1))
Eq(F_83(x, k_0, k_1), -F_84(x, 1, k_1) + (k_0*F_84(x, k_0, k_1) - F_84(x, 1, k_1))/(k_0 - 1))
Eq(F_84(x, k_0, k_1), F_80(x, k_0, k_1) + F_85(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), k_0*F_86(x, k_1))
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_88(x, k_0), F_100(x, k_0) + F_87(x, k_0))
Eq(F_89(x, k_0), F_88(x, k_0) + F_97(x, k_0))
Eq(F_90(x, k_0), F_4(x)*F_89(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_92(x, k_0), F_91(x, k_0) + F_94(x, k_0))
Eq(F_93(x, k_0), F_16(x, k_0)*F_92(x, k_0))
Eq(F_93(x, k_0), F_7(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0, 1))
Eq(F_95(x, k_0, k_1), F_96(x, k_0, k_0*k_1))
Eq(F_96(x, k_0, k_1), F_72(x, k_0, k_1) + F_79(x, k_1))
Eq(F_97(x, k_0), F_98(x, k_0, 1))
Eq(F_98(x, k_0, k_1), F_99(x, k_0, k_0*k_1))
Eq(F_99(x, k_0, k_1), (k_0*F_77(x, k_0, k_1) - F_77(x, 1, k_1))/(k_0 - 1))
Eq(F_101(x, k_0), F_100(x, k_0)*F_16(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0) + F_7(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0) + F_106(x, k_0))
Eq(F_105(x, k_0), F_104(x, k_0)*F_4(x))
Eq(F_105(x, k_0), F_49(x, k_0))
Eq(F_107(x, k_0), F_106(x, k_0) + F_110(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_4(x))
Eq(F_108(x, k_0), F_109(x, k_0))
Eq(F_109(x, k_0), F_2(x) + F_49(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_66(x, k_0))
Eq(F_111(x, k_0), F_0(x) + F_7(x, k_0))
Eq(F_112(x, k_0), k_0*F_113(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0) + F_115(x, k_0))
Eq(F_114(x, k_0), F_4(x)*F_79(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0)*F_4(x))
Eq(F_117(x, k_0), F_118(x, k_0) + F_66(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0)*F_4(x))
Eq(F_120(x, k_0), F_121(x, 1, k_0))
Eq(F_122(x, k_0, k_1), F_121(x, k_0, k_1) + F_124(x, k_0, k_1))
Eq(F_123(x, k_0, k_1), F_122(x, k_0, k_1)*F_16(x, k_0))
Eq(F_123(x, k_0, k_1), F_84(x, k_0, k_1))
Eq(F_125(x, k_0, k_1), F_124(x, k_0, k_1) + F_127(x, k_0, k_1))
Eq(F_126(x, k_0, k_1), F_125(x, k_0, k_1)*F_16(x, k_0))
Eq(F_126(x, k_0, k_1), F_80(x, k_0, k_1))
Eq(F_127(x, k_0, k_1), F_128(x, k_0, k_1) + F_69(x, k_0, k_1))
Eq(F_128(x, k_0, k_1), F_129(x, k_0, k_1))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1)*F_4(x))
Eq(F_130(x, k_0, k_1), (k_0*F_121(x, k_0, k_1) - F_121(x, 1, k_1))/(k_0 - 1))
Eq(F_132(x, k_0, k_1), F_131(x, k_0, k_1) + F_135(x, k_0, k_1))
Eq(F_133(x, k_0, k_1), F_132(x, k_0, k_1)*F_16(x, k_1))
Eq(F_133(x, k_0, k_1), F_134(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), F_111(x, k_0) + F_134(x, k_0, k_1))
Eq(F_136(x, k_0, k_1), F_135(x, k_0, k_1) + F_138(x, k_0, k_1))
Eq(F_137(x, k_0, k_1), F_136(x, k_0, k_1)*F_16(x, k_1))
Eq(F_137(x, k_0, k_1), F_134(x, k_0, k_1))
Eq(F_138(x, k_0, k_1), F_139(x, k_0, k_1))
Eq(F_139(x, k_0, k_1), k_1*F_140(x, k_0, k_1))
Eq(F_140(x, k_0, k_1), F_141(x, k_0, k_1) + F_143(x, k_0, k_1))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1))
Eq(F_142(x, k_0, k_1), F_11(x, k_1)*F_111(x, k_0)*F_4(x))
Eq(F_143(x, k_0, k_1), F_144(x, k_0, k_1))
Eq(F_144(x, k_0, k_1), F_111(x, k_0)*F_145(x, k_1)*F_4(x))
Eq(F_146(x, k_0), F_0(x)*F_145(x, k_0)*F_4(x))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, 1, k_0))
Eq(F_149(x, k_0, k_1), F_148(x, k_0, k_1) + F_157(x, k_0, k_1))
Eq(F_149(x, k_0, k_1), F_150(x, k_0, k_1) + F_154(x, k_0, k_1))
Eq(F_150(x, k_0, k_1), k_0*F_151(x, k_1))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0)*F_4(x))
Eq(F_153(x, k_0), F_60(x, k_0) + F_66(x, k_0))
Eq(F_154(x, k_0, k_1), k_0*F_155(x, k_1))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_118(x, k_0)*F_4(x))
Eq(F_157(x, k_0, k_1), F_158(x, k_0, k_1))
Eq(F_158(x, k_0, k_1), F_11(x, k_1)*F_16(x, k_0)*F_2(x))
Eq(F_159(x, k_0), k_0*F_115(x, k_0))
Eq(F_160(x, k_0, k_1), F_161(x, k_1, k_0))
Eq(F_161(x, k_0, k_1), F_16(x, k_1)*F_162(x, k_0, k_1))
Eq(F_162(x, k_0, k_1), F_163(x, k_1, k_0) + F_167(x, k_0))
Eq(F_163(x, k_0, k_1), (-k_0*F_164(x, k_0, 1) + k_1*F_164(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_164(x, k_0, k_1), F_165(x, k_0, k_1) + F_58(x, k_0, k_1))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_0*k_1))
Eq(F_166(x, k_0, k_1), F_66(x, k_1) + F_81(x, k_0, k_1))
Eq(F_167(x, k_0), F_159(x, k_0) + F_168(x, k_0))
Eq(F_168(x, k_0), F_16(x, k_0)*F_60(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, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "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, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]]}], "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, 2, 3], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 1], [2, 3]]}, {"patt": [2, 0, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 3], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 3], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 3], [2, 3], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 3], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, 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"requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 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, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "indices": [0, 0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25906/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[50,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[15,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[11,x,k[0]]+F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[12,x,k[0]]*F[14,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[33,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[14,x,k[0]]*F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[24,x,k[0]]
F[23,x,k[0]] = F[1,x]+F[14,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[28,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[14,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]+F[32,x,k[0]]
F[29,x] = 0
F[30,x,k[0]] = F[14,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[14,x,k[0]]+F[28,x,k[0]]
F[32,x,k[0]] = F[14,x,k[0]]*F[25,x,k[0]]
F[33,x,k[0]] = F[29,x]+F[34,x,k[0]]+F[42,x,k[0]]
F[34,x,k[0]] = F[14,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[38,x,k[0]]
F[36,x,k[0]] = F[12,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = F[18,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[46,x,k[0]]
F[39,x,k[0]] = F[29,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[14,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[12,x,k[0]]+F[39,x,k[0]]
F[42,x,k[0]] = F[14,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[25,x,k[0]]+F[39,x,k[0]]
F[45,x,k[0]] = F[28,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = 2*F[29,x]+F[47,x,k[0]]+F[49,x,k[0]]
F[47,x,k[0]] = F[14,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[37,x,k[0]]+F[46,x,k[0]]
F[49,x,k[0]] = F[14,x,k[0]]*F[39,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[4,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[54,x,k[0]]
F[53,x,k[0]] = -k[0]*(F[7,x,1]-F[7,x,k[0]])/(-1+k[0])
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[14,x,k[0]]*F[56,x,k[0]]
F[57,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0],1]
F[59,x,k[0],k[1]] = F[60,x,k[0],k[0]*k[1]]
F[60,x,k[0],k[1]] = F[161,x,k[0],k[1]]+F[61,x,k[1]]
F[61,x,k[0]] = F[2,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[14,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[66,x,k[0]]
F[65,x,k[0]] = F[23,x,k[0]]*F[61,x,k[0]]
F[66,x,k[0]] = F[160,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,1,k[0]]
F[71,x,k[0],k[1]] = F[132,x,k[0],k[1]]+F[70,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[14,x,k[0]]*F[71,x,k[0],k[1]]
F[72,x,k[0],k[1]] = F[73,x,k[0],k[1]]
F[73,x,k[0],k[1]] = F[74,x,k[1],k[0]]
F[74,x,k[0],k[1]] = F[14,x,k[1]]*F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = F[113,x,k[0]]+F[76,x,k[1],k[0]]
F[76,x,k[0],k[1]] = (F[77,x,k[0],1]*k[0]-F[77,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[77,x,k[0],k[1]] = F[78,x,k[0],k[0]*k[1]]
F[78,x,k[0],k[1]] = F[79,x,k[1]]+F[81,x,k[0],k[1]]
F[79,x,k[0]] = F[67,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = F[11,x,k[0]]+F[61,x,k[0]]
F[81,x,k[0],k[1]] = F[73,x,k[0],k[1]]+F[82,x,k[0],k[1]]
F[82,x,k[0],k[1]] = F[83,x,k[0],k[1]]
F[83,x,k[0],k[1]] = F[4,x]*F[84,x,k[0],k[1]]
F[84,x,k[0],k[1]] = -k[0]*(F[85,x,1,k[1]]-F[85,x,k[0],k[1]])/(-1+k[0])
F[85,x,k[0],k[1]] = F[81,x,k[0],k[1]]+F[86,x,k[0],k[1]]
F[86,x,k[0],k[1]] = k[0]*F[87,x,k[1]]
F[87,x,k[0]] = F[88,x,k[0]]
F[89,x,k[0]] = F[101,x,k[0]]+F[88,x,k[0]]
F[90,x,k[0]] = F[89,x,k[0]]+F[98,x,k[0]]
F[91,x,k[0]] = F[4,x]*F[90,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[93,x,k[0]] = F[92,x,k[0]]+F[95,x,k[0]]
F[94,x,k[0]] = F[14,x,k[0]]*F[93,x,k[0]]
F[94,x,k[0]] = F[7,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0],1]
F[96,x,k[0],k[1]] = F[97,x,k[0],k[0]*k[1]]
F[97,x,k[0],k[1]] = F[73,x,k[0],k[1]]+F[80,x,k[1]]
F[98,x,k[0]] = F[99,x,k[0],1]
F[99,x,k[0],k[1]] = F[100,x,k[0],k[0]*k[1]]
F[100,x,k[0],k[1]] = 1/(-1+k[0])*(F[78,x,k[0],k[1]]*k[0]-F[78,x,1,k[1]])
F[102,x,k[0]] = F[101,x,k[0]]*F[14,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[104,x,k[0]] = F[103,x,k[0]]+F[7,x,k[0]]
F[105,x,k[0]] = F[104,x,k[0]]+F[107,x,k[0]]
F[106,x,k[0]] = F[105,x,k[0]]*F[4,x]
F[106,x,k[0]] = F[50,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]+F[111,x,k[0]]
F[109,x,k[0]] = F[108,x,k[0]]*F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[2,x]+F[50,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[67,x,k[0]]
F[112,x,k[0]] = F[0,x]+F[7,x,k[0]]
F[113,x,k[0]] = k[0]*F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[116,x,k[0]]
F[115,x,k[0]] = F[4,x]*F[80,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]*F[4,x]
F[118,x,k[0]] = F[119,x,k[0]]+F[67,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[4,x]
F[121,x,k[0]] = F[122,x,1,k[0]]
F[123,x,k[0],k[1]] = F[122,x,k[0],k[1]]+F[125,x,k[0],k[1]]
F[124,x,k[0],k[1]] = F[123,x,k[0],k[1]]*F[14,x,k[0]]
F[124,x,k[0],k[1]] = F[85,x,k[0],k[1]]
F[126,x,k[0],k[1]] = F[125,x,k[0],k[1]]+F[128,x,k[0],k[1]]
F[127,x,k[0],k[1]] = F[126,x,k[0],k[1]]*F[14,x,k[0]]
F[127,x,k[0],k[1]] = F[81,x,k[0],k[1]]
F[128,x,k[0],k[1]] = F[129,x,k[0],k[1]]+F[70,x,k[0],k[1]]
F[129,x,k[0],k[1]] = F[130,x,k[0],k[1]]
F[130,x,k[0],k[1]] = F[131,x,k[0],k[1]]*F[4,x]
F[131,x,k[0],k[1]] = 1/(-1+k[0])*(F[122,x,k[0],k[1]]*k[0]-F[122,x,1,k[1]])
F[133,x,k[0],k[1]] = F[132,x,k[0],k[1]]+F[136,x,k[0],k[1]]
F[134,x,k[0],k[1]] = F[133,x,k[0],k[1]]*F[14,x,k[1]]
F[134,x,k[0],k[1]] = F[135,x,k[0],k[1]]
F[97,x,k[0],k[1]] = F[112,x,k[0]]+F[135,x,k[0],k[1]]
F[137,x,k[0],k[1]] = F[136,x,k[0],k[1]]+F[139,x,k[0],k[1]]
F[138,x,k[0],k[1]] = F[137,x,k[0],k[1]]*F[14,x,k[1]]
F[138,x,k[0],k[1]] = F[135,x,k[0],k[1]]
F[139,x,k[0],k[1]] = F[140,x,k[0],k[1]]
F[140,x,k[0],k[1]] = k[1]*F[141,x,k[0],k[1]]
F[141,x,k[0],k[1]] = F[142,x,k[0],k[1]]+F[144,x,k[0],k[1]]
F[142,x,k[0],k[1]] = F[143,x,k[0],k[1]]
F[143,x,k[0],k[1]] = F[11,x,k[1]]*F[112,x,k[0]]*F[4,x]
F[144,x,k[0],k[1]] = F[145,x,k[0],k[1]]
F[145,x,k[0],k[1]] = F[112,x,k[0]]*F[146,x,k[1]]*F[4,x]
F[147,x,k[0]] = F[0,x]*F[146,x,k[0]]*F[4,x]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,1,k[0]]
F[150,x,k[0],k[1]] = F[149,x,k[0],k[1]]+F[158,x,k[0],k[1]]
F[150,x,k[0],k[1]] = F[151,x,k[0],k[1]]+F[155,x,k[0],k[1]]
F[151,x,k[0],k[1]] = k[0]*F[152,x,k[1]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]*F[4,x]
F[154,x,k[0]] = F[61,x,k[0]]+F[67,x,k[0]]
F[155,x,k[0],k[1]] = k[0]*F[156,x,k[1]]
F[156,x,k[0]] = F[157,x,k[0]]
F[157,x,k[0]] = F[119,x,k[0]]*F[4,x]
F[158,x,k[0],k[1]] = F[159,x,k[0],k[1]]
F[159,x,k[0],k[1]] = F[11,x,k[1]]*F[14,x,k[0]]*F[2,x]
F[160,x,k[0]] = k[0]*F[116,x,k[0]]
F[161,x,k[0],k[1]] = F[162,x,k[1],k[0]]
F[162,x,k[0],k[1]] = F[14,x,k[1]]*F[163,x,k[0],k[1]]
F[163,x,k[0],k[1]] = F[164,x,k[1],k[0]]+F[168,x,k[0]]
F[164,x,k[0],k[1]] = (F[165,x,k[0],1]*k[0]-F[165,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[165,x,k[0],k[1]] = F[166,x,k[0],k[1]]+F[59,x,k[0],k[1]]
F[166,x,k[0],k[1]] = F[167,x,k[0],k[0]*k[1]]
F[167,x,k[0],k[1]] = F[67,x,k[1]]+F[82,x,k[0],k[1]]
F[168,x,k[0]] = F[160,x,k[0]]+F[169,x,k[0]]
F[169,x,k[0]] = F[14,x,k[0]]*F[61,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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y , 1\right)
F_{59}\! \left(x , y , z\right) = F_{60}\! \left(x , y , y z \right)
F_{60}\! \left(x , y , z\right) = F_{161}\! \left(x , y , z\right)+F_{61}\! \left(x , z\right)
F_{61}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{61}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , 1, y\right)
F_{71}\! \left(x , y , z\right) = F_{132}\! \left(x , y , z\right)+F_{70}\! \left(x , y , z\right)
F_{72}\! \left(x , y , z\right) = F_{14}\! \left(x , y\right) F_{71}\! \left(x , y , z\right)
F_{72}\! \left(x , y , z\right) = F_{73}\! \left(x , y , z\right)
F_{73}\! \left(x , y , z\right) = F_{74}\! \left(x , z , y\right)
F_{74}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{75}\! \left(x , y , z\right)
F_{75}\! \left(x , y , z\right) = F_{113}\! \left(x , y\right)+F_{76}\! \left(x , z , y\right)
F_{76}\! \left(x , y , z\right) = \frac{F_{77}\! \left(x , y , 1\right) y -F_{77}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{77}\! \left(x , y , z\right) = F_{78}\! \left(x , y , y z \right)
F_{78}\! \left(x , y , z\right) = F_{79}\! \left(x , z\right)+F_{81}\! \left(x , y , z\right)
F_{79}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{81}\! \left(x , y , z\right) = F_{73}\! \left(x , y , z\right)+F_{82}\! \left(x , y , z\right)
F_{82}\! \left(x , y , z\right) = F_{83}\! \left(x , y , z\right)
F_{83}\! \left(x , y , z\right) = F_{4}\! \left(x \right) F_{84}\! \left(x , y , z\right)
F_{84}\! \left(x , y , z\right) = -\frac{y \left(F_{85}\! \left(x , 1, z\right)-F_{85}\! \left(x , y , z\right)\right)}{-1+y}
F_{85}\! \left(x , y , z\right) = F_{81}\! \left(x , y , z\right)+F_{86}\! \left(x , y , z\right)
F_{86}\! \left(x , y , z\right) = y F_{87}\! \left(x , z\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y , 1\right)
F_{96}\! \left(x , y , z\right) = F_{97}\! \left(x , y , y z \right)
F_{97}\! \left(x , y , z\right) = F_{73}\! \left(x , y , z\right)+F_{80}\! \left(x , z\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y , 1\right)
F_{99}\! \left(x , y , z\right) = F_{100}\! \left(x , y , y z \right)
F_{100}\! \left(x , y , z\right) = -\frac{-y F_{78}\! \left(x , y , z\right)+F_{78}\! \left(x , 1, z\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{107}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{50}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = y F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , 1, y\right)
F_{123}\! \left(x , y , z\right) = F_{122}\! \left(x , y , z\right)+F_{125}\! \left(x , y , z\right)
F_{124}\! \left(x , y , z\right) = F_{123}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)
F_{124}\! \left(x , y , z\right) = F_{85}\! \left(x , y , z\right)
F_{126}\! \left(x , y , z\right) = F_{125}\! \left(x , y , z\right)+F_{128}\! \left(x , y , z\right)
F_{127}\! \left(x , y , z\right) = F_{126}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)
F_{127}\! \left(x , y , z\right) = F_{81}\! \left(x , y , z\right)
F_{128}\! \left(x , y , z\right) = F_{129}\! \left(x , y , z\right)+F_{70}\! \left(x , y , z\right)
F_{129}\! \left(x , y , z\right) = F_{130}\! \left(x , y , z\right)
F_{130}\! \left(x , y , z\right) = F_{131}\! \left(x , y , z\right) F_{4}\! \left(x \right)
F_{131}\! \left(x , y , z\right) = -\frac{-y F_{122}\! \left(x , y , z\right)+F_{122}\! \left(x , 1, z\right)}{-1+y}
F_{133}\! \left(x , y , z\right) = F_{132}\! \left(x , y , z\right)+F_{136}\! \left(x , y , z\right)
F_{134}\! \left(x , y , z\right) = F_{133}\! \left(x , y , z\right) F_{14}\! \left(x , z\right)
F_{134}\! \left(x , y , z\right) = F_{135}\! \left(x , y , z\right)
F_{97}\! \left(x , y , z\right) = F_{112}\! \left(x , y\right)+F_{135}\! \left(x , y , z\right)
F_{137}\! \left(x , y , z\right) = F_{136}\! \left(x , y , z\right)+F_{139}\! \left(x , y , z\right)
F_{138}\! \left(x , y , z\right) = F_{137}\! \left(x , y , z\right) F_{14}\! \left(x , z\right)
F_{138}\! \left(x , y , z\right) = F_{135}\! \left(x , y , z\right)
F_{139}\! \left(x , y , z\right) = F_{140}\! \left(x , y , z\right)
F_{140}\! \left(x , y , z\right) = z F_{141}\! \left(x , y , z\right)
F_{141}\! \left(x , y , z\right) = F_{142}\! \left(x , y , z\right)+F_{144}\! \left(x , y , z\right)
F_{142}\! \left(x , y , z\right) = F_{143}\! \left(x , y , z\right)
F_{143}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{112}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{144}\! \left(x , y , z\right) = F_{145}\! \left(x , y , z\right)
F_{145}\! \left(x , y , z\right) = F_{112}\! \left(x , y\right) F_{146}\! \left(x , z\right) F_{4}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{146}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , 1, y\right)
F_{150}\! \left(x , y , z\right) = F_{149}\! \left(x , y , z\right)+F_{158}\! \left(x , y , z\right)
F_{150}\! \left(x , y , z\right) = F_{151}\! \left(x , y , z\right)+F_{155}\! \left(x , y , z\right)
F_{151}\! \left(x , y , z\right) = y F_{152}\! \left(x , z\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{154}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{155}\! \left(x , y , z\right) = y F_{156}\! \left(x , z\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{158}\! \left(x , y , z\right) = F_{159}\! \left(x , y , z\right)
F_{159}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{14}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{160}\! \left(x , y\right) = y F_{116}\! \left(x , y\right)
F_{161}\! \left(x , y , z\right) = F_{162}\! \left(x , z , y\right)
F_{162}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{163}\! \left(x , y , z\right)
F_{163}\! \left(x , y , z\right) = F_{164}\! \left(x , z , y\right)+F_{168}\! \left(x , y\right)
F_{164}\! \left(x , y , z\right) = \frac{y F_{165}\! \left(x , y , 1\right)-z F_{165}\! \left(x , y , \frac{z}{y}\right)}{-z +y}
F_{165}\! \left(x , y , z\right) = F_{166}\! \left(x , y , z\right)+F_{59}\! \left(x , y , z\right)
F_{166}\! \left(x , y , z\right) = F_{167}\! \left(x , y , y z \right)
F_{167}\! \left(x , y , z\right) = F_{67}\! \left(x , z\right)+F_{82}\! \left(x , y , z\right)
F_{168}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{61}\! \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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_50(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_14(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_15(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_11(x, k_0) + F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_12(x, k_0)*F_14(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_33(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_14(x, k_0)*F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_24(x, k_0))
Eq(F_23(x, k_0), F_1(x) + F_14(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_28(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_14(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0) + F_32(x, k_0))
Eq(F_29(x), 0)
Eq(F_30(x, k_0), F_14(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_14(x, k_0) + F_28(x, k_0))
Eq(F_32(x, k_0), F_14(x, k_0)*F_25(x, k_0))
Eq(F_33(x, k_0), F_29(x) + F_34(x, k_0) + F_42(x, k_0))
Eq(F_34(x, k_0), F_14(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_38(x, k_0))
Eq(F_36(x, k_0), F_12(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), F_18(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_46(x, k_0))
Eq(F_39(x, k_0), F_29(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_14(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_12(x, k_0) + F_39(x, k_0))
Eq(F_42(x, k_0), F_14(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_25(x, k_0) + F_39(x, k_0))
Eq(F_45(x, k_0), F_28(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), 2*F_29(x) + F_47(x, k_0) + F_49(x, k_0))
Eq(F_47(x, k_0), F_14(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_37(x, k_0) + F_46(x, k_0))
Eq(F_49(x, k_0), F_14(x, k_0)*F_39(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_4(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_54(x, k_0))
Eq(F_53(x, k_0), -F_7(x, 1) + (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_14(x, k_0)*F_56(x, k_0))
Eq(F_57(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0, 1))
Eq(F_59(x, k_0, k_1), F_60(x, k_0, k_0*k_1))
Eq(F_60(x, k_0, k_1), F_161(x, k_0, k_1) + F_61(x, k_1))
Eq(F_61(x, k_0), F_2(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_14(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_66(x, k_0))
Eq(F_65(x, k_0), F_23(x, k_0)*F_61(x, k_0))
Eq(F_66(x, k_0), F_160(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, 1, k_0))
Eq(F_71(x, k_0, k_1), F_132(x, k_0, k_1) + F_70(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_14(x, k_0)*F_71(x, k_0, k_1))
Eq(F_72(x, k_0, k_1), F_73(x, k_0, k_1))
Eq(F_73(x, k_0, k_1), F_74(x, k_1, k_0))
Eq(F_74(x, k_0, k_1), F_14(x, k_1)*F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), F_113(x, k_0) + F_76(x, k_1, k_0))
Eq(F_76(x, k_0, k_1), (-k_0*F_77(x, k_0, 1) + k_1*F_77(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_77(x, k_0, k_1), F_78(x, k_0, k_0*k_1))
Eq(F_78(x, k_0, k_1), F_79(x, k_1) + F_81(x, k_0, k_1))
Eq(F_79(x, k_0), F_67(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), F_11(x, k_0) + F_61(x, k_0))
Eq(F_81(x, k_0, k_1), F_73(x, k_0, k_1) + F_82(x, k_0, k_1))
Eq(F_82(x, k_0, k_1), F_83(x, k_0, k_1))
Eq(F_83(x, k_0, k_1), F_4(x)*F_84(x, k_0, k_1))
Eq(F_84(x, k_0, k_1), -F_85(x, 1, k_1) + (k_0*F_85(x, k_0, k_1) - F_85(x, 1, k_1))/(k_0 - 1))
Eq(F_85(x, k_0, k_1), F_81(x, k_0, k_1) + F_86(x, k_0, k_1))
Eq(F_86(x, k_0, k_1), k_0*F_87(x, k_1))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_89(x, k_0), F_101(x, k_0) + F_88(x, k_0))
Eq(F_90(x, k_0), F_89(x, k_0) + F_98(x, k_0))
Eq(F_91(x, k_0), F_4(x)*F_90(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_93(x, k_0), F_92(x, k_0) + F_95(x, k_0))
Eq(F_94(x, k_0), F_14(x, k_0)*F_93(x, k_0))
Eq(F_94(x, k_0), F_7(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0, 1))
Eq(F_96(x, k_0, k_1), F_97(x, k_0, k_0*k_1))
Eq(F_97(x, k_0, k_1), F_73(x, k_0, k_1) + F_80(x, k_1))
Eq(F_98(x, k_0), F_99(x, k_0, 1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_0*k_1))
Eq(F_100(x, k_0, k_1), (k_0*F_78(x, k_0, k_1) - F_78(x, 1, k_1))/(k_0 - 1))
Eq(F_102(x, k_0), F_101(x, k_0)*F_14(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_104(x, k_0), F_103(x, k_0) + F_7(x, k_0))
Eq(F_105(x, k_0), F_104(x, k_0) + F_107(x, k_0))
Eq(F_106(x, k_0), F_105(x, k_0)*F_4(x))
Eq(F_106(x, k_0), F_50(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0) + F_111(x, k_0))
Eq(F_109(x, k_0), F_108(x, k_0)*F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_2(x) + F_50(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_67(x, k_0))
Eq(F_112(x, k_0), F_0(x) + F_7(x, k_0))
Eq(F_113(x, k_0), k_0*F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_116(x, k_0))
Eq(F_115(x, k_0), F_4(x)*F_80(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0)*F_4(x))
Eq(F_118(x, k_0), F_119(x, k_0) + F_67(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_4(x))
Eq(F_121(x, k_0), F_122(x, 1, k_0))
Eq(F_123(x, k_0, k_1), F_122(x, k_0, k_1) + F_125(x, k_0, k_1))
Eq(F_124(x, k_0, k_1), F_123(x, k_0, k_1)*F_14(x, k_0))
Eq(F_124(x, k_0, k_1), F_85(x, k_0, k_1))
Eq(F_126(x, k_0, k_1), F_125(x, k_0, k_1) + F_128(x, k_0, k_1))
Eq(F_127(x, k_0, k_1), F_126(x, k_0, k_1)*F_14(x, k_0))
Eq(F_127(x, k_0, k_1), F_81(x, k_0, k_1))
Eq(F_128(x, k_0, k_1), F_129(x, k_0, k_1) + F_70(x, k_0, k_1))
Eq(F_129(x, k_0, k_1), F_130(x, k_0, k_1))
Eq(F_130(x, k_0, k_1), F_131(x, k_0, k_1)*F_4(x))
Eq(F_131(x, k_0, k_1), (k_0*F_122(x, k_0, k_1) - F_122(x, 1, k_1))/(k_0 - 1))
Eq(F_133(x, k_0, k_1), F_132(x, k_0, k_1) + F_136(x, k_0, k_1))
Eq(F_134(x, k_0, k_1), F_133(x, k_0, k_1)*F_14(x, k_1))
Eq(F_134(x, k_0, k_1), F_135(x, k_0, k_1))
Eq(F_97(x, k_0, k_1), F_112(x, k_0) + F_135(x, k_0, k_1))
Eq(F_137(x, k_0, k_1), F_136(x, k_0, k_1) + F_139(x, k_0, k_1))
Eq(F_138(x, k_0, k_1), F_137(x, k_0, k_1)*F_14(x, k_1))
Eq(F_138(x, k_0, k_1), F_135(x, k_0, k_1))
Eq(F_139(x, k_0, k_1), F_140(x, k_0, k_1))
Eq(F_140(x, k_0, k_1), k_1*F_141(x, k_0, k_1))
Eq(F_141(x, k_0, k_1), F_142(x, k_0, k_1) + F_144(x, k_0, k_1))
Eq(F_142(x, k_0, k_1), F_143(x, k_0, k_1))
Eq(F_143(x, k_0, k_1), F_11(x, k_1)*F_112(x, k_0)*F_4(x))
Eq(F_144(x, k_0, k_1), F_145(x, k_0, k_1))
Eq(F_145(x, k_0, k_1), F_112(x, k_0)*F_146(x, k_1)*F_4(x))
Eq(F_147(x, k_0), F_0(x)*F_146(x, k_0)*F_4(x))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, 1, k_0))
Eq(F_150(x, k_0, k_1), F_149(x, k_0, k_1) + F_158(x, k_0, k_1))
Eq(F_150(x, k_0, k_1), F_151(x, k_0, k_1) + F_155(x, k_0, k_1))
Eq(F_151(x, k_0, k_1), k_0*F_152(x, k_1))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0)*F_4(x))
Eq(F_154(x, k_0), F_61(x, k_0) + F_67(x, k_0))
Eq(F_155(x, k_0, k_1), k_0*F_156(x, k_1))
Eq(F_156(x, k_0), F_157(x, k_0))
Eq(F_157(x, k_0), F_119(x, k_0)*F_4(x))
Eq(F_158(x, k_0, k_1), F_159(x, k_0, k_1))
Eq(F_159(x, k_0, k_1), F_11(x, k_1)*F_14(x, k_0)*F_2(x))
Eq(F_160(x, k_0), k_0*F_116(x, k_0))
Eq(F_161(x, k_0, k_1), F_162(x, k_1, k_0))
Eq(F_162(x, k_0, k_1), F_14(x, k_1)*F_163(x, k_0, k_1))
Eq(F_163(x, k_0, k_1), F_164(x, k_1, k_0) + F_168(x, k_0))
Eq(F_164(x, k_0, k_1), (-k_0*F_165(x, k_0, 1) + k_1*F_165(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_165(x, k_0, k_1), F_166(x, k_0, k_1) + F_59(x, k_0, k_1))
Eq(F_166(x, k_0, k_1), F_167(x, k_0, k_0*k_1))
Eq(F_167(x, k_0, k_1), F_67(x, k_1) + F_82(x, k_0, k_1))
Eq(F_168(x, k_0), F_160(x, k_0) + F_169(x, k_0))
Eq(F_169(x, k_0), F_14(x, k_0)*F_61(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, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "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, 2, 3], [0, 1, 4, 3, 2], [0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]]}], "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, 2, 3], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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