01243_01342_02143_10243_10342_12043_20143_20341_21043_30142_30241_31042
Counting sequence:
1, 1, 2, 6, 24, 108, 512, 2501, 12469, 63117, 323302, 1671958, 8715360, 45736091, 241402304, 1280603408, 6823766712, 36505829481, 196000221628, 1055753103958, 5703695476643, 30898137957678, 167802344738747, 913424294068838, 4982925370558436, 27237662753631018, 149166709507890233, 818350303123129654, 4497025749343470849, 24750731121549864196, 136423330156104744630, 752994626110022603169, 4161646998085036938812, 23029196734529535527528, 127586537091249841610626, 707648800993391552836796, 3929106054715171546618022, 21837887363715030607200386, 121492013851618249023530442, 676528026699653453693647889, 3770567935309045720102112597, 21032639020627479051197771484, 117416989987959490769791624526, 655999358974414859559916213978, 3667728624460196429543567596533, 20521028049477238826021678914411, 114893845304343827287534395343664, 643692491436122624468516914907368, 3608553086714396895858553844454933, 20241854008462943546161460612158103, 113610934864203622245144952528390965, 638018516208198766852068609654545510, 3584931611122509221251258862807975247, 20153686951319149959251707739720803769, 113356442666129026177345958193568592605, 637893831737350162628142703103313763089, 3591318257671296770167779384022327274048, 20228134621360531504228811131450937013237, 113985002466062209514882423222523267435253, 642574254853034800079611734295139054326248, 3623904517422804282611503472307817870299855, 20445717151440132121788782409353001173206757, 115397060310726822907310460553051027512487700, 651551574520758340469699234068827113006036926, 3680099811675589984012952837315945353700673669, 20793253528431446166935589236103975681060172791, 117525704099550073121648364786344860151269100948, 664487076284762987275457933437007126925296677670, 3758195464327411074061057149003178363067829332228, 21262160605074645572515494119749636120686049640745, 120328041676830585364261886688086275147628064181832, 681167785624726060730110496938983981899857245516943, 3857142378127374778624166242783495758551142636882667, 21847322285581792361561696286292194672704252501389732, 123779443487458073876874468607868915494340986560337817, 701477129358332742559457306006528298643222333060729846, 3976401410278802822231319322914748529960186792293681325, 22546325919435710546134321883005987761570062296888121581, 127869643188431335067114850237464025843672867129015732868, 725375013445418992845868191006005126618296807207802186262, 4115841550299843331915548308406444518818509196735655129343, 23358941755916615785108971903237167873252494015990257601822, 132600076130370424469723151623920922637111286813195615440740, 752884215043020185835589643186763544896268024660268073551256, 4275670356792538249773085220700491916554622094433415813586567, 24286767463545617354507434995291026503654782999527702860850055, 137982063770473291611483093250121767573072612666047699548257031, 784081116568284596109853057785042523967634335846598638781459956, 4456386715672594102745631952264385327843716546785324597257131986, 25332987579807544243748183993802398427190597150327918823013724394, 144035590780367668258373705864300103200814812394904750077960667902, 819089501157694971055463250052613692007323682051560197885301730950, 4658749436680710854342260452291881470843132426887877457514373062105, 26502215035119117089171878467138202302893525037476556867969759976784, 150788508171947239411123689890226612600968671540794451480400533977393, 858076563181945495291344689568158765631094104559906067219699354048388, 4883757386871706514287649169788522697066098761456298854992821490626832, 27800392872663845905261923009504338705437741284374699601653214483069017, 158276051072201138895979240147346205295957528481528380446509774125519781, 901250566506459402358203946021847261412317148210094639570684210836678942, 5132638269368732702158982066997609012649903171269518388910349158341218302
Implicit equation for the generating function in Maple syntax:
x*(-2+x)^3*F(x)^4-(-2+x)*(2*x^3-5*x^2+7*x+2)*F(x)^3+(x^4-4*x^3-x^2+5*x-12)*F(x)^2+(x^3+6*x^2-13*x+12)*F(x)-(-2+x)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(-2+x \right)^{3} F \! \left(x \right)^{4}-\left(-2+x \right) \left(2 x^{3}-5 x^{2}+7 x +2\right) F \! \left(x \right)^{3}+\left(x^{4}-4 x^{3}-x^{2}+5 x -12\right) F \! \left(x \right)^{2}+\left(x^{3}+6 x^{2}-13 x +12\right) F \! \left(x \right)-\left(-2+x \right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 512
a(7) = 2501
a(8) = 12469
a(9) = 63117
a(10) = 323302
a(11) = 1671958
a(12) = 8715360
a(13) = 45736091
a(14) = 241402304
a(15) = 1280603408
a(16) = 6823766712
a(17) = 36505829481
a(18) = 196000221628
a(19) = 1055753103958
a(20) = 5703695476643
a(21) = 30898137957678
a(22) = 167802344738747
a(23) = 913424294068838
a(24) = 4982925370558436
a(25) = 27237662753631018
a(26) = 149166709507890233
a(27) = 818350303123129654
a(n+28) = -1/30720*(31516778278*n^3+841462557981*n^2+7496579138537*n+22287597464106)/(2*n+55)/(n+29)/(n+27)*a(n+9)-1/30720*(741983406041*n^3+32890936371861*n^2+485448799376962*n+2385545264638644)/(2*n+55)/(n+29)/(n+27)*a(n+15)+1/30720*(700784092055*n^3+32941685418648*n^2+515374537405225*n+2683433893055406)/(2*n+55)/(n+29)/(n+27)*a(n+16)+1/30720*(297483730202*n^3+10640720094825*n^2+126836603311975*n+503847945646062)/(2*n+55)/(n+29)/(n+27)*a(n+12)-1/15360*(237664284106*n^3+9197509610028*n^2+118578908298797*n+509313370025646)/(2*n+55)/(n+29)/(n+27)*a(n+13)+1/30720*(647849616911*n^3+26920950651375*n^2+372579311384284*n+1717360306380432)/(2*n+55)/(n+29)/(n+27)*a(n+14)+1/3072*(4386446*n^3+58007511*n^2+255672610*n+375332838)/(2*n+55)/(n+29)/(n+27)*a(n+4)-5/6144*(283018*n^3+3076239*n^2+11053949*n+13119282)/(2*n+55)/(n+29)/(n+27)*a(n+3)-1/3072*(22674653*n^3+354467859*n^2+1851588214*n+3230615070)/(2*n+55)/(n+29)/(n+27)*a(n+5)-1/10240*(1210250547*n^3+25267196910*n^2+176205532001*n+410472808158)/(2*n+55)/(n+29)/(n+27)*a(n+7)+1/10240*(328599474*n^3+5972655641*n^2+36279549427*n+73639719230)/(2*n+55)/(n+29)/(n+27)*a(n+6)+875/6144*n*(n+2)*(n+1)/(2*n+55)/(n+29)/(n+27)*a(n)-25/2048*(228*n+625)*(n+2)*(n+1)/(2*n+55)/(n+29)/(n+27)*a(n+1)-1/30720*(531001369961*n^3+26306786644710*n^2+433489777776679*n+2375586259876506)/(2*n+55)/(n+29)/(n+27)*a(n+17)+5/2048*(n+2)*(12219*n^2+78434*n+124405)/(2*n+55)/(n+29)/(n+27)*a(n+2)+1/30720*(75974323358*n^3+2258935692363*n^2+22401001460167*n+74094508634898)/(2*n+55)/(n+29)/(n+27)*a(n+10)+1/2560*(955935121*n^3+22683724790*n^2+179700955093*n+475308321231)/(2*n+55)/(n+29)/(n+27)*a(n+8)-1/30720*(160879333307*n^3+5272307058660*n^2+57601354945165*n+209805861629610)/(2*n+55)/(n+29)/(n+27)*a(n+11)+1/30720*(307298183668*n^3+15912614787105*n^2+273706497937685*n+1563295725282534)/(2*n+55)/(n+29)/(n+27)*a(n+18)-1/30720*(120507824759*n^3+6398751887964*n^2+112355150114875*n+651437342346234)/(2*n+55)/(n+29)/(n+27)*a(n+19)+1/15360*(8552975023*n^3+388012621785*n^2+5187819208514*n+16996336585704)/(2*n+55)/(n+29)/(n+27)*a(n+20)+1/30720*(14877233195*n^3+1037532442962*n^2+23941077793165*n+182972002172190)/(2*n+55)/(n+29)/(n+27)*a(n+21)-1/5120*(2189485589*n^3+149351061358*n^2+3393952568051*n+25693998013522)/(2*n+55)/(n+29)/(n+27)*a(n+22)+1/2560*(468972551*n^3+32838058058*n^2+766326045129*n+5960132903878)/(2*n+55)/(n+29)/(n+27)*a(n+23)-1/960*(47712497*n^3+3456891525*n^2+83470483981*n+671705393211)/(2*n+55)/(n+29)/(n+27)*a(n+24)+1/960*(8502071*n^3+638684184*n^2+15988566751*n+133383489654)/(2*n+55)/(n+29)/(n+27)*a(n+25)-1/960*(969455*n^3+75521514*n^2+1960413373*n+16957668738)/(2*n+55)/(n+29)/(n+27)*a(n+26)+1/120*(8069*n^3+651303*n^2+17516788*n+156978780)/(2*n+55)/(n+29)/(n+27)*a(n+27), n >= 28
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 512
a(7) = 2501
a(8) = 12469
a(9) = 63117
a(10) = 323302
a(11) = 1671958
a(12) = 8715360
a(13) = 45736091
a(14) = 241402304
a(15) = 1280603408
a(16) = 6823766712
a(17) = 36505829481
a(18) = 196000221628
a(19) = 1055753103958
a(20) = 5703695476643
a(21) = 30898137957678
a(22) = 167802344738747
a(23) = 913424294068838
a(24) = 4982925370558436
a(25) = 27237662753631018
a(26) = 149166709507890233
a(27) = 818350303123129654
a{\left(n + 28 \right)} = \frac{875 n \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{6144 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{25 \left(n + 1\right) \left(n + 2\right) \left(228 n + 625\right) a{\left(n + 1 \right)}}{2048 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{5 \left(n + 2\right) \left(12219 n^{2} + 78434 n + 124405\right) a{\left(n + 2 \right)}}{2048 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(8069 n^{3} + 651303 n^{2} + 17516788 n + 156978780\right) a{\left(n + 27 \right)}}{120 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{5 \left(283018 n^{3} + 3076239 n^{2} + 11053949 n + 13119282\right) a{\left(n + 3 \right)}}{6144 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(969455 n^{3} + 75521514 n^{2} + 1960413373 n + 16957668738\right) a{\left(n + 26 \right)}}{960 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(4386446 n^{3} + 58007511 n^{2} + 255672610 n + 375332838\right) a{\left(n + 4 \right)}}{3072 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(8502071 n^{3} + 638684184 n^{2} + 15988566751 n + 133383489654\right) a{\left(n + 25 \right)}}{960 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(22674653 n^{3} + 354467859 n^{2} + 1851588214 n + 3230615070\right) a{\left(n + 5 \right)}}{3072 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(47712497 n^{3} + 3456891525 n^{2} + 83470483981 n + 671705393211\right) a{\left(n + 24 \right)}}{960 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(328599474 n^{3} + 5972655641 n^{2} + 36279549427 n + 73639719230\right) a{\left(n + 6 \right)}}{10240 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(468972551 n^{3} + 32838058058 n^{2} + 766326045129 n + 5960132903878\right) a{\left(n + 23 \right)}}{2560 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(955935121 n^{3} + 22683724790 n^{2} + 179700955093 n + 475308321231\right) a{\left(n + 8 \right)}}{2560 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(1210250547 n^{3} + 25267196910 n^{2} + 176205532001 n + 410472808158\right) a{\left(n + 7 \right)}}{10240 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(2189485589 n^{3} + 149351061358 n^{2} + 3393952568051 n + 25693998013522\right) a{\left(n + 22 \right)}}{5120 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(8552975023 n^{3} + 388012621785 n^{2} + 5187819208514 n + 16996336585704\right) a{\left(n + 20 \right)}}{15360 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(14877233195 n^{3} + 1037532442962 n^{2} + 23941077793165 n + 182972002172190\right) a{\left(n + 21 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(31516778278 n^{3} + 841462557981 n^{2} + 7496579138537 n + 22287597464106\right) a{\left(n + 9 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(75974323358 n^{3} + 2258935692363 n^{2} + 22401001460167 n + 74094508634898\right) a{\left(n + 10 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(120507824759 n^{3} + 6398751887964 n^{2} + 112355150114875 n + 651437342346234\right) a{\left(n + 19 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(160879333307 n^{3} + 5272307058660 n^{2} + 57601354945165 n + 209805861629610\right) a{\left(n + 11 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(237664284106 n^{3} + 9197509610028 n^{2} + 118578908298797 n + 509313370025646\right) a{\left(n + 13 \right)}}{15360 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(297483730202 n^{3} + 10640720094825 n^{2} + 126836603311975 n + 503847945646062\right) a{\left(n + 12 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(307298183668 n^{3} + 15912614787105 n^{2} + 273706497937685 n + 1563295725282534\right) a{\left(n + 18 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(531001369961 n^{3} + 26306786644710 n^{2} + 433489777776679 n + 2375586259876506\right) a{\left(n + 17 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(647849616911 n^{3} + 26920950651375 n^{2} + 372579311384284 n + 1717360306380432\right) a{\left(n + 14 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} + \frac{\left(700784092055 n^{3} + 32941685418648 n^{2} + 515374537405225 n + 2683433893055406\right) a{\left(n + 16 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)} - \frac{\left(741983406041 n^{3} + 32890936371861 n^{2} + 485448799376962 n + 2385545264638644\right) a{\left(n + 15 \right)}}{30720 \left(n + 27\right) \left(n + 29\right) \left(2 n + 55\right)}, \quad n \geq 28
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24489/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = 1/F[15,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]+F[84,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = -F[84,x]+F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[13,x]*F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[21,x]
F[21,x] = F[22,x]+F[76,x]
F[22,x] = F[23,x]+F[48,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = -F[26,x]+F[11,x]
F[26,x] = F[27,x]+F[36,x]
F[27,x] = -F[33,x]+F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[32,x]+F[31,x]
F[31,x] = -F[0,x]+F[13,x]
F[32,x] = (x*F[32,x]+x-1)*(x*F[32,x]+x-2*F[32,x])
F[33,x] = -F[12,x]+F[34,x]
F[34,x] = 1/F[15,x]*F[35,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[27,x]*F[38,x]
F[38,x] = F[39,x]+F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]*F[41,x]
F[41,x] = F[42,x]+F[7,x]
F[42,x] = F[43,x]
F[43,x] = F[15,x]*F[44,x]
F[44,x] = F[25,x]+F[42,x]
F[45,x] = F[46,x]+F[9,x]
F[46,x] = F[47,x]
F[47,x] = F[15,x]*F[42,x]
F[48,x] = F[49,x]
F[49,x] = F[15,x]*F[44,x]*F[50,x]
F[50,x] = F[13,x]+F[51,x]
F[51,x] = 1/F[15,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[15,x]*F[55,x]
F[55,x] = F[56,x]+F[61,x]
F[56,x] = F[57,x]
F[57,x] = F[15,x]*F[50,x]*F[58,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[15,x]*F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[15,x]*F[58,x]*F[63,x]
F[63,x] = 1/F[15,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[66,x]
F[66,x] = F[67,x]+F[72,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]
F[69,x] = -F[0,x]+F[70,x]
F[70,x] = 1/F[15,x]*F[71,x]
F[71,x] = F[2,x]
F[72,x] = F[73,x]*F[75,x]
F[73,x] = F[53,x]+F[74,x]
F[74,x] = F[14,x]
F[75,x] = F[68,x]+F[70,x]
F[76,x] = F[77,x]
F[77,x] = F[15,x]*F[44,x]*F[78,x]
F[78,x] = -F[81,x]+F[79,x]
F[79,x] = 1/F[15,x]*F[80,x]
F[80,x] = F[31,x]
F[81,x] = F[82,x]
F[82,x] = 1/F[15,x]*F[83,x]
F[83,x] = F[53,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[15,x]*F[38,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{84}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{76}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{48}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}+2 x^{2} F_{32}\! \left(x \right)-2 x F_{32} \left(x \right)^{2}+x^{2}-3 x F_{32}\! \left(x \right)-x +2 F_{32}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{7}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{9}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right) F_{50}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{15}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right) F_{58}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{2}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{53}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right)
F_{75}\! \left(x \right) = F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{53}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{38}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_15(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_15(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x) + F_84(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) - F_84(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_13(x)*F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_76(x))
Eq(F_22(x), F_23(x) + F_48(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_11(x) - F_26(x))
Eq(F_26(x), F_27(x) + F_36(x))
Eq(F_27(x), F_28(x) - F_33(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_32(x))
Eq(F_31(x), -F_0(x) + F_13(x))
Eq(F_32(x), x*(x - 2)*(F_32(x) + 1)**2 + (x + 1)*(F_32(x) + 1) + F_32(x) - 1)
Eq(F_33(x), -F_12(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_15(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_27(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_7(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_15(x)*F_44(x))
Eq(F_44(x), F_25(x) + F_42(x))
Eq(F_45(x), F_46(x) + F_9(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_15(x)*F_42(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_15(x)*F_44(x)*F_50(x))
Eq(F_50(x), F_13(x) + F_51(x))
Eq(F_51(x), F_52(x)/F_15(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_15(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_61(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_15(x)*F_50(x)*F_58(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_15(x)*F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_15(x)*F_58(x)*F_63(x))
Eq(F_63(x), F_64(x)/F_15(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_72(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), -F_0(x) + F_70(x))
Eq(F_70(x), F_71(x)/F_15(x))
Eq(F_71(x), F_2(x))
Eq(F_72(x), F_73(x)*F_75(x))
Eq(F_73(x), F_53(x) + F_74(x))
Eq(F_74(x), F_14(x))
Eq(F_75(x), F_68(x) + F_70(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_15(x)*F_44(x)*F_78(x))
Eq(F_78(x), F_79(x) - F_81(x))
Eq(F_79(x), F_80(x)/F_15(x))
Eq(F_80(x), F_31(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x)/F_15(x))
Eq(F_83(x), F_53(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_15(x)*F_38(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 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0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 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": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24836/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = 1/F[15,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]+F[80,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = -F[80,x]+F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[13,x]*F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[21,x]
F[21,x] = F[22,x]+F[75,x]
F[22,x] = F[23,x]+F[50,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[47,x]
F[25,x] = -F[26,x]+F[11,x]
F[26,x] = F[27,x]+F[38,x]
F[27,x] = -F[33,x]+F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[32,x]+F[13,x]
F[32,x] = -1+(x^2-2*x)*F[32,x]^2+(2+x)*F[32,x]
F[33,x] = -F[12,x]+F[34,x]
F[34,x] = 1/F[15,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = (x*F[37,x]+x-2*F[37,x])*(x*F[37,x]+x-1)
F[38,x] = F[39,x]
F[39,x] = F[15,x]*F[27,x]*F[40,x]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[15,x]*F[43,x]
F[43,x] = F[44,x]+F[7,x]
F[44,x] = F[45,x]
F[45,x] = F[15,x]*F[46,x]
F[46,x] = F[25,x]+F[44,x]
F[47,x] = F[48,x]+F[9,x]
F[48,x] = F[49,x]
F[49,x] = F[15,x]*F[44,x]
F[50,x] = F[51,x]
F[51,x] = F[15,x]*F[46,x]*F[52,x]
F[52,x] = -F[55,x]+F[53,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[36,x]
F[55,x] = F[56,x]
F[56,x] = 1/F[15,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[15,x]*F[60,x]
F[60,x] = F[61,x]+F[74,x]
F[61,x] = F[62,x]+F[64,x]
F[62,x] = F[58,x]+F[63,x]
F[63,x] = F[14,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[66,x]
F[66,x] = F[67,x]+F[72,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]
F[69,x] = -F[0,x]+F[70,x]
F[70,x] = 1/F[15,x]*F[71,x]
F[71,x] = F[2,x]
F[72,x] = F[62,x]*F[73,x]
F[73,x] = F[68,x]+F[70,x]
F[74,x] = F[58,x]
F[75,x] = F[76,x]
F[76,x] = F[15,x]*F[46,x]*F[77,x]
F[77,x] = F[13,x]+F[78,x]
F[78,x] = 1/F[15,x]*F[79,x]
F[79,x] = F[58,x]
F[80,x] = F[81,x]
F[81,x] = F[12,x]*F[15,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{80}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{75}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{50}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{47}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{38}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}-2 x F_{32} \left(x \right)^{2}+x F_{32}\! \left(x \right)+2 F_{32}\! \left(x \right)-1
F_{33}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = x^{2} F_{37} \left(x \right)^{2}+2 x^{2} F_{37}\! \left(x \right)-2 x F_{37} \left(x \right)^{2}+x^{2}-3 x F_{37}\! \left(x \right)-x +2 F_{37}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{25}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{74}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{2}\! \left(x \right)
F_{72}\! \left(x \right) = F_{62}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{58}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{13}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{58}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_15(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_15(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x) + F_80(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) - F_80(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_13(x)*F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_75(x))
Eq(F_22(x), F_23(x) + F_50(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_47(x))
Eq(F_25(x), F_11(x) - F_26(x))
Eq(F_26(x), F_27(x) + F_38(x))
Eq(F_27(x), F_28(x) - F_33(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_13(x) - F_32(x))
Eq(F_32(x), x*(x - 2)*F_32(x)**2 + (x + 2)*F_32(x) - 1)
Eq(F_33(x), -F_12(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_15(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), x*(x - 2)*(F_37(x) + 1)**2 + (x + 1)*(F_37(x) + 1) + F_37(x) - 1)
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_15(x)*F_27(x)*F_40(x))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_15(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_7(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_15(x)*F_46(x))
Eq(F_46(x), F_25(x) + F_44(x))
Eq(F_47(x), F_48(x) + F_9(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_15(x)*F_44(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_15(x)*F_46(x)*F_52(x))
Eq(F_52(x), F_53(x) - F_55(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_36(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x)/F_15(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_15(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_74(x))
Eq(F_61(x), F_62(x) + F_64(x))
Eq(F_62(x), F_58(x) + F_63(x))
Eq(F_63(x), F_14(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_72(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), -F_0(x) + F_70(x))
Eq(F_70(x), F_71(x)/F_15(x))
Eq(F_71(x), F_2(x))
Eq(F_72(x), F_62(x)*F_73(x))
Eq(F_73(x), F_68(x) + F_70(x))
Eq(F_74(x), F_58(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_15(x)*F_46(x)*F_77(x))
Eq(F_77(x), F_13(x) + F_78(x))
Eq(F_78(x), F_79(x)/F_15(x))
Eq(F_79(x), F_58(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_12(x)*F_15(x)*F_40(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 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[1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 0]]}]}}]}, {"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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": true}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24837/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = 1/F[15,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]+F[86,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = -F[86,x]+F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[13,x]*F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[21,x]
F[21,x] = F[22,x]+F[84,x]
F[22,x] = F[23,x]+F[50,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[47,x]
F[25,x] = -F[26,x]+F[11,x]
F[26,x] = F[27,x]+F[38,x]
F[27,x] = -F[33,x]+F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[32,x]+F[13,x]
F[32,x] = -1+(x^2-2*x)*F[32,x]^2+(2+x)*F[32,x]
F[33,x] = -F[12,x]+F[34,x]
F[34,x] = 1/F[15,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = (x*F[37,x]+x-2*F[37,x])*(x*F[37,x]+x-1)
F[38,x] = F[39,x]
F[39,x] = F[15,x]*F[27,x]*F[40,x]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[15,x]*F[43,x]
F[43,x] = F[44,x]+F[7,x]
F[44,x] = F[45,x]
F[45,x] = F[15,x]*F[46,x]
F[46,x] = F[25,x]+F[44,x]
F[47,x] = F[48,x]+F[9,x]
F[48,x] = F[49,x]
F[49,x] = F[15,x]*F[44,x]
F[50,x] = F[51,x]
F[51,x] = F[15,x]*F[46,x]*F[52,x]
F[52,x] = -F[55,x]+F[53,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[36,x]
F[55,x] = F[56,x]
F[56,x] = 1/F[15,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[15,x]*F[60,x]
F[60,x] = F[61,x]+F[69,x]
F[61,x] = F[62,x]
F[62,x] = F[15,x]*F[63,x]*F[66,x]
F[63,x] = F[1,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[63,x]
F[66,x] = F[13,x]+F[67,x]
F[67,x] = 1/F[15,x]*F[68,x]
F[68,x] = F[58,x]
F[69,x] = F[70,x]
F[70,x] = F[15,x]*F[63,x]*F[71,x]
F[71,x] = 1/F[15,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[15,x]*F[74,x]
F[74,x] = F[75,x]+F[80,x]
F[75,x] = F[76,x]
F[76,x] = F[77,x]
F[77,x] = -F[0,x]+F[78,x]
F[78,x] = 1/F[15,x]*F[79,x]
F[79,x] = F[2,x]
F[80,x] = F[81,x]*F[83,x]
F[81,x] = F[58,x]+F[82,x]
F[82,x] = F[14,x]
F[83,x] = F[76,x]+F[78,x]
F[84,x] = F[85,x]
F[85,x] = F[15,x]*F[46,x]*F[66,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[15,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{86}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{84}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{50}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{47}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{38}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}-2 x F_{32} \left(x \right)^{2}+F_{32}\! \left(x \right) x +2 F_{32}\! \left(x \right)-1
F_{33}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = x^{2} F_{37} \left(x \right)^{2}+2 x^{2} F_{37}\! \left(x \right)-2 x F_{37} \left(x \right)^{2}+x^{2}-3 x F_{37}\! \left(x \right)-x +2 F_{37}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{25}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{69}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right) F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{13}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{58}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{80}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right) F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{58}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right)
F_{83}\! \left(x \right) = F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{66}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_15(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_15(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x) + F_86(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) - F_86(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_13(x)*F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_84(x))
Eq(F_22(x), F_23(x) + F_50(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_47(x))
Eq(F_25(x), F_11(x) - F_26(x))
Eq(F_26(x), F_27(x) + F_38(x))
Eq(F_27(x), F_28(x) - F_33(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_13(x) - F_32(x))
Eq(F_32(x), x*(x - 2)*F_32(x)**2 + (x + 2)*F_32(x) - 1)
Eq(F_33(x), -F_12(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_15(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), x*(x - 2)*(F_37(x) + 1)**2 + (x + 1)*(F_37(x) + 1) + F_37(x) - 1)
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_15(x)*F_27(x)*F_40(x))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_15(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_7(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_15(x)*F_46(x))
Eq(F_46(x), F_25(x) + F_44(x))
Eq(F_47(x), F_48(x) + F_9(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_15(x)*F_44(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_15(x)*F_46(x)*F_52(x))
Eq(F_52(x), F_53(x) - F_55(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_36(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x)/F_15(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_15(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_69(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_15(x)*F_63(x)*F_66(x))
Eq(F_63(x), F_1(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_63(x))
Eq(F_66(x), F_13(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_15(x))
Eq(F_68(x), F_58(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_15(x)*F_63(x)*F_71(x))
Eq(F_71(x), F_72(x)/F_15(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_15(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_80(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), -F_0(x) + F_78(x))
Eq(F_78(x), F_79(x)/F_15(x))
Eq(F_79(x), F_2(x))
Eq(F_80(x), F_81(x)*F_83(x))
Eq(F_81(x), F_58(x) + F_82(x))
Eq(F_82(x), F_14(x))
Eq(F_83(x), F_76(x) + F_78(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_15(x)*F_46(x)*F_66(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_15(x)*F_40(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], 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0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 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": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25168/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = 1/F[15,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]+F[84,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = -F[84,x]+F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[13,x]*F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[21,x]
F[21,x] = F[22,x]+F[76,x]
F[22,x] = F[23,x]+F[48,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = -F[26,x]+F[11,x]
F[26,x] = F[27,x]+F[36,x]
F[27,x] = -F[33,x]+F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[32,x]+F[31,x]
F[31,x] = -F[0,x]+F[13,x]
F[32,x] = (x*F[32,x]+x-1)*(x*F[32,x]+x-2*F[32,x])
F[33,x] = -F[12,x]+F[34,x]
F[34,x] = 1/F[15,x]*F[35,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[27,x]*F[38,x]
F[38,x] = F[39,x]+F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]*F[41,x]
F[41,x] = F[42,x]+F[7,x]
F[42,x] = F[43,x]
F[43,x] = F[15,x]*F[44,x]
F[44,x] = F[25,x]+F[42,x]
F[45,x] = F[46,x]+F[9,x]
F[46,x] = F[47,x]
F[47,x] = F[15,x]*F[42,x]
F[48,x] = F[49,x]
F[49,x] = F[15,x]*F[44,x]*F[50,x]
F[50,x] = F[13,x]+F[51,x]
F[51,x] = 1/F[15,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[15,x]*F[55,x]
F[55,x] = F[56,x]+F[61,x]
F[56,x] = F[57,x]
F[57,x] = F[15,x]*F[50,x]*F[58,x]
F[58,x] = F[1,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[15,x]*F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[15,x]*F[58,x]*F[63,x]
F[63,x] = 1/F[15,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[66,x]
F[66,x] = F[67,x]+F[72,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x]
F[69,x] = -F[0,x]+F[70,x]
F[70,x] = 1/F[15,x]*F[71,x]
F[71,x] = F[2,x]
F[72,x] = F[73,x]*F[75,x]
F[73,x] = F[53,x]+F[74,x]
F[74,x] = F[14,x]
F[75,x] = F[68,x]+F[70,x]
F[76,x] = F[77,x]
F[77,x] = F[15,x]*F[44,x]*F[78,x]
F[78,x] = -F[81,x]+F[79,x]
F[79,x] = 1/F[15,x]*F[80,x]
F[80,x] = F[31,x]
F[81,x] = F[82,x]
F[82,x] = 1/F[15,x]*F[83,x]
F[83,x] = F[53,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[15,x]*F[38,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{84}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{76}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{48}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}+2 x^{2} F_{32}\! \left(x \right)-2 x F_{32} \left(x \right)^{2}+x^{2}-3 x F_{32}\! \left(x \right)-x +2 F_{32}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{7}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{9}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right) F_{50}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{1}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{15}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right) F_{58}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{72}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{2}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{53}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right)
F_{75}\! \left(x \right) = F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{53}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{38}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_15(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_15(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x) + F_84(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) - F_84(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_13(x)*F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_76(x))
Eq(F_22(x), F_23(x) + F_48(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_11(x) - F_26(x))
Eq(F_26(x), F_27(x) + F_36(x))
Eq(F_27(x), F_28(x) - F_33(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_32(x))
Eq(F_31(x), -F_0(x) + F_13(x))
Eq(F_32(x), x*(x - 2)*(F_32(x) + 1)**2 + (x + 1)*(F_32(x) + 1) + F_32(x) - 1)
Eq(F_33(x), -F_12(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_15(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_27(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_7(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_15(x)*F_44(x))
Eq(F_44(x), F_25(x) + F_42(x))
Eq(F_45(x), F_46(x) + F_9(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_15(x)*F_42(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_15(x)*F_44(x)*F_50(x))
Eq(F_50(x), F_13(x) + F_51(x))
Eq(F_51(x), F_52(x)/F_15(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_15(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_61(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_15(x)*F_50(x)*F_58(x))
Eq(F_58(x), F_1(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_15(x)*F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_15(x)*F_58(x)*F_63(x))
Eq(F_63(x), F_64(x)/F_15(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_72(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), -F_0(x) + F_70(x))
Eq(F_70(x), F_71(x)/F_15(x))
Eq(F_71(x), F_2(x))
Eq(F_72(x), F_73(x)*F_75(x))
Eq(F_73(x), F_53(x) + F_74(x))
Eq(F_74(x), F_14(x))
Eq(F_75(x), F_68(x) + F_70(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_15(x)*F_44(x)*F_78(x))
Eq(F_78(x), F_79(x) - F_81(x))
Eq(F_79(x), F_80(x)/F_15(x))
Eq(F_80(x), F_31(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x)/F_15(x))
Eq(F_83(x), F_53(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_15(x)*F_38(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": 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1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 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": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25240/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = 1/F[15,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]+F[86,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = -F[86,x]+F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[13,x]*F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[15,x]*F[21,x]
F[21,x] = F[22,x]+F[84,x]
F[22,x] = F[23,x]+F[50,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[47,x]
F[25,x] = -F[26,x]+F[11,x]
F[26,x] = F[27,x]+F[38,x]
F[27,x] = -F[33,x]+F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[32,x]+F[13,x]
F[32,x] = -1+(x^2-2*x)*F[32,x]^2+(2+x)*F[32,x]
F[33,x] = -F[12,x]+F[34,x]
F[34,x] = 1/F[15,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = (x*F[37,x]+x-1)*(x*F[37,x]+x-2*F[37,x])
F[38,x] = F[39,x]
F[39,x] = F[15,x]*F[27,x]*F[40,x]
F[40,x] = F[4,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[15,x]*F[43,x]
F[43,x] = F[44,x]+F[7,x]
F[44,x] = F[45,x]
F[45,x] = F[15,x]*F[46,x]
F[46,x] = F[25,x]+F[44,x]
F[47,x] = F[48,x]+F[9,x]
F[48,x] = F[49,x]
F[49,x] = F[15,x]*F[44,x]
F[50,x] = F[51,x]
F[51,x] = F[15,x]*F[46,x]*F[52,x]
F[52,x] = -F[55,x]+F[53,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[36,x]
F[55,x] = F[56,x]
F[56,x] = 1/F[15,x]*F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[15,x]*F[60,x]
F[60,x] = F[61,x]+F[69,x]
F[61,x] = F[62,x]
F[62,x] = F[15,x]*F[63,x]*F[66,x]
F[63,x] = F[1,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[63,x]
F[66,x] = F[13,x]+F[67,x]
F[67,x] = 1/F[15,x]*F[68,x]
F[68,x] = F[58,x]
F[69,x] = F[70,x]
F[70,x] = F[15,x]*F[63,x]*F[71,x]
F[71,x] = 1/F[15,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[15,x]*F[74,x]
F[74,x] = F[75,x]+F[80,x]
F[75,x] = F[76,x]
F[76,x] = F[77,x]
F[77,x] = -F[0,x]+F[78,x]
F[78,x] = 1/F[15,x]*F[79,x]
F[79,x] = F[2,x]
F[80,x] = F[81,x]*F[83,x]
F[81,x] = F[58,x]+F[82,x]
F[82,x] = F[14,x]
F[83,x] = F[76,x]+F[78,x]
F[84,x] = F[85,x]
F[85,x] = F[15,x]*F[46,x]*F[66,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[15,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{86}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{84}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{50}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{47}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{11}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{38}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = x^{2} F_{32} \left(x \right)^{2}-2 x F_{32} \left(x \right)^{2}+F_{32}\! \left(x \right) x +2 F_{32}\! \left(x \right)-1
F_{33}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = x^{2} F_{37} \left(x \right)^{2}+2 x^{2} F_{37}\! \left(x \right)-2 x F_{37} \left(x \right)^{2}+x^{2}-3 x F_{37}\! \left(x \right)-x +2 F_{37}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{25}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{69}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right) F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{13}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{58}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{63}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{80}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{2}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right) F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{58}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right)
F_{83}\! \left(x \right) = F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{15}\! \left(x \right) F_{46}\! \left(x \right) F_{66}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_15(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_15(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x) + F_86(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x) - F_86(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_13(x)*F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_15(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_84(x))
Eq(F_22(x), F_23(x) + F_50(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_47(x))
Eq(F_25(x), F_11(x) - F_26(x))
Eq(F_26(x), F_27(x) + F_38(x))
Eq(F_27(x), F_28(x) - F_33(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_13(x) - F_32(x))
Eq(F_32(x), x*(x - 2)*F_32(x)**2 + (x + 2)*F_32(x) - 1)
Eq(F_33(x), -F_12(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_15(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), x*(x - 2)*(F_37(x) + 1)**2 + (x + 1)*(F_37(x) + 1) + F_37(x) - 1)
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_15(x)*F_27(x)*F_40(x))
Eq(F_40(x), F_4(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_15(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_7(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_15(x)*F_46(x))
Eq(F_46(x), F_25(x) + F_44(x))
Eq(F_47(x), F_48(x) + F_9(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_15(x)*F_44(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_15(x)*F_46(x)*F_52(x))
Eq(F_52(x), F_53(x) - F_55(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_36(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x)/F_15(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_15(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_69(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_15(x)*F_63(x)*F_66(x))
Eq(F_63(x), F_1(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_63(x))
Eq(F_66(x), F_13(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_15(x))
Eq(F_68(x), F_58(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_15(x)*F_63(x)*F_71(x))
Eq(F_71(x), F_72(x)/F_15(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_15(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_80(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), -F_0(x) + F_78(x))
Eq(F_78(x), F_79(x)/F_15(x))
Eq(F_79(x), F_2(x))
Eq(F_80(x), F_81(x)*F_83(x))
Eq(F_81(x), F_58(x) + F_82(x))
Eq(F_82(x), F_14(x))
Eq(F_83(x), F_76(x) + F_78(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_15(x)*F_46(x)*F_66(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_15(x)*F_40(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 2, 0, 4, 3], [2, 0, 1, 4, 3], [2, 0, 3, 4, 1], [2, 1, 0, 4, 3], [3, 0, 1, 4, 2], [3, 0, 2, 4, 1], [3, 1, 0, 4, 2]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "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], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "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, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 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