02341_03241_03421_20341_23041_23401_30241_30421_32041_32401_34021_34201
Counting sequence:
1, 1, 2, 6, 24, 108, 512, 2506, 12560, 64148, 332704, 1747748, 9280416, 49731768, 268613568, 1460847018, 7992819600, 43965495588, 242989734432, 1348696517964, 7514649244128, 42016005233352, 235665924826176, 1325673785058180, 7477059086539424, 42275419332388168, 239567065205029952, 1360430550201086216, 7740541529962849600, 44121903718663304816, 251926012956167788416, 1440723346709420323050, 8251526397226054378896, 47325506341456085391044, 271786623474630428921632, 1562788803506076123276092, 8996677655300269717462880, 51849710099274003611880232, 299135253656989772968570688, 1727518371379928454124795692, 9985964362150530485633093856, 57776286878192693593012410072, 334566888415810890109628624064, 1938977296357297668690780126072, 11246122791729048828273340522176, 65276702838022040177312854687248, 379162018386459854897967213964416, 2203887896727351931462092857872452, 12818578802907040062728896459099296, 74604385827938481830036016591676968, 434462240601801508475329890307377984, 2531585750986910546600168334851175288, 14759664794912254679344147270042228416, 86098276565704160505129878429889486288, 502502127052964432971614450309457836672, 2934260529558409958200729899476504572104, 17142297742809733369814446663673080838976, 100193989631846794863438089051656145000208, 585881298957241605707816302422627915922560, 3427412198959300374395229820786600381361424, 20058826079181414729753761725433868754829952, 117441395210113950495431812877518683380531424, 687872163841724453951139456406351988547211008, 4030507285692431229515124627225048578233718634, 23625008778897280982203179989975157970298999184, 138528657830353603112437099415657127651658695684, 812564723246756738736447014995906058542838925600, 4767849187430588997060167064242521466517468492444, 27985236389160897737863521028316080227410024056416, 164313510870831784437152863574548534884231700590312, 965053683684004124265974996517414356176349874494784, 5669696529192648956770750786472761652195311574048796, 33319210031880638533346118531197139691350794765717088, 195863118372582883099492463436163691613210954486406200, 1151676232712791061247592012442399710904386521245396928, 6773680872226457523721023267251852796666142168213246488, 39850391241666605844724772639656670444790011733840246720, 234504422853756838917247747013666828721095231919952413648, 1380311960252026234533905517248856496072783427694817258112, 8126592987747720439234773223955537594539386154771072879852, 47856638959472017530990431480339382696406105977645766642400, 281887478810888775481208067097163656208822685984896167665464, 1660759912179625919782323379294456881712523319721615284746176, 9786627447438641209074951322774802915192612274435322325567336, 57683570672143779423382512641302661677397642084593499454417984, 340064982333224833479996003127128079800709441144935651792656496, 2005211958269693399853156628133485927467451178551251126985140096, 11826200085609889873780660499839146735994771144737530364027183800, 69761331545278897919058782352151346381868238971868725790142673088, 411592077809463680288535127338566893823404742420916427669783530224, 2428846822056866792706535049244189739654069228558939325773621531520, 14335483562801876293914111020224695847541584418479628599704196471408, 84625637675796166669772601999607632349398732803958861799548809996672, 499651606454183581127269015671181972775669113720617756349050932170272, 2950575566619383450873896792722924871437695755786574863788787290761472, 17426844619940691203062420740910668586130860741147730301770153055364548, 102944187920369954062827878916073761421914578758564675417624856213823648, 608211320850328169365686702434380699182156515406286277494091470148815080, 3593977426329137610994692434217117322949885631731520586787962875498041664, 21240414835820696095710002540784456876372219653125555025000684553687707544, 125549826043436215314932204120654409881660015237404901275197222335558351808
Generating function in Maple syntax:
(2*x^3-5*x^2-(12*x^2-8*x+1)^(1/2)+5*x+1)/x/(2*x-3)^2
Generating function in latex syntax:
\frac{2 x^{3}-5 x^{2}-\sqrt{12 x^{2}-8 x +1}+5 x +1}{x \left(2 x -3\right)^{2}}
Generating function in sympy syntax:
(2*x**3 - 5*x**2 + 5*x - sqrt(12*x**2 - 8*x + 1) + 1)/(x*(2*x - 3)**2)
Implicit equation for the generating function in Maple syntax:
x*(2*x-3)^2*F(x)^2+(-4*x^3+10*x^2-10*x-2)*F(x)+x^3-2*x^2+3*x+2 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -3\right)^{2} F \! \left(x \right)^{2}+\left(-4 x^{3}+10 x^{2}-10 x -2\right) F \! \left(x \right)+x^{3}-2 x^{2}+3 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = 8*(n+2)/(n+4)*a(n)-4/3*(13*n+23)/(n+4)*a(1+n)+2/3*(13*n+35)/(n+4)*a(n+2), n >= 4
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a{\left(n + 3 \right)} = \frac{8 \left(n + 2\right) a{\left(n \right)}}{n + 4} - \frac{4 \left(13 n + 23\right) a{\left(n + 1 \right)}}{3 \left(n + 4\right)} + \frac{2 \left(13 n + 35\right) a{\left(n + 2 \right)}}{3 \left(n + 4\right)}, \quad n \geq 4
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24796/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[110,x]+F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[11,x,k[0]]+F[35,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[19,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[20,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[20,x]*F[21,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x] = x
F[21,x,k[0]] = F[22,x]+F[24,x,k[0]]
F[22,x] = 1/F[20,x]*F[23,x]
F[23,x] = F[2,x]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[19,x,k[0]]*F[26,x,k[0]]
F[27,x,k[0]] = F[105,x,k[0]]+F[26,x,k[0]]
F[28,x,k[0]] = F[19,x,k[0]]*F[27,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[30,x,k[0]] = F[22,x]+F[29,x,k[0]]
F[31,x,k[0]] = F[30,x,k[0]]+F[57,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[31,x,k[0]]*k[0]-F[31,x,1])
F[33,x,k[0]] = F[20,x]*F[32,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[5,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[20,x]*F[37,x,k[0]]
F[37,x,k[0]] = -k[0]*(F[38,x,1]-F[38,x,k[0]])/(-1+k[0])
F[38,x,k[0]] = F[10,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[19,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[51,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[45,x,k[0]]
F[44,x,k[0]] = F[16,x,k[0]]*F[20,x]*F[43,x,k[0]]
F[44,x,k[0]] = F[15,x,k[0]]
F[45,x,k[0]] = F[16,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[19,x,k[0]]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x]+F[49,x,k[0]]+F[50,x,k[0]]
F[48,x] = 0
F[49,x,k[0]] = F[17,x,k[0]]*F[19,x,k[0]]
F[50,x,k[0]] = F[19,x,k[0]]*F[46,x,k[0]]
F[51,x,k[0]] = F[16,x,k[0]]*F[52,x,k[0]]
F[52,x,k[0]] = k[0]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[20,x]*F[55,x,k[0]]
F[56,x,k[0]] = F[19,x,k[0]]*F[55,x,k[0]]
F[56,x,k[0]] = F[10,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[74,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[22,x]+F[61,x,k[0]]
F[61,x,k[0]] = F[17,x,k[0]]*F[62,x]
F[62,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[20,x]*F[63,x]
F[66,x] = F[67,x]+F[70,x]
F[67,x] = F[68,x]
F[68,x] = F[20,x]*F[69,x]
F[69,x] = F[1,x]+F[67,x]
F[70,x] = F[48,x]+F[71,x]+F[73,x]
F[71,x] = F[20,x]*F[72,x]
F[72,x] = F[64,x]+F[70,x]
F[73,x] = F[20,x]*F[66,x]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[19,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]+F[80,x,k[0]]
F[77,x,k[0]] = F[17,x,k[0]]*F[78,x,k[0]]
F[79,x,k[0]] = F[19,x,k[0]]*F[78,x,k[0]]
F[79,x,k[0]] = F[29,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]*F[85,x,k[0]]
F[82,x,k[0]] = k[0]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[16,x,k[0]]*F[20,x]*F[60,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[92,x,k[0]]
F[86,x,k[0]] = F[16,x,k[0]]+F[87,x,k[0]]
F[87,x,k[0]] = F[64,x]+F[88,x,k[0]]
F[88,x,k[0]] = F[48,x]+F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[20,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[17,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[19,x,k[0]]*F[87,x,k[0]]
F[92,x,k[0]] = F[93,x,k[0]]+F[98,x,k[0]]
F[93,x,k[0]] = F[67,x]+F[94,x,k[0]]
F[94,x,k[0]] = F[48,x]+F[95,x,k[0]]+F[97,x,k[0]]
F[95,x,k[0]] = F[20,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[17,x,k[0]]+F[94,x,k[0]]
F[97,x,k[0]] = F[19,x,k[0]]*F[93,x,k[0]]
F[98,x,k[0]] = F[70,x]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[102,x,k[0]]+F[104,x,k[0]]+F[48,x]
F[100,x,k[0]] = F[101,x,k[0]]*F[20,x]
F[101,x,k[0]] = F[88,x,k[0]]+F[99,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[20,x]
F[103,x,k[0]] = F[94,x,k[0]]+F[99,x,k[0]]
F[104,x,k[0]] = F[19,x,k[0]]*F[98,x,k[0]]
F[105,x,k[0]] = k[0]*F[106,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[20,x]*F[62,x]
F[109,x,k[0]] = F[108,x,k[0]]*F[19,x,k[0]]
F[109,x,k[0]] = F[29,x,k[0]]
F[110,x] = F[39,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{20}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{110}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x \right) = x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}
F_{33}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{32}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = -\frac{y \left(F_{38}\! \left(x , 1\right)-F_{38}\! \left(x , y\right)\right)}{-1+y}
F_{38}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x \right) = 0
F_{49}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{46}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = y F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{62}\! \left(x \right)
F_{62}\! \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_{20}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{70}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{1}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{48}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{64}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{20}\! \left(x \right) F_{66}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{78}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = y F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{64}\! \left(x \right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{67}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{48}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{70}\! \left(x \right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{48}\! \left(x \right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{20}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{98}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = y F_{106}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{20}\! \left(x \right) F_{62}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{110}\! \left(x \right) = F_{39}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_110(x) + F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_11(x, k_0) + F_35(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_19(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_20(x))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_20(x)*F_21(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_16(x, k_0)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x), x)
Eq(F_21(x, k_0), F_22(x) + F_24(x, k_0))
Eq(F_22(x), F_23(x)/F_20(x))
Eq(F_23(x), F_2(x))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_19(x, k_0)*F_26(x, k_0))
Eq(F_27(x, k_0), F_105(x, k_0) + F_26(x, k_0))
Eq(F_28(x, k_0), F_19(x, k_0)*F_27(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_30(x, k_0), F_22(x) + F_29(x, k_0))
Eq(F_31(x, k_0), F_30(x, k_0) + F_57(x, k_0))
Eq(F_32(x, k_0), (k_0*F_31(x, k_0) - F_31(x, 1))/(k_0 - 1))
Eq(F_33(x, k_0), F_20(x)*F_32(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_5(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_20(x)*F_37(x, k_0))
Eq(F_37(x, k_0), -F_38(x, 1) + (k_0*F_38(x, k_0) - F_38(x, 1))/(k_0 - 1))
Eq(F_38(x, k_0), F_10(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_19(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_51(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_45(x, k_0))
Eq(F_44(x, k_0), F_16(x, k_0)*F_20(x)*F_43(x, k_0))
Eq(F_44(x, k_0), F_15(x, k_0))
Eq(F_45(x, k_0), F_16(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_19(x, k_0) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x) + F_49(x, k_0) + F_50(x, k_0))
Eq(F_48(x), 0)
Eq(F_49(x, k_0), F_17(x, k_0)*F_19(x, k_0))
Eq(F_50(x, k_0), F_19(x, k_0)*F_46(x, k_0))
Eq(F_51(x, k_0), F_16(x, k_0)*F_52(x, k_0))
Eq(F_52(x, k_0), k_0*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_20(x)*F_55(x, k_0))
Eq(F_56(x, k_0), F_19(x, k_0)*F_55(x, k_0))
Eq(F_56(x, k_0), F_10(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_74(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_16(x, k_0)*F_19(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_22(x) + F_61(x, k_0))
Eq(F_61(x, k_0), F_17(x, k_0)*F_62(x))
Eq(F_62(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_20(x)*F_63(x))
Eq(F_66(x), F_67(x) + F_70(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_20(x)*F_69(x))
Eq(F_69(x), F_1(x) + F_67(x))
Eq(F_70(x), F_48(x) + F_71(x) + F_73(x))
Eq(F_71(x), F_20(x)*F_72(x))
Eq(F_72(x), F_64(x) + F_70(x))
Eq(F_73(x), F_20(x)*F_66(x))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_19(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0) + F_80(x, k_0))
Eq(F_77(x, k_0), F_17(x, k_0)*F_78(x, k_0))
Eq(F_79(x, k_0), F_19(x, k_0)*F_78(x, k_0))
Eq(F_79(x, k_0), F_29(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0)*F_85(x, k_0))
Eq(F_82(x, k_0), k_0*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_16(x, k_0)*F_20(x)*F_60(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_92(x, k_0))
Eq(F_86(x, k_0), F_16(x, k_0) + F_87(x, k_0))
Eq(F_87(x, k_0), F_64(x) + F_88(x, k_0))
Eq(F_88(x, k_0), F_48(x) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_20(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_17(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_19(x, k_0)*F_87(x, k_0))
Eq(F_92(x, k_0), F_93(x, k_0) + F_98(x, k_0))
Eq(F_93(x, k_0), F_67(x) + F_94(x, k_0))
Eq(F_94(x, k_0), F_48(x) + F_95(x, k_0) + F_97(x, k_0))
Eq(F_95(x, k_0), F_20(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_17(x, k_0) + F_94(x, k_0))
Eq(F_97(x, k_0), F_19(x, k_0)*F_93(x, k_0))
Eq(F_98(x, k_0), F_70(x) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_102(x, k_0) + F_104(x, k_0) + F_48(x))
Eq(F_100(x, k_0), F_101(x, k_0)*F_20(x))
Eq(F_101(x, k_0), F_88(x, k_0) + F_99(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_20(x))
Eq(F_103(x, k_0), F_94(x, k_0) + F_99(x, k_0))
Eq(F_104(x, k_0), F_19(x, k_0)*F_98(x, k_0))
Eq(F_105(x, k_0), k_0*F_106(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_20(x)*F_62(x))
Eq(F_109(x, k_0), F_108(x, k_0)*F_19(x, k_0))
Eq(F_109(x, k_0), F_29(x, k_0))
Eq(F_110(x), F_39(x, 1))
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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "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, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "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, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 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[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": "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24848/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[50,x]+F[9,x]
F[9,x] = F[10,x]+F[36,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = -1+(x^2-2*x)*F[11,x]^2+(2+x)*F[11,x]
F[12,x] = F[13,x]+F[28,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[4,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[24,x]+F[25,x]+F[27,x]
F[24,x] = 0
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[23,x]
F[27,x] = F[19,x]*F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[43,x]
F[31,x] = F[32,x]
F[32,x] = F[15,x]*F[33,x]*F[4,x]
F[33,x] = 1/F[38,x]/F[4,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[41,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]*F[40,x]
F[38,x] = 1/F[4,x]*F[39,x]
F[39,x] = F[2,x]
F[40,x] = F[15,x]+F[31,x]
F[41,x] = F[42,x]
F[42,x] = F[33,x]*F[36,x]*F[4,x]
F[43,x] = -F[48,x]+F[44,x]
F[44,x] = 1/F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[47,x]+F[6,x]
F[47,x] = (x*F[47,x]+x-1)*(x*F[47,x]+x-2*F[47,x])
F[48,x] = F[49,x]
F[49,x] = F[33,x]*F[4,x]*F[5,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[40,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{50}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{36}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}-2 x F_{11} \left(x \right)^{2}+F_{11}\! \left(x \right) x +2 F_{11}\! \left(x \right)-1
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{43}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{38}\! \left(x \right) F_{4}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{33}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{6}\! \left(x \right)
F_{47}\! \left(x \right) = x^{2} F_{47} \left(x \right)^{2}+2 x^{2} F_{47}\! \left(x \right)-2 x F_{47} \left(x \right)^{2}+x^{2}-3 x F_{47}\! \left(x \right)-x +2 F_{47}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_50(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_36(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x*(x - 2)*F_11(x)**2 + (x + 2)*F_11(x) - 1)
Eq(F_12(x), F_13(x) + F_28(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_27(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_23(x))
Eq(F_27(x), F_19(x)*F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_43(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_15(x)*F_33(x)*F_4(x))
Eq(F_33(x), F_34(x)/(F_38(x)*F_4(x)))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_41(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x)*F_40(x))
Eq(F_38(x), F_39(x)/F_4(x))
Eq(F_39(x), F_2(x))
Eq(F_40(x), F_15(x) + F_31(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_33(x)*F_36(x)*F_4(x))
Eq(F_43(x), F_44(x) - F_48(x))
Eq(F_44(x), F_45(x)/F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), -F_47(x) + F_6(x))
Eq(F_47(x), x*(x - 2)*(F_47(x) + 1)**2 + (x + 1)*(F_47(x) + 1) + F_47(x) - 1)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_33(x)*F_4(x)*F_5(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_40(x)*F_8(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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "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, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "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, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25400/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[47,x]+F[9,x]
F[9,x] = F[10,x]+F[34,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = -1+F[11,x]^2*(x^2-2*x)+(2+x)*F[11,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[40,x]
F[15,x] = F[16,x]+F[29,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[1,x]+F[21,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[18,x]+F[24,x]
F[28,x] = F[20,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[16,x]*F[31,x]*F[4,x]
F[31,x] = 1/F[36,x]/F[4,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[38,x]
F[34,x] = F[35,x]
F[35,x] = F[15,x]*F[36,x]*F[4,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[31,x]*F[34,x]*F[4,x]
F[40,x] = -F[45,x]+F[41,x]
F[41,x] = 1/F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[2,x]+F[44,x]
F[44,x] = -F[11,x]+F[5,x]
F[45,x] = F[46,x]
F[46,x] = F[31,x]*F[4,x]*F[5,x]
F[47,x] = F[48,x]
F[48,x] = F[15,x]*F[4,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{47}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{34}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}-2 x F_{11} \left(x \right)^{2}+F_{11}\! \left(x \right) x +2 F_{11}\! \left(x \right)-1
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{40}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{29}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right) F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{36}\! \left(x \right) F_{4}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_47(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_34(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x*(x - 2)*F_11(x)**2 + (x + 2)*F_11(x) - 1)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_40(x))
Eq(F_15(x), F_16(x) + F_29(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_1(x) + F_21(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_18(x) + F_24(x))
Eq(F_28(x), F_20(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_16(x)*F_31(x)*F_4(x))
Eq(F_31(x), F_32(x)/(F_36(x)*F_4(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_38(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_15(x)*F_36(x)*F_4(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_31(x)*F_34(x)*F_4(x))
Eq(F_40(x), F_41(x) - F_45(x))
Eq(F_41(x), F_42(x)/F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_2(x) + F_44(x))
Eq(F_44(x), -F_11(x) + F_5(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_31(x)*F_4(x)*F_5(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_15(x)*F_4(x)*F_8(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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "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, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "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, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"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, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 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0], "pos": [[3, 4], [3, 4], [3, 3]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [3, 6], [3, 4]]}, {"patt": [1, 2, 0], "pos": [[3, 6], [3, 6], [3, 4]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[3, 6], [3, 4], [3, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 6], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 6], [2, 6], [2, 4]]}, {"patt": [2, 1, 0], "pos": [[2, 6], [2, 4], [2, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "requirements": [[{"patt": [0], "pos": [[1, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25623/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[47,x]+F[9,x]
F[9,x] = F[10,x]+F[34,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = -1+(x^2-2*x)*F[11,x]^2+(2+x)*F[11,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[40,x]
F[15,x] = F[16,x]+F[29,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[1,x]+F[21,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[18,x]+F[24,x]
F[28,x] = F[20,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[16,x]*F[31,x]*F[4,x]
F[31,x] = 1/F[36,x]/F[4,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[38,x]
F[34,x] = F[35,x]
F[35,x] = F[15,x]*F[36,x]*F[4,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,x] = F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[31,x]*F[34,x]*F[4,x]
F[40,x] = -F[45,x]+F[41,x]
F[41,x] = 1/F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[2,x]+F[44,x]
F[44,x] = -F[11,x]+F[5,x]
F[45,x] = F[46,x]
F[46,x] = F[31,x]*F[4,x]*F[5,x]
F[47,x] = F[48,x]
F[48,x] = F[15,x]*F[4,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{47}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{34}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}-2 x F_{11} \left(x \right)^{2}+F_{11}\! \left(x \right) x +2 F_{11}\! \left(x \right)-1
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{40}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{29}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right) F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{36}\! \left(x \right) F_{4}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_47(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_34(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x*(x - 2)*F_11(x)**2 + (x + 2)*F_11(x) - 1)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_40(x))
Eq(F_15(x), F_16(x) + F_29(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_1(x) + F_21(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_18(x) + F_24(x))
Eq(F_28(x), F_20(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_16(x)*F_31(x)*F_4(x))
Eq(F_31(x), F_32(x)/(F_36(x)*F_4(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_38(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_15(x)*F_36(x)*F_4(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_31(x)*F_34(x)*F_4(x))
Eq(F_40(x), F_41(x) - F_45(x))
Eq(F_41(x), F_42(x)/F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), -F_2(x) + F_44(x))
Eq(F_44(x), -F_11(x) + F_5(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_31(x)*F_4(x)*F_5(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_15(x)*F_4(x)*F_8(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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "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, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "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, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"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, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"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], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "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, 2], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 2], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": 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[2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[2, 6], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 6], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 6], [2, 6], [2, 4]]}, {"patt": [2, 1, 0], "pos": [[2, 6], [2, 4], [2, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 6], [2, 6], [2, 6], [2, 6]]}], "requirements": [[{"patt": [0], "pos": [[1, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25818/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[50,x]+F[9,x]
F[9,x] = F[10,x]+F[36,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = -1+(x^2-2*x)*F[11,x]^2+(2+x)*F[11,x]
F[12,x] = F[13,x]+F[28,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[4,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[24,x]+F[25,x]+F[27,x]
F[24,x] = 0
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[23,x]
F[27,x] = F[19,x]*F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[43,x]
F[31,x] = F[32,x]
F[32,x] = F[15,x]*F[33,x]*F[4,x]
F[33,x] = 1/F[38,x]/F[4,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[41,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]*F[40,x]
F[38,x] = 1/F[4,x]*F[39,x]
F[39,x] = F[2,x]
F[40,x] = F[15,x]+F[31,x]
F[41,x] = F[42,x]
F[42,x] = F[33,x]*F[36,x]*F[4,x]
F[43,x] = -F[48,x]+F[44,x]
F[44,x] = 1/F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[47,x]+F[6,x]
F[47,x] = (x*F[47,x]+x-2*F[47,x])*(x*F[47,x]+x-1)
F[48,x] = F[49,x]
F[49,x] = F[33,x]*F[4,x]*F[5,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[40,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{50}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{36}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}-2 x F_{11} \left(x \right)^{2}+F_{11}\! \left(x \right) x +2 F_{11}\! \left(x \right)-1
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{43}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{38}\! \left(x \right) F_{4}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{33}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{6}\! \left(x \right)
F_{47}\! \left(x \right) = x^{2} F_{47} \left(x \right)^{2}+2 x^{2} F_{47}\! \left(x \right)-2 x F_{47} \left(x \right)^{2}+x^{2}-3 x F_{47}\! \left(x \right)-x +2 F_{47}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_50(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_36(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x*(x - 2)*F_11(x)**2 + (x + 2)*F_11(x) - 1)
Eq(F_12(x), F_13(x) + F_28(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_27(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_23(x))
Eq(F_27(x), F_19(x)*F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_43(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_15(x)*F_33(x)*F_4(x))
Eq(F_33(x), F_34(x)/(F_38(x)*F_4(x)))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_41(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x)*F_40(x))
Eq(F_38(x), F_39(x)/F_4(x))
Eq(F_39(x), F_2(x))
Eq(F_40(x), F_15(x) + F_31(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_33(x)*F_36(x)*F_4(x))
Eq(F_43(x), F_44(x) - F_48(x))
Eq(F_44(x), F_45(x)/F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), -F_47(x) + F_6(x))
Eq(F_47(x), x*(x - 2)*(F_47(x) + 1)**2 + (x + 1)*(F_47(x) + 1) + F_47(x) - 1)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_33(x)*F_4(x)*F_5(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_40(x)*F_8(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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1], [3, 4, 0, 2, 1], [3, 4, 2, 0, 1]], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "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, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "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, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 4, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"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, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": 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[]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], 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