01243_01342_01432_02143_02341_02431_03142_03241_03421_04132_04231_04321
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_req_corrob
Tree: http://permpal.com/tree/25374/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[8,x]+F[96,x]
F[8,x] = F[9,x]+F[94,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = F[13,x]+F[84,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = 1/F[23,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = -F[77,x]+F[17,x]
F[17,x] = F[18,x]+F[28,x]
F[18,x] = F[19,x]+F[24,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[23,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = x
F[24,x] = F[23,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[29,x]
F[29,x] = F[23,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[17,x]+F[32,x]
F[32,x] = F[25,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[13,x]*F[23,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = F[38,x]+F[76,x]
F[38,x] = F[33,x]+F[39,x]
F[39,x] = F[40,x]+F[75,x]
F[40,x] = F[41,x]+F[73,x]
F[41,x] = F[27,x]*F[42,x]
F[42,x] = 1/F[58,x]*F[43,x]
F[43,x] = -F[53,x]+F[44,x]
F[44,x] = 1/F[23,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[8,x]+F[47,x]
F[47,x] = 1/F[23,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[5,x]
F[53,x] = F[54,x]
F[54,x] = F[23,x]*F[42,x]*F[55,x]
F[55,x] = 1/F[23,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[58,x]+F[8,x]
F[58,x] = F[59,x]+F[71,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[62,x]
F[62,x] = F[22,x]+F[63,x]
F[63,x] = F[60,x]+F[64,x]
F[64,x] = F[65,x]+F[66,x]+F[70,x]
F[65,x] = 0
F[66,x] = F[23,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[23,x]
F[69,x] = F[64,x]
F[70,x] = F[23,x]*F[60,x]
F[71,x] = F[72,x]
F[72,x] = F[23,x]*F[27,x]*F[4,x]*F[59,x]
F[73,x] = F[74,x]
F[74,x] = F[23,x]*F[42,x]
F[75,x] = F[73,x]
F[76,x] = F[33,x]
F[77,x] = F[78,x]
F[78,x] = F[23,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[81,x]+F[9,x]
F[81,x] = F[82,x]
F[82,x] = F[13,x]*F[23,x]
F[83,x] = F[81,x]
F[84,x] = -F[88,x]+F[85,x]
F[85,x] = 1/F[23,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[2,x]+F[49,x]
F[88,x] = F[89,x]
F[89,x] = F[23,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[0,x]*F[42,x]
F[92,x] = F[93,x]
F[93,x] = F[23,x]*F[42,x]*F[51,x]
F[94,x] = F[95,x]
F[95,x] = F[13,x]*F[23,x]*F[4,x]
F[96,x] = F[94,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[23,x]*F[99,x]
F[99,x] = F[100,x]+F[118,x]
F[100,x] = F[101,x]*F[13,x]
F[101,x] = -F[105,x]+F[102,x]
F[102,x] = 1/F[23,x]*F[103,x]
F[103,x] = F[104,x]
F[104,x] = -F[2,x]+F[5,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[23,x]
F[107,x] = F[108,x]+F[116,x]
F[108,x] = F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[27,x]
F[110,x] = F[111,x]+F[4,x]
F[111,x] = F[112,x]
F[112,x] = F[107,x]*F[23,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[23,x]*F[27,x]
F[115,x] = F[101,x]+F[4,x]
F[116,x] = F[117,x]
F[117,x] = F[110,x]*F[23,x]*F[27,x]
F[118,x] = F[119,x]
F[119,x] = F[107,x]*F[13,x]*F[23,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{96}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)+F_{94}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{84}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{76}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{75}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{41}\! \left(x \right) = F_{27}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{58}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{5}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{8}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{71}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = 0
F_{66}\! \left(x \right) = F_{23}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{75}\! \left(x \right) = F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{33}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{9}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{83}\! \left(x \right) = F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{23}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{42}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{51}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{96}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{118}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{23}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{116}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{27}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{107}\! \left(x \right) F_{23}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{115}\! \left(x \right) = F_{101}\! \left(x \right)+F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{107}\! \left(x \right) F_{13}\! \left(x \right) F_{23}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_23(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_96(x))
Eq(F_8(x), F_9(x) + F_94(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x) + F_84(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x)/F_23(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) - F_77(x))
Eq(F_17(x), F_18(x) + F_28(x))
Eq(F_18(x), F_19(x) + F_24(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_23(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), x)
Eq(F_24(x), F_23(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_23(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_17(x) + F_32(x))
Eq(F_32(x), F_25(x)*F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_13(x)*F_23(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_76(x))
Eq(F_38(x), F_33(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_75(x))
Eq(F_40(x), F_41(x) + F_73(x))
Eq(F_41(x), F_27(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_58(x))
Eq(F_43(x), F_44(x) - F_53(x))
Eq(F_44(x), F_45(x)/F_23(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_8(x))
Eq(F_47(x), F_48(x)/F_23(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_5(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_23(x)*F_42(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), -F_58(x) + F_8(x))
Eq(F_58(x), F_59(x) + F_71(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_62(x))
Eq(F_62(x), F_22(x) + F_63(x))
Eq(F_63(x), F_60(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_66(x) + F_70(x))
Eq(F_65(x), 0)
Eq(F_66(x), F_23(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_23(x))
Eq(F_69(x), F_64(x))
Eq(F_70(x), F_23(x)*F_60(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_23(x)*F_27(x)*F_4(x)*F_59(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_23(x)*F_42(x))
Eq(F_75(x), F_73(x))
Eq(F_76(x), F_33(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_23(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_81(x) + F_9(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_13(x)*F_23(x))
Eq(F_83(x), F_81(x))
Eq(F_84(x), F_85(x) - F_88(x))
Eq(F_85(x), F_86(x)/F_23(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), -F_2(x) + F_49(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_23(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_0(x)*F_42(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_23(x)*F_42(x)*F_51(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_13(x)*F_23(x)*F_4(x))
Eq(F_96(x), F_94(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_23(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_118(x))
Eq(F_100(x), F_101(x)*F_13(x))
Eq(F_101(x), F_102(x) - F_105(x))
Eq(F_102(x), F_103(x)/F_23(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), -F_2(x) + F_5(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_23(x))
Eq(F_107(x), F_108(x) + F_116(x))
Eq(F_108(x), F_109(x) + F_113(x))
Eq(F_109(x), F_110(x)*F_27(x))
Eq(F_110(x), F_111(x) + F_4(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_107(x)*F_23(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_23(x)*F_27(x))
Eq(F_115(x), F_101(x) + F_4(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_110(x)*F_23(x)*F_27(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_107(x)*F_13(x)*F_23(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "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": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}], "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]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"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": "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": [], "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/25380/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[8,x]+F[96,x]
F[8,x] = F[9,x]+F[94,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = F[13,x]+F[84,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = 1/F[23,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = -F[77,x]+F[17,x]
F[17,x] = F[18,x]+F[28,x]
F[18,x] = F[19,x]+F[24,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[23,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = x
F[24,x] = F[23,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[29,x]
F[29,x] = F[23,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[17,x]+F[32,x]
F[32,x] = F[25,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[13,x]*F[23,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = F[38,x]+F[76,x]
F[38,x] = F[33,x]+F[39,x]
F[39,x] = F[40,x]+F[75,x]
F[40,x] = F[41,x]+F[73,x]
F[41,x] = F[27,x]*F[42,x]
F[42,x] = 1/F[58,x]*F[43,x]
F[43,x] = -F[53,x]+F[44,x]
F[44,x] = 1/F[23,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[8,x]+F[47,x]
F[47,x] = 1/F[23,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[5,x]
F[53,x] = F[54,x]
F[54,x] = F[23,x]*F[42,x]*F[55,x]
F[55,x] = 1/F[23,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[58,x]+F[8,x]
F[58,x] = F[59,x]+F[71,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[62,x]
F[62,x] = F[22,x]+F[63,x]
F[63,x] = F[60,x]+F[64,x]
F[64,x] = F[65,x]+F[66,x]+F[70,x]
F[65,x] = 0
F[66,x] = F[23,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[23,x]
F[69,x] = F[64,x]
F[70,x] = F[23,x]*F[60,x]
F[71,x] = F[72,x]
F[72,x] = F[23,x]*F[27,x]*F[4,x]*F[59,x]
F[73,x] = F[74,x]
F[74,x] = F[23,x]*F[42,x]
F[75,x] = F[73,x]
F[76,x] = F[33,x]
F[77,x] = F[78,x]
F[78,x] = F[23,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[81,x]+F[9,x]
F[81,x] = F[82,x]
F[82,x] = F[13,x]*F[23,x]
F[83,x] = F[81,x]
F[84,x] = -F[88,x]+F[85,x]
F[85,x] = 1/F[23,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[2,x]+F[49,x]
F[88,x] = F[89,x]
F[89,x] = F[23,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[0,x]*F[42,x]
F[92,x] = F[93,x]
F[93,x] = F[23,x]*F[42,x]*F[51,x]
F[94,x] = F[95,x]
F[95,x] = F[13,x]*F[23,x]*F[4,x]
F[96,x] = F[94,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[23,x]*F[99,x]
F[99,x] = F[100,x]+F[118,x]
F[100,x] = F[101,x]*F[13,x]
F[101,x] = -F[105,x]+F[102,x]
F[102,x] = 1/F[23,x]*F[103,x]
F[103,x] = F[104,x]
F[104,x] = -F[2,x]+F[5,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[23,x]
F[107,x] = F[108,x]+F[116,x]
F[108,x] = F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[27,x]
F[110,x] = F[111,x]+F[4,x]
F[111,x] = F[112,x]
F[112,x] = F[107,x]*F[23,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[23,x]*F[27,x]
F[115,x] = F[101,x]+F[4,x]
F[116,x] = F[117,x]
F[117,x] = F[110,x]*F[23,x]*F[27,x]
F[118,x] = F[119,x]
F[119,x] = F[107,x]*F[13,x]*F[23,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{96}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)+F_{94}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{84}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{76}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{75}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{41}\! \left(x \right) = F_{27}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{58}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{5}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{8}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{71}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = 0
F_{66}\! \left(x \right) = F_{23}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{75}\! \left(x \right) = F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{33}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{9}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{83}\! \left(x \right) = F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{23}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{42}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{51}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{96}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{118}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{23}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{116}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{27}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{107}\! \left(x \right) F_{23}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{115}\! \left(x \right) = F_{101}\! \left(x \right)+F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{107}\! \left(x \right) F_{13}\! \left(x \right) F_{23}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_23(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_96(x))
Eq(F_8(x), F_9(x) + F_94(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x) + F_84(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x)/F_23(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) - F_77(x))
Eq(F_17(x), F_18(x) + F_28(x))
Eq(F_18(x), F_19(x) + F_24(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_23(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), x)
Eq(F_24(x), F_23(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_23(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_17(x) + F_32(x))
Eq(F_32(x), F_25(x)*F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_13(x)*F_23(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_76(x))
Eq(F_38(x), F_33(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_75(x))
Eq(F_40(x), F_41(x) + F_73(x))
Eq(F_41(x), F_27(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_58(x))
Eq(F_43(x), F_44(x) - F_53(x))
Eq(F_44(x), F_45(x)/F_23(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_8(x))
Eq(F_47(x), F_48(x)/F_23(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_5(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_23(x)*F_42(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), -F_58(x) + F_8(x))
Eq(F_58(x), F_59(x) + F_71(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_62(x))
Eq(F_62(x), F_22(x) + F_63(x))
Eq(F_63(x), F_60(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_66(x) + F_70(x))
Eq(F_65(x), 0)
Eq(F_66(x), F_23(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_23(x))
Eq(F_69(x), F_64(x))
Eq(F_70(x), F_23(x)*F_60(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_23(x)*F_27(x)*F_4(x)*F_59(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_23(x)*F_42(x))
Eq(F_75(x), F_73(x))
Eq(F_76(x), F_33(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_23(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_81(x) + F_9(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_13(x)*F_23(x))
Eq(F_83(x), F_81(x))
Eq(F_84(x), F_85(x) - F_88(x))
Eq(F_85(x), F_86(x)/F_23(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), -F_2(x) + F_49(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_23(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_0(x)*F_42(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_23(x)*F_42(x)*F_51(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_13(x)*F_23(x)*F_4(x))
Eq(F_96(x), F_94(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_23(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_118(x))
Eq(F_100(x), F_101(x)*F_13(x))
Eq(F_101(x), F_102(x) - F_105(x))
Eq(F_102(x), F_103(x)/F_23(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), -F_2(x) + F_5(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_23(x))
Eq(F_107(x), F_108(x) + F_116(x))
Eq(F_108(x), F_109(x) + F_113(x))
Eq(F_109(x), F_110(x)*F_27(x))
Eq(F_110(x), F_111(x) + F_4(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_107(x)*F_23(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_23(x)*F_27(x))
Eq(F_115(x), F_101(x) + F_4(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_110(x)*F_23(x)*F_27(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_107(x)*F_13(x)*F_23(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 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:
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"obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}], "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]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"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": "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": [], "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/25558/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[8,x]+F[98,x]
F[8,x] = F[9,x]+F[96,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = F[13,x]+F[84,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = 1/F[23,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = -F[77,x]+F[17,x]
F[17,x] = F[18,x]+F[28,x]
F[18,x] = F[19,x]+F[24,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[23,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = x
F[24,x] = F[23,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[29,x]
F[29,x] = F[23,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[17,x]+F[32,x]
F[32,x] = F[25,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[13,x]*F[23,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = F[38,x]+F[76,x]
F[38,x] = F[33,x]+F[39,x]
F[39,x] = F[40,x]+F[75,x]
F[40,x] = F[41,x]+F[73,x]
F[41,x] = F[27,x]*F[42,x]
F[42,x] = 1/F[58,x]*F[43,x]
F[43,x] = -F[53,x]+F[44,x]
F[44,x] = 1/F[23,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[8,x]+F[47,x]
F[47,x] = 1/F[23,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[5,x]
F[53,x] = F[54,x]
F[54,x] = F[23,x]*F[42,x]*F[55,x]
F[55,x] = 1/F[23,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[58,x]+F[8,x]
F[58,x] = F[59,x]+F[71,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[62,x]
F[62,x] = F[22,x]+F[63,x]
F[63,x] = F[60,x]+F[64,x]
F[64,x] = F[65,x]+F[66,x]+F[70,x]
F[65,x] = 0
F[66,x] = F[23,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[23,x]
F[69,x] = F[64,x]
F[70,x] = F[23,x]*F[60,x]
F[71,x] = F[72,x]
F[72,x] = F[23,x]*F[27,x]*F[4,x]*F[59,x]
F[73,x] = F[74,x]
F[74,x] = F[23,x]*F[42,x]
F[75,x] = F[73,x]
F[76,x] = F[33,x]
F[77,x] = F[78,x]
F[78,x] = F[23,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[81,x]+F[9,x]
F[81,x] = F[82,x]
F[82,x] = F[13,x]*F[23,x]
F[83,x] = F[81,x]
F[84,x] = -F[90,x]+F[85,x]
F[85,x] = 1/F[23,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[2,x]+F[88,x]
F[88,x] = -F[0,x]+F[89,x]
F[89,x] = F[0,x]+F[49,x]
F[90,x] = F[91,x]
F[91,x] = F[23,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[0,x]*F[42,x]
F[94,x] = F[95,x]
F[95,x] = F[23,x]*F[42,x]*F[51,x]
F[96,x] = F[97,x]
F[97,x] = F[13,x]*F[23,x]*F[4,x]
F[98,x] = F[96,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[23,x]
F[101,x] = F[102,x]+F[121,x]
F[102,x] = F[103,x]*F[13,x]
F[103,x] = -F[108,x]+F[104,x]
F[104,x] = 1/F[23,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[2,x]+F[107,x]
F[107,x] = -F[0,x]+F[4,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[23,x]
F[110,x] = F[111,x]+F[119,x]
F[111,x] = F[112,x]+F[116,x]
F[112,x] = F[113,x]*F[27,x]
F[113,x] = F[114,x]+F[4,x]
F[114,x] = F[115,x]
F[115,x] = F[110,x]*F[23,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[23,x]*F[27,x]
F[118,x] = F[103,x]+F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[113,x]*F[23,x]*F[27,x]
F[121,x] = F[122,x]
F[122,x] = F[110,x]*F[13,x]*F[23,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{98}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)+F_{96}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{84}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{76}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{75}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{41}\! \left(x \right) = F_{27}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{58}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{5}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{8}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{71}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = 0
F_{66}\! \left(x \right) = F_{23}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{75}\! \left(x \right) = F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{33}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{9}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{83}\! \left(x \right) = F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{0}\! \left(x \right)+F_{49}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{23}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{0}\! \left(x \right) F_{42}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{51}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{98}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{23}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{121}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{13}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{119}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{116}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{27}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{118}\! \left(x \right) = F_{103}\! \left(x \right)+F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{113}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{110}\! \left(x \right) F_{13}\! \left(x \right) F_{23}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_23(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_98(x))
Eq(F_8(x), F_9(x) + F_96(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x) + F_84(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x)/F_23(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) - F_77(x))
Eq(F_17(x), F_18(x) + F_28(x))
Eq(F_18(x), F_19(x) + F_24(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_23(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), x)
Eq(F_24(x), F_23(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_23(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_17(x) + F_32(x))
Eq(F_32(x), F_25(x)*F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_13(x)*F_23(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_76(x))
Eq(F_38(x), F_33(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_75(x))
Eq(F_40(x), F_41(x) + F_73(x))
Eq(F_41(x), F_27(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_58(x))
Eq(F_43(x), F_44(x) - F_53(x))
Eq(F_44(x), F_45(x)/F_23(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_8(x))
Eq(F_47(x), F_48(x)/F_23(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_5(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_23(x)*F_42(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), -F_58(x) + F_8(x))
Eq(F_58(x), F_59(x) + F_71(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_62(x))
Eq(F_62(x), F_22(x) + F_63(x))
Eq(F_63(x), F_60(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_66(x) + F_70(x))
Eq(F_65(x), 0)
Eq(F_66(x), F_23(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_23(x))
Eq(F_69(x), F_64(x))
Eq(F_70(x), F_23(x)*F_60(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_23(x)*F_27(x)*F_4(x)*F_59(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_23(x)*F_42(x))
Eq(F_75(x), F_73(x))
Eq(F_76(x), F_33(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_23(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_81(x) + F_9(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_13(x)*F_23(x))
Eq(F_83(x), F_81(x))
Eq(F_84(x), F_85(x) - F_90(x))
Eq(F_85(x), F_86(x)/F_23(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), -F_2(x) + F_88(x))
Eq(F_88(x), -F_0(x) + F_89(x))
Eq(F_89(x), F_0(x) + F_49(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_23(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_0(x)*F_42(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_23(x)*F_42(x)*F_51(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_13(x)*F_23(x)*F_4(x))
Eq(F_98(x), F_96(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_23(x))
Eq(F_101(x), F_102(x) + F_121(x))
Eq(F_102(x), F_103(x)*F_13(x))
Eq(F_103(x), F_104(x) - F_108(x))
Eq(F_104(x), F_105(x)/F_23(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) - F_2(x))
Eq(F_107(x), -F_0(x) + F_4(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_23(x))
Eq(F_110(x), F_111(x) + F_119(x))
Eq(F_111(x), F_112(x) + F_116(x))
Eq(F_112(x), F_113(x)*F_27(x))
Eq(F_113(x), F_114(x) + F_4(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_110(x)*F_23(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_23(x)*F_27(x))
Eq(F_118(x), F_103(x) + F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_113(x)*F_23(x)*F_27(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_110(x)*F_13(x)*F_23(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "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": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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"tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"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": "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 2], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": [], "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/25942/
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[23,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[23,x]*F[7,x]
F[7,x] = F[8,x]+F[98,x]
F[8,x] = F[9,x]+F[96,x]
F[9,x] = F[0,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[23,x]
F[12,x] = F[13,x]+F[84,x]
F[13,x] = F[14,x]+F[9,x]
F[14,x] = 1/F[23,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = -F[77,x]+F[17,x]
F[17,x] = F[18,x]+F[28,x]
F[18,x] = F[19,x]+F[24,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[23,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = x
F[24,x] = F[23,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[23,x]*F[27,x]
F[27,x] = F[1,x]+F[25,x]
F[28,x] = F[29,x]
F[29,x] = F[23,x]*F[30,x]
F[30,x] = F[31,x]+F[35,x]
F[31,x] = F[17,x]+F[32,x]
F[32,x] = F[25,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[13,x]*F[23,x]
F[35,x] = F[36,x]
F[36,x] = F[23,x]*F[37,x]
F[37,x] = F[38,x]+F[76,x]
F[38,x] = F[33,x]+F[39,x]
F[39,x] = F[40,x]+F[75,x]
F[40,x] = F[41,x]+F[73,x]
F[41,x] = F[27,x]*F[42,x]
F[42,x] = 1/F[58,x]*F[43,x]
F[43,x] = -F[53,x]+F[44,x]
F[44,x] = 1/F[23,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[8,x]+F[47,x]
F[47,x] = 1/F[23,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[23,x]*F[51,x]
F[51,x] = 1/F[23,x]*F[52,x]
F[52,x] = F[5,x]
F[53,x] = F[54,x]
F[54,x] = F[23,x]*F[42,x]*F[55,x]
F[55,x] = 1/F[23,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[58,x]+F[8,x]
F[58,x] = F[59,x]+F[71,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[23,x]*F[62,x]
F[62,x] = F[22,x]+F[63,x]
F[63,x] = F[60,x]+F[64,x]
F[64,x] = F[65,x]+F[66,x]+F[70,x]
F[65,x] = 0
F[66,x] = F[23,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[23,x]
F[69,x] = F[64,x]
F[70,x] = F[23,x]*F[60,x]
F[71,x] = F[72,x]
F[72,x] = F[23,x]*F[27,x]*F[4,x]*F[59,x]
F[73,x] = F[74,x]
F[74,x] = F[23,x]*F[42,x]
F[75,x] = F[73,x]
F[76,x] = F[33,x]
F[77,x] = F[78,x]
F[78,x] = F[23,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[81,x]+F[9,x]
F[81,x] = F[82,x]
F[82,x] = F[13,x]*F[23,x]
F[83,x] = F[81,x]
F[84,x] = -F[90,x]+F[85,x]
F[85,x] = 1/F[23,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = -F[2,x]+F[88,x]
F[88,x] = -F[0,x]+F[89,x]
F[89,x] = F[0,x]+F[49,x]
F[90,x] = F[91,x]
F[91,x] = F[23,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[0,x]*F[42,x]
F[94,x] = F[95,x]
F[95,x] = F[23,x]*F[42,x]*F[51,x]
F[96,x] = F[97,x]
F[97,x] = F[13,x]*F[23,x]*F[4,x]
F[98,x] = F[96,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[23,x]
F[101,x] = F[102,x]+F[121,x]
F[102,x] = F[103,x]*F[13,x]
F[103,x] = -F[108,x]+F[104,x]
F[104,x] = 1/F[23,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[2,x]+F[107,x]
F[107,x] = -F[0,x]+F[4,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[23,x]
F[110,x] = F[111,x]+F[119,x]
F[111,x] = F[112,x]+F[116,x]
F[112,x] = F[113,x]*F[27,x]
F[113,x] = F[114,x]+F[4,x]
F[114,x] = F[115,x]
F[115,x] = F[110,x]*F[23,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[23,x]*F[27,x]
F[118,x] = F[103,x]+F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[113,x]*F[23,x]*F[27,x]
F[121,x] = F[122,x]
F[122,x] = F[110,x]*F[13,x]*F[23,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_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{98}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)+F_{96}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{84}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = x
F_{24}\! \left(x \right) = F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{25}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{76}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{75}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{73}\! \left(x \right)
F_{41}\! \left(x \right) = F_{27}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{58}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{5}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{8}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{71}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = 0
F_{66}\! \left(x \right) = F_{23}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{23}\! \left(x \right) F_{60}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{23}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right)
F_{75}\! \left(x \right) = F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{33}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{23}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{9}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{83}\! \left(x \right) = F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{0}\! \left(x \right)+F_{49}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{23}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{0}\! \left(x \right) F_{42}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{23}\! \left(x \right) F_{42}\! \left(x \right) F_{51}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{98}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{23}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{121}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{13}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{23}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{119}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{116}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{27}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{110}\! \left(x \right) F_{23}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{118}\! \left(x \right) = F_{103}\! \left(x \right)+F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{113}\! \left(x \right) F_{23}\! \left(x \right) F_{27}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{110}\! \left(x \right) F_{13}\! \left(x \right) F_{23}\! \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_23(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_23(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_98(x))
Eq(F_8(x), F_9(x) + F_96(x))
Eq(F_9(x), F_0(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_23(x))
Eq(F_12(x), F_13(x) + F_84(x))
Eq(F_13(x), F_14(x) + F_9(x))
Eq(F_14(x), F_15(x)/F_23(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x) - F_77(x))
Eq(F_17(x), F_18(x) + F_28(x))
Eq(F_18(x), F_19(x) + F_24(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_23(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), x)
Eq(F_24(x), F_23(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_23(x)*F_27(x))
Eq(F_27(x), F_1(x) + F_25(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_23(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_35(x))
Eq(F_31(x), F_17(x) + F_32(x))
Eq(F_32(x), F_25(x)*F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_13(x)*F_23(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_23(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_76(x))
Eq(F_38(x), F_33(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_75(x))
Eq(F_40(x), F_41(x) + F_73(x))
Eq(F_41(x), F_27(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_58(x))
Eq(F_43(x), F_44(x) - F_53(x))
Eq(F_44(x), F_45(x)/F_23(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_47(x) - F_8(x))
Eq(F_47(x), F_48(x)/F_23(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_23(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_23(x))
Eq(F_52(x), F_5(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_23(x)*F_42(x)*F_55(x))
Eq(F_55(x), F_56(x)/F_23(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), -F_58(x) + F_8(x))
Eq(F_58(x), F_59(x) + F_71(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_23(x)*F_62(x))
Eq(F_62(x), F_22(x) + F_63(x))
Eq(F_63(x), F_60(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_66(x) + F_70(x))
Eq(F_65(x), 0)
Eq(F_66(x), F_23(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_23(x))
Eq(F_69(x), F_64(x))
Eq(F_70(x), F_23(x)*F_60(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_23(x)*F_27(x)*F_4(x)*F_59(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_23(x)*F_42(x))
Eq(F_75(x), F_73(x))
Eq(F_76(x), F_33(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_23(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_81(x) + F_9(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_13(x)*F_23(x))
Eq(F_83(x), F_81(x))
Eq(F_84(x), F_85(x) - F_90(x))
Eq(F_85(x), F_86(x)/F_23(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), -F_2(x) + F_88(x))
Eq(F_88(x), -F_0(x) + F_89(x))
Eq(F_89(x), F_0(x) + F_49(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_23(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_0(x)*F_42(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_23(x)*F_42(x)*F_51(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_13(x)*F_23(x)*F_4(x))
Eq(F_98(x), F_96(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_23(x))
Eq(F_101(x), F_102(x) + F_121(x))
Eq(F_102(x), F_103(x)*F_13(x))
Eq(F_103(x), F_104(x) - F_108(x))
Eq(F_104(x), F_105(x)/F_23(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) - F_2(x))
Eq(F_107(x), -F_0(x) + F_4(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_23(x))
Eq(F_110(x), F_111(x) + F_119(x))
Eq(F_111(x), F_112(x) + F_116(x))
Eq(F_112(x), F_113(x)*F_27(x))
Eq(F_113(x), F_114(x) + F_4(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_110(x)*F_23(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_23(x)*F_27(x))
Eq(F_118(x), F_103(x) + F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_113(x)*F_23(x)*F_27(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_110(x)*F_13(x)*F_23(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [0, 4, 2, 3, 1], [0, 4, 3, 2, 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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "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": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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