02341_03241_20341_23041_30241_32041

Counting sequence:
1, 1, 2, 6, 24, 114, 600, 3366, 19704, 118890, 733836, 4610514, 29382564, 189463698, 1233776172, 8101888338, 53588885928, 356696620974, 2387426484576, 16058143143690, 108484256384424, 735785128422678, 5008217585603652, 34199611501872198, 234229555308364692, 1608559441318555662, 11074212975410058228, 76416199546979224566, 528421700659390745064, 3661275036313260903498, 25414485028196810254056, 176715334701359882941182, 1230730680840707880140952, 8584284811940699602850418, 59959489351241696757762300, 419361320153007573793508442, 2936719588893225894367744164, 20589700832278548097934873706, 144518444827706643072957581436, 1015445563263992959726935143178, 7142110168447722430366961750568, 50281839311170124350283924584758, 354315587369528022662354571051504, 2498878149473323806896166125173746, 17638358118115669418252507609754600, 124598615692680427632719624640033102, 880836044975144997759385522205037684, 6231456169746448908452185528383935934, 44114699865326077901146996201287636084, 312510039515848539504170020590702105270, 2215234902389613170123174418241837886340, 15712300306836803660682155233290692328702, 111509940796215074644635654151543500554376, 791829137326390193430656005916821320826434, 5625799551143255511014964048877167241126968, 39991088479701325694824850271485983144107414, 284420030332385468180692256035289436716874552, 2023798833831770553927267596062365819627400890, 14407125837212025333467408350613351351534792556, 102608471764474004150713754716319643420990451170, 731102589653971257449455217066342534813643138852, 5211423423986871275730984174519494717913481132482, 37163049745712169424211239333307688597924037392588, 265117003087780029735313547277159184591380281594754, 1892037059059384592666974231946357976165061711662504, 13507729155905068155358636241381272334303552105300862, 96469663422865821587750270656732643064798781009752192, 689207803376866336030949765649417929922889640630380122, 4925565653828310679144905011918858413458203320712697000, 35213098418225029570829831582217877681450985105217900678, 251820137199574395718874152756012585529526657012893939364, 1801402747237876029323601777431568433328586384142350928758, 12890256572775386939831021802770843820919261200901412729172, 92265441485694355935802580873405096548158956272205996288670, 660601964577698045549371935391433623568638845786596886899988, 4731083636109118632552250665532756267591018127114846138858502, 33892075450419094297880688958120670848083951676896163216284840, 242856320184895888712790036113040764364231489472452159981720762, 1740649838755073908267313348407373685220307434035316326769497480, 12479044733516641472047637909771182659476274716932956678624405486, 89486282083714107655104182763970117768397693537768220602035774680, 641850905612529949309387964810851893580041218452916500876979295426, 4604811895555959683703615981020824328205602931589728084549267228636, 33043590878980367904581608855284090111477322918553449422218801414634, 237168953416931809335101825232086222334759578598451349621663749092900, 1702634511776894292593671584700432590092408649207342834213229190661402, 12225759184573324600426158148671429579675352383336638056236905812504860, 87804938629102827969896074225242657369594696116275087900101267487728954, 630737592830423606339394115423563824522645238912475364528470880770370856, 4531721254415633582598876606114158028606512446653517567943381474009124870, 32565703199228584555040382216421168915851266043363271654576014232080491280, 234066194798480314732651399483283666166623415929289934084649959592620235202, 1682659010853626702534078717747804918470903546337489748661240674041095447272, 12098485376012341190895406007437968283459668226470736720043266643961236353854, 87004496211602491892781569069928031873064219923038234997237867210118016081108, 625787067330476328058413939981923011322918540817613969136513073633192525250542, 4501778322352134394260080121176620905833293787248001692222892175993880643865396, 32390134511337074800061046027610598379121369861230653539246403674656814891301190, 233083246020917397319761993121366913760961705058062603343049319303196398860797604, 1677558231811535845013437324304632235335077437960938425556401373872448879553285262, 12075663865062923417535273691525079131671486495571223974874226842321673348078657864

Implicit equation for the generating function in Maple syntax:
(-3*x+2)*F(x)^3+(6*x^3-2*x^2+11*x-7)*F(x)^2+(2*x^4-x^3-8*x^2-11*x+8)*F(x)+3*(x+1)*(x^2+2*x-1) = 0

Implicit equation for the generating function in latex syntax:
\left(-3 x +2\right) F \! \left(x \right)^{3}+\left(6 x^{3}-2 x^{2}+11 x -7\right) F \! \left(x \right)^{2}+\left(2 x^{4}-x^{3}-8 x^{2}-11 x +8\right) F \! \left(x \right)+3 \left(x +1\right) \left(x^{2}+2 x -1\right) = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a(6) = 600
a(7) = 3366
a(8) = 19704
a(9) = 118890
a(10) = 733836
a(11) = 4610514
a(12) = 29382564
a(13) = 189463698
a(14) = 1233776172
a(15) = 8101888338
a(16) = 53588885928
a(17) = 356696620974
a(18) = 2387426484576
a(n+19) = -3*(n-2)*(n-1)/(n+19)/(n+17)*a(n)+1/2*(25*n+4)*(n-1)/(n+19)/(n+17)*a(n+1)+1/4*(881*n^2+1965*n+52)/(n+19)/(n+17)*a(n+2)-3/8*(103*n^2-611*n-946)/(n+19)/(n+17)*a(n+3)-1/8*(39317*n^2+250521*n+340678)/(n+19)/(n+17)*a(n+4)-1/4*(53533*n^2+440622*n+847553)/(n+19)/(n+17)*a(n+5)-3/8*(18039*n^2+155809*n+382624)/(n+19)/(n+17)*a(n+6)+1/4*(105335*n^2+1257150*n+3573277)/(n+19)/(n+17)*a(n+7)+1/8*(519949*n^2+6661017*n+21756170)/(n+19)/(n+17)*a(n+8)-1/8*(114821*n^2+828021*n-755486)/(n+19)/(n+17)*a(n+9)-1/4*(915742*n^2+16112157*n+71041430)/(n+19)/(n+17)*a(n+10)+1/8*(2172833*n^2+40612287*n+188788006)/(n+19)/(n+17)*a(n+11)-1/8*(627745*n^2+11089899*n+45562286)/(n+19)/(n+17)*a(n+12)-1/4*(214913*n^2+5845476*n+39369805)/(n+19)/(n+17)*a(n+13)+1/8*(420973*n^2+11389173*n+77003036)/(n+19)/(n+17)*a(n+14)-1/4*(78593*n^2+2249898*n+16092175)/(n+19)/(n+17)*a(n+15)+1/8*(32441*n^2+987339*n+7503658)/(n+19)/(n+17)*a(n+16)-1/8*(3923*n^2+126627*n+1020082)/(n+19)/(n+17)*a(n+17)+1/4*(133*n^2+4539*n+38636)/(n+19)/(n+17)*a(n+18), n >= 19

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 114
a(6) = 600
a(7) = 3366
a(8) = 19704
a(9) = 118890
a(10) = 733836
a(11) = 4610514
a(12) = 29382564
a(13) = 189463698
a(14) = 1233776172
a(15) = 8101888338
a(16) = 53588885928
a(17) = 356696620974
a(18) = 2387426484576
a{\left(n + 19 \right)} = - \frac{3 \left(n - 2\right) \left(n - 1\right) a{\left(n \right)}}{\left(n + 17\right) \left(n + 19\right)} + \frac{\left(n - 1\right) \left(25 n + 4\right) a{\left(n + 1 \right)}}{2 \left(n + 17\right) \left(n + 19\right)} - \frac{3 \left(103 n^{2} - 611 n - 946\right) a{\left(n + 3 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(133 n^{2} + 4539 n + 38636\right) a{\left(n + 18 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(881 n^{2} + 1965 n + 52\right) a{\left(n + 2 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(3923 n^{2} + 126627 n + 1020082\right) a{\left(n + 17 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} - \frac{3 \left(18039 n^{2} + 155809 n + 382624\right) a{\left(n + 6 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(32441 n^{2} + 987339 n + 7503658\right) a{\left(n + 16 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(39317 n^{2} + 250521 n + 340678\right) a{\left(n + 4 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(53533 n^{2} + 440622 n + 847553\right) a{\left(n + 5 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(78593 n^{2} + 2249898 n + 16092175\right) a{\left(n + 15 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(105335 n^{2} + 1257150 n + 3573277\right) a{\left(n + 7 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(114821 n^{2} + 828021 n - 755486\right) a{\left(n + 9 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(214913 n^{2} + 5845476 n + 39369805\right) a{\left(n + 13 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(420973 n^{2} + 11389173 n + 77003036\right) a{\left(n + 14 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(519949 n^{2} + 6661017 n + 21756170\right) a{\left(n + 8 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(627745 n^{2} + 11089899 n + 45562286\right) a{\left(n + 12 \right)}}{8 \left(n + 17\right) \left(n + 19\right)} - \frac{\left(915742 n^{2} + 16112157 n + 71041430\right) a{\left(n + 10 \right)}}{4 \left(n + 17\right) \left(n + 19\right)} + \frac{\left(2172833 n^{2} + 40612287 n + 188788006\right) a{\left(n + 11 \right)}}{8 \left(n + 17\right) \left(n + 19\right)}, \quad n \geq 19

Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24410/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[39,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[32,x]
F[13,x] = F[14,x]*F[5,x]
F[14,x] = F[0,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[17,x]*F[4,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[14,x]*F[20,x]*F[4,x]
F[20,x] = 1/F[10,x]/F[4,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[10,x]+F[23,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[4,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]+F[5,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[12,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[29,x]*F[4,x]
F[32,x] = F[33,x]+F[38,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = -F[15,x]+F[27,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = -F[14,x]+F[17,x]
F[38,x] = F[37,x]*F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[10,x]*F[17,x]
F[44,x] = F[17,x]*F[39,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{39}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{10}\! \left(x \right) F_{4}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{38}\! \left(x \right) = F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right) F_{39}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_39(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_32(x))
Eq(F_13(x), F_14(x)*F_5(x))
Eq(F_14(x), F_0(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_17(x)*F_4(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_20(x)*F_4(x))
Eq(F_20(x), F_21(x)/(F_10(x)*F_4(x)))
Eq(F_21(x), F_22(x))
Eq(F_22(x), -F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_4(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x) + F_5(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_12(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_29(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_38(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), -F_15(x) + F_27(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), -F_14(x) + F_17(x))
Eq(F_38(x), F_37(x)*F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_10(x)*F_17(x))
Eq(F_44(x), F_17(x)*F_39(x))
Pack JSON:
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Specification JSON:
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{"patt": [1, 2, 0], "pos": [[3, 6], [3, 8], [3, 6]]}, {"patt": [1, 2, 0], "pos": [[3, 8], [3, 8], [3, 6]]}, {"patt": [2, 1, 0], "pos": [[0, 5], [0, 5], [2, 5]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 4], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 4], [2, 4], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 8], [3, 8], [3, 8], [3, 8]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 4], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 8], [3, 8], [3, 8], [3, 8]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 7]]}]], "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"}}]}

Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25144/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[39,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[32,x]
F[13,x] = F[14,x]*F[5,x]
F[14,x] = F[0,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[17,x]*F[4,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[14,x]*F[20,x]*F[4,x]
F[20,x] = 1/F[10,x]/F[4,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[10,x]+F[23,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[4,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]+F[5,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[12,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[29,x]*F[4,x]
F[32,x] = F[33,x]+F[38,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = -F[15,x]+F[27,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = -F[14,x]+F[17,x]
F[38,x] = F[37,x]*F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[10,x]*F[17,x]
F[44,x] = F[17,x]*F[39,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{39}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{10}\! \left(x \right) F_{4}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{38}\! \left(x \right) = F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right) F_{39}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_39(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_32(x))
Eq(F_13(x), F_14(x)*F_5(x))
Eq(F_14(x), F_0(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_17(x)*F_4(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_20(x)*F_4(x))
Eq(F_20(x), F_21(x)/(F_10(x)*F_4(x)))
Eq(F_21(x), F_22(x))
Eq(F_22(x), -F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_4(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x) + F_5(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_12(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_29(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_38(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), -F_15(x) + F_27(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), -F_14(x) + F_17(x))
Eq(F_38(x), F_37(x)*F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_10(x)*F_17(x))
Eq(F_44(x), F_17(x)*F_39(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 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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[0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], 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1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 4], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 8], [3, 8], [3, 8], [3, 8]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 7]]}]], "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"}}]}

Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25541/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[39,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[32,x]
F[13,x] = F[14,x]*F[5,x]
F[14,x] = F[0,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[17,x]*F[4,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[14,x]*F[20,x]*F[4,x]
F[20,x] = 1/F[10,x]/F[4,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[10,x]+F[23,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[4,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]+F[5,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[12,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[29,x]*F[4,x]
F[32,x] = F[33,x]+F[38,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = -F[15,x]+F[27,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = -F[14,x]+F[17,x]
F[38,x] = F[37,x]*F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[10,x]*F[17,x]
F[44,x] = F[17,x]*F[39,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{39}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{10}\! \left(x \right) F_{4}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{38}\! \left(x \right) = F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right) F_{39}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_39(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_32(x))
Eq(F_13(x), F_14(x)*F_5(x))
Eq(F_14(x), F_0(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_17(x)*F_4(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_20(x)*F_4(x))
Eq(F_20(x), F_21(x)/(F_10(x)*F_4(x)))
Eq(F_21(x), F_22(x))
Eq(F_22(x), -F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_4(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x) + F_5(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_12(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_29(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_38(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), -F_15(x) + F_27(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), -F_14(x) + F_17(x))
Eq(F_38(x), F_37(x)*F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_10(x)*F_17(x))
Eq(F_44(x), F_17(x)*F_39(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 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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[0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], 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1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 4], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 8], [3, 8], [3, 8], [3, 8]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 7]]}]], "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"}}]}

Specification 4
Strategy pack name: insertion_point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25714/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[129,x]
F[10,x] = F[11,x]+F[128,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = (1+F[12,x])*x+F[12,x]^2
F[13,x] = F[14,x]+F[2,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[8,x]
F[16,x] = F[17,x]+F[97,x]
F[17,x] = F[13,x]+F[18,x]
F[18,x] = F[19,x]+F[20,x]
F[19,x] = F[12,x]*F[2,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[8,x]
F[22,x] = F[23,x]+F[96,x]
F[23,x] = F[24,x]+F[95,x]
F[24,x] = F[25,x]+F[71,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[8,x]
F[27,x] = F[28,x]+F[60,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[2,x]+F[25,x]
F[30,x] = F[19,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[53,x]*F[8,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = 2+F[34,x]^2+(-2+x)*F[34,x]
F[35,x] = F[12,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[33,x]*F[38,x]*F[8,x]
F[38,x] = F[12,x]+F[39,x]
F[39,x] = F[12,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]*F[8,x]
F[42,x] = F[39,x]+F[43,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[34,x]+F[39,x]
F[46,x] = F[40,x]+F[47,x]
F[47,x] = -F[52,x]+F[48,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[8,x]*F[50,x]
F[50,x] = F[36,x]
F[51,x] = F[36,x]+F[38,x]
F[52,x] = F[12,x]*F[38,x]
F[53,x] = F[25,x]+F[54,x]
F[54,x] = -F[29,x]+F[55,x]
F[55,x] = -F[58,x]+F[56,x]
F[56,x] = 1/F[8,x]*F[57,x]
F[57,x] = F[25,x]
F[58,x] = F[2,x]*F[59,x]
F[59,x] = F[45,x]+F[55,x]
F[60,x] = F[61,x]+F[63,x]
F[61,x] = F[2,x]*F[62,x]
F[62,x] = F[29,x]+F[34,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[25,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[27,x]*F[38,x]*F[8,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[2,x]*F[25,x]
F[69,x] = F[70,x]
F[70,x] = F[27,x]*F[53,x]*F[8,x]
F[71,x] = F[14,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]*F[8,x]
F[74,x] = F[75,x]+F[82,x]
F[75,x] = F[71,x]+F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[12,x]*F[55,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[2,x]*F[40,x]
F[80,x] = F[81,x]
F[81,x] = F[42,x]*F[53,x]*F[8,x]
F[82,x] = F[83,x]+F[85,x]
F[83,x] = F[2,x]*F[84,x]
F[84,x] = F[39,x]+F[54,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[14,x]*F[59,x]
F[87,x] = F[88,x]+F[91,x]
F[88,x] = F[72,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[38,x]*F[74,x]*F[8,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[2,x]*F[72,x]
F[93,x] = F[94,x]
F[94,x] = F[53,x]*F[74,x]*F[8,x]
F[95,x] = F[12,x]*F[53,x]
F[96,x] = F[35,x]*F[53,x]
F[97,x] = F[119,x]+F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[2,x]*F[34,x]
F[100,x] = F[101,x]+F[108,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[8,x]
F[103,x] = F[104,x]+F[107,x]
F[104,x] = F[105,x]+F[11,x]
F[105,x] = F[106,x]*F[2,x]
F[106,x] = F[12,x]+F[29,x]
F[107,x] = F[106,x]*F[5,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[8,x]
F[110,x] = F[111,x]+F[118,x]
F[111,x] = F[112,x]+F[114,x]
F[112,x] = F[113,x]+F[40,x]
F[113,x] = F[25,x]+F[72,x]
F[114,x] = F[115,x]*F[2,x]
F[115,x] = F[116,x]+F[40,x]
F[116,x] = F[117,x]+F[25,x]
F[117,x] = -F[25,x]+F[54,x]
F[118,x] = F[115,x]*F[5,x]
F[119,x] = F[120,x]+F[123,x]
F[120,x] = F[121,x]+F[14,x]
F[121,x] = F[122,x]
F[122,x] = F[16,x]*F[38,x]*F[8,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[125,x]
F[125,x] = F[16,x]*F[2,x]*F[8,x]
F[126,x] = F[127,x]
F[127,x] = F[16,x]*F[53,x]*F[8,x]
F[128,x] = F[18,x]+F[36,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[100,x]+F[131,x]
F[131,x] = F[12,x]*F[2,x]
F[132,x] = F[121,x]+F[123,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{129}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{128}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = F_{12}\! \left(x \right) x +F_{12} \left(x \right)^{2}+x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{2}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{97}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{96}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{95}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{71}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{60}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{34}\! \left(x \right) x +F_{34} \left(x \right)^{2}-2 F_{34}\! \left(x \right)+2
F_{35}\! \left(x \right) = F_{12}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right) F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{42}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{36}\! \left(x \right)
F_{51}\! \left(x \right) = F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{53}\! \left(x \right) = F_{25}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{25}\! \left(x \right)
F_{58}\! \left(x \right) = F_{2}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{45}\! \left(x \right)+F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{29}\! \left(x \right)+F_{34}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{25}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{27}\! \left(x \right) F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{2}\! \left(x \right) F_{25}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{27}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right) F_{8}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{82}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{2}\! \left(x \right) F_{40}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{42}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{85}\! \left(x \right)
F_{83}\! \left(x \right) = F_{2}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{39}\! \left(x \right)+F_{54}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{59}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{72}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{38}\! \left(x \right) F_{74}\! \left(x \right) F_{8}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{2}\! \left(x \right) F_{72}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{53}\! \left(x \right) F_{74}\! \left(x \right) F_{8}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{96}\! \left(x \right) = F_{35}\! \left(x \right) F_{53}\! \left(x \right)
F_{97}\! \left(x \right) = F_{119}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{2}\! \left(x \right) F_{34}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{108}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{8}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{11}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{2}\! \left(x \right)
F_{106}\! \left(x \right) = F_{12}\! \left(x \right)+F_{29}\! \left(x \right)
F_{107}\! \left(x \right) = F_{106}\! \left(x \right) F_{5}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{8}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{118}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{114}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{40}\! \left(x \right)
F_{113}\! \left(x \right) = F_{25}\! \left(x \right)+F_{72}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{2}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{40}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{25}\! \left(x \right)
F_{117}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{54}\! \left(x \right)
F_{118}\! \left(x \right) = F_{115}\! \left(x \right) F_{5}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{123}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{14}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{16}\! \left(x \right) F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right) F_{8}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{16}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
F_{128}\! \left(x \right) = F_{18}\! \left(x \right)+F_{36}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{100}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{132}\! \left(x \right) = F_{121}\! \left(x \right)+F_{123}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_129(x))
Eq(F_10(x), F_11(x) + F_128(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), (x - 3)*(F_12(x) + 1) + (F_12(x) + 1)**2 + F_12(x) + 2)
Eq(F_13(x), F_14(x) + F_2(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_97(x))
Eq(F_17(x), F_13(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), F_12(x)*F_2(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_8(x))
Eq(F_22(x), F_23(x) + F_96(x))
Eq(F_23(x), F_24(x) + F_95(x))
Eq(F_24(x), F_25(x) + F_71(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_8(x))
Eq(F_27(x), F_28(x) + F_60(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_2(x) + F_25(x))
Eq(F_30(x), F_19(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_53(x)*F_8(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), (x - 2)*F_34(x) + F_34(x)**2 + 2)
Eq(F_35(x), F_12(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_33(x)*F_38(x)*F_8(x))
Eq(F_38(x), F_12(x) + F_39(x))
Eq(F_39(x), F_12(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x)*F_8(x))
Eq(F_42(x), F_39(x) + F_43(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_34(x) + F_39(x))
Eq(F_46(x), F_40(x) + F_47(x))
Eq(F_47(x), F_48(x) - F_52(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_8(x))
Eq(F_50(x), F_36(x))
Eq(F_51(x), F_36(x) + F_38(x))
Eq(F_52(x), F_12(x)*F_38(x))
Eq(F_53(x), F_25(x) + F_54(x))
Eq(F_54(x), -F_29(x) + F_55(x))
Eq(F_55(x), F_56(x) - F_58(x))
Eq(F_56(x), F_57(x)/F_8(x))
Eq(F_57(x), F_25(x))
Eq(F_58(x), F_2(x)*F_59(x))
Eq(F_59(x), F_45(x) + F_55(x))
Eq(F_60(x), F_61(x) + F_63(x))
Eq(F_61(x), F_2(x)*F_62(x))
Eq(F_62(x), F_29(x) + F_34(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_25(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_27(x)*F_38(x)*F_8(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_2(x)*F_25(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_27(x)*F_53(x)*F_8(x))
Eq(F_71(x), F_14(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x)*F_8(x))
Eq(F_74(x), F_75(x) + F_82(x))
Eq(F_75(x), F_71(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_12(x)*F_55(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_2(x)*F_40(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_42(x)*F_53(x)*F_8(x))
Eq(F_82(x), F_83(x) + F_85(x))
Eq(F_83(x), F_2(x)*F_84(x))
Eq(F_84(x), F_39(x) + F_54(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_14(x)*F_59(x))
Eq(F_87(x), F_88(x) + F_91(x))
Eq(F_88(x), F_72(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_38(x)*F_74(x)*F_8(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_2(x)*F_72(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_53(x)*F_74(x)*F_8(x))
Eq(F_95(x), F_12(x)*F_53(x))
Eq(F_96(x), F_35(x)*F_53(x))
Eq(F_97(x), F_119(x) + F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_2(x)*F_34(x))
Eq(F_100(x), F_101(x) + F_108(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_8(x))
Eq(F_103(x), F_104(x) + F_107(x))
Eq(F_104(x), F_105(x) + F_11(x))
Eq(F_105(x), F_106(x)*F_2(x))
Eq(F_106(x), F_12(x) + F_29(x))
Eq(F_107(x), F_106(x)*F_5(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_8(x))
Eq(F_110(x), F_111(x) + F_118(x))
Eq(F_111(x), F_112(x) + F_114(x))
Eq(F_112(x), F_113(x) + F_40(x))
Eq(F_113(x), F_25(x) + F_72(x))
Eq(F_114(x), F_115(x)*F_2(x))
Eq(F_115(x), F_116(x) + F_40(x))
Eq(F_116(x), F_117(x) + F_25(x))
Eq(F_117(x), -F_25(x) + F_54(x))
Eq(F_118(x), F_115(x)*F_5(x))
Eq(F_119(x), F_120(x) + F_123(x))
Eq(F_120(x), F_121(x) + F_14(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_16(x)*F_38(x)*F_8(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_16(x)*F_2(x)*F_8(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_16(x)*F_53(x)*F_8(x))
Eq(F_128(x), F_18(x) + F_36(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_100(x) + F_131(x))
Eq(F_131(x), F_12(x)*F_2(x))
Eq(F_132(x), F_121(x) + F_123(x))
Pack JSON:
{"name": "insertion_point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 4], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], 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"pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0], "pos": [[3, 7]]}, {"patt": [0, 1], "pos": [[1, 7], [1, 7]]}, {"patt": [1, 0], "pos": [[0, 5], [2, 4]]}, {"patt": [1, 0], "pos": [[1, 7], [1, 7]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 5], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 5], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 6], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 8], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 5], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [0, 5], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 5], [0, 5], [2, 5]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 5], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[2, 5], [2, 5], [2, 4]]}, {"patt": [1, 2, 0], "pos": [[3, 6], [3, 8], [3, 6]]}, {"patt": [1, 2, 0], "pos": [[3, 8], [3, 8], [3, 6]]}, {"patt": [2, 1, 0], "pos": [[0, 5], [0, 5], [2, 5]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 3], [0, 3], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 4], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 4], [2, 4], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 8], [3, 8], [3, 8], [3, 8]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [0, 2], [0, 3], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 3], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 4], [2, 1], [2, 4], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 5], [2, 5], [2, 5], [2, 5]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 8], [3, 8], [3, 8], [3, 8]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[1, 7]]}], [{"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[3, 6]]}, {"patt": [0], "pos": [[3, 8]]}]], "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": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1]], "symmetry": true}}]}

Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25739/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[39,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[32,x]
F[13,x] = F[14,x]*F[5,x]
F[14,x] = F[0,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[0,x]*F[17,x]*F[4,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[14,x]*F[20,x]*F[4,x]
F[20,x] = 1/F[10,x]/F[4,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[10,x]+F[23,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[4,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]+F[5,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[12,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[29,x]*F[4,x]
F[32,x] = F[33,x]+F[38,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[35,x]+F[6,x]
F[35,x] = -F[15,x]+F[27,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = -F[14,x]+F[17,x]
F[38,x] = F[37,x]*F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[12,x]+F[43,x]
F[43,x] = F[10,x]*F[17,x]
F[44,x] = F[17,x]*F[39,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{39}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{10}\! \left(x \right) F_{4}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{5}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{38}\! \left(x \right) = F_{37}\! \left(x \right) F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right) F_{39}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_39(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_32(x))
Eq(F_13(x), F_14(x)*F_5(x))
Eq(F_14(x), F_0(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_0(x)*F_17(x)*F_4(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_14(x)*F_20(x)*F_4(x))
Eq(F_20(x), F_21(x)/(F_10(x)*F_4(x)))
Eq(F_21(x), F_22(x))
Eq(F_22(x), -F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_4(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x) + F_5(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_12(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_29(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_38(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_35(x) + F_6(x))
Eq(F_35(x), -F_15(x) + F_27(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), -F_14(x) + F_17(x))
Eq(F_38(x), F_37(x)*F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_12(x) + F_43(x))
Eq(F_43(x), F_10(x)*F_17(x))
Eq(F_44(x), F_17(x)*F_39(x))
Pack JSON:
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Specification JSON:
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