Summary

You searched for: sol=1

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1

New Number: 9.6 |  AESZ:  |  Superseeker: 95/102 1421/102  |  Hash: 04982735f3d6178049251771352a0277  

Degree: 9

\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\left(1238\theta^4+2434\theta^3+1931\theta^2+714\theta+102\right)-x^{2}\left(1905719\theta^4+7435898\theta^3+11481377\theta^2+8054838\theta+2175150\right)-x^{3}\left(65375064\theta+31069026\theta^3+4568070\theta^4+22153074+70031651\theta^2\right)+x^{4}\left(4512344\theta^4-46914039-80101802\theta^2-111691663\theta-9395414\theta^3\right)+x^{5}\left(36577126+121266438\theta^3+23432568\theta^4+137186363\theta+194777323\theta^2\right)+x^{6}\left(69502656\theta^3-1312570+57037497\theta+121320734\theta^2+4255715\theta^4\right)-3 13 x^{7}\left(877789\theta^4+3969932\theta^3+7763293\theta^2+7084011\theta+2438016\right)-3^{2} 5 13^{2} x^{8}(\theta+1)(1514\theta^3+4164\theta^2+3373\theta+681)+3^{3} 5^{2} 13^{3} x^{9}(3\theta+5)(3\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, 1, 17, 163, 2233, ...
--> OEIS
Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...

Discriminant

\((1-12z-181z^2-510z^3-328z^4+351z^5)(-102+7z+195z^2)^2\)

Local exponents

\(-\frac{ 7}{ 390}-\frac{ 1}{ 390}\sqrt{ 79609}\)\(0\)\(-\frac{ 7}{ 390}+\frac{ 1}{ 390}\sqrt{ 79609}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(3\)\(0\)\(3\)\(1\)\(\frac{ 5}{ 3}\)
\(4\)\(0\)\(4\)\(2\)\(2\)

Note:

This is operator "9.6" from ...

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2

New Number: 24.12 |  AESZ:  |  Superseeker: 1/3 1289597/39366  |  Hash: 9f410e240839dfb2c31e0d9ab21bcf92  

Degree: 24

\(3^{3} \theta^4-3^{2} x\left(21\theta^4+26\theta^3+27\theta^2+14\theta+3\right)+2^{4} 3 x^{2}\left(1375\theta^4+1228\theta^3+1487\theta^2+614\theta+93\right)+2^{7} x^{3}\left(5593\theta^4-4894\theta^3-15283\theta^2-10592\theta-3189\right)-2^{10} x^{4}\left(1755\theta^4+11130\theta^3-55892\theta^2-47479\theta-15219\right)-2^{12} x^{5}\left(35483\theta^4-933060\theta^3+194605\theta^2+201774\theta+76539\right)+2^{14} x^{6}\left(105307\theta^4-637672\theta^3-308501\theta^2-310872\theta-167723\right)-2^{17} x^{7}\left(59541\theta^4-937902\theta^3-1250911\theta^2-1406132\theta-697865\right)+2^{20} x^{8}\left(150991\theta^4+759264\theta^3+3007976\theta^2+4226730\theta+2232921\right)-2^{23} x^{9}\left(303262\theta^4+2599208\theta^3+7447674\theta^2+10796900\theta+6015357\right)+2^{26} x^{10}\left(26658\theta^4-69132\theta^3-5869072\theta^2-9790622\theta-5785043\right)+2^{29} x^{11}\left(52403\theta^4+5485920\theta^3+20238530\theta^2+32576052\theta+19443807\right)-2^{32} x^{12}\left(676638\theta^4+4352088\theta^3+7488880\theta^2+5678926\theta+1126215\right)+2^{35} x^{13}\left(144814\theta^4-1215584\theta^3-10922414\theta^2-24907140\theta-173936401\right)+2^{38} x^{14}\left(464128\theta^4+5192664\theta^3+16987014\theta^2+25566882\theta+1450055\right)-2^{41} x^{15}\left(393556\theta^4+2778212\theta^3+7715696\theta^2+9949084\theta+4920079\right)+2^{44} x^{16}\left(1992\theta^4-1014792\theta^3-4709600\theta^2-7958386\theta-4559197\right)+2^{47} x^{17}\left(171070\theta^4+1455864\theta^3+5007722\theta^2+7771956\theta+4461993\right)-2^{50} x^{18}\left(80590\theta^4+559352\theta^3+1994028\theta^2+3689138\theta+2550645\right)-2^{53} x^{19}\left(38226\theta^4+30444\theta^3+878182\theta^2+886100\theta+185855\right)+2^{56} x^{20}\left(20906\theta^4+165792\theta^3+493376\theta^2+554010\theta+178671\right)+2^{59} x^{21}\left(5072\theta^4+33772\theta^3+69936\theta^2+56704\theta+16563\right)-2^{62} x^{22}\left(1691\theta^4+12560\theta^3+32617\theta^2+37570\theta+16816\right)-2^{65} 5 x^{23}\left(59\theta^4+306\theta^3+563\theta^2+408\theta+78\right)+2^{68} 5^{2} x^{24}\left((\theta+2)^4\right)\)

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Coefficients of the holomorphic solution: 1, 1, -135/16, 672377/11664, 759635299/995328, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/3, -15611/576, 1289597/39366, 2808573854873/859963392, 25331648080663241/1259712000000, ... ; Common denominator:...

Discriminant

\(27-189z-7798361057160712945664z^22-10883579003488635453440z^23+7378697629483820646400z^24+1725349888z^6-7804157952z^7+158325538816z^8-2543946039296z^9+1788988096512z^10+35043634600476672z^16+24075962132945960960z^17+66000z^2+715904z^3-1797120z^4-145338368z^5-90736273492447068160z^18+28133646401536z^11-2906138081230848z^12+4975771152023552z^13+127578533194104832z^14-865438796362022912z^15-344309198711729160192z^19+1506436060956921430016z^20+2923808935682963931136z^21\)

No data for singularities

Note:

This is operator "24.12" from ...

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