1
New Number: 5.113 | AESZ: 403 | Superseeker: -29/5 -1481/5 | Hash: 492c8a69e87d470c87b9557834f0fc5b
Degree: 5
\(5^{2} \theta^4+5 x\left(487\theta^4+878\theta^3+709\theta^2+270\theta+40\right)+2^{5} x^{2}\left(1013\theta^4+2639\theta^3+2943\theta^2+1520\theta+280\right)-2^{8} x^{3}\left(2169\theta^4+14880\theta^3+30789\theta^2+22440\theta+5240\right)-2^{12} x^{4}(2\theta+1)(518\theta^3+2397\theta^2+2940\theta+1048)-2^{16} 3 x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -8, 216, -8000, 359800, ... --> OEIS Normalized instanton numbers (n0=1): -29/5, 229/5, -1481/5, 43173/5, -155267, ... ; Common denominator:...
\(-(27z+1)(1024z^2-64z-1)(5+16z)^2\)
| \(-\frac{ 5}{ 16}\) | \(-\frac{ 1}{ 27}\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 2}{ 3}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(\frac{ 4}{ 3}\) |
| \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 12.4 | AESZ: | Superseeker: 4 -228/5 | Hash: c24070a1d4a449404cd7b46398fa6d6e
Degree: 12
\(5^{2} \theta^4-2^{2} 5^{2} x\left(16\theta^4+32\theta^3+31\theta^2+15\theta+3\right)+2^{4} 5 x^{2}\left(736\theta^4+2368\theta^3+3848\theta^2+2960\theta+915\right)-2^{10} 5 x^{3}\left(304\theta^4+1176\theta^3+2337\theta^2+2313\theta+891\right)+2^{12} 3 x^{4}\left(2608\theta^4+10688\theta^3+21652\theta^2+23580\theta+9945\right)-2^{16} 3 x^{5}\left(2784\theta^4+11616\theta^3+21812\theta^2+22396\theta+9191\right)+2^{21} 3 x^{6}\left(1232\theta^4+5232\theta^3+9332\theta^2+7968\theta+2649\right)-2^{25} 3^{2} x^{7}\left(304\theta^4+1312\theta^3+2472\theta^2+1992\theta+559\right)+2^{30} 3 x^{8}\left(280\theta^4+1216\theta^3+2491\theta^2+2337\theta+827\right)-2^{32} x^{9}\left(1664\theta^4+7200\theta^3+13692\theta^2+11988\theta+3951\right)+2^{38} x^{10}\left(164\theta^4+832\theta^3+1751\theta^2+1731\theta+663\right)-2^{40} x^{11}\left(160\theta^4+928\theta^3+2072\theta^2+2072\theta+777\right)+2^{44} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 108, 688, 3564, ... --> OEIS Normalized instanton numbers (n0=1): 4, -29/5, -228/5, 3724/5, -31856/5, ... ; Common denominator:...
\((16z-1)^2(256z^2-16z+1)^2(4096z^3-768z^2-5)^2\)
| ≈\(-0.013312-0.074322I\) | ≈\(-0.013312+0.074322I\) | \(0\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 3}I\) | \(\frac{ 1}{ 16}\) | ≈\(0.214124\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(4\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) | \(\frac{ 3}{ 2}\) |