1
New Number: 3.4 | AESZ: | Superseeker: -9 -748 | Hash: 350ef7c6e038467a3f50bfbe164fa73a
Degree: 3
\(\theta^4+3^{2} x\left(33\theta^4+66\theta^3+57\theta^2+24\theta+4\right)+2^{3} 3^{6} x^{2}(\theta+1)^2(5\theta^2+10\theta+4)+2^{2} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -36, 2268, -168840, 13664700, ... --> OEIS Normalized instanton numbers (n0=1): -9, -279/4, -748, -9612, -155448, ... ; Common denominator:...
\((81z+1)(1+108z)^2\)
| \(-\frac{ 1}{ 81}\) | \(-\frac{ 1}{ 108}\) | \(0\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(2\) |
| \(2\) | \(1\) | \(0\) | \(\frac{ 5}{ 2}\) |
2
New Number: 6.7 | AESZ: | Superseeker: -9 217/3 | Hash: 9492f991c909a6774f5546668ff53b6a
Degree: 6
\(\theta^4-3 x\left(42\theta^4+84\theta^3+77\theta^2+35\theta+6\right)+3^{3} x^{2}\left(291\theta^4+1164\theta^3+1747\theta^2+1166\theta+264\right)-2^{2} 3^{5} x^{3}\left(360\theta^4+2160\theta^3+4553\theta^2+3939\theta+1035\right)+2^{3} 3^{8} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{4} 3^{11} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{4} 3^{14} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 8820, 266490, ... --> OEIS Normalized instanton numbers (n0=1): -9, 18, 217/3, -9, -146079, ... ; Common denominator:...
\((27z-1)(34992z^3-1944z^2+27z-1)(-1+36z)^2\)
| \(0\) | ≈\(0.002095-0.023494I\) | ≈\(0.002095+0.023494I\) | \(\frac{ 1}{ 36}\) | \(\frac{ 1}{ 27}\) | ≈\(0.051365\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |
3
New Number: 8.21 | AESZ: 251 | Superseeker: -9 -3145/3 | Hash: dd2b60d18804c72129ba319fc8b50023
Degree: 8
\(\theta^4-3 x\theta(-2-11\theta-18\theta^2+27\theta^3)-2 3^{2} x^{2}\left(39\theta^4+480\theta^3+474\theta^2+276\theta+64\right)+2^{3} 3^{4} x^{3}\left(348\theta^4+1152\theta^3+1759\theta^2+1110\theta+260\right)-2^{3} 3^{5} x^{4}\left(3420\theta^4+15912\theta^3+28437\theta^2+20544\theta+5296\right)+2^{4} 3^{7} x^{5}\left(1125\theta^4+12546\theta^3+31089\theta^2+26448\theta+7480\right)+2^{5} 3^{9} x^{6}\left(1395\theta^4+3240\theta^3-3378\theta^2-7146\theta-2696\right)-2^{7} 3^{11} x^{7}\left(351\theta^4+2646\theta^3+4767\theta^2+3309\theta+800\right)-2^{7} 3^{13} x^{8}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, -1440, 48600, ... --> OEIS Normalized instanton numbers (n0=1): -9, -27/4, -3145/3, -20907/4, -327348, ... ; Common denominator:...
\(-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2\)
| \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 2}\) | \(-\frac{ 1}{ 54}\) | \(0\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 2}\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(2\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |