1
New Number: 3.24 | AESZ: | Superseeker: -2 -108 | Hash: 3c89cc2017daa2eba88c016b8ae5865c
Degree: 3
\(\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ... --> OEIS Normalized instanton numbers (n0=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:...
\((16z-1)(112z^2-40z-1)\)
\(\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 2}\) |
2
New Number: 8.12 | AESZ: 175 | Superseeker: 17 1387 | Hash: f6db11b5e593983f455489d5bb1003c5
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+3^{4} x^{2}\left(89\theta^4+452\theta^3+633\theta^2+362\theta+80\right)+2^{3} 3^{4} x^{3}\left(170\theta^4-1020\theta^3-3119\theta^2-2373\theta-648\right)-2^{4} 3^{8} x^{4}\left(97\theta^4+194\theta^3-238\theta^2-335\theta-114\right)+2^{6} 3^{8} x^{5}\left(170\theta^4+1700\theta^3+961\theta^2-125\theta-204\right)+2^{6} 3^{12} x^{6}\left(89\theta^4-96\theta^3-189\theta^2-96\theta-12\right)-2^{9} 3^{12} x^{7}(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{16} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 630, 29016, 1529766, ... --> OEIS Normalized instanton numbers (n0=1): 17, -299/4, 1387, -47623/2, 500282, ... ; Common denominator:...
\((81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2\)
\(-\frac{ 1}{ 36}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 36}\sqrt{ 2}\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
\(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |