1
New Number: 13.7 | AESZ: | Superseeker: 10 7709/9 | Hash: 47093f7f3b7ab4544ef6b418bdae778b
Degree: 13
\(\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ... --> OEIS Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...
\(-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3\)
≈\(-0.100198\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}\) | \(\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(0\) | ≈\(0.043849-0.05194I\) | ≈\(0.043849+0.05194I\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(\infty\) |
---|---|---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
\(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) | \(3\) | \(3\) |
\(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) |
2
New Number: 8.15 | AESZ: 178 | Superseeker: 18 9799/3 | Hash: e748913f322a008ae5c350f96f1cd860
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+3^{3} x^{2}\left(217\theta^4+1732\theta^3+2441\theta^2+1418\theta+336\right)+2^{3} 3^{6} x^{3}\left(51\theta^4-306\theta^3-934\theta^2-717\theta-204\right)-2^{4} 3^{8} x^{4}\left(289\theta^4+578\theta^3-1310\theta^2-1599\theta-570\right)+2^{6} 3^{11} x^{5}\left(51\theta^4+510\theta^3+290\theta^2-29\theta-64\right)+2^{6} 3^{13} x^{6}\left(217\theta^4-864\theta^3-1453\theta^2-864\theta-156\right)-2^{9} 3^{16} x^{7}(3\theta^2+3\theta+1)(17\theta^2+17\theta+6)+2^{12} 3^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 378, 6552, 21546, ... --> OEIS Normalized instanton numbers (n0=1): 18, -423/2, 9799/3, -150003/2, 1914237, ... ; Common denominator:...
\((1728z^2-72z+1)(2187z^2-81z+1)(-1+1944z^2)^2\)
\(-\frac{ 1}{ 108}\sqrt{ 6}\) | \(0\) | \(\frac{ 1}{ 54}-\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 54}+\frac{ 1}{ 162}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 108}\sqrt{ 6}\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
\(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |