1
New Number: 7.21 | AESZ: | Superseeker: 90 413926 | Hash: f2cdf32038c22a3da2f5752ad59eaa27
Degree: 7
\(\theta^4-3^{2} x\left(27\theta^4+216\theta^3+234\theta^2+126\theta+28\right)-3^{6} x^{2}\left(75\theta^4-672\theta^3-2378\theta^2-2602\theta-1076\right)+3^{9} x^{3}\left(1843\theta^4+6360\theta^3-2836\theta^2-13692\theta-9828\right)-3^{14} x^{4}\left(373\theta^4+9344\theta^3+16396\theta^2+10260\theta+540\right)-3^{19} x^{5}\left(875\theta^4+152\theta^3-6794\theta^2-11462\theta-5400\right)+3^{26} x^{6}\left(71\theta^4+480\theta^3+1218\theta^2+1386\theta+600\right)+3^{33} x^{7}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 252, 40419, 2460816, -1025424441, ... --> OEIS Normalized instanton numbers (n0=1): 90, -4365, 413926, -38862153, 4502063682, ... ; Common denominator:...
\((1+27z)(243z+1)^2(59049z^2-378z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 243}\) | \(0\) | \(\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(2\) | \(4\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(2\) |
2
New Number: 9.4 | AESZ: | Superseeker: -90 -413926 | Hash: e2329b2f9cd1e3f65d29644e6ce39d24
Degree: 9
\(\theta^4+3^{2} x\left(69\theta^4+132\theta^3+108\theta^2+42\theta+7\right)+2 3^{5} x^{2}\left(198\theta^4+1656\theta^3+2235\theta^2+1203\theta+271\right)-2 3^{9} x^{3}\left(1082\theta^4-4032\theta^3-10621\theta^2-6257\theta-1523\right)-2 3^{12} x^{4}\left(17617\theta^4+21400\theta^3-72757\theta^2-59353\theta-17391\right)-2 3^{17} x^{5}\left(6967\theta^4+54948\theta^3-16949\theta^2-32367\theta-12734\right)+2 3^{22} x^{6}\left(7322\theta^4-27080\theta^3-389\theta^2+8651\theta+4395\right)+2 3^{29} x^{7}\left(894\theta^4+368\theta^3+311\theta^2+323\theta+137\right)+3^{36} x^{8}\left(57\theta^4+112\theta^3+78\theta^2+22\theta+2\right)-3^{43} x^{9}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -63, 4455, 34551, -114913161, ... --> OEIS Normalized instanton numbers (n0=1): -90, -8685/2, -413926, -38862153, -4502063682, ... ; Common denominator:...
\(-(-1+27z)(-1+243z)^2(59049z^2+378z+1)^3\)
| \(-\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(-\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\) | \(0\) | \(\frac{ 1}{ 243}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |