Summary

You searched for: sol=5

Your search produced 8 matches

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1

New Number: 3.1 |  AESZ: 34  |  Superseeker: 1 28/3  |  Hash: e5461c5f5ae4d929328f66b8955a31f5  

Degree: 3

\(\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...

Discriminant

\(-(z-1)(25z-1)(9z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 25}\)\(\frac{ 1}{ 9}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(2\)\(2\)\(2\)\(2\)

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2

New Number: 5.18 |  AESZ: 124  |  Superseeker: 163/61 4795/61  |  Hash: 394b401a3162e31c79ede5b46973791d  

Degree: 5

\(61^{2} \theta^4-61 x\left(3029\theta^4+5572\theta^3+4677\theta^2+1891\theta+305\right)+x^{2}\left(1215215\theta^4+3428132\theta^3+4267228\theta^2+2572675\theta+611586\right)-3^{4} x^{3}\left(39370\theta^4+140178\theta^3+206807\theta^2+142191\theta+37332\right)+3^{8} x^{4}\left(566\theta^4+2230\theta^3+3356\theta^2+2241\theta+558\right)-3^{13} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 69, 1427, 35749, ...
--> OEIS
Normalized instanton numbers (n0=1): 163/61, 630/61, 4795/61, 48422/61, 599809/61, ... ; Common denominator:...

Discriminant

\(-(243z^3-200z^2+47z-1)(-61+81z)^2\)

Local exponents

\(0\) ≈\(0.023574\) ≈\(0.399736-0.121575I\) ≈\(0.399736+0.121575I\)\(\frac{ 61}{ 81}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "5.18" from ...

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3

New Number: 5.7 |  AESZ: 27  |  Superseeker: 14/3 910/3  |  Hash: 3671a1760894e9030e36de89070612e8  

Degree: 5

\(3^{2} \theta^4-3 x\left(173\theta^4+340\theta^3+272\theta^2+102\theta+15\right)-2 x^{2}\left(1129\theta^4+5032\theta^3+7597\theta^2+4773\theta+1083\right)+2 x^{3}\left(843\theta^4+2628\theta^3+2353\theta^2+675\theta+6\right)-x^{4}\left(295\theta^4+608\theta^3+478\theta^2+174\theta+26\right)+x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 109, 3317, 121501, ...
--> OEIS
Normalized instanton numbers (n0=1): 14/3, 175/6, 910/3, 14147/3, 265496/3, ... ; Common denominator:...

Discriminant

\((z^3-289z^2-57z+1)(z-3)^2\)

Local exponents

≈\(-0.213297\)\(0\) ≈\(0.016211\)\(3\) ≈\(289.197085\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

A-incarnation: X(1,1,1,1,1,1,1) in G(2,7)
There is a second MUM point at infinity related to
the Pfaffian in P^7, AESZ 243/5.46

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4

New Number: 10.5 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: 26cb7b62aea8fead9548cb08c510d8cc  

Degree: 10

\(\theta^4-x\left(5+36\theta+102\theta^2+132\theta^3+42\theta^4\right)+x^{2}\left(321+2500\theta+5078\theta^2+2676\theta^3-126\theta^4\right)+x^{3}\left(58511+193314\theta+255284\theta^2+165228\theta^3+36750\theta^4\right)+3 x^{4}\left(149076\theta^4+788140\theta^3+1818454\theta^2+1636604\theta+537147\right)+x^{5}\left(18978161+48287282\theta+41352784\theta^2+10485348\theta^3-282726\theta^4\right)+x^{6}\left(75240839+129474252\theta+18361102\theta^2-64936644\theta^3-20164434\theta^4\right)-x^{7}\left(192652267+790586058\theta+1080753300\theta^2+555817116\theta^3+53729334\theta^4\right)-x^{8}\left(1469856277+3396870740\theta+2385867946\theta^2+267688500\theta^3-184083363\theta^4\right)+2 5 13 x^{9}(2\theta+3)(3678542\theta^3+13483935\theta^2+14333215\theta+4727112)+2^{2} 3 5^{2} 13^{2} 73^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 5, 79, 791, -9329, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

Discriminant

\((3z+1)(5329z^3+1587z^2-69z+1)(13z+1)^2(4z+1)^2(5z-1)^2\)

Local exponents

≈\(-0.337782\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 13}\)\(0\) ≈\(0.019989-0.01249I\) ≈\(0.019989+0.01249I\)\(\frac{ 1}{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 5}{ 2}\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(3\)

Note:

This is operator "10.5" from ...

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5

New Number: 11.16 |  AESZ:  |  Superseeker: 211/35 19279/35  |  Hash: dc993c4f73af62a0915341e2b6d1f81f  

Degree: 11

\(5^{2} 7^{2} \theta^4-5 7 x\left(2658\theta^4+4272\theta^3+3361\theta^2+1225\theta+175\right)-x^{2}\left(482475+2058700\theta+2927049\theta^2+1102432\theta^3-364211\theta^4\right)+x^{3}\left(1107645+7584675\theta+17848802\theta^2+16891206\theta^3+3547267\theta^4\right)-x^{4}\left(5628891+26546780\theta+46592338\theta^2+38194636\theta^3+16110878\theta^4\right)-3 x^{5}\left(2019469\theta^4+2698822\theta^3+453746\theta^2+985337\theta+832575\right)+3^{2} x^{6}\left(3186847\theta^4+10570488\theta^3+13101727\theta^2+7620366\theta+1780951\right)+3^{3} x^{7}\left(515831\theta^4+2708278\theta^3+5879206\theta^2+4986803\theta+1463799\right)-3^{4} x^{8}\left(94081\theta^4+60208\theta^3-440794\theta^2-635338\theta-240009\right)-3^{6} x^{9}\left(4919\theta^4+23958\theta^3+26539\theta^2+8334\theta-480\right)+2 3^{6} x^{10}\left(392\theta^4-674\theta^3-2747\theta^2-2410\theta-663\right)+2^{2} 3^{10} x^{11}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 129, 4523, 191329, ...
--> OEIS
Normalized instanton numbers (n0=1): 211/35, 1643/35, 19279/35, 69901/7, 7789913/35, ... ; Common denominator:...

Discriminant

\((1-66z-379z^2+427z^3+439z^4+81z^5)(35-174z-81z^2+54z^3)^2\)

Local exponents

≈\(-1.31797\)\(0\) ≈\(0.186913\) ≈\(2.631057\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(3\)\(3\)\(1\)\(1\)
\(4\)\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This is operator "11.16" from ...

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6

New Number: 12.15 |  AESZ:  |  Superseeker: 27/5 1619/5  |  Hash: f7297f2850190f8613d1cbc3a7363a23  

Degree: 12

\(5^{2} \theta^4-5 x\left(296\theta^4+574\theta^3+457\theta^2+170\theta+25\right)-x^{2}\left(4531\theta^4+24118\theta^3+37791\theta^2+23710\theta+5550\right)+2^{2} x^{3}\left(559\theta^4+9744\theta^3+19448\theta^2+14280\theta+4055\right)+x^{4}\left(1455\theta^4-636\theta^3+151398\theta^2+254100\theta+114136\right)+x^{5}\left(80304\theta^4+79818\theta^3-776517\theta^2-952026\theta-338569\right)-x^{6}\left(18597\theta^4-67050\theta^3-680097\theta^2-608202\theta-164470\right)-2 x^{7}\left(19086\theta^4+454818\theta^3+525507\theta^2-112266\theta-235189\right)-2^{2} x^{8}\left(52779\theta^4-252492\theta^3-39867\theta^2+316368\theta+192050\right)-2^{3} x^{9}\left(27325\theta^4+45630\theta^3-118827\theta^2-223839\theta-101599\right)+2^{2} 17 x^{10}\left(8047\theta^4+9182\theta^3-8905\theta^2-20876\theta-9476\right)+2^{5} 17^{2} x^{11}(\theta+1)(19\theta^3+129\theta^2+246\theta+145)-2^{4} 17^{3} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 109, 3329, 122581, ...
--> OEIS
Normalized instanton numbers (n0=1): 27/5, 158/5, 1619/5, 51193/10, 485082/5, ... ; Common denominator:...

Discriminant

\(-(4z+1)(z+1)(68z^2+61z-1)(z-1)^2(34z^3-12z^2+3z-5)^2\)

Local exponents

\(-1\)\(-\frac{ 61}{ 136}-\frac{ 11}{ 136}\sqrt{ 33}\)\(-\frac{ 1}{ 4}\) ≈\(-0.126959-0.475615I\) ≈\(-0.126959+0.475615I\)\(0\)\(-\frac{ 61}{ 136}+\frac{ 11}{ 136}\sqrt{ 33}\) ≈\(0.606859\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(2\)\(4\)\(4\)\(0\)\(2\)\(4\)\(1\)\(2\)

Note:

This is operator "12.15" from ...

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7

New Number: 8.16 |  AESZ: 196  |  Superseeker: 189/47 9277/47  |  Hash: fdeee36c14d9c003b59c1738c024d479  

Degree: 8

\(47^{2} \theta^4-47 x\left(2489\theta^4+4984\theta^3+4043\theta^2+1551\theta+235\right)-x^{2}\left(161022+701851\theta+1135848\theta^2+790072\theta^3+208867\theta^4\right)+x^{3}\left(38352+149319\theta+383912\theta^2+637644\theta^3+370857\theta^4\right)-x^{4}\left(1770676+5161283\theta+4424049\theta^2+511820\theta^3-291161\theta^4\right)+x^{5}\left(2151-260936\theta-750755\theta^2-749482\theta^3-406192\theta^4\right)+3^{3} x^{6}\left(5305\theta^4+90750\theta^3+152551\theta^2+91194\theta+17914\right)+2 3^{6} x^{7}\left(106\theta^4+230\theta^3+197\theta^2+82\theta+15\right)-2^{2} 3^{10} x^{8}\left((\theta+1)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 93, 2507, 81229, ...
--> OEIS
Normalized instanton numbers (n0=1): 189/47, 979/47, 9277/47, 124795/47, 2049020/47, ... ; Common denominator:...

Discriminant

\(-(-1+53z+90z^2-50z^3+81z^4)(-47-z+54z^2)^2\)

Local exponents

\(\frac{ 1}{ 108}-\frac{ 1}{ 108}\sqrt{ 10153}\)\(0\)\(\frac{ 1}{ 108}+\frac{ 1}{ 108}\sqrt{ 10153}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(3\)\(1\)\(1\)
\(4\)\(0\)\(4\)\(2\)\(1\)

Note:

The operator has a second MUM-point at infinity, corresponding to operator 8.17 .

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8

New Number: 32.1 |  AESZ:  |  Superseeker: 13 1275  |  Hash: 5c2e3e1d3e85022a77a9136d2272db2f  

Degree: 32

\(\theta^4+x\left(52\theta^4-36\theta-142\theta^3-5-107\theta^2\right)-x^{2}\left(620\theta+8686\theta^3+170+2477\theta^2+1603\theta^4\right)-2 x^{3}\left(57842\theta^4+88182\theta^3+89923\theta^2+53586\theta+14064\right)-x^{4}\left(2697348\theta^3+3016956\theta+1218741\theta^4+4034478\theta^2+1011862\right)+x^{5}\left(4154284\theta^4-36611635\theta^2-9502094\theta^3-20359939-44530432\theta\right)-x^{6}\left(337605744\theta-48775967\theta^4+194246629\theta^2-5346306\theta^3+193227408\right)-2^{2} x^{7}\left(20258471\theta^4-183191522\theta^3-458704813\theta^2-332600094\theta-41903870\right)-2^{3} x^{8}\left(66325647\theta^4-411353730\theta^3-1541171000\theta^2-2130504013\theta-1105449340\right)+2^{5} 3 x^{9}\left(1066771\theta^4-131777420\theta^3+79983198\theta^2+543150745\theta+463708954\right)-2^{4} x^{10}\left(143783659\theta^4+4053640514\theta^3+9858746999\theta^2+7077509476\theta-502326500\right)+2^{7} x^{11}\left(138368083\theta^4+183238033\theta^3-3310018192\theta^2-6653286340\theta-3889203872\right)+2^{7} x^{12}\left(496481718\theta^4+4322462304\theta^3+199787519\theta^2-15317512629\theta-16640068710\right)-2^{8} x^{13}\left(289743462\theta^4-4401242298\theta^3-13355918183\theta^2-7397020754\theta+6375065509\right)-2^{10} x^{14}\left(396133743\theta^4-1333996518\theta^3-15885985865\theta^2-33541445647\theta-23107708481\right)-2^{11} x^{15}\left(453981938\theta^4+4435638750\theta^3+3949663684\theta^2-11263025013\theta-17739853167\right)-2^{12} x^{16}\left(227785391\theta^4+9832817848\theta^3+42310236910\theta^2+74461395968\theta+49621401789\right)+2^{15} x^{17}\left(198897592\theta^4+11771212\theta^3-3867168178\theta^2-11297299537\theta-10235944704\right)+2^{16} x^{18}\left(383086368\theta^4+3420815388\theta^3+11952116012\theta^2+20508953472\theta+14439167835\right)+2^{17} x^{19}\left(190788296\theta^4+2425061392\theta^3+10401497028\theta^2+20606177314\theta+16211593657\right)-2^{19} x^{20}\left(54126314\theta^4+419989028\theta^3+1520710075\theta^2+2841733138\theta+2156782988\right)-2^{21} 3 x^{21}\left(13401434\theta^4+146502422\theta^3+639965165\theta^2+1327396637\theta+1086335005\right)-2^{22} x^{22}\left(10981880\theta^4+141779260\theta^3+691712182\theta^2+1569642590\theta+1393845167\right)+2^{23} x^{23}\left(6721988\theta^4+71373164\theta^3+305959012\theta^2+607082692\theta+457859591\right)+2^{24} x^{24}\left(5172254\theta^4+63781560\theta^3+312564510\theta^2+712915992\theta+628949703\right)+2^{27} x^{25}\left(151244\theta^4+2505628\theta^3+15500094\theta^2+43116865\theta+45072668\right)-2^{28} x^{26}\left(133829\theta^4+1536890\theta^3+6680129\theta^2+12566244\theta+8313095\right)-2^{29} x^{27}\left(54212\theta^4+746052\theta^3+3929140\theta^2+9277842\theta+8249757\right)-2^{31} x^{28}\left(1640\theta^4+35404\theta^3+249484\theta^2+728729\theta+767131\right)+2^{32} x^{29}\left(1266\theta^4+15354\theta^3+69999\theta^2+141732\theta+107131\right)+2^{34} x^{30}\left(187\theta^4+2670\theta^3+14509\theta^2+35511\theta+32982\right)+2^{35} x^{31}\left(22\theta^4+338\theta^3+1960\theta^2+5079\theta+4958\right)+2^{36} x^{32}\left((\theta+4)^4\right)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 85, 2033, 56701, ...
--> OEIS
Normalized instanton numbers (n0=1): 13, -305/4, 1275, -82705/4, 456346, ... ; Common denominator:...

Discriminant

\((2z+1)(z+1)(8z^2+16z+1)(8z^3+28z^2+46z-1)(8z^3+8z^2+z-1)(z-1)^2(8z^2+1)^2(1024z^8+2560z^7-1792z^6-3520z^5-1616z^4+920z^3+36z^2-41z-1)^2\)

Local exponents

\(-1\)\(-\frac{ 1}{ 2}\)\(0\)\(s_18\)\(s_15\)\(s_14\)\(s_17\)\(s_16\)\(s_11\)\(s_10\)\(s_13\)\(s_12\)\(s_1\)\(s_3\)\(s_2\)\(s_5\)\(s_4\)\(s_7\)\(s_6\)\(s_9\)\(s_8\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(4\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(1\)\(1\)\(0\)\(3\)\(3\)\(3\)\(3\)\(3\)\(3\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(4\)
\(2\)\(2\)\(0\)\(4\)\(4\)\(4\)\(4\)\(4\)\(4\)\(2\)\(4\)\(4\)\(1\)\(2\)\(1\)\(2\)\(2\)\(2\)\(2\)\(2\)\(2\)\(1\)\(4\)

Note:

This is operator "32.1" from ...

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