{"count": 10, "status":"OK", "data":[{"pols": "[X^4, -12*(2*X+1)^2*(18*X^2+18*X+7), 11664*(2*X+1)^2*(2*X+3)^2]", "text": "Hadamard product $A \\ast$", "degz": 2, "h3": null, "sol": "1 84 17820 4868400 1499003100 494961035184 171107639586576 61103337391736640 22354350543240615900 8332724377700866743600", "n_discr_factors": "1", "c3": null, "operator": "4 2 0 0 0 0 1 -84 -552 -1416 -1728 -864 104976 559872 1026432 746496 186624", "new_number": "2.28", "id": 20, "operator_tex": "\\theta^4-2^{2} 3 x(2\\theta+1)^2(18\\theta^2+18\\theta+7)+2^{4} 3^{6} x^{2}(2\\theta+1)^2(2\\theta+3)^2", "superseek": "48 2864", "discriminant": "2 1 -864 186624", "aesz": "49", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "0a357a8c4fd703ab062148eadcd94daa", "dim_h": null, "inst": " 48 -438 2864 77958 -4942032 151245290 -1996758480 -88714438074 7950912054320 -337859845694358", "cleanlist": "True", "n_sing_real": "2", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "2", "laurent": null, 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2598156*X^4+9447840*X^3+13568148*X^2+8608032*X+2006208, -1417176*(X+1)^2*(3*X+2)*(3*X+4)]", "text": "A-Incarnation: (3,0),(0,3),(1,1) intersection in $P^3 \\times \\P^3$.", "degz": 5, "h3": "54", "sol": "1 12 252 6600 198540 6616512 238795704 9174387024 370128617100 15513158060400", "n_discr_factors": "3", "c3": "-18", "operator": "4 5 0 0 0 0 1 -12 -69 -159 -180 -144 2736 12096 20871 17820 7857 -129600 -542376 -851958 -629856 -205578 2006208 8608032 13568148 9447840 2598156 -11337408 -48183984 -75110328 -51018336 -12754584", "new_number": "5.3", "id": 249, "operator_tex": "\\theta^4-3 x\\left(48\\theta^4+60\\theta^3+53\\theta^2+23\\theta+4\\right)+3^{2} x^{2}\\left(873\\theta^4+1980\\theta^3+2319\\theta^2+1344\\theta+304\\right)-2 3^{4} x^{3}\\left(1269\\theta^4+3888\\theta^3+5259\\theta^2+3348\\theta+800\\right)+2^{2} 3^{6} x^{4}\\left(891\\theta^4+3240\\theta^3+4653\\theta^2+2952\\theta+688\\right)-2^{3} 3^{11} x^{5}(\\theta+1)^2(3\\theta+2)(3\\theta+4)", "superseek": "3 245/3", 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x^{4}\\left(309\\theta^4+2472\\theta^3+7618\\theta^2+10696\\theta+5311\\right)-2^{2} 3^{3} 5 7^{2} x^{5}(\\theta+4)(\\theta+1)(22\\theta^2+110\\theta+123)-3^{5} 5^{2} 7^{2} x^{6}(\\theta+5)(\\theta+4)(\\theta+2)(\\theta+1)", "superseek": "5/4 35/2", "discriminant": "6 4096 -108544 4864 573696 133488 -582120 -297675", "aesz": "376", "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "24fee66b67ff1a8a852f7a562f7665c1", "dim_h": null, "inst": " 5/4 57/16 35/2 459/4 3615/4 97217/12 317945/4 833711 110476691/12 1694285265/16", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "-(7z+4)(5z-4)(105z-4)(9z-4)(4+3z)^2", "discr_factors": "-297675, z-4/5, (4/3+z)^2, z-4/105, z+4/7, z-4/9", "dm_basis": null, "q": "0 1 -25/4 81/16 -713/64 -73087/256 -1774713/1024 -94067023/4096 -4335269673/16384 -209855999007/65536", "yuk": "1 5/4 119/4 1895/4 29495/4 112970 7001633/4 27263785 1707469623/4 6711459452", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-4/3","im":"0","approx_re":"-1.33333333333","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-4/7","im":"0","approx_re":"-0.571428571429","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"4/105","im":"0","approx_re":"0.0380952380952","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"4/9","im":"0","approx_re":"0.444444444444","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"4/5","im":"0","approx_re":"0.8","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","4","5"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[49*X^4, -20832*X^4-20328*X^3-15750*X^2-5586*X-784, 3065568*X^4+4739808*X^3+4043188*X^2+1816304*X+335104, -207097856*X^4-453667200*X^3-491369152*X^2-256875696*X-51444064, 6782284032*X^4+21334995456*X^3+27915672384*X^2+16721014848*X+3660106624, -260096*(X+1)*(390972*X^3+1350660*X^2+1486781*X+460439), 139792236544*(X+1)*(X+2)*(2*X+1)*(2*X+5)]", "text": "This is operator \"6.3\" from ...", "degz": 6, "h3": null, "sol": "1 16 864 80800 9624160 1298457216 189187469856 29065426625664 4642948645077600 764217020993620480", "n_discr_factors": "3", "c3": null, "operator": "4 6 0 0 0 0 49 -784 -5586 -15750 -20328 -20832 335104 1816304 4043188 4739808 3065568 -51444064 -256875696 -491369152 -453667200 -207097856 3660106624 16721014848 27915672384 21334995456 6782284032 -119758342144 -506464133120 -738007054336 -452991516672 -101690253312 1397922365440 5451897225216 6849819590656 3355013677056 559168946176", "new_number": "6.3", "id": 425, "operator_tex": "7^{2} \\theta^4-2 7 x\\left(1488\\theta^4+1452\\theta^3+1125\\theta^2+399\\theta+56\\right)+2^{2} x^{2}\\left(766392\\theta^4+1184952\\theta^3+1010797\\theta^2+454076\\theta+83776\\right)-2^{4} x^{3}\\left(12943616\\theta^4+28354200\\theta^3+30710572\\theta^2+16054731\\theta+3215254\\right)+2^{6} x^{4}\\left(105973188\\theta^4+333359304\\theta^3+436182381\\theta^2+261265857\\theta+57189166\\right)-2^{11} 127 x^{5}(\\theta+1)(390972\\theta^3+1350660\\theta^2+1486781\\theta+460439)+2^{14} 23^{2} 127^{2} x^{6}(\\theta+1)(\\theta+2)(2\\theta+1)(2\\theta+5)", "superseek": "178/7 129516/7", "discriminant": "6 49 -20832 3065568 -207097856 6782284032 -101690253312 559168946176", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "ec9e21dc2ccd3b4b4156ae1438454b96", "dim_h": null, "inst": " 178/7 3375/7 129516/7 6515900/7 409239710/7 29732192762/7 2381477190166/7 204433165592840/7 18494912599411778/7 1743947625117701865/7", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "5", "laurent": null, "discriminant_tex": "(1-248z+8464z^2)(508z-7)^2(16z-1)^2", "discr_factors": "559168946176, 1/8464-31/1058*z+z^2, (z-7/508)^2, (z-1/16)^2", "dm_basis": null, "q": "0 1 -50 857 -43532 -275940 -100383426 -7088749302 -728504871752 -71513069258332", "yuk": "1 178/7 27178/7 3497110/7 417044778/7 51154963928/7 6422157160702/7 816846676227116/7 104669781200578858/7 13482791284974683272/7", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"31/2116-3/529*3^(1/2)","im":"0","approx_re":"0.004828","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"7/508","im":"0","approx_re":"0.0137795275591","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"31/2116+3/529*3^(1/2)","im":"0","approx_re":"0.024473","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","1","2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -288*X^4-360*X^3-381*X^2-201*X-42, 35073*X^4+85860*X^3+118881*X^2+83214*X+23472, -2340090*X^4-8424324*X^3-14284998*X^2-11871036*X-3875040, 92352636*X^4+435545424*X^3+869227524*X^2+817972992*X+293874480, -4251528*(X+1)*(507*X^3+2439*X^2+4306*X+2704), 306110016*(X+1)*(X+2)*(90*X^2+351*X+370), -148769467776*(X+1)*(X+2)^2*(X+3)]", "text": "This is operator \"7.9\" from ...", "degz": 7, "h3": null, "sol": "1 42 1872 86712 4126716 200324232 9870518664 491971281984 24744102202764 1253607240829272", "n_discr_factors": "3", "c3": null, "operator": "4 7 0 0 0 0 1 -42 -201 -381 -360 -288 23472 83214 118881 85860 35073 -3875040 -11871036 -14284998 -8424324 -2340090 293874480 817972992 869227524 435545424 92352636 -11496131712 -29803211280 -28676556360 -12525001488 -2155524696 226521411840 554671348992 490694355648 190094319936 27549901440 -1785233613312 -4165545097728 -3421697758848 -1190155742208 -148769467776", "new_number": "7.9", "id": 452, "operator_tex": "\\theta^4-3 x\\left(96\\theta^4+120\\theta^3+127\\theta^2+67\\theta+14\\right)+3^{2} x^{2}\\left(3897\\theta^4+9540\\theta^3+13209\\theta^2+9246\\theta+2608\\right)-2 3^{4} x^{3}\\left(14445\\theta^4+52002\\theta^3+88179\\theta^2+73278\\theta+23920\\right)+2^{2} 3^{6} x^{4}\\left(31671\\theta^4+149364\\theta^3+298089\\theta^2+280512\\theta+100780\\right)-2^{3} 3^{12} x^{5}(\\theta+1)(507\\theta^3+2439\\theta^2+4306\\theta+2704)+2^{6} 3^{14} x^{6}(\\theta+1)(\\theta+2)(90\\theta^2+351\\theta+370)-2^{7} 3^{19} x^{7}(\\theta+1)(\\theta+2)^2(\\theta+3)", "superseek": "-3 -245/3", "discriminant": "7 1 -288 35073 -2340090 92352636 -2155524696 27549901440 -148769467776", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "5641c09b76662b0741e41b41b0c6f105", "dim_h": null, "inst": " -3 69/4 -245/3 879 -11829 1987219/12 -2570790 43196640 -2285716376/3 55956638451/4", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(36z-1)^2(27z-1)^2(54z-1)^3", "discr_factors": "-148769467776, (z-1/54)^3, (z-1/36)^2, (z-1/27)^2", "dm_basis": null, "q": "0 1 -33 954 -26687 733938 -19944846 537750017 -14419345233 385065685188", "yuk": "1 -3 135 -2208 56391 -1478628 35767872 -881780973 22116736071 -555429081576", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/54","im":"0","approx_re":"0.0185185185185","approx_im":"0.0","exponents":["0","0","-1/3","1/3"],"monodromy":[],"monodromy_dm":[]},{"re":"1/36","im":"0","approx_re":"0.0277777777778","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/27","im":"0","approx_re":"0.037037037037","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","2","3"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[16*X^4, -4*X*(2*X^3+82*X^2+53*X+12), -4895*X^4-18410*X^3-26199*X^2-18308*X-5120, -60679*X^4-272424*X^3-497452*X^2-430092*X-143808, -344527*X^4-1870838*X^3-4034628*X^2-3987101*X-1478544, -(X+1)*(1076509*X^3+5847783*X^2+11226106*X+7492832), -2*(X+1)*(X+2)*(944887*X^2+4249317*X+5045304), -3328*(X+3)*(X+2)*(X+1)*(518*X+1381), -621920*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.40\" from ...", "degz": 8, "h3": null, "sol": "1 0 20 168 2652 40080 666920 11536560 207013660 3816224160", "n_discr_factors": "6", "c3": null, "operator": "4 8 0 0 0 0 16 0 -48 -212 -328 -8 -5120 -18308 -26199 -18410 -4895 -143808 -430092 -497452 -272424 -60679 -1478544 -3987101 -4034628 -1870838 -344527 -7492832 -18718938 -17073889 -6924292 -1076509 -20181216 -47269092 -39366058 -14167956 -1889774 -27575808 -60899072 -46538752 -14939392 -1723904 -14926080 -31096000 -21767200 -6219200 -621920", "new_number": "8.40", "id": 486, "operator_tex": "2^{4} \\theta^4-2^{2} x\\theta(2\\theta^3+82\\theta^2+53\\theta+12)-x^{2}\\left(4895\\theta^4+18410\\theta^3+26199\\theta^2+18308\\theta+5120\\right)-x^{3}\\left(60679\\theta^4+272424\\theta^3+497452\\theta^2+430092\\theta+143808\\right)-x^{4}\\left(344527\\theta^4+1870838\\theta^3+4034628\\theta^2+3987101\\theta+1478544\\right)-x^{5}(\\theta+1)(1076509\\theta^3+5847783\\theta^2+11226106\\theta+7492832)-2 x^{6}(\\theta+1)(\\theta+2)(944887\\theta^2+4249317\\theta+5045304)-2^{8} 13 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(518\\theta+1381)-2^{5} 5 13^{2} 23 x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "5/4 35/2", "discriminant": "8 16 -8 -4895 -60679 -344527 -1076509 -1889774 -1723904 -621920", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "d3cb0fbbc65d6c5dace733d3d1ca181b", "dim_h": null, "inst": " 5/4 57/16 35/2 459/4 3615/4 97217/12 317945/4 833711 110476691/12 1694285265/16", "cleanlist": "True", "n_sing_real": "7", "sol_explicit": "", "n_sing_rational": "7", "n_sing": "7", "laurent": null, "discriminant_tex": "-(23z-1)(5z+1)(2z+1)(z+1)(13z+4)^2(4z+1)^2", "discr_factors": "-621920, z+1/5, z+1/2, (z+4/13)^2, (z+1/4)^2, z-1/23, z+1", "dm_basis": null, "q": "0 1 -3 -25 -15 88 -2373 -34656 -361587 -4196900", "yuk": "1 5/4 119/4 1895/4 29495/4 112970 7001633/4 27263785 1707469623/4 6711459452", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1","im":"0","approx_re":"-1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-4/13","im":"0","approx_re":"-0.307692307692","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/4","im":"0","approx_re":"-0.25","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/5","im":"0","approx_re":"-0.2","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/23","im":"0","approx_re":"0.0434782608696","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[1849*X^4, -43*X*(142*X^3+890*X^2+574*X+129), -647269*X^4-2441818*X^3-3538503*X^2-2423953*X-650848, -7200000*X^4-34423908*X^3-65337898*X^2-57379329*X-19251960, -37610765*X^4-220029964*X^3-499781264*X^2-511393545*X-194039928, -2*(X+1)*(54978121*X^3+324737370*X^2+665066226*X+466789876), -(X+1)*(X+2)*(185181547*X^2+915931425*X+1176131796), -1212*(X+3)*(X+2)*(X+1)*(138979*X+413408), -64266300*(X+1)*(X+2)*(X+3)*(X+4)]", "text": "This is operator \"8.51\" from ...", "degz": 8, "h3": null, "sol": "1 0 22 204 3474 57000 1031080 19368720 377712370 7565838000", "n_discr_factors": "5", "c3": null, "operator": "4 8 0 0 0 0 1849 0 -5547 -24682 -38270 -6106 -650848 -2423953 -3538503 -2441818 -647269 -19251960 -57379329 -65337898 -34423908 -7200000 -194039928 -511393545 -499781264 -220029964 -37610765 -933579752 -2263712204 -1979607192 -759430982 -109956242 -2352263592 -5360258238 -4294289165 -1471476066 -185181547 -3006302976 -6522210744 -4859171004 -1511705784 -168442548 -1542391200 -3213315000 -2249320500 -642663000 -64266300", "new_number": "8.51", "id": 498, "operator_tex": "43^{2} \\theta^4-43 x\\theta(142\\theta^3+890\\theta^2+574\\theta+129)-x^{2}\\left(647269\\theta^4+2441818\\theta^3+3538503\\theta^2+2423953\\theta+650848\\right)-x^{3}\\left(7200000\\theta^4+34423908\\theta^3+65337898\\theta^2+57379329\\theta+19251960\\right)-x^{4}\\left(37610765\\theta^4+220029964\\theta^3+499781264\\theta^2+511393545\\theta+194039928\\right)-2 x^{5}(\\theta+1)(54978121\\theta^3+324737370\\theta^2+665066226\\theta+466789876)-x^{6}(\\theta+1)(\\theta+2)(185181547\\theta^2+915931425\\theta+1176131796)-2^{2} 3 101 x^{7}(\\theta+3)(\\theta+2)(\\theta+1)(138979\\theta+413408)-2^{2} 3^{2} 5^{2} 7 101^{2} x^{8}(\\theta+1)(\\theta+2)(\\theta+3)(\\theta+4)", "superseek": "58/43 1024/43", "discriminant": "8 1849 -6106 -647269 -7200000 -37610765 -109956242 -185181547 -168442548 -64266300", "aesz": null, "n_sing_complex": "0", "inst_int": "", "c2h": null, "hash": "85b9064701880ae8e0518e47cff1b030", "dim_h": null, "inst": " 58/43 211/43 1024/43 7544/43 64880/43 642512/43 6932348/43 80121364/43 974406940/43 12346791976/43", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "6", "n_sing": "6", "laurent": null, "discriminant_tex": "-(7z+1)(25z-1)(2z+1)^2(101z+43)^2(3z+1)^2", "discr_factors": "-64266300, (z+1/3)^2, (z+1/2)^2, (z+43/101)^2, z+1/7, z-1/25", "dm_basis": null, "q": "0 1 -3 -32 -33 135 -3440 -63577 -746051 -9406920", "yuk": "1 58/43 1746/43 27706/43 484562/43 188606 138811986/43 2377795422/43 41022622930/43 710342686966/43", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/2","im":"0","approx_re":"-0.5","approx_im":"0.0","exponents":["0","1/3","2/3","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-43/101","im":"0","approx_re":"-0.425742574257","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/3","im":"0","approx_re":"-0.333333333333","approx_im":"0.0","exponents":["0","1/2","1/2","1"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/7","im":"0","approx_re":"-0.142857142857","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/25","im":"0","approx_re":"0.04","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","2","3","4"],"monodromy":[],"monodromy_dm":[]}]}]}