back to table · edit · history · where entries came from · files · download
5417 bytes, as of the version from 2026-11-02 11:01 (current). Recorded here, not run.
/home/sage/sage/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/sage/rings/qqbar.py:2988: UserWarning: Resolving lazy import SymbolicRing during startup
roots = p.roots(ring, False)
{
"CM_checks": [
{
"t": "-216",
"D": -3,
"interior": false,
"degree": 1,
"j_minpoly": "x"
},
{
"t": "24",
"D": -27,
"interior": true,
"degree": 1,
"j_minpoly": "x + 12288000"
},
{
"t": "54",
"D": -12,
"interior": false,
"degree": 1,
"j_minpoly": "x - 54000"
},
{
"t": "108+54*sqrt(2)",
"D": -24,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 4834944*x + 14670139392"
},
{
"t": "108-54*sqrt(2)",
"D": -24,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 4834944*x + 14670139392"
},
{
"t": "18+6*sqrt(3)",
"D": -36,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 153542016*x - 1790957481984"
},
{
"t": "18-6*sqrt(3)",
"D": -36,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 - 153542016*x - 1790957481984"
},
{
"t": "270+162*sqrt(3)",
"D": -4,
"interior": false,
"degree": 2,
"j_minpoly": "x - 1728"
},
{
"t": "270-162*sqrt(3)",
"D": -4,
"interior": false,
"degree": 2,
"j_minpoly": "x - 1728"
},
{
"t": "729+405*sqrt(3)",
"D": -48,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 2835810000*x + 6549518250000"
},
{
"t": "729-405*sqrt(3)",
"D": -48,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 2835810000*x + 6549518250000"
},
{
"t": "-27/2-27/2*sqrt(5)",
"D": -15,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 191025*x - 121287375"
},
{
"t": "-27/2+27/2*sqrt(5)",
"D": -15,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 191025*x - 121287375"
},
{
"t": "3375/2+1485/2*sqrt(5)",
"D": -60,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 37018076625*x + 153173312762625"
},
{
"t": "3375/2-1485/2*sqrt(5)",
"D": -60,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 37018076625*x + 153173312762625"
},
{
"t": "-4320-1944*sqrt(5)",
"D": -75,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 654403829760*x + 5209253090426880"
},
{
"t": "-4320+1944*sqrt(5)",
"D": -75,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 654403829760*x + 5209253090426880"
},
{
"t": "32+2*sqrt(6)",
"D": -72,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 377674768000*x + 232381513792000000"
},
{
"t": "32-2*sqrt(6)",
"D": -72,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 - 377674768000*x + 232381513792000000"
},
{
"t": "3672+1458*sqrt(6)",
"D": -8,
"interior": false,
"degree": 2,
"j_minpoly": "x - 8000"
},
{
"t": "3672-1458*sqrt(6)",
"D": -8,
"interior": false,
"degree": 2,
"j_minpoly": "x - 8000"
},
{
"t": "-864-216*sqrt(17)",
"D": -51,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 5541101568*x + 6262062317568"
},
{
"t": "-864+216*sqrt(17)",
"D": -51,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 5541101568*x + 6262062317568"
},
{
"t": "-163296-35640*sqrt(21)",
"D": -147,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 34848505552896000*x + 11356800389480448000000"
},
{
"t": "-163296+35640*sqrt(21)",
"D": -147,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 34848505552896000*x + 11356800389480448000000"
},
{
"t": "4-4*sqrt(33)",
"D": -99,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 37616060956672*x - 56171326053810176"
},
{
"t": "4+4*sqrt(33)",
"D": -99,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 37616060956672*x - 56171326053810176"
},
{
"t": "-16740-2916*sqrt(33)",
"D": -11,
"interior": false,
"degree": 2,
"j_minpoly": "x + 32768"
},
{
"t": "-16740+2916*sqrt(33)",
"D": -11,
"interior": true,
"degree": 2,
"j_minpoly": "x + 32768"
},
{
"t": "-55296-8640*sqrt(41)",
"D": -123,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 1354146840576000*x + 148809594175488000000"
},
{
"t": "-55296+8640*sqrt(41)",
"D": -123,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 1354146840576000*x + 148809594175488000000"
},
{
"t": "-13500000-1431000*sqrt(89)",
"D": -267,
"interior": false,
"degree": 2,
"j_minpoly": "x^2 + 19683091854079488000000*x + 531429662672621376897024000000"
},
{
"t": "-13500000+1431000*sqrt(89)",
"D": -267,
"interior": true,
"degree": 2,
"j_minpoly": "x^2 + 19683091854079488000000*x + 531429662672621376897024000000"
}
],
"passed": true
}