[0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, -2, 0, 2, 0, -6, 0, -1, 0]
x^3 + 12*x + 12
19
[0, 1, 0, 3, 0, -2, 0, 4, 0, 6, 0, -2, 0, -5, 0, -6, 0, 4, 0, 2, 0]
1.35165039003399
x^3 - 1/3*x - 29/27
Galois group PARI group [12, -1, 3, "D(6) = S(3)[x]2"] of degree 6 of the Number Field in a with defining polynomial x^2 - 31 over its base field
z^3 - z^2 - 1
[1/3*a^2 + 1/3*a + 1/3, a, a^2]
(Fractional ideal (3, 1/3*a^2 + 1/3*a + 1/3))^2 * (Fractional ideal (3, 1/3*a^2 + 1/3*a - 2/3))
(Fractional ideal (3, 1/3*a^2 + 1/3*a + 1/3)) * (Fractional ideal (3, 1/3*a^2 + 1/3*a - 2/3))
9
Class group of order 1 of Number Field in a with defining polynomial x^4 + x^3 + x^2 + 1
Class group of order 2 with structure C2 of Number Field in a with defining polynomial x^2 - 10
Fractional ideal (3)
-1
(Fractional ideal (3, a + 1))^2
Error in lines 10-10
Traceback (most recent call last):
File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "/projects/sage/sage-7.5/local/lib/python/site.py", line 351, in __call__
raise SystemExit(code)
SystemExit: 0