Rewriting number field related Magma code in Sage
I have the following Magma code, which I want to rewrite in Sage:
G := Sz(8);
T := CharacterTable(G);
M := GModule(T[2]:SparseCyclo := false);
N := AbsoluteModuleOverMinimalField(M);
Currently, I have something like this:
from sage.all import *
proof.arithmetic(False)
G = SuzukiGroup(8)
T = gap(G).CharacterTable()
print(gap.eval("Display(%s)"%T.name()))
Though, I do not know how to rewrite the rest in Sage. Sz
in Magma is Suzuki group. The result of M
here is GModule M of dimension 14 over Cyclotomic Field of order 52 and degree 24
. Also, the result of T[2]
in Magma is T[2] = ( 14, -2, 2*zeta(4)_4, -2*zeta(4)_4, -1, 0, 0, 0, 1, 1, 1 )
. AbsoluteModuleOverMinimalField
is defined here.
Unfortunately, it is hard to extract the needed information from the documentation of
GModule
starting from here: GModuleThe following extracts the character table:
with results:
and
T[1]
has for instance for its last componentWhich is question in this context?