Rewriting number field related Magma code in Sage

asked 2018-02-21 14:39:53 -0500

ninho gravatar image

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.

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Comments

Unfortunately, it is hard to extract the needed information from the documentation of GModule starting from here: GModule

The following extracts the character table:

G = SuzukiGroup(8)
T = G.character_table()
for k in range(3): # 3 instead of 11 here, no space 4 more
    print T[k]

with results:

(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
(14, 0, 0, 0, -1, 1, 1, 1, -2, -2*zeta364^91, 2*zeta364^91)
(14, 0, 0, 0, -1, 1, 1, 1, -2, 2*zeta364^91, -2*zeta364^91)

and T[1] has for instance for its last component

sage: a = T[1][-1]; a
2*zeta364^91
sage: a.parent()
Cyclotomic Field of order 364 and degree 144
sage: a.absolute_minpoly()
x^2 + 4

Which is question in this context?

dan_fulea gravatar imagedan_fulea ( 2018-03-07 11:59:01 -0500 )edit