Basic invariants
Defining polynomial
f(x) | = |
x4−2x3−5x2+6x+10
. |
The roots of f are computed in Q41 to precision 5.
Generators of the action on the roots
r1,…,r4
Cycle notation |
(1,4) |
(1,2)(3,4) |
Size | Order | Action on
r1,…,r4
| Character value | Complex conjugation |
1 | 1 | () | 2 |
|
1 | 2 | (1,4)(2,3) | −2 |
|
2 | 2 | (1,2)(3,4) | 0 |
✓ |
2 | 2 | (1,4) | 0 |
|
2 | 4 | (1,3,4,2) | 0 |
|