Table 1 The generators of the Galois group, and how they act
u | r | \(\sqrt{5}\) | \(\sqrt{2}\) | \(i\sqrt{1+\sqrt{5}}\) | i | \(\tau \) | |
|---|---|---|---|---|---|---|---|
\(g_1\) | 1 / u | r | \(\sqrt{5}\) | \(\sqrt{2}\) | \(-i\sqrt{1+\sqrt{5}}\) | \(-i\) | \(1/\tau \) |
\(g_2\) | \(-u\) | \(-r\) | \(\sqrt{5}\) | \(-\sqrt{2}\) | \(-i\sqrt{1+\sqrt{5}}\) | i | \(-\tau \) |
\(g_3\) | u | 1 / r | \(\sqrt{5}\) | \(\sqrt{2}\) | \(i\sqrt{1+\sqrt{5}}\) | \(-i\) | \(1/\tau \) |
\(g_4\) | r | u | \(-\sqrt{5}\) | \(-\sqrt{2}\) | \(\sqrt{\sqrt{5}-1}\) | i | \(-\tau \) |