sage: zeta84 in Q1092
True
sage: zeta12 in Q84
True
sage: zeta12 in Q1092
False
sage: Q12.embeddings(Q1092)
[
Ring morphism:
From: Cyclotomic Field of order 12 and degree 4
To: Cyclotomic Field of order 1092 and degree 288
Defn: zeta12 |--> zeta1092^91,
Ring morphism:
From: Cyclotomic Field of order 12 and degree 4
To: Cyclotomic Field of order 1092 and degree 288
Defn: zeta12 |--> -zeta1092^91,
Ring morphism:
From: Cyclotomic Field of order 12 and degree 4
To: Cyclotomic Field of order 1092 and degree 288
Defn: zeta12 |--> zeta1092^273 - zeta1092^91,
Ring morphism:
From: Cyclotomic Field of order 12 and degree 4
To: Cyclotomic Field of order 1092 and degree 288
Defn: zeta12 |--> -zeta1092^273 + zeta1092^91
]
Perhaps Sage now wants you to choose an embedding.
sage: (zeta1092^13) == zeta84
True
sage: zeta84^7 == zeta12
True
sage: (zeta1092^13)^7 == zeta12
False