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Hello,
In Sage there is the universal cyclotomic field implemented. It would be much faster than QQbar as proposed by @tmonteil
sage: UCF = UniversalCyclotomicField()
sage: UCF.gen(3)
E(3)
sage: e3 = UCF.gen(3)
sage: e4 = UCF.gen(4)
sage: e3 + e4
E(12)^4 - E(12)^7 - E(12)^11
Vincent
