Why don't you just work with the quotientring of a polynmial ring? sage: Rx.<x>=RR[] sage: K.<a>=Rx.quo(x^6+1) sage: j=a^4 sage: i=a^3 sage: j^3 1.00000000000000 sage: i^2 -1.00000000000000 sage: (1+j+j^2) * j a^4 - a^2 + 1.00000000000000 sage: (1+j+j^2) a^4 - a^2 + 1.00000000000000
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