> R<x> := PolynomialRing(RationalField()); > K<a> := NumberField(x^3-2); > OK := RingOfIntegers(K); > I := Factorization(3*OK)[1][1]; > J := Factorization(5*OK)[1][1]; > I; Prime Ideal of OK Two element generators: [3, 0, 0] [4, 1, 0] > J; Prime Ideal of OK Two element generators: [5, 0, 0] [7, 1, 0] > b := ChineseRemainderTheorem(I, J, OK!a, OK!1); > K!b; -4 > b - a in I; true > b - 1 in J; true