Ideals of the integers can be constructed using the ideal constructor as outlined in Section Defining Ideals and Quotient Rings. Such ideals will have type RngInt the same as the ring of integers itself (ideal<Integers() | 1>).
A collection of functions are provided that make Z behave like an order of a number field. Note however, that Z is not of type RngOrd. If complete compatibility is necessary, the user should create the maximal order of a degree 1 extension of Q.
Returns the ideal decomposition of the prime p, i.e. a list [ < ideal<Z|p>, 1> ] as in the number field case.
Returns a generator for the ideal I.
The ramification index of I over Z which is always 1.
The inertia degree of the ideal I, which is always 1.
Two integers that generate the ideal I. In this case the generator is returned twice.
The Chinese remainder theorem for ideals. Given ideals I and J of Z together with integers a and b, an integer x such that x - a in I and x - b in J is returned.
The valuation of the integer x at the prime ideal I.
The representative of the ideal I of Z in the basis of the class group.[Next][Prev] [Right] [Left] [Up] [Index] [Root]