Ideals of Index

IdealsOfIndex(O, N): RngOrd, RngIntElt -> SeqEnum[RngOrdIdl]

Given an order \(O\) in a number field and a positive integer \(N\), returns all the ideals \(I\) of index \([O:I]=N\).

IdealsOfIndex(I, N): RngOrdIdl, RngIntElt -> SeqEnum[RngOrdIdl]

Given an ideal \(I\) in an order \(O\) in a number field and a positive integer \(N\), with \(N\) coprime with the conductor, returns all the ideals \(J\) contained in \(I\) with index \([I:J]=N\).

IdealsOfIndex(I, N): RngOrdFracIdl, RngIntElt -> SeqEnum[RngOrdFracIdl]

Given an ideal \(I\) in an order \(O\) in a number field and a positive integer \(N\), with \(N\) coprime with the conductor, returns all the ideals \(J\) contained in \(I\) with index \([I:J]=N\).

IdealsOfIndex(I, N): AlgEtQIdl, RngIntElt -> SeqEnum[AlgEtQIdl]

Method: MonStgElt                    Default: "Default"

Given an \(O\)-ideal \(I\) in \(O\) and a positive integer \(N\), returns all the subideals \(J\) of \(I\) with index \([I:J]=N\). The function is very fast if \(N\) is coprime to the conductor of \(O\). If this condition is not satisfied a slow algorithm is used which doesn’t require additional hypothesis. One can force the slow algorithm by setting the parameter Method:="Slow".

IdealsOfIndex(O, N): AlgEtQOrd, RngIntElt -> SeqEnum[AlgEtQIdl]

Method: MonStgElt                    Default: "Default"

Given an order \(O\) and a positive integer \(N\), returns all the \(O\)-ideals \(J\) with index \([O:J]=N\). The function is very fast if \(N\) is coprime to the conductor of \(O\). If this condition is not satisfied a slow algorithm is used which doesn’t require additional hypothesis. One can force the slow-naive algorithm by setting the parameter Method:="Slow".