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".
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Version: V2.29 of Fri Nov 28 15:14:01 AEDT 2025