Over Orders

IsMaximalAtPrime(R, P) : AlgEtQOrd, AlgEtQIdl -> BoolElt
Returns whether R is maximal at the prime P, that is, if (R:O) is not contained in P, where O is the maximal order.
MinimalOverOrdersAtPrime(R, P) : AlgEtQOrd, AlgEtQIdl -> SetIndx[AlgEtQOrd]
Given an order R and prime P of R, it returns the minimal overorders S of R with conductor (R:S) which is P-primary. The minimality assumption forces the conductor (R:S) to be exactly P. Based on [HS20].
MinimalOverOrders(R) : AlgEtQOrd -> SetIndx[AlgEtQOrd]
Computes the minimal overorders of R.
OverOrdersAtPrime(R, P) : AlgEtQOrd, AlgEtQIdl -> SeqEnum[AlgEtQOrd]
Given an order R and prime P of R, it returns R and the overorders S of R with conductor (R:S) which is P-primary. We recursively produce the minimal PP-overorders where PP are primes above P. Based on [HS20].
OverOrders(R) : AlgEtQOrd -> SeqEnum[AlgEtQOrd]
    populateoo_in_oo: BoolElt           Default: false
We compute all the overorders of R. The parameter populateoo_in_oo (default false) determines whether we should fill the attribute T`OverOrders for every overorder T of R. The computation is based on [HS20].
FindOverOrders(R) : AlgEtQOrd -> SetIndx[AlgEtQOrd]
    populateoo_in_oo: BoolElt           Default: false
We compute all the overorders of R. The parameter populateoo_in_oo (default false) determines whether we should fill the attribute T`OverOrders for every overorder T of R. The computation is based on [HS20].
V2.29, 21 October 2025