Given an integral S-ideal I coprime with the conductor of S
(hence invertible in S), returns its factorization into a product
of primes of S.
Given an integral S-ideal I, returns the sequence of maximal
ideals P of S above I.
Returns the non-invertible primes of the order R.
Given an étale algebra and a rational prime, returns the primes of the maximal order of the algebra containing the rational prime.
Returns the non-invertible primes of the order R.
Given an integral S-ideal I, returns if the ideal is a prime fractional
ideal of S, that is a maximal S ideal.
Valuation(I, P) : AlgEtQIdl, AlgEtQIdl -> RngIntElt
Valuation at the prime P of an element x or of a fractional ideal I of the maximal order.
RamificationIndex(P) : AlgEtQIdl -> RngIntElt
For a prime P of the maximal order mathcal O, returns its inertia degree and ramification index.
Check if the order is Bass at the prime ideal P, that is, if every overorder
of S is Gorenstein at the primes above P.
Check if the order S is Bass, that is, if every overorder of S is Gorenstein.
Check if the order S is Gorenstein at the prime ideal P, that is, if every
fractional ideal I with (I:I)=S is locally principal at P.
Checks if the order O is Gorenstein, that is if the TraceDualIdeal
of O is invertible, or equivalently, if all fractional ideals I with
(I:I)=O are invertible.
Given a sequence of primes P of the maximal order, returns a sequence of elements tP such that tP is a uniformizer at P and a unit at every other prime in the sequence.
V2.29, 28 November 2025