Introduction

 
Creation of Modules
      Module(O, n) : RngOrd, RngIntElt -> ModDed
      Module(O) : RngOrd -> ModDed, Map
      Module(I) : RngOrdFracIdl -> ModDed, Map
      Module(S) : SeqEnum[Tup] -> ModDed, Map
      Module(S) : SeqEnum[RngOrdFracIdl] -> ModDed
      Module(S) : SeqEnum[ModElt] -> ModDed, Map
      Example ModDed_create (H61E1)
      sub<M | m> : ModDed, SeqEnum[ModDedElt] -> ModDed, Map
      quo<M | S> : ModDed, ModDed -> ModDed, Map
      Example ModDed_sub-quo (H61E2)

 
Elementary Functions
      BaseRing(M) : ModDed -> Rng
      Degree(M) : ModDed -> RngIntElt
      Ngens(M) : ModDed -> RngIntElt
      M . i : ModDed, RngIntElt -> ModTupRngElt
      Determinant(M) : ModDed -> RngOrdIdl
      Dimension(M) : ModDed -> RngIntElt
      Contents(M) : ModDed -> RngOrdFracIdl
      Simplify(M) : ModDed -> ModDed
      EmbeddingSpace(M) : ModDed -> Mod
      Example ModDed_elementary (H61E3)

 
Predicates on Modules
      M eq N : ModDed, ModDed -> BoolElt
      x in M : Any, ModDed -> BoolElt
      M subset N : ModDed, ModDed -> BoolElt
      IsFree(M) : ModDed -> BoolElt

 
Arithmetic with Modules
      I * M : RngOrdIdl, ModDed -> ModDed
      M1 + M2 : ModDed, ModDed -> ModDed
      DirectSum(M1, M2) : ModDed, ModDed -> ModDed, Map, Map, Map, Map
      u * I : ModDedElt, RngOrdIdl -> ModDed
      Example ModDed_ops_arith (H61E4)

 
Basis of a Module
      Basis(M) : ModDed -> SeqEnum
      PseudoBasis(M) : ModDed -> SeqEnum
      PseudoGenerators(M): ModDed -> SeqEnum
      LocalBasis(M, p) : ModDed, RngOrdIdl -> [ ModTupFldElt ]

 
Other Functions on Modules
      M1 meet M2 : ModDed, ModDed -> ModDed
      Dual(M) : ModDed -> ModDed
      ElementaryDivisors(M, N) : ModDed, ModDed -> SeqEnum
      SteinitzClass(M) : ModDed -> RngOrdIdl
      SteinitzForm(M) : ModDed -> ModDed
      Example ModDed_basis-other (H61E5)

 
Homomorphisms between Modules
      hom<M -> N | T> : ModDed, ModDed, Map -> Map
      Hom(M, N) : ModDed, ModDed -> ModDed, Map
      IsSubmodule(M, N) : ModDed, ModDed -> BoolElt, Map
      Morphism(M, N) : ModDed, ModDed -> Map
      Example ModDed_hom (H61E6)

 
Elements of Modules

      Creation of Elements
            M ! v : ModDed, SeqEnum -> ModDedElt
            Example ModDed_coerce-quo (H61E7)

      Arithmetic with Elements
            x + y : ModDedElt, ModDedElt -> ModDedElt
            x - y : ModDedElt, ModDedElt -> ModDedElt
            u * c : ModDedElt, RngElt -> ModDedElt
            u / c : ModDedElt, RngElt -> ModDedElt
            I * u : RngOrdIdl, ModDedElt -> ModDed

      Other Functions on Elements
            x eq y : ModDedElt, ModDedElt -> Bool
            IsZero(a) : ModDedElt -> BoolElt
            ElementToSequence(a) : ModDedElt -> SeqEnum

 
Pseudo Matrices

      Construction of a Pseudo Matrix
            PseudoMatrix(I, m) : [RngOrdFracIdl], MtrxSpcElt -> PMat
            PseudoMatrix(m) : Mtrx[FldOrd] -> PMat
            PseudoMatrix(M) : ModDed -> PMat
            AbsoluteBasis(M) : ModDed -> SeqEnum

      Elementary Functions
            CoefficientIdeals(P): PMat -> SeqEnum
            Matrix(P) : PMat -> Mtrx
            Order(pm) : PMat -> Rng
            Dimension(pm) : PMat -> RngIntElt
            Length(pm) : PMat -> RngIntElt

      Basis of a Pseudo Matrix
            Basis(P) : PMat -> SeqEnum

      Predicates
            p1 eq p2 : PMat, PMat -> BoolElt

      Operations with Pseudo Matrices
            Transpose(P) : PMat -> PMat
            HermiteForm(X) : PMat -> PMat, AlgMatElt
            VerticalJoin(X, Y) : PMat, PMat -> PMat
            X meet Y : PMat, PMat -> PMat
            Module(X) : PMat -> ModDed
            I * X : RngOrdFracIdl, PMat -> PMat

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