Introduction

 
Representation

 
Creation of Structures
      AlgebraicClosure(K) : Fld -> FldAC
      AlgebraicClosure() : -> FldAC
      AssignNamePrefix(A, S) : FldAC, MonStgElt ->

 
Creation of Elements

      Coercion
            A ! a : FldAC, RngElt -> FldACElt

      Roots
            Roots(f) : RngUPolElt -> [ < FldACElt, RngIntElt> ]
            RootOfUnity(n, A) : RngIntElt, FldAC -> FldACElt
            SquareRoot(a) : FldACElt -> FldACElt
            IsSquare(a) : FldACElt -> BoolElt
            Root(a, n) : FldACElt, RngIntElt -> FldACElt
            IsPower(a, n) : FldACElt, RngIntElt -> BoolElt, FldACElt

      Variables
            A . i : FldAC, RngIntElt -> FldACElt
            Example FldAC_Create (H44E1)
            Example FldAC_SwinnertonDyer (H44E2)
            Example FldAC_Puiseux (H44E3)

 
Related Structures

 
Properties
      BaseField(A) : FldAC -> Fld
      Rank(A) : FldAC -> RngIntElt
      Degree(A, v) : FldAC, RngIntElt -> RngIntElt
      Degree(A) : FldAC -> RngIntElt
      AffineAlgebra(A) : FldAC -> RngMPolRes
      Ideal(A) : FldAC -> RngMPol

 
Ring Predicates and Properties

 
Element Operations

      Arithmetic Operators

      Equality and Membership

      Parent and Category

      Predicates on Ring Elements
            IsZero(a) : FldACElt -> BoolElt
            IsOne(a) : FldACElt -> BoolElt
            IsMinusOne(a) : FldACElt -> BoolElt
            a eq b : FldACElt, FldACElt -> BoolElt

      Minimal Polynomial, Norm and Trace
            MinimalPolynomial(a) : FldACElt -> RngUPolElt
            Norm(a) : FldACElt -> FldACElt
            Trace(a) : FldACElt -> FldACElt
            Conjugates(a) : FldACElt -> [ FldACElt ]
            Example FldAC_Functions (H44E4)

 
Simplification
      Simplify(A) : FldAC ->
      Prune(A) : FldAC ->

 
Absolute Field
      AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
      AbsolutePolynomial(A) : FldAC ->
      Absolutize(A) : FldAC ->
      Example FldAC_Cyclic6 (H44E5)
      Example FldAC_Split (H44E6)

 
Bibliography

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