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 (H36E1) Example FldAC_SwinnertonDyer (H36E2) Example FldAC_Puiseux (H36E3)
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 (H36E4)
Simplification Simplify(A) : FldAC -> Prune(A) : FldAC ->
Absolute Field AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes AbsolutePolynomial(A) : FldAC -> Absolutize(A) : FldAC -> Example FldAC_Cyclic6 (H36E5)
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