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Magma
Computer • algebra
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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 (H43E1)
Example
FldAC_SwinnertonDyer (H43E2)
Example
FldAC_Puiseux (H43E3)
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 (H43E4)
Simplification
Simplify(A) : FldAC ->
Prune(A) : FldAC ->
Absolute Field
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AbsolutePolynomial(A) : FldAC ->
Absolutize(A) : FldAC ->
Example
FldAC_Cyclic6 (H43E5)
Example
FldAC_Split (H43E6)
Bibliography
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V2.28, 28 February 2025