Creation of Structures
AlgebraicClosure(K) : Fld -> FldAC
AlgebraicClosure() : -> FldAC
AssignNamePrefix(A, S) : FldAC, MonStgElt ->
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 (H40E1)
Example FldAC_SwinnertonDyer (H40E2)
Example FldAC_Puiseux (H40E3)
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
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 (H40E4)
Simplification
Simplify(A) : FldAC ->
Prune(A) : FldAC ->
Absolute Field
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AbsolutePolynomial(A) : FldAC ->
Absolutize(A) : FldAC ->
Example FldAC_Cyclic6 (H40E5)
Example FldAC_Split (H40E6)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012