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################################
# SQRTFIELD ELEMENTS
DeclareCategory( "IsSqrtFieldElement",
IsMultiplicativeElementWithInverse
and IsAdditiveElementWithInverse and IsZDFRE);
DeclareCategoryFamily( "IsSqrtFieldElement" );
DeclareCategoryCollections( "IsSqrtFieldElement" );
DeclareCategoryFamily( "IsSqrtFieldElementCollection" );
DeclareCategoryCollections( "IsSqrtFieldElementCollection" );
DeclareRepresentation( "IsSqrtFieldElementRep",
IsPositionalObjectRep,
[1] );
fam_SqrtFieldElt := NewFamily("SqrtFieldElt",IsSqrtFieldElement);
SqrtFieldType := NewType( fam_SqrtFieldElt,
IsSqrtFieldElement and IsSqrtFieldElementRep );
################################
# SQRTFIELD
DeclareCategory( "IsSqrtField", IsField );
BindGlobal( "SqrtField", Objectify( NewType(
CollectionsFamily( fam_SqrtFieldElt ),
IsField and
IsAttributeStoringRep and
IsSqrtField), rec() ) );
SetName( SqrtField, "SqrtField" );
SetIsLeftActedOnByDivisionRing( SqrtField, true );
SetSize( SqrtField, infinity );
SetIsFiniteDimensional( SqrtField, false);
SetLeftActingDomain( SqrtField, GaussianRationals );
SetCharacteristic( SqrtField, 0);
SetPrimeField( SqrtField, Rationals );
SqrtFieldFam:= ElementsFamily( FamilyObj( SqrtField ) );
##################################
# GLOBAL FUNCTIONS AND ATTRIBUTES
DeclareGlobalFunction("Sqroot");
DeclareGlobalFunction("SqrtFieldIsGaussRat");
DeclareGlobalFunction("SqrtFieldMakeRational");
DeclareGlobalFunction("SqrtFieldMinimalPolynomial");
DeclareGlobalFunction("SqrtFieldEltByRationalSqrt");
DeclareGlobalFunction("SqrtFieldEltRealAndComplexPart");
DeclareGlobalFunction("IsPosSqrtFieldElt");
DeclareGlobalFunction("CoefficientsOfSqrtFieldElt");
DeclareGlobalFunction("SqrtFieldEltByCoefficients");
DeclareGlobalFunction("SqrtFieldEltToCyclotomic");
DeclareGlobalFunction("SqrtFieldEltByCyclotomic");
DeclareGlobalFunction("SqrtFieldPolynomialToRationalPolynomial");
DeclareGlobalFunction("SqrtFieldRationalPolynomialToSqrtFieldPolynomial");
DeclareAttribute( "AbsoluteValue" , IsSqrtFieldElement );
[ Dauer der Verarbeitung: 0.20 Sekunden
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