public override GaSymMultivector BasisBladeSignature(int id)
{
var basisBlade = GaSymMultivector.CreateBasisBlade(GaSpaceDimension, id);
var sig = Gp[basisBlade, basisBlade];
return(id.BasisBladeIdHasNegativeReverse() ? -sig : sig);
}
public override IEnumerable <Tuple <int, IGaSymMultivector> > BasisBladeMaps()
{
return(Enumerable.Range(0, TargetGaSpaceDimension)
.Select(id => new Tuple <int, IGaSymMultivector>(
id,
GaSymMultivector.CreateBasisBlade(TargetGaSpaceDimension, id)
)));
}
/// <summary>
/// Convert this basis blade into a multivector value with unity coefficient of its single term
/// </summary>
/// <returns></returns>
public AstValueMultivector ToMultivectorValue()
{
return(new AstValueMultivector(
GMacValueMultivector.Create(
AssociatedFrame.MultivectorType,
GaSymMultivector.CreateBasisBlade(
AssociatedFrame.GaSpaceDimension,
BasisBladeId
)
)
));
}
public IEnumerable <GaSymMultivector> RotorProduct(GaSymMultivector rotorVersor, IEnumerable <int> basisBladeIDs)
{
var rotorVersorInverse = rotorVersor.Reverse();
return(basisBladeIDs.Select(id =>
{
var mv = GaSymMultivector.CreateBasisBlade(GaSpaceDimension, id);
return
Gp[Gp[rotorVersor, mv], rotorVersorInverse]
.GetKVectorPart(id.BasisBladeGrade());
}));
}
public IEnumerable <GaSymMultivector> EvenVersorProduct(GaSymMultivector evenVersor, IEnumerable <int> basisBladeIDs)
{
var evenVersorReverse = evenVersor.Reverse();
var evenVersorNorm2Inverse =
SymbolicUtils.Constants.One / Sp[evenVersor, evenVersorReverse][0]
.ToMathematicaScalar();
var evenVersorInverse = evenVersorReverse * evenVersorNorm2Inverse;
return(basisBladeIDs.Select(id =>
{
var mv = GaSymMultivector.CreateBasisBlade(GaSpaceDimension, id);
return
Gp[Gp[evenVersor, mv], evenVersorInverse]
.GetKVectorPart(id.BasisBladeGrade());
}));
}
internal static GMacValueMultivector CreateBasisBlade(GMacFrameMultivector mvType, int id)
{
var mvCoefs = GaSymMultivector.CreateBasisBlade(mvType.ParentFrame.GaSpaceDimension, id);
return(new GMacValueMultivector(mvType, mvCoefs));
}
public GaSymMultivector CreateUnitPseudoScalar()
{
return(GaSymMultivector.CreateBasisBlade(GaSpaceDimension, MaxBasisBladeId));
}
public override IGaSymMultivectorTemp MapToTemp(int id1)
{
var mv1 = GaSymMultivector.CreateBasisBlade(TargetGaSpaceDimension, id1);
return(MapToTemp(mv1));
}
public override IGaSymMultivector this[int id1] => GaSymMultivector.CreateBasisBlade(TargetGaSpaceDimension, id1);