public override IEnumerable <Tuple <int, IGaNumMultivector> > BasisBladeMaps()
{
return(Enumerable.Range(0, TargetGaSpaceDimension)
.Select(id => new Tuple <int, IGaNumMultivector>(
id,
GaNumMultivector.CreateBasisBlade(TargetGaSpaceDimension, id)
)));
}
public override GaNumMultivector BasisBladeSignature(int id)
{
var basisBlade = GaNumMultivector.CreateBasisBlade(GaSpaceDimension, id);
var sig = Gp[basisBlade, basisBlade];
return(id.BasisBladeIdHasNegativeReverse() ? -sig : sig);
}
public IEnumerable <GaNumMultivector> RotorProduct(GaNumMultivector rotorVersor, IEnumerable <int> basisBladeIDs)
{
var rotorVersorInverse = rotorVersor.Reverse();
return(basisBladeIDs.Select(id =>
{
var mv = GaNumMultivector.CreateBasisBlade(GaSpaceDimension, id);
return
Gp[Gp[rotorVersor, mv], rotorVersorInverse]
.GetKVectorPart(id.BasisBladeGrade());
}));
}
public IEnumerable <GaNumMultivector> EvenVersorProduct(GaNumMultivector evenVersor, IEnumerable <int> basisBladeIDs)
{
var evenVersorReverse = evenVersor.Reverse();
var evenVersorNorm2Inverse = 1.0d / Sp[evenVersor, evenVersorReverse][0];
var evenVersorInverse = evenVersorReverse * evenVersorNorm2Inverse;
return(basisBladeIDs.Select(id =>
{
var mv = GaNumMultivector.CreateBasisBlade(GaSpaceDimension, id);
return
Gp[Gp[evenVersor, mv], evenVersorInverse]
.GetKVectorPart(id.BasisBladeGrade());
}));
}
public override IGaNumMultivector this[int id1] => GaNumMultivector.CreateBasisBlade(TargetGaSpaceDimension, id1);
public GaNumMultivector CreateUnitPseudoScalar()
{
return(GaNumMultivector.CreateBasisBlade(GaSpaceDimension, MaxBasisBladeId));
}
