/// <summary>
/// Even Versor Product
/// </summary>
/// <param name="evenVersor"></param>
/// <param name="mv"></param>
/// <returns></returns>
public GaSymMultivector EvenVersorProduct(GaSymMultivector evenVersor, GaSymMultivector mv)
{
var evenVersorReverse = evenVersor.Reverse();
var evenVersorNorm2Inverse =
SymbolicUtils.Constants.One / Sp[evenVersor, evenVersorReverse][0]
.ToMathematicaScalar();
var evenVersorInverse = evenVersorReverse * evenVersorNorm2Inverse;
return(Gp[Gp[evenVersor, mv], evenVersorInverse]);
}
/// <summary>
/// Odd Versor Product
/// </summary>
/// <param name="oddVersor"></param>
/// <param name="mv"></param>
/// <returns></returns>
public GaSymMultivector OddVersorProduct(GaSymMultivector oddVersor, GaSymMultivector mv)
{
var oddVersorReverse = oddVersor.Reverse();
var oddVersorNorm2Inverse =
SymbolicUtils.Constants.One / Sp[oddVersor, oddVersorReverse][0]
.ToMathematicaScalar();
var oddVersorInverse = oddVersorReverse * oddVersorNorm2Inverse;
return(Gp[Gp[oddVersor, mv.GradeInv()], oddVersorInverse]);
}
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());
}));
}
/// <summary>
/// Odd Versor Product of a list of basis blades given by their IDs
/// </summary>
/// <param name="oddVersor"></param>
/// <param name="basisBladeIDs"></param>
/// <returns></returns>
public IEnumerable <GaSymMultivector> OddVersorProduct(GaSymMultivector oddVersor, IEnumerable <int> basisBladeIDs)
{
var oddVersorReverse = oddVersor.Reverse();
var oddVersorNorm2Inverse =
SymbolicUtils.Constants.One / Sp[oddVersor, oddVersorReverse][0]
.ToMathematicaScalar();
var oddVersorInverse = oddVersorReverse * oddVersorNorm2Inverse;
return(basisBladeIDs.Select(id =>
{
var mv = GaSymMultivector.CreateTerm(
GaSpaceDimension,
id,
id.BasisBladeIdHasNegativeGradeInv() ? Expr.INT_MINUSONE : Expr.INT_ONE
);
return
Gp[Gp[oddVersor, mv], oddVersorInverse]
.GetKVectorPart(id.BasisBladeGrade());
}));
}
public static MathematicaScalar EMagnitude2(this GaSymMultivector mv)
{
return(ESp(mv, mv.Reverse())[0].ToMathematicaScalar());
}
/// <summary>
/// Rotor Product
/// </summary>
/// <param name="rotorVersor"></param>
/// <param name="mv"></param>
/// <returns></returns>
public GaSymMultivector RotorProduct(GaSymMultivector rotorVersor, GaSymMultivector mv)
{
return(Gp[Gp[rotorVersor, mv], rotorVersor.Reverse()]);
}
public MathematicaScalar Norm2(GaSymMultivector mv)
{
return(Sp[mv, mv.Reverse()][0].ToMathematicaScalar());
}