protected override void ComputeUnitPseudoScalarCoef()
{
InnerUnitPseudoScalarCoef =
(_basisBladesSignatures[MaxBasisBladeId] == 1) == !MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? CasConstants.One
: CasConstants.MinusOne;
}
protected override void ComputeUnitPseudoScalarCoef()
{
if (MaxBasisBladeId.BasisBladeIdHasNegativeReverse())
{
InnerUnitPseudoScalarCoef = CasConstants.MinusOne / _basisBladesSignatures[MaxBasisBladeId];
}
else
{
InnerUnitPseudoScalarCoef = CasConstants.One / _basisBladesSignatures[MaxBasisBladeId];
}
}
internal GaNumFrameOrthogonal(IEnumerable <double> basisVectorsSignaturesList)
{
BasisVectorsSignatures = basisVectorsSignaturesList.ToArray();
OrthogonalMetric = GaNumMetricOrthogonal.Create(BasisVectorsSignatures);
Op = ComputedOp = new GaNumOp(VSpaceDimension);
Gp = ComputedGp = new GaNumOrthogonalGp(OrthogonalMetric);
Sp = ComputedSp = new GaNumOrthogonalSp(OrthogonalMetric);
Lcp = ComputedLcp = new GaNumOrthogonalLcp(OrthogonalMetric);
Rcp = ComputedRcp = new GaNumOrthogonalRcp(OrthogonalMetric);
Fdp = ComputedFdp = new GaNumOrthogonalFdp(OrthogonalMetric);
Hip = ComputedHip = new GaNumOrthogonalHip(OrthogonalMetric);
Acp = ComputedAcp = new GaNumOrthogonalAcp(OrthogonalMetric);
Cp = ComputedCp = new GaNumOrthogonalCp(OrthogonalMetric);
UnitPseudoScalarCoef =
(MaxBasisBladeId.BasisBladeIdHasNegativeReverse() ? -1.0d : 1.0d) /
OrthogonalMetric[MaxBasisBladeId];
}
internal GaSymFrameOrthogonal(IEnumerable <MathematicaScalar> basisVectorsSignaturesList)
{
BasisVectorsSignatures = basisVectorsSignaturesList.ToArray();
OrthogonalMetric = GaSymMetricOrthogonal.Create(BasisVectorsSignatures);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = new GaSymOrthogonalGp(OrthogonalMetric);
Sp = ComputedSp = new GaSymOrthogonalSp(OrthogonalMetric);
Lcp = ComputedLcp = new GaSymOrthogonalLcp(OrthogonalMetric);
Rcp = ComputedRcp = new GaSymOrthogonalRcp(OrthogonalMetric);
Fdp = ComputedFdp = new GaSymOrthogonalFdp(OrthogonalMetric);
Hip = ComputedHip = new GaSymOrthogonalHip(OrthogonalMetric);
Acp = ComputedAcp = new GaSymOrthogonalAcp(OrthogonalMetric);
Cp = ComputedCp = new GaSymOrthogonalCp(OrthogonalMetric);
UnitPseudoScalarCoef = (
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? CasConstants.MinusOne
: CasConstants.One
) / OrthogonalMetric.GetSignature(MaxBasisBladeId);
}
internal GaSymFrameNonOrthogonal(GaSymFrame baseOrthoFrame, ISymbolicMatrix ipm, GaSymOutermorphism derivedToBaseOm, GaSymOutermorphism baseToDerivedOm)
{
if (baseOrthoFrame.IsOrthogonal == false)
{
throw new GMacSymbolicException("Base frame must be orthogonal");
}
if (ipm.IsSymmetric() == false || ipm.IsDiagonal())
{
throw new GMacSymbolicException("Inner product matrix must be symmetric and non-diagonal");
}
InnerProductMatrix = ipm.ToMathematicaMatrix();
NonOrthogonalMetric =
new GaSymMetricNonOrthogonal(
baseOrthoFrame,
this,
derivedToBaseOm,
baseToDerivedOm
);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = GaSymBilinearProductCba.CreateGp(NonOrthogonalMetric);
Sp = ComputedSp = GaSymBilinearProductCba.CreateSp(NonOrthogonalMetric);
Lcp = ComputedLcp = GaSymBilinearProductCba.CreateLcp(NonOrthogonalMetric);
Rcp = ComputedRcp = GaSymBilinearProductCba.CreateRcp(NonOrthogonalMetric);
Fdp = ComputedFdp = GaSymBilinearProductCba.CreateFdp(NonOrthogonalMetric);
Hip = ComputedHip = GaSymBilinearProductCba.CreateHip(NonOrthogonalMetric);
Acp = ComputedAcp = GaSymBilinearProductCba.CreateAcp(NonOrthogonalMetric);
Cp = ComputedCp = GaSymBilinearProductCba.CreateCp(NonOrthogonalMetric);
UnitPseudoScalarCoef =
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? CasConstants.MinusOne / BasisBladeSignature(MaxBasisBladeId)[0].ToMathematicaScalar()
: CasConstants.One / BasisBladeSignature(MaxBasisBladeId)[0].ToMathematicaScalar();
}
/// <summary>
/// frameSigList must have all items equal to 1 (false) or -1 (true) with at least one negative item
/// </summary>
/// <param name="frameSigList"></param>
internal GaSymFrameOrthonormal(IEnumerable <bool> frameSigList)
{
BasisVectorsSignatures = frameSigList.Select(b => b ? -1 : 1).ToArray();
OrthonormalMetric = GaSymMetricOrthonormal.Create(BasisVectorsSignatures);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = new GaSymOrthonormalGp(OrthonormalMetric);
Sp = ComputedSp = new GaSymOrthonormalSp(OrthonormalMetric);
Lcp = ComputedLcp = new GaSymOrthonormalLcp(OrthonormalMetric);
Rcp = ComputedRcp = new GaSymOrthonormalRcp(OrthonormalMetric);
Fdp = ComputedFdp = new GaSymOrthonormalFdp(OrthonormalMetric);
Hip = ComputedHip = new GaSymOrthonormalHip(OrthonormalMetric);
Acp = ComputedAcp = new GaSymOrthonormalAcp(OrthonormalMetric);
Cp = ComputedCp = new GaSymOrthonormalCp(OrthonormalMetric);
UnitPseudoScalarCoef =
MathematicaScalar.Create(
SymbolicUtils.Cas,
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? -1.0d / OrthonormalMetric[MaxBasisBladeId]
: 1.0d / OrthonormalMetric[MaxBasisBladeId]
);
}
internal GaNumFrameNonOrthogonal(GaNumFrame baseOrthoFrame, Matrix ipm, GaNumOutermorphism derivedToBaseOm, GaNumOutermorphism baseToDerivedOm)
{
if (baseOrthoFrame.IsOrthogonal == false)
{
throw new GMacNumericException("Base frame must be orthogonal");
}
if (ipm.IsDiagonal())
{
throw new GMacNumericException("Inner product matrix must be non-diagonal");
}
InnerProductMatrix = ipm;
NonOrthogonalMetric =
new GaNumMetricNonOrthogonal(
baseOrthoFrame,
this,
derivedToBaseOm,
baseToDerivedOm
);
Op = ComputedOp = new GaNumOp(VSpaceDimension);
Gp = ComputedGp = GaNumBilinearProductCba.CreateGp(NonOrthogonalMetric);
Sp = ComputedSp = GaNumBilinearProductCba.CreateSp(NonOrthogonalMetric);
Lcp = ComputedLcp = GaNumBilinearProductCba.CreateLcp(NonOrthogonalMetric);
Rcp = ComputedRcp = GaNumBilinearProductCba.CreateRcp(NonOrthogonalMetric);
Fdp = ComputedFdp = GaNumBilinearProductCba.CreateFdp(NonOrthogonalMetric);
Hip = ComputedHip = GaNumBilinearProductCba.CreateHip(NonOrthogonalMetric);
Acp = ComputedAcp = GaNumBilinearProductCba.CreateAcp(NonOrthogonalMetric);
Cp = ComputedCp = GaNumBilinearProductCba.CreateCp(NonOrthogonalMetric);
UnitPseudoScalarCoef =
(MaxBasisBladeId.BasisBladeIdHasNegativeReverse() ? -1.0d : 1.0d) /
BasisBladeSignature(MaxBasisBladeId)[0];
}
