private static int[] ComputeBasisBladesSignatures(int[] frameSigList)
{
var vSpaceDim = frameSigList.Length;
var bbsList = new int[FrameUtils.GaSpaceDimension(vSpaceDim)];
bbsList[0] = 1;
for (var m = 0; m < vSpaceDim; m++)
{
bbsList[1 << m] = frameSigList[m];
}
var idsSeq = FrameUtils.BasisBladeIDsSortedByGrade(vSpaceDim, 2);
foreach (var id in idsSeq)
{
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
bbsList[id] = bbsList[id1] * bbsList[id2];
}
return(bbsList);
}
private static MathematicaScalar[] ComputeBasisBladesSignatures(MathematicaScalar[] basisVectorsSignaturesList)
{
var vspacedim = basisVectorsSignaturesList.Length;
var bbsList = new MathematicaScalar[FrameUtils.GaSpaceDimension(vspacedim)];
bbsList[0] = SymbolicUtils.Constants.One;
for (var m = 0; m < vspacedim; m++)
{
bbsList[1 << m] = basisVectorsSignaturesList[m];
}
var idsSeq = FrameUtils.BasisBladeIDsSortedByGrade(vspacedim, 2);
foreach (var id in idsSeq)
{
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
bbsList[id] = bbsList[id1] * bbsList[id2];
}
return(bbsList);
}
private static string EuclideanSample(int vSpaceDim)
{
Composer.Clear();
var basisBladeIds = FrameUtils.BasisBladeIDsSortedByGrade(vSpaceDim).ToArray();
Composer
.AppendLine("Involution Tables, " + vSpaceDim + "D Space:")
.IncreaseIndentation()
.AppendLine(InvolutionTables(basisBladeIds))
.DecreaseIndentation()
.AppendLineAtNewLine(PageSeparator)
.AppendLine();
Composer
.AppendLine("Geometric Product Table, " + vSpaceDim + "D Space:")
.IncreaseIndentation()
.AppendLine(EuclideanBilinearProductTable(basisBladeIds, EuclideanUtils.IsZeroEuclideanGp))
.DecreaseIndentation()
.AppendLineAtNewLine(PageSeparator)
.AppendLine();
Composer
.AppendLine("Outer Product Table, " + vSpaceDim + "D Space:")
.IncreaseIndentation()
.AppendLine(EuclideanBilinearProductTable(basisBladeIds, EuclideanUtils.IsZeroOp))
.DecreaseIndentation()
.AppendLineAtNewLine(PageSeparator)
.AppendLine();
Composer
.AppendLine("Scalar Product Table, " + vSpaceDim + "D Space:")
.IncreaseIndentation()
.AppendLine(EuclideanBilinearProductTable(basisBladeIds, EuclideanUtils.IsZeroEuclideanSp))
.DecreaseIndentation()
.AppendLineAtNewLine(PageSeparator)
.AppendLine();
Composer
.AppendLine("Left Contraction Product Table, " + vSpaceDim + "D Space:")
.IncreaseIndentation()
.AppendLine(EuclideanBilinearProductTable(basisBladeIds, EuclideanUtils.IsZeroEuclideanLcp))
.DecreaseIndentation()
.AppendLineAtNewLine(PageSeparator)
.AppendLine();
Composer
.AppendLine("Right Contraction Product Table, " + vSpaceDim + "D Space:")
.IncreaseIndentation()
.AppendLine(EuclideanBilinearProductTable(basisBladeIds, EuclideanUtils.IsZeroEuclideanRcp))
.DecreaseIndentation()
.AppendLineAtNewLine(PageSeparator)
.AppendLine();
return(Composer.ToString());
}