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);
}
public static GaOuterMorphismFull Create(ISymbolicMatrix vectorTransformMatrix)
{
var domainGaSpaceDim = FrameUtils.GaSpaceDimension(vectorTransformMatrix.Columns);
var codomainGaSpaceDim = FrameUtils.GaSpaceDimension(vectorTransformMatrix.Rows);
var transformedBasisBlades = new GaMultivector[domainGaSpaceDim];
transformedBasisBlades[0] = GaMultivector.CreateScalar(codomainGaSpaceDim, MathematicaScalar.Create(vectorTransformMatrix.CasInterface, 1));
for (var id = 1; id <= domainGaSpaceDim - 1; id++)
{
if (id.IsValidBasisVectorId())
{
transformedBasisBlades[id] = CreateFromMatrixColumn(vectorTransformMatrix, id.BasisBladeIndex());
}
else
{
int id1, id2;
id.SplitBySmallestBasicPattern(out id1, out id2);
transformedBasisBlades[id] = transformedBasisBlades[id1].OuterProduct(transformedBasisBlades[id2]);
}
}
return(new GaOuterMorphismFull(transformedBasisBlades));
}
private static GaMultivector CreateFromMatrixColumn(ISymbolicMatrix matrix, int col)
{
var gaSpaceDim = FrameUtils.GaSpaceDimension(matrix.Rows);
var mv = GaMultivector.CreateZero(gaSpaceDim);
for (var index = 0; index < matrix.Rows; index++)
{
mv[1, index] = matrix[index, col];
}
return(mv);
}