public static Dictionary <int, GaSymMultivector> ToOutermorphismDictionary(this ISymbolicMatrix linearVectorMapMatrix)
{
var domainGaSpaceDim =
linearVectorMapMatrix.ColumnCount.ToGaSpaceDimension();
var targetGaSpaceDim =
linearVectorMapMatrix.RowCount.ToGaSpaceDimension();
var omMapDict = new Dictionary <int, GaSymMultivector>();
//Add unit scalar as the image of the 0-basis blade
omMapDict.Add(0, GaSymMultivector.CreateUnitScalar(targetGaSpaceDim));
for (var id = 1; id <= domainGaSpaceDim - 1; id++)
{
GaSymMultivector basisBladeImage;
if (id.IsValidBasisVectorId())
{
//Add images of vector basis blades
basisBladeImage =
GaSymMultivector.CreateVectorFromColumn(
linearVectorMapMatrix,
id.BasisBladeIndex()
);
}
else
{
//Add images of a higher dimensional basis blade using the outer product
//of the images of two lower dimensional basis blades
int id1, id2;
id.SplitBySmallestBasicPattern(out id1, out id2);
basisBladeImage =
omMapDict[id1].Op(omMapDict[id2]);
}
if (!basisBladeImage.IsZero())
{
omMapDict.Add(id, basisBladeImage);
}
}
return(omMapDict);
}
public static Dictionary <int, GaSymMultivector> ToOutermorphismDictionary(this Dictionary <int, IGaSymMultivector> linearVectorMaps, int domainVSpaceDim, int targetVSpaceDim)
{
var domainGaSpaceDim =
domainVSpaceDim.ToGaSpaceDimension();
var targetGaSpaceDim =
targetVSpaceDim.ToGaSpaceDimension();
var omMapDict = new Dictionary <int, GaSymMultivector>();
//Add unit scalar as the image of the 0-basis blade
omMapDict.Add(0, GaSymMultivector.CreateUnitScalar(targetGaSpaceDim));
for (var id = 1; id <= domainGaSpaceDim - 1; id++)
{
GaSymMultivector basisBladeImage;
if (id.IsValidBasisVectorId())
{
//Add images of vector basis blades
IGaSymMultivector mv;
linearVectorMaps.TryGetValue(id.BasisBladeIndex(), out mv);
basisBladeImage = mv?.GetVectorPart()
?? GaSymMultivector.CreateZero(targetGaSpaceDim);
}
else
{
//Add images of a higher dimensional basis blade using the outer product
//of the images of two lower dimensional basis blades
int id1, id2;
id.SplitBySmallestBasicPattern(out id1, out id2);
basisBladeImage =
omMapDict[id1].Op(omMapDict[id2]);
}
if (!basisBladeImage.IsZero())
{
omMapDict.Add(id, basisBladeImage);
}
}
return(omMapDict);
}
public static Dictionary <int, GaSymMultivector> ToOutermorphismDictionary(this IEnumerable <IGaSymMultivector> linearVectorMaps)
{
var linearVectorMapsArray = linearVectorMaps.ToArray();
var domainGaSpaceDim =
linearVectorMapsArray.Length.ToGaSpaceDimension();
var targetGaSpaceDim =
linearVectorMapsArray[0].GaSpaceDimension;
var omMapDict = new Dictionary <int, GaSymMultivector>();
//Add unit scalar as the image of the 0-basis blade
omMapDict.Add(0, GaSymMultivector.CreateUnitScalar(targetGaSpaceDim));
for (var id = 1; id <= domainGaSpaceDim - 1; id++)
{
GaSymMultivector basisBladeImage;
if (id.IsValidBasisVectorId())
{
//Add images of vector basis blades
basisBladeImage =
linearVectorMapsArray[id.BasisBladeIndex()].GetVectorPart();
}
else
{
//Add images of a higher dimensional basis blade using the outer product
//of the images of two lower dimensional basis blades
int id1, id2;
id.SplitBySmallestBasicPattern(out id1, out id2);
basisBladeImage =
omMapDict[id1].Op(omMapDict[id2]);
}
if (!basisBladeImage.IsZero())
{
omMapDict.Add(id, basisBladeImage);
}
}
return(omMapDict);
}
