/// <summary>
/// Find all basis blade IDs with the given grade in a given frame
/// </summary>
/// <param name="frame"></param>
/// <param name="grade"></param>
/// <returns></returns>
public static IEnumerable <int> BasisBladeIDsOfGrade(this IGMacFrame frame, int grade)
{
var kvDim = frame.KvSpaceDimension(grade);
return
(Enumerable
.Range(0, kvDim)
.Select(index => BasisBladeId(grade, index)));
}
public static string BasisBladeGradeIndexName(this IGMacFrame frame, int basisBladeId)
{
return
(new StringBuilder(32)
.Append('G')
.Append(basisBladeId.BasisBladeGrade())
.Append('I')
.Append(basisBladeId.BasisBladeIndex())
.ToString());
}
public static string BasisBladeGradeIndexName(this IGMacFrame frame, int grade, int index)
{
return
(new StringBuilder(32)
.Append('G')
.Append(grade)
.Append('I')
.Append(index)
.ToString());
}
public static bool IsValidBasisBladeGradeIndex(this IGMacFrame frame, int grade, int index)
{
if (grade < 0 || grade > frame.VSpaceDimension)
{
return(false);
}
var kvDim = KvSpaceDimension(frame.VSpaceDimension, grade);
return(index >= 0 && index <= kvDim);
}
/// <summary>
/// Returns the basis blade IDs of having the given grades
/// </summary>
/// <param name="frame"></param>
/// <param name="gradesSeq"></param>
/// <returns></returns>
public static IEnumerable <int> BasisBladeIDsOfGrades(this IGMacFrame frame, params int[] gradesSeq)
{
foreach (var grade in gradesSeq.OrderBy(g => g))
{
var kvSpaceDim = frame.KvSpaceDimension(grade);
for (var index = 0; index < kvSpaceDim; index++)
{
yield return(BasisBladeId(grade, index));
}
}
}
/// <summary>
/// The basis blade IDs of the given frame sorted by their grade and index
/// </summary>
/// <param name="frame"></param>
/// <param name="startGrade"></param>
/// <returns></returns>
public static IEnumerable <int> BasisBladeIDsSortedByGrade(this IGMacFrame frame, int startGrade = 0)
{
for (var grade = startGrade; grade <= frame.VSpaceDimension; grade++)
{
var kvSpaceDim = frame.KvSpaceDimension(grade);
for (var index = 0; index < kvSpaceDim; index++)
{
yield return(BasisBladeId(grade, index));
}
}
}
/// <summary>
/// Get all possible grades of the meet of two blades grades
/// </summary>
/// <param name="frame"></param>
/// <param name="grade1"></param>
/// <param name="grade2"></param>
/// <returns></returns>
public static IEnumerable <int> GradesOfMeet(this IGMacFrame frame, int grade1, int grade2)
{
if (grade1 > frame.VSpaceDimension || grade2 > frame.VSpaceDimension || grade1 < 0 || grade2 < 0)
{
yield break;
}
var maxGrade = Math.Min(grade1, grade2);
//TODO: Should this be grade++ instead of grade += 2 ?
for (var grade = 0; grade <= maxGrade; grade += 2)
{
yield return(grade);
}
}
/// <summary>
/// Return a list of all possible grades in the geometric product of two k-vectors with
/// the given grades
/// </summary>
/// <param name="frame"></param>
/// <param name="grade1"></param>
/// <param name="grade2"></param>
/// <returns></returns>
public static IEnumerable <int> GradesOfEGp(this IGMacFrame frame, int grade1, int grade2)
{
if (grade1 > frame.VSpaceDimension || grade2 > frame.VSpaceDimension || grade1 < 0 || grade2 < 0)
{
yield break;
}
var minGrade = Math.Abs(grade1 - grade2);
var maxGrade = Math.Min(frame.VSpaceDimension, grade1 + grade2);
for (var grade = minGrade; grade <= maxGrade; grade += 2)
{
yield return(grade);
}
}
/// <summary>
/// Returns the basis blade IDs of having the given grades grouped by their grade
/// </summary>
/// <param name="frame"></param>
/// <param name="gradesSeq"></param>
/// <returns></returns>
public static Dictionary <int, List <int> > BasisBladeIDsGroupedByGrade(this IGMacFrame frame, params int[] gradesSeq)
{
var result = new Dictionary <int, List <int> >();
foreach (var grade in gradesSeq)
{
var kvSpaceDim = frame.KvSpaceDimension(grade);
var newList = new List <int>(kvSpaceDim);
for (var index = 0; index < kvSpaceDim; index++)
{
newList.Add(BasisBladeId(grade, index));
}
result.Add(grade, newList);
}
return(result);
}
/// <summary>
/// Returns the basis blade IDs of having the given grades grouped by their grade
/// </summary>
/// <param name="frame"></param>
/// <param name="startGrade"></param>
/// <returns></returns>
public static Dictionary <int, List <int> > BasisBladeIDsGroupedByGrade(this IGMacFrame frame, int startGrade = 0)
{
var result = new Dictionary <int, List <int> >();
for (var grade = startGrade; grade <= frame.VSpaceDimension; grade++)
{
var kvSpaceDim = frame.KvSpaceDimension(grade);
var newList = new List <int>(kvSpaceDim);
for (var index = 0; index < kvSpaceDim; index++)
{
newList.Add(BasisBladeId(grade, index));
}
result.Add(grade, newList);
}
return(result);
}
public static IEnumerable <int> BasisBladeIDsInside(this IGMacFrame frame, int basisBladeId)
{
return(basisBladeId.GetSubPatterns());
}
public static IEnumerable <int> BasisVectorIndexesInside(this IGMacFrame frame, int grade, int index)
{
return(BasisBladeId(grade, index).PatternToPositions());
}
/// <summary>
/// The grades of k-vectors in the given frame
/// </summary>
/// <param name="frame"></param>
/// <returns></returns>
public static IEnumerable <int> Grades(this IGMacFrame frame)
{
return(Enumerable.Range(0, frame.VSpaceDimension + 1));
}
/// <summary>
/// The Basis blade IDs of the given frame
/// </summary>
/// <param name="frame"></param>
/// <returns></returns>
public static IEnumerable <int> BasisBladeIDs(this IGMacFrame frame)
{
return(Enumerable.Range(0, frame.GaSpaceDimension));
}
/// <summary>
/// The basis vectors IDs of the given frame
/// </summary>
/// <param name="frame"></param>
/// <returns></returns>
public static IEnumerable <int> BasisVectorIDs(this IGMacFrame frame)
{
return(Enumerable.Range(0, frame.VSpaceDimension).Select(i => (1 << i)));
}
public static bool IsValidBasisBladeId(this IGMacFrame frame, int basisBladeId)
{
return(basisBladeId >= 0 && basisBladeId <= frame.MaxBasisBladeId);
}
public static bool IsValidBasisVectorId(this IGMacFrame frame, int basisBladeId)
{
return(frame.IsValidBasisBladeId(basisBladeId) && basisBladeId.IsBasicPattern());
}
public static GaNumMapBilinearArray CreateFromOuterProduct(IGMacFrame frame)
{
return(new GaNumOp(frame.VSpaceDimension).ToArrayMap());
}
/// <summary>
/// Find the index of a basis blade given its ID
/// </summary>
/// <param name="frame"></param>
/// <param name="basisBladeId"></param>
/// <returns></returns>
public static int BasisBladeIndex(this IGMacFrame frame, int basisBladeId)
{
return(GMacLookupTables.IdToIndexTable[basisBladeId]);
}
/// <summary>
/// Find the ID of a basis vector given its index
/// </summary>
/// <param name="frame"></param>
/// <param name="index"></param>
/// <returns></returns>
public static int BasisVectorId(this IGMacFrame frame, int index)
{
return(GMacLookupTables.GradeIndexToIdTable[1][index]);
}
/// <summary>
/// Find the ID of a basis blade given its grade and index
/// </summary>
/// <param name="frame"></param>
/// <param name="grade"></param>
/// <param name="index"></param>
/// <returns></returns>
public static int BasisBladeId(this IGMacFrame frame, int grade, int index)
{
return(GMacLookupTables.GradeIndexToIdTable[grade][index]);
}
public static IEnumerable <int> BasisBladeIDsInside(this IGMacFrame frame, int grade, int index)
{
return(BasisBladeId(grade, index).GetSubPatterns());
}
public static IEnumerable <int> BasisBladeIDsContaining(this IGMacFrame frame, int grade, int index)
{
return(BasisBladeId(grade, index).GetSuperPatterns(frame.VSpaceDimension));
}
public static string BasisBladeIndexedName(this IGMacFrame frame, int grade, int index)
{
return("E" + BasisBladeId(grade, index));
}
public static bool IsValidBasisVectorIndex(this IGMacFrame frame, int index)
{
return(index >= 0 && index <= frame.VSpaceDimension);
}
public static string BasisBladeBinaryIndexedName(this IGMacFrame frame, int grade, int index)
{
return("B" + BasisBladeId(grade, index).PatternToString(frame.VSpaceDimension));
}
/// <summary>
/// Find the grade and index of a basis blade given its ID
/// </summary>
/// <param name="frame"></param>
/// <param name="basisBladeId"></param>
/// <param name="grade"></param>
/// <param name="index"></param>
public static void BasisBladeGradeIndex(this IGMacFrame frame, int basisBladeId, out int grade, out int index)
{
basisBladeId.BasisBladeGradeIndex(out grade, out index);
}
/// <summary>
/// Find all basis blade IDs with the given grade and indexes in a given frame
/// </summary>
/// <param name="frame"></param>
/// <param name="grade"></param>
/// <param name="indexSeq"></param>
/// <returns></returns>
public static IEnumerable <int> BasisBladeIDsOfGrade(this IGMacFrame frame, int grade, params int[] indexSeq)
{
return(indexSeq.Select(index => BasisBladeId(grade, index)));
}
public static GaSymMapBilinearTree CreateFromOuterProduct(IGMacFrame frame)
{
return(new GaSymOp(frame.VSpaceDimension).ToTreeMap());
}
public static string BasisBladeIndexedName(this IGMacFrame frame, int basisBladeId)
{
return("E" + basisBladeId);
}
