/// <summary>
/// Return true if the anti-commutator product of the given euclidean basis blades ids is always zero
/// </summary>
/// <param name="id1"></param>
/// <param name="id2"></param>
/// <returns></returns>
public static bool IsZeroEuclideanAcp(int id1, int id2)
{
return(FrameUtils.IsNegativeEGp(id1, id2) == !FrameUtils.IsNegativeEGp(id2, id1));
}
/// <summary>
/// Compute and fill all GA lookup tables
/// </summary>
private static void ComputeGaLookupTables()
{
const int c = 1;
const int d = 1;
var gaSpaceDim = (c << FrameUtils.MaxVSpaceDimension);
var maxId = gaSpaceDim - 1;
var gradeCount = new int[FrameUtils.MaxVSpaceDimension + 1];
//Initialize all tables
IdToGradeTable = new int[gaSpaceDim];
IdToIndexTable = new int[gaSpaceDim];
IsNegativeReverseTable = new BitArray(gaSpaceDim);
IsNegativeGradeInvTable = new BitArray(gaSpaceDim);
IsNegativeClifConjTable = new BitArray(gaSpaceDim);
IsNegativeEGpTable = new BitArray(d << (2 * FrameUtils.MaxVSpaceDimension));
GradeIndexToIdTable = new List <int[]>(FrameUtils.MaxVSpaceDimension);
//var stopWatch = new Stopwatch();
//long ticks = 0;
for (var id = 0; id <= maxId; id++)
{
var grade = id.CountOnes();
IdToGradeTable[id] = grade;
//Calculate grade inversion sign
if (grade.GradeHasNegativeGradeInv())
{
IsNegativeGradeInvTable.Set(id, true);
}
//Calculate reversion sign
if (grade.GradeHasNegativeReverse())
{
IsNegativeReverseTable.Set(id, true);
}
//Calculate Clifford conjugate sign
if (grade.GradeHasNegativeClifConj())
{
IsNegativeClifConjTable.Set(id, true);
}
//Calculate index of basis blade ID
IdToIndexTable[id] = gradeCount[grade];
gradeCount[grade] += 1;
//stopWatch.Start();
//Calculate the sign of the geometric product of basis blades
var id1 = id;
for (var id2 = 0; id2 <= maxId; id2++)
{
if (FrameUtils.ComputeIsNegativeEGp(id1, id2))
{
IsNegativeEGpTable.Set(FrameUtils.JoinIDs(id1, id2), true);
}
}
//stopWatch.Stop();
//ticks += stopWatch.ElapsedTicks;
}
//MessageBox.Show(ticks.ToString("###,###,###,###,###"));
//Calculate inverse index table: (grade, index) to ID table
gradeCount = new int[gaSpaceDim];
for (var id = 0; id <= maxId; id++)
{
var grade = IdToGradeTable[id];
var index = gradeCount[grade];
gradeCount[grade] += 1;
if (gradeCount[grade] == 1)
{
GradeIndexToIdTable.Add(new int[Choose(FrameUtils.MaxVSpaceDimension, grade)]);
}
GradeIndexToIdTable[grade][index] = id;
}
}