public static GaNumMetricOrthonormal Create(IReadOnlyList <int> basisVectorsSignaturesList)
{
var vSpaceDim = basisVectorsSignaturesList.Count;
var bbsList = new GaNumMetricOrthonormal(vSpaceDim);
bbsList[0] = 1;
for (var m = 0; m < vSpaceDim; m++)
{
var bvs = basisVectorsSignaturesList[m];
if (bvs == 0)
{
continue;
}
bbsList[1 << m] = bvs;
}
var idsSeq = GMacMathUtils.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 GaSymMetricOrthogonal Create(IReadOnlyList <Expr> basisVectorsSignaturesList)
{
var vSpaceDim = basisVectorsSignaturesList.Count;
var bbsList = new GaSymMetricOrthogonal(vSpaceDim);
bbsList[0] = Expr.INT_ONE;
for (var m = 0; m < vSpaceDim; m++)
{
var bvs = basisVectorsSignaturesList[m];
if (bvs.IsNullOrZero())
{
continue;
}
bbsList[1 << m] = bvs;
}
var idsSeq = GMacMathUtils.BasisBladeIDsSortedByGrade(vSpaceDim, 2);
foreach (var id in idsSeq)
{
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
var bvs1 = bbsList[id1];
if (bvs1.IsNullOrZero())
{
continue;
}
var bvs2 = bbsList[id2];
if (bvs2.IsNullOrZero())
{
continue;
}
bbsList[id] = SymbolicUtils.Cas[Mfs.Times[bvs1, bvs2]];
}
return(bbsList);
}
//public static BinaryTreeNode<MathematicaScalar> ComputeBasisBladesSignatures(this IReadOnlyList<MathematicaScalar> basisVectorsSignaturesList)
//{
// var vSpaceDim = basisVectorsSignaturesList.Count;
// var bbsList = new BinaryTreeNode<MathematicaScalar>(vSpaceDim);
// bbsList.SetValue(0ul, Constants.One);
// for (var m = 0; m < vSpaceDim; m++)
// {
// var bvs = basisVectorsSignaturesList[m];
// if (bvs.IsNullOrZero()) continue;
// bbsList.SetValue(1ul << m, bvs);
// }
// var idsSeq = FrameUtils.BasisBladeIDsSortedByGrade(vSpaceDim, 2);
// foreach (var id in idsSeq)
// {
// int id1, id2;
// id.SplitBySmallestBasisVectorId(out id1, out id2);
// var bvs1 = bbsList.GetValue((ulong)id1);
// if (bvs1.IsNullOrZero()) continue;
// var bvs2 = bbsList.GetValue((ulong)id2);
// if (bvs2.IsNullOrZero()) continue;
// bbsList.SetValue((ulong)id, bvs1 * bvs2);
// }
// return bbsList;
//}
public static GMacBinaryTree <int> ComputeBasisBladesSignatures(this IReadOnlyList <int> basisVectorsSignaturesList)
{
var vSpaceDim = basisVectorsSignaturesList.Count;
var bbsList = new GMacBinaryTree <int>(vSpaceDim);
bbsList.SetLeafValue(0ul, 1);
for (var m = 0; m < vSpaceDim; m++)
{
var bvs = basisVectorsSignaturesList[m];
if (bvs == 0)
{
continue;
}
bbsList.SetLeafValue(1ul << m, bvs);
}
var idsSeq = GMacMathUtils.BasisBladeIDsSortedByGrade(vSpaceDim, 2);
foreach (var id in idsSeq)
{
int id1, id2;
id.SplitBySmallestBasisVectorId(out id1, out id2);
var bvs1 = bbsList.GetLeafValue((ulong)id1);
if (bvs1 == 0)
{
continue;
}
var bvs2 = bbsList.GetLeafValue((ulong)id2);
if (bvs2 == 0)
{
continue;
}
bbsList.SetLeafValue((ulong)id, bvs1 * bvs2);
}
return(bbsList);
}