public static GaTreeMultivector EGp(this GaTreeMultivector mv1, GaTreeMultivector mv2)
{
if (mv1.GaSpaceDimension != mv2.GaSpaceDimension)
{
throw new GMacSymbolicException("Multivector size mismatch");
}
var resultMv = GaSymMultivector.CreateZeroTemp(mv1.GaSpaceDimension);
var indexList = Enumerable.Range(0, mv1.GaSpaceDimension).Reverse().ToList();
for (var k = 0; k < mv1.GaSpaceDimension; k++)
{
var coefId = k.ReverseBits(mv1.VSpaceDimension);
var signList = GpSign(mv1.VSpaceDimension, coefId);
foreach (var index in indexList)
{
var id1 = index.ReverseBits(mv1.VSpaceDimension);
var id2 = id1 ^ coefId;
resultMv.AddFactor(
coefId,
signList[mv1.GaSpaceDimension - index - 1],
Mfs.Times[mv1[id1], mv2[id2]]
);
}
}
return(resultMv.ToTreeMultivector());
}
public static GaTreeMultivector CreatePseudoScalar(int gaSpaceDim, MathematicaScalar coef)
{
var resultMv = new GaTreeMultivector(gaSpaceDim)
{
[gaSpaceDim - 1] = coef.Expression
};
return(resultMv);
}
public static GaTreeMultivector CreateBasisBlade(int gaSpaceDim, int id)
{
var resultMv = new GaTreeMultivector(gaSpaceDim)
{
[id] = Expr.INT_ONE
};
return(resultMv);
}
public static GaTreeMultivector CreateTerm(int gaSpaceDim, int id, MathematicaScalar coef)
{
var resultMv = new GaTreeMultivector(gaSpaceDim)
{
[id] = coef.Expression
};
return(resultMv);
}
public static GaTreeMultivector CreateMapped(GaTreeMultivector mv, Func <MathematicaScalar, MathematicaScalar> scalarMap)
{
var resultMv = CreateZero(mv.GaSpaceDimension);
foreach (var term in mv.Terms)
{
resultMv[term.Key] = scalarMap(term.Value).Expression;
}
return(resultMv);
}
public static GaTreeMultivector CreateSymbolic(int gaSpaceDim, string baseCoefName, IEnumerable <int> idsList)
{
var resultMv = new GaTreeMultivector(gaSpaceDim);
var vSpaceDim = gaSpaceDim.ToVSpaceDimension();
foreach (var id in idsList)
{
resultMv[id] =
MathematicaScalar.CreateSymbol(
SymbolicUtils.Cas,
baseCoefName + id.PatternToString(vSpaceDim)
).Expression;
}
return(resultMv);
}
public static GaTreeMultivector Op(this GaTreeMultivector mv1, GaTreeMultivector mv2)
{
if (mv1.GaSpaceDimension != mv2.GaSpaceDimension)
{
throw new GMacSymbolicException("Multivector size mismatch");
}
var resultMv = GaSymMultivector.CreateZeroTemp(mv1.GaSpaceDimension);
var signList = OpSign(mv1.VSpaceDimension);
for (var basisBladeId = 0; basisBladeId < mv1.GaSpaceDimension; basisBladeId++)
{
var indexList = new List <int>();
indexList =
basisBladeId
.PatternToBooleans(mv1.VSpaceDimension)
.Aggregate(
indexList,
(currentList, bitFlag) =>
OpOneLevel(currentList, bitFlag).ToList()
)
.Select(idx => idx.ReverseBits(mv1.VSpaceDimension))
.ToList();
var i = 0;
foreach (var index in indexList)
{
resultMv.AddFactor(
basisBladeId,
signList[i],
Mfs.Times[mv1[index], mv2[basisBladeId ^ index]]
);
i++;
}
}
return(resultMv.ToTreeMultivector());
}
public static GaTreeMultivector CreateCopy(GaTreeMultivector mv)
{
var resultMv = new GaTreeMultivector(mv.GaSpaceDimension);
var sourceNodeStack = new Stack <IGaTreeMultivectorNode>();
var targetNodeStack = new Stack <IGaTreeMultivectorNode>();
sourceNodeStack.Push(mv);
targetNodeStack.Push(resultMv);
while (sourceNodeStack.Count > 0)
{
var sourceNode = sourceNodeStack.Pop();
var targetNode = targetNodeStack.Pop();
var childNode = sourceNode.GetLeftChild();
if (!ReferenceEquals(childNode, null))
{
targetNodeStack.Push(
childNode.IsInternal
? (IGaTreeMultivectorNode)targetNode.SetLeftChildToInternalNode()
: targetNode.SetLeftChildToLeafNode(childNode.AsLeafNode().Value)
);
}
childNode = sourceNode.GetRightChild();
if (!ReferenceEquals(childNode, null))
{
targetNodeStack.Push(
childNode.IsInternal
? (IGaTreeMultivectorNode)targetNode.SetRightChildToInternalNode()
: targetNode.SetRightChildToLeafNode(childNode.AsLeafNode().Value)
);
}
}
return(resultMv);
}