public static Operand CalculateJoin(List <Operand> operandList, Context context)
{
OuterProduct[] bladeArray = new OuterProduct[operandList.Count];
int j = -1;
for (int i = 0; i < bladeArray.Length; i++)
{
try
{
bladeArray[i] = FactorBlade.Factor(operandList[i], context);
if (j < 0 || bladeArray[i].Grade > bladeArray[j].Grade)
{
j = i;
}
}
catch (MathException exc)
{
throw new MathException($"Failed to factor argument {i} as blade.", exc);
}
}
OuterProduct join = bladeArray[j];
for (int i = 0; i < bladeArray.Length; i++)
{
if (i != j)
{
foreach (Operand vector in bladeArray[i].operandList)
{
Operand operand = Operand.ExhaustEvaluation(new Trim(new List <Operand>()
{
new OuterProduct(new List <Operand>()
{
vector.Copy(), join.Copy()
})
}), context);
if (!operand.IsAdditiveIdentity)
{
join.operandList.Add(vector);
}
}
}
}
return(join);
}
// The algorithm implemented here comes straight out of Christian Perwass' book.
// TODO: Also, as noted by Perwass, this algorithm doesn't work for null versors.
public static GeometricProduct Factor(Operand operand, Context context)
{
Operand currentVersor = operand.Copy();
GeometricProduct versorFactorization = new GeometricProduct();
while (true)
{
HashSet <int> gradeSet = DiscoverGrades(currentVersor, context);
int maxGrade = gradeSet.ToList().Aggregate(0, (currentMaxGrade, grade) => grade > currentMaxGrade ? grade : currentMaxGrade);
if (maxGrade <= 0)
{
break;
}
Operand blade = Operand.ExhaustEvaluation(new GradePart(new List <Operand>()
{
currentVersor.Copy(), new NumericScalar(maxGrade)
}), context);
OuterProduct bladeFactorization = null;
try
{
bladeFactorization = FactorBlade.Factor(blade, context);
}
catch (MathException exc)
{
throw new MathException("Highest-grade-part of multivector does not factor as a blade.", exc);
}
Operand nonNullVector = null, magnitude = null;
foreach (Operand vector in bladeFactorization.operandList)
{
if (vector.Grade == 1)
{
magnitude = Operand.ExhaustEvaluation(new Trim(new List <Operand>()
{
new Magnitude(new List <Operand>()
{
vector.Copy()
})
}), context);
if (!magnitude.IsAdditiveIdentity)
{
nonNullVector = vector;
break;
}
}
}
if (nonNullVector == null)
{
throw new MathException("Failed to find non-null vector in blade factorization.");
}
Operand unitVector = Operand.ExhaustEvaluation(new Normalize(new List <Operand>()
{
nonNullVector
}), context);
versorFactorization.operandList.Insert(0, unitVector);
currentVersor = Operand.ExhaustEvaluation(new Trim(new List <Operand>()
{
new GeometricProduct(new List <Operand>()
{
currentVersor, unitVector.Copy()
})
}), context);
}
versorFactorization.operandList.Add(currentVersor);
return(versorFactorization);
}