public override Operand Copy()
{
Blade clone = base.Copy() as Blade;
clone.vectorList = (from vectorName in this.vectorList select vectorName).ToList();
return(clone);
}
public override Operand EvaluationStep(Context context)
{
Operand operand = base.EvaluationStep(context);
if (operand != null)
{
return(operand);
}
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA != null && bladeB != null)
{
Blade blade = new Blade(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar
}));
blade.vectorList = bladeA.vectorList.Concat(bladeB.vectorList).ToList();
operandList.RemoveAt(i);
operandList[i] = blade;
return(this);
}
}
return(null);
}
public static OuterProduct Factor(Operand operand, Context context)
{
// TODO: Support symbolic factorization? For example, it would be quite useful
// to be able to evaluate factor(n*(a^b)*n). I wouldn't expect any kind
// of miracle, though, like finding (n*a*n)^(n*b*n).
Sum multivector = CanonicalizeMultivector(operand);
OuterProduct factorization = FactorMultivectorAsBlade(multivector, context);
operand = Operand.ExhaustEvaluation(factorization.Copy(), context);
Sum expansion = CanonicalizeMultivector(operand);
if (expansion.operandList.Count != multivector.operandList.Count)
{
throw new MathException("The multivector is not a blade.");
}
// Note that this should work by the sorting performed by the sum operation.
double commonRatio = 0.0;
for (int i = 0; i < expansion.operandList.Count; i++)
{
Blade bladeA = multivector.operandList[i] as Blade;
Blade bladeB = expansion.operandList[i] as Blade;
if (!bladeA.IsLike(bladeB))
{
throw new MathException("The multivector is not a blade.");
}
double ratio = 0.0;
try
{
ratio = (bladeA.scalar as NumericScalar).value / (bladeB.scalar as NumericScalar).value;
}
catch (DivideByZeroException)
{
ratio = 1.0;
}
if (Double.IsNaN(ratio))
{
ratio = 1.0;
}
if (commonRatio == 0.0)
{
commonRatio = ratio;
}
else if (Math.Abs(ratio - commonRatio) >= context.epsilon)
{
throw new MathException("The multivector is not a blade.");
}
}
factorization.operandList.Insert(0, new NumericScalar(commonRatio));
return(factorization);
}
public override bool IsLike(Collectable collectable)
{
Blade blade = collectable as Blade;
if (blade == null)
{
return(false);
}
// This works because blades are sorted as part of their evaluation.
return(Enumerable.SequenceEqual <string>(vectorList, blade.vectorList));
}
public Blade MakeSubBlade(int i)
{
Blade subBlade = new Blade();
subBlade.scalar = this.scalar;
string removedVectorName = this.vectorList[i];
subBlade.vectorList = (from vectorName in this.vectorList where vectorName != removedVectorName select vectorName).ToList();
return(subBlade);
}
public static IEnumerable <Blade> GenerateBasisBlades(List <string> basisVectorList)
{
for (int i = 0; i <= basisVectorList.Count; i++)
{
List <string> vectorList = new List <string>();
foreach (List <string> vectorComboList in GenerateVectorCombinations(basisVectorList, vectorList, 0, i, 0))
{
vectorComboList.Sort();
Blade basisBlade = new Blade(new NumericScalar(1.0), vectorComboList);
yield return(basisBlade);
}
}
}
private IEnumerable <List <int> > IteratePotentiallyFactorableBladesLists(List <int> bladeOffsetList, Sum sum, List <string> basisVectorList, string vectorName)
{
if (bladeOffsetList.Count == basisVectorList.Count)
{
yield return(bladeOffsetList);
}
else
{
string basisVectorName = basisVectorList[bladeOffsetList.Count];
for (int i = 0; i < sum.operandList.Count; i++)
{
if (bladeOffsetList.Contains(i))
{
continue;
}
Blade blade = sum.operandList[i] as Blade;
if (blade.vectorList.Contains(basisVectorName))
{
if (blade.scalar is SymbolicScalarTerm term)
{
if (term.factorList.Any(factor => factor is SymbolicScalarTerm.SymbolicDot symbolicDot && symbolicDot.InvolvesVectors(vectorName, basisVectorName)))
{
bladeOffsetList.Add(i);
foreach (List <int> otherBladeOffsetList in IteratePotentiallyFactorableBladesLists(bladeOffsetList, sum, basisVectorList, vectorName))
{
yield return(otherBladeOffsetList);
}
bladeOffsetList.Remove(i);
}
}
}
}
}
}
public override Operand EvaluationStep(Context context)
{
Operand operand = base.EvaluationStep(context);
if (operand != null)
{
return(operand);
}
// To avoid infinite evaluation looping, we must apply...
// 1) vB = v.B + v^B, and
// 2) v^B = vB - v.B,
// ...according to rules that dictate when and where they're appropriate.
// Also to avoid infinite looping, the distributive property must take
// precedence over anything we do here.
// All reduction cases must be eliminated before it is safe to handle the expansion cases.
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA != null && bladeB != null && bladeA.Grade > 1 && bladeB.Grade > 1)
{
GeometricProduct geometricProduct;
if (context.useOperandCache)
{
geometricProduct = new GeometricProduct(new List <Operand>()
{
new Blade(new NumericScalar(1.0), bladeA.vectorList.ToList()), new Blade(new NumericScalar(1.0), bladeB.vectorList.ToList())
});
string key = geometricProduct.Print(Format.PARSEABLE, context);
Operand cachedResult = null;
if (!context.operandCache.GetStorage(key, ref cachedResult))
{
context.useOperandCache = false;
cachedResult = Operand.ExhaustEvaluation(geometricProduct, context);
context.useOperandCache = true;
context.operandCache.SetStorage(key, cachedResult);
}
return(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, cachedResult
}));
}
// Here our choice of which blade to reduce is arbitrary from a stand-point of correctness.
// However, we might converge faster by choosing the blade with smaller grade.
// Note there is also something arbitrary about how we're reducing the blades.
int j = bladeA.Grade <= bladeB.Grade ? i : i + 1;
Blade blade = operandList[j] as Blade;
Blade subBlade = blade.MakeSubBlade(0);
Blade vector = new Blade(blade.vectorList[0]);
geometricProduct = new GeometricProduct(new List <Operand>()
{
vector, subBlade
});
InnerProduct innerProduct = new InnerProduct(new List <Operand>()
{
vector.Copy(), subBlade.Copy()
});
operandList[j] = new Sum(new List <Operand>()
{
geometricProduct, new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), innerProduct
})
});
return(this);
}
}
// All reduction cases eliminated, it is now safe to handle some expansion cases.
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA == null || bladeB == null)
{
continue;
}
if ((bladeA.Grade == 1 && bladeB.Grade > 1) || (bladeA.Grade > 1 && bladeB.Grade == 1))
{
InnerProduct innerProduct = new InnerProduct(new List <Operand>()
{
bladeA, bladeB
});
OuterProduct outerProduct = new OuterProduct(new List <Operand>()
{
bladeA.Copy(), bladeB.Copy()
});
operandList[i] = new Sum(new List <Operand>()
{
innerProduct, outerProduct
});
operandList.RemoveAt(i + 1);
return(this);
}
}
// It is now safe to handle the remaining expansion cases.
for (int i = 0; i < operandList.Count - 1; i++)
{
Blade bladeA = operandList[i] as Blade;
Blade bladeB = operandList[i + 1] as Blade;
if (bladeA == null || bladeB == null)
{
continue;
}
if (bladeA.Grade == 1 && bladeB.Grade == 1)
{
operandList.RemoveAt(i + 1);
GeometricProduct innerProduct = new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, context.BilinearForm(bladeA.vectorList[0], bladeB.vectorList[0])
});
Blade outerProduct = new Blade(new GeometricProduct(new List <Operand>()
{
bladeA.scalar.Copy(), bladeB.scalar.Copy()
}));
outerProduct.vectorList.Add(bladeA.vectorList[0]);
outerProduct.vectorList.Add(bladeB.vectorList[0]);
operandList[i] = new Sum(new List <Operand>()
{
innerProduct, outerProduct
});
return(this);
}
}
return(null);
}
public override Operand EvaluationStep(Context context)
{
if (operandList.Count != 1)
{
throw new MathException(string.Format("Exponential function expected exactly 1 argument, got {0}.", operandList.Count));
}
Operand operand = base.EvaluationStep(context);
if (operand != null)
{
return(operand);
}
Operand exponentOperand = operandList[0];
if (exponentOperand is Sum sumExponent)
{
GeometricProduct geometricProduct = new GeometricProduct();
for (int i = 0; i < sumExponent.operandList.Count; i++)
{
geometricProduct.operandList.Add(new Exponent(new List <Operand>()
{
sumExponent.operandList[i]
}));
}
return(geometricProduct);
}
if (exponentOperand is NumericScalar numericScalar)
{
return(new NumericScalar(Math.Exp(numericScalar.value)));
}
else if (exponentOperand is Blade blade)
{
Blade basisBlade = new Blade(new NumericScalar(1.0), blade.vectorList.ToList());
InnerProduct innerProduct = new InnerProduct();
innerProduct.operandList.Add(new NumericScalar(-1.0));
innerProduct.operandList.Add(basisBlade.Copy());
innerProduct.operandList.Add(basisBlade.Copy());
Operand result = Operand.ExhaustEvaluation(innerProduct, context);
if (result.IsMultiplicativeIdentity)
{
Sum sum = new Sum();
sum.operandList.Add(new Cosine(new List <Operand>()
{
blade.scalar.Copy()
}));
sum.operandList.Add(new GeometricProduct(new List <Operand>()
{
basisBlade.Copy(), new Sine(new List <Operand>()
{
blade.scalar.Copy()
})
}));
return(sum);
}
else if (result.IsAdditiveIdentity)
{
// What if it's a null blade?
}
else
{
// Hyperbolic cosine/sine?
}
}
return(null);
}
public override Operand EvaluationStep(Context context)
{
Operand operand = base.EvaluationStep(context);
if (operand != null)
{
return(operand);
}
if (operandList.Count == 2)
{
Blade bladeA = operandList[0] as Blade;
Blade bladeB = operandList[1] as Blade;
if (bladeA != null && bladeB != null)
{
if (bladeA.Grade == 1 && bladeB.Grade == 1)
{
return(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, context.BilinearForm(bladeA.vectorList[0], bladeB.vectorList[0])
}));
}
else if (bladeA.Grade == 1 && bladeB.Grade > 1)
{
Sum sum = new Sum();
for (int i = 0; i < bladeB.vectorList.Count; i++)
{
Blade subBlade = bladeB.MakeSubBlade(i);
subBlade.scalar = new GeometricProduct(new List <Operand>()
{
new NumericScalar(i % 2 == 1 ? -1.0 : 1.0), bladeA.scalar, bladeB.scalar, context.BilinearForm(bladeA.vectorList[0], bladeB.vectorList[i])
});
sum.operandList.Add(subBlade);
}
return(sum);
}
else if (bladeA.Grade > 1 && bladeB.Grade == 1)
{
operandList[0] = bladeB;
operandList[1] = bladeA;
if (bladeA.Grade % 2 == 0)
{
operandList.Add(new NumericScalar(-1.0));
}
return(this);
}
else if (bladeA.Grade > 1 && bladeB.Grade > 1)
{
if (context.useOperandCache)
{
InnerProduct innerProduct = new InnerProduct(new List <Operand>()
{
new Blade(new NumericScalar(1.0), bladeA.vectorList.ToList()), new Blade(new NumericScalar(1.0), bladeB.vectorList.ToList())
});
string key = innerProduct.Print(Format.PARSEABLE, context);
Operand cachedResult = null;
if (!context.operandCache.GetStorage(key, ref cachedResult))
{
context.useOperandCache = false;
cachedResult = Operand.ExhaustEvaluation(innerProduct, context);
context.useOperandCache = true;
context.operandCache.SetStorage(key, cachedResult);
}
return(new GeometricProduct(new List <Operand>()
{
bladeA.scalar, bladeB.scalar, cachedResult
}));
}
if (bladeA.Grade <= bladeB.Grade)
{
return(new InnerProduct(new List <Operand>()
{
bladeA.MakeSubBlade(bladeA.Grade - 1), new InnerProduct(new List <Operand>()
{
new Blade(bladeA.vectorList[bladeA.Grade - 1]), bladeB
})
}));
}
else
{
return(new InnerProduct(new List <Operand>()
{
new InnerProduct(new List <Operand>()
{
bladeA, new Blade(bladeB.vectorList[0])
}), bladeB.MakeSubBlade(0)
}));
}
}
}
}
return(null);
}
private Operand FactorBlade(string vectorName, Sum sum, Context context)
{
List <string> basisVectorList = context.ReturnBasisVectors();
basisVectorList = basisVectorList.Where(basisVectorName => !context.BilinearForm(vectorName, basisVectorName).IsAdditiveIdentity).ToList();
List <int> emptyBladeOffsetList = new List <int>();
foreach (List <int> bladeOffsetList in this.IteratePotentiallyFactorableBladesLists(emptyBladeOffsetList, sum, basisVectorList, vectorName))
{
List <Operand> modifiedOperandList = new List <Operand>();
for (int i = 0; i < bladeOffsetList.Count; i++)
{
string basisVectorName = basisVectorList[i];
Blade blade = sum.operandList[bladeOffsetList[i]].Copy() as Blade;
SymbolicScalarTerm term = blade.scalar as SymbolicScalarTerm;
int j = blade.vectorList.IndexOf(basisVectorName);
if (j % 2 == 1)
{
term.scalar = new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), term.scalar
});
}
blade.vectorList.Remove(basisVectorName);
term.factorList = term.factorList.Where(factor => !(factor is SymbolicScalarTerm.SymbolicDot symbolicDot && symbolicDot.InvolvesVectors(vectorName, basisVectorName))).ToList();
modifiedOperandList.Add(ExhaustEvaluation(blade, context));
}
bool canFactor = Enumerable.Range(0, modifiedOperandList.Count - 1).All(j => {
Operand bladeA = modifiedOperandList[j];
Operand bladeB = modifiedOperandList[j + 1];
Operand difference = new Sum(new List <Operand>()
{
bladeA.Copy(), new GeometricProduct(new List <Operand>()
{
new NumericScalar(-1.0), bladeB.Copy()
})
});
difference = ExhaustEvaluation(difference, context);
return(difference.IsAdditiveIdentity);
});
if (canFactor)
{
Sum remainderSum = new Sum(sum.operandList.Where(operand => !bladeOffsetList.Contains(sum.operandList.IndexOf(operand))).ToList());
Sum resultSum = new Sum();
resultSum.operandList.Add(new OuterProduct(new List <Operand>()
{
new Blade(vectorName), modifiedOperandList[0]
}));
resultSum.operandList.Add(new FactorDot(new List <Operand>()
{
remainderSum
}));
return(resultSum);
}
}
return(null);
}