public double this[Basis basis]
{
get
{
if (blades.ContainsKey(basis))
{
return(blades[basis].Value);
}
else
{
return(0.0);
}
}
set
{
// HACK
if (Math.Abs(value) < 1E-3)
{
if (blades.ContainsKey(basis))
{
blades.Remove(basis);
}
}
else
{
if (blades.ContainsKey(basis))
{
blades[basis] = new Blade(basis, value);
}
else
{
blades.Add(basis, new Blade(basis, value));
}
}
}
}
public static int Order(Basis e1, Basis e2)
{
int a = e1.bitMask;
int b = e2.bitMask;
int n = 0;
do
{
a >>= 1;
n += (new Basis(a & b, false)).Grade;
} while (a != 0);
if (n % 2 == 0)
return 1;
else
return -1;
}
public static bool IsCompatible(Basis e1, Basis e2)
{
return !(e1.IsNullMetric && e2.IsMinkowskiMetric ||
e1.IsMinkowskiMetric && e2.IsNullMetric);
}
public static int GetHashPair(Basis e1, Basis e2)
{
return (e1.GetHashCode() << 16) | e2.GetHashCode();
}
public static MultiVector GeometricProduct(Basis e1, Basis e2)
{
int hashPair = Basis.GetHashPair(e1, e2);
if (geometricProductCache.ContainsKey(hashPair))
return geometricProductCache[hashPair];
MultiVector result;
if (e1.IsNullMetric || e2.IsNullMetric)
{
MultiVector m1 = e1.ToMinkowskiMetric();
MultiVector m2 = e2.ToMinkowskiMetric();
result = (m1 * m2).ToNullMetric();
}
else
{
int rBitMask = e1.bitMask ^ e2.bitMask;
double rValue = Basis.Order(e1, e2);
int common = e1.bitMask & e2.bitMask;
int i = 0;
while (common != 0)
{
if ((common & 0x1) != 0)
rValue *= Basis.minkowskiSignature[i];
common >>= 1;
i++;
}
result = new Blade(new Basis(rBitMask, false), rValue);
}
geometricProductCache.Add(hashPair, result);
return result;
}
public static int DisplayOrder(Basis e1, Basis e2)
{
if (e1.Grade != e2.Grade)
{
return e1.Grade - e2.Grade;
}
else
{
return (int)(e1.bitMask - e2.bitMask);
}
}
public static MultiVector GeometricProduct(Blade b1, Blade b2)
{
return((b1.Value * b2.Value) * Basis.GeometricProduct(b1.Basis, b2.Basis));
}
public MultiVector ToMinkowskiMetric()
{
if (!this.IsNullMetric)
return this;
if (this.Contains(Basis.EPLANE))
return this;
int b = this.bitMask & ~Basis.EPLANE.bitMask;
Basis bp = new Basis(b | Basis.EPLUS.bitMask, false);
Basis bm = new Basis(b | Basis.EMINUS.bitMask, false);
if (this.Contains(Basis.E0))
return 0.5 * (bm + bp);
if (this.Contains(Basis.E8))
return bm - bp;
// not possible
return this;
}
public static bool IsCompatible(Basis e1, Basis e2)
{
return(!(e1.IsNullMetric && e2.IsMinkowskiMetric ||
e1.IsMinkowskiMetric && e2.IsNullMetric));
}
public static int GetHashPair(Basis e1, Basis e2)
{
return((e1.GetHashCode() << 16) | e2.GetHashCode());
}
public static Blade operator ^(Basis e1, Basis e2)
{
return(Basis.OuterProduct(e1, e2));
}
public static MultiVector operator *(Basis e1, Basis e2)
{
return(Basis.GeometricProduct(e1, e2));
}
public Blade(Basis basis, double value)
{
this.basis = basis;
this.value = value;
}
public override string ToString()
{
string basis = this.Basis.ToString();
return((basis != "") ? "(" + Value.ToString() + "*" + Basis.ToString() + ")" : "(" + Value.ToString() + ")");
}
public static Blade InnerProduct(Blade b1, Blade b2)
{
return((b1.Value * b2.Value) * Basis.InnerProduct(b1.Basis, b2.Basis));
}
public static Blade OuterProduct(Basis e1, Basis e2)
{
int hashPair = Basis.GetHashPair(e1, e2);
if (outerProductCache.ContainsKey(hashPair))
return outerProductCache[hashPair];
Blade result;
if (e1.IsNullMetric || e2.IsNullMetric)
{
MultiVector m1 = e1.ToMinkowskiMetric();
MultiVector m2 = e2.ToMinkowskiMetric();
result = (Blade)(m1 ^ m2).ToNullMetric();
}
else
{
if ((e1.bitMask & e2.bitMask) == 0)
result = (Blade)(e1 * e2);
else
result = Blade.Zero;
}
outerProductCache.Add(hashPair, result);
return result;
}
public bool Contains(Basis basis)
{
if (!Basis.IsCompatible(this, basis))
return false;
return (this.bitMask & basis.bitMask) == basis.bitMask;
}
public double this[Basis basis]
{
get
{
if (blades.ContainsKey(basis))
return blades[basis].Value;
else
return 0.0;
}
set
{
// HACK
if (Math.Abs(value) < 1E-3)
{
if (blades.ContainsKey(basis))
blades.Remove(basis);
}
else
{
if (blades.ContainsKey(basis))
blades[basis] = new Blade(basis, value);
else
blades.Add(basis, new Blade(basis, value));
}
}
}
public MultiVector ToNullMetric()
{
if (!this.IsMinkowskiMetric)
return this;
if (this.Contains(Basis.EPLANE))
return this;
int b = this.bitMask & ~Basis.EPLANE.bitMask;
Basis b0 = new Basis(b | Basis.E0.bitMask, true);
Basis b8 = new Basis(b | Basis.E8.bitMask, true);
if (this.Contains(Basis.EPLUS))
return b0 - 0.5 * b8;
if (this.Contains(Basis.EMINUS))
return b0 + 0.5 * b8;
return this;
}
public Blade(Basis basis, double value)
{
this.basis = basis;
this.value = value;
}
