public double this[Blade blade]
{
get
{
return(blade.Value * this[blade.Basis]);
}
set
{
this[blade.Basis] = blade.Value * value;
}
}
public static MultiVector InnerProduct(MultiVector v1, MultiVector v2)
{
MultiVector result = new MultiVector();
foreach (Blade b1 in v1.Blades)
{
foreach (Blade b2 in v2.Blades)
{
result += Blade.InnerProduct(b1, b2);
}
}
return(result);
}
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 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 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 double this[Blade blade]
{
get
{
return blade.Value * this[blade.Basis];
}
set
{
this[blade.Basis] = blade.Value * value;
}
}
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 Blade InnerProduct(Blade b1, Blade b2)
{
return((b1.Value * b2.Value) * Basis.InnerProduct(b1.Basis, b2.Basis));
}
public static MultiVector GeometricProduct(Blade b1, Blade b2)
{
return((b1.Value * b2.Value) * Basis.GeometricProduct(b1.Basis, b2.Basis));
}
public static Blade operator ^(Blade b1, Blade b2)
{
return(Blade.OuterProduct(b1, b2));
}
public static MultiVector operator *(Blade b1, Blade b2)
{
return(Blade.GeometricProduct(b1, b2));
}
public static Blade OuterProduct(Blade b1, Blade b2)
{
return (b1.Value * b2.Value) * Basis.OuterProduct(b1.Basis, b2.Basis);
}
public static MultiVector GeometricProduct(Blade b1, Blade b2)
{
return (b1.Value * b2.Value) * Basis.GeometricProduct(b1.Basis, b2.Basis);
}
