public static Blade InnerProduct(Basis e1, Basis e2)
{
int hashPair = Basis.GetHashPair(e1, e2);
if (innerProductCache.ContainsKey(hashPair))
{
return(innerProductCache[hashPair]);
}
Blade result;
if (e1.IsNullMetric || e2.IsNullMetric)
{
MultiVector m1 = e1.ToMinkowskiMetric();
MultiVector m2 = e2.ToMinkowskiMetric();
result = (Blade)MultiVector.InnerProduct(m1, m2).ToNullMetric();
}
else
{
if ((e1.bitMask & ~e2.bitMask) == 0)
{
result = (Blade)(e1 * e2);
}
else
{
result = Blade.Zero;
}
}
innerProductCache.Add(hashPair, result);
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);
}