// Exterior product (or wedge product)
/// <summary>Wedge multiply two multivectors a and b and add the result to c.</summary>
/// <param name="c">The exterior product of a and b will be added to this multivector.</param>
/// <returns>Returns c for chaining.</returns>
public static Multivector Wedge(Multivector a, Multivector b, ref Multivector c)
{
if (a.Space != b.Space || a.Space != c.Space)
{
throw new ArgumentException("Cannot wedge multiply two multivectors from different spaces.");
}
var space = a.Space;
var l = (ulong)a.Count;
for (ulong i = 0; i < l; i++)
{
for (ulong j = 0; j < l; j++)
{
if ((i & j) != 0)
{
continue; //skip linearly dependent components
}
var(e, sign) = space.BasisMultiply(i, j);
c[(int)e] += sign * a[(int)i] * b[(int)j];
}
}
return(c);
}
public Space(int positive, int negative = 0, int nil = 0) : this()
{
if (positive < 0 || negative < 0 || nil < 0)
{
throw new ArgumentOutOfRangeException();
}
var dimension = positive + negative + nil;
if (dimension <= 30)
{
Dimension = (int)dimension;
PositiveDimension = (int)positive;
NegativeDimension = (int)negative;
NilpotentDimension = (int)nil;
}
else
{
throw new ArgumentOutOfRangeException("The total dimension cannot be greater than 30.");
}
// “No one will ever need 34.3 T of memory.” —Bill Gates
SetUpConversionBetweenIndexAndBladeBasis();
Zero = new Multivector(this, ImmutableArray.CreateRange(Enumerable.Repeat(0.0, Dimension)));
}
public Multivector Subtract(Multivector M)
{
if (Space != M.Space)
{
throw new ArgumentException("Cannot subtract two multivectors from different spaces.");
}
for (int i = 0, l = Count; i < l; i++)
{
this[i] -= M[i];
}
return(this);
}
/// <summary>Multiply two multivectors a and b and add the result to c.</summary>
/// <param name="c">The result of multiplication will be added to this multivector.</param>
/// <returns>Returns c for chaining.</returns>
public static Multivector Multiply(Multivector a, Multivector b, ref Multivector c)
{
if (a.Space != b.Space || a.Space != c.Space)
{
throw new ArgumentException("Cannot multiply two multivectors from different spaces.");
}
var space = a.Space;
var l = (ulong)a.Count;
for (ulong i = 0; i < l; i++)
{
for (ulong j = 0; j < l; j++)
{
var(e, sign) = space.BasisMultiply(i, j);
c[(int)e] += sign * a[(int)i] * b[(int)j];
}
}
return(c);
}
public Multivector Wedge(Multivector M) => Wedge(this, M);
public static Multivector Involute(Multivector M) => (new Multivector(M.Space)).Copy(M).Involute();
public static Multivector Add(Multivector a, double b) => a.Clone().Add(b);
public static Multivector Wedge(Multivector a, Multivector b)
{
var c = new Multivector(a.Space);
return(Wedge(a, b, ref c));
}
public Multivector Mul(Multivector M) => Multiply(M);
public Multivector Multiply(Multivector M)
{
return(Multiply(this, M));
}
public static Multivector Mul(Multivector a, Multivector b) => Multiply(a, b);
public static Multivector Subtract(double a, Multivector b) => b.Clone().Negate().Add(a);
public static Multivector Negate(Multivector M) => M.Clone().Negate();
public static Multivector Add(double a, Multivector b) => b.Clone().Add(a);
public static Multivector Sub(Multivector a, double b) => Subtract(a, b);
public static Multivector Sub(double a, Multivector b) => Subtract(a, b);
public static Multivector Subtract(Multivector a, double b) => a.Clone().Sub(b);
public static Multivector Reverse(Multivector M) => M.Clone().Reverse();
public static Multivector Multiply(Multivector a, Multivector b)
{
var c = new Multivector(a.Space);
return(Multiply(a, b, ref c));
}
public static Multivector Conjugate(Multivector M) => M.Clone().Conjugate();
public Multivector Sub(Multivector M) => Subtract(M);
