Linq and Cross Products

Question

I am trying to perform a Calculus Cross Product calculation using Linq and trying to figure out the pattern for the below code:

static void Main(string[] args)
    {
        double[] a = { 1, -1, -1 };
        double[] b = {.5,1,.5};

        var cross = from x in a
                    from y in b
                    select new {x,y};
        List<double> LeftSide = new List<double>();

        foreach (var c in cross) {             
            Console.WriteLine("x = " + c.x + " y = " + c.y);
            double res = c.x * c.y;
            Console.WriteLine("");
            LeftSide.Add(res);
        }

        double i = LeftSide[5] - LeftSide[7];
        double j = LeftSide[2] - LeftSide[6];
        double k = LeftSide[1] - LeftSide[3];
        Console.WriteLine("("+ i + "i) - (" + j + "j) +(" + k + "k)"  );
        Console.ReadLine();
    }

Once I cross join the a and b, I need to perform the following calculations:

  double i = LeftSide[5] - LeftSide[7];
  double j = LeftSide[2] - LeftSide[6];
  double k = LeftSide[1] - LeftSide[3];

This works and I get the desired output, put I know it can be written more efficiently. I am looking for any suggestions, to point me in the right direction.

Note: This is not a homework question, but is related to Calculus III Cross Products. I am a CS Major

Answer 1

You are making this way, way, way too complicated. The cross product of vectors (a0, a1, a2) and (b0, b1, b2) is (a1 * b2 - a2 * b1, a2 * b0 - a0 * b2, a0 * b1 - a1 * b0). So just compute that:

double[] a = { 1.0, -1.0, -1.0 };         
double[] b = { 0.5,  1.0,  0.5 };
double[] cross = 
{ 
    a[1] * b[2] - a[2] * b[1], 
    a[2] * b[0] - a[0] * b[2], 
    a[0] * b[1] - a[1] * b[0]
};

And you're done in a single statement. There's no need to involve LINQ.

Answer 2

You are defining cross as a sequence of {x,y} elements, only to convert it to a sequence of x*y elements in the next step. This is redundant; you could generate your LeftSide immediately using:

double[] a = { 1, -1, -1 };
double[] b = { .5, 1, .5 };

var LeftSide =
    (
        from x in a
        from y in b
        select x * y
    ).ToArray();