Geometric algebra: Difference between revisions

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=={{header|C#|C sharp}}==

{{trans|D}}

<lang csharp>using System;

using System.Text;

namespace GeometricAlgebra {

struct Vector {

private readonly double[] dims;

public Vector(double[] da) {

dims = da;

}

public static Vector operator -(Vector v) {

return v * -1.0;

}

public static Vector operator +(Vector lhs, Vector rhs) {

var result = new double[32];

Array.Copy(lhs.dims, 0, result, 0, lhs.Length);

for (int i = 0; i < result.Length; i++) {

result[i] = lhs[i] + rhs[i];

}

return new Vector(result);

}

public static Vector operator *(Vector lhs, Vector rhs) {

var result = new double[32];

for (int i = 0; i < lhs.Length; i++) {

if (lhs[i] != 0.0) {

for (int j = 0; j < lhs.Length; j++) {

if (rhs[j] != 0.0) {

var s = ReorderingSign(i, j) * lhs[i] * rhs[j];

var k = i ^ j;

result[k] += s;//there is an index out of bounds here

}

}

}

}

return new Vector(result);

}

public static Vector operator *(Vector v, double scale) {

var result = (double[])v.dims.Clone();

for (int i = 0; i < result.Length; i++) {

result[i] *= scale;

}

return new Vector(result);

}

public double this[int key] {

get {

return dims[key];

}

set {

dims[key] = value;

}

}

public int Length {

get {

return dims.Length;

}

}

public Vector Dot(Vector rhs) {

return (this * rhs + rhs * this) * 0.5;

}

private static int BitCount(int i) {

i -= ((i >> 1) & 0x55555555);

i = (i & 0x33333333) + ((i >> 2) & 0x33333333);

i = (i + (i >> 4)) & 0x0F0F0F0F;

i += (i >> 8);

i += (i >> 16);

return i & 0x0000003F;

}

private static double ReorderingSign(int i, int j) {

int k = i >> 1;

int sum = 0;

while (k != 0) {

sum += BitCount(k & j);

k >>= 1;

}

return ((sum & 1) == 0) ? 1.0 : -1.0;

}

public override string ToString() {

var it = dims.GetEnumerator();

StringBuilder sb = new StringBuilder("[");

if (it.MoveNext()) {

sb.Append(it.Current);

}

while (it.MoveNext()) {

sb.Append(", ");

sb.Append(it.Current);

}

sb.Append(']');

return sb.ToString();

}

}

class Program {

static double[] DoubleArray(uint size) {

double[] result = new double[size];

for (int i = 0; i < size; i++) {

result[i] = 0.0;

}

return result;

}

static Vector E(int n) {

if (n > 4) {

throw new ArgumentException("n must be less than 5");

}

var result = new Vector(DoubleArray(32));

result[1 << n] = 1.0;

return result;

}

static readonly Random r = new Random();

static Vector RandomVector() {

var result = new Vector(DoubleArray(32));

for (int i = 0; i < 5; i++) {

var singleton = new double[] { r.NextDouble() };

result += new Vector(singleton) * E(i);

}

return result;

}

static Vector RandomMultiVector() {

var result = new Vector(DoubleArray(32));

for (int i = 0; i < result.Length; i++) {

result[i] = r.NextDouble();

}

return result;

}

static void Main() {

for (int i = 0; i < 5; i++) {

for (int j = 0; j < 5; j++) {

if (i < j) {

if (E(i).Dot(E(j))[0] != 0.0) {

Console.WriteLine("Unexpected non-null sclar product.");

return;

}

} else if (i == j) {

if ((E(i).Dot(E(j)))[0] == 0.0) {

Console.WriteLine("Unexpected null sclar product.");

}

}

}

}

var a = RandomMultiVector();

var b = RandomMultiVector();

var c = RandomMultiVector();

var x = RandomVector();

// (ab)c == a(bc)

Console.WriteLine((a * b) * c);

Console.WriteLine(a * (b * c));

Console.WriteLine();

// a(b+c) == ab + ac

Console.WriteLine(a * (b + c));

Console.WriteLine(a * b + a * c);

Console.WriteLine();

// (a+b)c == ac + bc

Console.WriteLine((a + b) * c);

Console.WriteLine(a * c + b * c);

Console.WriteLine();

// x^2 is real

Console.WriteLine(x * x);

}

}

}</lang>

{{out}}

<pre>[-2.7059639813936, -2.65443237395364, -1.03355975191747, 5.431067101183, 9.57183741787636, 7.41390675997241, -8.09043009371666, -7.30180304927878, -1.50642825479215, -4.14594595273162, -1.78857280373918, -0.484382016930444, -7.42401696794793, -4.78491995868705, -8.43252648860165, -4.47485336471182, -2.3458119817208, 3.6184495826099, -7.50802924695147, -2.10106278080463, 7.15782745037037, 7.60049996423655, -10.6945339837475, -6.9874232887485, -4.85603010723139, -9.8225346377117, 3.50534384939214, 3.08239272713895, -9.92019737517891, -10.1065306142574, -8.79795495448311, -4.01442257971653]

[-2.70596398139361, -2.65443237395364, -1.03355975191747, 5.43106710118299, 9.57183741787636, 7.41390675997241, -8.09043009371666, -7.30180304927878, -1.50642825479215, -4.14594595273162, -1.78857280373917, -0.484382016930444, -7.42401696794793, -4.78491995868705, -8.43252648860165, -4.47485336471182, -2.3458119817208, 3.6184495826099, -7.50802924695147, -2.10106278080463, 7.15782745037036, 7.60049996423655, -10.6945339837475, -6.9874232887485, -4.85603010723139, -9.8225346377117, 3.50534384939214, 3.08239272713894, -9.9201973751789, -10.1065306142574, -8.79795495448311, -4.01442257971653]

[-5.35792362178344, -2.83992055857095, -0.00435065203934659, 0.548701864561436, 7.31905167177133, 2.98280880755406, 2.54042778638867, -1.82513292511705, -4.07944497473881, -3.87206774796269, 2.05320674506366, 1.00599045579458, -3.72912260067605, -3.4226426940923, 1.62806109332525, 3.26554642532303, -2.2232872618717, -2.06401927877361, 3.31046340349916, 3.21397515180161, 4.84963949791875, 1.98923326842668, 2.28775873178049, -0.927084258496161, -3.99100687576943, -1.67065148926557, 2.70438629346319, 0.400654313359669, -0.74522009023782, 0.737528754412463, 4.53246775536051, 5.82111882775243]

[-5.35792362178344, -2.83992055857095, -0.0043506520393467, 0.548701864561437, 7.31905167177133, 2.98280880755406, 2.54042778638867, -1.82513292511705, -4.0794449747388, -3.87206774796269, 2.05320674506366, 1.00599045579458, -3.72912260067605, -3.4226426940923, 1.62806109332525, 3.26554642532303, -2.2232872618717, -2.06401927877361, 3.31046340349916, 3.21397515180161, 4.84963949791875, 1.98923326842668, 2.28775873178049, -0.92708425849616, -3.99100687576943, -1.67065148926557, 2.70438629346319, 0.40065431335967, -0.745220090237821, 0.737528754412463, 4.53246775536051, 5.82111882775243]

[-6.85152530876464, -2.6466613868296, -0.814269203555543, -2.63807771948643, 6.89540453623166, 4.70804372948965, 2.78512631505336, 2.03877626337364, -1.77047482836463, 1.52836763170898, 0.71565745873906, 0.886707645932111, -2.25661460785133, -1.08891196061849, 3.44949857952115, 5.8645384965889, -3.09249704978979, -1.41518183096078, 1.87603297737169, 2.45042504250642, 3.66908389117503, 1.85358883025892, 1.23206155683761, -0.216105143607701, -1.88866851071821, -0.131570581491294, 5.7355274883507, 4.22029797577044, -0.212906215521922, -0.323884694190184, 4.41630150883192, 5.94513377054442]

[-6.85152530876464, -2.6466613868296, -0.814269203555542, -2.63807771948643, 6.89540453623166, 4.70804372948965, 2.78512631505335, 2.03877626337364, -1.77047482836463, 1.52836763170898, 0.715657458739061, 0.886707645932111, -2.25661460785133, -1.08891196061849, 3.44949857952115, 5.8645384965889, -3.09249704978979, -1.41518183096078, 1.87603297737169, 2.45042504250642, 3.66908389117503, 1.85358883025892, 1.23206155683761, -0.216105143607701, -1.88866851071821, -0.131570581491294, 5.7355274883507, 4.22029797577044, -0.212906215521922, -0.323884694190183, 4.41630150883192, 5.94513377054442]