struct Vec example

struct Vec example.ipynb

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      "source": "using LinearAlgebra\n\nstruct Vec{T} x::T; y::T; z::T end\n\nfor op in (:+, :-)\n    @eval Base.$op(v::Vec) = Vec($op(v.x), $op(v.y), $op(v.z))\n    @eval Base.$op(v::Vec, w::Vec) = Vec($op(v.x, w.x), $op(v.y, w.y), $op(v.z, w.z))\nend\n\nfor op in (:*, :/)\n    @eval Base.$op(v::Vec, c) = Vec($op(v.x, c), $op(v.y, c), $op(v.z, c))\nend\n\nfor op in (:*, :\\)\n    @eval Base.$op(c, v::Vec) = Vec($op(c, v.x), $op(c, v.y), $op(c, v.z))\nend\n\nLinearAlgebra.dot(v::Vec, w::Vec) = v.x*w.x + v.y*w.y + v.z*w.z\nLinearAlgebra.cross(v::Vec, w::Vec) = Vec(v.y*w.z-v.z*w.y, v.z*w.z-v.x*w.z, v.x*w.y-v.y*w.x)\n\nBase.Vector(v::Vec) = [v.x, v.y, v.z]",
      "execution_count": 1,
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      "cell_type": "code",
      "source": "v = Vec(1, 2, 3)\nw = Vec(4, 5, 6)\n[+v, -v, v+w, v-w]",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/plain": "4-element Vector{Vec{Int64}}:\n Vec{Int64}(1, 2, 3)\n Vec{Int64}(-1, -2, -3)\n Vec{Int64}(5, 7, 9)\n Vec{Int64}(-3, -3, -3)"
          },
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    {
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      "cell_type": "code",
      "source": "[3v, v*3, v/3, 3\\v]",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/plain": "4-element Vector{Vec}:\n Vec{Int64}(3, 6, 9)\n Vec{Int64}(3, 6, 9)\n Vec{Float64}(0.3333333333333333, 0.6666666666666666, 1.0)\n Vec{Float64}(0.3333333333333333, 0.6666666666666666, 1.0)"
          },
          "metadata": {}
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      ]
    },
    {
      "metadata": {
        "trusted": true
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      "cell_type": "code",
      "source": "[dot(v, w), v⋅w, Vector(v)⋅Vector(w)]",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 4,
          "data": {
            "text/plain": "3-element Vector{Int64}:\n 32\n 32\n 32"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
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      "cell_type": "code",
      "source": "[cross(v, w), v×w, Vector(v)×Vector(w)]",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 5,
          "data": {
            "text/plain": "3-element Vector{Any}:\n Vec{Int64}(-3, 12, -3)\n Vec{Int64}(-3, 12, -3)\n [-3, 6, -3]"
          },
          "metadata": {}
        }
      ]
    },
    {
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      "source": "methods(cross)",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 6,
          "data": {
            "text/plain": "# 2 methods for generic function \"cross\":\n[1] cross(a::AbstractVector{T} where T, b::AbstractVector{T} where T) in LinearAlgebra at C:\\Julia-1.7.0-DEV\\share\\julia\\stdlib\\v1.7\\LinearAlgebra\\src\\generic.jl:310\n[2] cross(v::Vec, w::Vec) in Main at In[1]:19",
            "text/html": "# 2 methods for generic function <b>cross</b>:<ul><li> cross(a::<b>AbstractVector{T} where T</b>, b::<b>AbstractVector{T} where T</b>) in LinearAlgebra at <a href=\"file://C:/buildbot/worker/package_win64/build/usr/share/julia/stdlib/v1.7/LinearAlgebra/src/generic.jl\" target=\"_blank\">C:\\Julia-1.7.0-DEV\\share\\julia\\stdlib\\v1.7\\LinearAlgebra\\src\\generic.jl:310</a></li> <li> cross(v::<b>Vec</b>, w::<b>Vec</b>) in Main at In[1]:19</li> </ul>"
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    },
    {
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      "cell_type": "code",
      "source": "*(v, 3)",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": "Vec{Int64}(3, 6, 9)"
          },
          "metadata": {}
        }
      ]
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      "source": "",
      "execution_count": null,
      "outputs": []
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        "description": "struct Vec example",
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