Lz のお話

Lz.ipynb

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     "data": {
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       "v\"1.7.2\""
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    "VERSION"
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   "source": [
    "using SymPy"
   ]
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       "(x, y, px, py, θ)"
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   "source": [
    "@vars x y px py θ"
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       "(x, y, px, py)"
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   "source": [
    "t = (x,y,px,py)"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lz (generic function with 2 methods)"
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   "source": [
    "Lz(x,y,px,py) = x * py - y * px\n",
    "Lz(t::Tuple) = Lz(t...)"
   ]
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     "data": {
      "text/plain": [
       "tfm1 (generic function with 2 methods)"
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   "source": [
    "tfm1(x,y,px,py) = px,py,-x,-y\n",
    "tfm1(t::Tuple) = tfm1(t...)"
   ]
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   "outputs": [],
   "source": [
    "@assert (Lz∘tfm1)(t) == Lz(t)\n",
    "@assert iszero((Lz∘tfm1)(t) - Lz(t)) # 差がゼロであることでも確認できる."
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       "tfm2 (generic function with 2 methods)"
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   "source": [
    "c = cos(θ)\n",
    "s = sin(θ)\n",
    "\n",
    "tfm2(x,y,px,py) = x*c+px*s,y*c+py*s,px*c-x*s,py*c-y*s\n",
    "tfm2(t::NTuple) = tfm2(t...)"
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   "outputs": [],
   "source": [
    "ex = (Lz∘tfm2)(t) - Lz(t)\n",
    "# sin^2 + cos^2 = 1 のルールで簡約化しないとゼロまで持っていけない.\n",
    "@assert ex |> expand |> simplify |> iszero"
   ]
  }
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