diff --git a/computations/projector_after_commute_C_L.ipynb b/computations/projector_after_commute_C_L.ipynb
new file mode 100644
index 0000000..1a3fda5
--- /dev/null
+++ b/computations/projector_after_commute_C_L.ipynb
@@ -0,0 +1,261 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$\\displaystyle \\left[ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & i\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & -1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right]\\right]$"
+      ],
+      "text/plain": [
+       "⎡⎡√2   √2 ⎤                  ⎡ √2     √2  ⎤  ⎡√2   √2⋅ⅈ ⎤           ⎡ √2   √2⋅\n",
+       "⎢⎢──   ── ⎥                  ⎢ ──     ──  ⎥  ⎢──   ──── ⎥           ⎢ ──   ───\n",
+       "⎢⎢2    2  ⎥  ⎡1  0⎤  ⎡1  0⎤  ⎢ 2      2   ⎥  ⎢2     2   ⎥  ⎡1  0 ⎤  ⎢ 2     2 \n",
+       "⎢⎢        ⎥, ⎢    ⎥, ⎢    ⎥, ⎢            ⎥, ⎢          ⎥, ⎢     ⎥, ⎢         \n",
+       "⎢⎢√2  -√2 ⎥  ⎣0  ⅈ⎦  ⎣0  1⎦  ⎢√2⋅ⅈ  -√2⋅ⅈ ⎥  ⎢√2  -√2⋅ⅈ ⎥  ⎣0  -1⎦  ⎢√2⋅ⅈ   √2\n",
+       "⎢⎢──  ────⎥                  ⎢────  ──────⎥  ⎢──  ──────⎥           ⎢────   ──\n",
+       "⎣⎣2    2  ⎦                  ⎣ 2      2   ⎦  ⎣2     2   ⎦           ⎣ 2     2 \n",
+       "\n",
+       "ⅈ⎤  ⎡√2  -√2 ⎤           ⎡ √2   -√2 ⎤  ⎡√2  -√2⋅ⅈ ⎤  ⎡ √2   -√2⋅ⅈ ⎤  ⎡1   ⅈ  1\n",
+       "─⎥  ⎢──  ────⎥           ⎢ ──   ────⎥  ⎢──  ──────⎥  ⎢ ──   ──────⎥  ⎢─ + ─  ─\n",
+       " ⎥  ⎢2    2  ⎥  ⎡1  0 ⎤  ⎢ 2     2  ⎥  ⎢2     2   ⎥  ⎢ 2      2   ⎥  ⎢2   2  2\n",
+       " ⎥, ⎢        ⎥, ⎢     ⎥, ⎢          ⎥, ⎢          ⎥, ⎢            ⎥, ⎢        \n",
+       " ⎥  ⎢√2   √2 ⎥  ⎣0  -ⅈ⎦  ⎢√2⋅ⅈ  √2⋅ⅈ⎥  ⎢√2   √2⋅ⅈ ⎥  ⎢√2⋅ⅈ   -√2  ⎥  ⎢1   ⅈ  1\n",
+       " ⎥  ⎢──   ── ⎥           ⎢────  ────⎥  ⎢──   ──── ⎥  ⎢────   ──── ⎥  ⎢─ - ─  ─\n",
+       " ⎦  ⎣2    2  ⎦           ⎣ 2     2  ⎦  ⎣2     2   ⎦  ⎣ 2      2   ⎦  ⎣2   2  2\n",
+       "\n",
+       "   ⅈ⎤  ⎡ √2   √2⎤          ⎡  √2     √2 ⎤          ⎡ 1   ⅈ   1   ⅈ⎤          ⎡\n",
+       " - ─⎥  ⎢ ──   ──⎥          ⎢  ──     ── ⎥          ⎢ ─ - ─   ─ + ─⎥          ⎢\n",
+       "   2⎥  ⎢ 2    2 ⎥  ⎡0  1⎤  ⎢  2      2  ⎥  ⎡0  1⎤  ⎢ 2   2   2   2⎥  ⎡0  ⅈ⎤  ⎢\n",
+       "    ⎥, ⎢        ⎥, ⎢    ⎥, ⎢            ⎥, ⎢    ⎥, ⎢              ⎥, ⎢    ⎥, ⎢\n",
+       "   ⅈ⎥  ⎢-√2   √2⎥  ⎣1  0⎦  ⎢-√2⋅ⅈ   √2⋅ⅈ⎥  ⎣ⅈ  0⎦  ⎢  1   ⅈ  1   ⅈ⎥  ⎣1  0⎦  ⎢\n",
+       " + ─⎥  ⎢────  ──⎥          ⎢──────  ────⎥          ⎢- ─ + ─  ─ + ─⎥          ⎢\n",
+       "   2⎦  ⎣ 2    2 ⎦          ⎣  2      2  ⎦          ⎣  2   2  2   2⎦          ⎣\n",
+       "\n",
+       "  √2    √2⋅ⅈ⎤  ⎡ 1   ⅈ     1   ⅈ⎤           ⎡  √2     -√2  ⎤  ⎡ 1   ⅈ   ⅈ⋅(-1 \n",
+       "  ──    ────⎥  ⎢ ─ - ─   - ─ + ─⎥           ⎢  ──     ──── ⎥  ⎢ ─ - ─   ──────\n",
+       "  2      2  ⎥  ⎢ 2   2     2   2⎥  ⎡0  -1⎤  ⎢  2       2   ⎥  ⎢ 2   2       2 \n",
+       "            ⎥, ⎢                ⎥, ⎢     ⎥, ⎢              ⎥, ⎢               \n",
+       "-√2⋅ⅈ   -√2 ⎥  ⎢  1   ⅈ    1   ⅈ⎥  ⎣1  0 ⎦  ⎢-√2⋅ⅈ   -√2⋅ⅈ ⎥  ⎢  1   ⅈ  ⅈ⋅(-1 \n",
+       "──────  ────⎥  ⎢- ─ + ─  - ─ + ─⎥           ⎢──────  ──────⎥  ⎢- ─ + ─  ──────\n",
+       "  2      2  ⎦  ⎣  2   2    2   2⎦           ⎣  2       2   ⎦  ⎣  2   2      2 \n",
+       "\n",
+       "+ ⅈ)⎤⎤\n",
+       "────⎥⎥\n",
+       "    ⎥⎥\n",
+       "    ⎥⎥\n",
+       "+ ⅈ)⎥⎥\n",
+       "────⎥⎥\n",
+       "    ⎦⎦"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import sympy\n",
+    "import numpy as np\n",
+    "\n",
+    "from collections import defaultdict\n",
+    "from itertools import product\n",
+    "\n",
+    "M = sympy.Matrix\n",
+    "simplify = sympy.simplify\n",
+    "sqrt = sympy.sqrt\n",
+    "i = sympy.I\n",
+    "i_ = i\n",
+    "\n",
+    "from sympy.physics.quantum import Dagger\n",
+    "from sympy.physics.quantum import tensorproduct\n",
+    "\n",
+    "sympy.init_printing()\n",
+    "H = simplify(M([[1, 1], [1, -1]]) / sqrt(2))\n",
+    "S = M([[1, 0], [0, i]])\n",
+    "C_L = [H, S]\n",
+    "basis_vectors = [M([1, 0]), M([0, 1])]\n",
+    "\n",
+    "def getitem(m, i, j):\n",
+    "    # Note that sympy uses an extremely weird way to store the matrices,\n",
+    "    # in particular the internal representation is vastly different from what\n",
+    "    # is printed. For instance the H matrix is stored as a Mul object\n",
+    "    # (even after using simplify) instead of a matrix. \n",
+    "    # Therefore m[i][j] will NOT work. This is a workaround.\n",
+    "    return (Dagger(basis_vectors[i]) * m * basis_vectors[j])[0]\n",
+    "\n",
+    "def is_known(C_L, a):\n",
+    "    for c in C_L:\n",
+    "        test = c * Dagger(a)\n",
+    "        if(simplify(getitem(test, 0, 1)) != 0):\n",
+    "            continue\n",
+    "        if(simplify(getitem(test, 0, 0) / getitem(test, 1, 1)) == 1):\n",
+    "            return True\n",
+    "    return False\n",
+    "for i in range(5):\n",
+    "    for m in (H, S):\n",
+    "        for c in C_L:\n",
+    "            c = simplify(c*m)\n",
+    "            if(is_known(C_L, c)):\n",
+    "                continue\n",
+    "            C_L.append(c)\n",
+    "C_L"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "⎡1  0 ⎤\n",
+       "⎢     ⎥\n",
+       "⎣0  -1⎦"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Z = C_L[5]\n",
+    "Z"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$\\displaystyle \\left[ \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & i\\\\- i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & i\\\\- i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & -1\\\\-1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & -1\\\\-1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}-1 & 0\\\\0 & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}-1 & 0\\\\0 & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & i\\\\- i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}-1 & 0\\\\0 & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & i\\\\- i & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & -1\\\\-1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}-1 & 0\\\\0 & 1\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & -1\\\\-1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right]\\right]$"
+      ],
+      "text/plain": [
+       "⎡⎡0  1⎤  ⎡1  0 ⎤  ⎡1  0 ⎤  ⎡0  1⎤  ⎡0   ⅈ⎤  ⎡1  0 ⎤  ⎡0   ⅈ⎤  ⎡0   -1⎤  ⎡1  0 \n",
+       "⎢⎢    ⎥, ⎢     ⎥, ⎢     ⎥, ⎢    ⎥, ⎢     ⎥, ⎢     ⎥, ⎢     ⎥, ⎢      ⎥, ⎢     \n",
+       "⎣⎣1  0⎦  ⎣0  -1⎦  ⎣0  -1⎦  ⎣1  0⎦  ⎣-ⅈ  0⎦  ⎣0  -1⎦  ⎣-ⅈ  0⎦  ⎣-1  0 ⎦  ⎣0  -1\n",
+       "\n",
+       "⎤  ⎡0   -1⎤  ⎡0  -ⅈ⎤  ⎡0  -ⅈ⎤  ⎡0  -ⅈ⎤  ⎡0  1⎤  ⎡-1  0⎤  ⎡0  1⎤  ⎡-1  0⎤  ⎡0  \n",
+       "⎥, ⎢      ⎥, ⎢     ⎥, ⎢     ⎥, ⎢     ⎥, ⎢    ⎥, ⎢     ⎥, ⎢    ⎥, ⎢     ⎥, ⎢   \n",
+       "⎦  ⎣-1  0 ⎦  ⎣ⅈ  0 ⎦  ⎣ⅈ  0 ⎦  ⎣ⅈ  0 ⎦  ⎣1  0⎦  ⎣0   1⎦  ⎣1  0⎦  ⎣0   1⎦  ⎣-ⅈ \n",
+       "\n",
+       " ⅈ⎤  ⎡-1  0⎤  ⎡0   ⅈ⎤  ⎡0   -1⎤  ⎡-1  0⎤  ⎡0   -1⎤  ⎡0  -ⅈ⎤⎤\n",
+       "  ⎥, ⎢     ⎥, ⎢     ⎥, ⎢      ⎥, ⎢     ⎥, ⎢      ⎥, ⎢     ⎥⎥\n",
+       " 0⎦  ⎣0   1⎦  ⎣-ⅈ  0⎦  ⎣-1  0 ⎦  ⎣0   1⎦  ⎣-1  0 ⎦  ⎣ⅈ  0 ⎦⎦"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "resulting_matrices = [simplify(Dagger(C)*Z*C) for C in C_L]\n",
+    "resulting_matrices"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALYAAAAzCAYAAAA6jfJvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAILUlEQVR4Ae2djVHcOBTHIUMBDOkAOiBHBYEOLrkKQjq4DBVkSAfcVXBHOoBUwIUOoIMQOuD+P0XPY3tlr3ct+WNXmhFry9L7+Pv56UmWxe7Ly8tOn7S7u7sfai+6z6HyqZVNSf4pyTLUfUql86suCoj5tfJpQ93vKv9Zy5cNdadYfF2THV0oGyPNHct1MOuMPw+B8g2/yxgtNWwRgfGNPPBtC7EzXd8t5Y8tdSd1STJXZJdwY8tekUfyjS1P0vu1Cv6qSxTwSfnbMuNuNWxv1I8i+FdS7TLxjEBHBGSL96r6WZnerTHtNV2RUZ/r2rEIvWuq07VctCw0+aE2R8qXovvYtX3feuJ/LBr0PG/Edxaxf5POY2PZJFfXcsn/p+oe6T6s3ROp7VfROVO+1nHQPoOGrQaHYn6l/KarwE31RIsn6zPCUEfnxEff9UuXm8y4PZ+/xetJ+TdldJp1GgvLyKBh0M4W+tCV7XwUHg/K5zpeiCiaQpEbMf2iBrj9tRNM1XhfdApFdIzH5JwHJ1mCj/I7ZYD8JxmjgQiPiWVMFXU/8NbEyTESdC6FDc6ykhYM2wN4EIk53UTo4bhT+WlIoIp0+aSMQMayjIaOZaM4SHp9C3WLGguG7SstuPaixWoHTBESCtSTxblNU4j1+vlcjkAgZCwXLQGvfS4nWQk1K4atiwT2uHVGnb1SR2980IvJljSeO5bIj20pX/Eb87bJazMNTVRQCW8qhq2LLrBXZfOofWQwow3RMs/DQ5TTcgTmjuWFbOqL1GRm6mK5uivXwBHjtQt7KgxbhUyJ4c57e+sVxHq9Qt1ctR2BSWIpu8KmGFORGCekmAmzl4dMVrhUnu7jSWImAbceI5lXDtEyD8S8dk7LERgVS+8Jv0nMwiMuF3mHGSls6Um/NiuG4VVChg50llYR/WfJiHETcdAz7JQNm8GJWT7XeiXPDBohMKwsxdPbS+4pNh4bS/gLl7Xeafi2vL/43WMba2KifqsIc4jhD8Xz0YUiOiEMwdiYv46ZeFDoiurJPHa0B6nOYAPP544lEcFXM/QE9+dfTxMHveMMW79/+MLYhsZTxFu/euLpv0+oZJ3fJpzPFks5TpwmztO9KNP5wrxz3xvkbYme5QxaZtgwJb6OGhqIHt3OkxSxbsheqb9X+QflnDoiMHMsnXOTDqzxoAd/6Kj2qtX+UwNsuYixYUxhioR3vvAKQf9E+a2UjDVIhWYwiSdeDm9hvQZrVOB7J/5ukBFsON3C0bDsA4mwvhXuZOawcaCp4mzurQtF9sSMG0+O6q1FzyUpQfcQfSTsybf+iDfTSxuTxsSyL4iS3YUIfeksae96Atn0KaEIXQMpVffwi3r+mxFIj4BFHcdlw07isdPrkjlkBAoEzIaPMGyberPColY+yAjMCQEfqiHyAYZNfE0iFs4pI7AJCOxj2K+9Jk+boFHWYesRwEFXPPbWI5IB2AgEcNDOY7sYuxSfbIR2WYmtRsB57K1GICu/mQgQY7vY2r+o2Uwts1bbhsAThm2zITbtt20g9NI3O4Re8KVojB0/sx7bFvvbtF8KZix+OhZh1m4MummN+NpKsuib9Xij/qlfViqyjmPQJL6svei1+UwsgVPivIaMjxi2eew12rc38Td+tE1rxD/pZj0MuMWDF1t8rLo/wgDcfaPafhfSX02N84oa4KCfMGybv44eivgb7RYiSXm8C157kCR+wc16VM5nSmzWE2VRjnQ8Es1iWe4gynkm8B6SX4jXUDiHeNfLJItFHc/E2PYq/bBecebnPFD3AR3uVBZ7s56TEbx1QLVRiobEeZmCZsM/XumG2M0fPEZcJmXP66zLtd6oTMpCL673Tt5L2DilN70ZEhgE5464mGG7GJs2eG1bjN+RxnSrlbqkNiFjhV7v5RwG+2jB60aYRRjyMCTvOpgD41xnHzo3w75/5a/ita0w1GBuZWa05p3L8psXt3isfG3lYxlWqq9BmmRJvflME99Q+WA4h5gHyk4o0z359ZW6jvk63Y3subAlyRZ/zUZdeUicD2MEErGtjY9cwUT/DIkzYZH7IN08tn15ECXunADA5pVDopiXmWNcXN98xn31HVJyoLLJ4Owfenpht4WIM2y5bkIRum3bhmEgXNKwkT4WgoTCDSubg7erAGR66Sba9OLQYVBQHhUapuXrVjYUzuaUmc4ttl/gmA1H7CLnc09z32CmDf/Um8+08a5fmwrOvJfg/yW5B8lCEYR1WxXIG2yKcaNPaKaHac3Zbtaj+4MnPFZOtvmMaK+SpoIzvRgv3lwqDFuWzpOHtTMomX2SPpu6WY97WKVf6s1nOtnAFHDWw267rBah2V5NehYMsbHfJwn8XLu21qlouZ5Ajc17DrlpDd55lM161gKrQyPdl6E2n+kgTVFlbJzZt6ayL2DFsHn6ZIgYNzFclE1uRHO0HsA/nFH0KG7hBA6kV5R1LrFUGRNn2Suh86FyBZMiFCkpiSHwbxVsVFu6lA8zApNDwLx1ZfZlwbD19BGnMP2H184pIzBZBLy3xmN/qAu5YNi+AhUX/hNTvXE+zwiMjADjN/5zwsJ4MGjYqojH5n/R0DCnjMDkEJC3xjZvZavuhUxdwKBhU0kNWLH2KAIMJnPKCEwGAdkkc9b8S47GiYnKrEhdchqKyI1y8P9Vl+ofqk5lsKm2C91Dqf5kDutyS7CKHiMIOlss18FqVfxVn5dTjP/etvKTAeKdW7MIsLDkNFRP5Ww//FLLV6G6UyyT3OhWl/9mDFklx6yxXAezVfBXXZwO37HyfWmrzf4Pa6TvwXQmOPQAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$\\displaystyle \\left( \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right]\\right)$"
+      ],
+      "text/plain": [
+       "⎛⎡0  1⎤  ⎡0  -ⅈ⎤⎞\n",
+       "⎜⎢    ⎥, ⎢     ⎥⎟\n",
+       "⎝⎣1  0⎦  ⎣ⅈ  0 ⎦⎠"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "X = C_L[14]\n",
+    "Y = i_ * C_L[21]\n",
+    "X, Y"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "matrices = [Z, Y, X, -Z, -Y, -X]\n",
+    "\n",
+    "def get_matrix_index(m):\n",
+    "    for i,p in enumerate(matrices):\n",
+    "        if(simplify(m - p) == M([[0, 0], [0, 0]])):\n",
+    "            return i\n",
+    "    raise ValueError()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/latex": [
+       "$\\displaystyle \\left[ 2, \\  0, \\  0, \\  2, \\  4, \\  0, \\  4, \\  5, \\  0, \\  5, \\  1, \\  1, \\  1, \\  2, \\  3, \\  2, \\  3, \\  4, \\  3, \\  4, \\  5, \\  3, \\  5, \\  1\\right]$"
+      ],
+      "text/plain": [
+       "[2, 0, 0, 2, 4, 0, 4, 5, 0, 5, 1, 1, 1, 2, 3, 2, 3, 4, 3, 4, 5, 3, 5, 1]"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "resulting_indices = [get_matrix_index(m) for m in resulting_matrices]\n",
+    "resulting_indices"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}