Invariants And CrossRatio2.ipynb

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   "execution_count": 45,
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   "source": [
    "import numpy as np\n",
    "from clifford.cga import CGA\n",
    "N=2\n",
    "cga = CGA(N)\n",
    "locals().update(cga.blades)\n",
    "\n",
    "v2c = lambda x: float(x|e1)+ float(x|e2)*1j\n",
    "c2v = lambda x: x.real*e1+ x.imag*e2\n",
    "cr = lambda a,b,c,d: (a-b)*(c-d)/\\\n",
    "                    ((a-d)*(c-b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
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     "data": {
      "text/plain": [
       "(-0.4436773975341889-0.03838763391718519j)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "w = np.random.rand(4)+  np.random.rand(4)*1j \n",
    "cr(*w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.44368 + (0.03839^e1234)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "a,b,c,d = map(cga.up, map(c2v, w))\n",
    "1 + (a*c*d*b)(0,4)/\\\n",
    "    (a*d*c*b)(0,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretty close,  but  would be nice to remove the conj(), and make sense of expression"
   ]
  }
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