SymmetricSpinors2D.ipynb

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   "source": [
    "### Spinors for Symmetric matrix , 2D for starters"
   ]
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   "id": "decreased-world",
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       "[(2.0^e1), (6.0^e2)]"
      ]
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   "source": [
    "\n",
    "from pylab import * \n",
    "from clifford import Cl\n",
    "\n",
    "l,b = Cl(sig=[-1,1,1],firstIdx=0)\n",
    "locals().update(b)\n",
    "\n",
    "up = lambda x: x + abs(x)*e0\n",
    "dn = lambda X: (X^e0)/e0\n",
    "    \n",
    "x = l.randomV()(e12)\n",
    "assert(dn(up(x))==x)\n",
    "\n",
    "d = 2           # size of smallest eigenval\n",
    "r = 3           # ratio of eigenval 1 to eigenval2\n",
    "\n",
    "\n",
    "B = up(e1)^up(e2)  # plane of rotation, squeeze map between e1,e2\n",
    "D = sqrt(d)*sqrt(sqrt(r))*e**(log(sqrt(r))/2*B) # the spinor\n",
    "\n",
    "Y = [dn(D*up(x)*~D) for x in [e1,e2]]\n",
    "Y"
   ]
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     "data": {
      "text/plain": [
       "array([[2., 0.],\n",
       "       [0., 6.]])"
      ]
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     "execution_count": 6,
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   "source": [
    "# Convert to a matrix \n",
    "X = e12.basis()\n",
    "y = array([float(x|y) for x in X for y in Y]).reshape(2,2)\n",
    "y"
   ]
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