DirectionalScalingInBalancedAlgebra.ipynb

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    "## G(n,n) ( balanced algebra)\n",
    "\n",
    "Implementation of directional scaling in G3, by using rotors in G(3,3)."
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       "(3.0^e1) + (8.0^e2) + (15.0^e3)"
      ]
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    "from clifford import Cl \n",
    "from pylab import *\n",
    "\n",
    "\n",
    "layout,blades = Cl(3,3)\n",
    "locals().update(blades)\n",
    "\n",
    "\n",
    "J1,J2,J3 = e14,e25,e36\n",
    "Js       = [J1,J2,J3] # list of J's\n",
    "J        = sum(Js)\n",
    "\n",
    "\n",
    "up = lambda x: x + (x|J ) # put it on the null cones\n",
    "dn = lambda x: x(e123)    # project back into original space\n",
    "\n",
    "x = 1*e1 + 2*e2 + 3*e3\n",
    "X = up(x)\n",
    "\n",
    "D  = e**(-log(sqrt(3))*J1 - log(sqrt(4))*J2- log(sqrt(5))*J3  )\n",
    "\n",
    "dn(D*X*~D)"
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