reverse a vector.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import * \n",
      "from galgebra.ga import Ga"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "2D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(ga,e1,e2) = Ga.build('e1 e2',g=[1,1])\n",
      "a=ga.mv('a','vector')\n",
      "\n",
      "n = sqrt(2)/2*(e1+e2)\n",
      "n*a*n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation*} a^{2} e_{1} + a^{1} e_{2} \\end{equation*}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "a__2*e1 + a__1*e2"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "3D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(ga,e1,e2,e3) = Ga.build('e1 e2 e3',g=[1,1,1])\n",
      "a=ga.mv('a','vector')\n",
      "\n",
      "n = sqrt(2)/2*(e1-e3)\n",
      "-n*a*n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation*} a^{3} e_{1} + a^{2} e_{2} + a^{1} e_{3} \\end{equation*}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 77,
       "text": [
        "a__3*e1 + a__2*e2 + a__1*e3"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "4D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(ga,e1,e2,e3,e4) = Ga.build('e1 e2 e3 e4',g=[1,1,1,1])\n",
      "a=ga.mv('a','vector')\n",
      "n = sqrt(2)/2*(e2-e3)\n",
      "m = sqrt(2)/2*(e1-e4)\n",
      "R = m*n\n",
      "R*a*R.rev()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation*} a^{4} e_{1} + a^{3} e_{2} + a^{2} e_{3} + a^{1} e_{4} \\end{equation*}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 78,
       "text": [
        "a__4*e1 + a__3*e2 + a__2*e3 + a__1*e4"
       ]
      }
     ],
     "prompt_number": 78
    }
   ],
   "metadata": {}
  }
 ]
}