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": [],
     "prompt_number": 79
    },
    {
     "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": 134,
       "text": [
        "a__2*e1 + a__1*e2"
       ]
      }
     ],
     "prompt_number": 134
    },
    {
     "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",
      "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": 135,
       "text": [
        "a__3*e1 + a__2*e2 + a__1*e3"
       ]
      }
     ],
     "prompt_number": 135
    },
    {
     "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*(e1-e4)\n",
      "m = sqrt(2)/2*(e2-e3)\n",
      "\n",
      "m*n*a*n*m"
     ],
     "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": 161,
       "text": [
        "a__4*e1 + a__3*e2 + a__2*e3 + a__1*e4"
       ]
      }
     ],
     "prompt_number": 161
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "5D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(ga,e1,e2,e3,e4, e5) = Ga.build('e1 e2 e3 e4 e5',g=[1,1,1,1,1])\n",
      "a=ga.mv('a','vector')\n",
      "n = sqrt(2)/2*(e1-e5)\n",
      "m = sqrt(2)/2*(e2-e4)\n",
      "\n",
      "m*n*a*n*m"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation*} a^{5} e_{1} + a^{4} e_{2} + a^{3} e_{3} + a^{2} e_{4} + a^{1} e_{5} \\end{equation*}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 163,
       "text": [
        "a__5*e1 + a__4*e2 + a__3*e3 + a__2*e4 + a__1*e5"
       ]
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "6D"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(ga,e1,e2,e3,e4, e5, e6) = Ga.build('e1 e2 e3 e4 e5 e6',g=[1,1,1,1,1,1])\n",
      "a=ga.mv('a','vector')\n",
      "n = sqrt(2)/2*(e1-e6)\n",
      "m = sqrt(2)/2*(e2-e5)\n",
      "o = sqrt(2)/2*(e3-e4)\n",
      "\n",
      "-m*n*o*a*o*n*m"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation*} a^{6} e_{1} + a^{5} e_{2} + a^{4} e_{3} + a^{3} e_{4} + a^{2} e_{5} + a^{1} e_{6} \\end{equation*}"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 164,
       "text": [
        "a__6*e1 + a__5*e2 + a__4*e3 + a__3*e4 + a__2*e5 + a__1*e6"
       ]
      }
     ],
     "prompt_number": 164
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}