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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Object Oriented CGA "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This is a shelled out demo for a object-oriented approach to CGA with `clifford`.  The `CGA` object holds the original layout for an arbitrary geometric algebra , and the conformalized version. It provides up/down projections, as well as easy ways to generate objects and operators. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick Use Demo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0^e1235)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from clifford.cga import CGA, Sphere, Translation\n",
    "from clifford import Cl\n",
    "\n",
    "ga,blades = Cl(3)     #  you can change  dimensions\n",
    "cga = CGA(ga)\n",
    "\n",
    "locals().update(ga.blades)        # put ga's blades in local namespace\n",
    "\n",
    "C = cga.sphere(e1,e2,e3,-e2)      # generate unit sphere from points \n",
    "C.mv                              # any CGA object/operator has a multivector repr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1.0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cga.down(C.center),C.radius # some properties of spheres"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0^e1) + (1.0^e2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = cga.translation(e1+e2) # make a translation \n",
    "C_ = T(C)                  # translate the sphere \n",
    "cga.down(C_.center)        # compute center again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<clifford.cga.Translation at 0x7f55e0eea358>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cga.sphere()      #  no args == random sphere \n",
    "cga.translation() #             random translation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  more details "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objects "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vectors "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.11758^e1) - (1.49541^e2) - (0.77589^e3)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = cga.lower_vector() # exists in ga,  not cga \n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.11758^e1) - (1.49541^e2) - (0.77589^e3) + (1.54362^e4) + (2.54362^e5)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = cga.up(a) # exists in  cga, not ga \n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_ = cga.down(A) # back in ga\n",
    "assert(a_.layout ==a.layout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-(0.66034^e1) - (1.36113^e2) - (1.71379^e3) + (2.1129^e4) + (3.1129^e5)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cga.null_vector()  # create null vector directly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sphere (point pair, circles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0^e125)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = cga.sphere(e1, e2,-e1,e3) # generates sphere from points\n",
    "C = cga.sphere(e1, e2,-e1)    # generates circle from points\n",
    "C2 = cga.sphere(2)            # random 2-sphere  (sphere)\n",
    "C1 = cga.sphere(1)            # random 1-sphere, (circle)\n",
    "C0 = cga.sphere(0)            # random 0-sphere, (point pair)\n",
    "\n",
    "cga.down(C1.center)\n",
    "C.mv                       # access the multivector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-(1.0^e4) + (1.0^e5)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.center         # spheres have properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cga.down(C.center) == C.center_down #down projected center"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0 - (0.5^e14) - (0.5^e15)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = cga.translation(e1) # generate translation \n",
    "T.mv "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-(0.5^e1234) + (0.5^e1235) + (1.0^e2345)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T.mv*C.mv*~T.mv         # translate a sphere "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-(0.5^e1234) + (0.5^e1235) + (1.0^e2345)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T(C).mv                 # shorthand call, same as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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