{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from clifford.g3c import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Metric\n",
    "print(e1*e1)\n",
    "print(e2*e2)\n",
    "print(e3*e3)\n",
    "print(e4*e4)\n",
    "print(e5*e5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example\n",
    "a = (2 + 5.7*e2)*(e1 + e3*e4)\n",
    "b = 5*e2 - 3.5*e1\n",
    "print(a)\n",
    "print(b)\n",
    "\n",
    "# Projection\n",
    "print(a(2))\n",
    "\n",
    "# Outer product\n",
    "print(a^b)\n",
    "\n",
    "# Inner product\n",
    "print(a|b)\n",
    "\n",
    "# Left contraction\n",
    "print(a.lc(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mapping points from euclidean to conformal \n",
    "b_up = up(5*e2 - 3.5*e1)\n",
    "print(b_up)\n",
    "\n",
    "# And back again\n",
    "print( down(b_up) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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