{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from vecs import *\n",
    "from sympy import *\n",
    "import random\n",
    "init_printing(use_unicode=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1\n",
    "b = -1\n",
    "v1 = Vector(2,1,1)\n",
    "v2 = Vector(0,1,1)\n",
    "\n",
    "v3 = a * v1 + b * v2\n",
    "\n",
    "v3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "draw(\n",
    "    arrow(a * v1, color='blue'),\n",
    "    arrow(b * v2, start=v1, color='red'),\n",
    "    arrow(v3, color='green'),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "marks = []\n",
    "v1 = Vector(1,3,1)\n",
    "v2 = Vector(1,-1,2)\n",
    "\n",
    "a = 1\n",
    "b = -1\n",
    "v3 = a * v1 + b * v2\n",
    "marks.append(mark(v3))\n",
    "\n",
    "a = 2\n",
    "b = 3\n",
    "v3 = a * v1 + b * v2\n",
    "marks.append(mark(v3))\n",
    "\n",
    "a = 0\n",
    "b = 2.5\n",
    "v3 = a * v1 + b * v2\n",
    "marks.append(mark(v3))\n",
    "\n",
    "a = -1\n",
    "b = 3\n",
    "v3 = a * v1 + b * v2\n",
    "marks.append(mark(v3))\n",
    "\n",
    "\n",
    "for i in range(200):\n",
    "    a = random.random() * 3 - 1.5\n",
    "    b = random.random() * 3 - 1.5\n",
    "    v3 = a * v1 + b * v2\n",
    "    marks.append(mark(v3))\n",
    "\n",
    "\n",
    "draw(\n",
    "    marks,\n",
    "    arrow(a * v1, color='blue'),\n",
    "    arrow(b * v2, start=a * v1, color='red'),\n",
    "    #arrow(v3, color='green')\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}