01_presburger_sets.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import isl\n",
    "from plot.plotter import plot_set_points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# (Quasi) Affine Expressions \n",
    "\n",
    "<!-- An affine expression is recursively constructed from the following elements -->\n",
    "Quasi-affine表达式, 即通过常量、变量以及对应基础操作构成的表达式.\n",
    "\n",
    "**Base** \n",
    "- Constants ($(c_i)$) \n",
    "- Parameters ($(p_i)$) \n",
    "- Variables ($(v_i)$) \n",
    "\n",
    "**Operations** \n",
    "- Unary negation $( (-e) )$ \n",
    "- Addition $( ( e\\_0 + e\\_1 ) )$ \n",
    "- Multiplication by a constant $( (c * e) )$ \n",
    "- Constant division $( (e / c) )$ \n",
    "- Constant remainder $( (e \\mod c) )$ \n",
    "\n",
    "### Examples \n",
    "\n",
    "#### Valid Expressions \n",
    "\n",
    "- 42 \n",
    "- n, m \n",
    "- i, j \n",
    "- -i, 3 * i + 4 \n",
    "- i / 2, i % 3 \n",
    "\n",
    "#### Invalid Expressions \n",
    "\n",
    "- i * n, n * m \n",
    "- 5 / n, i % j "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Presburger Formula \n",
    "\n",
    "<!-- A Presburger Formula is a boolean combination of comparisons between (Quasi) Affine Expressions. It is recursively constructed from the following elements:  -->\n",
    "Presburger 公式就是affine表达式进行二元关系组合:\n",
    "\n",
    "**Base** \n",
    "- Boolean constants (&#8868;, &#8869;) \n",
    "\n",
    "**Operations** \n",
    "- Comparisions between quasi-affine expressions \n",
    "  \n",
    "  $(e0 \\oplus e1, \\oplus \\in)$ $\\{(<, \\le, =, \\ne, \\ge, >) \\}$ \n",
    "\n",
    "- Boolean operations between Presburger Formulas \n",
    "  \n",
    "  $(e0 \\otimes e1, \\otimes \\in)$ $\\{(\\land, \\lor, not, \\Rightarrow, \\Leftarrow, \\Leftrightarrow ) \\}$ \n",
    "\n",
    "- Quantified variables \n",
    "  \n",
    "  $( \\exists x: p(x, ...) )$  \n",
    "  \n",
    "  $( \\forall x: p(x, ...) )$  \n",
    "\n",
    "### Examples \n",
    "#### Valid Expressions \n",
    "\n",
    "- $1 < 0$\n",
    "- $(j + 3 \\le 0 \\land 0 \\le n)$  \n",
    "\n",
    "#### Invalid Expressions \n",
    "- 42 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Presburger Sets \n",
    "<!-- A Presburger Set S, is a set of integer vectors described by a Presburger formula. It is formally described as a set S = $( \\{ \\vec{v} \\mid \\vec{v} \\in \\mathbb{Z}^n : p (\\vec{v}, \\vec{p})\\} )$, where \"p\" is a Presburger Formular that evaluates to true, if a tuple $(\\vec{v})$ is element of S. -->\n",
    "\n",
    "Presburger 集合S, 是一个通过Presburger公式定义的整数向量集合. 通常$p$作为Presburger公式会被执行为true, 然后$(\\vec{v})$则是集合包含的所有元素."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Set \n",
    "\n",
    "<!-- A Basic Set is the simplest form of a Presburger Set and allows only Presburger Formula that describe a single convex (but possibly sparse) set.  -->\n",
    "Basic Set 是 Presburger Set的最简单形式,仅允许描述单个凸（但可能是稀疏）集的 Presburger 公式.\n",
    "\n",
    "<!-- The **space** of a set is defined by the dimensionality of the tuples it contains. A set containing pairs is called a two-dimensional space. Spaces can be **named**, which means a name is written in front of each tuple that allows to distinguish different spaces with identical dimensionality.  -->\n",
    "\n",
    "集合的**space**被tuple的维度定义.一个集合包含pair被称为2维space. \n",
    "\n",
    "\n",
    "### Examples \n",
    "\n",
    "<!-- The following two basic sets **Triangle** and **Square** describe an upper-left triangle as well as a square.  -->\n",
    "以下两个基本集合 **Triangle** 和 **Square** :\n",
    "\n",
    "- Triangle: $(\\{A[i,j] \\mid 0 < i < j < 10\\})$ \n",
    "\n",
    "- Square: $(\\{ A[i,j] \\mid 5 < i < 10 \\land 0 < j < 5 \\})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Triangle = isl.basic_set(\"{A[i,j] : 0 < i < j < 10}\")\n",
    "Square = isl.basic_set(\"{A[i,j] : 5 < i < 10 and 0 < j < 5}\")\n",
    "plot_set_points(Triangle,color='blue')\n",
    "plot_set_points(Square,color='orange')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparse Basic Sets \n",
    "\n",
    "<!-- In case the Presburger Formula describing the Basic Set contains modulo constraints, the set of points may become sparse. -->\n",
    "\n",
    "这个例子中展示了集合中存在取模约束,这样集合元素会变成稀疏的.\n",
    "\n",
    "### Example \n",
    "\n",
    "<!-- The basic set **Sparse** is a square where certain diagonals are excluded. -->\n",
    "basic set **Sparse** 是排除某些对角线的正方形."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Sparse = isl.basic_set(\"{A[i,j] : 0 < i,j < 10 and (i + j) % 3 != 0}\")\n",
    "plot_set_points(Sparse,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "a) Plot a set **UpperTriangle** with a base of width 7. \n",
    "\n",
    "```\n",
    "       x\n",
    "     x x x\n",
    "   x x x x x\n",
    " x x x x x x x\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = isl.basic_set(\"{A[x,y] : 0 <= x < 7 and 0 <= y < 4 and y <= x < 7-y }\")\n",
    "plot_set_points(s,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Plot a set **LowerTriangle** with a base of width 7 \n",
    "```\n",
    "x x x x x x x\n",
    "  x x x x x\n",
    "    x x x\n",
    "      x\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Xnl9jcfToUa1du1aHDh3S9OnTexzX3t6uSCTSZUlWS4vU0JDYgZTc8Q0N0sGDSe8aAxh9Ba/QW/CC3/sq4WCxfft25ebmKjs7W/Pnz9dzzz2nM844o8fxNTU1CgQCnUtpaWnSxba2Jr2pJCka7d/2GJjoK3iF3oIX/N5XCQeLSZMmqb6+Xps3b9btt9+uefPmaceOHT2OX7p0qcLhcOfS1NSUdLG5uUlvKknKy+vf9hiY6Ct4hd6CF/zeV/2+xuKKK67QxIkT9dhjj8U1nmss4Df0FbxCb8ELA/Yaiw7GGLW3t/f3n4mL40gLFiS37cKF/IKie/QVvEJvwQt+76uEZizuuecezZo1S6WlpYpGo1q7dq2WLVumV155RVdeeWVc/0Z/n7wZCkklJe4DP+K5zSYrSxo5UmpulgoKEt4dBgn6Cl6ht+CFdPSVJzMWH330kebOnatJkybp8ssv15YtWxIKFTYUFLiPJnUc90D1JivLHVdbyy8oekdfwSv0Frzg574a8J8VUlsrVVb2o2AMKvQVvEJvwQup7KsB/VkhkvthKs3N0vLl7sUoxyovd9fv2cMvKBJDX8Er9Ba84Me+ytgZi2MZ4z7wIxp1b6MpLOSiJ/QffQWv0Fvwgtd9Fe/791B7u0wfx5GKitwFsIW+glfoLXjBL32VsadCAACA/xAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFhDsAAAANYQLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFhDsAAAANYQLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFhDsAAAANYQLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANUPTXQDgV8ZILS1Sa6uUmysVFUmOk+6qMBDQW/CCX/qKGQvgOKGQtGKFVFEhjR4tlZW5f1ZUuOtDoXRXiExFb8ELfusrxxhjUrnDSCSiQCCgcDis/Pz8VO4a6FMwKFVXS4cPu18f+9vRkfxzcqR166SqqtTXh8xFb8ELqeyreN+/mbEA/l8wKM2eLbW1ub+cx0fujnVtbe64YDA9dSLz0Fvwgl/7KqFgUVNTo3PPPVd5eXkaM2aMrr32Wr3//vte1QakTCjkpn5jpFis97GxmDuuupqpa/SN3oIX/NxXCQWLDRs26I477tDmzZu1fv16ff7556qsrNShQ4e8qg9IidWr3anEvn5BO8Ri7vg1a7ytC5mP3oIX/NxX/brG4pNPPtGYMWO0YcMGffWrX41rG66xgN8Y417k1Nh44lRibxxHKi+Xdu7kin50j96CF9LVVym5xiIcDkuSCgsLexzT3t6uSCTSZQH8pKVFamhI7BdUcsc3NEgHD3pTFzIfvQUv+L2vkg4WxhgtWbJEF110kSZPntzjuJqaGgUCgc6ltLQ02V0Cnmht7d/20aidOjDw0Fvwgt/7Kulgceedd+rtt9/WM8880+u4pUuXKhwOdy5NTU3J7hLwRG5u/7bPy7NTBwYeegte8HtfJRUsFixYoBdffFGvv/66SkpKeh2bnZ2t/Pz8LgvgJ0VF0sSJiZ9zdBx3u17OBGKQo7fgBb/3VULBwhijO++8U7W1tXrttddUVlbmVV1AyjiOtGBBctsuXMjFdegZvQUv+L2vEror5Pvf/76efvppvfDCC5o0aVLn+kAgoJEjR8b1b3BXCPwoFJJKStwHycRz+1ZWljRypNTcLBUUeF0dMhm9BS+ko688uStk5cqVCofDuvTSSzVu3LjO5dlnn02uSsAnCgrcR946jvsL2JusLHdcbS0v/OgbvQUv+LmvEj4V0t1y6623elQekDpVVdLf/+6mesc5cbqwY93IkdJLL0mVlempE5mH3oIX/NpXfFYIcIyqKneqcPly90Eyxyovd9fv2cMLPxJHb8ELfuwrPt0U6IEx7oNkolH39qzCQi6mgx30FrzgdV/F+/491N4ugYHFcdzbuoqK0l0JBhp6C17wS19xKgQAAFhDsAAAANYQLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFhDsAAAANYQLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFhDsAAAANYQLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFhDsAAAANYMTXcBADDYGCO1tEitrVJurlRUJDlOuqtCpvNLXzFjAQApEgpJK1ZIFRXS6NFSWZn7Z0WFuz4USneFyER+6yvHGGNSucNIJKJAIKBwOKz8/PxU7hoA0iYYlKqrpcOH3a+PfeXt+F9lTo60bp1UVZX6+pCZUtlX8b5/M2MBAB4LBqXZs6W2NveF//j/znWsa2tzxwWD6akTmcWvfZVwsPjHP/6hq6++WuPHj5fjOHr++ec9KAsABoZQyP0fpTFSLNb72FjMHVddzWkR9M7PfZVwsDh06JC+8pWv6OGHH/aiHgAYUFavdqep+3rx7xCLuePXrPG2LmQ2P/dVv66xcBxHzz33nK699tq4t+EaCwCDhTHuBXSNjSdOU/fGcaTycmnnTu4WwYnS1Vfxvn97frtpe3u72tvbuxQGAINBS4vU0JD4dsa42x086N4yCBzL733l+cWbNTU1CgQCnUtpaanXuwQAX2ht7d/20aidOjCw+L2vPA8WS5cuVTgc7lyampq83iUA+EJubv+2z8uzUwcGFr/3leenQrKzs5Wdne31bgDAd4qKpIkTkz8XXljoXW3IXH7vK55jAQAecRxpwYLktl24kAs30T2/91XCwaK1tVX19fWqr6+XJO3atUv19fXavXu37doAIOPNm+c++TArzlfbrCx3/C23eFsXMpuf+yrhYLFt2zZNmTJFU6ZMkSQtWbJEU6ZM0U9/+lPrxQFApisocB+n7Dh9vwlkZbnjamvd7YCe+Lmv+KwQAEiBeD/TobZWqqxMfX3ITKnsKz4rBAB8pKpKam6Wli93L6A7Vnm5u37PHkIFEuPHvmLGAgBSzBj3IUXRqHvrX2EhF2qi/7zuK988eRMA0JXjuLcM8lRN2OSXvuJUCAAAsIZgAQAArCFYAAAAawgWAADAGoIFAACwhmABAACsIVgAAABrCBYAAMAaggUAALCGYAEAAKwhWAAAAGsIFgAAwBqCBQAAsIZgAQAArCFYAAAAawgWAADAGoIFAACwhmABAACsIVgAAABrCBYAAMAaggUAALCGYAEAAKwhWAAAAGsIFgAAwBqCBQAAsIZgAQAArCFYAAAAawgWAADAGoIFAACwhmABAACsIVgAAABrCBYAAMAaggUAALCGYAEAAKwhWAAAAGsIFgAAwBqCBQAAsIZgAQAArBma7gIAAED/GSO1tEitrVJurlRUJDlO6utgxgIAgAwWCkkrVkgVFdLo0VJZmftnRYW7PhRKbT0ECwAAMlQwKJWUSIsXS42NXb/X2OiuLylxx6UKwQIAgAwUDEqzZ0ttbe5pEGO6fr9jXVubOy5V4SKpYPHII4+orKxMI0aM0NSpU/Xmm2/argsAAPQgFJKqq93gEIv1PjYWc8dVV6fmtEjCweLZZ5/VokWLdO+996qurk4XX3yxZs2apd27d3tRHwAAOM7q1dLhw32Hig6xmDt+zRpv65Ikx5jjJ096d/755+ucc87RypUrO9edfvrpuvbaa1VTU9Pn9pFIRIFAQOFwWPn5+YlXDADAIGaMe2FmY+OJpz964zhSebm0c2dyd4vE+/6d0IzFkSNH9NZbb6mysrLL+srKSm3cuLHbbdrb2xWJRLosAAAgOS0tUkNDYqFCcsc3NEgHD3pTV4eEgsWBAwd09OhRjR07tsv6sWPHav/+/d1uU1NTo0Ag0LmUlpYmXy0AAINca2v/to9G7dTRk6Qu3nSOm0MxxpywrsPSpUsVDoc7l6ampmR2CQAA5D78qj/y8uzU0ZOEnrw5atQoDRky5ITZiY8//viEWYwO2dnZys7OTr5CAADQqahImjgx+WssCgu9q01KcMZi+PDhmjp1qtavX99l/fr16zVjxgyrhQEAgBM5jrRgQXLbLlzo/WO+Ez4VsmTJEv3xj3/Un/70J7377rtavHixdu/erfnz53tRHwAAOM68eVJOjpQV57t4VpY7/pZbvK1LSuJDyG688Ua1tLTo5z//ufbt26fJkyfrpZde0oQJE7yoDwAAHKegQFq3zn2iZlZW78+zyMpyZylqa93tvJbwcyz6i+dYAABgRzDoPlHz8GH362Pf0TtOeeTkuKHiuCdFJMyT51gAAAD/qKqSmpul5cvdCzOPVV7urt+zp/+hIhHMWAAAMAAY4z78Khp1byktLLR7oWa8798JX2MBAAD8x3HcW1GLitJbB6dCAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGBNym837XhsRiQSSfWuAQBAkjret/t6/FXKg0U0GpUklZaWpnrXAACgn6LRqAKBQI/fT/mTN2OxmPbu3au8vDw5Fh8JFolEVFpaqqamJp7o2QeOVfw4VonheMWPYxU/jlX8vDxWxhhFo1GNHz9eWb18rGrKZyyysrJUUlLi2b+fn59P48WJYxU/jlViOF7x41jFj2MVP6+OVW8zFR24eBMAAFhDsAAAANYMmGCRnZ2t++67T9nZ2ekuxfc4VvHjWCWG4xU/jlX8OFbx88OxSvnFmwAAYOAaMDMWAAAg/QgWAADAGoIFAACwhmABAACsyehg8Y1vfEMnn3yyRowYoXHjxmnu3Lnau3dvr9sYY3T//fdr/PjxGjlypC699FK98847Kao4PT788EPddtttKisr08iRIzVx4kTdd999OnLkSK/b3XrrrXIcp8tywQUXpKjq9Ej2WA3GvpKkX/7yl5oxY4ZycnJUUFAQ1zaDsa+k5I7VYO0rSfr00081d+5cBQIBBQIBzZ07V6FQqNdtBktvPfLIIyorK9OIESM0depUvfnmm72O37Bhg6ZOnaoRI0aovLxcjz76qKf1ZXSwmDlzpv7yl7/o/fff17p169TQ0KDrr7++120eeOAB/fa3v9XDDz+srVu3qri4WFdeeWXnZ5gMRO+9955isZgee+wxvfPOO/rd736nRx99VPfcc0+f21511VXat29f5/LSSy+loOL0SfZYDca+kqQjR47ohhtu0O23357QdoOtr6TkjtVg7StJ+ta3vqX6+nq98soreuWVV1RfX6+5c+f2ud1A761nn31WixYt0r333qu6ujpdfPHFmjVrlnbv3t3t+F27dulrX/uaLr74YtXV1emee+7RwoULtW7dOu+KNAPICy+8YBzHMUeOHOn2+7FYzBQXF5tly5Z1rvvss89MIBAwjz76aKrK9IUHHnjAlJWV9Tpm3rx55pprrklNQT7W17Gir4xZtWqVCQQCcY0d7H0V77EazH21Y8cOI8ls3ry5c92mTZuMJPPee+/1uN1g6K3zzjvPzJ8/v8u60047zdx9993djr/rrrvMaaed1mXd9773PXPBBRd4VmNGz1gc6+DBg3rqqac0Y8YMDRs2rNsxu3bt0v79+1VZWdm5Ljs7W5dccok2btyYqlJ9IRwOq7CwsM9xb7zxhsaMGaNTTz1V3/3ud/Xxxx+noDp/6etY0VeJo6/6Npj7atOmTQoEAjr//PM7111wwQUKBAJ9/uwDubeOHDmit956q0tPSFJlZWWPx2XTpk0njK+qqtK2bdv0v//9z5M6Mz5Y/OQnP9FJJ52koqIi7d69Wy+88EKPY/fv3y9JGjt2bJf1Y8eO7fzeYNDQ0KCHHnpI8+fP73XcrFmz9NRTT+m1117Tgw8+qK1bt+qyyy5Te3t7iipNv3iOFX2VGPoqPoO5r/bv368xY8acsH7MmDG9/uwDvbcOHDigo0ePJtQT+/fv73b8559/rgMHDnhSp++Cxf3333/CxTfHL9u2besc/+Mf/1h1dXV69dVXNWTIEN1yyy0yfTxM9PiPazfGWP0I91RJ9FhJ0t69e3XVVVfphhtu0He+851e//0bb7xRs2fP1uTJk3X11Vfr5Zdf1gcffKC///3vXv5YnvD6WEmDu68SMdj7KlEDpa+kxI5Xdz9jXz/7QOqt3iTaE92N7269LSn/2PS+3Hnnnbrpppt6HXPKKad0/n3UqFEaNWqUTj31VJ1++ukqLS3V5s2bNX369BO2Ky4uluQmuHHjxnWu//jjj09IdJkg0WO1d+9ezZw5U9OnT9fjjz+e8P7GjRunCRMmaOfOnQlvm25eHqvB3lf9NZj6KhEDra+k+I/X22+/rY8++uiE733yyScJ/eyZ3FvdGTVqlIYMGXLC7ERvPVFcXNzt+KFDh6qoqMiTOn0XLDqCQjI6UlhP015lZWUqLi7W+vXrNWXKFEnuOasNGzbo17/+dXIFp1Eix2rPnj2aOXOmpk6dqlWrVikrK/HJqpaWFjU1NXV5kcsUXh6rwdxXNgyWvkrUQOsrKf7jNX36dIXDYf3rX//SeeedJ0nasmWLwuGwZsyYEff+Mrm3ujN8+HBNnTpV69ev13XXXde5fv369brmmmu63Wb69On629/+1mXdq6++qmnTpvV4PWK/eXZZqMe2bNliHnroIVNXV2c+/PBD89prr5mLLrrITJw40Xz22Wed4yZNmmRqa2s7v162bJkJBAKmtrbWbN++3dx8881m3LhxJhKJpOPHSIk9e/aYL33pS+ayyy4zzc3NZt++fZ3LsY49VtFo1Pzwhz80GzduNLt27TKvv/66mT59uvniF7/IsTL0VYf//ve/pq6uzvzsZz8zubm5pq6uztTV1ZloNNo5hr5yJXqsjBm8fWWMMVdddZU566yzzKZNm8ymTZvMmWeeab7+9a93GTMYe2vt2rVm2LBh5sknnzQ7duwwixYtMieddJL58MMPjTHG3H333Wbu3Lmd4xsbG01OTo5ZvHix2bFjh3nyySfNsGHDzF//+lfPaszYYPH222+bmTNnmsLCQpOdnW1OOeUUM3/+fNPc3NxlnCSzatWqzq9jsZi57777THFxscnOzjZf/epXzfbt21NcfWqtWrXKSOp2Odaxx+rw4cOmsrLSjB492gwbNsycfPLJZt68eWb37t1p+AlSJ5ljZczg7Ctj3Nv7ujtWr7/+eucY+sqV6LEyZvD2lTHGtLS0mDlz5pi8vDyTl5dn5syZYz799NMuYwZrb/3hD38wEyZMMMOHDzfnnHOO2bBhQ+f35s2bZy655JIu49944w0zZcoUM3z4cHPKKaeYlStXelofH5sOAACs8d1dIQAAIHMRLAAAgDUECwAAYA3BAgAAWEOwAAAA1hAsAACANQQLAABgDcECAABYQ7AAAADWECwAAIA1BAsAAGANwQIAAFjzfxYhaZCSuMTiAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = isl.basic_set(\"{A[x,y] : 0 <= x < 7 and -4 < y <= 0 and  (-y) <= x < 7+y }\")\n",
    "plot_set_points(s,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Plot a set **Diamond** with a width and height of 7. \n",
    "```\n",
    "       x\n",
    "     x x x\n",
    "   x x x x x\n",
    " x x x x x x x\n",
    "   x x x x x\n",
    "     x x x\n",
    "       x\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = isl.basic_set(\"{A[x,y] : 0 <= x < 7 and -4 < y < 4 and (-y) <= x < 7+y and y <= x < 7-y }\")\n",
    "plot_set_points(s,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Plot a set **Parallelogram** with a height of 4 and a width of 7 with a slope of 1/2. \n",
    "```\n",
    "      x x x x x x x\n",
    "    x x x x x x x  \n",
    "  x x x x x x x\n",
    "x x x x x x x\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = isl.basic_set(\"{A[x,y] : 0 <= y < 4 and y <= x < y + 7 }\")\n",
    "plot_set_points(s,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sets \n",
    "<!-- A set is a finite union of basic sets that all belong to the same named space. This means all basic sets have identical dimensionality and carry the same name.  -->\n",
    "\n",
    "集合是有限的基础集合的联合, 他们都属于相同的named space中, 也就是他们的标识维度名都相同.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Combined: { A[i, j] : i > 0 and j <= 9 and (j > i or (6 <= i <= 9 and 0 < j <= 4)) }\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Combined = Triangle.union(Square)\n",
    "print(\"Combined: \" + str(Combined))\n",
    "plot_set_points(Combined,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Union Set \n",
    "\n",
    "<!-- A union set is a finite union of sets that belong to differently named spaces. -->\n",
    "\n",
    "不同named spaces的有限集合组成的是union set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = isl.union_set(\"{A[i,j] : 0 < i,j and  j + i < 10; B[i,j] : 5 <= i,j < 10 }\")\n",
    "plot_set_points(u,color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Presburger Relations\n",
    "<!-- A Presburger Map M, is a set of tuples of integer vectors described by a Presburger formula.  -->\n",
    "\n",
    "<!-- It is formally described as a map M = $( \\{ \\vec{v_1} \\to \\vec{v\\_2} \\mid \\vec{v\\_1}, \\vec{v\\_2} \\in \\mathbb{Z}^n : p (\\vec{v\\_1}, \\vec{v\\_2}, \\vec{p})\\} )$, where \"p\" is a Presburger Formular that evaluates to true, if the pair of tuples $(\\vec{v\\_1})$ and $(\\vec{v\\_2})$ is element of M.  -->\n",
    "\n",
    "Presburger Relations 是一种映射关系, 将多个Presburger formula描述的set映射起来.\n",
    "\n",
    "通常可以表示为M = $( \\{ \\vec{v_1} \\to \\vec{v\\_2} \\mid \\vec{v\\_1}, \\vec{v\\_2} \\in \\mathbb{Z}^n : p (\\vec{v\\_1}, \\vec{v\\_2}, \\vec{p})\\} )$,其中`p`是一个 Presburger 公式，如果元组对 $(\\vec{v\\_1})$ 和 $(\\vec{v\\_2})$ 是 M 的元素，则计算结果为真."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Map \n",
    "\n",
    "<!-- A basic map relates two basic sets. The relations are simple enough to be described with a union of affine inequalities (and modulo constraints).  -->\n",
    "\n",
    "basic map关联了basic set.\n",
    "\n",
    "### Example\n",
    "\n",
    "<!-- A simple relation that translates a basic set **A** to position **X**.  -->\n",
    "比如下面关联set A和position X.\n",
    "\n",
    "Translate = $(\\{A[i,j] \\to X[i+10,j+1]\\})$\n",
    "\n",
    "To visualize this set, we use it to translate the earlier defined set **Triangle**. Without constraining **Translate** to **Triangle** the map is infinite and cannot be rendered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot.plotter import plot_map\n",
    "\n",
    "\n",
    "Translate = isl.basic_map(\"{A[i,j] -> X[i+10,j+1]}\")\n",
    "b  = Triangle.apply(Translate)\n",
    "Translate = Translate.intersect_domain(Triangle)\n",
    "\n",
    "plot_map(Translate)\n",
    "plot_set_points(Triangle,color='blue')\n",
    "plot_set_points(b,color='orange')"
   ]
  }
 ],
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