{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2493461",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "import sympy\n",
    "\n",
    "x = sympy.symbols('x')\n",
    "h = 2\n",
    "relu = sympy.Max(0, h) + sympy.Max(0, -h)\n",
    "print(sympy.Max(h,0))\n",
    "print(relu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "de59fd98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x_{1} \\left(11 x_{1} - 12 x_{2}\\right) - 20 x_{1} + x_{2} \\left(- 12 x_{1} + 4 x_{2}\\right) + 40 x_{2} - 60\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[x_1*(11*x_1 - 12*x_2) - 20*x_1 + x_2*(-12*x_1 + 4*x_2) + 40*x_2 - 60]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x_{1} \\left(11 x_{1} - 24 x_{2}\\right) - 20 x_{1} + 4 x_{2}^{2} + 40 x_{2} - 60\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[x_1*(11*x_1 - 24*x_2) - 20*x_1 + 4*x_2**2 + 40*x_2 - 60]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x_{1} \\left(14.6 x_{1} - 7.2 x_{2}\\right) - 44 x_{1} + x_{2} \\left(- 7.2 x_{1} + 10.4 x_{2}\\right) + 8 x_{2} - 60\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[x_1*(14.6*x_1 - 7.2*x_2) - 44*x_1 + x_2*(-7.2*x_1 + 10.4*x_2) + 8*x_2 - 60]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy as sp\n",
    "import numpy\n",
    "\n",
    "x_1, x_2 = sp.symbols('x_1, x_2')\n",
    "\n",
    "A_1 = sp.Matrix([[11,-12],[-12,4]])\n",
    "A_2 = sp.Matrix([[11,0],[-24,4]])\n",
    "A_3 = sp.Matrix([[73/5,-36/5],[-36/5,52/5]])\n",
    "\n",
    "b_1 = sp.Matrix([-20,40])\n",
    "b_2 = b_1\n",
    "b_3 = sp.Matrix([-44,8])\n",
    "\n",
    "x = sp.Matrix([x_1,x_2])\n",
    "\n",
    "c = sp.Matrix([-60])\n",
    "\n",
    "q_1 = x.T * A_1 * x + b_1.T * x + c\n",
    "\n",
    "q_2 = x.T * A_2 * x + b_2.T * x + c\n",
    "\n",
    "q_3 = x.T * A_3 * x + b_3.T * x + c\n",
    "\n",
    "display(q_1)\n",
    "\n",
    "display(q_2)\n",
    "\n",
    "display(q_3)\n"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
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    "version": 3
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   "file_extension": ".py",
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