Sympy_2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sy\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{55}{32}$"
      ],
      "text/plain": [
       "55/32"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R(1.71875)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.71875"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = sy.Symbol(\"n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exp(-pi/2)\n"
     ]
    }
   ],
   "source": [
    "print(sy.limit(sy.cos(1/sy.sqrt(n)) ** (n*sy.pi), n, sy.oo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = sy.eye(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.gridspec import GridSpec\n",
    "import networkx as nx\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.random_geometric_graph(10, 0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a33c20cd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# m = [[1, 1, 1, 1, 1, 1, 1],\n",
    "#      [1, 1, 0, 1, 1, 1, 1],\n",
    "#      [1, 0, 1, 1, 0, 0, 1],\n",
    "#      [1, 1, 1, 1, 0, 0, 1],\n",
    "#      [1, 1, 0, 0, 1, 1, 0],\n",
    "#      [1, 1, 0, 0, 1, 1, 0],\n",
    "#      [1, 1, 1, 1, 0, 0, 1]]\n",
    "\n",
    "def matrix2graph(N):\n",
    "    edglist=[]\n",
    "    G=nx.Graph()\n",
    "    point = range(len(N))\n",
    "    G.add_nodes_from(point)\n",
    "    for i in range(len(N)):\n",
    "        for j in range(len(N)):\n",
    "            if N[i][j]:\n",
    "                edglist.append((i, j))\n",
    "    \n",
    "    G.add_edges_from(edglist)\n",
    "    return G\n",
    "\n",
    "nx.draw_networkx(matrix2graph(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a33d2ebf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_networkx(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 不等关系推导"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.abc import *\n",
    "from sympy import Poly\n",
    "from sympy.solvers.inequalities import solve_rational_inequalities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "too many values to unpack (expected 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-12-76ebc2c469ff>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m solve_rational_inequalities([[(Poly(-x+1), Poly(1, x), \">=\"),\n\u001b[1;32m----> 2\u001b[1;33m                              (Poly(-x+1), Poly(1, x), '<=')]])\n\u001b[0m",
      "\u001b[1;32mD:\\software\\Anaconda3\\envs\\py36\\lib\\site-packages\\sympy\\solvers\\inequalities.py\u001b[0m in \u001b[0;36msolve_rational_inequalities\u001b[1;34m(eqs)\u001b[0m\n\u001b[0;32m    162\u001b[0m         \u001b[0mglobal_intervals\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mInterval\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNegativeInfinity\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mS\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mInfinity\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    163\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 164\u001b[1;33m         \u001b[1;32mfor\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnumer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdenom\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrel\u001b[0m \u001b[1;32min\u001b[0m \u001b[0m_eqs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    165\u001b[0m             \u001b[0mnumer_intervals\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msolve_poly_inequality\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumer\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mdenom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    166\u001b[0m             \u001b[0mdenom_intervals\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msolve_poly_inequality\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdenom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'=='\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: too many values to unpack (expected 2)"
     ]
    }
   ],
   "source": [
    "solve_rational_inequalities([[(Poly(-x+1), Poly(1, x), \">=\"),\n",
    "                             (Poly(-x+1), Poly(1, x), '<=')]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left\\{2\\right\\}$"
      ],
      "text/plain": [
       "{2}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_rational_inequalities([[\n",
    "((Poly(-x + 2), Poly(2, x)), '>='),\n",
    "((Poly(-x + 2), Poly(2, x)), '<=')]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = solve_rational_inequalities([[\n",
    "((Poly(-x + 2), Poly(2, x)), '>=')]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left\\{2\\right\\}$"
      ],
      "text/plain": [
       "{2}"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = sy.Interval(2, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3$"
      ],
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.sup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[6, 9\\right]$"
      ],
      "text/plain": [
       "Interval(6, 9)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.imageset(x, 3*x, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\text{False}$"
      ],
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.Equality(n, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = sy.GreaterThan(y, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = sy.Interval(1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = sy.Symbol(\"x\")\n",
    "y = x + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = sy.Interval(0, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\text{False}$"
      ],
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.as_relational(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[-2, 2\\right]$"
      ],
      "text/plain": [
       "Interval(-2, 2)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.Interval(-2, 1) + k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.solvers.inequalities import solve_rational_inequalities\n",
    "from sympy.solvers import inequalities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Piecewise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Piecewise((0, x < -1), (f, x<=1), (x, True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "b1, b2 = sy.symbols(\"b1:3\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(-\\infty, -1\\right] \\cup \\left(0, \\infty\\right)$"
      ],
      "text/plain": [
       "Union(Interval(-oo, -1), Interval.open(0, oo))"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_rational_inequalities([[\n",
    "    ((sy.Poly(x+1) ,sy.Poly(x)), '>=')\n",
    "]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Abs',\n",
       " 'And',\n",
       " 'Dummy',\n",
       " 'EmptySet',\n",
       " 'Eq',\n",
       " 'FiniteSet',\n",
       " 'Ge',\n",
       " 'ImageSet',\n",
       " 'Intersection',\n",
       " 'Interval',\n",
       " 'Lt',\n",
       " 'Ne',\n",
       " 'Poly',\n",
       " 'PolynomialError',\n",
       " 'Relational',\n",
       " 'S',\n",
       " 'Symbol',\n",
       " 'Union',\n",
       " '__builtins__',\n",
       " '__cached__',\n",
       " '__doc__',\n",
       " '__file__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " '_nsort',\n",
       " '_pt',\n",
       " '_reduce_inequalities',\n",
       " '_solve_inequality',\n",
       " 'division',\n",
       " 'expand_mul',\n",
       " 'factor_terms',\n",
       " 'filldedent',\n",
       " 'iterable',\n",
       " 'parallel_poly_from_expr',\n",
       " 'print_function',\n",
       " 'reduce_abs_inequalities',\n",
       " 'reduce_abs_inequality',\n",
       " 'reduce_inequalities',\n",
       " 'reduce_rational_inequalities',\n",
       " 'sift',\n",
       " 'solve_poly_inequalities',\n",
       " 'solve_poly_inequality',\n",
       " 'solve_rational_inequalities',\n",
       " 'solve_univariate_inequality',\n",
       " 'sympify']"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(inequalities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{0}]"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "inequalities.solve_poly_inequality(Poly(x, x, domain=\"ZZ\"), \"==\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[-1, 0\\right) \\cup \\left(0, \\infty\\right)$"
      ],
      "text/plain": [
       "Union(Interval.Ropen(-1, 0), Interval.open(0, oo))"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solveset(p > 0, x, sy.S.Reals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = symbols(\"x\", real=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = Piecewise((6*x/5, sy.And(0<=x, x<=S(1)/6)), (9*x/5-S(1)/10, x<=S(1)/3), \n",
    "              (6*x/5 + S(1)/10, x<=S(1)/2), (1, x<=1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "Wa = W.subs(x, alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{cases} \\frac{6 \\alpha}{5} & \\text{for}\\: \\alpha \\geq 0 \\wedge \\alpha \\leq \\frac{1}{6} \\\\\\frac{9 \\alpha}{5} - \\frac{1}{10} & \\text{for}\\: \\alpha \\leq \\frac{1}{3} \\\\\\frac{6 \\alpha}{5} + \\frac{1}{10} & \\text{for}\\: \\alpha \\leq \\frac{1}{2} \\\\1 & \\text{for}\\: \\alpha \\leq 1 \\end{cases}$"
      ],
      "text/plain": [
       "Piecewise((6*alpha/5, (alpha >= 0) & (alpha <= 1/6)), (9*alpha/5 - 1/10, alpha <= 1/3), (6*alpha/5 + 1/10, alpha <= 1/2), (1, alpha <= 1))"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Wa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [],
   "source": [
    "b1, b2, b3, b4 = sy.symbols(\"b1:5\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(0, \\frac{1}{2}\\right]$"
      ],
      "text/plain": [
       "Interval.Lopen(0, 1/2)"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solveset(Wa.subs(alpha ,b1) > 0, b1, S.Reals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sympy无法做非多项式不等式分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = \"'asdf'\\\" a\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'asdf\\'\" a'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.strip(\"\\'\\\"\\n \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "codemirror_mode": {
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