sympy-test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
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    {
     "name": "stdout",
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     "text": [
      "['d:\\\\Users\\\\John\\\\Documents\\\\IPython Notebooks\\\\sympy\\\\sympy-notes', 'D:\\\\Users\\\\John\\\\Documents\\\\IPython Notebooks\\\\sympy\\\\sympy-notes', 'D:\\\\Users\\\\John\\\\Documents\\\\IPython Notebooks\\\\sympy\\\\sympy-notes\\\\sympy_support', 'D:\\\\Users\\\\John\\\\Documents\\\\IPython Notebooks\\\\sympy\\\\sympy-notes\\\\kronecker_levi', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\python310.zip', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\DLLs', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\lib', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy', '', 'C:\\\\Users\\\\John\\\\AppData\\\\Roaming\\\\Python\\\\Python310\\\\site-packages', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\lib\\\\site-packages', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\lib\\\\site-packages\\\\win32', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\lib\\\\site-packages\\\\win32\\\\lib', 'd:\\\\Users\\\\John\\\\miniconda3\\\\envs\\\\sympy\\\\lib\\\\site-packages\\\\Pythonwin']\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f =  x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    analyse_critical_points(f, x, y)\n",
      "Expecting:\n",
      "    [((-1, 5/2), 'SADDLEPOINT'), ((3, -3/2), 'LOCAL_MINIMUM')]\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    critical_points(x**2 + y**2, x, y)\n",
      "Expecting:\n",
      "    [{x: 0, y: 0}]\n",
      "ok\n",
      "Trying:\n",
      "    critical_points(sp.sqrt(4*y**2 -9*x**2 +24*y+36*x+36), x, y)\n",
      "Expecting:\n",
      "    [{x: 2, y: -3}]\n",
      "ok\n",
      "Trying:\n",
      "    critical_points(x**2+2*x*y-4*y**2+4*x-6*y+4, x, y)\n",
      "Expecting:\n",
      "    [{x: -1, y: -1}]\n",
      "ok\n",
      "Trying:\n",
      "    critical_points(x**3+2*x*y-2*x-4*y, x, y)\n",
      "Expecting:\n",
      "    [{x: 2, y: -5}]\n",
      "ok\n",
      "Trying:\n",
      "    critical_points(4*x**2 + 9*y**2 + 8*x - 36*y + 24, x, y)\n",
      "Expecting:\n",
      "    [{x: -1, y: 2}]\n",
      "ok\n",
      "Trying:\n",
      "    critical_points(x**3/3 + y**2 +2*x*y -6*x - 3*y +4, x, y)\n",
      "Expecting:\n",
      "    [{x: -1, y: 5/2}, {x: 3, y: -3/2}]\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f = x**2 + y**2\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    discriminant(f, x, y)\n",
      "Expecting:\n",
      "    4\n",
      "ok\n",
      "Trying:\n",
      "    f = x**2 + y**2 + x*y\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    discriminant(f, x, y)\n",
      "Expecting:\n",
      "    3\n",
      "ok\n",
      "Trying:\n",
      "    f = 4*x**2 + 9*y**2 + 8*x - 36*y + 24\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    discriminant(f, x, y)\n",
      "Expecting:\n",
      "    144\n",
      "ok\n",
      "Trying:\n",
      "    f = x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    discriminant(f, x, y)\n",
      "Expecting:\n",
      "    4*x - 4\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f = 4*x**2 + 9*y**2 + 8*x - 36*y + 24\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    evaluate_discriminant(f, x, y, -1, 2)\n",
      "Expecting:\n",
      "    144\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f = x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    evaluate_discriminant(f, x, y, -1, 5/2)\n",
      "Expecting:\n",
      "    -8\n",
      "ok\n",
      "Trying:\n",
      "    evaluate_discriminant(f, x, y, 3, -3/2)\n",
      "Expecting:\n",
      "    8\n",
      "ok\n",
      "Trying:\n",
      "    from sympy import symbols, diff\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    x, y = symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f = x**2 + y**2\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    hessian(f, x, y)\n",
      "Expecting:\n",
      "    Matrix([\n",
      "    [2, 0],\n",
      "    [0, 2]])\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f = 4*x**2 + 9*y**2 + 8*x - 36*y + 24\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    second_derivative_test(f, x, y, -1, 2)\n",
      "Expecting:\n",
      "    'LOCAL_MINIMUM'\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f =  x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    second_derivative_test(f, x, y, 3, 3/2)\n",
      "Expecting:\n",
      "    'LOCAL_MINIMUM'\n",
      "ok\n",
      "Trying:\n",
      "    second_derivative_test(f, x, y, -1, 5/2)\n",
      "Expecting:\n",
      "    'SADDLEPOINT'\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f = x**2 + y**2\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    fxx, fyy, fxy = second_order_partial_derivatives(f, x, y)\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    fxx\n",
      "Expecting:\n",
      "    2\n",
      "ok\n",
      "Trying:\n",
      "    fyy\n",
      "Expecting:\n",
      "    2\n",
      "ok\n",
      "Trying:\n",
      "    fxy\n",
      "Expecting:\n",
      "    0\n",
      "ok\n",
      "Trying:\n",
      "    f = 4*x**2 + 9*y**2 + 8*x - 36*y + 24\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    fxx, fyy, fxy = second_order_partial_derivatives(f, x, y)\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    fxx\n",
      "Expecting:\n",
      "    8\n",
      "ok\n",
      "Trying:\n",
      "    fyy\n",
      "Expecting:\n",
      "    18\n",
      "ok\n",
      "Trying:\n",
      "    fxy\n",
      "Expecting:\n",
      "    0\n",
      "ok\n",
      "Trying:\n",
      "    f = x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    fxx, fyy, fxy = second_order_partial_derivatives(f, x, y)\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    fxx\n",
      "Expecting:\n",
      "    2*x\n",
      "ok\n",
      "Trying:\n",
      "    fyy\n",
      "Expecting:\n",
      "    2\n",
      "ok\n",
      "Trying:\n",
      "    fxy\n",
      "Expecting:\n",
      "    2\n",
      "ok\n",
      "Trying:\n",
      "    sgn(5)\n",
      "Expecting:\n",
      "    1\n",
      "ok\n",
      "Trying:\n",
      "    sgn(-5)\n",
      "Expecting:\n",
      "    -1\n",
      "ok\n",
      "Trying:\n",
      "    sgn(0)\n",
      "Expecting:\n",
      "    0\n",
      "ok\n",
      "1 items had no tests:\n",
      "    critical_points_2d\n",
      "8 items passed all tests:\n",
      "   3 tests in critical_points_2d.analyse_critical_points\n",
      "   7 tests in critical_points_2d.critical_points\n",
      "   9 tests in critical_points_2d.discriminant\n",
      "   7 tests in critical_points_2d.evaluate_discriminant\n",
      "   4 tests in critical_points_2d.hessian\n",
      "   7 tests in critical_points_2d.second_derivative_test\n",
      "  16 tests in critical_points_2d.second_order_partial_derivatives\n",
      "   3 tests in critical_points_2d.sgn\n",
      "56 tests in 9 items.\n",
      "56 passed and 0 failed.\n",
      "Test passed.\n",
      "Trying:\n",
      "    import sympy as sp\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    x, y = sp.symbols('x y')\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    f =  x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
      "Expecting nothing\n",
      "ok\n",
      "Trying:\n",
      "    sycp.analyse_critical_points(f, x, y)\n",
      "Expecting:\n",
      "    [((-1, 5/2), 'SADDLEPOINT'), ((3, -3/2), 'LOCAL_MINIMUM')]\n",
      "ok\n",
      "1 items passed all tests:\n",
      "   4 tests in __main__\n",
      "4 tests in 1 items.\n",
      "4 passed and 0 failed.\n",
      "Test passed.\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import critical_points_2d as sycp\n",
    "\n",
    "print(sys.path)\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "    >>> import sympy as sp\n",
    "    >>> x, y = sp.symbols('x y')\n",
    "    >>> f =  x**3/3 + y**2 +2*x*y -6*x - 3*y + 4\n",
    "    >>> sycp.analyse_critical_points(f, x, y)\n",
    "    [((-1, 5/2), 'SADDLEPOINT'), ((3, -3/2), 'LOCAL_MINIMUM')]\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    import doctest\n",
    "    \n",
    "    verbose = True\n",
    "    doctest.testmod(sycp, verbose=verbose)\n",
    "    doctest.testmod(verbose=verbose)\n"
   ]
  }
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