{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b21d3072-49a3-47c8-b6ed-5926fc165ad5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.vector import CoordSys3D, Del, express\n",
    "from sympy import vector\n",
    "from sympy import symbols\n",
    "from sympy.abc import x, y, z, r, theta\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "941cd86f-95b3-4d6b-98b4-e94fe9391bac",
   "metadata": {},
   "outputs": [],
   "source": [
    "a1, a2, a3 = symbols(\"a1 a2 a3\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "97495bbf-c436-416c-9746-4ebf454a4137",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = CoordSys3D('N')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ac3437bd-5da2-4663-b056-a4a9ee407a8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\mathbf{\\hat{i}_{N}}$"
      ],
      "text/plain": [
       "N.i"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N.i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d88ed004-11a8-4b21-8fe8-c40e55d77b92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{Point}\\left(N.origin, \\mathbf{\\hat{0}}\\right)$"
      ],
      "text/plain": [
       "N.origin"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N.origin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43946e3c-6b3b-4a95-a857-ccb2e98374a7",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\operatorname{Point}\\left(A, \\left(a_{1}\\right)\\mathbf{\\hat{i}_{N}} + \\left(a_{2}\\right)\\mathbf{\\hat{j}_{N}} + \\left(a_{3}\\right)\\mathbf{\\hat{k}_{N}}, \\operatorname{Point}\\left(N.origin, \\mathbf{\\hat{0}}\\right)\\right)$"
      ],
      "text/plain": [
       "A"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = N.origin.locate_new(\"A\", a1*N.i + a2*N.j + a3*N.k)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bf493bda-b7c5-4f27-b190-6a94ab9adae1",
   "metadata": {},
   "outputs": [],
   "source": [
    "C = CoordSys3D('C')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b008fe56-e9c8-4b57-8f2a-32f778f329c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "delop = Del()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8816c468-b001-492e-95ef-cb3b17b71bbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(\\mathbf{{x}_{C}} \\mathbf{{y}_{C}}\\right)\\mathbf{\\hat{j}_{C}} + \\left(- \\mathbf{{x}_{C}} \\mathbf{{z}_{C}}\\right)\\mathbf{\\hat{k}_{C}}$"
      ],
      "text/plain": [
       "C.x*C.y*C.j + (-C.x*C.z)*C.k"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(delop ^ C.x*C.y*C.z*C.i).doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3963fcc1-4476-4934-a4e3-7575bddbe5d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "C = N.create_new('C', transformation='cylindrical', variable_names=(\"r\", \"theta\", \"z\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7868851b-1291-4f21-afc0-334f740619cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(x\\right)\\mathbf{\\hat{i}_{N}} + \\left(y\\right)\\mathbf{\\hat{j}_{N}} + \\left(z\\right)\\mathbf{\\hat{k}_{N}}$"
      ],
      "text/plain": [
       "x*N.i + y*N.j + z*N.k"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1 = x*N.i + y*N.j+ z*N.k\n",
    "v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e55937ab-31d1-4cfe-ae65-ccd99dc3d800",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(- \\frac{d}{d \\mathbf{{z}_{N}}} y + \\frac{d}{d \\mathbf{{y}_{N}}} z\\right)\\mathbf{\\hat{i}_{N}} + \\left(\\frac{d}{d \\mathbf{{z}_{N}}} x - \\frac{d}{d \\mathbf{{x}_{N}}} z\\right)\\mathbf{\\hat{j}_{N}} + \\left(- \\frac{d}{d \\mathbf{{y}_{N}}} x + \\frac{d}{d \\mathbf{{x}_{N}}} y\\right)\\mathbf{\\hat{k}_{N}}$"
      ],
      "text/plain": [
       "(-Derivative(y, N.z) + Derivative(z, N.y))*N.i + (Derivative(x, N.z) - Derivative(z, N.x))*N.j + (-Derivative(x, N.y) + Derivative(y, N.x))*N.k"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv1 = delop.cross(v1)\n",
    "cv1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d2fce40e-292e-495e-b0d9-6db9529487bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(- \\frac{d}{d \\mathbf{{z}_{N}}} y + \\frac{d}{d \\mathbf{{y}_{N}}} z\\right)\\mathbf{\\hat{i}_{C}} + \\left(\\frac{d}{d \\mathbf{{z}_{N}}} x - \\frac{d}{d \\mathbf{{x}_{N}}} z\\right)\\mathbf{\\hat{j}_{C}} + \\left(- \\frac{d}{d \\mathbf{{y}_{N}}} x + \\frac{d}{d \\mathbf{{x}_{N}}} y\\right)\\mathbf{\\hat{k}_{C}}$"
      ],
      "text/plain": [
       "(-Derivative(y, N.z) + Derivative(z, N.y))*C.i + (Derivative(x, N.z) - Derivative(z, N.x))*C.j + (-Derivative(x, N.y) + Derivative(y, N.x))*C.k"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "express(cv1, C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fee5ea69-87af-4bf3-95df-b807f05688f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(np.array((1,2,3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "14aaf5d0-b984-4638-88cb-169fc3cbecee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type((1,2,3)) == tuple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5482e5cb-d850-429b-b80a-744afcfee2c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type((1,2,3)) == list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "535a8ca7-2ca5-4820-b312-34b6a451f845",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(super(tuple)) == super"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b1a7fe52-84b8-4f58-90af-f5fc1a5027d8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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