{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symbolic Coord System Notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "\n",
    "from mechpy.core.symbolic.coord import (\n",
    "    SymbolicCoordSystem,\n",
    "    SymbolicCartesianCoordSystem,\n",
    "    SymbolicCylindricalCoordSystem,\n",
    "    SymbolicSphericalCoordSystem,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cartesian Coord System"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SymbolicCartesianCoordSystem(origin=(0, 0, 0), basis=(x, y, z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cartesian_system = SymbolicCartesianCoordSystem()\n",
    "display(cartesian_system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cylindrical Coord System"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(r, theta, z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cylindrical_system = SymbolicCylindricalCoordSystem()\n",
    "display(cylindrical_system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cartesian/Cylindrical Conversion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(r, theta, z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "SymbolicCartesianCoordSystem(origin=(0, 0, 0), basis=(r*cos(theta), r*sin(theta), z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(r*cos(theta), r*sin(theta), z)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "symbolic_cylindrical_system = SymbolicCylindricalCoordSystem()\n",
    "display(symbolic_cylindrical_system)\n",
    "new_coord_system = symbolic_cylindrical_system.to_cartesian()\n",
    "display(new_coord_system)\n",
    "display(new_coord_system.basis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SymbolicCartesianCoordSystem(origin=(0, 0, 0), basis=(x, y, z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(sqrt(x**2 + y**2), atan2(y, x), z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(sqrt(x**2 + y**2), atan2(y, x), z)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "symbolic_cartesian_system = SymbolicCartesianCoordSystem()\n",
    "display(symbolic_cartesian_system)\n",
    "new_coord_system = symbolic_cartesian_system.to_cylindrical()\n",
    "display(new_coord_system)\n",
    "display(new_coord_system.basis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5/2, 5*sqrt(3)/2, 2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cylindrical_coord = (5, sp.pi/3, 2)\n",
    "symbolic_cylindrical_system = SymbolicCylindricalCoordSystem()\n",
    "cartesian_coord = symbolic_cylindrical_system.get_cartesian_coords(cylindrical_coord)\n",
    "display(cartesian_coord)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, pi/2, 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cartesian_coord = (0, 1, 1)\n",
    "symbolic_cartesian_system = SymbolicCartesianCoordSystem()\n",
    "cylindrical_coord = symbolic_cartesian_system.get_cylindrical_coord(cartesian_coord)\n",
    "display(cylindrical_coord)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### using params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(r, theta, z))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(a/2, sqrt(3)*a/2, b)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "symbolic_cylindrical_system = SymbolicCylindricalCoordSystem()\n",
    "display(symbolic_cylindrical_system)\n",
    "a, b = sp.symbols(\"a b\", positive=True)\n",
    "cylindrical_coord = (a, sp.pi/3, b)\n",
    "cartesian_coord = symbolic_cylindrical_system.get_cartesian_coords(cylindrical_coord)\n",
    "display(cartesian_coord)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.50000000000000, 2.59807621135332, 5.00000000000000)\n"
     ]
    }
   ],
   "source": [
    "eval_coord = SymbolicCoordSystem.coord_eval(cartesian_coord, subs={a: 3, b: 5})\n",
    "print(eval_coord)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(a, pi/2, b)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = sp.symbols(\"a b\", positive=True)\n",
    "cartesian_coord = (0, a, b)\n",
    "symbolic_cartesian_system = SymbolicCartesianCoordSystem()\n",
    "cylindrical_coord = symbolic_cartesian_system.get_cylindrical_coord(cartesian_coord)\n",
    "display(cylindrical_coord)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3.00000000000000, 1.57079632679490, 5.00000000000000)\n"
     ]
    }
   ],
   "source": [
    "eval_coord = SymbolicCoordSystem.coord_eval(cylindrical_coord, subs={a: 3, b: 5})\n",
    "print(eval_coord)"
   ]
  }
 ],
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