initial look at using sympy CAS to replace maple worksheets (UNFINISHED)

SR/buried_2d_dipoles.ipynb

@@ -0,0 +1,143 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Preamble\n",
+    "from sympy import * \n",
+    "from sympy.vector import *\n",
+    "init_printing() # gives latex formatted output"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "N = vector.CoordSys3D(\"\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "moment_vec = 0 * N.i + 1 * N.j + 0 * N.k"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x0,y0,z0 = symbols(\"x0, y0, z0\") # declare some symbols associated with coordinate translation\n",
+    "N.z = 0 # reduce to 2d\n",
+    "z0 = 0 # reduce to 2d\n",
+    "position_vec = (N.x - x0) * N.i + (N.y - y0) * N.j + (N.z -z0) * N.k"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "position_abs = sqrt(position_vec.dot(position_vec))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "surface = 1 / position_abs  # In 3d should have surface area of sphere (don't need factors of 4pi), something like 1/rabs^2.\n",
+    "                            # In 2d you drop a factgor of r so associate it with the side area of a cylinder of unit height??? seems to work"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Flux function associated with such a dipole\n",
+    "A_dip_vec = surface * moment_vec.cross(position_vec) / position_abs\n",
+    "A_dip_vec "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Magnetic field associated with such a dipole \n",
+    "B_dip_vec = curl(A_dip_vec)\n",
+    "B_dip_vec"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Plot the field - unfortunately this isn't the one-liner it would be in Maple but at least its free\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "# Do this later\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}