ShwarzchildConnection.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import *\n",
    "from sympy import *\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Time( radius, mass ):\n",
    "    return simplify( 1 - ( 2.0 * mass ) / radius )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Radius( radius, mass ):\n",
    "    return simplify( Time( radius, mass ) ** ( -1 ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Theta( radius ):\n",
    "    return ( radius ** 2 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Phi( radius, theta ):\n",
    "    return ( ( radius **2 ) * ( sin( theta ) ** 2 ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ShwarzchildMetric( mass, radius, theta ):\n",
    "    return [ [ -Time( radius, mass ), 0.0, 0.0, 0.0 ], \n",
    "               [ 0.0, Radius( radius, mass ), 0.0, 0.0 ], \n",
    "               [ 0.0, 0.0, Theta( radius ), 0.0 ], \n",
    "               [ 0.0, 0.0, 0.0, Phi( radius, theta ) ] ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "time = Symbol( 'time' )\n",
    "radius = Symbol( 'radius' ) \n",
    "theta = Symbol( 'theta' )\n",
    "phi = Symbol( 'phi' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "symboles = [ time, radius, theta, phi ]\n",
    "display = [ 't', 'r', 'theta', 'phi' ]#[ u't', u'r', u'u0398', u'u03D5' ]\n",
    "def CoordinateString( a, b, c ):\n",
    "    return display[ a ] + u', ' + display[ b ] + u', ' + display[ c ] + u': '"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DeriveCoordinate( metric, x, y, withRespectTo ):\n",
    "    if( type( metric[ x ][ y ] ) != float ):\n",
    "        metric[ x ][ y ] += metric[ x ][ y ].diff( withRespectTo )\n",
    "    else:\n",
    "        metric[ x ][ y ] += 0.0\n",
    "    return metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def IntermediateConnection( mass, radius, theta, a, b, c, symboles ):\n",
    "    metric0 = ShwarzchildMetric( mass, radius, theta )\n",
    "    metric1 = ShwarzchildMetric( mass, radius, theta )\n",
    "    metric2 = ShwarzchildMetric( mass, radius, theta )\n",
    "    metric3 = ShwarzchildMetric( mass, radius, theta )\n",
    "    result = 0.0\n",
    "    for i in range( 4 ):\n",
    "        metric1 = DeriveCoordinate( metric1, b, i, symboles[ c ] )\n",
    "        metric2 = DeriveCoordinate( metric2, c, i, symboles[ b ] )\n",
    "        metric3 = DeriveCoordinate( metric3, b, c, symboles[ i ] )\n",
    "        result += 0.5 * metric0[ a ][ i ] * ( metric1[ b ][ i ] + metric2[ c ][ i ] - metric3[ b ][ c ] )\n",
    "    return result\n",
    "\n",
    "\n",
    "def DeriveMetricParameter( metric, x, y, withRespectTo ):\n",
    "    if( type( metric[ x ][ y ] ) != float ):\n",
    "        return metric[ x ][ y ].diff( withRespectTo )\n",
    "    return 0.0\n",
    "\n",
    "def DebugPrint( toPrint, debug ):\n",
    "    if debug == True:\n",
    "        if isinstance( toPrint, tuple ):\n",
    "            print( *toPrint )\n",
    "        else:\n",
    "            print( toPrint )\n",
    "\n",
    "def Connection( mass, radius, theta, a, b, c, symboles, debug = True ):\n",
    "    global DeriveMetricParameter\n",
    "    Derive = DeriveMetricParameter\n",
    "    metric = ShwarzchildMetric( mass, radius, theta )\n",
    "    result = [ [ 0.0, 0.0, 0.0, 0.0 ], \n",
    "                [ 0.0, 0.0, 0.0, 0.0 ], \n",
    "                [ 0.0, 0.0, 0.0, 0.0 ], \n",
    "                [ 0.0, 0.0, 0.0, 0.0 ] ]\n",
    "    results = []\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    for l in range( 4 ):\n",
    "        DebugPrint( '<matrix' + str( l ) + '>', debug )\n",
    "        for m in range( 4 ):\n",
    "            DebugPrint( '\\t<row' + str( m ) + '>', debug )\n",
    "            for n in range( 4 ):\n",
    "                DebugPrint( '\\t\\t<number' + str( m ) + 'x' + str( n ) + '>', debug )\n",
    "                for p in range ( 4 ):\n",
    "                    #print( \"Deriving0: \", symboles[ n ], \": \", metric[ m ][ p ], \"::\", Derive( metric, m, p, symboles[ n ] ) )\n",
    "                    #print( \"Deriving1: \", symboles[ m ], \": \", metric[ n ][ p ], \"::\", Derive( metric, n, p, symboles[ m ] ) )\n",
    "                    #print( \"Deriving2: \", symboles[ p ], \": \",  metric[ m ][ n ], \"::\",Derive( metric, m, n, symboles[ p ] ) )\n",
    "                    DebugPrint( ( '\\t\\t\\t', 0.5 * metric[ l ][ p ], ' * ( ', \n",
    "                                               Derive( metric, m, p, symboles[ n ] ), '+', \n",
    "                                               Derive( metric, n, p, symboles[ m ] ), '-', \n",
    "                                               Derive( metric, m, n, symboles[ p ] ), ' )', 'l: ', l, ' m: ', m, ' n: ', n, ' p: ', p ), debug )\n",
    "                    results[ l ][ m ][ n ] += ( 0.5 * metric[ l ][ p ] * \n",
    "                                               ( Derive( metric, m, p, symboles[ n ] ) + \n",
    "                                               Derive( metric, n, p, symboles[ m ] ) - \n",
    "                                               Derive( metric, m, n, symboles[ p ] ) ) )\n",
    "                DebugPrint( ( '\\t\\t\\tresult: ', results[ l ][ m ][ n ], '\\n' ), debug )\n",
    "                DebugPrint( '\\t\\t\\t<ncurrently>', debug )\n",
    "                for o in results[ l ]:\n",
    "                    DebugPrint( ( '\\t\\t\\t\\t', o ), debug )\n",
    "                DebugPrint( '\\t\\t\\t</ncurrently>', debug )\n",
    "                DebugPrint( '\\t\\t</number' + str( m ) + 'x' + str( n ) + '>', debug )\n",
    "            DebugPrint( '\\t\\t<rcurrently>', debug )\n",
    "            #for i in range( 4 ):\n",
    "            #    results[ i ] = ( 0.5 * Matrix( metric ) * Matrix( results[ i ] ) ).tolist()\n",
    "            for o in results[ l ]:\n",
    "                DebugPrint( ( '\\t\\t\\t', o ), debug )\n",
    "            DebugPrint( '\\t\\t</rcurrently>', debug )\n",
    "            DebugPrint( '\\t</row' + str( m ) + '>', debug )\n",
    "        DebugPrint( '</matrix' + str( l ) + '>\\n\\n', debug )\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phi, r, phi:  0.5*radius**2*(radius**2*sin(theta)**2 + 2*radius*sin(theta)**2)*sin(theta)**2\n",
      "phi, theta, phi:  0.5*radius**2*(radius**2*sin(theta)**2 + 2*radius**2*sin(theta)*cos(theta))*sin(theta)**2\n",
      "theta, theta, theta:  0.5*radius**2*(radius**2 - 2*radius)\n",
      "theta, r, phi:  0\n",
      "t, t, phi:  -0.5*(radius - 2.0)*(-(radius - 2.0)/radius - 1/radius + (radius - 2.0)/radius**2)/radius\n",
      "r, t, t:  0.5*radius*((radius - 2.0)/radius + 1/radius - (radius - 2.0)/radius**2)/(radius - 2.0)\n",
      "r, r, r:  0.5*radius*(radius/(radius - 2.0) - radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0)\n",
      "r, phi, phi:  0.5*radius*(-radius**2*sin(theta)**2 - 2*radius*sin(theta)**2)/(radius - 2.0)\n",
      "r, theta, theta:  0.5*radius*(-radius**2 - 2*radius)/(radius - 2.0)\n",
      "-----Direct Calculation-----\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "<matrix0>\n",
      "\t<row0>\n",
      "\t\t<number0x0>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0 + 0 - 0  ) l:  0  m:  0  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - -1/radius + (radius - 2.0)/radius**2  ) l:  0  m:  0  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  0  m:  0  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  0  m:  0  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x0>\n",
      "\t\t<number0x1>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  -1/radius + (radius - 2.0)/radius**2 + 0.0 - 0.0  ) l:  0  m:  0  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  0  m:  0  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  0  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  0  n:  1  p:  3\n",
      "\t\t\tresult:  -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x1>\n",
      "\t\t<number0x2>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0 + 0.0 - 0.0  ) l:  0  m:  0  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  0  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  0  m:  0  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  0  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x2>\n",
      "\t\t<number0x3>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0 + 0.0 - 0.0  ) l:  0  m:  0  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  0  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  0  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  0  m:  0  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row0>\n",
      "\t<row1>\n",
      "\t\t<number1x0>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + -1/radius + (radius - 2.0)/radius**2 - 0.0  ) l:  0  m:  1  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  0  m:  1  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  1  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  1  n:  0  p:  3\n",
      "\t\t\tresult:  -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x0>\n",
      "\t\t<number1x1>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0  ) l:  0  m:  1  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  -radius/(radius - 2.0)**2 + 1/(radius - 2.0) + -radius/(radius - 2.0)**2 + 1/(radius - 2.0) - -radius/(radius - 2.0)**2 + 1/(radius - 2.0)  ) l:  0  m:  1  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  0  m:  1  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  0  m:  1  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x1>\n",
      "\t\t<number1x2>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  1  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  0  m:  1  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius - 0.0  ) l:  0  m:  1  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  1  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x2>\n",
      "\t\t<number1x3>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  1  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  0  m:  1  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  1  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius*sin(theta)**2 - 0.0  ) l:  0  m:  1  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row1>\n",
      "\t<row2>\n",
      "\t\t<number2x0>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0 - 0.0  ) l:  0  m:  2  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  2  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  0  m:  2  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  2  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x0>\n",
      "\t\t<number2x1>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  2  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  0  m:  2  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  2*radius + 0.0 - 0.0  ) l:  0  m:  2  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  2  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x1>\n",
      "\t\t<number2x2>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0  ) l:  0  m:  2  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius  ) l:  0  m:  2  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  0  m:  2  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  0  m:  2  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x2>\n",
      "\t\t<number2x3>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  2  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  2  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  0  m:  2  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius**2*sin(theta)*cos(theta) - 0.0  ) l:  0  m:  2  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row2>\n",
      "\t<row3>\n",
      "\t\t<number3x0>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0 - 0.0  ) l:  0  m:  3  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  3  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  3  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  0  m:  3  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x0>\n",
      "\t\t<number3x1>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  3  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  0  m:  3  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  3  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  2*radius*sin(theta)**2 + 0.0 - 0.0  ) l:  0  m:  3  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x1>\n",
      "\t\t<number3x2>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  3  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  0  m:  3  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  0  m:  3  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  2*radius**2*sin(theta)*cos(theta) + 0.0 - 0.0  ) l:  0  m:  3  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x2>\n",
      "\t\t<number3x3>\n",
      "\t\t\t -0.5*(radius - 2.0)/radius  * (  0.0 + 0.0 - 0  ) l:  0  m:  3  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius*sin(theta)**2  ) l:  0  m:  3  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius**2*sin(theta)*cos(theta)  ) l:  0  m:  3  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  0  m:  3  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "\t\t\t [-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t</rcurrently>\n",
      "\t</row3>\n",
      "</matrix0>\n",
      "\n",
      "\n",
      "<matrix1>\n",
      "\t<row0>\n",
      "\t\t<number0x0>\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  1  m:  0  n:  0  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - -1/radius + (radius - 2.0)/radius**2  ) l:  1  m:  0  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  0  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  0  n:  0  p:  3\n",
      "\t\t\tresult:  0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x0>\n",
      "\t\t<number0x1>\n",
      "\t\t\t 0.0  * (  -1/radius + (radius - 2.0)/radius**2 + 0.0 - 0.0  ) l:  1  m:  0  n:  1  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0 - 0.0  ) l:  1  m:  0  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  0  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  0  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x1>\n",
      "\t\t<number0x2>\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  1  m:  0  n:  2  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  0  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  1  m:  0  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  0  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x2>\n",
      "\t\t<number0x3>\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  1  m:  0  n:  3  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  0  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  0  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  1  m:  0  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row0>\n",
      "\t<row1>\n",
      "\t\t<number1x0>\n",
      "\t\t\t 0.0  * (  0.0 + -1/radius + (radius - 2.0)/radius**2 - 0.0  ) l:  1  m:  1  n:  0  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0 + 0.0 - 0.0  ) l:  1  m:  1  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  1  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  1  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x0>\n",
      "\t\t<number1x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  1  n:  1  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  -radius/(radius - 2.0)**2 + 1/(radius - 2.0) + -radius/(radius - 2.0)**2 + 1/(radius - 2.0) - -radius/(radius - 2.0)**2 + 1/(radius - 2.0)  ) l:  1  m:  1  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  1  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  1  n:  1  p:  3\n",
      "\t\t\tresult:  0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x1>\n",
      "\t\t<number1x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  1  n:  2  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0 + 0.0 - 0.0  ) l:  1  m:  1  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius - 0.0  ) l:  1  m:  1  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  1  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x2>\n",
      "\t\t<number1x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  1  n:  3  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0 + 0.0 - 0.0  ) l:  1  m:  1  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  1  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius*sin(theta)**2 - 0.0  ) l:  1  m:  1  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row1>\n",
      "\t<row2>\n",
      "\t\t<number2x0>\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  1  m:  2  n:  0  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  2  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  1  m:  2  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  2  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x0>\n",
      "\t\t<number2x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  2  n:  1  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0 - 0.0  ) l:  1  m:  2  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  2*radius + 0.0 - 0.0  ) l:  1  m:  2  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  2  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x1>\n",
      "\t\t<number2x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  2  n:  2  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 2*radius  ) l:  1  m:  2  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  1  m:  2  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  2  n:  2  p:  3\n",
      "\t\t\tresult:  -1.0*radius**2/(radius - 2.0) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x2>\n",
      "\t\t<number2x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  2  n:  3  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  2  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  1  m:  2  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius**2*sin(theta)*cos(theta) - 0.0  ) l:  1  m:  2  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row2>\n",
      "\t<row3>\n",
      "\t\t<number3x0>\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  1  m:  3  n:  0  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  3  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  3  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  1  m:  3  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x0>\n",
      "\t\t<number3x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  3  n:  1  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0 - 0.0  ) l:  1  m:  3  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  3  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  2*radius*sin(theta)**2 + 0.0 - 0.0  ) l:  1  m:  3  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x1>\n",
      "\t\t<number3x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  3  n:  2  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 0.0  ) l:  1  m:  3  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  1  m:  3  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  2*radius**2*sin(theta)*cos(theta) + 0.0 - 0.0  ) l:  1  m:  3  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x2>\n",
      "\t\t<number3x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  1  m:  3  n:  3  p:  0\n",
      "\t\t\t 0.5*radius/(radius - 2.0)  * (  0.0 + 0.0 - 2*radius*sin(theta)**2  ) l:  1  m:  3  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius**2*sin(theta)*cos(theta)  ) l:  1  m:  3  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  1  m:  3  n:  3  p:  3\n",
      "\t\t\tresult:  -1.0*radius**2*sin(theta)**2/(radius - 2.0) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t\t [0, 0, 0, -1.0*radius**2*sin(theta)**2/(radius - 2.0)]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "\t\t\t [0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "\t\t\t [0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "\t\t\t [0, 0, 0, -1.0*radius**2*sin(theta)**2/(radius - 2.0)]\n",
      "\t\t</rcurrently>\n",
      "\t</row3>\n",
      "</matrix1>\n",
      "\n",
      "\n",
      "<matrix2>\n",
      "\t<row0>\n",
      "\t\t<number0x0>\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  2  m:  0  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - -1/radius + (radius - 2.0)/radius**2  ) l:  2  m:  0  n:  0  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0  ) l:  2  m:  0  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  2  m:  0  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x0>\n",
      "\t\t<number0x1>\n",
      "\t\t\t 0.0  * (  -1/radius + (radius - 2.0)/radius**2 + 0.0 - 0.0  ) l:  2  m:  0  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  2  m:  0  n:  1  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  0  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  0  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x1>\n",
      "\t\t<number0x2>\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  2  m:  0  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  0  n:  2  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0 - 0.0  ) l:  2  m:  0  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  0  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x2>\n",
      "\t\t<number0x3>\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  2  m:  0  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  0  n:  3  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  0  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  2  m:  0  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row0>\n",
      "\t<row1>\n",
      "\t\t<number1x0>\n",
      "\t\t\t 0.0  * (  0.0 + -1/radius + (radius - 2.0)/radius**2 - 0.0  ) l:  2  m:  1  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  2  m:  1  n:  0  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  1  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  1  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x0>\n",
      "\t\t<number1x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  2  m:  1  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  -radius/(radius - 2.0)**2 + 1/(radius - 2.0) + -radius/(radius - 2.0)**2 + 1/(radius - 2.0) - -radius/(radius - 2.0)**2 + 1/(radius - 2.0)  ) l:  2  m:  1  n:  1  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0  ) l:  2  m:  1  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  2  m:  1  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x1>\n",
      "\t\t<number1x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  1  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  2  m:  1  n:  2  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 2*radius - 0.0  ) l:  2  m:  1  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  1  n:  2  p:  3\n",
      "\t\t\tresult:  1.0*radius**3 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x2>\n",
      "\t\t<number1x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  1  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  2  m:  1  n:  3  p:  1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  1  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius*sin(theta)**2 - 0.0  ) l:  2  m:  1  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row1>\n",
      "\t<row2>\n",
      "\t\t<number2x0>\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  2  m:  2  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  2  n:  0  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0 + 0.0 - 0.0  ) l:  2  m:  2  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  2  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x0>\n",
      "\t\t<number2x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  2  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  2  m:  2  n:  1  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  2*radius + 0.0 - 0.0  ) l:  2  m:  2  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  2  n:  1  p:  3\n",
      "\t\t\tresult:  1.0*radius**3 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x1>\n",
      "\t\t<number2x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  2  m:  2  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius  ) l:  2  m:  2  n:  2  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0 + 0 - 0  ) l:  2  m:  2  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  2  m:  2  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x2>\n",
      "\t\t<number2x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  2  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  2  n:  3  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0 + 0.0 - 0.0  ) l:  2  m:  2  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius**2*sin(theta)*cos(theta) - 0.0  ) l:  2  m:  2  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row2>\n",
      "\t<row3>\n",
      "\t\t<number3x0>\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  2  m:  3  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  3  n:  0  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  3  n:  0  p:  2\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  2  m:  3  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x0>\n",
      "\t\t<number3x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  3  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  2  m:  3  n:  1  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  3  n:  1  p:  2\n",
      "\t\t\t 0.0  * (  2*radius*sin(theta)**2 + 0.0 - 0.0  ) l:  2  m:  3  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x1>\n",
      "\t\t<number3x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  3  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  2  m:  3  n:  2  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0 - 0.0  ) l:  2  m:  3  n:  2  p:  2\n",
      "\t\t\t 0.0  * (  2*radius**2*sin(theta)*cos(theta) + 0.0 - 0.0  ) l:  2  m:  3  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x2>\n",
      "\t\t<number3x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  2  m:  3  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius*sin(theta)**2  ) l:  2  m:  3  n:  3  p:  1\n",
      "\t\t\t 0.5*radius**2  * (  0.0 + 0.0 - 2*radius**2*sin(theta)*cos(theta)  ) l:  2  m:  3  n:  3  p:  2\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  2  m:  3  n:  3  p:  3\n",
      "\t\t\tresult:  -1.0*radius**4*sin(theta)*cos(theta) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, -1.0*radius**4*sin(theta)*cos(theta)]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 1.0*radius**3, 0]\n",
      "\t\t\t [0, 1.0*radius**3, 0, 0]\n",
      "\t\t\t [0, 0, 0, -1.0*radius**4*sin(theta)*cos(theta)]\n",
      "\t\t</rcurrently>\n",
      "\t</row3>\n",
      "</matrix2>\n",
      "\n",
      "\n",
      "<matrix3>\n",
      "\t<row0>\n",
      "\t\t<number0x0>\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  3  m:  0  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - -1/radius + (radius - 2.0)/radius**2  ) l:  3  m:  0  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  3  m:  0  n:  0  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0  ) l:  3  m:  0  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x0>\n",
      "\t\t<number0x1>\n",
      "\t\t\t 0.0  * (  -1/radius + (radius - 2.0)/radius**2 + 0.0 - 0.0  ) l:  3  m:  0  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  0  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  0  n:  1  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  0  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x1>\n",
      "\t\t<number0x2>\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  0  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  0  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  0  n:  2  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  0  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x2>\n",
      "\t\t<number0x3>\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  0  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  0  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  0  n:  3  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0 - 0.0  ) l:  3  m:  0  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number0x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row0>\n",
      "\t<row1>\n",
      "\t\t<number1x0>\n",
      "\t\t\t 0.0  * (  0.0 + -1/radius + (radius - 2.0)/radius**2 - 0.0  ) l:  3  m:  1  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  1  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  1  n:  0  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  1  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x0>\n",
      "\t\t<number1x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  3  m:  1  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  -radius/(radius - 2.0)**2 + 1/(radius - 2.0) + -radius/(radius - 2.0)**2 + 1/(radius - 2.0) - -radius/(radius - 2.0)**2 + 1/(radius - 2.0)  ) l:  3  m:  1  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  3  m:  1  n:  1  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0  ) l:  3  m:  1  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x1>\n",
      "\t\t<number1x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  1  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  1  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 2*radius - 0.0  ) l:  3  m:  1  n:  2  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  1  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x2>\n",
      "\t\t<number1x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  1  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  1  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  1  n:  3  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 2*radius*sin(theta)**2 - 0.0  ) l:  3  m:  1  n:  3  p:  3\n",
      "\t\t\tresult:  1.0*radius**3*sin(theta)**4 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number1x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row1>\n",
      "\t<row2>\n",
      "\t\t<number2x0>\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  2  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  2  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  2  n:  0  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  2  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x0>\n",
      "\t\t<number2x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  2  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  2  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  2*radius + 0.0 - 0.0  ) l:  3  m:  2  n:  1  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  2  n:  1  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0.0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x1>\n",
      "\t\t<number2x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  3  m:  2  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius  ) l:  3  m:  2  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0 - 0  ) l:  3  m:  2  n:  2  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 0.0 - 0  ) l:  3  m:  2  n:  2  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0, 0.0]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x2>\n",
      "\t\t<number2x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  2  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  2  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0 + 0.0 - 0.0  ) l:  3  m:  2  n:  3  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0.0 + 2*radius**2*sin(theta)*cos(theta) - 0.0  ) l:  3  m:  2  n:  3  p:  3\n",
      "\t\t\tresult:  1.0*radius**4*sin(theta)**3*cos(theta) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number2x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t [0.0, 0.0, 0.0, 0.0]\n",
      "\t\t</rcurrently>\n",
      "\t</row2>\n",
      "\t<row3>\n",
      "\t\t<number3x0>\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  3  n:  0  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  3  n:  0  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  3  n:  0  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0 + 0.0 - 0.0  ) l:  3  m:  3  n:  0  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t\t [0, 0.0, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x0>\n",
      "\t\t<number3x1>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  3  n:  1  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  3  n:  1  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  3  n:  1  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  2*radius*sin(theta)**2 + 0.0 - 0.0  ) l:  3  m:  3  n:  1  p:  3\n",
      "\t\t\tresult:  1.0*radius**3*sin(theta)**4 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t\t [0, 1.0*radius**3*sin(theta)**4, 0.0, 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x1>\n",
      "\t\t<number3x2>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  3  n:  2  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0.0  ) l:  3  m:  3  n:  2  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0 - 0.0  ) l:  3  m:  3  n:  2  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  2*radius**2*sin(theta)*cos(theta) + 0.0 - 0.0  ) l:  3  m:  3  n:  2  p:  3\n",
      "\t\t\tresult:  1.0*radius**4*sin(theta)**3*cos(theta) \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t\t [0, 1.0*radius**3*sin(theta)**4, 1.0*radius**4*sin(theta)**3*cos(theta), 0.0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x2>\n",
      "\t\t<number3x3>\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 0  ) l:  3  m:  3  n:  3  p:  0\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius*sin(theta)**2  ) l:  3  m:  3  n:  3  p:  1\n",
      "\t\t\t 0.0  * (  0.0 + 0.0 - 2*radius**2*sin(theta)*cos(theta)  ) l:  3  m:  3  n:  3  p:  2\n",
      "\t\t\t 0.5*radius**2*sin(theta)**2  * (  0 + 0 - 0  ) l:  3  m:  3  n:  3  p:  3\n",
      "\t\t\tresult:  0 \n",
      "\n",
      "\t\t\t<ncurrently>\n",
      "\t\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t\t [0, 1.0*radius**3*sin(theta)**4, 1.0*radius**4*sin(theta)**3*cos(theta), 0]\n",
      "\t\t\t</ncurrently>\n",
      "\t\t</number3x3>\n",
      "\t\t<rcurrently>\n",
      "\t\t\t [0, 0, 0, 0]\n",
      "\t\t\t [0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "\t\t\t [0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "\t\t\t [0, 1.0*radius**3*sin(theta)**4, 1.0*radius**4*sin(theta)**3*cos(theta), 0]\n",
      "\t\t</rcurrently>\n",
      "\t</row3>\n",
      "</matrix3>\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "[0, -0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0]\n",
      "[-0.5*(-1/radius + (radius - 2.0)/radius**2)*(radius - 2.0)/radius, 0, 0, 0]\n",
      "[0, 0, 0, 0]\n",
      "[0, 0, 0, 0]\n",
      "\n",
      "\n",
      "\n",
      "[0.5*radius*(1/radius - (radius - 2.0)/radius**2)/(radius - 2.0), 0, 0, 0]\n",
      "[0, 0.5*radius*(-radius/(radius - 2.0)**2 + 1/(radius - 2.0))/(radius - 2.0), 0, 0]\n",
      "[0, 0, -1.0*radius**2/(radius - 2.0), 0]\n",
      "[0, 0, 0, -1.0*radius**2*sin(theta)**2/(radius - 2.0)]\n",
      "\n",
      "\n",
      "\n",
      "[0, 0, 0, 0]\n",
      "[0, 0, 1.0*radius**3, 0]\n",
      "[0, 1.0*radius**3, 0, 0]\n",
      "[0, 0, 0, -1.0*radius**4*sin(theta)*cos(theta)]\n",
      "\n",
      "\n",
      "\n",
      "[0, 0, 0, 0]\n",
      "[0, 0, 0, 1.0*radius**3*sin(theta)**4]\n",
      "[0, 0, 0, 1.0*radius**4*sin(theta)**3*cos(theta)]\n",
      "[0, 1.0*radius**3*sin(theta)**4, 1.0*radius**4*sin(theta)**3*cos(theta), 0]\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print( CoordinateString( 3, 1, 3 ), IntermediateConnection( 1.0, radius, theta, 3, 1, 3, symboles ) )\n",
    "print( CoordinateString( 3, 2, 3 ), IntermediateConnection( 1.0, radius, theta, 3, 2, 3, symboles ) )\n",
    "print( CoordinateString( 2, 2, 2 ), IntermediateConnection( 1.0, radius, theta, 2, 2, 2, symboles ) )\n",
    "print( CoordinateString( 2, 1, 3 ), IntermediateConnection( 1.0, radius, theta, 2, 1, 3, symboles ) )\n",
    "#print( CoordinateString( 3, 1, 3 ), IntermediateConnection( 1.0, radius, theta, 3, 1, 3, symboles ) )\n",
    "#print( CoordinateString( 3, 2, 3 ), IntermediateConnection( 1.0, radius, theta, 3, 2, 3, symboles ) )\n",
    "print( CoordinateString( 0, 0, 3 ), IntermediateConnection( 1.0, radius, theta, 0, 0, 1, symboles ) )\n",
    "print( CoordinateString( 1, 0, 0 ), IntermediateConnection( 1.0, radius, theta, 1, 0, 0, symboles ) )\n",
    "print( CoordinateString( 1, 1, 1 ), IntermediateConnection( 1.0, radius, theta, 1, 1, 1, symboles ) )\n",
    "print( CoordinateString( 1, 3, 3 ), IntermediateConnection( 1.0, radius, theta, 1, 3, 3, symboles ) )\n",
    "print( CoordinateString( 1, 2, 2 ), IntermediateConnection( 1.0, radius, theta, 1, 2, 2, symboles ) )\n",
    "print( '-----Direct Calculation-----\\n\\n\\n\\n' )\n",
    "connection = Connection( 1.0, radius, theta, 3, 1, 3, symboles )\n",
    "print( \"\\n\\n\" )\n",
    "for i in connection:\n",
    "    for j in i:\n",
    "        print( simplify( j ) )\n",
    "    print( '\\n\\n' )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeConnection( mass, radius, theta, symboles ):\n",
    "    #coords = [ 'time', 'radius', 'theta', 'phi' ]\n",
    "    result = [ [ 0.0, 0.0, 0.0, 0.0 ], \n",
    "    [ 0.0, 0.0, 0.0, 0.0 ], \n",
    "    [ 0.0, 0.0, 0.0, 0.0 ], \n",
    "    [ 0.0, 0.0, 0.0, 0.0 ] ]\n",
    "    results = []\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    results.append( copy.deepcopy( result ) )\n",
    "    for i in range( 4 ):\n",
    "        for j in range( 4 ):\n",
    "            #print( 'x: ' + coords[ i ] + ' y: ' + coords[ j ] )\n",
    "            for k in range( 4 ):\n",
    "                results[ k ][ i ][ j ] += IntermediateConnection( mass, radius, theta, k, i, j, symboles )\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "newLine = 0\n",
    "for i in MakeConnection( 1.0, radius, theta, symboles ):\n",
    "    print( i )\n",
    "    for j in i:\n",
    "        print( j )\n",
    "        q = j\n",
    "        for k in q:\n",
    "            k = simplify( k )\n",
    "        print( q )\n",
    "        if newLine >= 3:\n",
    "            print( '\\n\\n\\n\\n\\n\\n\\n\\n' )\n",
    "            newLine = 0\n",
    "        else:\n",
    "            newLine += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def GenerateDerivedMetric( metric, symboles ):\n",
    "    global DeriveMetricParameter\n",
    "    Derive = DeriveMetricParameter\n",
    "    for i in range( 4 ):\n",
    "        for j in range( 4 ):\n",
    "            metric[ i ][ j ] = Derive( metric, i, j, symboles[ j ] )\n",
    "    return metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 0.0, 0.0, 0.0],\n",
       " [0.0, -radius/(radius - 2.0)**2 + 1/(radius - 2.0), 0.0, 0.0],\n",
       " [0.0, 0.0, 0, 0.0],\n",
       " [0.0, 0.0, 0.0, 0]]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GenerateDerivedMetric( ShwarzchildMetric( 1.0, symboles[ 1 ], symboles[ 2 ] ), symboles )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = Matrix( [ [ 0, 1 ], [ 1, 0 ] ] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 1], [1, 0]]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 1], [1, 0]]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.__array__().tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = Matrix( [ [ 1, 3 ], [ 6, 8 ] ] )\n",
    "B = Matrix( [ [ 2, 8 ], [ 4, 6 ] ] )\n",
    "C = Matrix( [ [ 9, 3 ], [ 7, 5 ] ] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Matrix([\n",
       "[ 44,  44],\n",
       "[154, 154]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "( A * B ) + ( A * C )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Matrix([\n",
       "[ 44,  44],\n",
       "[154, 154]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * ( B + C )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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