tricky_determinant.ipynb

{
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  "name": "",
  "signature": "sha256:7c46df537ad8dbd089e78fb490cf55e050f9a51e9fe09c7e1e9a593472ea6322"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load SymPy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "from __future__ import division, print_function, with_statement\n",
      "\n",
      "init_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define symbols"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x, r, s, alpha, beta, gamma = symbols('x, r, s, \\\\alpha, \\\\beta, \\\\gamma', real=True)\n",
      "\n",
      "u11, u12, u13 = symbols('U_11, U_12, U_13', real=True)\n",
      "u21, u22, u23 = symbols('U_21, U_22, U_23', real=True)\n",
      "u31, u32, u33 = symbols('U_31, U_32, U_33', real=True)\n",
      "\n",
      "v11, v12, v13 = symbols('V_11, V_12, V_13', real=True)\n",
      "v21, v22, v23 = symbols('V_21, V_22, V_23', real=True)\n",
      "v31, v32, v33 = symbols('V_31, V_32, V_33', real=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define the matrices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m1 = Matrix(((u11 * v13, u12 * v13, u13 * v13, r * u11 * v11 + s * u12 * v12),\n",
      "             (u11 * v23, u12 * v23, u13 * v23, r * u11 * v21 + s * u12 * v22),\n",
      "             (u21 * v13, u22 * v13, u23 * v13, r * u21 * v11 + s * u22 * v12),\n",
      "             (u21 * v23, u22 * v23, u23 * v23, r * u21 * v21 + s * u22 * v22)))\n",
      "\n",
      "mx = Matrix(((-s * u13 * v11, -r * u13 * v12, r * u12 * v12 + s * u11 * v11, r * s * u13 * v13),\n",
      "             (-s * u13 * v21, -r * u13 * v22, r * u12 * v22 + s * u11 * v21, r * s * u13 * v23),\n",
      "             (-s * u23 * v11, -r * u23 * v12, r * u22 * v12 + s * u21 * v11, r * s * u23 * v13),\n",
      "             (-s * u23 * v21, -r * u23 * v22, r * u22 * v22 + s * u21 * v21, r * s * u23 * v23)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check stated properties (may take a while)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(det(mx))\n",
      "print(det(m1))\n",
      "print(det(m1 + mx) + det(m1 - mx))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0\n",
        "0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now compute that determinant (as a polynomial in x)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = Poly(det(m1 - x * mx), x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check expected properties (it is a polynomial with degree 3 and terms only on x and x<sup>3</sup>)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(d.degree())\n",
      "print(d.coeff_monomial(1))\n",
      "print(d.coeff_monomial(x * x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3\n",
        "0\n",
        "0\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And so the expressions for a1 and a2 are:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a1 = d.coeff_monomial(x)\n",
      "a2 = d.coeff_monomial(x * x * x)\n",
      "a1, a2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left ( - U_{11}^{2} U_{22}^{2} V_{11} V_{12} V_{23}^{2} r^{2} + U_{11}^{2} U_{22}^{2} V_{11} V_{12} V_{23}^{2} s^{2} + U_{11}^{2} U_{22}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} - U_{11}^{2} U_{22}^{2} V_{11} V_{13} V_{22} V_{23} s^{2} + U_{11}^{2} U_{22}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} - U_{11}^{2} U_{22}^{2} V_{12} V_{13} V_{21} V_{23} s^{2} - U_{11}^{2} U_{22}^{2} V_{13}^{2} V_{21} V_{22} r^{2} + U_{11}^{2} U_{22}^{2} V_{13}^{2} V_{21} V_{22} s^{2} - U_{11}^{2} U_{23}^{2} V_{11} V_{12} V_{23}^{2} r^{2} + U_{11}^{2} U_{23}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} + U_{11}^{2} U_{23}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} - U_{11}^{2} U_{23}^{2} V_{13}^{2} V_{21} V_{22} r^{2} + 2 U_{11} U_{12} U_{21} U_{22} V_{11} V_{12} V_{23}^{2} r^{2} - 2 U_{11} U_{12} U_{21} U_{22} V_{11} V_{12} V_{23}^{2} s^{2} - 2 U_{11} U_{12} U_{21} U_{22} V_{11} V_{13} V_{22} V_{23} r^{2} + 2 U_{11} U_{12} U_{21} U_{22} V_{11} V_{13} V_{22} V_{23} s^{2} - 2 U_{11} U_{12} U_{21} U_{22} V_{12} V_{13} V_{21} V_{23} r^{2} + 2 U_{11} U_{12} U_{21} U_{22} V_{12} V_{13} V_{21} V_{23} s^{2} + 2 U_{11} U_{12} U_{21} U_{22} V_{13}^{2} V_{21} V_{22} r^{2} - 2 U_{11} U_{12} U_{21} U_{22} V_{13}^{2} V_{21} V_{22} s^{2} + U_{11} U_{12} U_{23}^{2} V_{11}^{2} V_{23}^{2} r s - 2 U_{11} U_{12} U_{23}^{2} V_{11} V_{13} V_{21} V_{23} r s - U_{11} U_{12} U_{23}^{2} V_{12}^{2} V_{23}^{2} r s + 2 U_{11} U_{12} U_{23}^{2} V_{12} V_{13} V_{22} V_{23} r s + U_{11} U_{12} U_{23}^{2} V_{13}^{2} V_{21}^{2} r s - U_{11} U_{12} U_{23}^{2} V_{13}^{2} V_{22}^{2} r s + 2 U_{11} U_{13} U_{21} U_{23} V_{11} V_{12} V_{23}^{2} r^{2} - 2 U_{11} U_{13} U_{21} U_{23} V_{11} V_{13} V_{22} V_{23} r^{2} - 2 U_{11} U_{13} U_{21} U_{23} V_{12} V_{13} V_{21} V_{23} r^{2} + 2 U_{11} U_{13} U_{21} U_{23} V_{13}^{2} V_{21} V_{22} r^{2} - U_{11} U_{13} U_{22} U_{23} V_{11}^{2} V_{23}^{2} r s + 2 U_{11} U_{13} U_{22} U_{23} V_{11} V_{13} V_{21} V_{23} r s + U_{11} U_{13} U_{22} U_{23} V_{12}^{2} V_{23}^{2} r s - 2 U_{11} U_{13} U_{22} U_{23} V_{12} V_{13} V_{22} V_{23} r s - U_{11} U_{13} U_{22} U_{23} V_{13}^{2} V_{21}^{2} r s + U_{11} U_{13} U_{22} U_{23} V_{13}^{2} V_{22}^{2} r s - U_{12}^{2} U_{21}^{2} V_{11} V_{12} V_{23}^{2} r^{2} + U_{12}^{2} U_{21}^{2} V_{11} V_{12} V_{23}^{2} s^{2} + U_{12}^{2} U_{21}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} - U_{12}^{2} U_{21}^{2} V_{11} V_{13} V_{22} V_{23} s^{2} + U_{12}^{2} U_{21}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} - U_{12}^{2} U_{21}^{2} V_{12} V_{13} V_{21} V_{23} s^{2} - U_{12}^{2} U_{21}^{2} V_{13}^{2} V_{21} V_{22} r^{2} + U_{12}^{2} U_{21}^{2} V_{13}^{2} V_{21} V_{22} s^{2} + U_{12}^{2} U_{23}^{2} V_{11} V_{12} V_{23}^{2} s^{2} - U_{12}^{2} U_{23}^{2} V_{11} V_{13} V_{22} V_{23} s^{2} - U_{12}^{2} U_{23}^{2} V_{12} V_{13} V_{21} V_{23} s^{2} + U_{12}^{2} U_{23}^{2} V_{13}^{2} V_{21} V_{22} s^{2} - U_{12} U_{13} U_{21} U_{23} V_{11}^{2} V_{23}^{2} r s + 2 U_{12} U_{13} U_{21} U_{23} V_{11} V_{13} V_{21} V_{23} r s + U_{12} U_{13} U_{21} U_{23} V_{12}^{2} V_{23}^{2} r s - 2 U_{12} U_{13} U_{21} U_{23} V_{12} V_{13} V_{22} V_{23} r s - U_{12} U_{13} U_{21} U_{23} V_{13}^{2} V_{21}^{2} r s + U_{12} U_{13} U_{21} U_{23} V_{13}^{2} V_{22}^{2} r s - 2 U_{12} U_{13} U_{22} U_{23} V_{11} V_{12} V_{23}^{2} s^{2} + 2 U_{12} U_{13} U_{22} U_{23} V_{11} V_{13} V_{22} V_{23} s^{2} + 2 U_{12} U_{13} U_{22} U_{23} V_{12} V_{13} V_{21} V_{23} s^{2} - 2 U_{12} U_{13} U_{22} U_{23} V_{13}^{2} V_{21} V_{22} s^{2} - U_{13}^{2} U_{21}^{2} V_{11} V_{12} V_{23}^{2} r^{2} + U_{13}^{2} U_{21}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} + U_{13}^{2} U_{21}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} - U_{13}^{2} U_{21}^{2} V_{13}^{2} V_{21} V_{22} r^{2} + U_{13}^{2} U_{21} U_{22} V_{11}^{2} V_{23}^{2} r s - 2 U_{13}^{2} U_{21} U_{22} V_{11} V_{13} V_{21} V_{23} r s - U_{13}^{2} U_{21} U_{22} V_{12}^{2} V_{23}^{2} r s + 2 U_{13}^{2} U_{21} U_{22} V_{12} V_{13} V_{22} V_{23} r s + U_{13}^{2} U_{21} U_{22} V_{13}^{2} V_{21}^{2} r s - U_{13}^{2} U_{21} U_{22} V_{13}^{2} V_{22}^{2} r s + U_{13}^{2} U_{22}^{2} V_{11} V_{12} V_{23}^{2} s^{2} - U_{13}^{2} U_{22}^{2} V_{11} V_{13} V_{22} V_{23} s^{2} - U_{13}^{2} U_{22}^{2} V_{12} V_{13} V_{21} V_{23} s^{2} + U_{13}^{2} U_{22}^{2} V_{13}^{2} V_{21} V_{22} s^{2}, \\quad U_{11}^{2} U_{23}^{2} V_{11} V_{12} V_{23}^{2} r^{2} s^{2} - U_{11}^{2} U_{23}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} s^{2} - U_{11}^{2} U_{23}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} s^{2} + U_{11}^{2} U_{23}^{2} V_{13}^{2} V_{21} V_{22} r^{2} s^{2} + U_{11} U_{12} U_{23}^{2} V_{11}^{2} V_{22}^{2} r^{3} s - U_{11} U_{12} U_{23}^{2} V_{11}^{2} V_{22}^{2} r s^{3} - U_{11} U_{12} U_{23}^{2} V_{11}^{2} V_{23}^{2} r s^{3} - 2 U_{11} U_{12} U_{23}^{2} V_{11} V_{12} V_{21} V_{22} r^{3} s + 2 U_{11} U_{12} U_{23}^{2} V_{11} V_{12} V_{21} V_{22} r s^{3} + 2 U_{11} U_{12} U_{23}^{2} V_{11} V_{13} V_{21} V_{23} r s^{3} + U_{11} U_{12} U_{23}^{2} V_{12}^{2} V_{21}^{2} r^{3} s - U_{11} U_{12} U_{23}^{2} V_{12}^{2} V_{21}^{2} r s^{3} + U_{11} U_{12} U_{23}^{2} V_{12}^{2} V_{23}^{2} r^{3} s - 2 U_{11} U_{12} U_{23}^{2} V_{12} V_{13} V_{22} V_{23} r^{3} s - U_{11} U_{12} U_{23}^{2} V_{13}^{2} V_{21}^{2} r s^{3} + U_{11} U_{12} U_{23}^{2} V_{13}^{2} V_{22}^{2} r^{3} s - 2 U_{11} U_{13} U_{21} U_{23} V_{11} V_{12} V_{23}^{2} r^{2} s^{2} + 2 U_{11} U_{13} U_{21} U_{23} V_{11} V_{13} V_{22} V_{23} r^{2} s^{2} + 2 U_{11} U_{13} U_{21} U_{23} V_{12} V_{13} V_{21} V_{23} r^{2} s^{2} - 2 U_{11} U_{13} U_{21} U_{23} V_{13}^{2} V_{21} V_{22} r^{2} s^{2} - U_{11} U_{13} U_{22} U_{23} V_{11}^{2} V_{22}^{2} r^{3} s + U_{11} U_{13} U_{22} U_{23} V_{11}^{2} V_{22}^{2} r s^{3} + U_{11} U_{13} U_{22} U_{23} V_{11}^{2} V_{23}^{2} r s^{3} + 2 U_{11} U_{13} U_{22} U_{23} V_{11} V_{12} V_{21} V_{22} r^{3} s - 2 U_{11} U_{13} U_{22} U_{23} V_{11} V_{12} V_{21} V_{22} r s^{3} - 2 U_{11} U_{13} U_{22} U_{23} V_{11} V_{13} V_{21} V_{23} r s^{3} - U_{11} U_{13} U_{22} U_{23} V_{12}^{2} V_{21}^{2} r^{3} s + U_{11} U_{13} U_{22} U_{23} V_{12}^{2} V_{21}^{2} r s^{3} - U_{11} U_{13} U_{22} U_{23} V_{12}^{2} V_{23}^{2} r^{3} s + 2 U_{11} U_{13} U_{22} U_{23} V_{12} V_{13} V_{22} V_{23} r^{3} s + U_{11} U_{13} U_{22} U_{23} V_{13}^{2} V_{21}^{2} r s^{3} - U_{11} U_{13} U_{22} U_{23} V_{13}^{2} V_{22}^{2} r^{3} s - U_{12}^{2} U_{23}^{2} V_{11} V_{12} V_{23}^{2} r^{2} s^{2} + U_{12}^{2} U_{23}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} s^{2} + U_{12}^{2} U_{23}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} s^{2} - U_{12}^{2} U_{23}^{2} V_{13}^{2} V_{21} V_{22} r^{2} s^{2} - U_{12} U_{13} U_{21} U_{23} V_{11}^{2} V_{22}^{2} r^{3} s + U_{12} U_{13} U_{21} U_{23} V_{11}^{2} V_{22}^{2} r s^{3} + U_{12} U_{13} U_{21} U_{23} V_{11}^{2} V_{23}^{2} r s^{3} + 2 U_{12} U_{13} U_{21} U_{23} V_{11} V_{12} V_{21} V_{22} r^{3} s - 2 U_{12} U_{13} U_{21} U_{23} V_{11} V_{12} V_{21} V_{22} r s^{3} - 2 U_{12} U_{13} U_{21} U_{23} V_{11} V_{13} V_{21} V_{23} r s^{3} - U_{12} U_{13} U_{21} U_{23} V_{12}^{2} V_{21}^{2} r^{3} s + U_{12} U_{13} U_{21} U_{23} V_{12}^{2} V_{21}^{2} r s^{3} - U_{12} U_{13} U_{21} U_{23} V_{12}^{2} V_{23}^{2} r^{3} s + 2 U_{12} U_{13} U_{21} U_{23} V_{12} V_{13} V_{22} V_{23} r^{3} s + U_{12} U_{13} U_{21} U_{23} V_{13}^{2} V_{21}^{2} r s^{3} - U_{12} U_{13} U_{21} U_{23} V_{13}^{2} V_{22}^{2} r^{3} s + 2 U_{12} U_{13} U_{22} U_{23} V_{11} V_{12} V_{23}^{2} r^{2} s^{2} - 2 U_{12} U_{13} U_{22} U_{23} V_{11} V_{13} V_{22} V_{23} r^{2} s^{2} - 2 U_{12} U_{13} U_{22} U_{23} V_{12} V_{13} V_{21} V_{23} r^{2} s^{2} + 2 U_{12} U_{13} U_{22} U_{23} V_{13}^{2} V_{21} V_{22} r^{2} s^{2} + U_{13}^{2} U_{21}^{2} V_{11} V_{12} V_{23}^{2} r^{2} s^{2} - U_{13}^{2} U_{21}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} s^{2} - U_{13}^{2} U_{21}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} s^{2} + U_{13}^{2} U_{21}^{2} V_{13}^{2} V_{21} V_{22} r^{2} s^{2} + U_{13}^{2} U_{21} U_{22} V_{11}^{2} V_{22}^{2} r^{3} s - U_{13}^{2} U_{21} U_{22} V_{11}^{2} V_{22}^{2} r s^{3} - U_{13}^{2} U_{21} U_{22} V_{11}^{2} V_{23}^{2} r s^{3} - 2 U_{13}^{2} U_{21} U_{22} V_{11} V_{12} V_{21} V_{22} r^{3} s + 2 U_{13}^{2} U_{21} U_{22} V_{11} V_{12} V_{21} V_{22} r s^{3} + 2 U_{13}^{2} U_{21} U_{22} V_{11} V_{13} V_{21} V_{23} r s^{3} + U_{13}^{2} U_{21} U_{22} V_{12}^{2} V_{21}^{2} r^{3} s - U_{13}^{2} U_{21} U_{22} V_{12}^{2} V_{21}^{2} r s^{3} + U_{13}^{2} U_{21} U_{22} V_{12}^{2} V_{23}^{2} r^{3} s - 2 U_{13}^{2} U_{21} U_{22} V_{12} V_{13} V_{22} V_{23} r^{3} s - U_{13}^{2} U_{21} U_{22} V_{13}^{2} V_{21}^{2} r s^{3} + U_{13}^{2} U_{21} U_{22} V_{13}^{2} V_{22}^{2} r^{3} s - U_{13}^{2} U_{22}^{2} V_{11} V_{12} V_{23}^{2} r^{2} s^{2} + U_{13}^{2} U_{22}^{2} V_{11} V_{13} V_{22} V_{23} r^{2} s^{2} + U_{13}^{2} U_{22}^{2} V_{12} V_{13} V_{21} V_{23} r^{2} s^{2} - U_{13}^{2} U_{22}^{2} V_{13}^{2} V_{21} V_{22} r^{2} s^{2}\\right )$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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4KZ+CYj2UWgb1e1sa1YJzwrlnfLUWs+ZiHYzD4clahAFr08B28IahRiKDNfda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\n",
       "prompt_number": 10,
       "text": [
        "\u239b     2    2            2  2      2    2            2  2      2    2          \n",
        "\u239d- U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r  + U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5s  + U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\n",
        "\n",
        "        2      2    2                  2      2    2                  2      2\n",
        "\u2082\u2082\u22c5V\u2082\u2083\u22c5r  - U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5s  + U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r  - U\u2081\u2081 \n",
        "\n",
        "    2                  2      2    2    2          2      2    2    2         \n",
        "\u22c5U\u2082\u2082 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5s  - U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r  + U\u2081\u2081 \u22c5U\u2082\u2082 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5\n",
        "\n",
        " 2      2    2            2  2      2    2                  2      2    2     \n",
        "s  - U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r  + U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r  + U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2082\u22c5\n",
        "\n",
        "             2      2    2    2          2                                2  2\n",
        "V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r  - U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \n",
        "\n",
        "                                2  2                                      2   \n",
        " - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5s  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r  + \n",
        "\n",
        "                                   2                                      2   \n",
        "2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5s  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r  + \n",
        "\n",
        "                                   2                        2          2      \n",
        "2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5s  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r  - 2\u22c5U\n",
        "\n",
        "                  2          2              2    2    2                    2  \n",
        "\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5s  + U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\n",
        "\n",
        "                                2    2    2                    2              \n",
        "\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s - U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r\u22c5s + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\n",
        "\n",
        "                    2    2    2                  2    2    2                  \n",
        "\u2082\u2083\u22c5r\u22c5s + U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s - U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r\u22c5s + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\n",
        "\n",
        "                  2  2                                      2                 \n",
        "\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5\n",
        "\n",
        "                     2                        2          2                    \n",
        "U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r  - U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\n",
        "\n",
        "  2    2                                                                  2   \n",
        "\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s + U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\n",
        "\n",
        " 2                                                                  2    2    \n",
        "\u2083 \u22c5r\u22c5s - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r\u22c5s - U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s\n",
        "\n",
        "                      2    2          2    2            2  2      2    2      \n",
        " + U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r\u22c5s - U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r  + U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\n",
        "\n",
        "      2  2      2    2                  2      2    2                  2      \n",
        "\u2081\u2082\u22c5V\u2082\u2083 \u22c5s  + U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r  - U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5s  + U\u2081\u2082\n",
        "\n",
        "2    2                  2      2    2                  2      2    2    2     \n",
        " \u22c5U\u2082\u2081 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r  - U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5s  - U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5\n",
        "\n",
        "     2      2    2    2          2      2    2            2  2      2    2    \n",
        "V\u2082\u2082\u22c5r  + U\u2081\u2082 \u22c5U\u2082\u2081 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5s  + U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5s  - U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\n",
        "\n",
        "              2      2    2                  2      2    2    2          2    \n",
        "\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5s  - U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5s  + U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5s  - U\n",
        "\n",
        "                  2    2                                                      \n",
        "\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s + 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s + U\u2081\u2082\u22c5U\u2081\u2083\n",
        "\n",
        "            2    2                                                            \n",
        "\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r\u22c5s - 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r\u22c5s - U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\n",
        "\n",
        "      2    2                          2    2                                  \n",
        "\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s + U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r\u22c5s - 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\n",
        "\n",
        "  2  2                                      2                                 \n",
        "\u2082\u2083 \u22c5s  + 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5s  + 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5\n",
        "\n",
        "     2                        2          2      2    2            2  2      2 \n",
        "V\u2082\u2083\u22c5s  - 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5s  - U\u2081\u2083 \u22c5U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r  + U\u2081\u2083 \u22c5\n",
        "\n",
        "   2                  2      2    2                  2      2    2    2       \n",
        "U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r  + U\u2081\u2083 \u22c5U\u2082\u2081 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r  - U\u2081\u2083 \u22c5U\u2082\u2081 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\n",
        "\n",
        "   2      2            2    2            2                                  2 \n",
        "\u2082\u22c5r  + U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s - 2\u22c5U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s - U\u2081\u2083 \u22c5\n",
        "\n",
        "           2    2            2                                  2            2\n",
        "U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r\u22c5s + 2\u22c5U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r\u22c5s + U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2083 \n",
        "\n",
        "    2          2            2    2          2    2            2  2      2    2\n",
        "\u22c5V\u2082\u2081 \u22c5r\u22c5s - U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r\u22c5s + U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5s  - U\u2081\u2083 \u22c5U\u2082\u2082 \n",
        "\n",
        "                  2      2    2                  2      2    2    2          2\n",
        "\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5s  - U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5s \n",
        "\n",
        "     2    2            2  2  2      2    2                  2  2      2    2  \n",
        ", U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \u22c5s  - U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s  - U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\n",
        "\n",
        "                2  2      2    2    2          2  2              2    2    2  \n",
        "\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r \u22c5s  + U\u2081\u2081 \u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s  + U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r\n",
        "\n",
        "3                2    2    2    3              2    2    2    3               \n",
        " \u22c5s - U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r\u22c5s  - U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\n",
        "\n",
        " 2                  3                  2                    3                2\n",
        "\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r\u22c5s  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \n",
        "\n",
        "                    3              2    2    2  3                2    2    2  \n",
        "\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s  + U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r \u22c5s - U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r\n",
        "\n",
        "  3              2    2    2  3                  2                  3         \n",
        "\u22c5s  + U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r \u22c5s - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s - U\u2081\u2081\u22c5\n",
        "\n",
        "       2    2    2    3              2    2    2  3                           \n",
        "U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s  + U\u2081\u2081\u22c5U\u2081\u2082\u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r \u22c5s - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5\n",
        "\n",
        "       2  2  2                                      2  2                      \n",
        "V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \u22c5s  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\n",
        "\n",
        "                2  2                        2          2  2                   \n",
        "\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r \u22c5s  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s  - U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5\n",
        "\n",
        "   2    2  3                        2    2    3                      2    2   \n",
        "V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r \u22c5s + U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r\u22c5s  + U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5\n",
        "\n",
        " 3                                      3                                     \n",
        "s  + 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\n",
        "\n",
        "     3                                        3                      2    2  3\n",
        "\u2082\u22c5r\u22c5s  - 2\u22c5U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s  - U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r \n",
        "\n",
        "                        2    2    3                      2    2  3            \n",
        "\u22c5s + U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r\u22c5s  - U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r \u22c5s + 2\u22c5U\u2081\u2081\u22c5U\n",
        "\n",
        "                            3                        2    2    3              \n",
        "\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s + U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s  - U\u2081\u2081\u22c5U\u2081\u2083\u22c5U\u2082\u2082\n",
        "\n",
        "        2    2  3        2    2            2  2  2      2    2                \n",
        "\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r \u22c5s - U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \u22c5s  + U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\n",
        "\n",
        "  2  2      2    2                  2  2      2    2    2          2  2       \n",
        "\u22c5r \u22c5s  + U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r \u22c5s  - U\u2081\u2082 \u22c5U\u2082\u2083 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s  - U\u2081\u2082\u22c5\n",
        "\n",
        "               2    2  3                        2    2    3                   \n",
        "U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r \u22c5s + U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r\u22c5s  + U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5\n",
        "\n",
        "   2    2    3                                      3                         \n",
        "V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s  + 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s - 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\n",
        "\n",
        "                 3                                        3                   \n",
        "\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r\u22c5s  - 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s  - U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5\n",
        "\n",
        "   2    2  3                        2    2    3                      2    2  3\n",
        "V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r \u22c5s + U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r\u22c5s  - U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r \n",
        "\n",
        "                                        3                        2    2    3  \n",
        "\u22c5s + 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s + U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s  -\n",
        "\n",
        "                    2    2  3                                  2  2  2        \n",
        " U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2081\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r \u22c5s + 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \u22c5s  - 2\u22c5U\u2081\u2082\n",
        "\n",
        "                              2  2                                      2  2  \n",
        "\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s  - 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r \u22c5s  +\n",
        "\n",
        "                      2          2  2      2    2            2  2  2      2   \n",
        " 2\u22c5U\u2081\u2082\u22c5U\u2081\u2083\u22c5U\u2082\u2082\u22c5U\u2082\u2083\u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \u22c5s  - U\u2081\u2083 \u22c5U\u2082\n",
        "\n",
        " 2                  2  2      2    2                  2  2      2    2    2   \n",
        "\u2081 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s  - U\u2081\u2083 \u22c5U\u2082\u2081 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r \u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2081 \u22c5V\u2081\u2083 \u22c5V\u2082\n",
        "\n",
        "       2  2      2            2    2  3        2            2    2    3      2\n",
        "\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r \u22c5s - U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081 \u22c5V\u2082\u2082 \u22c5r\u22c5s  - U\u2081\u2083 \n",
        "\n",
        "            2    2    3        2                          3          2        \n",
        "\u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081 \u22c5V\u2082\u2083 \u22c5r\u22c5s  - 2\u22c5U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s + 2\u22c5U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\n",
        "\n",
        "                    3        2                            3      2            \n",
        "\u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r\u22c5s  + 2\u22c5U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r\u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082\n",
        "\n",
        "2    2  3        2            2    2    3      2            2    2  3         \n",
        " \u22c5V\u2082\u2081 \u22c5r \u22c5s - U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082 \u22c5V\u2082\u2081 \u22c5r\u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082 \u22c5V\u2082\u2083 \u22c5r \u22c5s - 2\u22c5U\u2081\n",
        "\n",
        " 2                          3        2            2    2    3      2          \n",
        "\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s - U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\u2081\u2083 \u22c5V\u2082\u2081 \u22c5r\u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2081\u22c5U\u2082\u2082\u22c5V\n",
        "\n",
        "  2    2  3        2    2            2  2  2      2    2                  2  2\n",
        "\u2081\u2083 \u22c5V\u2082\u2082 \u22c5r \u22c5s - U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2082\u22c5V\u2082\u2083 \u22c5r \u22c5s  + U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2081\u22c5V\u2081\u2083\u22c5V\u2082\u2082\u22c5V\u2082\u2083\u22c5r \u22c5s \n",
        "\n",
        "      2    2                  2  2      2    2    2          2  2\u239e\n",
        " + U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2082\u22c5V\u2081\u2083\u22c5V\u2082\u2081\u22c5V\u2082\u2083\u22c5r \u22c5s  - U\u2081\u2083 \u22c5U\u2082\u2082 \u22c5V\u2081\u2083 \u22c5V\u2082\u2081\u22c5V\u2082\u2082\u22c5r \u22c5s \u23a0"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Welp.\n",
      "\n",
      "That was not too useful. Luckily, SymPy has some neat code generation capabilities."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.utilities.codegen import codegen\n",
      "\n",
      "[(cName, cCode), (hName, cHeader)] = codegen((('a1', a1), ('a2', a2)), 'C', 'functions', 'Project name')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cName, hName"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "('functions.c', 'functions.h')"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(cHeader)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "/******************************************************************************\n",
        " *                     Code generated with sympy 0.7.6.1                      *\n",
        " *                                                                            *\n",
        " *              See http://www.sympy.org/ for more information.               *\n",
        " *                                                                            *\n",
        " *                    This file is part of 'Project name'                     *\n",
        " ******************************************************************************/\n",
        "\n",
        "\n",
        "#ifndef PROJECT_NAME__FUNCTIONS__H\n",
        "#define PROJECT_NAME__FUNCTIONS__H\n",
        "\n",
        "double a1(double U_11, double U_12, double U_13, double U_21, double U_22, double U_23, double V_11, double V_12, double V_13, double V_21, double V_22, double V_23, double r, double s);\n",
        "double a2(double U_11, double U_12, double U_13, double U_21, double U_22, double U_23, double V_11, double V_12, double V_13, double V_21, double V_22, double V_23, double r, double s);\n",
        "\n",
        "#endif\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(cCode)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "/******************************************************************************\n",
        " *                     Code generated with sympy 0.7.6.1                      *\n",
        " *                                                                            *\n",
        " *              See http://www.sympy.org/ for more information.               *\n",
        " *                                                                            *\n",
        " *                    This file is part of 'Project name'                     *\n",
        " ******************************************************************************/\n",
        "#include \"functions.h\"\n",
        "#include <math.h>\n",
        "\n",
        "double a1(double U_11, double U_12, double U_13, double U_21, double U_22, double U_23, double V_11, double V_12, double V_13, double V_21, double V_22, double V_23, double r, double s) {\n",
        "\n",
        "   double a1_result;\n",
        "   a1_result = -pow(U_11, 2)*pow(U_22, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2) + pow(U_11, 2)*pow(U_22, 2)*V_11*V_12*pow(V_23, 2)*pow(s, 2) + pow(U_11, 2)*pow(U_22, 2)*V_11*V_13*V_22*V_23*pow(r, 2) - pow(U_11, 2)*pow(U_22, 2)*V_11*V_13*V_22*V_23*pow(s, 2) + pow(U_11, 2)*pow(U_22, 2)*V_12*V_13*V_21*V_23*pow(r, 2) - pow(U_11, 2)*pow(U_22, 2)*V_12*V_13*V_21*V_23*pow(s, 2) - pow(U_11, 2)*pow(U_22, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2) + pow(U_11, 2)*pow(U_22, 2)*pow(V_13, 2)*V_21*V_22*pow(s, 2) - pow(U_11, 2)*pow(U_23, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2) + pow(U_11, 2)*pow(U_23, 2)*V_11*V_13*V_22*V_23*pow(r, 2) + pow(U_11, 2)*pow(U_23, 2)*V_12*V_13*V_21*V_23*pow(r, 2) - pow(U_11, 2)*pow(U_23, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2) + 2*U_11*U_12*U_21*U_22*V_11*V_12*pow(V_23, 2)*pow(r, 2) - 2*U_11*U_12*U_21*U_22*V_11*V_12*pow(V_23, 2)*pow(s, 2) - 2*U_11*U_12*U_21*U_22*V_11*V_13*V_22*V_23*pow(r, 2) + 2*U_11*U_12*U_21*U_22*V_11*V_13*V_22*V_23*pow(s, 2) - 2*U_11*U_12*U_21*U_22*V_12*V_13*V_21*V_23*pow(r, 2) + 2*U_11*U_12*U_21*U_22*V_12*V_13*V_21*V_23*pow(s, 2) + 2*U_11*U_12*U_21*U_22*pow(V_13, 2)*V_21*V_22*pow(r, 2) - 2*U_11*U_12*U_21*U_22*pow(V_13, 2)*V_21*V_22*pow(s, 2) + U_11*U_12*pow(U_23, 2)*pow(V_11, 2)*pow(V_23, 2)*r*s - 2*U_11*U_12*pow(U_23, 2)*V_11*V_13*V_21*V_23*r*s - U_11*U_12*pow(U_23, 2)*pow(V_12, 2)*pow(V_23, 2)*r*s + 2*U_11*U_12*pow(U_23, 2)*V_12*V_13*V_22*V_23*r*s + U_11*U_12*pow(U_23, 2)*pow(V_13, 2)*pow(V_21, 2)*r*s - U_11*U_12*pow(U_23, 2)*pow(V_13, 2)*pow(V_22, 2)*r*s + 2*U_11*U_13*U_21*U_23*V_11*V_12*pow(V_23, 2)*pow(r, 2) - 2*U_11*U_13*U_21*U_23*V_11*V_13*V_22*V_23*pow(r, 2) - 2*U_11*U_13*U_21*U_23*V_12*V_13*V_21*V_23*pow(r, 2) + 2*U_11*U_13*U_21*U_23*pow(V_13, 2)*V_21*V_22*pow(r, 2) - U_11*U_13*U_22*U_23*pow(V_11, 2)*pow(V_23, 2)*r*s + 2*U_11*U_13*U_22*U_23*V_11*V_13*V_21*V_23*r*s + U_11*U_13*U_22*U_23*pow(V_12, 2)*pow(V_23, 2)*r*s - 2*U_11*U_13*U_22*U_23*V_12*V_13*V_22*V_23*r*s - U_11*U_13*U_22*U_23*pow(V_13, 2)*pow(V_21, 2)*r*s + U_11*U_13*U_22*U_23*pow(V_13, 2)*pow(V_22, 2)*r*s - pow(U_12, 2)*pow(U_21, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2) + pow(U_12, 2)*pow(U_21, 2)*V_11*V_12*pow(V_23, 2)*pow(s, 2) + pow(U_12, 2)*pow(U_21, 2)*V_11*V_13*V_22*V_23*pow(r, 2) - pow(U_12, 2)*pow(U_21, 2)*V_11*V_13*V_22*V_23*pow(s, 2) + pow(U_12, 2)*pow(U_21, 2)*V_12*V_13*V_21*V_23*pow(r, 2) - pow(U_12, 2)*pow(U_21, 2)*V_12*V_13*V_21*V_23*pow(s, 2) - pow(U_12, 2)*pow(U_21, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2) + pow(U_12, 2)*pow(U_21, 2)*pow(V_13, 2)*V_21*V_22*pow(s, 2) + pow(U_12, 2)*pow(U_23, 2)*V_11*V_12*pow(V_23, 2)*pow(s, 2) - pow(U_12, 2)*pow(U_23, 2)*V_11*V_13*V_22*V_23*pow(s, 2) - pow(U_12, 2)*pow(U_23, 2)*V_12*V_13*V_21*V_23*pow(s, 2) + pow(U_12, 2)*pow(U_23, 2)*pow(V_13, 2)*V_21*V_22*pow(s, 2) - U_12*U_13*U_21*U_23*pow(V_11, 2)*pow(V_23, 2)*r*s + 2*U_12*U_13*U_21*U_23*V_11*V_13*V_21*V_23*r*s + U_12*U_13*U_21*U_23*pow(V_12, 2)*pow(V_23, 2)*r*s - 2*U_12*U_13*U_21*U_23*V_12*V_13*V_22*V_23*r*s - U_12*U_13*U_21*U_23*pow(V_13, 2)*pow(V_21, 2)*r*s + U_12*U_13*U_21*U_23*pow(V_13, 2)*pow(V_22, 2)*r*s - 2*U_12*U_13*U_22*U_23*V_11*V_12*pow(V_23, 2)*pow(s, 2) + 2*U_12*U_13*U_22*U_23*V_11*V_13*V_22*V_23*pow(s, 2) + 2*U_12*U_13*U_22*U_23*V_12*V_13*V_21*V_23*pow(s, 2) - 2*U_12*U_13*U_22*U_23*pow(V_13, 2)*V_21*V_22*pow(s, 2) - pow(U_13, 2)*pow(U_21, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2) + pow(U_13, 2)*pow(U_21, 2)*V_11*V_13*V_22*V_23*pow(r, 2) + pow(U_13, 2)*pow(U_21, 2)*V_12*V_13*V_21*V_23*pow(r, 2) - pow(U_13, 2)*pow(U_21, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2) + pow(U_13, 2)*U_21*U_22*pow(V_11, 2)*pow(V_23, 2)*r*s - 2*pow(U_13, 2)*U_21*U_22*V_11*V_13*V_21*V_23*r*s - pow(U_13, 2)*U_21*U_22*pow(V_12, 2)*pow(V_23, 2)*r*s + 2*pow(U_13, 2)*U_21*U_22*V_12*V_13*V_22*V_23*r*s + pow(U_13, 2)*U_21*U_22*pow(V_13, 2)*pow(V_21, 2)*r*s - pow(U_13, 2)*U_21*U_22*pow(V_13, 2)*pow(V_22, 2)*r*s + pow(U_13, 2)*pow(U_22, 2)*V_11*V_12*pow(V_23, 2)*pow(s, 2) - pow(U_13, 2)*pow(U_22, 2)*V_11*V_13*V_22*V_23*pow(s, 2) - pow(U_13, 2)*pow(U_22, 2)*V_12*V_13*V_21*V_23*pow(s, 2) + pow(U_13, 2)*pow(U_22, 2)*pow(V_13, 2)*V_21*V_22*pow(s, 2);\n",
        "   return a1_result;\n",
        "\n",
        "}\n",
        "\n",
        "double a2(double U_11, double U_12, double U_13, double U_21, double U_22, double U_23, double V_11, double V_12, double V_13, double V_21, double V_22, double V_23, double r, double s) {\n",
        "\n",
        "   double a2_result;\n",
        "   a2_result = pow(U_11, 2)*pow(U_23, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2)*pow(s, 2) - pow(U_11, 2)*pow(U_23, 2)*V_11*V_13*V_22*V_23*pow(r, 2)*pow(s, 2) - pow(U_11, 2)*pow(U_23, 2)*V_12*V_13*V_21*V_23*pow(r, 2)*pow(s, 2) + pow(U_11, 2)*pow(U_23, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2)*pow(s, 2) + U_11*U_12*pow(U_23, 2)*pow(V_11, 2)*pow(V_22, 2)*pow(r, 3)*s - U_11*U_12*pow(U_23, 2)*pow(V_11, 2)*pow(V_22, 2)*r*pow(s, 3) - U_11*U_12*pow(U_23, 2)*pow(V_11, 2)*pow(V_23, 2)*r*pow(s, 3) - 2*U_11*U_12*pow(U_23, 2)*V_11*V_12*V_21*V_22*pow(r, 3)*s + 2*U_11*U_12*pow(U_23, 2)*V_11*V_12*V_21*V_22*r*pow(s, 3) + 2*U_11*U_12*pow(U_23, 2)*V_11*V_13*V_21*V_23*r*pow(s, 3) + U_11*U_12*pow(U_23, 2)*pow(V_12, 2)*pow(V_21, 2)*pow(r, 3)*s - U_11*U_12*pow(U_23, 2)*pow(V_12, 2)*pow(V_21, 2)*r*pow(s, 3) + U_11*U_12*pow(U_23, 2)*pow(V_12, 2)*pow(V_23, 2)*pow(r, 3)*s - 2*U_11*U_12*pow(U_23, 2)*V_12*V_13*V_22*V_23*pow(r, 3)*s - U_11*U_12*pow(U_23, 2)*pow(V_13, 2)*pow(V_21, 2)*r*pow(s, 3) + U_11*U_12*pow(U_23, 2)*pow(V_13, 2)*pow(V_22, 2)*pow(r, 3)*s - 2*U_11*U_13*U_21*U_23*V_11*V_12*pow(V_23, 2)*pow(r, 2)*pow(s, 2) + 2*U_11*U_13*U_21*U_23*V_11*V_13*V_22*V_23*pow(r, 2)*pow(s, 2) + 2*U_11*U_13*U_21*U_23*V_12*V_13*V_21*V_23*pow(r, 2)*pow(s, 2) - 2*U_11*U_13*U_21*U_23*pow(V_13, 2)*V_21*V_22*pow(r, 2)*pow(s, 2) - U_11*U_13*U_22*U_23*pow(V_11, 2)*pow(V_22, 2)*pow(r, 3)*s + U_11*U_13*U_22*U_23*pow(V_11, 2)*pow(V_22, 2)*r*pow(s, 3) + U_11*U_13*U_22*U_23*pow(V_11, 2)*pow(V_23, 2)*r*pow(s, 3) + 2*U_11*U_13*U_22*U_23*V_11*V_12*V_21*V_22*pow(r, 3)*s - 2*U_11*U_13*U_22*U_23*V_11*V_12*V_21*V_22*r*pow(s, 3) - 2*U_11*U_13*U_22*U_23*V_11*V_13*V_21*V_23*r*pow(s, 3) - U_11*U_13*U_22*U_23*pow(V_12, 2)*pow(V_21, 2)*pow(r, 3)*s + U_11*U_13*U_22*U_23*pow(V_12, 2)*pow(V_21, 2)*r*pow(s, 3) - U_11*U_13*U_22*U_23*pow(V_12, 2)*pow(V_23, 2)*pow(r, 3)*s + 2*U_11*U_13*U_22*U_23*V_12*V_13*V_22*V_23*pow(r, 3)*s + U_11*U_13*U_22*U_23*pow(V_13, 2)*pow(V_21, 2)*r*pow(s, 3) - U_11*U_13*U_22*U_23*pow(V_13, 2)*pow(V_22, 2)*pow(r, 3)*s - pow(U_12, 2)*pow(U_23, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2)*pow(s, 2) + pow(U_12, 2)*pow(U_23, 2)*V_11*V_13*V_22*V_23*pow(r, 2)*pow(s, 2) + pow(U_12, 2)*pow(U_23, 2)*V_12*V_13*V_21*V_23*pow(r, 2)*pow(s, 2) - pow(U_12, 2)*pow(U_23, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2)*pow(s, 2) - U_12*U_13*U_21*U_23*pow(V_11, 2)*pow(V_22, 2)*pow(r, 3)*s + U_12*U_13*U_21*U_23*pow(V_11, 2)*pow(V_22, 2)*r*pow(s, 3) + U_12*U_13*U_21*U_23*pow(V_11, 2)*pow(V_23, 2)*r*pow(s, 3) + 2*U_12*U_13*U_21*U_23*V_11*V_12*V_21*V_22*pow(r, 3)*s - 2*U_12*U_13*U_21*U_23*V_11*V_12*V_21*V_22*r*pow(s, 3) - 2*U_12*U_13*U_21*U_23*V_11*V_13*V_21*V_23*r*pow(s, 3) - U_12*U_13*U_21*U_23*pow(V_12, 2)*pow(V_21, 2)*pow(r, 3)*s + U_12*U_13*U_21*U_23*pow(V_12, 2)*pow(V_21, 2)*r*pow(s, 3) - U_12*U_13*U_21*U_23*pow(V_12, 2)*pow(V_23, 2)*pow(r, 3)*s + 2*U_12*U_13*U_21*U_23*V_12*V_13*V_22*V_23*pow(r, 3)*s + U_12*U_13*U_21*U_23*pow(V_13, 2)*pow(V_21, 2)*r*pow(s, 3) - U_12*U_13*U_21*U_23*pow(V_13, 2)*pow(V_22, 2)*pow(r, 3)*s + 2*U_12*U_13*U_22*U_23*V_11*V_12*pow(V_23, 2)*pow(r, 2)*pow(s, 2) - 2*U_12*U_13*U_22*U_23*V_11*V_13*V_22*V_23*pow(r, 2)*pow(s, 2) - 2*U_12*U_13*U_22*U_23*V_12*V_13*V_21*V_23*pow(r, 2)*pow(s, 2) + 2*U_12*U_13*U_22*U_23*pow(V_13, 2)*V_21*V_22*pow(r, 2)*pow(s, 2) + pow(U_13, 2)*pow(U_21, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2)*pow(s, 2) - pow(U_13, 2)*pow(U_21, 2)*V_11*V_13*V_22*V_23*pow(r, 2)*pow(s, 2) - pow(U_13, 2)*pow(U_21, 2)*V_12*V_13*V_21*V_23*pow(r, 2)*pow(s, 2) + pow(U_13, 2)*pow(U_21, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2)*pow(s, 2) + pow(U_13, 2)*U_21*U_22*pow(V_11, 2)*pow(V_22, 2)*pow(r, 3)*s - pow(U_13, 2)*U_21*U_22*pow(V_11, 2)*pow(V_22, 2)*r*pow(s, 3) - pow(U_13, 2)*U_21*U_22*pow(V_11, 2)*pow(V_23, 2)*r*pow(s, 3) - 2*pow(U_13, 2)*U_21*U_22*V_11*V_12*V_21*V_22*pow(r, 3)*s + 2*pow(U_13, 2)*U_21*U_22*V_11*V_12*V_21*V_22*r*pow(s, 3) + 2*pow(U_13, 2)*U_21*U_22*V_11*V_13*V_21*V_23*r*pow(s, 3) + pow(U_13, 2)*U_21*U_22*pow(V_12, 2)*pow(V_21, 2)*pow(r, 3)*s - pow(U_13, 2)*U_21*U_22*pow(V_12, 2)*pow(V_21, 2)*r*pow(s, 3) + pow(U_13, 2)*U_21*U_22*pow(V_12, 2)*pow(V_23, 2)*pow(r, 3)*s - 2*pow(U_13, 2)*U_21*U_22*V_12*V_13*V_22*V_23*pow(r, 3)*s - pow(U_13, 2)*U_21*U_22*pow(V_13, 2)*pow(V_21, 2)*r*pow(s, 3) + pow(U_13, 2)*U_21*U_22*pow(V_13, 2)*pow(V_22, 2)*pow(r, 3)*s - pow(U_13, 2)*pow(U_22, 2)*V_11*V_12*pow(V_23, 2)*pow(r, 2)*pow(s, 2) + pow(U_13, 2)*pow(U_22, 2)*V_11*V_13*V_22*V_23*pow(r, 2)*pow(s, 2) + pow(U_13, 2)*pow(U_22, 2)*V_12*V_13*V_21*V_23*pow(r, 2)*pow(s, 2) - pow(U_13, 2)*pow(U_22, 2)*pow(V_13, 2)*V_21*V_22*pow(r, 2)*pow(s, 2);\n",
        "   return a2_result;\n",
        "\n",
        "}\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, this may or may not be the most convenient form of expressing this for your code, but you get the idea. You can adapt it to your needs, but in any case you can ask me if you don't knonw how to do something in particular. SymPy has support for a few languages, but not for Java... C is mostly the same, but you may need to search replace some stuff, like \"pow\" -> \"Math.pow\", etc."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}