{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<p>\n",
    "<img src=\"http://www.cerm.unifi.it/chianti/images/logo%20unifi_positivo.jpg\" \n",
    "        alt=\"UniFI logo\" style=\"float: left; width: 20%; height: 20%;\">\n",
    "<div align=\"right\">\n",
    "Massimo Nocentini<br>\n",
    "<small>\n",
    "<br>April 20, 2018: cleanup, `sin` and `cos` $g$ poly\n",
    "<br>November 16 and 18, 2016: `expt` and `log` $g$ poly\n",
    "<br>November 9, 2016: splitting from \"big\" notebook\n",
    "</small>\n",
    "</div>\n",
    "</p>\n",
    "<br>\n",
    "<br>\n",
    "<div align=\"center\">\n",
    "<b>Abstract</b><br>\n",
    "Theory of matrix functions, with applications to Catalan array $\\mathcal{C}$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import n, i, N, x, lamda, phi, z, j, r, k, a, alpha\n",
    "\n",
    "from commons import *\n",
    "from matrix_functions import *\n",
    "from sequences import *\n",
    "import functions_catalog\n",
    "\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Catalan array $\\mathcal{C}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "m=8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\mathcal{C}_{ 8 } = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\2 & 2 & 1 & 0 & 0 & 0 & 0 & 0\\\\5 & 5 & 3 & 1 & 0 & 0 & 0 & 0\\\\14 & 14 & 9 & 4 & 1 & 0 & 0 & 0\\\\42 & 42 & 28 & 14 & 5 & 1 & 0 & 0\\\\132 & 132 & 90 & 48 & 20 & 6 & 1 & 0\\\\429 & 429 & 297 & 165 & 75 & 27 & 7 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                    ⎡ 1    0    0    0   0   0   0  0⎤\n",
       "                    ⎢                                ⎥\n",
       "                    ⎢ 1    1    0    0   0   0   0  0⎥\n",
       "                    ⎢                                ⎥\n",
       "                    ⎢ 2    2    1    0   0   0   0  0⎥\n",
       "                    ⎢                                ⎥\n",
       "                    ⎢ 5    5    3    1   0   0   0  0⎥\n",
       "\\mathcal{C}_{ 8 } = ⎢                                ⎥\n",
       "                    ⎢14   14    9    4   1   0   0  0⎥\n",
       "                    ⎢                                ⎥\n",
       "                    ⎢42   42   28   14   5   1   0  0⎥\n",
       "                    ⎢                                ⎥\n",
       "                    ⎢132  132  90   48   20  6   1  0⎥\n",
       "                    ⎢                                ⎥\n",
       "                    ⎣429  429  297  165  75  27  7  1⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = define(let=Symbol(r'\\mathcal{{C}}_{{ {} }}'.format(m)), \n",
    "           be=Matrix(m, m, lambda n,k: (k+1)*binomial(2*n-k, n-k)/(n+1) if n > 0 else int(not k)))\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb8AAAAVBAMAAAAkzf19AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/wACo2UNvnaDTAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\sigma{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left ( \\left \\{ 1 : \\left ( \\lambda_{1}, \\quad m_{1}\\right )\\right \\}, \\quad \\left \\{ \\lambda_{1} : 1\\right \\}, \\quad \\left \\{ m_{1} : 8\\right \\}\\right )$$"
      ],
      "text/plain": [
       "\\sigma(\\mathcal{C}_{ 8 }) = ({1: (\\lambda[1], m[1])}, {\\lambda[1]: 1}, {m[1]: \n",
       "8})"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigendata = spectrum(C)\n",
    "eigendata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data, eigenvals, multiplicities = eigendata.rhs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAskAAAAaBAMAAAC3Ltx2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
      "text/latex": [
       "$$\\Phi{\\left (z,i,j \\right )} = z^{7} \\phi_{i,j,0} + z^{6} \\phi_{i,j,1} + z^{5} \\phi_{i,j,2} + z^{4} \\phi_{i,j,3} + z^{3} \\phi_{i,j,4} + z^{2} \\phi_{i,j,5} + z \\phi_{i,j,6} + \\phi_{i,j,7}$$"
      ],
      "text/plain": [
       "                 7                  6                  5                  4   \n",
       "\\Phi(z, i, j) = z ⋅\\phi[i, j, 0] + z ⋅\\phi[i, j, 1] + z ⋅\\phi[i, j, 2] + z ⋅\\p\n",
       "\n",
       "               3                  2                                           \n",
       "hi[i, j, 3] + z ⋅\\phi[i, j, 4] + z ⋅\\phi[i, j, 5] + z⋅\\phi[i, j, 6] + \\phi[i, \n",
       "\n",
       "     \n",
       "j, 7]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi_poly = Phi_poly_ctor(deg=m-1)\n",
    "Phi_poly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0oWVCiR6lTse/TI9a0f/WSSc1Gr2BVSGeCirsK5huznlpZjvjUZwjdIa6u3GKsXK+Tn4Y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\n",
      "text/latex": [
       "$$\\left \\{ \\left ( 1, \\quad 1\\right ) : \\Phi_{ 1, 1 }{\\left (z \\right )} = 1, \\quad \\left ( 1, \\quad 2\\right ) : \\Phi_{ 1, 2 }{\\left (z \\right )} = z - 1, \\quad \\left ( 1, \\quad 3\\right ) : \\Phi_{ 1, 3 }{\\left (z \\right )} = \\frac{z^{2}}{2} - z + \\frac{1}{2}, \\quad \\left ( 1, \\quad 4\\right ) : \\Phi_{ 1, 4 }{\\left (z \\right )} = \\frac{z^{3}}{6} - \\frac{z^{2}}{2} + \\frac{z}{2} - \\frac{1}{6}, \\quad \\left ( 1, \\quad 5\\right ) : \\Phi_{ 1, 5 }{\\left (z \\right )} = \\frac{z^{4}}{24} - \\frac{z^{3}}{6} + \\frac{z^{2}}{4} - \\frac{z}{6} + \\frac{1}{24}, \\quad \\left ( 1, \\quad 6\\right ) : \\Phi_{ 1, 6 }{\\left (z \\right )} = \\frac{z^{5}}{120} - \\frac{z^{4}}{24} + \\frac{z^{3}}{12} - \\frac{z^{2}}{12} + \\frac{z}{24} - \\frac{1}{120}, \\quad \\left ( 1, \\quad 7\\right ) : \\Phi_{ 1, 7 }{\\left (z \\right )} = \\frac{z^{6}}{720} - \\frac{z^{5}}{120} + \\frac{z^{4}}{48} - \\frac{z^{3}}{36} + \\frac{z^{2}}{48} - \\frac{z}{120} + \\frac{1}{720}, \\quad \\left ( 1, \\quad 8\\right ) : \\Phi_{ 1, 8 }{\\left (z \\right )} = \\frac{z^{7}}{5040} - \\frac{z^{6}}{720} + \\frac{z^{5}}{240} - \\frac{z^{4}}{144} + \\frac{z^{3}}{144} - \\frac{z^{2}}{240} + \\frac{z}{720} - \\frac{1}{5040}\\right \\}$$"
      ],
      "text/plain": [
       "⎧                                                                             \n",
       "⎪                                                                             \n",
       "⎨(1, 1): \\Phi_{ 1, 1 }(z) = 1, (1, 2): \\Phi_{ 1, 2 }(z) = z - 1, (1, 3): \\Phi_\n",
       "⎪                                                                             \n",
       "⎩                                                                             \n",
       "\n",
       "               2                                      3    2                  \n",
       "              z        1                             z    z    z   1          \n",
       "{ 1, 3 }(z) = ── - z + ─, (1, 4): \\Phi_{ 1, 4 }(z) = ── - ── + ─ - ─, (1, 5): \n",
       "              2        2                             6    2    2   6          \n",
       "                                                                              \n",
       "\n",
       "                    4    3    2                                        5    4 \n",
       "                   z    z    z    z   1                               z    z  \n",
       "\\Phi_{ 1, 5 }(z) = ── - ── + ── - ─ + ──, (1, 6): \\Phi_{ 1, 6 }(z) = ─── - ── \n",
       "                   24   6    4    6   24                             120   24 \n",
       "                                                                              \n",
       "\n",
       "   3    2                                          6     5    4    3    2     \n",
       "  z    z    z     1                               z     z    z    z    z     z\n",
       "+ ── - ── + ── - ───, (1, 7): \\Phi_{ 1, 7 }(z) = ─── - ─── + ── - ── + ── - ──\n",
       "  12   12   24   120                             720   120   48   36   48   12\n",
       "                                                                              \n",
       "\n",
       "                                      7      6     5     4     3     2        \n",
       "     1                               z      z     z     z     z     z     z   \n",
       "─ + ───, (1, 8): \\Phi_{ 1, 8 }(z) = ──── - ─── + ─── - ─── + ─── - ─── + ─── -\n",
       "0   720                             5040   720   240   144   144   240   720  \n",
       "                                                                              \n",
       "\n",
       "     ⎫\n",
       "  1  ⎪\n",
       " ────⎬\n",
       " 5040⎪\n",
       "     ⎭"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi_polynomials = component_polynomials(eigendata, early_eigenvals_subs=True)\n",
    "Phi_polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i3Wg/X3L9+OTcP1iCQdh1CXlrPAzdm+KJ+ATm7ehp6MvuCcYpugymFvVJdRZj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\nrkJggg==\n",
      "text/latex": [
       "$$\\left [ Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,1} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,2} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\2 & 2 & 0 & 0 & 0 & 0 & 0 & 0\\\\5 & 5 & 3 & 0 & 0 & 0 & 0 & 0\\\\14 & 14 & 9 & 4 & 0 & 0 & 0 & 0\\\\42 & 42 & 28 & 14 & 5 & 0 & 0 & 0\\\\132 & 132 & 90 & 48 & 20 & 6 & 0 & 0\\\\429 & 429 & 297 & 165 & 75 & 27 & 7 & 0\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,3} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{11}{2} & 3 & 0 & 0 & 0 & 0 & 0 & 0\\\\26 & 19 & 6 & 0 & 0 & 0 & 0 & 0\\\\119 & 98 & \\frac{87}{2} & 10 & 0 & 0 & 0 & 0\\\\542 & 476 & 246 & 82 & 15 & 0 & 0 & 0\\\\2478 & \\frac{4527}{2} & 1278 & 507 & \\frac{275}{2} & 21 & 0 & 0\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,4} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{31}{3} & 4 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{235}{3} & \\frac{137}{3} & 10 & 0 & 0 & 0 & 0 & 0\\\\\\frac{1588}{3} & \\frac{1112}{3} & 127 & 20 & 0 & 0 & 0 & 0\\\\\\frac{20323}{6} & \\frac{7898}{3} & \\frac{2231}{2} & \\frac{844}{3} & 35 & 0 & 0 & 0\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,5} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{197}{12} & 5 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{1087}{6} & \\frac{177}{2} & 15 & 0 & 0 & 0 & 0 & 0\\\\\\frac{20281}{12} & \\frac{12383}{12} & \\frac{1159}{4} & 35 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,6} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{237}{10} & 6 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{21437}{60} & \\frac{1509}{10} & 21 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,7} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{643}{20} & 7 & 0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\quad Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}_{1,8} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right]\\right ]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢                                             ⎡1  0  0  0  0  0  0  0⎤        \n",
       "⎢                                             ⎢                      ⎥        \n",
       "⎢                                             ⎢0  1  0  0  0  0  0  0⎥        \n",
       "⎢                                             ⎢                      ⎥        \n",
       "⎢                                             ⎢0  0  1  0  0  0  0  0⎥        \n",
       "⎢                                             ⎢                      ⎥        \n",
       "⎢                                             ⎢0  0  0  1  0  0  0  0⎥        \n",
       "⎢Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 1] = ⎢                      ⎥, Z^{\\le\n",
       "⎢                                             ⎢0  0  0  0  1  0  0  0⎥        \n",
       "⎢                                             ⎢                      ⎥        \n",
       "⎢                                             ⎢0  0  0  0  0  1  0  0⎥        \n",
       "⎢                                             ⎢                      ⎥        \n",
       "⎢                                             ⎢0  0  0  0  0  0  1  0⎥        \n",
       "⎢                                             ⎢                      ⎥        \n",
       "⎢                                             ⎣0  0  0  0  0  0  0  1⎦        \n",
       "⎢                                                                             \n",
       "⎣                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                       ⎡ 0    0    0    0   0   0   0  0⎤     \n",
       "                                       ⎢                                ⎥     \n",
       "                                       ⎢ 1    0    0    0   0   0   0  0⎥     \n",
       "                                       ⎢                                ⎥     \n",
       "                                       ⎢ 2    2    0    0   0   0   0  0⎥     \n",
       "                                       ⎢                                ⎥     \n",
       "                                       ⎢ 5    5    3    0   0   0   0  0⎥     \n",
       "ft[ \\mathcal{C}_{ 8 } \\right]}[1, 2] = ⎢                                ⎥, Z^{\n",
       "                                       ⎢14   14    9    4   0   0   0  0⎥     \n",
       "                                       ⎢                                ⎥     \n",
       "                                       ⎢42   42   28   14   5   0   0  0⎥     \n",
       "                                       ⎢                                ⎥     \n",
       "                                       ⎢132  132  90   48   20  6   0  0⎥     \n",
       "                                       ⎢                                ⎥     \n",
       "                                       ⎣429  429  297  165  75  27  7  0⎦     \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          ⎡ 0      0      0     0     0    0  \n",
       "                                          ⎢                                   \n",
       "                                          ⎢ 0      0      0     0     0    0  \n",
       "                                          ⎢                                   \n",
       "                                          ⎢ 1      0      0     0     0    0  \n",
       "                                          ⎢                                   \n",
       "                                          ⎢11/2    3      0     0     0    0  \n",
       "\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 3] = ⎢                                   \n",
       "                                          ⎢ 26     19     6     0     0    0  \n",
       "                                          ⎢                                   \n",
       "                                          ⎢119     98    87/2  10     0    0  \n",
       "                                          ⎢                                   \n",
       "                                          ⎢542    476    246   82    15    0  \n",
       "                                          ⎢                                   \n",
       "                                          ⎣2478  4527/2  1278  507  275/2  21 \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       " 0  0⎤                                               ⎡   0       0       0    \n",
       "     ⎥                                               ⎢                        \n",
       " 0  0⎥                                               ⎢   0       0       0    \n",
       "     ⎥                                               ⎢                        \n",
       " 0  0⎥                                               ⎢   0       0       0    \n",
       "     ⎥                                               ⎢                        \n",
       " 0  0⎥                                               ⎢   1       0       0    \n",
       "     ⎥, Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 4] = ⎢                        \n",
       " 0  0⎥                                               ⎢ 31/3      4       0    \n",
       "     ⎥                                               ⎢                        \n",
       " 0  0⎥                                               ⎢ 235/3   137/3     10   \n",
       "     ⎥                                               ⎢                        \n",
       " 0  0⎥                                               ⎢1588/3   1112/3   127   \n",
       "     ⎥                                               ⎢                        \n",
       " 0  0⎦                                               ⎣20323/6  7898/3  2231/2 \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                   ⎡  0       \n",
       "                                                                   ⎢          \n",
       "   0    0   0  0  0⎤                                               ⎢  0       \n",
       "                   ⎥                                               ⎢          \n",
       "   0    0   0  0  0⎥                                               ⎢  0       \n",
       "                   ⎥                                               ⎢          \n",
       "   0    0   0  0  0⎥                                               ⎢  0       \n",
       "                   ⎥                                               ⎢          \n",
       "   0    0   0  0  0⎥                                               ⎢  1       \n",
       "                   ⎥, Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 5] = ⎢          \n",
       "   0    0   0  0  0⎥                                               ⎢ 197      \n",
       "                   ⎥                                               ⎢ ───      \n",
       "   0    0   0  0  0⎥                                               ⎢  12      \n",
       "                   ⎥                                               ⎢          \n",
       "  20    0   0  0  0⎥                                               ⎢1087/6  17\n",
       "                   ⎥                                               ⎢          \n",
       " 844/3  35  0  0  0⎦                                               ⎢20281   12\n",
       "                                                                   ⎢─────   ──\n",
       "                                                                   ⎣  12      \n",
       "\n",
       "0      0     0   0  0  0  0⎤                                               ⎡  \n",
       "                           ⎥                                               ⎢  \n",
       "0      0     0   0  0  0  0⎥                                               ⎢  \n",
       "                           ⎥                                               ⎢  \n",
       "0      0     0   0  0  0  0⎥                                               ⎢  \n",
       "                           ⎥                                               ⎢  \n",
       "0      0     0   0  0  0  0⎥                                               ⎢  \n",
       "                           ⎥                                               ⎢  \n",
       "0      0     0   0  0  0  0⎥                                               ⎢  \n",
       "                           ⎥, Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 6] = ⎢  \n",
       "                           ⎥                                               ⎢  \n",
       "5      0     0   0  0  0  0⎥                                               ⎢  \n",
       "                           ⎥                                               ⎢ 2\n",
       "                           ⎥                                               ⎢ ─\n",
       "7/2    15    0   0  0  0  0⎥                                               ⎢  \n",
       "                           ⎥                                               ⎢  \n",
       "383                        ⎥                                               ⎢21\n",
       "───  1159/4  35  0  0  0  0⎥                                               ⎢──\n",
       "12                         ⎦                                               ⎣  \n",
       "\n",
       "0     0    0   0  0  0  0  0⎤                                                 \n",
       "                            ⎥                                               ⎡ \n",
       "0     0    0   0  0  0  0  0⎥                                               ⎢ \n",
       "                            ⎥                                               ⎢ \n",
       "0     0    0   0  0  0  0  0⎥                                               ⎢ \n",
       "                            ⎥                                               ⎢ \n",
       "0     0    0   0  0  0  0  0⎥                                               ⎢ \n",
       "                            ⎥                                               ⎢ \n",
       "0     0    0   0  0  0  0  0⎥                                               ⎢ \n",
       "                            ⎥, Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 7] = ⎢ \n",
       "1     0    0   0  0  0  0  0⎥                                               ⎢ \n",
       "                            ⎥                                               ⎢ \n",
       "37                          ⎥                                               ⎢ \n",
       "──    6    0   0  0  0  0  0⎥                                               ⎢ \n",
       "10                          ⎥                                               ⎢ \n",
       "                            ⎥                                               ⎢6\n",
       "437  1509                   ⎥                                               ⎢─\n",
       "───  ────  21  0  0  0  0  0⎥                                               ⎣ \n",
       "60    10                    ⎦                                                 \n",
       "\n",
       "                                                                              \n",
       "0   0  0  0  0  0  0  0⎤                                                      \n",
       "                       ⎥                                               ⎡0  0  \n",
       "0   0  0  0  0  0  0  0⎥                                               ⎢      \n",
       "                       ⎥                                               ⎢0  0  \n",
       "0   0  0  0  0  0  0  0⎥                                               ⎢      \n",
       "                       ⎥                                               ⎢0  0  \n",
       "0   0  0  0  0  0  0  0⎥                                               ⎢      \n",
       "                       ⎥                                               ⎢0  0  \n",
       "0   0  0  0  0  0  0  0⎥, Z^{\\left[ \\mathcal{C}_{ 8 } \\right]}[1, 8] = ⎢      \n",
       "                       ⎥                                               ⎢0  0  \n",
       "0   0  0  0  0  0  0  0⎥                                               ⎢      \n",
       "                       ⎥                                               ⎢0  0  \n",
       "1   0  0  0  0  0  0  0⎥                                               ⎢      \n",
       "                       ⎥                                               ⎢0  0  \n",
       "43                     ⎥                                               ⎢      \n",
       "──  7  0  0  0  0  0  0⎥                                               ⎣1  0  \n",
       "20                     ⎦                                                      \n",
       "                                                                              \n",
       "\n",
       "                 ⎤\n",
       "                 ⎥\n",
       "0  0  0  0  0  0⎤⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎥⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎥⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎥⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎥⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎥⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎥⎥\n",
       "                ⎥⎥\n",
       "0  0  0  0  0  0⎦⎥\n",
       "                 ⎥\n",
       "                 ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmatrices = component_matrices(C, Phi_polynomials)\n",
    "list(cmatrices.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `power` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f_power, g_power, G_power = functions_catalog.power(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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eBqhqfUntlN9EqTCA+6a5PMOmUu8TrEcnrtvKhIHgJN2e8raBmyL0vsvktJJ9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\n0igDyoAyoAwoA8qAMtDLwP8DtFSx01kfIAEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\operatorname{P_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\r & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\r \\left(r + 1\\right) & 2 r & 1 & 0 & 0 & 0 & 0 & 0\\\\\\frac{r}{2} \\left(2 r^{2} + 5 r + 3\\right) & r \\left(3 r + 2\\right) & 3 r & 1 & 0 & 0 & 0 & 0\\\\\\frac{r}{3} \\left(3 r^{3} + 13 r^{2} + 18 r + 8\\right) & r \\left(4 r^{2} + 7 r + 3\\right) & 3 r \\left(2 r + 1\\right) & 4 r & 1 & 0 & 0 & 0\\\\\\frac{r}{12} \\left(12 r^{4} + 77 r^{3} + 178 r^{2} + 175 r + 62\\right) & \\frac{r}{3} \\left(15 r^{3} + 47 r^{2} + 48 r + 16\\right) & \\frac{r}{2} \\left(20 r^{2} + 27 r + 9\\right) & 2 r \\left(5 r + 2\\right) & 5 r & 1 & 0 & 0\\\\\\frac{r}{30} \\left(30 r^{5} + 261 r^{4} + 875 r^{3} + 1405 r^{2} + 1075 r + 314\\right) & \\frac{r}{6} \\left(36 r^{4} + 171 r^{3} + 298 r^{2} + 225 r + 62\\right) & r \\left(15 r^{3} + 37 r^{2} + 30 r + 8\\right) & 2 r \\left(10 r^{2} + 11 r + 3\\right) & 5 r \\left(3 r + 1\\right) & 6 r & 1 & 0\\\\\\frac{r}{60} \\left(60 r^{6} + 669 r^{5} + 3002 r^{4} + 6900 r^{3} + 8510 r^{2} + 5301 r + 1298\\right) & \\frac{r}{60} \\left(420 r^{5} + 2754 r^{4} + 7075 r^{3} + 8860 r^{2} + 5375 r + 1256\\right) & \\frac{r}{4} \\left(84 r^{4} + 319 r^{3} + 448 r^{2} + 275 r + 62\\right) & \\frac{r}{3} \\left(105 r^{3} + 214 r^{2} + 144 r + 32\\right) & \\frac{5 r}{2} \\left(14 r^{2} + 13 r + 3\\right) & 3 r \\left(7 r + 2\\right) & 7 r & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡                               1                \n",
       "                             ⎢                                                \n",
       "                             ⎢                               r                \n",
       "                             ⎢                                                \n",
       "                             ⎢                           r⋅(r + 1)            \n",
       "                             ⎢                                                \n",
       "                             ⎢                         ⎛   2          ⎞       \n",
       "                             ⎢                       r⋅⎝2⋅r  + 5⋅r + 3⎠       \n",
       "                             ⎢                       ──────────────────       \n",
       "                             ⎢                               2                \n",
       "                             ⎢                                                \n",
       "                             ⎢                    ⎛   3       2           ⎞   \n",
       "                             ⎢                  r⋅⎝3⋅r  + 13⋅r  + 18⋅r + 8⎠   \n",
       "                             ⎢                  ───────────────────────────   \n",
       "                             ⎢                               3                \n",
       "P_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                                                \n",
       "                             ⎢              ⎛    4       3        2           \n",
       "                             ⎢            r⋅⎝12⋅r  + 77⋅r  + 178⋅r  + 175⋅r + \n",
       "                             ⎢            ────────────────────────────────────\n",
       "                             ⎢                               12               \n",
       "                             ⎢                                                \n",
       "                             ⎢        ⎛    5        4        3         2      \n",
       "                             ⎢      r⋅⎝30⋅r  + 261⋅r  + 875⋅r  + 1405⋅r  + 107\n",
       "                             ⎢      ──────────────────────────────────────────\n",
       "                             ⎢                               30               \n",
       "                             ⎢                                                \n",
       "                             ⎢  ⎛    6        5         4         3         2 \n",
       "                             ⎢r⋅⎝60⋅r  + 669⋅r  + 3002⋅r  + 6900⋅r  + 8510⋅r  \n",
       "                             ⎢────────────────────────────────────────────────\n",
       "                             ⎣                               60               \n",
       "\n",
       "                                             0                                \n",
       "                                                                              \n",
       "                                             1                                \n",
       "                                                                              \n",
       "                                            2⋅r                               \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                        r⋅(3⋅r + 2)                           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                       ⎛   2          ⎞                       \n",
       "                                     r⋅⎝4⋅r  + 7⋅r + 3⎠                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "  ⎞                              ⎛    3       2            ⎞                  \n",
       "62⎠                            r⋅⎝15⋅r  + 47⋅r  + 48⋅r + 16⎠                  \n",
       "───                            ─────────────────────────────                  \n",
       "                                             3                                \n",
       "                                                                              \n",
       "         ⎞                  ⎛    4        3        2             ⎞            \n",
       "5⋅r + 314⎠                r⋅⎝36⋅r  + 171⋅r  + 298⋅r  + 225⋅r + 62⎠            \n",
       "──────────                ────────────────────────────────────────            \n",
       "                                             6                                \n",
       "                                                                              \n",
       "               ⎞    ⎛     5         4         3         2                ⎞    \n",
       "+ 5301⋅r + 1298⎠  r⋅⎝420⋅r  + 2754⋅r  + 7075⋅r  + 8860⋅r  + 5375⋅r + 1256⎠  r⋅\n",
       "────────────────  ────────────────────────────────────────────────────────  ──\n",
       "                                             60                               \n",
       "\n",
       "                 0                                     0                      \n",
       "                                                                              \n",
       "                 0                                     0                      \n",
       "                                                                              \n",
       "                 1                                     0                      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                3⋅r                                    1                      \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "           3⋅r⋅(2⋅r + 1)                              4⋅r                     \n",
       "                                                                              \n",
       "                                                                              \n",
       "          ⎛    2           ⎞                                                  \n",
       "        r⋅⎝20⋅r  + 27⋅r + 9⎠                                                  \n",
       "        ────────────────────                     2⋅r⋅(5⋅r + 2)                \n",
       "                 2                                                            \n",
       "                                                                              \n",
       "                                                                              \n",
       "      ⎛    3       2           ⎞                 ⎛    2           ⎞           \n",
       "    r⋅⎝15⋅r  + 37⋅r  + 30⋅r + 8⎠             2⋅r⋅⎝10⋅r  + 11⋅r + 3⎠           \n",
       "                                                                              \n",
       "                                                                              \n",
       "⎛    4        3        2             ⎞    ⎛     3        2             ⎞      \n",
       "⎝84⋅r  + 319⋅r  + 448⋅r  + 275⋅r + 62⎠  r⋅⎝105⋅r  + 214⋅r  + 144⋅r + 32⎠  5⋅r⋅\n",
       "──────────────────────────────────────  ────────────────────────────────  ────\n",
       "                 4                                     3                      \n",
       "\n",
       "      0                   0         0   0⎤\n",
       "                                         ⎥\n",
       "      0                   0         0   0⎥\n",
       "                                         ⎥\n",
       "      0                   0         0   0⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "      0                   0         0   0⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "      1                   0         0   0⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "     5⋅r                  1         0   0⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "5⋅r⋅(3⋅r + 1)            6⋅r        1   0⎥\n",
       "                                         ⎥\n",
       "                                         ⎥\n",
       "⎛    2           ⎞                       ⎥\n",
       "⎝14⋅r  + 13⋅r + 3⎠                       ⎥\n",
       "──────────────────  3⋅r⋅(7⋅r + 2)  7⋅r  1⎥\n",
       "      2                                  ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_power = G_power(C)\n",
    "C_power"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HtvTRr9sVuEEwxSiQUqyqVi/h4YdQBkT+LsoA04vKqRRip61pcdWAiqA7EkXPL6qXF+SL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\n",
      "text/latex": [
       "$$\\operatorname{P_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\r & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\r \\left(r + 1\\right) & 2 r & 1 & 0 & 0 & 0 & 0 & 0\\\\\\frac{r}{2} \\left(r + 1\\right) \\left(2 r + 3\\right) & r \\left(3 r + 2\\right) & 3 r & 1 & 0 & 0 & 0 & 0\\\\\\frac{r}{3} \\left(r + 1\\right) \\left(r + 2\\right) \\left(3 r + 4\\right) & r \\left(r + 1\\right) \\left(4 r + 3\\right) & 3 r \\left(2 r + 1\\right) & 4 r & 1 & 0 & 0 & 0\\\\\\frac{r}{12} \\left(r + 1\\right) \\left(r + 2\\right) \\left(12 r^{2} + 41 r + 31\\right) & \\frac{r}{3} \\left(r + 1\\right) \\left(3 r + 4\\right) \\left(5 r + 4\\right) & \\frac{r}{2} \\left(4 r + 3\\right) \\left(5 r + 3\\right) & 2 r \\left(5 r + 2\\right) & 5 r & 1 & 0 & 0\\\\\\frac{r}{30} \\left(r + 1\\right) \\left(r + 2\\right) \\left(30 r^{3} + 171 r^{2} + 302 r + 157\\right) & \\frac{r}{6} \\left(r + 1\\right) \\left(36 r^{3} + 135 r^{2} + 163 r + 62\\right) & r \\left(r + 1\\right) \\left(3 r + 2\\right) \\left(5 r + 4\\right) & 2 r \\left(2 r + 1\\right) \\left(5 r + 3\\right) & 5 r \\left(3 r + 1\\right) & 6 r & 1 & 0\\\\\\frac{r}{60} \\left(r + 1\\right) \\left(r + 2\\right) \\left(4 r + 11\\right) \\left(15 r^{3} + 81 r^{2} + 131 r + 59\\right) & \\frac{r}{60} \\left(r + 1\\right) \\left(420 r^{4} + 2334 r^{3} + 4741 r^{2} + 4119 r + 1256\\right) & \\frac{r}{4} \\left(r + 1\\right)^{2} \\left(84 r^{2} + 151 r + 62\\right) & \\frac{r}{3} \\left(3 r + 2\\right) \\left(5 r + 4\\right) \\left(7 r + 4\\right) & \\frac{5 r}{2} \\left(2 r + 1\\right) \\left(7 r + 3\\right) & 3 r \\left(7 r + 2\\right) & 7 r & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡                            1                   \n",
       "                             ⎢                                                \n",
       "                             ⎢                            r                   \n",
       "                             ⎢                                                \n",
       "                             ⎢                        r⋅(r + 1)               \n",
       "                             ⎢                                                \n",
       "                             ⎢                   r⋅(r + 1)⋅(2⋅r + 3)          \n",
       "                             ⎢                   ───────────────────          \n",
       "                             ⎢                            2                   \n",
       "                             ⎢                                                \n",
       "                             ⎢               r⋅(r + 1)⋅(r + 2)⋅(3⋅r + 4)      \n",
       "                             ⎢               ───────────────────────────      \n",
       "                             ⎢                            3                   \n",
       "                             ⎢                                                \n",
       "P_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                            ⎛    2            ⎞ \n",
       "                             ⎢          r⋅(r + 1)⋅(r + 2)⋅⎝12⋅r  + 41⋅r + 31⎠ \n",
       "                             ⎢          ───────────────────────────────────── \n",
       "                             ⎢                            12                  \n",
       "                             ⎢                                                \n",
       "                             ⎢                      ⎛    3        2           \n",
       "                             ⎢    r⋅(r + 1)⋅(r + 2)⋅⎝30⋅r  + 171⋅r  + 302⋅r + \n",
       "                             ⎢    ────────────────────────────────────────────\n",
       "                             ⎢                           30                   \n",
       "                             ⎢                                                \n",
       "                             ⎢                             ⎛    3       2     \n",
       "                             ⎢r⋅(r + 1)⋅(r + 2)⋅(4⋅r + 11)⋅⎝15⋅r  + 81⋅r  + 13\n",
       "                             ⎢────────────────────────────────────────────────\n",
       "                             ⎣                            60                  \n",
       "\n",
       "                                     0                                        \n",
       "                                                                              \n",
       "                                     1                                        \n",
       "                                                                              \n",
       "                                    2⋅r                                       \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                r⋅(3⋅r + 2)                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                            r⋅(r + 1)⋅(4⋅r + 3)                             3⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                       r⋅(r + 1)⋅(3⋅r + 4)⋅(5⋅r + 4)                    r⋅(4⋅r\n",
       "                       ─────────────────────────────                    ──────\n",
       "                                     3                                        \n",
       "                                                                              \n",
       "   ⎞                        ⎛    3        2             ⎞                     \n",
       "157⎠              r⋅(r + 1)⋅⎝36⋅r  + 135⋅r  + 163⋅r + 62⎠                     \n",
       "────              ───────────────────────────────────────           r⋅(r + 1)⋅\n",
       "                                     6                                        \n",
       "                                                                              \n",
       "        ⎞            ⎛     4         3         2                ⎞           2 \n",
       "1⋅r + 59⎠  r⋅(r + 1)⋅⎝420⋅r  + 2334⋅r  + 4741⋅r  + 4119⋅r + 1256⎠  r⋅(r + 1) ⋅\n",
       "─────────  ──────────────────────────────────────────────────────  ───────────\n",
       "                                     60                                       \n",
       "\n",
       "    0                                0                            0           \n",
       "                                                                              \n",
       "    0                                0                            0           \n",
       "                                                                              \n",
       "    1                                0                            0           \n",
       "                                                                              \n",
       "                                                                              \n",
       "   3⋅r                               1                            0           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "r⋅(2⋅r + 1)                         4⋅r                           1           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " + 3)⋅(5⋅r + 3)                                                               \n",
       "───────────────                2⋅r⋅(5⋅r + 2)                     5⋅r          \n",
       "    2                                                                         \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(3⋅r + 2)⋅(5⋅r + 4)       2⋅r⋅(2⋅r + 1)⋅(5⋅r + 3)           5⋅r⋅(3⋅r + 1)     \n",
       "                                                                              \n",
       "                                                                              \n",
       "⎛    2             ⎞                                                          \n",
       "⎝84⋅r  + 151⋅r + 62⎠  r⋅(3⋅r + 2)⋅(5⋅r + 4)⋅(7⋅r + 4)  5⋅r⋅(2⋅r + 1)⋅(7⋅r + 3)\n",
       "────────────────────  ───────────────────────────────  ───────────────────────\n",
       "    4                                3                            2           \n",
       "\n",
       "        0         0   0⎤\n",
       "                       ⎥\n",
       "        0         0   0⎥\n",
       "                       ⎥\n",
       "        0         0   0⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "        0         0   0⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "        0         0   0⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "        1         0   0⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "       6⋅r        1   0⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "                       ⎥\n",
       "  3⋅r⋅(7⋅r + 2)  7⋅r  1⎥\n",
       "                       ⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "define(C_power.lhs, C_power.rhs.applyfunc(factor)) # factored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "assert C_power.rhs == (C.rhs**r).applyfunc(simplify)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nature(is_ordinary=True, is_exponential=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(C_power.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UlEZCay3q42PCmt1jVQ4pFBoJtNOxucIw5S3/ncghqBdbs0mUTyWwWNOFb33V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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}r & 1 & 0 & 0 & 0 & 0 & 0\\\\r & r & 1 & 0 & 0 & 0 & 0\\\\- \\frac{r}{2} \\left(r - 3\\right) & r & r & 1 & 0 & 0 & 0\\\\\\frac{r}{3} \\left(r - 4\\right) \\left(r - 2\\right) & - \\frac{r}{2} \\left(r - 3\\right) & r & r & 1 & 0 & 0\\\\- \\frac{r}{12} \\left(r - 2\\right) \\left(3 r^{2} - 22 r + 31\\right) & \\frac{r}{3} \\left(r - 4\\right) \\left(r - 2\\right) & - \\frac{r}{2} \\left(r - 3\\right) & r & r & 1 & 0\\\\\\frac{r}{60} \\left(12 r^{4} - 155 r^{3} + 650 r^{2} - 1075 r + 628\\right) & - \\frac{r}{12} \\left(r - 2\\right) \\left(3 r^{2} - 22 r + 31\\right) & \\frac{r}{3} \\left(r - 4\\right) \\left(r - 2\\right) & - \\frac{r}{2} \\left(r - 3\\right) & r & r & 1\\\\- \\frac{r}{60} \\left(10 r^{5} - 167 r^{4} + 975 r^{3} - 2525 r^{2} + 2945 r - 1298\\right) & \\frac{r}{60} \\left(12 r^{4} - 155 r^{3} + 650 r^{2} - 1075 r + 628\\right) & - \\frac{r}{12} \\left(r - 2\\right) \\left(3 r^{2} - 22 r + 31\\right) & \\frac{r}{3} \\left(r - 4\\right) \\left(r - 2\\right) & - \\frac{r}{2} \\left(r - 3\\right) & r & r\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                           r                                                 \n",
       "⎢                                                                             \n",
       "⎢                           r                                                 \n",
       "⎢                                                                             \n",
       "⎢                      -r⋅(r - 3)                                             \n",
       "⎢                      ───────────                                            \n",
       "⎢                           2                                                 \n",
       "⎢                                                                             \n",
       "⎢                   r⋅(r - 4)⋅(r - 2)                                    -r⋅(r\n",
       "⎢                   ─────────────────                                    ─────\n",
       "⎢                           3                                                 \n",
       "⎢                                                                             \n",
       "⎢                       ⎛   2            ⎞                                    \n",
       "⎢            -r⋅(r - 2)⋅⎝3⋅r  - 22⋅r + 31⎠                            r⋅(r - 4\n",
       "⎢            ──────────────────────────────                           ────────\n",
       "⎢                          12                                                 \n",
       "⎢                                                                             \n",
       "⎢        ⎛    4        3        2               ⎞                          ⎛  \n",
       "⎢      r⋅⎝12⋅r  - 155⋅r  + 650⋅r  - 1075⋅r + 628⎠               -r⋅(r - 2)⋅⎝3⋅\n",
       "⎢      ──────────────────────────────────────────               ──────────────\n",
       "⎢                          60                                                 \n",
       "⎢                                                                             \n",
       "⎢   ⎛    5        4        3         2                ⎞     ⎛    4        3   \n",
       "⎢-r⋅⎝10⋅r  - 167⋅r  + 975⋅r  - 2525⋅r  + 2945⋅r - 1298⎠   r⋅⎝12⋅r  - 155⋅r  + \n",
       "⎢───────────────────────────────────────────────────────  ────────────────────\n",
       "⎣                           60                                                \n",
       "\n",
       "1                                     0                         0             \n",
       "                                                                              \n",
       "r                                     1                         0             \n",
       "                                                                              \n",
       "                                                                              \n",
       "r                                     r                         1             \n",
       "                                                                              \n",
       "                                                                              \n",
       " - 3)                                                                         \n",
       "──────                                r                         r             \n",
       "2                                                                             \n",
       "                                                                              \n",
       "                                                                              \n",
       ")⋅(r - 2)                        -r⋅(r - 3)                                   \n",
       "─────────                        ───────────                    r             \n",
       "3                                     2                                       \n",
       "                                                                              \n",
       " 2            ⎞                                                               \n",
       "r  - 22⋅r + 31⎠               r⋅(r - 4)⋅(r - 2)            -r⋅(r - 3)         \n",
       "────────────────              ─────────────────            ───────────        \n",
       "12                                    3                         2             \n",
       "                                                                              \n",
       "     2               ⎞             ⎛   2            ⎞                         \n",
       "650⋅r  - 1075⋅r + 628⎠  -r⋅(r - 2)⋅⎝3⋅r  - 22⋅r + 31⎠   r⋅(r - 4)⋅(r - 2)  -r⋅\n",
       "──────────────────────  ──────────────────────────────  ─────────────────  ───\n",
       "60                                    12                        3             \n",
       "\n",
       "  0       0  0⎤\n",
       "              ⎥\n",
       "  0       0  0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "  0       0  0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "  1       0  0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "  r       1  0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "  r       r  1⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "(r - 3)       ⎥\n",
       "────────  r  r⎥\n",
       "  2           ⎦"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "production_matrix(C_power.rhs).applyfunc(factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `inverse` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "f_inverse, g_inverse, G_inverse = functions_catalog.inverse(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dFr6GFOUMcTO1A06bwwTRKd1rOMZLna6ocIJ6PNbImLk75Y/X6wJW+kQbNTgT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\na8+KzxNEMuAYn6n/Pxr0gE7IpOUFAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( \\operatorname{I_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & -2 & 1 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & -3 & 1 & 0 & 0 & 0 & 0\\\\0 & 0 & 3 & -4 & 1 & 0 & 0 & 0\\\\0 & 0 & -1 & 6 & -5 & 1 & 0 & 0\\\\0 & 0 & 0 & -4 & 10 & -6 & 1 & 0\\\\0 & 0 & 0 & 1 & -10 & 15 & -7 & 1\\end{matrix}\\right], \\quad \\operatorname{I_{ 8 }}{\\left (\\operatorname{I_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} \\right )} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\2 & 2 & 1 & 0 & 0 & 0 & 0 & 0\\\\5 & 5 & 3 & 1 & 0 & 0 & 0 & 0\\\\14 & 14 & 9 & 4 & 1 & 0 & 0 & 0\\\\42 & 42 & 28 & 14 & 5 & 1 & 0 & 0\\\\132 & 132 & 90 & 48 & 20 & 6 & 1 & 0\\\\429 & 429 & 297 & 165 & 75 & 27 & 7 & 1\\end{matrix}\\right]\\right )$$"
      ],
      "text/plain": [
       "⎛                             ⎡1   0   0   0    0   0   0   0⎤                \n",
       "⎜                             ⎢                              ⎥                \n",
       "⎜                             ⎢-1  1   0   0    0   0   0   0⎥                \n",
       "⎜                             ⎢                              ⎥                \n",
       "⎜                             ⎢0   -2  1   0    0   0   0   0⎥                \n",
       "⎜                             ⎢                              ⎥                \n",
       "⎜                             ⎢0   1   -3  1    0   0   0   0⎥                \n",
       "⎜I_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                              ⎥, I_{ 8 }(I_{ 8 \n",
       "⎜                             ⎢0   0   3   -4   1   0   0   0⎥                \n",
       "⎜                             ⎢                              ⎥                \n",
       "⎜                             ⎢0   0   -1  6   -5   1   0   0⎥                \n",
       "⎜                             ⎢                              ⎥                \n",
       "⎜                             ⎢0   0   0   -4  10   -6  1   0⎥                \n",
       "⎜                             ⎢                              ⎥                \n",
       "⎝                             ⎣0   0   0   1   -10  15  -7  1⎦                \n",
       "\n",
       "                        ⎡ 1    0    0    0   0   0   0  0⎤⎞\n",
       "                        ⎢                                ⎥⎟\n",
       "                        ⎢ 1    1    0    0   0   0   0  0⎥⎟\n",
       "                        ⎢                                ⎥⎟\n",
       "                        ⎢ 2    2    1    0   0   0   0  0⎥⎟\n",
       "                        ⎢                                ⎥⎟\n",
       "                        ⎢ 5    5    3    1   0   0   0  0⎥⎟\n",
       "}(\\mathcal{C}_{ 8 })) = ⎢                                ⎥⎟\n",
       "                        ⎢14   14    9    4   1   0   0  0⎥⎟\n",
       "                        ⎢                                ⎥⎟\n",
       "                        ⎢42   42   28   14   5   1   0  0⎥⎟\n",
       "                        ⎢                                ⎥⎟\n",
       "                        ⎢132  132  90   48   20  6   1  0⎥⎟\n",
       "                        ⎢                                ⎥⎟\n",
       "                        ⎣429  429  297  165  75  27  7  1⎦⎠"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_inverse = G_inverse(C)\n",
    "C_inverse, G_inverse(C_inverse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nature(is_ordinary=True, is_exponential=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(C_inverse.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAACvCAMAAADT2HVDAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\ne87N/8nIoTxwogLjAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-1 & 1 & 0 & 0 & 0 & 0 & 0\\\\-1 & -1 & 1 & 0 & 0 & 0 & 0\\\\-2 & -1 & -1 & 1 & 0 & 0 & 0\\\\-5 & -2 & -1 & -1 & 1 & 0 & 0\\\\-14 & -5 & -2 & -1 & -1 & 1 & 0\\\\-42 & -14 & -5 & -2 & -1 & -1 & 1\\\\-132 & -42 & -14 & -5 & -2 & -1 & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡ -1    1    0   0   0   0   0 ⎤\n",
       "⎢                              ⎥\n",
       "⎢ -1   -1    1   0   0   0   0 ⎥\n",
       "⎢                              ⎥\n",
       "⎢ -2   -1   -1   1   0   0   0 ⎥\n",
       "⎢                              ⎥\n",
       "⎢ -5   -2   -1   -1  1   0   0 ⎥\n",
       "⎢                              ⎥\n",
       "⎢-14   -5   -2   -1  -1  1   0 ⎥\n",
       "⎢                              ⎥\n",
       "⎢-42   -14  -5   -2  -1  -1  1 ⎥\n",
       "⎢                              ⎥\n",
       "⎣-132  -42  -14  -5  -2  -1  -1⎦"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "production_matrix(C_inverse.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "assert C_inverse.rhs*C.rhs == Matrix(m, m, identity_matrix())\n",
    "assert C_inverse.rhs == C_power.rhs.subs({r:-1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `sqrt` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "f_sqrt, g_sqrt, G_sqrt = functions_catalog.square_root(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eBJ2hoIIhoZqq1M/EnKNy3Ued4nmlnbQK6I1BK0H2XvAG+7Th+vHZqaz4j4FyD3X/stp2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\nsM7kAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\operatorname{R_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{3}{4} & 1 & 1 & 0 & 0 & 0 & 0 & 0\\\\\\frac{3}{2} & \\frac{7}{4} & \\frac{3}{2} & 1 & 0 & 0 & 0 & 0\\\\\\frac{55}{16} & \\frac{15}{4} & 3 & 2 & 1 & 0 & 0 & 0\\\\\\frac{545}{64} & \\frac{143}{16} & \\frac{55}{8} & \\frac{9}{2} & \\frac{5}{2} & 1 & 0 & 0\\\\\\frac{709}{32} & \\frac{727}{32} & \\frac{273}{16} & 11 & \\frac{25}{4} & 3 & 1 & 0\\\\\\frac{15249}{256} & \\frac{3855}{64} & \\frac{2853}{64} & \\frac{455}{16} & \\frac{65}{4} & \\frac{33}{4} & \\frac{7}{2} & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡  1     0     0     0    0     0     0   0⎤\n",
       "                             ⎢                                          ⎥\n",
       "                             ⎢ 1/2    1     0     0    0     0     0   0⎥\n",
       "                             ⎢                                          ⎥\n",
       "                             ⎢ 3/4    1     1     0    0     0     0   0⎥\n",
       "                             ⎢                                          ⎥\n",
       "                             ⎢ 3/2   7/4   3/2    1    0     0     0   0⎥\n",
       "                             ⎢                                          ⎥\n",
       "                             ⎢ 55                                       ⎥\n",
       "                             ⎢ ──    15/4   3     2    1     0     0   0⎥\n",
       "                             ⎢ 16                                       ⎥\n",
       "R_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                                          ⎥\n",
       "                             ⎢ 545   143                                ⎥\n",
       "                             ⎢ ───   ───   55/8  9/2  5/2    1     0   0⎥\n",
       "                             ⎢  64    16                                ⎥\n",
       "                             ⎢                                          ⎥\n",
       "                             ⎢ 709   727   273                          ⎥\n",
       "                             ⎢ ───   ───   ───   11   25/4   3     1   0⎥\n",
       "                             ⎢  32    32    16                          ⎥\n",
       "                             ⎢                                          ⎥\n",
       "                             ⎢15249  3855  2853  455                    ⎥\n",
       "                             ⎢─────  ────  ────  ───  65/4  33/4  7/2  1⎥\n",
       "                             ⎣ 256    64    64    16                    ⎦"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_sqrt = G_sqrt(C)\n",
    "C_sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nature(is_ordinary=True, is_exponential=False)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(C_sqrt.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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,
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & 0\\\\\\frac{1}{2} & \\frac{1}{2} & 1 & 0 & 0 & 0 & 0\\\\\\frac{5}{8} & \\frac{1}{2} & \\frac{1}{2} & 1 & 0 & 0 & 0\\\\\\frac{7}{8} & \\frac{5}{8} & \\frac{1}{2} & \\frac{1}{2} & 1 & 0 & 0\\\\\\frac{83}{64} & \\frac{7}{8} & \\frac{5}{8} & \\frac{1}{2} & \\frac{1}{2} & 1 & 0\\\\\\frac{125}{64} & \\frac{83}{64} & \\frac{7}{8} & \\frac{5}{8} & \\frac{1}{2} & \\frac{1}{2} & 1\\\\\\frac{23}{8} & \\frac{125}{64} & \\frac{83}{64} & \\frac{7}{8} & \\frac{5}{8} & \\frac{1}{2} & \\frac{1}{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1/2    1    0    0    0    0    0 ⎤\n",
       "⎢                                  ⎥\n",
       "⎢1/2   1/2   1    0    0    0    0 ⎥\n",
       "⎢                                  ⎥\n",
       "⎢5/8   1/2  1/2   1    0    0    0 ⎥\n",
       "⎢                                  ⎥\n",
       "⎢7/8   5/8  1/2  1/2   1    0    0 ⎥\n",
       "⎢                                  ⎥\n",
       "⎢ 83                               ⎥\n",
       "⎢ ──   7/8  5/8  1/2  1/2   1    0 ⎥\n",
       "⎢ 64                               ⎥\n",
       "⎢                                  ⎥\n",
       "⎢125   83                          ⎥\n",
       "⎢───   ──   7/8  5/8  1/2  1/2   1 ⎥\n",
       "⎢ 64   64                          ⎥\n",
       "⎢                                  ⎥\n",
       "⎢      125  83                     ⎥\n",
       "⎢23/8  ───  ──   7/8  5/8  1/2  1/2⎥\n",
       "⎣       64  64                     ⎦"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "production_matrix(C_sqrt.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "assert C.rhs**(S(1)/2) == C_sqrt.rhs\n",
    "assert C_sqrt.rhs == C_power.rhs.subs({r:S(1)/2})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `expt` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "f_exp, g_exp, G_exp = functions_catalog.exp(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CgCAgCAgCgoAgIAgIAgUISDhaANJbsjx6WDJvP0z/lhpEqCAgCAgCgoAgIAgIAl+AgISj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\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\operatorname{E_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}e^{\\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0 & 0 & 0 & 0\\\\\\alpha \\left(\\alpha + 2\\right) e^{\\alpha} & 2 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0 & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{2} \\left(2 \\alpha^{2} + 11 \\alpha + 10\\right) & \\alpha \\left(3 \\alpha + 5\\right) e^{\\alpha} & 3 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{3} \\left(3 \\alpha^{3} + 31 \\alpha^{2} + 78 \\alpha + 42\\right) & \\alpha \\left(4 \\alpha^{2} + 19 \\alpha + 14\\right) e^{\\alpha} & 3 \\alpha \\left(2 \\alpha + 3\\right) e^{\\alpha} & 4 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{12} \\left(12 \\alpha^{4} + 197 \\alpha^{3} + 940 \\alpha^{2} + 1428 \\alpha + 504\\right) & \\frac{\\alpha e^{\\alpha}}{3} \\left(15 \\alpha^{3} + 137 \\alpha^{2} + 294 \\alpha + 126\\right) & \\frac{\\alpha e^{\\alpha}}{2} \\left(20 \\alpha^{2} + 87 \\alpha + 56\\right) & 2 \\alpha \\left(5 \\alpha + 7\\right) e^{\\alpha} & 5 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{30} \\left(30 \\alpha^{5} + 711 \\alpha^{4} + 5435 \\alpha^{3} + 15880 \\alpha^{2} + 16260 \\alpha + 3960\\right) & \\frac{\\alpha e^{\\alpha}}{6} \\left(36 \\alpha^{4} + 531 \\alpha^{3} + 2224 \\alpha^{2} + 2856 \\alpha + 792\\right) & \\alpha \\left(15 \\alpha^{3} + 127 \\alpha^{2} + 246 \\alpha + 90\\right) e^{\\alpha} & 2 \\alpha \\left(10 \\alpha^{2} + 41 \\alpha + 24\\right) e^{\\alpha} & 5 \\alpha \\left(3 \\alpha + 4\\right) e^{\\alpha} & 6 \\alpha e^{\\alpha} & e^{\\alpha} & 0\\\\\\frac{\\alpha e^{\\alpha}}{60} \\left(60 \\alpha^{6} + 1929 \\alpha^{5} + 21437 \\alpha^{4} + 101405 \\alpha^{3} + 203230 \\alpha^{2} + 148680 \\alpha + 25740\\right) & \\frac{\\alpha e^{\\alpha}}{60} \\left(420 \\alpha^{5} + 9054 \\alpha^{4} + 61915 \\alpha^{3} + 157960 \\alpha^{2} + 135810 \\alpha + 25740\\right) & \\frac{\\alpha e^{\\alpha}}{4} \\left(84 \\alpha^{4} + 1159 \\alpha^{3} + 4462 \\alpha^{2} + 5112 \\alpha + 1188\\right) & \\frac{\\alpha e^{\\alpha}}{3} \\left(105 \\alpha^{3} + 844 \\alpha^{2} + 1521 \\alpha + 495\\right) & \\frac{5 \\alpha}{2} \\left(14 \\alpha^{2} + 55 \\alpha + 30\\right) e^{\\alpha} & 3 \\alpha \\left(7 \\alpha + 9\\right) e^{\\alpha} & 7 \\alpha e^{\\alpha} & e^{\\alpha}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡                                      α         \n",
       "                             ⎢                                     ℯ          \n",
       "                             ⎢                                                \n",
       "                             ⎢                                       α        \n",
       "                             ⎢                                    α⋅ℯ         \n",
       "                             ⎢                                                \n",
       "                             ⎢                                           α    \n",
       "                             ⎢                                α⋅(α + 2)⋅ℯ     \n",
       "                             ⎢                                                \n",
       "                             ⎢                            ⎛   2            ⎞  \n",
       "                             ⎢                          α⋅⎝2⋅α  + 11⋅α + 10⎠⋅ℯ\n",
       "                             ⎢                          ──────────────────────\n",
       "                             ⎢                                     2          \n",
       "                             ⎢                                                \n",
       "                             ⎢                        ⎛   3       2           \n",
       "                             ⎢                      α⋅⎝3⋅α  + 31⋅α  + 78⋅α + 4\n",
       "E_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                      ──────────────────────────\n",
       "                             ⎢                                     3          \n",
       "                             ⎢                                                \n",
       "                             ⎢                 ⎛    4        3        2       \n",
       "                             ⎢               α⋅⎝12⋅α  + 197⋅α  + 940⋅α  + 1428\n",
       "                             ⎢               ─────────────────────────────────\n",
       "                             ⎢                                     12         \n",
       "                             ⎢                                                \n",
       "                             ⎢          ⎛    5        4         3          2  \n",
       "                             ⎢        α⋅⎝30⋅α  + 711⋅α  + 5435⋅α  + 15880⋅α  +\n",
       "                             ⎢        ────────────────────────────────────────\n",
       "                             ⎢                                     30         \n",
       "                             ⎢                                                \n",
       "                             ⎢  ⎛    6         5          4           3       \n",
       "                             ⎢α⋅⎝60⋅α  + 1929⋅α  + 21437⋅α  + 101405⋅α  + 2032\n",
       "                             ⎢────────────────────────────────────────────────\n",
       "                             ⎣                                     60         \n",
       "\n",
       "                                                                              \n",
       "                                                              0               \n",
       "                                                                              \n",
       "                                                              α               \n",
       "                                                             ℯ                \n",
       "                                                                              \n",
       "                                                                α             \n",
       "                                                           2⋅α⋅ℯ              \n",
       "                                                                              \n",
       "α                                                                             \n",
       "                                                                    α         \n",
       "─                                                      α⋅(3⋅α + 5)⋅ℯ          \n",
       "                                                                              \n",
       "                                                                              \n",
       " ⎞  α                                                                         \n",
       "2⎠⋅ℯ                                                 ⎛   2            ⎞  α    \n",
       "─────                                              α⋅⎝4⋅α  + 19⋅α + 14⎠⋅ℯ     \n",
       "                                                                              \n",
       "                                                                              \n",
       "        ⎞  α                                   ⎛    3        2              ⎞ \n",
       "⋅α + 504⎠⋅ℯ                                  α⋅⎝15⋅α  + 137⋅α  + 294⋅α + 126⎠⋅\n",
       "────────────                                 ─────────────────────────────────\n",
       "                                                              3               \n",
       "                                                                              \n",
       "               ⎞  α                      ⎛    4        3         2            \n",
       " 16260⋅α + 3960⎠⋅ℯ                     α⋅⎝36⋅α  + 531⋅α  + 2224⋅α  + 2856⋅α + \n",
       "───────────────────                    ───────────────────────────────────────\n",
       "                                                             6                \n",
       "                                                                              \n",
       "    2                   ⎞  α    ⎛     5         4          3           2      \n",
       "30⋅α  + 148680⋅α + 25740⎠⋅ℯ   α⋅⎝420⋅α  + 9054⋅α  + 61915⋅α  + 157960⋅α  + 135\n",
       "────────────────────────────  ────────────────────────────────────────────────\n",
       "                                                              60              \n",
       "\n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                           α                                  \n",
       "                                          ℯ                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                             α                                \n",
       "                                        3⋅α⋅ℯ                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                  α                           \n",
       "                                   3⋅α⋅(2⋅α + 3)⋅ℯ                            \n",
       "                                                                              \n",
       "                                                                              \n",
       " α                               ⎛    2            ⎞  α                       \n",
       "ℯ                              α⋅⎝20⋅α  + 87⋅α + 56⎠⋅ℯ                        \n",
       "──                             ────────────────────────                       \n",
       "                                          2                                   \n",
       "                                                                              \n",
       "   ⎞  α                                                                       \n",
       "792⎠⋅ℯ                      ⎛    3        2             ⎞  α                  \n",
       "───────                   α⋅⎝15⋅α  + 127⋅α  + 246⋅α + 90⎠⋅ℯ               2⋅α⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "             ⎞  α    ⎛    4         3         2                ⎞  α    ⎛     3\n",
       "810⋅α + 25740⎠⋅ℯ   α⋅⎝84⋅α  + 1159⋅α  + 4462⋅α  + 5112⋅α + 1188⎠⋅ℯ   α⋅⎝105⋅α \n",
       "─────────────────  ────────────────────────────────────────────────  ─────────\n",
       "                                          4                                   \n",
       "\n",
       "                                                                              \n",
       "         0                                0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                                0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                                0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "         α                                                                    \n",
       "        ℯ                                 0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "           α                               α                                  \n",
       "      4⋅α⋅ℯ                               ℯ                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                α                            α                    α           \n",
       " 2⋅α⋅(5⋅α + 7)⋅ℯ                        5⋅α⋅ℯ                    ℯ            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⎛    2            ⎞  α                            α                 α         \n",
       "⎝10⋅α  + 41⋅α + 24⎠⋅ℯ              5⋅α⋅(3⋅α + 4)⋅ℯ             6⋅α⋅ℯ          \n",
       "                                                                              \n",
       "                                                                              \n",
       "        2               ⎞  α      ⎛    2            ⎞  α                      \n",
       " + 844⋅α  + 1521⋅α + 495⎠⋅ℯ   5⋅α⋅⎝14⋅α  + 55⋅α + 30⎠⋅ℯ                  α    \n",
       "────────────────────────────  ──────────────────────────  3⋅α⋅(7⋅α + 9)⋅ℯ   7⋅\n",
       "         3                                2                                   \n",
       "\n",
       "        ⎤\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       " α      ⎥\n",
       "ℯ     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "   α   α⎥\n",
       "α⋅ℯ   ℯ ⎥\n",
       "        ⎦"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_exp = G_exp(C)\n",
    "C_exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CgCAgCAgCgoAgIAgIAgUISDhaANJbsjx6WDJvP0z/lhpEqCAgCAgCgoAgIAgIAl+AgISj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\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\operatorname{E_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}e^{\\alpha} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0 & 0 & 0 & 0\\\\\\alpha \\left(\\alpha + 2\\right) e^{\\alpha} & 2 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0 & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{2} \\left(2 \\alpha^{2} + 11 \\alpha + 10\\right) & \\alpha \\left(3 \\alpha + 5\\right) e^{\\alpha} & 3 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{3} \\left(3 \\alpha^{3} + 31 \\alpha^{2} + 78 \\alpha + 42\\right) & \\alpha \\left(4 \\alpha^{2} + 19 \\alpha + 14\\right) e^{\\alpha} & 3 \\alpha \\left(2 \\alpha + 3\\right) e^{\\alpha} & 4 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{12} \\left(12 \\alpha^{4} + 197 \\alpha^{3} + 940 \\alpha^{2} + 1428 \\alpha + 504\\right) & \\frac{\\alpha e^{\\alpha}}{3} \\left(15 \\alpha^{3} + 137 \\alpha^{2} + 294 \\alpha + 126\\right) & \\frac{\\alpha e^{\\alpha}}{2} \\left(20 \\alpha^{2} + 87 \\alpha + 56\\right) & 2 \\alpha \\left(5 \\alpha + 7\\right) e^{\\alpha} & 5 \\alpha e^{\\alpha} & e^{\\alpha} & 0 & 0\\\\\\frac{\\alpha e^{\\alpha}}{30} \\left(30 \\alpha^{5} + 711 \\alpha^{4} + 5435 \\alpha^{3} + 15880 \\alpha^{2} + 16260 \\alpha + 3960\\right) & \\frac{\\alpha e^{\\alpha}}{6} \\left(36 \\alpha^{4} + 531 \\alpha^{3} + 2224 \\alpha^{2} + 2856 \\alpha + 792\\right) & \\alpha \\left(15 \\alpha^{3} + 127 \\alpha^{2} + 246 \\alpha + 90\\right) e^{\\alpha} & 2 \\alpha \\left(10 \\alpha^{2} + 41 \\alpha + 24\\right) e^{\\alpha} & 5 \\alpha \\left(3 \\alpha + 4\\right) e^{\\alpha} & 6 \\alpha e^{\\alpha} & e^{\\alpha} & 0\\\\\\frac{\\alpha e^{\\alpha}}{60} \\left(60 \\alpha^{6} + 1929 \\alpha^{5} + 21437 \\alpha^{4} + 101405 \\alpha^{3} + 203230 \\alpha^{2} + 148680 \\alpha + 25740\\right) & \\frac{\\alpha e^{\\alpha}}{60} \\left(420 \\alpha^{5} + 9054 \\alpha^{4} + 61915 \\alpha^{3} + 157960 \\alpha^{2} + 135810 \\alpha + 25740\\right) & \\frac{\\alpha e^{\\alpha}}{4} \\left(84 \\alpha^{4} + 1159 \\alpha^{3} + 4462 \\alpha^{2} + 5112 \\alpha + 1188\\right) & \\frac{\\alpha e^{\\alpha}}{3} \\left(105 \\alpha^{3} + 844 \\alpha^{2} + 1521 \\alpha + 495\\right) & \\frac{5 \\alpha}{2} \\left(14 \\alpha^{2} + 55 \\alpha + 30\\right) e^{\\alpha} & 3 \\alpha \\left(7 \\alpha + 9\\right) e^{\\alpha} & 7 \\alpha e^{\\alpha} & e^{\\alpha}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡                                      α         \n",
       "                             ⎢                                     ℯ          \n",
       "                             ⎢                                                \n",
       "                             ⎢                                       α        \n",
       "                             ⎢                                    α⋅ℯ         \n",
       "                             ⎢                                                \n",
       "                             ⎢                                           α    \n",
       "                             ⎢                                α⋅(α + 2)⋅ℯ     \n",
       "                             ⎢                                                \n",
       "                             ⎢                            ⎛   2            ⎞  \n",
       "                             ⎢                          α⋅⎝2⋅α  + 11⋅α + 10⎠⋅ℯ\n",
       "                             ⎢                          ──────────────────────\n",
       "                             ⎢                                     2          \n",
       "                             ⎢                                                \n",
       "                             ⎢                        ⎛   3       2           \n",
       "                             ⎢                      α⋅⎝3⋅α  + 31⋅α  + 78⋅α + 4\n",
       "E_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                      ──────────────────────────\n",
       "                             ⎢                                     3          \n",
       "                             ⎢                                                \n",
       "                             ⎢                 ⎛    4        3        2       \n",
       "                             ⎢               α⋅⎝12⋅α  + 197⋅α  + 940⋅α  + 1428\n",
       "                             ⎢               ─────────────────────────────────\n",
       "                             ⎢                                     12         \n",
       "                             ⎢                                                \n",
       "                             ⎢          ⎛    5        4         3          2  \n",
       "                             ⎢        α⋅⎝30⋅α  + 711⋅α  + 5435⋅α  + 15880⋅α  +\n",
       "                             ⎢        ────────────────────────────────────────\n",
       "                             ⎢                                     30         \n",
       "                             ⎢                                                \n",
       "                             ⎢  ⎛    6         5          4           3       \n",
       "                             ⎢α⋅⎝60⋅α  + 1929⋅α  + 21437⋅α  + 101405⋅α  + 2032\n",
       "                             ⎢────────────────────────────────────────────────\n",
       "                             ⎣                                     60         \n",
       "\n",
       "                                                                              \n",
       "                                                              0               \n",
       "                                                                              \n",
       "                                                              α               \n",
       "                                                             ℯ                \n",
       "                                                                              \n",
       "                                                                α             \n",
       "                                                           2⋅α⋅ℯ              \n",
       "                                                                              \n",
       "α                                                                             \n",
       "                                                                    α         \n",
       "─                                                      α⋅(3⋅α + 5)⋅ℯ          \n",
       "                                                                              \n",
       "                                                                              \n",
       " ⎞  α                                                                         \n",
       "2⎠⋅ℯ                                                 ⎛   2            ⎞  α    \n",
       "─────                                              α⋅⎝4⋅α  + 19⋅α + 14⎠⋅ℯ     \n",
       "                                                                              \n",
       "                                                                              \n",
       "        ⎞  α                                   ⎛    3        2              ⎞ \n",
       "⋅α + 504⎠⋅ℯ                                  α⋅⎝15⋅α  + 137⋅α  + 294⋅α + 126⎠⋅\n",
       "────────────                                 ─────────────────────────────────\n",
       "                                                              3               \n",
       "                                                                              \n",
       "               ⎞  α                      ⎛    4        3         2            \n",
       " 16260⋅α + 3960⎠⋅ℯ                     α⋅⎝36⋅α  + 531⋅α  + 2224⋅α  + 2856⋅α + \n",
       "───────────────────                    ───────────────────────────────────────\n",
       "                                                             6                \n",
       "                                                                              \n",
       "    2                   ⎞  α    ⎛     5         4          3           2      \n",
       "30⋅α  + 148680⋅α + 25740⎠⋅ℯ   α⋅⎝420⋅α  + 9054⋅α  + 61915⋅α  + 157960⋅α  + 135\n",
       "────────────────────────────  ────────────────────────────────────────────────\n",
       "                                                              60              \n",
       "\n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                          0                                   \n",
       "                                                                              \n",
       "                                           α                                  \n",
       "                                          ℯ                                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                             α                                \n",
       "                                        3⋅α⋅ℯ                                 \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                  α                           \n",
       "                                   3⋅α⋅(2⋅α + 3)⋅ℯ                            \n",
       "                                                                              \n",
       "                                                                              \n",
       " α                               ⎛    2            ⎞  α                       \n",
       "ℯ                              α⋅⎝20⋅α  + 87⋅α + 56⎠⋅ℯ                        \n",
       "──                             ────────────────────────                       \n",
       "                                          2                                   \n",
       "                                                                              \n",
       "   ⎞  α                                                                       \n",
       "792⎠⋅ℯ                      ⎛    3        2             ⎞  α                  \n",
       "───────                   α⋅⎝15⋅α  + 127⋅α  + 246⋅α + 90⎠⋅ℯ               2⋅α⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "             ⎞  α    ⎛    4         3         2                ⎞  α    ⎛     3\n",
       "810⋅α + 25740⎠⋅ℯ   α⋅⎝84⋅α  + 1159⋅α  + 4462⋅α  + 5112⋅α + 1188⎠⋅ℯ   α⋅⎝105⋅α \n",
       "─────────────────  ────────────────────────────────────────────────  ─────────\n",
       "                                          4                                   \n",
       "\n",
       "                                                                              \n",
       "         0                                0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                                0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "         0                                0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "         α                                                                    \n",
       "        ℯ                                 0                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "           α                               α                                  \n",
       "      4⋅α⋅ℯ                               ℯ                      0            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                α                            α                    α           \n",
       " 2⋅α⋅(5⋅α + 7)⋅ℯ                        5⋅α⋅ℯ                    ℯ            \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⎛    2            ⎞  α                            α                 α         \n",
       "⎝10⋅α  + 41⋅α + 24⎠⋅ℯ              5⋅α⋅(3⋅α + 4)⋅ℯ             6⋅α⋅ℯ          \n",
       "                                                                              \n",
       "                                                                              \n",
       "        2               ⎞  α      ⎛    2            ⎞  α                      \n",
       " + 844⋅α  + 1521⋅α + 495⎠⋅ℯ   5⋅α⋅⎝14⋅α  + 55⋅α + 30⎠⋅ℯ                  α    \n",
       "────────────────────────────  ──────────────────────────  3⋅α⋅(7⋅α + 9)⋅ℯ   7⋅\n",
       "         3                                2                                   \n",
       "\n",
       "        ⎤\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "0     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       " α      ⎥\n",
       "ℯ     0 ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "   α   α⎥\n",
       "α⋅ℯ   ℯ ⎥\n",
       "        ⎦"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "define(C_exp.lhs, C_exp.rhs.applyfunc(factor))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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etZlaNgypWVUqez02D7m9mpaOcSoim0TdyJDpvLwyfn8AElJhstmzRERl5Apc\nJGJJ7U0y6yCuXhUgix57xTC+XBHZcIIZDp4Mcj/Uhbls+AFIuFHYX2H5ruqzOJWbd+AfJIdkqfxF\nZh3E1WsCZOpmIvaKYXS5IrK5qBue5nZhR6qifG30AUh4wYYwJZzbKD5ohi0fxeJhnn/3Jc96yCZR\nNz6AZyk7aec+AAkJkCiotLR8tS7d33l72znXQzaJuokCeL5WUcqZD0DCnNETnvQmLRsGFucfG9zO\nuR6ykTigGVsfwJNfD97TBfJYQoZIH3+X7C8l+ztvcTvnisgmUTeGvdEPQPpIn2yKkaOPiMqE2eR2\nzhWRTaJuJIAnsxqmbh+ARHiK9JneJ+O7RERluIKLRCzleX/Ka1Nko2k90kwtZtdH3cieCItWSSc/\nACmRPknp+GosEVFfr2jOSMSSxvZbbE48Zfst99LcBNQWeGAM+H78aSXQcuU2/wGEyMOA3wkj7AAA\nAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left. \\operatorname{E_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} \\right|_{\\substack{ \\alpha=1 }} = \\left[\\begin{matrix}e & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\e & e & 0 & 0 & 0 & 0 & 0 & 0\\\\3 e & 2 e & e & 0 & 0 & 0 & 0 & 0\\\\\\frac{23 e}{2} & 8 e & 3 e & e & 0 & 0 & 0 & 0\\\\\\frac{154 e}{3} & 37 e & 15 e & 4 e & e & 0 & 0 & 0\\\\\\frac{1027 e}{4} & \\frac{572 e}{3} & \\frac{163 e}{2} & 24 e & 5 e & e & 0 & 0\\\\\\frac{7046 e}{5} & \\frac{6439 e}{6} & 478 e & 150 e & 35 e & 6 e & e & 0\\\\\\frac{502481 e}{60} & \\frac{390899 e}{60} & \\frac{12005 e}{4} & \\frac{2965 e}{3} & \\frac{495 e}{2} & 48 e & 7 e & e\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                                   ⎡   ℯ         0         0       0       0  \n",
       "                                   ⎢                                          \n",
       "                                   ⎢   ℯ         ℯ         0       0       0  \n",
       "                                   ⎢                                          \n",
       "                                   ⎢  3⋅ℯ       2⋅ℯ        ℯ       0       0  \n",
       "                                   ⎢                                          \n",
       "                                   ⎢  23⋅ℯ                                    \n",
       "                                   ⎢  ────      8⋅ℯ       3⋅ℯ      ℯ       0  \n",
       "                                   ⎢   2                                      \n",
       "                                   ⎢                                          \n",
       "                                   ⎢ 154⋅ℯ                                    \n",
       "                                   ⎢ ─────      37⋅ℯ     15⋅ℯ     4⋅ℯ      ℯ  \n",
       "(E_{ 8 }(\\mathcal{C}_{ 8 }))│    = ⎢   3                                      \n",
       "                            │α=1   ⎢                                          \n",
       "                                   ⎢ 1027⋅ℯ    572⋅ℯ     163⋅ℯ                \n",
       "                                   ⎢ ──────    ─────     ─────    24⋅ℯ    5⋅ℯ \n",
       "                                   ⎢   4         3         2                  \n",
       "                                   ⎢                                          \n",
       "                                   ⎢ 7046⋅ℯ    6439⋅ℯ                         \n",
       "                                   ⎢ ──────    ──────    478⋅ℯ   150⋅ℯ   35⋅ℯ \n",
       "                                   ⎢   5         6                            \n",
       "                                   ⎢                                          \n",
       "                                   ⎢502481⋅ℯ  390899⋅ℯ  12005⋅ℯ  2965⋅ℯ  495⋅ℯ\n",
       "                                   ⎢────────  ────────  ───────  ──────  ─────\n",
       "                                   ⎣   60        60        4       3       2  \n",
       "\n",
       "   0     0   0⎤\n",
       "              ⎥\n",
       "   0     0   0⎥\n",
       "              ⎥\n",
       "   0     0   0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "   0     0   0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "   0     0   0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "   ℯ     0   0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "  6⋅ℯ    ℯ   0⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "              ⎥\n",
       "  48⋅ℯ  7⋅ℯ  ℯ⎥\n",
       "              ⎦"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_exp1 = define(let=Subs(C_exp.lhs, alpha, 1), be=C_exp.rhs.subs({alpha:1}))\n",
    "C_exp1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nature(is_ordinary=False, is_exponential=False)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(C_exp.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nature(is_ordinary=False, is_exponential=False)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(C_exp1.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhUAAAAaBAMAAADyA7OxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ntcbA38FUzMtMJGaYAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\sigma{\\left (\\left. \\operatorname{E_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} \\right|_{\\substack{ \\alpha=1 }} \\right )} = \\left ( \\left \\{ 1 : \\left ( \\lambda_{1}, \\quad m_{1}\\right )\\right \\}, \\quad \\left \\{ \\lambda_{1} : e\\right \\}, \\quad \\left \\{ m_{1} : 8\\right \\}\\right )$$"
      ],
      "text/plain": [
       "\\sigma⎛(E_{ 8 }(\\mathcal{C}_{ 8 }))│   ⎞ = ({1: (\\lambda[1], m[1])}, {\\lambda[\n",
       "      ⎝                            │α=1⎠                                      \n",
       "\n",
       "1]: ℯ}, {m[1]: 8})\n",
       "                  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigendata_Cexpt = spectrum(C_exp1)\n",
    "eigendata_Cexpt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aPMY/+I1/5kYOnVDMq7+EPfFw6bB0YLM3rB7065VHJhythiFsno5gc039/1pR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\n",
      "text/latex": [
       "$$\\left \\{ \\left ( 1, \\quad 1\\right ) : \\Phi_{ 1, 1 }{\\left (z \\right )} = 1, \\quad \\left ( 1, \\quad 2\\right ) : \\Phi_{ 1, 2 }{\\left (z \\right )} = z - e, \\quad \\left ( 1, \\quad 3\\right ) : \\Phi_{ 1, 3 }{\\left (z \\right )} = \\frac{z^{2}}{2} - e z + \\frac{e^{2}}{2}, \\quad \\left ( 1, \\quad 4\\right ) : \\Phi_{ 1, 4 }{\\left (z \\right )} = \\frac{z^{3}}{6} - \\frac{e z^{2}}{2} + \\frac{z e^{2}}{2} - \\frac{e^{3}}{6}, \\quad \\left ( 1, \\quad 5\\right ) : \\Phi_{ 1, 5 }{\\left (z \\right )} = \\frac{z^{4}}{24} - \\frac{e z^{3}}{6} + \\frac{z^{2} e^{2}}{4} - \\frac{z e^{3}}{6} + \\frac{e^{4}}{24}, \\quad \\left ( 1, \\quad 6\\right ) : \\Phi_{ 1, 6 }{\\left (z \\right )} = \\frac{z^{5}}{120} - \\frac{e z^{4}}{24} + \\frac{z^{3} e^{2}}{12} - \\frac{z^{2} e^{3}}{12} + \\frac{z e^{4}}{24} - \\frac{e^{5}}{120}, \\quad \\left ( 1, \\quad 7\\right ) : \\Phi_{ 1, 7 }{\\left (z \\right )} = \\frac{z^{6}}{720} - \\frac{e z^{5}}{120} + \\frac{z^{4} e^{2}}{48} - \\frac{z^{3} e^{3}}{36} + \\frac{z^{2} e^{4}}{48} - \\frac{z e^{5}}{120} + \\frac{e^{6}}{720}, \\quad \\left ( 1, \\quad 8\\right ) : \\Phi_{ 1, 8 }{\\left (z \\right )} = \\frac{z^{7}}{5040} - \\frac{e z^{6}}{720} + \\frac{z^{5} e^{2}}{240} - \\frac{z^{4} e^{3}}{144} + \\frac{z^{3} e^{4}}{144} - \\frac{z^{2} e^{5}}{240} + \\frac{z e^{6}}{720} - \\frac{e^{7}}{5040}\\right \\}$$"
      ],
      "text/plain": [
       "⎧                                                                             \n",
       "⎪                                                                             \n",
       "⎨(1, 1): \\Phi_{ 1, 1 }(z) = 1, (1, 2): \\Phi_{ 1, 2 }(z) = z - ℯ, (1, 3): \\Phi_\n",
       "⎪                                                                             \n",
       "⎩                                                                             \n",
       "\n",
       "               2          2                              3      2      2    3 \n",
       "              z          ℯ                              z    ℯ⋅z    z⋅ℯ    ℯ  \n",
       "{ 1, 3 }(z) = ── - ℯ⋅z + ──, (1, 4): \\Phi_{ 1, 4 }(z) = ── - ──── + ──── - ──,\n",
       "              2          2                              6     2      2     6  \n",
       "                                                                              \n",
       "\n",
       "                             4      3    2  2      3    4                     \n",
       "                            z    ℯ⋅z    z ⋅ℯ    z⋅ℯ    ℯ                      \n",
       " (1, 5): \\Phi_{ 1, 5 }(z) = ── - ──── + ───── - ──── + ──, (1, 6): \\Phi_{ 1, 6\n",
       "                            24    6       4      6     24                     \n",
       "                                                                              \n",
       "\n",
       "          5      4    3  2    2  3      4     5                               \n",
       "         z    ℯ⋅z    z ⋅ℯ    z ⋅ℯ    z⋅ℯ     ℯ                               z\n",
       " }(z) = ─── - ──── + ───── - ───── + ──── - ───, (1, 7): \\Phi_{ 1, 7 }(z) = ──\n",
       "        120    24      12      12     24    120                             72\n",
       "                                                                              \n",
       "\n",
       "6      5    4  2    3  3    2  4      5     6                               7 \n",
       "    ℯ⋅z    z ⋅ℯ    z ⋅ℯ    z ⋅ℯ    z⋅ℯ     ℯ                               z  \n",
       "─ - ──── + ───── - ───── + ───── - ──── + ───, (1, 8): \\Phi_{ 1, 8 }(z) = ────\n",
       "0   120      48      36      48    120    720                             5040\n",
       "                                                                              \n",
       "\n",
       "      6    5  2    4  3    3  4    2  5      6     7 ⎫\n",
       "   ℯ⋅z    z ⋅ℯ    z ⋅ℯ    z ⋅ℯ    z ⋅ℯ    z⋅ℯ     ℯ  ⎪\n",
       " - ──── + ───── - ───── + ───── - ───── + ──── - ────⎬\n",
       "   720     240     144     144     240    720    5040⎪\n",
       "                                                     ⎭"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi_polynomials_Cexpt = component_polynomials(eigendata_Cexpt, early_eigenvals_subs=True)\n",
    "Phi_polynomials_Cexpt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `log` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "f_log, g_log, G_log = functions_catalog.log(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NNNg7qf95WyFypEK9LPV6T/fQAWsQiDdBKuSD/wECPA/xqOdzmE2tZBDKkgoPddeicRZg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\ndTXZwEkd3Mvl9Ww+K+XVOK36P0erRE02HquFAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\operatorname{L_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 2 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{3}{2} & 2 & 3 & 0 & 0 & 0 & 0 & 0\\\\\\frac{8}{3} & 3 & 3 & 4 & 0 & 0 & 0 & 0\\\\\\frac{31}{6} & \\frac{16}{3} & \\frac{9}{2} & 4 & 5 & 0 & 0 & 0\\\\\\frac{157}{15} & \\frac{31}{3} & 8 & 6 & 5 & 6 & 0 & 0\\\\\\frac{649}{30} & \\frac{314}{15} & \\frac{31}{2} & \\frac{32}{3} & \\frac{15}{2} & 6 & 7 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡ 0     0     0     0     0    0  0  0⎤\n",
       "                             ⎢                                     ⎥\n",
       "                             ⎢ 1     0     0     0     0    0  0  0⎥\n",
       "                             ⎢                                     ⎥\n",
       "                             ⎢ 1     2     0     0     0    0  0  0⎥\n",
       "                             ⎢                                     ⎥\n",
       "                             ⎢3/2    2     3     0     0    0  0  0⎥\n",
       "                             ⎢                                     ⎥\n",
       "                             ⎢8/3    3     3     4     0    0  0  0⎥\n",
       "L_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                                     ⎥\n",
       "                             ⎢31/6  16/3  9/2    4     5    0  0  0⎥\n",
       "                             ⎢                                     ⎥\n",
       "                             ⎢157                                  ⎥\n",
       "                             ⎢───   31/3   8     6     5    6  0  0⎥\n",
       "                             ⎢ 15                                  ⎥\n",
       "                             ⎢                                     ⎥\n",
       "                             ⎢649   314                            ⎥\n",
       "                             ⎢───   ───   31/2  32/3  15/2  6  7  0⎥\n",
       "                             ⎣ 30    15                            ⎦"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_log = G_log(C)\n",
    "C_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nature(is_ordinary=False, is_exponential=True)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(C_log.rhs[1:,:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 2 & 0 & 0 & 0 & 0\\\\\\frac{1}{4} & 0 & \\frac{3}{2} & 0 & 0 & 0\\\\\\frac{2}{9} & 0 & 0 & \\frac{4}{3} & 0 & 0\\\\\\frac{13}{48} & 0 & 0 & 0 & \\frac{5}{4} & 0\\\\\\frac{113}{300} & 0 & 0 & 0 & 0 & \\frac{6}{5}\\\\\\frac{1187}{2160} & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡ 1    2   0    0    0    0 ⎤\n",
       "⎢                           ⎥\n",
       "⎢1/4   0  3/2   0    0    0 ⎥\n",
       "⎢                           ⎥\n",
       "⎢2/9   0   0   4/3   0    0 ⎥\n",
       "⎢                           ⎥\n",
       "⎢ 13                        ⎥\n",
       "⎢ ──   0   0    0   5/4   0 ⎥\n",
       "⎢ 48                        ⎥\n",
       "⎢                           ⎥\n",
       "⎢113                        ⎥\n",
       "⎢───   0   0    0    0   6/5⎥\n",
       "⎢300                        ⎥\n",
       "⎢                           ⎥\n",
       "⎢1187                       ⎥\n",
       "⎢────  0   0    0    0    0 ⎥\n",
       "⎣2160                       ⎦"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "production_matrix(C_log.rhs[1:,:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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P9CMYFnW9uERatuhwqY1qs88vve4/2bOtA13fNQBhv6SD2ZmmeTdr7tmStSCfSskcf2I4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\nrkJggg==\n",
      "text/latex": [
       "$$\\operatorname{L_{ 8 }}{\\left (z \\right )} = \\frac{z^{7}}{7 \\lambda_{1}^{7}} + z^{6} \\left(- \\frac{1}{6 \\lambda_{1}^{6}} - \\frac{e}{\\lambda_{1}^{7}}\\right) + z^{5} \\left(\\frac{1}{5 \\lambda_{1}^{5}} + \\frac{e}{\\lambda_{1}^{6}} + \\frac{3 e^{2}}{\\lambda_{1}^{7}}\\right) + z^{4} \\left(- \\frac{1}{4 \\lambda_{1}^{4}} - \\frac{e}{\\lambda_{1}^{5}} - \\frac{5 e^{2}}{2 \\lambda_{1}^{6}} - \\frac{5 e^{3}}{\\lambda_{1}^{7}}\\right) + z^{3} \\left(\\frac{1}{3 \\lambda_{1}^{3}} + \\frac{e}{\\lambda_{1}^{4}} + \\frac{2 e^{2}}{\\lambda_{1}^{5}} + \\frac{10 e^{3}}{3 \\lambda_{1}^{6}} + \\frac{5 e^{4}}{\\lambda_{1}^{7}}\\right) + z^{2} \\left(- \\frac{1}{2 \\lambda_{1}^{2}} - \\frac{e}{\\lambda_{1}^{3}} - \\frac{3 e^{2}}{2 \\lambda_{1}^{4}} - \\frac{2 e^{3}}{\\lambda_{1}^{5}} - \\frac{5 e^{4}}{2 \\lambda_{1}^{6}} - \\frac{3 e^{5}}{\\lambda_{1}^{7}}\\right) + z \\left(\\frac{1}{\\lambda_{1}} + \\frac{e}{\\lambda_{1}^{2}} + \\frac{e^{2}}{\\lambda_{1}^{3}} + \\frac{e^{3}}{\\lambda_{1}^{4}} + \\frac{e^{4}}{\\lambda_{1}^{5}} + \\frac{e^{5}}{\\lambda_{1}^{6}} + \\frac{e^{6}}{\\lambda_{1}^{7}}\\right) + \\log{\\left (\\lambda_{1} \\right )} - \\frac{e}{\\lambda_{1}} - \\frac{e^{2}}{2 \\lambda_{1}^{2}} - \\frac{e^{3}}{3 \\lambda_{1}^{3}} - \\frac{e^{4}}{4 \\lambda_{1}^{4}} - \\frac{e^{5}}{5 \\lambda_{1}^{5}} - \\frac{e^{6}}{6 \\lambda_{1}^{6}} - \\frac{e^{7}}{7 \\lambda_{1}^{7}}$$"
      ],
      "text/plain": [
       "                    7                                                ⎛        \n",
       "                   z          6 ⎛        1              ℯ     ⎞    5 ⎜      1 \n",
       "L_{ 8 }(z) = ───────────── + z ⋅⎜- ───────────── - ───────────⎟ + z ⋅⎜────────\n",
       "                         7      ⎜              6             7⎟      ⎜        \n",
       "             7⋅\\lambda[1]       ⎝  6⋅\\lambda[1]    \\lambda[1] ⎠      ⎝5⋅\\lambd\n",
       "\n",
       "                             2   ⎞      ⎛                                     \n",
       "             ℯ            3⋅ℯ    ⎟    4 ⎜        1              ℯ             \n",
       "───── + ─────────── + ───────────⎟ + z ⋅⎜- ───────────── - ─────────── - ─────\n",
       "    5             6             7⎟      ⎜              4             5        \n",
       "a[1]    \\lambda[1]    \\lambda[1] ⎠      ⎝  4⋅\\lambda[1]    \\lambda[1]    2⋅\\la\n",
       "\n",
       "   2              3   ⎞      ⎛                                     2          \n",
       "5⋅ℯ            5⋅ℯ    ⎟    3 ⎜      1              ℯ            2⋅ℯ           \n",
       "──────── - ───────────⎟ + z ⋅⎜───────────── + ─────────── + ─────────── + ────\n",
       "       6             7⎟      ⎜            3             4             5       \n",
       "mbda[1]    \\lambda[1] ⎠      ⎝3⋅\\lambda[1]    \\lambda[1]    \\lambda[1]    3⋅\\l\n",
       "\n",
       "    3              4   ⎞      ⎛                                        2      \n",
       "10⋅ℯ            5⋅ℯ    ⎟    2 ⎜        1              ℯ             3⋅ℯ       \n",
       "───────── + ───────────⎟ + z ⋅⎜- ───────────── - ─────────── - ───────────── -\n",
       "        6             7⎟      ⎜              2             3               4  \n",
       "ambda[1]    \\lambda[1] ⎠      ⎝  2⋅\\lambda[1]    \\lambda[1]    2⋅\\lambda[1]   \n",
       "\n",
       "        3              4              5   ⎞     ⎛                             \n",
       "     2⋅ℯ            5⋅ℯ            3⋅ℯ    ⎟     ⎜    1             ℯ          \n",
       " ─────────── - ───────────── - ───────────⎟ + z⋅⎜────────── + ─────────── + ──\n",
       "           5               6             7⎟     ⎜\\lambda[1]             2     \n",
       " \\lambda[1]    2⋅\\lambda[1]    \\lambda[1] ⎠     ⎝             \\lambda[1]    \\l\n",
       "\n",
       "    2             3             4             5             6    ⎞            \n",
       "   ℯ             ℯ             ℯ             ℯ             ℯ     ⎟            \n",
       "───────── + ─────────── + ─────────── + ─────────── + ───────────⎟ + log(\\lamb\n",
       "        3             4             5             6             7⎟            \n",
       "ambda[1]    \\lambda[1]    \\lambda[1]    \\lambda[1]    \\lambda[1] ⎠            \n",
       "\n",
       "                             2               3               4               5\n",
       "             ℯ              ℯ               ℯ               ℯ               ℯ \n",
       "da[1]) - ────────── - ───────────── - ───────────── - ───────────── - ────────\n",
       "         \\lambda[1]               2               3               4           \n",
       "                      2⋅\\lambda[1]    3⋅\\lambda[1]    4⋅\\lambda[1]    5⋅\\lambd\n",
       "\n",
       "               6               7     \n",
       "              ℯ               ℯ      \n",
       "───── - ───────────── - ─────────────\n",
       "    5               6               7\n",
       "a[1]    6⋅\\lambda[1]    7⋅\\lambda[1] "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_log_Cexpt = Hermite_interpolation_polynomial(f_log, eigendata_Cexpt, Phi_polynomials_Cexpt)\n",
    "g_log_Cexpt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAAwBAMAAADqYs28AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\operatorname{L_{ 8 }}{\\left (z \\right )} = \\frac{z^{7}}{7 e^{7}} - \\frac{7 z^{6}}{6 e^{6}} + \\frac{21 z^{5}}{5 e^{5}} - \\frac{35 z^{4}}{4 e^{4}} + \\frac{35 z^{3}}{3 e^{3}} - \\frac{21 z^{2}}{2 e^{2}} + \\frac{7 z}{e} - \\frac{223}{140}$$"
      ],
      "text/plain": [
       "              7  -7      6  -6       5  -5       4  -4       3  -3       2  -2\n",
       "             z ⋅ℯ     7⋅z ⋅ℯ     21⋅z ⋅ℯ     35⋅z ⋅ℯ     35⋅z ⋅ℯ     21⋅z ⋅ℯ  \n",
       "L_{ 8 }(z) = ────── - ──────── + ───────── - ───────── + ───────── - ─────────\n",
       "               7         6           5           4           3           2    \n",
       "\n",
       "                \n",
       "        -1   223\n",
       " + 7⋅z⋅ℯ   - ───\n",
       "             140"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_log_Cexpt = g_log_Cexpt.subs(eigendata_Cexpt.rhs[1])\n",
    "g_log_Cexpt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/latex": [
       "$$\\operatorname{L_{ 8 }}{\\left (\\left. \\operatorname{E_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} \\right|_{\\substack{ \\alpha=1 }} \\right )} = \\left[\\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\2 & 2 & 1 & 0 & 0 & 0 & 0 & 0\\\\5 & 5 & 3 & 1 & 0 & 0 & 0 & 0\\\\14 & 14 & 9 & 4 & 1 & 0 & 0 & 0\\\\42 & 42 & 28 & 14 & 5 & 1 & 0 & 0\\\\132 & 132 & 90 & 48 & 20 & 6 & 1 & 0\\\\429 & 429 & 297 & 165 & 75 & 27 & 7 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                                            ⎡ 1    0    0    0   0   0   0  0⎤\n",
       "                                            ⎢                                ⎥\n",
       "                                            ⎢ 1    1    0    0   0   0   0  0⎥\n",
       "                                            ⎢                                ⎥\n",
       "                                            ⎢ 2    2    1    0   0   0   0  0⎥\n",
       "                                            ⎢                                ⎥\n",
       "                                            ⎢ 5    5    3    1   0   0   0  0⎥\n",
       "L_{ 8 }⎛(E_{ 8 }(\\mathcal{C}_{ 8 }))│   ⎞ = ⎢                                ⎥\n",
       "       ⎝                            │α=1⎠   ⎢14   14    9    4   1   0   0  0⎥\n",
       "                                            ⎢                                ⎥\n",
       "                                            ⎢42   42   28   14   5   1   0  0⎥\n",
       "                                            ⎢                                ⎥\n",
       "                                            ⎢132  132  90   48   20  6   1  0⎥\n",
       "                                            ⎢                                ⎥\n",
       "                                            ⎣429  429  297  165  75  27  7  1⎦"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with lift_to_matrix_function(g_log_Cexpt) as G_log_Cexpt:\n",
    "    CC = G_log_Cexpt(C_exp1)\n",
    "CC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `sin` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "f_sin, g_sin, G_sin = functions_catalog.sin(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dKgjVaAbLtJNPeNq2Nb5rz4G5a8GjDJLgs5YfLHtDK2QwbCD5FNW8dbqEl84a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\n6oA/dNJg7QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\operatorname{S_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}\\sin{\\left (1 \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )} & 0 & 0 & 0 & 0 & 0 & 0\\\\- \\sin{\\left (1 \\right )} + 2 \\cos{\\left (1 \\right )} & 2 \\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )} & 0 & 0 & 0 & 0 & 0\\\\- \\frac{11}{2} \\sin{\\left (1 \\right )} + 4 \\cos{\\left (1 \\right )} & - 3 \\sin{\\left (1 \\right )} + 5 \\cos{\\left (1 \\right )} & 3 \\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )} & 0 & 0 & 0 & 0\\\\- 25 \\sin{\\left (1 \\right )} + \\frac{11}{3} \\cos{\\left (1 \\right )} & - 19 \\sin{\\left (1 \\right )} + 10 \\cos{\\left (1 \\right )} & - 6 \\sin{\\left (1 \\right )} + 9 \\cos{\\left (1 \\right )} & 4 \\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )} & 0 & 0 & 0\\\\- \\frac{1231}{12} \\sin{\\left (1 \\right )} - \\frac{106}{3} \\cos{\\left (1 \\right )} & - 93 \\sin{\\left (1 \\right )} - \\frac{11}{3} \\cos{\\left (1 \\right )} & - \\frac{87}{2} \\sin{\\left (1 \\right )} + 18 \\cos{\\left (1 \\right )} & - 10 \\sin{\\left (1 \\right )} + 14 \\cos{\\left (1 \\right )} & 5 \\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )} & 0 & 0\\\\- \\frac{2171}{6} \\sin{\\left (1 \\right )} - \\frac{11209}{30} \\cos{\\left (1 \\right )} & - \\frac{775}{2} \\sin{\\left (1 \\right )} - \\frac{698}{3} \\cos{\\left (1 \\right )} & - 231 \\sin{\\left (1 \\right )} - 37 \\cos{\\left (1 \\right )} & - 82 \\sin{\\left (1 \\right )} + 28 \\cos{\\left (1 \\right )} & - 15 \\sin{\\left (1 \\right )} + 20 \\cos{\\left (1 \\right )} & 6 \\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )} & 0\\\\- \\frac{156113}{60} \\cos{\\left (1 \\right )} - \\frac{12301}{15} \\sin{\\left (1 \\right )} & - \\frac{61583}{30} \\cos{\\left (1 \\right )} - \\frac{14863}{12} \\sin{\\left (1 \\right )} & - \\frac{3953}{4} \\sin{\\left (1 \\right )} - \\frac{1595}{2} \\cos{\\left (1 \\right )} & - 472 \\sin{\\left (1 \\right )} - \\frac{349}{3} \\cos{\\left (1 \\right )} & - \\frac{275}{2} \\sin{\\left (1 \\right )} + 40 \\cos{\\left (1 \\right )} & - 21 \\sin{\\left (1 \\right )} + 27 \\cos{\\left (1 \\right )} & 7 \\cos{\\left (1 \\right )} & \\sin{\\left (1 \\right )}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡            sin(1)                            0 \n",
       "                             ⎢                                                \n",
       "                             ⎢            cos(1)                         sin(1\n",
       "                             ⎢                                                \n",
       "                             ⎢      -sin(1) + 2⋅cos(1)                  2⋅cos(\n",
       "                             ⎢                                                \n",
       "                             ⎢      11⋅sin(1)                                 \n",
       "                             ⎢    - ───────── + 4⋅cos(1)          -3⋅sin(1) + \n",
       "                             ⎢          2                                     \n",
       "                             ⎢                                                \n",
       "                             ⎢                 11⋅cos(1)                      \n",
       "                             ⎢    -25⋅sin(1) + ─────────         -19⋅sin(1) + \n",
       "S_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                     3                          \n",
       "                             ⎢                                                \n",
       "                             ⎢    1231⋅sin(1)   106⋅cos(1)                    \n",
       "                             ⎢  - ─────────── - ──────────       -93⋅sin(1) - \n",
       "                             ⎢         12           3                         \n",
       "                             ⎢                                                \n",
       "                             ⎢   2171⋅sin(1)   11209⋅cos(1)       775⋅sin(1)  \n",
       "                             ⎢ - ─────────── - ────────────     - ────────── -\n",
       "                             ⎢        6             30                2       \n",
       "                             ⎢                                                \n",
       "                             ⎢  156113⋅cos(1)   12301⋅sin(1)    61583⋅cos(1)  \n",
       "                             ⎢- ───────────── - ────────────  - ──────────── -\n",
       "                             ⎣        60             15              30       \n",
       "\n",
       "                            0                          0                      \n",
       "                                                                              \n",
       ")                           0                          0                      \n",
       "                                                                              \n",
       "1)                       sin(1)                        0                      \n",
       "                                                                              \n",
       "                                                                              \n",
       "5⋅cos(1)                3⋅cos(1)                     sin(1)                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "10⋅cos(1)         -6⋅sin(1) + 9⋅cos(1)              4⋅cos(1)                  \n",
       "                                                                              \n",
       "                                                                              \n",
       "11⋅cos(1)          87⋅sin(1)                                                  \n",
       "─────────        - ───────── + 18⋅cos(1)     -10⋅sin(1) + 14⋅cos(1)           \n",
       "    3                  2                                                      \n",
       "                                                                              \n",
       " 698⋅cos(1)                                                                   \n",
       " ──────────      -231⋅sin(1) - 37⋅cos(1)     -82⋅sin(1) + 28⋅cos(1)    -15⋅sin\n",
       "     3                                                                        \n",
       "                                                                              \n",
       " 14863⋅sin(1)    3953⋅sin(1)   1595⋅cos(1)                349⋅cos(1)    275⋅si\n",
       " ────────────  - ─────────── - ───────────  -472⋅sin(1) - ──────────  - ──────\n",
       "      12              4             2                         3             2 \n",
       "\n",
       "   0                        0                0        0   ⎤\n",
       "                                                          ⎥\n",
       "   0                        0                0        0   ⎥\n",
       "                                                          ⎥\n",
       "   0                        0                0        0   ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "   0                        0                0        0   ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       " sin(1)                     0                0        0   ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "5⋅cos(1)                  sin(1)             0        0   ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "(1) + 20⋅cos(1)          6⋅cos(1)          sin(1)     0   ⎥\n",
       "                                                          ⎥\n",
       "                                                          ⎥\n",
       "n(1)                                                      ⎥\n",
       "──── + 40⋅cos(1)  -21⋅sin(1) + 27⋅cos(1)  7⋅cos(1)  sin(1)⎥\n",
       "                                                          ⎦"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_sin = G_sin(C)    \n",
    "C_sin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "inspect(C_sin.rhs) # takes long to evaluate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## `cos` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "f_cos, g_cos, G_cos = functions_catalog.cos(eigendata, Phi_polynomials)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lure4jFt+lUMHBfzZmBWjyqcbcDSvrXHk5uMCWYWjbPufFFgTViZQDLaq0UDo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\ntS2807MJgYRAQiAhkBAYI5BLy5T9f01AQ3CyxKCwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\operatorname{C_{ 8 }}{\\left (\\mathcal{C}_{ 8 } \\right )} = \\left[\\begin{matrix}\\cos{\\left (1 \\right )} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\- \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )} & 0 & 0 & 0 & 0 & 0 & 0\\\\- 2 \\sin{\\left (1 \\right )} - \\cos{\\left (1 \\right )} & - 2 \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )} & 0 & 0 & 0 & 0 & 0\\\\- 4 \\sin{\\left (1 \\right )} - \\frac{11}{2} \\cos{\\left (1 \\right )} & - 5 \\sin{\\left (1 \\right )} - 3 \\cos{\\left (1 \\right )} & - 3 \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )} & 0 & 0 & 0 & 0\\\\- 25 \\cos{\\left (1 \\right )} - \\frac{11}{3} \\sin{\\left (1 \\right )} & - 19 \\cos{\\left (1 \\right )} - 10 \\sin{\\left (1 \\right )} & - 9 \\sin{\\left (1 \\right )} - 6 \\cos{\\left (1 \\right )} & - 4 \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )} & 0 & 0 & 0\\\\- \\frac{1231}{12} \\cos{\\left (1 \\right )} + \\frac{106}{3} \\sin{\\left (1 \\right )} & - 93 \\cos{\\left (1 \\right )} + \\frac{11}{3} \\sin{\\left (1 \\right )} & - \\frac{87}{2} \\cos{\\left (1 \\right )} - 18 \\sin{\\left (1 \\right )} & - 14 \\sin{\\left (1 \\right )} - 10 \\cos{\\left (1 \\right )} & - 5 \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )} & 0 & 0\\\\- \\frac{2171}{6} \\cos{\\left (1 \\right )} + \\frac{11209}{30} \\sin{\\left (1 \\right )} & - \\frac{775}{2} \\cos{\\left (1 \\right )} + \\frac{698}{3} \\sin{\\left (1 \\right )} & - 231 \\cos{\\left (1 \\right )} + 37 \\sin{\\left (1 \\right )} & - 82 \\cos{\\left (1 \\right )} - 28 \\sin{\\left (1 \\right )} & - 20 \\sin{\\left (1 \\right )} - 15 \\cos{\\left (1 \\right )} & - 6 \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )} & 0\\\\- \\frac{12301}{15} \\cos{\\left (1 \\right )} + \\frac{156113}{60} \\sin{\\left (1 \\right )} & - \\frac{14863}{12} \\cos{\\left (1 \\right )} + \\frac{61583}{30} \\sin{\\left (1 \\right )} & - \\frac{3953}{4} \\cos{\\left (1 \\right )} + \\frac{1595}{2} \\sin{\\left (1 \\right )} & - 472 \\cos{\\left (1 \\right )} + \\frac{349}{3} \\sin{\\left (1 \\right )} & - \\frac{275}{2} \\cos{\\left (1 \\right )} - 40 \\sin{\\left (1 \\right )} & - 27 \\sin{\\left (1 \\right )} - 21 \\cos{\\left (1 \\right )} & - 7 \\sin{\\left (1 \\right )} & \\cos{\\left (1 \\right )}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "                             ⎡            cos(1)                            0 \n",
       "                             ⎢                                                \n",
       "                             ⎢           -sin(1)                         cos(1\n",
       "                             ⎢                                                \n",
       "                             ⎢      -2⋅sin(1) - cos(1)                  -2⋅sin\n",
       "                             ⎢                                                \n",
       "                             ⎢                11⋅cos(1)                       \n",
       "                             ⎢    -4⋅sin(1) - ─────────           -5⋅sin(1) - \n",
       "                             ⎢                    2                           \n",
       "                             ⎢                                                \n",
       "                             ⎢                 11⋅sin(1)                      \n",
       "                             ⎢    -25⋅cos(1) - ─────────         -19⋅cos(1) - \n",
       "C_{ 8 }(\\mathcal{C}_{ 8 }) = ⎢                     3                          \n",
       "                             ⎢                                                \n",
       "                             ⎢    1231⋅cos(1)   106⋅sin(1)                    \n",
       "                             ⎢  - ─────────── + ──────────       -93⋅cos(1) + \n",
       "                             ⎢         12           3                         \n",
       "                             ⎢                                                \n",
       "                             ⎢   2171⋅cos(1)   11209⋅sin(1)       775⋅cos(1)  \n",
       "                             ⎢ - ─────────── + ────────────     - ────────── +\n",
       "                             ⎢        6             30                2       \n",
       "                             ⎢                                                \n",
       "                             ⎢  12301⋅cos(1)   156113⋅sin(1)    14863⋅cos(1)  \n",
       "                             ⎢- ──────────── + ─────────────  - ──────────── +\n",
       "                             ⎣       15              60              12       \n",
       "\n",
       "                            0                          0                      \n",
       "                                                                              \n",
       ")                           0                          0                      \n",
       "                                                                              \n",
       "(1)                      cos(1)                        0                      \n",
       "                                                                              \n",
       "                                                                              \n",
       "3⋅cos(1)                -3⋅sin(1)                    cos(1)                   \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "10⋅sin(1)         -9⋅sin(1) - 6⋅cos(1)             -4⋅sin(1)                  \n",
       "                                                                              \n",
       "                                                                              \n",
       "11⋅sin(1)          87⋅cos(1)                                                  \n",
       "─────────        - ───────── - 18⋅sin(1)     -14⋅sin(1) - 10⋅cos(1)          -\n",
       "    3                  2                                                      \n",
       "                                                                              \n",
       " 698⋅sin(1)                                                                   \n",
       " ──────────      -231⋅cos(1) + 37⋅sin(1)     -82⋅cos(1) - 28⋅sin(1)    -20⋅sin\n",
       "     3                                                                        \n",
       "                                                                              \n",
       " 61583⋅sin(1)    3953⋅cos(1)   1595⋅sin(1)                349⋅sin(1)    275⋅co\n",
       " ────────────  - ─────────── + ───────────  -472⋅cos(1) + ──────────  - ──────\n",
       "      30              4             2                         3             2 \n",
       "\n",
       "   0                        0                 0        0   ⎤\n",
       "                                                           ⎥\n",
       "   0                        0                 0        0   ⎥\n",
       "                                                           ⎥\n",
       "   0                        0                 0        0   ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "   0                        0                 0        0   ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       " cos(1)                     0                 0        0   ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "5⋅sin(1)                  cos(1)              0        0   ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "(1) - 15⋅cos(1)         -6⋅sin(1)          cos(1)      0   ⎥\n",
       "                                                           ⎥\n",
       "                                                           ⎥\n",
       "s(1)                                                       ⎥\n",
       "──── - 40⋅sin(1)  -27⋅sin(1) - 21⋅cos(1)  -7⋅sin(1)  cos(1)⎥\n",
       "                                                           ⎦"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_cos = G_cos(C)    \n",
    "C_cos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "inspect(C_sin.rhs) # takes long to evaluate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "assert (C_sin.rhs**2 + C_cos.rhs**2).applyfunc(trigsimp) == Matrix(m,m, identity_matrix())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "---\n",
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>."
   ]
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