{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "46be1ee8-65c3-46fc-b045-33f4de5f7f61",
   "metadata": {},
   "outputs": [],
   "source": [
    "n=6\n",
    "g=(n-1)*(n-2)/2;\n",
    "K=CyclotomicField(2*n)\n",
    "z=K.gen()\n",
    "zn=z^2\n",
    "PP.<T>=PolynomialRing(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "56307de0-af9e-45f7-b49e-2143f0c8e41c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def IMod(a,b):\n",
    "    ypol=a-b*floor(a/b)\n",
    "    return ypol\n",
    "def rat(x):\n",
    "    return numerator(x)/denominator(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "3e0f8e33-a387-4161-bd0a-d2656c740f10",
   "metadata": {},
   "outputs": [],
   "source": [
    "def polynom(V,Q,ka,la,nu,rho):\n",
    "    if not(3.divides(n)) and nu > 0:\n",
    "        print(\"3 does not divide\",n, \" and nu=\",nu)\n",
    "        return \"ERROR\"\n",
    "        print(\"XXXXXXXXXX\",V,Q,ka,la,nu,rho)\n",
    "    if Q == 0:\n",
    "        ex=IMod( nu*n/3,n)            \n",
    "        if V == 1:\n",
    "            if rho == \"triv\" and nu==0: \n",
    "                poly=1\n",
    "            if rho == \"sgn\"  and nu==0:\n",
    "                poly=T^n\n",
    "            if rho == \"triv\" and nu==1: \n",
    "                poly= T^(4*n/3)\n",
    "            if rho == \"sgn\"  and nu==1:\n",
    "                poly=T^(n/3)\n",
    "            if rho == \"triv\" and nu==2: \n",
    "                poly= T^(2*n/3)\n",
    "            if rho == \"sgn\"  and nu==2:\n",
    "                poly=T^(5*n/3)\n",
    "            # print(\"--\",poly)\n",
    "            return poly                                          \n",
    "            \n",
    "        if V == 2:\n",
    "            poly=T^(nu*n/3)+T^(n+nu*n/3)\n",
    "            # print(poly)\n",
    "            return poly\n",
    "                                 \n",
    "            \n",
    "        if V == 3:\n",
    "            if rho == \"triv\":\n",
    "                poly=T^ka+T^(n+ka)+T^(IMod(-2*ka,2*n))\n",
    "            if rho == \"sgn\":\n",
    "                # if ka <=floor(n/2):\n",
    "                #     poly=T^ka+T^(n+ka)+T^(n-2*ka)\n",
    "                # if ka >=ceil(n/2):\n",
    "                #     poly=T^ka+T^(n+ka)+T^(3*n-2*k)\n",
    "                poly=T^ka+T^(ka+n)+T^(IMod(-2*ka+n,2*n))\n",
    "            return poly\n",
    "            \n",
    "        if V == 6:\n",
    "            ee=IMod(-(ka+la),n)\n",
    "            poly=T^ka+T^la+T^(n+ka)+T^(n+la)+T^ee+T^(ee+n)\n",
    "            # if ka+la <=floor(n/2):\n",
    "            #     poly=T^ka+T^la+T^(n+ka)+T^(n+la)+T^(2*n-(ka+la))+T^(n-(ka+la))\n",
    "            # if ka+la >=ceil(n/2):\n",
    "            #     poly=T^ka+T^la+T^(n+ka)+T^(n+la)+T^(2*n-(ka+la))+T^(3*n-(ka+la))\n",
    "            return poly\n",
    "        \n",
    "    if Q == 1:\n",
    "        if V == 1 and rho == \"sgn\":\n",
    "            poly=T\n",
    "            return poly\n",
    "        if V == 1 and rho == \"triv\":\n",
    "            poly=1\n",
    "            return poly\n",
    "            \n",
    "        if V == 2:\n",
    "            poly=1+T\n",
    "            return poly\n",
    "            \n",
    "        if V == 3 and rho == \"sgn\":\n",
    "            poly=1+2*T\n",
    "            return poly\n",
    "        if V == 3 and rho == \"triv\":\n",
    "            poly=2+T\n",
    "            return poly\n",
    "        \n",
    "        if V == 6:\n",
    "            poly=3+3*T\n",
    "        \n",
    "    if Q == 2:\n",
    "            \n",
    "            pp=T^IMod(nu,3)\n",
    "            \n",
    "            if V == 1:\n",
    "                poly=pp\n",
    "                # poly=T^3\n",
    "\n",
    "            if V == 2:\n",
    "                poly=1+T+T^2 -pp\n",
    "\n",
    "            if V == 3:\n",
    "                poly=1+T+T^2\n",
    "                # poly=T^3+T+T^2\n",
    "\n",
    "            if V == 6:\n",
    "                poly=2*(1+T+T^2)\n",
    "                # poly=2*(T^3+T+T^2)\n",
    "    \n",
    "        \n",
    "    return poly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "c4757fb9-4da2-44f6-8b82-0f485612c314",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Hgen(V,ka,la,nu,rho):\n",
    "    pol0=polynom(V,0,ka,la,nu,rho)\n",
    "    pol1=polynom(V,1,ka,la,nu,rho)\n",
    "    pol2=polynom(V,2,ka,la,nu,rho)\n",
    "    # print(\"V=\",V,\"ka=\",ka,\"la=\",la,\"nu=\",nu,\"rho=\",rho)\n",
    "    # print(\"   pol0=\",pol0)\n",
    "    # print(\"   pol1=\",pol1)\n",
    "    # print(\"   pol2=\",pol2)\n",
    "    Dpol0=derivative(pol0,T)\n",
    "    Dpol1=derivative(pol1,T)\n",
    "    Dpol2=derivative(pol2,T)\n",
    "\n",
    "    sumD=Dpol0(T=1)/(2*n) + Dpol1(T=1)/2 +  Dpol2(T=1)/3\n",
    "    # print(\"            sumD=\",sumD)\n",
    "\n",
    "    sum1=pol0/(1-T^(2*n))+pol1/(1-T^2)+pol2/(1-T^3)\n",
    "\n",
    "    # print(sum)\n",
    "    H=V/(1-T)^2 -sumD/(1-T)-T*sum1/(1-T)\n",
    "    H=numerator(H)/denominator(H)\n",
    "    return H\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "15c31048-e2c4-426f-b483-01c8b780cec5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Costructing the indices of a basis of holomorphic 1-differentials\n",
    "L=[]  \n",
    "for i in range(n-3+1):\n",
    "    for j in range(n-3-i+1):\n",
    "        L.append([i,j])\n",
    "Ls=[]\n",
    "for el in L:\n",
    "    Ls.append([n-3-el[0]-el[1],el[0]])\n",
    "# create the matrix for the action on s\n",
    "M=matrix(g)\n",
    "for j in range(g):\n",
    "    for i in range(g):\n",
    "        if L[j] == Ls[i]:\n",
    "            # print(i,j)\n",
    "            M[i,j]=1\n",
    "Lts=[]\n",
    "for el in L:\n",
    "    Lts.append([el[1],el[0]])\n",
    "N=matrix(g)\n",
    "for j in range(g):\n",
    "    for i in range(g):\n",
    "        if L[j] == Lts[i]:\n",
    "            # print(i,j)\n",
    "            N[i,j]=1\n",
    "\n",
    "M=M.transpose()\n",
    "N=N.transpose()\n",
    "#-----acting on bases so need to take transpose, it makes a difference on multiplication \n",
    "\n",
    "# S3=[[M,\"s\"],[M^2,\"s^2\"],[M^3,\"id\"],[N,\"ts\"],[M*N,\"st\"],[N*M,\"t\"]]\n",
    "\n",
    "# S3=[[M,\"s\"],[M^2,\"s^2\"],[M^3,\"id\"],[N,\"ts\"],[M*N,\"st\"],[N*M,\"t\"]]\n",
    "# S3=[[M,\"s^2\"],[M^2,\"s\"],[M^3,\"id\"],[N,\"ts\"],[M*N,\"st\"],[N*M,\"t\"]]\n",
    "S3=[[M,\"s\"],[M^2,\"s^2\"],[M^3,\"id\"],[N,\"ts\"],[M*N,\"t\"],[N*M,\"st\"]] # <---\n",
    "\n",
    "\n",
    "Dlist=[]\n",
    "for k in range(n):\n",
    "    for l in range(n):\n",
    "        C=matrix(K,g)\n",
    "        for i in range(g):\n",
    "            el=L[i]\n",
    "            C[i,i]=zn^(k*(el[0]+1)+l*(el[1]+1))\n",
    "        C=C.transpose()\n",
    "        Dlist.append([k,l,C])\n",
    "        # print(C)\n",
    "\n",
    "        \n",
    "G=[]\n",
    "for i in Dlist:\n",
    "    for s in S3:\n",
    "        # print(i[2]*s)\n",
    "        # print(\"------------\")\n",
    "        G.append([s[0]*i[2],i[0],i[1],s[1]])\n",
    "        # In first position is the matrix, then k,l,string determining the element of S_3\n",
    "\n",
    "def chara(gg,V,ka,la,nu,rho):\n",
    "    if rho==\"triv\":\n",
    "        if V==1:\n",
    "            ch=zn^(nu*n/3*(gg[1]+gg[2]))\n",
    "            return ch\n",
    "        if V==3:\n",
    "            if gg[3]==\"id\":\n",
    "                ch=zn^(ka*(gg[1]+gg[2]))+zn^(ka*(gg[1]-2*gg[2]))+zn^(ka*(gg[2]-2*gg[1]))\n",
    "                return ch\n",
    "            if gg[3]==\"ts\":\n",
    "                ch=zn^(ka*(gg[1]+gg[2]))\n",
    "                return ch\n",
    "            if gg[3]==\"st\":\n",
    "                ch=zn^(ka*(gg[2]-2*gg[1]))\n",
    "                return ch\n",
    "            if gg[3]==\"t\":\n",
    "                ch=zn^(ka*(gg[1]-2*gg[2]))\n",
    "                return ch       \n",
    "            if gg[3]==\"s\" or gg[3]==\"s^2\":\n",
    "                ch=0\n",
    "                return ch\n",
    "        if V==6:\n",
    "            if gg[3]==\"id\":\n",
    "                ch=zn^(ka*gg[1]+la*gg[2])+zn^(-(ka+la)*gg[1]+ka*gg[2])+zn^(la*gg[1]-(ka+la)*gg[2])+zn^(la*gg[1]+ka*gg[2])+zn^(-(ka+la)*gg[1]+la*gg[2])+zn^(ka*gg[1]-(ka+la)*gg[2])\n",
    "                return ch\n",
    "            else:\n",
    "                return 0\n",
    "    if rho==\"sgn\":\n",
    "        if V==1:\n",
    "            # print(\"gg[3]=\",gg[3])\n",
    "            if gg[3]==\"id\" or gg[3]==\"s\" or gg[3]==\"s^2\":\n",
    "                ch=zn^(nu*n/3*(gg[1]+gg[2]))\n",
    "            if gg[3]==\"t\" or gg[3]==\"ts\" or gg[3]==\"st\":\n",
    "                ch=-zn^(nu*n/3*(gg[1]+gg[2]))\n",
    "            return ch\n",
    "        if V==3:\n",
    "            if gg[3]==\"id\":\n",
    "                ch=zn^(ka*(gg[1]+gg[2]))+zn^(ka*(gg[1]-2*gg[2]))+zn^(ka*(gg[2]-2*gg[1]))\n",
    "                return ch\n",
    "            if gg[3]==\"ts\":\n",
    "                ch=-zn^(ka*(gg[1]+gg[2]))\n",
    "                return ch\n",
    "            if gg[3]==\"st\":\n",
    "                ch=-zn^(ka*(gg[2]-2*gg[1]))\n",
    "                return ch\n",
    "            if gg[3]==\"t\":\n",
    "                ch=-zn^(ka*(gg[1]-2*gg[2]))\n",
    "                return ch       \n",
    "            if gg[3]==\"s\" or gg[3]==\"s^2\":\n",
    "                ch=0\n",
    "                return ch\n",
    "    if rho==\"stan\":\n",
    "        if gg[3]==\"id\":\n",
    "                cc=2\n",
    "        if gg[3]==\"ts\":\n",
    "                cc=0\n",
    "        if gg[3]==\"t\":\n",
    "                cc=0\n",
    "        if gg[3]==\"st\":\n",
    "                cc=0      \n",
    "        if gg[3]==\"s\" or gg[3]==\"s^2\":\n",
    "                cc=-1\n",
    "        ch=zn^(nu*n/3*(gg[1]+gg[2]))*cc\n",
    "        return ch\n",
    "\n",
    "def MolienF(V,ka,la,nu,rho):\n",
    "    sum=0\n",
    "    I=matrix.identity(K,g)\n",
    "    for gg in G:\n",
    "        de=(I-T*gg[0]).determinant()\n",
    "        sum=sum+chara(gg,V,ka,la,nu,rho).conjugate()/de\n",
    "        # sum=sum+chara(gg,V,ka,la,nu,rho)/de\n",
    "        # detList.append(de)\n",
    "    F=1/(6*n^2)*sum\n",
    "    # print(F)\n",
    "    # print(\"-------\")\n",
    "    # print(SR(F).series(T))\n",
    "    return [F,SR(F).series(T)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "3494925f-a315-4701-bbfe-1761b21f066f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reverse(nu,rho):\n",
    "    if nu !=0 or V==3:\n",
    "        if rho== \"triv\":\n",
    "            rr=\"sgn\"\n",
    "        if rho== \"sgn\":\n",
    "            rr=\"triv\"\n",
    "        if rho == \"stan\":\n",
    "            rr=\"stan\"\n",
    "    else:\n",
    "        rr=rho\n",
    "    return rr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "66989088-4c03-4c28-ba0c-92d0f8695015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V= 1 ka= 0 la= 0 nu= 0 rho= triv\n",
      " HH=   (T^8 - T^7 + T^6 + T^2 - 2*T + 1)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^14 - T^13 + T^8 - T^7 + T^6 - T + 1)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 1 ka= 0 la= 0 nu= 1 rho= triv\n",
      " HH=   (T^12 - T^11 + T^10 - T^9 + T^6 - T^5 + T^4)/((T^12 - 1)*(T - 1))\n",
      "MMdual= 0\n",
      "HHc= (T^12 - T^11 + T^10 - T^9 + T^6 - T^5 + T^4)/((T^12 - 1)*(T - 1))\n",
      "---------------------------------------------------------------------------\n",
      "V= 1 ka= 0 la= 0 nu= 2 rho= triv\n",
      " HH=   (T^10 - T^9 + T^8 - T^5 + T^4 - T^3 + T^2)/((T^12 - 1)*(T - 1))\n",
      "MMdual= 0\n",
      "HHc= (T^10 - T^9 + T^8 - T^5 + T^4 - T^3 + T^2)/((T^12 - 1)*(T - 1))\n",
      "---------------------------------------------------------------------------\n",
      "V= 1 ka= 0 la= 0 nu= 0 rho= sgn\n",
      " HH=   (T^11 - T^10 + T^9 - T^7 + T^5 - T^4 + T^3)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^11 - T^10 + T^9 - T^7 + T^5 - T^4 + T^3)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 1 ka= 0 la= 0 nu= 1 rho= sgn\n",
      " HH=   (T^9 - T^8 + T^7 - T^2 + T)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^9 - T^8 + T^7 - T^2 + T)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 1 ka= 0 la= 0 nu= 2 rho= sgn\n",
      " HH=   (T^7 - T^6 + T^5 + T - 1)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 1\n",
      "HHc= (T^13 - T^12 + T^7 - T^6 + T^5)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 2 ka= 0 la= 0 nu= 0 rho= stan\n",
      " HH=   T^4/(T^7 - T^6 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= T^4/(T^7 - T^6 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 2 ka= 0 la= 0 nu= 1 rho= stan\n",
      " HH=   (T^5 - T^3 + T^2)/(T^7 - T^6 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^5 - T^3 + T^2)/(T^7 - T^6 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 2 ka= 0 la= 0 nu= 2 rho= stan\n",
      " HH=   (T^6 - T^5 + T^3)/(T^7 - T^6 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^6 - T^5 + T^3)/(T^7 - T^6 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 3 ka= 3 la= 3 nu= 0 rho= triv\n",
      " HH=   (T^12 + T^8 - T^7 + T^6 + T^2)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^12 + T^8 - T^7 + T^6 + T^2)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 3 ka= 1 la= 1 nu= 0 rho= triv\n",
      " HH=   (T^12 - T^11 + T^10 + T^6 + T^4)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^12 - T^11 + T^10 + T^6 + T^4)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 3 ka= 5 la= 5 nu= 0 rho= triv\n",
      " HH=   (T^10 + T^8 + T^4 - T^3 + T^2)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^10 + T^8 + T^4 - T^3 + T^2)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 3 ka= 3 la= 3 nu= 0 rho= sgn\n",
      " HH=   (T^11 - T^10 + T^9 + T^7 + T^5 - T^4 + T^3)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^11 - T^10 + T^9 + T^7 + T^5 - T^4 + T^3)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 3 ka= 1 la= 1 nu= 0 rho= sgn\n",
      " HH=   (T^11 + T^9 - T^8 + T^7 + T^3 - T^2 + T)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^11 + T^9 - T^8 + T^7 + T^3 - T^2 + T)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 3 ka= 5 la= 5 nu= 0 rho= sgn\n",
      " HH=   (T^11 + T^7 - T^6 + T^5 + T^3 + T - 1)/(T^13 - T^12 - T + 1)\n",
      "MMdual= 1\n",
      "HHc= (T^13 - T^12 + T^11 + T^7 - T^6 + T^5 + T^3)/(T^13 - T^12 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 6 ka= 0 la= 1 nu= 0 rho= triv\n",
      " HH=   T^3/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)\n",
      "MMdual= 0\n",
      "HHc= T^3/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 6 ka= 0 la= 2 nu= 0 rho= triv\n",
      " HH=   T^2/(T^3 - T^2 - T + 1)\n",
      "MMdual= 0\n",
      "HHc= T^2/(T^3 - T^2 - T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 6 ka= 1 la= 2 nu= 0 rho= triv\n",
      " HH=   (T^4 - T^2 + T)/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)\n",
      "MMdual= 0\n",
      "HHc= (T^4 - T^2 + T)/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)\n",
      "---------------------------------------------------------------------------\n",
      "V= 6 ka= 3 la= 4 nu= 0 rho= triv\n",
      " HH=   (T^4 - T^3 + 2*T - 1)/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)\n",
      "MMdual= 1\n",
      "HHc= (T^5 - T^4 + T^2)/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)\n",
      "---------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "repList=[\n",
    "    [1,0,0,0,\"triv\"],\n",
    "    [1,0,0,1,\"triv\"],\n",
    "    [1,0,0,2,\"triv\"],\n",
    "    [1,0,0,0,\"sgn\"],\n",
    "    [1,0,0,1,\"sgn\"],\n",
    "    [1,0,0,2,\"sgn\"],\n",
    "    [2,0,0,0,\"stan\"],\n",
    "    [2,0,0,1,\"stan\"],\n",
    "    [2,0,0,2,\"stan\"],\n",
    "    [3,3,3,0,\"triv\"],\n",
    "    [3,1,1,0,\"triv\"],\n",
    "    [3,5,5,0,\"triv\"],\n",
    "    [3,3,3,0,\"sgn\"],\n",
    "    [3,1,1,0,\"sgn\"],\n",
    "    [3,5,5,0,\"sgn\"],\n",
    "    [6,0,1,0,\"triv\"],\n",
    "    [6,0,2,0,\"triv\"],\n",
    "    [6,1,2,0,\"triv\"],\n",
    "    [6,3,4,0,\"triv\"]]\n",
    "sum=0\n",
    "Msum=0\n",
    "for el in repList:\n",
    "        V=el[0]\n",
    "        ka=el[1]\n",
    "        la=el[2]\n",
    "        nu=el[3]\n",
    "        rho=el[4]\n",
    "        HH=Hgen(V,ka,la,nu,rho)\n",
    "        # print(\"V=\",V,\"ka=\",ka,\"la=\",la,\"nu=\",nu,\"rho=\",rho)\n",
    "        # print(\"  HH=  \",SR(HH).series(T))\n",
    "        \n",
    "        HHor=HH\n",
    "        \n",
    "        \n",
    "        rr=reverse(nu,rho)\n",
    "        \n",
    "        Moli=MolienF(V,-ka,-la,-nu,rr)\n",
    "        \n",
    "        MM=Moli[1].coefficients()[1][0]\n",
    "        # MM0=MolienF(V,ka,la,nu,rho)[1].coefficients()[1][0]\n",
    "        if el==[1,0,0,0,\"triv\"]:\n",
    "            HH=HH+T\n",
    "        HHc=rat(HH+MM)\n",
    "        \n",
    "        if V == 1 or V==2:\n",
    "            kk=n/3*nu\n",
    "            ll=kk\n",
    "        else:\n",
    "            kk=ka\n",
    "            ll=la\n",
    "        \n",
    "        # #------Uncoment for Latex output-----------\n",
    "        # # print(latex(rat(HHor)), \" & \", latex(rat(HH)), \" & \", latex(rat(Moli[0])), \" & \", latex(rat(HH-Moli[0])), \"EOL\")\n",
    "        # print( V , \" & \", kk , \" & \", ll, \" & RRho_{\\mathrm{\", rho , \"}} & \"  , latex(rat(HHor)), \" & \", latex(rat(HHc)), \"EOL\")\n",
    "        # # print(\"\\hline\")\n",
    "        # #------------------------------------------\n",
    "        \n",
    "        #-----------Uncomment for screen printing\n",
    "        print(\"V=\",V,\"ka=\",ka,\"la=\",la,\"nu=\",nu,\"rho=\",rho)\n",
    "        print(\" HH=  \",HHor)\n",
    "        print(\"MMdual=\",MM)\n",
    "        print(\"HHc=\",HHc)\n",
    "\n",
    "        print(\"---------------------------------------------------------------------------\")\n",
    "        #-----------\n",
    "\n",
    "        sum=sum+V*(HHc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "36daa113-4146-4b49-a376-f4db2a7a7dbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(T^3 + 8*T^2 + 8*T + 1)/(T^2 - 2*T + 1)"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rat(sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e911a327-5545-4b2e-ac15-71e9c9ec3f07",
   "metadata": {},
   "outputs": [],
   "source": [
    "Mollie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "5c5c6a41-e027-41d4-b0ce-6eff647969ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "Moli=MolienF(6,0,1,0,\"triv\")\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "9e3d0ec4-b733-44b9-bf3b-05587dc05fc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\\frac{3 T^{18} - 8 T^{17} + 3 T^{16} + 45 T^{15} - 76 T^{14} + 7 T^{13} + 134 T^{12} - 90 T^{11} - 103 T^{10} + 195 T^{9} - 44 T^{8} - 76 T^{7} + 58 T^{6} + 14 T^{5} - 23 T^{4} + 9 T^{3}}{T^{30} - 5 T^{29} + 8 T^{28} + T^{27} - 19 T^{26} + 22 T^{25} - 3 T^{24} - 7 T^{23} - 5 T^{22} - 4 T^{21} + 49 T^{20} - 61 T^{19} + 2 T^{18} + 51 T^{17} - 33 T^{16} + 6 T^{15} - 33 T^{14} + 51 T^{13} + 2 T^{12} - 61 T^{11} + 49 T^{10} - 4 T^{9} - 5 T^{8} - 7 T^{7} - 3 T^{6} + 22 T^{5} - 19 T^{4} + T^{3} + 8 T^{2} - 5 T + 1}"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latex(rat(Moli[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "79ca94b8-4abb-4960-ad32-7fa4763c4902",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9 T^{3} + 22 T^{4} + 52 T^{5} + 133 T^{6} + 322 T^{7} + 670 T^{8} + 1367 T^{9} + 2562 T^{10} + 4661 T^{11} + 8131 T^{12} + 13849 T^{13} + 22672 T^{14} + 36386 T^{15} + 56700 T^{16} + 86819 T^{17} + 130066 T^{18} + 191986 T^{19} + \\mathcal{O}\\left(T^{20}\\right)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latex(Moli[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "b13da049-7ff6-4bad-8440-c82475267130",
   "metadata": {},
   "outputs": [],
   "source": [
    "FFF=T^3/(T^5 - 2*T^4 + T^3 + T^2 - 2*T + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "9aa11346-7506-4c80-a340-94d24a6f4c6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8 T^{3} + 20 T^{4} + 49 T^{5} + 130 T^{6} + 319 T^{7} + 667 T^{8} + 1363 T^{9} + 2557 T^{10} + 4655 T^{11} + 8125 T^{12} + 13843 T^{13} + 22666 T^{14} + 36379 T^{15} + 56692 T^{16} + 86810 T^{17} + 130057 T^{18} + 191977 T^{19} + \\mathcal{O}\\left(T^{20}\\right)"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latex(SR(Moli[0]-FFF).series(T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fdbcf2e8-423e-4be3-bd95-cc05281f7836",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.5",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}