Hn2.ipynb

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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Kra(n,q,l,i): # K^{n,q}_l(i)\n",
    "   return sum([((-1)**j)*((q-1)**(l-j))*binomial(i,j)*binomial(n-i,l-j) \n",
    "                              for j in range(l+1)])\n",
    "\n",
    "def Pmat(n,q):\n",
    "   def f(i,j): return Kra(n,q,i,j)\n",
    "   return matrix(n+1,n+1,f).T\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "ep=[]\n",
    "for d in [1..18]:\n",
    "    n=2*d\n",
    "    P=Pmat(n,2)\n",
    "    2^n*P^-1==P; P\n",
    "    v=vector(([0]*d)+([1]*(d+1)))\n",
    "    eigdata=zip(P*v,P[0])\n",
    "    eplus=sum(map(lambda (_,m): m, filter(lambda (t,_): t>0, eigdata)))\n",
    "    eminus=sum(map(lambda (_,m): m, filter(lambda (t,_): t<0, eigdata)))\n",
    "    assert(eplus+eminus==2^n)\n",
    "    ep.append(eplus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " 34359607296]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ep"
   ]
  }
 ],
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