y^2=x^3+2

a.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "import sympy\n",
    "from spb import plot_implicit, plot_list  # sympy_plot_backends\n",
    "import matplotlib.font_manager as fm\n",
    "import matplotlib\n",
    "prop = fm.FontProperties(fname='/System/Library/Fonts/ヒラギノ角ゴシック W3.ttc')\n",
    "prop.set_weight = 'normal'\n",
    "matplotlib.rcParams['font.family'] = prop.get_name()\n",
    "matplotlib.rcParams['font.weight'] = 'normal'\n",
    "\n",
    "\n",
    "def step_imp(f, x, y, s0, s1):\n",
    "    if (s1[0] == s0[0]):\n",
    "        raise\n",
    "    a = (s1[1] - s0[1]) / (s1[0] - s0[0])\n",
    "    g = sympy.Eq(y, a * (x - s1[0]) + s1[1])\n",
    "    try:\n",
    "        result = sympy.nonlinsolve([f, g], [x, y])\n",
    "    except:\n",
    "        raise\n",
    "    return result\n",
    "\n",
    "\n",
    "def step(f, x, y, new_ps, ps):\n",
    "    results = set()\n",
    "    for s0 in list(new_ps):\n",
    "        for s1 in list(ps):\n",
    "            try:\n",
    "                results = results.union(step_imp(f, x, y, s0, s1))\n",
    "            except:\n",
    "                continue\n",
    "    ary = list(results)\n",
    "    for i in range(len(ary)-1):\n",
    "        for j in range(1, len(ary)):\n",
    "            try:\n",
    "                results = results.union(step_imp(f, x, y, ary[i], ary[j]))\n",
    "            except:\n",
    "                continue\n",
    "    return results\n",
    "\n",
    "\n",
    "def main():\n",
    "    x, y = sympy.symbols('x y')\n",
    "    f = sympy.Eq(y**2, x**3+2)\n",
    "    ps = {(-1, 1), (-1, -1)}\n",
    "    new_ps = {(sympy.Rational(17, 4), sympy.Rational(71, 8))}\n",
    "    for i in range(3):\n",
    "        new_new_ps = step(f, x, y, new_ps, ps)\n",
    "        ps = ps.union(new_ps)\n",
    "        new_ps = new_new_ps\n",
    "    ps = ps.union(new_ps)\n",
    "\n",
    "    p1 = plot_implicit(f, show=False)\n",
    "    xs = [point[0] for point in ps]\n",
    "    ys = [point[1] for point in ps]\n",
    "    p2 = plot_list((xs, ys, '有理点'), scatter=True, show=False)\n",
    "    (p1 + p2).show()\n",
    "    return ps\n",
    "\n",
    "\n",
    "main()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "{(-1, -1),\n",
       " (-1, 1),\n",
       " (-171804003687530192810198042838512424366412027182994348016212304543116691174005914152028115566393115098039741486535595290693353145176520338844652705343679900783/194053801888324560225268776200051065243053319489957665795255729413836001170883028796350680169230046040406763375871478175304409389066402103864482296570686124004, 3089311888954132756627355276786552544157272663915510709333053853951210257254735522338176687107830278927308859200801812600230381529994374194959956398705452131920486199770932162369405616117597808662433213292531516292658824088904048465428729/2703231464089788541556861581863739989052519379046591317219568246034341604903785017667065582354445877314712530600398355436396563249952149785562957626054602384366709078843016339981832349835815526054927833355869879921169736021122655941372008),\n",
       " (-174016613231/306196222500, -228355009922164103/169433679720375000),\n",
       " (-174016613231/306196222500, 228355009922164103/169433679720375000),\n",
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