задание 1

2 files changed, 244 insertions, 0 deletions

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..a40f1fd
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+.*
+!.gitignore
\ No newline at end of file
diff --git a/t4mk.ipynb b/t4mk.ipynb
new file mode 100644
index 0000000..1f12fc8
--- /dev/null
+++ b/t4mk.ipynb
@@ -0,0 +1,242 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Задание 1\n",
+    "\n",
+    "Изменяем значение `frac` на свою дробь."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\Large\\frac{157}{225}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 0 + \\Large\\frac{1}{\\Large\\frac{225}{157}}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 0 + \\Large\\frac{1}{1 + \\Large\\frac{1}{\\Large\\frac{157}{68}}}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 0 + \\Large\\frac{1}{1 + \\Large\\frac{1}{2 + \\Large\\frac{1}{\\Large\\frac{68}{21}}}}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 0 + \\Large\\frac{1}{1 + \\Large\\frac{1}{2 + \\Large\\frac{1}{3 + \\Large\\frac{1}{\\Large\\frac{21}{5}}}}}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 0 + \\Large\\frac{1}{1 + \\Large\\frac{1}{2 + \\Large\\frac{1}{3 + \\Large\\frac{1}{4 + \\Large\\frac{1}{5}}}}}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\begin{array}{ccccccccc}\n",
+       "i & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\\\\n",
+       "q_i &  &  & 0 & 1 & 2 & 3 & 4 & 5 \\\\\n",
+       "P_i & 0 & 1 & 0 & 1 & 2 & 7 & 30 & 157 \\\\\n",
+       "Q_i & 1 & 0 & 1 & 1 & 3 & 10 & 43 & 225 \\\\\n",
+       "\\end{array}$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "frac = (157, 225)\n",
+    "\n",
+    "from IPython.display import display, Math\n",
+    "\n",
+    "# Задание 1 - 157 225\n",
+    "def continued_fraction(a0, a1):\n",
+    "    if a1 > 0:\n",
+    "        qs = []\n",
+    "        while a1 != 0:\n",
+    "            r = a0 % a1\n",
+    "            qs.append((a0 - r) // a1)\n",
+    "            # print(f'{a0} / {a1} = {qs[-1]} + {a1} / {r}')\n",
+    "            a0 = a1\n",
+    "            a1 = r\n",
+    "        # print('Непрерывная дробь', qs)\n",
+    "        return qs\n",
+    "    else:\n",
+    "        return 'Знаменатель должен быть больше нуля!'\n",
+    "\n",
+    "\n",
+    "def successive_convergents(a0, a1):\n",
+    "    qs = [0, 0] + continued_fraction(a0, a1)\n",
+    "    big_ps = [0, 1]\n",
+    "    big_qs = [1, 0]\n",
+    "    for i in range(2, len(qs)):\n",
+    "        big_ps.append(big_ps[i - 1] * qs[i] + big_ps[i - 2])\n",
+    "        big_qs.append(big_qs[i - 1] * qs[i] + big_qs[i - 2])\n",
+    "    # print(f'P = {big_ps}')\n",
+    "    # print(f'Q = {big_qs}')\n",
+    "    qs[0] = qs[1] = None\n",
+    "    return qs, big_ps, big_qs\n",
+    "\n",
+    "\n",
+    "class Num:\n",
+    "  def __init__(self, val):\n",
+    "    self.val = val\n",
+    "\n",
+    "  def math(self):\n",
+    "    return str(self.val)\n",
+    "\n",
+    "class Fr:\n",
+    "  def __init__(self, den, num):\n",
+    "    self.val = None\n",
+    "    self.den = den\n",
+    "    self.num = num\n",
+    "  \n",
+    "  def math(self):\n",
+    "    if self.val is None:\n",
+    "      return f\"\\\\Large\\\\frac{{{self.den}}}{{{self.num}}}\"\n",
+    "    else:\n",
+    "      return f\"{self.val} + \\\\Large\\\\frac{{{self.den}}}{{{self.num.math()}}}\"\n",
+    "  \n",
+    "  def display(self):\n",
+    "    return display(Math(self.math()))\n",
+    "  \n",
+    "  def next(self):\n",
+    "    ret = True\n",
+    "    if self.val is None:\n",
+    "      self.val = self.den // self.num\n",
+    "      self.den = self.den % self.num\n",
+    "      if self.den == 1:\n",
+    "        f1 = Num(self.num)\n",
+    "        ret = False\n",
+    "      else:\n",
+    "        f1 = Fr(self.num, self.den)\n",
+    "      self.den = 1\n",
+    "      self.num = f1\n",
+    "    else:\n",
+    "      ret = self.num.next()\n",
+    "    return ret\n",
+    "\n",
+    "\n",
+    "def display_table(table):\n",
+    "  qs, bps, bqs = table\n",
+    "  res = [r\"\\begin{array}{\" + 'c' * (len(qs) + 1) + '}']\n",
+    "\n",
+    "  i_row = ['i'] + list(map(str, range(-1, len(qs) - 2 + 1)))\n",
+    "  q_row = ['q_i', '', '']\n",
+    "  bq_row = ['Q_i']\n",
+    "  bp_row = ['P_i']\n",
+    "  for (qi, bqi, bpi) in zip(qs, bqs, bps):\n",
+    "    if qi is not None:\n",
+    "      q_row.append(str(qi))\n",
+    "    bq_row.append(str(bqi))\n",
+    "    bp_row.append(str(bpi))\n",
+    "  res.append(' & '.join(i_row) + r' \\\\')\n",
+    "  res.append(' & '.join(q_row) + r' \\\\')\n",
+    "  res.append(' & '.join(bp_row) + r' \\\\')\n",
+    "  res.append(' & '.join(bq_row) + r' \\\\')\n",
+    "\n",
+    "  res.append(r\"\\end{array}\")\n",
+    "  res = '\\n'.join(res)\n",
+    "  return display(Math(res))\n",
+    "\n",
+    "f = Fr(*frac)\n",
+    "while True:\n",
+    "  f.display()\n",
+    "  if not f.next():\n",
+    "    break\n",
+    "f.display()\n",
+    "\n",
+    "table = successive_convergents(*frac)\n",
+    "display_table(table)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Задание 2"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}