{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing Jacobi symbols\n",
    "\n",
    "We use the function `jacobi` to compute the Jacobi symbols for the given numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from algorithms.modular import jacobi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7411 9283 1\n",
      "\t9283 mod 8 = 3\n",
      "\t7411 mod 4 = 3\n",
      "\t9283 mod 4 = 3\n",
      "9283 7411 -1\n",
      "1872 7411 -1\n",
      "\t7411 mod 8 = 3\n",
      "936 7411 1\n",
      "468 7411 -1\n",
      "234 7411 1\n",
      "117 7411 -1\n",
      "\t117 mod 4 = 1\n",
      "\t7411 mod 4 = 3\n",
      "7411 117 -1\n",
      "40 117 -1\n",
      "\t117 mod 8 = 5\n",
      "20 117 1\n",
      "10 117 -1\n",
      "5 117 1\n",
      "\t5 mod 4 = 1\n",
      "\t117 mod 4 = 1\n",
      "117 5 1\n",
      "2 5 1\n",
      "\t5 mod 8 = 5\n",
      "1 5 -1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobi(7411, 9283, trace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1094 1987 1\n",
      "\t1987 mod 8 = 3\n",
      "547 1987 -1\n",
      "\t547 mod 4 = 3\n",
      "\t1987 mod 4 = 3\n",
      "1987 547 1\n",
      "346 547 1\n",
      "\t547 mod 8 = 3\n",
      "173 547 -1\n",
      "\t173 mod 4 = 1\n",
      "\t547 mod 4 = 3\n",
      "547 173 -1\n",
      "28 173 -1\n",
      "\t173 mod 8 = 5\n",
      "14 173 1\n",
      "7 173 -1\n",
      "\t7 mod 4 = 3\n",
      "\t173 mod 4 = 1\n",
      "173 7 -1\n",
      "5 7 -1\n",
      "\t7 mod 8 = 7\n",
      "\t5 mod 4 = 1\n",
      "\t7 mod 4 = 3\n",
      "7 5 -1\n",
      "2 5 -1\n",
      "\t5 mod 8 = 5\n",
      "1 5 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobi(20964, 1987, trace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1234567 11111111 1\n",
      "\t11111111 mod 8 = 7\n",
      "\t1234567 mod 4 = 3\n",
      "\t11111111 mod 4 = 3\n",
      "11111111 1234567 -1\n",
      "8 1234567 -1\n",
      "\t1234567 mod 8 = 7\n",
      "4 1234567 -1\n",
      "2 1234567 -1\n",
      "1 1234567 -1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobi(1234567, 11111111, trace=True)"
   ]
  }
 ],
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