{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Améliorations du code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def f(n,k0):\n",
    "    k=k0\n",
    "    while n%k!=0 and k<=sqrt(n):\n",
    "        k=k+1\n",
    "    if k>sqrt(n):return(n)\n",
    "    else:return(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def f1(n,k0):\n",
    "    k=k0-k0%6\n",
    "    while k<=sqrt(n):\n",
    "        if n%(k+1)==0:return(k+1)\n",
    "        elif n%(k+5)==0:return(k+5)\n",
    "        else:k=k+6\n",
    "    return(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def fp(n,k0=7):\n",
    "    if n==1:return([])\n",
    "    else:\n",
    "        p=f(n,k0)\n",
    "        return([p]+fp(n/p,p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5, 31]\n",
      "811 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1  print(fp(465))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5, 89, 1049, 33223]\n",
      "4.3 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1  print(fp(46525987545))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5, 89, 1049, 33223]\n",
      "1.06 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1  print(fp(46525987545))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def fpp(n):\n",
    "    if n==0:return([0])\n",
    "    else:\n",
    "        l=[]\n",
    "        while n%2==0:\n",
    "            l=l+[2];n=n/2\n",
    "        while n%3==0:\n",
    "            l=l+[3];n=n/3\n",
    "        while n%5==0:\n",
    "            l=l+[5];n=n/5\n",
    "        return(l+fp(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5, 89, 1049, 33223]\n",
      "1.52 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1  print(fpp(46525987545))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5, 89, 1049, 33223]\n",
      "225 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1  print(fpp(46525987545))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 5, 89, 1049, 33223]\n",
      "1.22 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1  print(fpp(46525987545))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.2",
   "language": "sagemath",
   "metadata": {
    "cocalc": {
     "description": "Open-source mathematical software system",
     "priority": 10,
     "url": "https://www.sagemath.org/"
    }
   },
   "name": "sage-9.2",
   "resource_dir": "/ext/jupyter/kernels/sage-9.2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}