Initial commit of nbs.

Author: drvinceknight

nbs/00 - Studying Mathematics with Python.ipynb

@@ -0,0 +1,96 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook is used to generate data regarding the Goldbach conjecture: rows are of the form $N, a, b$ where $N$ is an even number, $a< b$ are prime and $N=a + b$.\n",
+    "\n",
+    "First we write a Python function `goldbach` that takes `N` and returns all pairs of numbers $a, b$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import sympy as sym\n",
+    "import pandas as pd\n",
+    "\n",
+    "def goldbach(N):\n",
+    "    \"\"\"Returns all pairs of primes that sum to give N\"\"\"\n",
+    "    primes = list(sym.primerange(1, N))\n",
+    "    sums = []\n",
+    "    for i, p1 in enumerate(primes):\n",
+    "        for p2 in primes[i:]:\n",
+    "            if p1 + p2 == N:\n",
+    "                sums.append((p1, p2))\n",
+    "    return sums"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us use the above function to create our data:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "maxN = 500\n",
+    "data = [[N, *pair] for N in range(4, maxN + 1) \n",
+    "        for pair in goldbach(N) if N % 2 == 0 ]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us write our data to an excel file:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "df = pd.DataFrame(data, columns=[\"N\",\"a\", \"b\"])  # Create a data frame\n",
+    "df.to_excel(\"data/goldbach.xlsx\")  # Write it to excel"
+   ]
+  }
+ ],
+ "metadata": {
+  "anaconda-cloud": {},
+  "kernelspec": {
+   "display_name": "Python [default]",
+   "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": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}