test notebook for latex render on github

github_render_test.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "this is a test no blank line after sentence.\n",
+    "$$x=y$$\n",
+    "\n",
+    "\n",
+    "blacksquare test\n",
+    "\n",
+    "$$ \n",
+    "\\begin{aligned}\n",
+    "P &= (1-K)P \\\\\n",
+    "&= (1-\\frac{P}{P+R})P \\\\\n",
+    "&= (\\frac{P+R}{P+R}-\\frac{P}{P+R})P \\\\\n",
+    "&= (\\frac{P+R-P}{P+R})P \\\\\n",
+    "&= \\frac{RP}{P+R}\\\\\n",
+    "&= \\frac{1}{\\frac{P+R}{RP}}\\\\\n",
+    "&= \\frac{1}{\\frac{R}{RP} + \\frac{P}{RP}} \\\\\n",
+    "&= \\frac{1}{\\frac{1}{P} + \\frac{1}{R}}\n",
+    "\\quad\\blacksquare\n",
+    "\\end{aligned}\n",
+    "$$\n",
+    "\n",
+    "alignment\n",
+    "\n",
+    "$$\\begin{aligned}\n",
+    "\\sigma_{i,j} &= \\mathrm{E}\\begin{bmatrix}(X_i - \\mu_i)(X_j - \\mu_j)\\end{bmatrix} \\\\ \n",
+    "&= \\mathrm{E}\\begin{bmatrix} (X_j - \\mu_j)(X_i - \\mu_i)\\end{bmatrix} \\\\ \n",
+    "&= \\sigma_{j,i}\n",
+    "\\end{aligned}$$\n"
+   ]
+  }
+ ],
+ "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": "3.4.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}