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authorkinitrupti2017-05-12 18:40:35 +0530
committerkinitrupti2017-05-12 18:40:35 +0530
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tree9806b0d68a708d2cfc4efc8ae3751423c56b7721 /sample_notebooks/SoumenGanguly/ncert_Maths.ipynb
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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Chapter 1: Sets\n",
- "========"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 1, Page 03:\n",
- "----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "collapsed": false,
- "scrolled": true
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Therefore, the solution set of the given equation can be written in roaster form as {-2,1}\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "coeff = [1,1,-2]\n",
- "\n",
- "#Calculations\n",
- "roots_array = np.roots(coeff)\n",
- "\n",
- "#Result\n",
- "print \"Therefore, the solution set of the given equation can be written in roaster form as {%d,%d}\"%(roots_array[0],roots_array[1])\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 2, Page 03:\n",
- "---------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The required numbers are 1,2,3,4,5,6\n",
- "So, the given set in the roster form is {1,2,3,4,5,6}\n"
- ]
- }
- ],
- "source": [
- "#Variable declaration\n",
- "pos_integer = []\n",
- "\n",
- "#Calculations\n",
- "for i in range(1,1000): #1000 is taken as the upper limit of a positive integer\n",
- " if i**2<40:\n",
- " pos_integer.append(i)\n",
- " \n",
- "#Result\n",
- "print \"The required numbers are %d,%d,%d,%d,%d,%d\"%(pos_integer[0],pos_integer[1],pos_integer[2],pos_integer[3],pos_integer[4],pos_integer[5])\n",
- "print \"So, the given set in the roster form is {%d,%d,%d,%d,%d,%d}\"%(pos_integer[0],pos_integer[1],pos_integer[2],pos_integer[3],pos_integer[4],pos_integer[5])\n",
- " "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 12, Page 14:\n",
- "-----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The union of the two given arrays is \n",
- "[ 2 4 6 8 10 12]\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "a = [2,4,6,8]\n",
- "b = [6,8,10,12]\n",
- "\n",
- "#Calculations\n",
- "union_array = np.union1d(a,b)\n",
- "\n",
- "#Result\n",
- "print \"The union of the two given arrays is \"\n",
- "print union_array"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 13, Page 14:\n",
- "-----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "A U B = ['a' 'e' 'i' 'o' 'u']\n",
- "A = ['a', 'e', 'i', 'o', 'u']\n",
- "Thus, A U B = A\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "a = ['a','e','i','o','u']\n",
- "b = ['a','i','u']\n",
- "\n",
- "#Calculations\n",
- "union_array = np.union1d(a,b)\n",
- "\n",
- "#Result\n",
- "print \"A U B = %s\"%(union_array)\n",
- "print \"A = %s\"%(a)\n",
- "print \"Thus, A U B = A\"\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 15, Page 15:\n",
- "----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "A intersection B = [6 8]\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "a = [2,4,6,8]\n",
- "b = [6,8,10,12]\n",
- "\n",
- "#Calculations\n",
- "intersect_array = np.intersect1d(a,b)\n",
- "\n",
- "#Result\n",
- "print \"A intersection B = %s\"%(intersect_array)\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 18, Page 17:\n",
- "-----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "A - B = [1 3 5]\n",
- "B - A = [8]\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "a = [1,2,3,4,5,6]\n",
- "b = [2,4,6,8]\n",
- "\n",
- "#Calculations\n",
- "diff_a = np.setdiff1d(a,b)\n",
- "diff_b = np.setdiff1d(b,a)\n",
- "\n",
- "#Result\n",
- "print \"A - B = %s\"%(diff_a)\n",
- "print \"B - A = %s\"%(diff_b)\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 20, Page 19:\n",
- "-----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "A' = [ 2 4 6 8 10]\n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "u = [1,2,3,4,5,6,7,8,9,10]\n",
- "a = [1,3,5,7,9]\n",
- "\n",
- "#Calculations\n",
- "complement_a = np.setdiff1d(u,a)\n",
- "\n",
- "#Result\n",
- "print \"A' = %s\"%(complement_a)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Example 22, Page 19:\n",
- "-----------------------"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "A' = [1 4 5 6]\n",
- "B' = [1 2 6]\n",
- "A' intersection B' = [1 6]\n",
- "A U B = [2 3 4 5]\n",
- "(A U B)' = [1 6]\n",
- "Therefore, (A U B)' = A' intersection B' \n"
- ]
- }
- ],
- "source": [
- "import numpy as np\n",
- "\n",
- "#Variable declaration\n",
- "u = [1,2,3,4,5,6]\n",
- "a = [2,3]\n",
- "b = [3,4,5]\n",
- "\n",
- "#Calculations\n",
- "complement_a = np.setdiff1d(u,a)\n",
- "complement_b = np.setdiff1d(u,b)\n",
- "intersect_ab = np.intersect1d(complement_a,complement_b)\n",
- "union_ab = np.union1d(a,b)\n",
- "complement_union_ab = np.setdiff1d(u,union_ab)\n",
- "\n",
- "#Result\n",
- "print \"A' = %s\"%(complement_a)\n",
- "print \"B' = %s\"%(complement_b)\n",
- "print \"A' intersection B' = %s\"%(intersect_ab)\n",
- "print \"A U B = %s\"%(union_ab)\n",
- "print \"(A U B)' = %s\"%(complement_union_ab)\n",
- "print \"Therefore, (A U B)\\' = A\\' intersection B\\' \"\n"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 2",
- "language": "python",
- "name": "python2"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 2
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython2",
- "version": "2.7.8"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}