{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 3: Functions and Algorithms"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.10: Polynomial_evaluation.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"x = poly(0, 'x');\n",
"p = 2*x^3-7*x^2+4*x-15;\n",
"disp(p,'the polynomial is')\n",
"k=horner(p,5);\n",
"disp(k,'value of the polynomial at x=5 is')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.11: Greatest_Common_Divisor.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"V=int32([258,60]);\n",
"thegcd=gcd(V);\n",
"disp(thegcd,'the gcd of the two numbers 258 and 60 is')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.8: Recursively_defined_functions.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"function[k]=fact(a)\n",
"k=-1;\n",
"if(a<0|a>200)\n",
"disp('Invalid');\n",
"break;\n",
" else\n",
"if(a==1|a==0)\n",
"k=1;\n",
" else\n",
"k=a*fact(a-1);\n",
"end\n",
"end\n",
"endfunction\n",
"a=4;\n",
"p=fact(a);\n",
"disp(p,'the value of 4! is')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.9: Cardinality.sci"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"x=1;\n",
"y=2;\n",
"z=3;\n",
"A=[x,y,z];\n",
"disp('cardinality of set A is:')\n",
"length(A)  \n",
"B=[1,3,5,7,9]\n",
"disp('cardinality of set B is:')\n",
"length(B)\n",
"\n",
"// 3.9 (b)\n",
"disp('the set E has the following elements)\n",
"E=[2,4,6 %inf]  //set E is the set of all positive even numbers and N is the set of all natural numbers\n",
"disp('function f:N to E is defined.So,E has the same cardinality as N')\n",
"disp('set E is countably infinite:')\n",
"for x=2:2:%inf\n",
"y=2*x;\n",
"disp(y)\n",
"end"
   ]
   }
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			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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