P-E-square root and Nthroot-edited-2

Author: ostad-ai

PE-Heron method for computing square root of positive number.ipynb

@@ -6,11 +6,11 @@
    "metadata": {},
    "source": [
     "# Python everything, exercise:\n",
-    "## Heron's method for computing $\\sqrt x$\n",
-    "**Heron's method** computes the *square root* of a given positive number $x$ by\n",
+    "## Heron's method for computing $\\sqrt a$\n",
+    "**Heron's method** computes the *square root* of a given positive number $a$ by\n",
     " 1) $x_0 \\leftarrow$ some initial guess <br>\n",
-    " 2) for $n=0,1,2...$ do: <br>\n",
-    "$\\;\\;\\;\\; x_{n+1}=\\frac{1}{2}(x_n+\\frac{x}{x_n})$\n",
+    " 2) for $k=0,1,2...$ do: <br>\n",
+    "$\\;\\;\\;\\;\\Large x_{k+1}=\\frac{1}{2}(x_k+\\frac{a}{x_k})$\n",
     "\n",
     "YouTube Channel: **@ostad-ai**\n",
     "<br>The Python code is at: https://github.com/ostad-ai/Python-Everything"
@@ -23,11 +23,11 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def heron(x,x0=1,iter=20):\n",
-    "    xn=x0\n",
-    "    for n in range(iter):\n",
-    "        xn=(xn+x/xn)/2\n",
-    "    return xn"
+    "def heron(a,x0=1,iter=20):\n",
+    "    xk=x0\n",
+    "    for _ in range(iter):\n",
+    "        xk=(xk+a/xk)/2\n",
+    "    return xk"
    ]
   },
   {
@@ -45,8 +45,8 @@
     }
    ],
    "source": [
-    "x=2\n",
-    "print(f'Square root of {x} = {heron(x)}')"
+    "a=2\n",
+    "print(f'Square root of {a} = {heron(a)}')"
    ]
   },
   {

PE-Nth root algorithm.ipynb

@@ -6,11 +6,11 @@
    "metadata": {},
    "source": [
     "# Python everything, exercise:\n",
-    "## Nth root algorithm for computing $\\sqrt[n] x$\n",
-    "**Nth root algorithm** computes the *nth root* of a given positive number $x$ by\n",
+    "## Nth root algorithm for computing $\\sqrt[n] a$\n",
+    "**Nth root algorithm** computes the *nth root* of a given positive number $a$ by\n",
     " 1) $x_0 \\leftarrow$ some initial guess <br>\n",
     " 2) for $k=0,1,2...$ do: <br>\n",
-    "$\\;\\;\\;\\; x_{k+1}=\\frac{1}{n}((n-1)x_k+\\frac{x}{x^{n-1}_k})$\n",
+    "$\\;\\;\\;\\;\\Large x_{k+1}=\\frac{1}{n}((n-1)x_k+\\frac{a}{x^{n-1}_k})$\n",
     "\n",
     "YouTube Channel: **@ostad-ai**\n",
     "<br>The Python code is at: https://github.com/ostad-ai/Python-Everything"
@@ -19,6 +19,21 @@
   {
    "cell_type": "code",
    "execution_count": 1,
+   "id": "80c175d2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def nth_root(a,n=2,x0=1,iter=20):\n",
+    "    xk=x0\n",
+    "    n1=n-1\n",
+    "    for _ in range(iter):\n",
+    "        xk=(n1*xk+a/xk**n1)/n\n",
+    "    return xk"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
    "id": "d757f8ac",
    "metadata": {},
    "outputs": [
@@ -31,15 +46,9 @@
     }
    ],
    "source": [
-    "def nth_root(x,n=2,x0=1,iter=20):\n",
-    "    xk=x0\n",
-    "    n1=n-1\n",
-    "    for _ in range(iter):\n",
-    "        xk=(n1*xk+x/xk**n1)/n\n",
-    "    return xk\n",
-    "x=2\n",
+    "a=2\n",
     "n=3\n",
-    "print(f'{n}th root of {x} is:{nth_root(x,n)}')"
+    "print(f'{n}th root of {a} is:{nth_root(a,n)}')"
    ]
   },
   {