Merge remote-tracking branch 'origin/main' into sympy

Author: rlanzafame

book/08/sympy.ipynb

@@ -409,14 +409,37 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Notice something in the above example. When we typed `expr - x`, we did not get $x + 2y - x$, but rather just $2y$. The $x$ and the $-x$ automatically canceled one another. This is similar to how $\\sqrt{8}$ automatically turned into $2\\sqrt{2}$ above. This isn’t always the case in SymPy;  Aside from obvious simplifications like $x - x = 0$ and $\\sqrt{8} = 2\\sqrt{2}$, most simplifications are not performed automatically. "
+    "Notice something in the above example. When we typed `expr - x`, we did not get $x + 2y - x$, but rather just $2y$. The $x$ and the $-x$ automatically canceled one another. This is similar to how $\\sqrt{8}$ automatically turned into $2\\sqrt{2}$ above. This isn’t always the case in SymPy, however; consider this example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAAAVCAYAAADCUymGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD3klEQVRYCd2Y0VEbMRCGL4wL8FCC6YCECmJ3QEgFCR04kyf8xjgdABVkQgeQCojpwO4gHndA/k8naWRZd8Hn9RCyM3uSVtKvvdXuSnfV09NTZc0XFxcDa8zXgFd674PKmCaTyViQx8awrwVu4N8/6vsGz7AigZ8K60TlFyvMfeJIz4Hwg67vVF/Slvyx67qai4OtVF6DYWZgAfaF91PlW4D/dZKeGPdK5SjoqvpUdQw0Uv0+yLctNXemOe9VrixTBMpdbavMLuP1AkPx544Y6HuezhUW3rwS/0jlHerYAfzK0sBnUtCFRQeFuk4hauAuNNSkuXTO5+O5fcnx8E7k7YA9+iYGFhC5d9FJm5ebhCEX0h2PLVFu+NKYNhn2OOuFEVhb9RBuJ6p/ErOLH8XQg8bc1tWNJ3msMWftiL2xmIVAOn1owHE3IPW7gy7R/UjjZ2rHKPV9NypLWNhjlHrwVAO/wep4EN+IyXHkJYzvcorKEnECz0sdXrYLdgusbZfeFePiVOFmwQJfvU3uVM9tcCYZ0Vsi7DFwHiwAPDedTNgwES+GDsVpvxMmDzaAK84GGWBvYO5RwOF26w1aqcTgOBtElObv2Ba5jK0NrMovgaU5lKvWo2QYmoVKIUBXIDbAjQ2CpNwVm/U5lTmUcmJd+tduA34Q+v9N74jn1yAnp3Nou1ShgXjrZZxQV9Apl4Uh2LMfPDiAhM4SWOjbqkwUDPO2xhZGyYCV5EQZX0+ktc6k+UTwoUo8MpLawcEwJFGa5l+8G1nT2eOcLs3BGuu8IYDFA00LcW0BrIkIh7Z+N08YXbCb1jSRSyc26Uhl9FzV2TRycSD6YkR7Ie/CF1vunGEO9lj2NIAKuYeDiN3AW5iYpgwSfZr4NWSNGJsq5DqNsNcWsmxIP7yw9GmP0aO3qs67pfZQ0+XkJu+lHw9e9PRgJ2C+wZ3VVY8kGX0h0Ud5VmEXTzIZTQvsAuzuIr0XRsOx7lXPv0CHkqVpB+NiMEfeJrxbMXX5Ye4c66nBLrBbTKg0+Vx8J2ZRvqmXqsd0wZgCfZcMZXOywM4xrdpcuzByuPunuHnYE73cd7lJ/RZzJ4baPLjeAKv/rPoXOhcfW+E9B0frnYrHzxlrOUZrTsWzJkz1DcRz+g/qjTB5srttIWOySAayUhveG+G1YiLZkeqkUbz+spYUn3i8+24wM7AWJs3kp29xdSuh1iR/poeRFXSKw4FHCgzEF+611i2mTclJO9jB6UUOtiSuM+Titfuk5QIvgIU3ckceqyT38g+5LfdydsVINvvhLlBHfgdPVaancOj+r0u/CXxqxyvdHwOidMKb8DIVAAAAAElFTkSuQmCC",
+      "text/latex": [
+       "$\\displaystyle x \\left(x + 2 y\\right)$"
+      ],
+      "text/plain": [
+       "x⋅(x + 2⋅y)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x*expr"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A general formula to simplify formulas is `sym.simplify`, which attempts to apply all of these functions in an intelligent way to arrive at the simplest form of an expression:"
+    "Aside from obvious simplifications like $x - x = 0$ and $\\sqrt{8} = 2\\sqrt{2}$, most simplifications are not performed automatically. A general formula to simplify formulas is `sym.simplify`, which attempts to apply all of these functions in an intelligent way to arrive at the simplest form of an expression:"
    ]
   },
   {

book/08/sympy_stripped.ipynb

@@ -313,7 +313,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Notice something in the above example. When we typed `expr - x`, we did not get $x + 2y - x$, but rather just $2y$. The $x$ and the $-x$ automatically canceled one another. This is similar to how $\\sqrt{8}$ automatically turned into $2\\sqrt{2}$ above. This isn’t always the case in SymPy, however:"
+    "Notice something in the above example. When we typed `expr - x`, we did not get $x + 2y - x$, but rather just $2y$. The $x$ and the $-x$ automatically canceled one another. This is similar to how $\\sqrt{8}$ automatically turned into $2\\sqrt{2}$ above. This isn’t always the case in SymPy, however; consider this example:"
    ]
   },
   {
@@ -344,14 +344,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Notice something in the above example. When we typed `expr - x`, we did not get $x + 2y - x$, but rather just $2y$. The $x$ and the $-x$ automatically canceled one another. This is similar to how $\\sqrt{8}$ automatically turned into $2\\sqrt{2}$ above. This isn’t always the case in SymPy;  Aside from obvious simplifications like $x - x = 0$ and $\\sqrt{8} = 2\\sqrt{2}$, most simplifications are not performed automatically. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A general formula to simplify formulas is `sym.simplify`, which attempts to apply all of these functions in an intelligent way to arrive at the simplest form of an expression:"
+    "Aside from obvious simplifications like $x - x = 0$ and $\\sqrt{8} = 2\\sqrt{2}$, most simplifications are not performed automatically. A general formula to simplify formulas is `sym.simplify`, which attempts to apply all of these functions in an intelligent way to arrive at the simplest form of an expression:"
    ]
   },
   {
@@ -516,7 +509,13 @@
     "\n",
     "Create an expression for the normal distribution function:\n",
     "\n",
-    "$$\\frac{1}{\\sqrt{2\\pi\\sigma}}e^{\\frac{(x-\\mu)^2}{2\\sigma^2}}$$"
+    "$$\\frac{1}{\\sqrt{2\\pi\\sigma}}e^{\\frac{(x-\\mu)^2}{2\\sigma^2}}$$\n",
+    "\n",
+    "First define variables with:\n",
+    "\n",
+    "```python\n",
+    "sym.var('x, sigma, mu')\n",
+    "```"
    ]
   },
   {
@@ -525,6 +524,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "# define variables\n",
     "expr = \n",
     "expr #displays expression"
    ]