update docs (#7714)

docs/extras/modules/chains/additional/llm_symbolic_math.ipynb

@@ -5,14 +5,47 @@
    "metadata": {},
    "source": [
     "# LLM Symbolic Math \n",
-    "This notebook showcases using LLMs and Python to Solve Algebraic Equations."
+    "This notebook showcases using LLMs and Python to Solve Algebraic Equations. Under the hood is makes use of [SymPy](https://www.sympy.org/en/index.html)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from langchain.llms import OpenAI\n",
+    "from langchain.chains.llm_symbolic_math.base import LLMSymbolicMathChain\n",
+    "\n",
+    "llm = OpenAI(temperature=0)\n",
+    "llm_symbolic_math = LLMSymbolicMathChain.from_llm(llm)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Calculating the limit of an equation"
+    "## Integrals and derivates"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'Answer: exp(x)*sin(x) + exp(x)*cos(x)'"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "llm_symbolic_math.run(\"What is the derivative of sin(x)*exp(x) with respect to x?\")"
    ]
   },
   {
@@ -20,21 +53,10 @@
    "execution_count": 18,
    "metadata": {},
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "\u001b[1m> Entering new LLMSymbolicMathChain chain...\u001b[0m\n",
-      "What is the limit of sin(x) / x as x goes to 0?\u001b[32;1m\u001b[1;3mAnswer: 1\u001b[0m\n",
-      "\u001b[1m> Finished chain.\u001b[0m\n"
-     ]
-    },
     {
      "data": {
       "text/plain": [
-       "'Answer: 1'"
+       "'Answer: exp(x)*sin(x)'"
       ]
      },
      "execution_count": 18,
@@ -43,20 +65,16 @@
     }
    ],
    "source": [
-    "from langchain.llms import OpenAI\n",
-    "from langchain.chains.llm_symbolic_math.base import LLMSymbolicMathChain\n",
-    "\n",
-    "llm = OpenAI(temperature=0)\n",
-    "llm_symbolic_math = LLMSymbolicMathChain.from_llm(llm, verbose=True)\n",
-    "\n",
-    "llm_symbolic_math.run(\"What is the limit of sin(x) / x as x goes to 0?\")"
+    "llm_symbolic_math.run(\n",
+    "    \"What is the integral of exp(x)*sin(x) + exp(x)*cos(x) with respect to x?\"\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Calculating an integral"
+    "## Solve linear and differential equations"
    ]
   },
   {
@@ -64,21 +82,10 @@
    "execution_count": 19,
    "metadata": {},
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "\u001b[1m> Entering new LLMSymbolicMathChain chain...\u001b[0m\n",
-      "What is the integral of e^-x from 0 to infinity?\u001b[32;1m\u001b[1;3mAnswer: 1\u001b[0m\n",
-      "\u001b[1m> Finished chain.\u001b[0m\n"
-     ]
-    },
     {
      "data": {
       "text/plain": [
-       "'Answer: 1'"
+       "'Answer: Eq(y(t), C2*exp(-t) + (C1 + t/2)*exp(t))'"
       ]
      },
      "execution_count": 19,
@@ -87,60 +94,55 @@
     }
    ],
    "source": [
-    "llm_symbolic_math.run(\"What is the integral of e^-x from 0 to infinity?\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Calculating an algebraic equation"
+    "llm_symbolic_math.run('Solve the differential equation y\" - y = e^t')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "\n",
-      "\u001b[1m> Entering new LLMSymbolicMathChain chain...\u001b[0m\n",
-      "What are the solutions to this equation x**2 - x?\u001b[32;1m\u001b[1;3mAnswer: 0 and 1.\u001b[0m\n",
-      "\u001b[1m> Finished chain.\u001b[0m\n"
-     ]
-    },
     {
      "data": {
       "text/plain": [
-       "'Answer: 0 and 1.'"
+       "'Answer: {0, -sqrt(3)*I/3, sqrt(3)*I/3}'"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "llm_symbolic_math.run(\"What are the solutions to this equation x**2 - x?\")"
+    "llm_symbolic_math.run(\"What are the solutions to this equation y^3 + 1/3y?\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'Answer: (3 - sqrt(7), -sqrt(7) - 2, 1 - sqrt(7)), (sqrt(7) + 3, -2 + sqrt(7), 1 + sqrt(7))'"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "llm_symbolic_math.run(\"x = y + 5, y = z - 3, z = x * y. Solve for x, y, z\")"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "venv",
    "language": "python",
-   "name": "python3"
+   "name": "venv"
   },
   "language_info": {
    "codemirror_mode": {
@@ -152,7 +154,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.4"
+   "version": "3.11.3"
   }
  },
  "nbformat": 4,