init

Author: noppoMan

.gitignore

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+notebook/npmath/__pycache__
+*.*~
+notebook/.ipynb_checkpoints

README.md

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+# Pythonコードを交えて学ぶ関数解析
+
+こちらは、Pythonコードを交えて学ぶ関数解析
+
+* Booth: https://noppoman.booth.pm/items/2698852
+
+のサポートページになります。
+
+## ソースコードについて
+
+[notebook](https://github.com/noppoMan/learning-functional-analysis-with-python/tree/master/notebook)以下に、各章に対応するソースコードがあります。
+
+## 誤植や理論の訂正について
+
+誤植や理論の訂正に関しては、各書籍リビジョンに対応する[正誤表](https://github.com/noppoMan/learning-functional-analysis-with-python/tree/master/typographical-error)をご確認ください。書籍リビジョンは巻末に記載があります。リビジョンが更新された場合は、過去のリビジョンに関する修正は行われず、最新のものに対してのみ修正が加わります。

notebook/L2Space.png

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "import os\n",
+    "import numpy as np\n",
+    "import sympy as sym\n",
+    "from IPython.display import display, Math, Image"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "A: [0, 1, 2, 3, 4]\n",
+      "B: [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n"
+     ]
+    }
+   ],
+   "source": [
+    "A = [0, 1, 2, 3, 4]\n",
+    "B = np.arange(0, 1, 0.1)\n",
+    "\n",
+    "print(\"A:\", A)\n",
+    "print(\"B:\", B)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 実数"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "R(1.0) R(2.0)\n",
+      "<class 'npmath.space.MathSet'>\n",
+      "R(1.1) R(1.4)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from npmath.space import R, MathSet, IncompatibleElementTypeError, NotInError\n",
+    "\n",
+    "RSet = MathSet(lambda x: R(x))\n",
+    "\n",
+    "# 𝑎, b ∈ R\n",
+    "a, b = RSet.take(1., 2.)\n",
+    "print(a, b)\n",
+    "\n",
+    "# 𝐴 ⊂ R\n",
+    "A = RSet.subset([1.1, 1.2, 1.3, 1.4, 1.5])\n",
+    "print(type(A))\n",
+    "a, b = A.take(1.1, 1.4)\n",
+    "print(a, b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 is not in the Set\n"
+     ]
+    }
+   ],
+   "source": [
+    "try:\n",
+    "    A.take(10)\n",
+    "except NotInError as e:\n",
+    "    print(e)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "R(3.0)\n",
+      "R(-1.0)\n",
+      "R(2.0)\n",
+      "R(0.5)\n",
+      "False\n",
+      "True\n"
+     ]
+    }
+   ],
+   "source": [
+    "a, b = RSet.take(1., 2.)\n",
+    "print(a + b)\n",
+    "print(a - b)\n",
+    "print(a * b)\n",
+    "print(a / b)\n",
+    "\n",
+    "print(a == b)\n",
+    "print(a < b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "element type should be a float or int. not <str>\n",
+      "element type should be a float or int. not <function>\n"
+     ]
+    }
+   ],
+   "source": [
+    "try:\n",
+    "    RSet.take(\"hello world\")\n",
+    "except IncompatibleElementTypeError as e:\n",
+    "    print(e)\n",
+    "    \n",
+    "try:\n",
+    "    RSet.subset([1, 2, 3, lambda: 1 + 2])\n",
+    "except IncompatibleElementTypeError as e:\n",
+    "    print(e)    "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 自然数"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "N(1) N(2)\n",
+      "N(3)\n",
+      "N(2)\n",
+      "element type should be a natural number. not <int>\n"
+     ]
+    }
+   ],
+   "source": [
+    "from npmath.space import AnyElement, MathSet, IncompatibleElementTypeError, NotInError\n",
+    "\n",
+    "class N(AnyElement):\n",
+    "    def validate(self):\n",
+    "        error = IncompatibleElementTypeError(f\"element type should be a natural number. not <{type(self.value).__name__}>\")\n",
+    "        if type(self.value) is not int:\n",
+    "            raise error\n",
+    "            \n",
+    "        if self.value < 0:\n",
+    "            raise error\n",
+    "            \n",
+    "    def __add__(self, other):\n",
+    "        return self._operate(other, \"__add__\")\n",
+    "    \n",
+    "    def __mul__(self, other):\n",
+    "        return self._operate(other, \"__mul__\")\n",
+    "        \n",
+    "NSet = MathSet(N)\n",
+    "a, b = NSet.take(1, 2)\n",
+    "print(a, b)\n",
+    "    \n",
+    "print(a + b)\n",
+    "print(a * b)\n",
+    "\n",
+    "try:\n",
+    "    NSet.take(-1)\n",
+    "except IncompatibleElementTypeError as e:\n",
+    "    print(e)"
+   ]
+  }
+ ],
+ "metadata": {
+  "hide_code_all_hidden": false,
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.0"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": false,
+   "sideBar": true,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": true,
+   "toc_window_display": false
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}