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notebooks neu generiert

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Meik Hellmund 2024-04-08 14:20:54 +02:00
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2
_quarto.yml
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@ -72,7 +72,7 @@ format:
highlight-style: github # arrow ????? highlight-style: github # arrow ?????
mainfont: "Roboto Condensed" # Ubuntu # "Atkinson Hyperlegible" # Verdana #Quicksand mainfont: "Roboto Condensed" # Ubuntu # "Atkinson Hyperlegible" # Verdana #Quicksand
toc: true # change for Vorlesung toc: false # change for Vorlesung
toc-depth: 3 toc-depth: 3
number-depth: 3 number-depth: 3
email-obfuscation: javascript email-obfuscation: javascript

172
nb/10_Strings.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "29fd19a8", "id": "7c21d452",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Zeichen, Strings und Unicode\n", "# Zeichen, Strings und Unicode\n",
@ -64,7 +64,7 @@
"- davon entfallen über 90 000 Zeichen auf die CJK-Schriften (Chinesisch/Japanisch/Koreanisch) \n", "- davon entfallen über 90 000 Zeichen auf die CJK-Schriften (Chinesisch/Japanisch/Koreanisch) \n",
" \n", " \n",
" \n", " \n",
"### technische Details\n", "### Technische Details\n",
"\n", "\n",
"- Jedem Zeichen wird ein `codepoint` zugeordnet. Das ist einfach eine fortlaufende Nummer.\n", "- Jedem Zeichen wird ein `codepoint` zugeordnet. Das ist einfach eine fortlaufende Nummer.\n",
"- Diese Nummer wird hexadezimal notiert\n", "- Diese Nummer wird hexadezimal notiert\n",
@ -93,7 +93,7 @@
" - Laufrichtung der Schrift \n", " - Laufrichtung der Schrift \n",
" - Kategorie: Großbuchstabe, Kleinbuchstabe, modifizierender Buchstabe, Ziffer, Satzzeichen, Symbol, Seperator,....\n", " - Kategorie: Großbuchstabe, Kleinbuchstabe, modifizierender Buchstabe, Ziffer, Satzzeichen, Symbol, Seperator,....\n",
"\n", "\n",
"Im Unicode-Standard sieht das dann so aus: (zur Vereinfachung nur Codepoint und Name)\n", "Im Unicode-Standard sieht das dann so aus (zur Vereinfachung nur Codepoint und Name):\n",
"```\n", "```\n",
"...\n", "...\n",
"U+0041 LATIN CAPITAL LETTER A\n", "U+0041 LATIN CAPITAL LETTER A\n",
@ -117,7 +117,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8eaf4a41", "id": "48697b80",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -126,7 +126,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1c1f742a", "id": "568c932d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Eine Auswahl an Schriften \n", "### Eine Auswahl an Schriften \n",
@ -148,7 +148,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "823bfab7", "id": "44eecb07",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -165,7 +165,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "50893728", "id": "9857ec8a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"__Kyrillisch__\n" "__Kyrillisch__\n"
@ -174,7 +174,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8caca4e0", "id": "d1827fb6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -183,7 +183,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "4400710f", "id": "1975b4c8",
"metadata": {}, "metadata": {},
"source": [ "source": [
"__Tamilisch__\n", "__Tamilisch__\n",
@ -194,7 +194,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "85bb89e4", "id": "0ac169a1",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -205,7 +205,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3904378b", "id": "cf47c3ec",
"metadata": {}, "metadata": {},
"source": [ "source": [
"\\begingroup\\setmonofont{Noto Sans Tamil}\n" "\\begingroup\\setmonofont{Noto Sans Tamil}\n"
@ -214,7 +214,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "13461be4", "id": "4c539418",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -225,7 +225,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e8ed18a7", "id": "57b1dd19",
"metadata": {}, "metadata": {},
"source": [ "source": [
"\\endgroup\n", "\\endgroup\n",
@ -238,7 +238,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8f6b4cee", "id": "6d474a65",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -247,7 +247,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f9ca81ef", "id": "9c31ea8a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"__Mathematische Operatoren__\n" "__Mathematische Operatoren__\n"
@ -256,7 +256,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "60c00c29", "id": "58aaf4c5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -265,7 +265,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1e023c33", "id": "9b6c63b0",
"metadata": {}, "metadata": {},
"source": [ "source": [
"__Runen__\n" "__Runen__\n"
@ -274,7 +274,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "361517d3", "id": "88859f95",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -283,7 +283,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "067f18ed", "id": "08203fd6",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::{.cellmerge}\n", ":::{.cellmerge}\n",
@ -298,7 +298,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "9ac8d6c5", "id": "640c2422",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -309,7 +309,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ab85dc8a", "id": "ee56718c",
"metadata": {}, "metadata": {},
"source": [ "source": [
"\\begingroup\\setmonofont{Phaistos.otf}\n" "\\begingroup\\setmonofont{Phaistos.otf}\n"
@ -318,7 +318,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "599a342d", "id": "0a728045",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -329,7 +329,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c5ccd262", "id": "cfcb78f6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"\\endgroup\n", "\\endgroup\n",
@ -376,7 +376,7 @@
"\n", "\n",
"Der Datentyp `Char` kodiert ein einzelnes Unicode-Zeichen. \n", "Der Datentyp `Char` kodiert ein einzelnes Unicode-Zeichen. \n",
"\n", "\n",
"- Julia verwendet dafür einfachen Anführungszeichen: `'a'`. \n", "- Julia verwendet dafür einfache Anführungszeichen: `'a'`. \n",
"- Ein `Char` belegt 4 Bytes Speicher und \n", "- Ein `Char` belegt 4 Bytes Speicher und \n",
"- repräsentiert einen Unicode-Codepoint.\n", "- repräsentiert einen Unicode-Codepoint.\n",
"- `Char`s können von/zu `UInt`s umgewandelt werden und \n", "- `Char`s können von/zu `UInt`s umgewandelt werden und \n",
@ -392,7 +392,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a8ea6e75", "id": "707c245e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -401,7 +401,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ab924ce4", "id": "ce463383",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- `Char`s können von/zu `UInt`s umgewandelt werden.\n" "- `Char`s können von/zu `UInt`s umgewandelt werden.\n"
@ -410,7 +410,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "dac49645", "id": "6488fdf6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -420,7 +420,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "98bd57af", "id": "2637de2b",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -429,7 +429,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "74470851", "id": "985adab7",
"metadata": {}, "metadata": {},
"source": [ "source": [
"__Bei einem Nicht-ASCII-String unterscheiden sich Anzahl der Bytes und Anzahl der Zeichen:__\n" "__Bei einem Nicht-ASCII-String unterscheiden sich Anzahl der Bytes und Anzahl der Zeichen:__\n"
@ -438,7 +438,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0edfc402", "id": "53c741c8",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -448,7 +448,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "2c2ce448", "id": "bf536c2d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(Das Leerzeichen zählt natürlich auch.)\n" "(Das Leerzeichen zählt natürlich auch.)\n"
@ -457,7 +457,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c171aa8d", "id": "37e36e85",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -467,7 +467,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e0467145", "id": "b9caf74d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"__Iteration über einen String iteriert über die Zeichen:__\n" "__Iteration über einen String iteriert über die Zeichen:__\n"
@ -476,7 +476,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "802e421f", "id": "0e8e04e3",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -487,7 +487,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b434c61b", "id": "ce0cfd1b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Verkettung von Strings\n", "### Verkettung von Strings\n",
@ -500,7 +500,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "dba97090", "id": "6f35d90f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -509,7 +509,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c2f3a520", "id": "898a6ea1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Damit sind auch Potenzen mit natürlichem Exponenten definiert.\n" "Damit sind auch Potenzen mit natürlichem Exponenten definiert.\n"
@ -518,7 +518,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e8804720", "id": "cb9d7217",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -527,7 +527,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ffd0fd4c", "id": "cc89a9ca",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Stringinterpolation\n", "### Stringinterpolation\n",
@ -539,7 +539,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b8248a55", "id": "16b8af0a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -551,7 +551,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b2039521", "id": "1ddcc1ad",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Backslash escape sequences \n", "### Backslash escape sequences \n",
@ -563,7 +563,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f896516b", "id": "64a50bab",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -573,7 +573,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6258cdb2", "id": "f8a758f6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Triple-Quotes\n", "### Triple-Quotes\n",
@ -585,7 +585,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e7913161", "id": "a042c5ed",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -600,7 +600,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "15de1886", "id": "7ff4c2dd",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Raw strings\n", "### Raw strings\n",
@ -611,7 +611,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a040859a", "id": "929529cf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -621,7 +621,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6e24746e", "id": "0040e4d6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Weitere Funktionen für Zeichen und Strings (Auswahl)\n", "## Weitere Funktionen für Zeichen und Strings (Auswahl)\n",
@ -632,7 +632,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f79e914f", "id": "195a2a3e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -642,7 +642,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d39076f7", "id": "2e50dae6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Anwendung auf Strings\n", "### Anwendung auf Strings\n",
@ -653,7 +653,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b6055040", "id": "c778a4ad",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -663,7 +663,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "29fd91ef", "id": "6a162d83",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -673,7 +673,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "73a589b9", "id": "c2d57533",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -682,7 +682,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "5bdff431", "id": "f6562800",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Weitere String-Funktionen\n" "### Weitere String-Funktionen\n"
@ -691,7 +691,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a24b1569", "id": "495799ef",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -702,7 +702,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "89003024", "id": "13e4d303",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -712,7 +712,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "01910748", "id": "36451c74",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -724,7 +724,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d618c466", "id": "a665d380",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -734,7 +734,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "da05d6b9", "id": "64967f02",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -743,7 +743,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "4e198e74", "id": "663832cf",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Indizierung von Strings\n", "## Indizierung von Strings\n",
@ -760,7 +760,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4686b303", "id": "23d51f20",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -769,7 +769,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6c1a2fe1", "id": "639c88fa",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Das erste Zeichen\n" "Das erste Zeichen\n"
@ -778,7 +778,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "eb0e9898", "id": "68ba5cb6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -787,7 +787,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "50049fee", "id": "44617a04",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Dieses Zeichen ist in UTF8-Kodierung 4 Bytes lang. Damit sind 2,3 und 4 ungültige Indizes. \n" "Dieses Zeichen ist in UTF8-Kodierung 4 Bytes lang. Damit sind 2,3 und 4 ungültige Indizes. \n"
@ -796,7 +796,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a6a3005a", "id": "c4575cca",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -805,7 +805,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "5c428767", "id": "e558202c",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Erst das 5. Byte ist ein neues Zeichen:\n" "Erst das 5. Byte ist ein neues Zeichen:\n"
@ -814,7 +814,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "29febb49", "id": "3813bbdf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -823,7 +823,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0daa1973", "id": "48f4cca9",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Auch bei der Adressierung von Substrings müssen Anfang und Ende jeweils gültige Indizes sein, d.h., der Endindex muss ebenfalls das erste Byte eines Zeichens indizieren und dieses Zeichen ist das letzte des Teilstrings. \n" "Auch bei der Adressierung von Substrings müssen Anfang und Ende jeweils gültige Indizes sein, d.h., der Endindex muss ebenfalls das erste Byte eines Zeichens indizieren und dieses Zeichen ist das letzte des Teilstrings. \n"
@ -832,7 +832,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "dbbc0c47", "id": "546d4ed2",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -841,7 +841,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b7fd7042", "id": "1007a717",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Funktion `eachindex()` liefert einen Iterator über die gültigen Indizes:\n" "Die Funktion `eachindex()` liefert einen Iterator über die gültigen Indizes:\n"
@ -850,7 +850,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6e2b8427", "id": "d01e440e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -862,7 +862,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f651e9bf", "id": "2f35e6bf",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Wie üblich macht collect() aus einem Iterator einen Vektor.\n" "Wie üblich macht collect() aus einem Iterator einen Vektor.\n"
@ -871,7 +871,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a591c148", "id": "b1644ea5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -880,7 +880,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "a7f9cb60", "id": "dc77d9e5",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Funktion `nextind()` liefert den nächsten gültigen Index.\n" "Die Funktion `nextind()` liefert den nächsten gültigen Index.\n"
@ -889,7 +889,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d568dd47", "id": "5c9f35e7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -898,7 +898,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "91af5e34", "id": "6d1e346b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Warum verwendet Julia einen Byte-Index und keinen Zeichenindex? Der Hauptgrund dürfte die Effizienz der Indizierung sein.\n", "Warum verwendet Julia einen Byte-Index und keinen Zeichenindex? Der Hauptgrund dürfte die Effizienz der Indizierung sein.\n",
@ -913,7 +913,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b62bbd82", "id": "e1ec4807",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -923,7 +923,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "93def2b5", "id": "2f8520fd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -933,7 +933,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e96565a7", "id": "0f07cff3",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -943,7 +943,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e251544c", "id": "19e5bcc4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -952,7 +952,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "be81789e", "id": "f614e688",
"metadata": {}, "metadata": {},
"source": [ "source": [
"So kann man ab dem nächsten nach `n=5` gültigen Index weitersuchen:\n" "So kann man ab dem nächsten nach `n=5` gültigen Index weitersuchen:\n"
@ -961,7 +961,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ad89b2c9", "id": "3f3b90b4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -971,15 +971,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.5"
} }
}, },
"nbformat": 4, "nbformat": 4,

391
nb/5_TricksHelp.ipynb
View File

@ -2,35 +2,29 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "2ffe347c", "id": "32301000",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Julia Dokumentation\n", "# Arbeit mit Julia: REPL, Pakete, Introspection\n",
"\n", "\n",
"[https://docs.julialang.org/](https://docs.julialang.org/) die offizielle Dokumentation\n",
"\n", "\n",
"Einige Seiten mit Übersichten:\n", "\n",
"## Dokumentation\n",
"\n",
"Die offizielle Julia-Dokumentation [https://docs.julialang.org/](https://docs.julialang.org/) enthält zahlreiche Übersichten, darunter:\n",
"\n", "\n",
" - [https://docs.julialang.org/en/v1/base/punctuation/](https://docs.julialang.org/en/v1/base/punctuation/) Verzeichnis der Symbole\n", " - [https://docs.julialang.org/en/v1/base/punctuation/](https://docs.julialang.org/en/v1/base/punctuation/) Verzeichnis der Symbole\n",
" - [https://docs.julialang.org/en/v1/manual/unicode-input/](https://docs.julialang.org/en/v1/manual/unicode-input/) Verzeichnis spezieller Unicode-Symbole und deren Eingabe in Julia via Tab-Vervollständigung\n", " - [https://docs.julialang.org/en/v1/manual/unicode-input/](https://docs.julialang.org/en/v1/manual/unicode-input/) Verzeichnis spezieller Unicode-Symbole und deren Eingabe in Julia via Tab-Vervollständigung\n",
" - [https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions](https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions) Liste mathematischer Funktionen \n", " - [https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions](https://docs.julialang.org/en/v1/manual/mathematical-operations/#Rounding-functions) Liste mathematischer Funktionen \n",
"\n", "\n",
"---------\n",
"\n", "\n",
"\n", "\n",
"\n", "\n",
"# Hilfe und praktische Tipps\n",
"\n",
"----\n",
"\n",
"\n",
"## Julia REPL (Read - Eval - Print - Loop)\n", "## Julia REPL (Read - Eval - Print - Loop)\n",
"\n", "\n",
"Start von Julia in einem Terminal:\n", "Nach dem Start von Julia in einem Terminal kann man neben Julia-Code auch verschiedene Kommandos eingeben \n",
"```\n",
"julia>\n",
"```\n",
"\n", "\n",
":::{.narrow}\n",
"| Kommando | Wirkung |\n", "| Kommando | Wirkung |\n",
"| :----------------------------| :------------------------ |\n", "| :----------------------------| :------------------------ |\n",
"| `exit()` oder `Ctrl-d` | exit Julia |\n", "| `exit()` oder `Ctrl-d` | exit Julia |\n",
@ -40,28 +34,23 @@
"| `include(\"filename.jl\")` | Datei mit Julia-Code einlesen und ausführen |\n", "| `include(\"filename.jl\")` | Datei mit Julia-Code einlesen und ausführen |\n",
"\n", "\n",
"\n", "\n",
"-----\n",
"\n", "\n",
"Der REPL hat verschiedene Modi: \n", "Der REPL hat verschiedene Modi: \n",
"\n", "\n",
"| Modus | Prompt | Modus starten | Modus verlassen |\n", "| Modus | Prompt | Modus starten | Modus verlassen |\n",
"| :- | :- | :- | :- |\n", "| :- | :- | :- | :- |\n",
"|||||\n", "| default| `julia>` | | `Ctrl-d`|\n",
"| default| `julia>` | | |\n",
"|||||\n",
"| Package manager | `pkg>` | `]` | `backspace` |\n", "| Package manager | `pkg>` | `]` | `backspace` |\n",
"|||||\n",
"| Help | `help?>` | `?`| `backspace `|\n", "| Help | `help?>` | `?`| `backspace `|\n",
"|||||\n",
"|Shell | `shell>` | `;` | `backspace`|\n", "|Shell | `shell>` | `;` | `backspace`|\n",
"|||||\n",
"\n", "\n",
"--------\n", ":::\n",
"\n", "\n",
"\n", "\n",
"## Jupyter notebooks (IJulia)\n", "## Jupyter-Notebooks (IJulia)\n",
"\n", "\n",
"Die Modi sind als Einzeiler in einer eigenen Input-Zelle nutzbar: \n", "\n",
"In einem Jupyter-Notebook sind die Modi sind als Einzeiler in einer eigenen Input-Zelle nutzbar: \n",
"\n", "\n",
"(i) ein Kommando des Paket-Managers:\n" "(i) ein Kommando des Paket-Managers:\n"
] ]
@ -69,16 +58,17 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d6c200e5", "id": "efacde4f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"#| eval: false\n",
"] status " "] status "
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "9caf3630", "id": "85fec425",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(ii) eine Help-Abfrage:\n" "(ii) eine Help-Abfrage:\n"
@ -87,16 +77,17 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c923aa16", "id": "80535b76",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"#| eval: false\n",
"?sin" "?sin"
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "bfc75d15", "id": "581aae68",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(iii) Ein Shell-Kommando:\n" "(iii) Ein Shell-Kommando:\n"
@ -105,44 +96,53 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3617aff8", "id": "c2438155",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
";ls .." "#| eval: false\n",
";ls "
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "bdce3ab2", "id": "bd2c64b7",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Der Paket-Manager\n", "## Der Paketmanager\n",
"\n", "\n",
"- Über 7000 Pakete, siehe [https://julialang.org/packages/](https://julialang.org/packages/)\n", "Wichtiger Teil des _Julia Ecosystems_ sind die zahlreichen Pakete, die Julia erweitern.\n",
"- Bevor sie mit `using Module` verwendet werden können, müssen sie heruntergeladen und installiert werden.\n", "\n",
"- Dazu dient der `package manager`\n", "- Einige Pakete sind Teil jeder Julia-Installation und müssen nur mit einer `using Paketname`-Anweisung aktiviert werden. \n",
"- 2 Betriebsarten: \n", " - Sie bilden die sogenannte _Standard Library_ und dazu gehören \n",
" - als normale Julia-Anweisungen, die auch in einer `.jl`-Programmdatei stehen können:\n", " - `LinearAlgebra`, `Statistics`, `SparseArrays`, `Printf`, `Pkg` und andere.\n",
"- Über 9000 Pakete sind offiziell registriert, siehe [https://julialang.org/packages/](https://julialang.org/packages/). \n",
" - Diese können mit wenigen Tastendrücken heruntergeladen und installiert werden.\n",
" - Dazu dient der _package manager_ `Pkg`.\n",
" - Man kann ihn auf zwei Arten verwenden: \n",
" - als normale Julia-Anweisungen, die auch in einer `.jl`-Programmdatei stehen können:\n",
" ```\n", " ```\n",
" using Pkg\n", " using Pkg\n",
" Pkg.add(\"TollesPaket\")\n", " Pkg.add(\"PaketXY\")\n",
" ```\n", " ```\n",
" - im speziellen pkg-Modus des Julia-REPLs:\n", " - im speziellen pkg-Modus des Julia-REPLs:\n",
" ```\n", " ```\n",
" ] add TollesPaket\n", " ] add PaketXY\n",
" ```\n", " ```\n",
"----- \n", " - Anschließend kann das Paket mit `using PaketXY` verwendet werden.\n",
"- Man kann auch Pakete aus anderen Quellen und selbstgeschriebene Pakete installieren.\n",
"\n", "\n",
"### Einige Funktionen\n", " \n",
"### Einige Funktionen des Paketmanagers\n",
"\n", "\n",
"| Funktion | `pkg` - Mode | Erklärung |\n", "| Funktion | `pkg` - Mode | Erklärung |\n",
"|:------------------------|:----------------------|:----------------------------------------------------------|\n", "|:------------------------|:--------------------------| :-------------------------------------------------------|\n",
"| `Pkg.add(\"MyPack\")` | `pkg> add MyPack` | add `MyPack.jl` to current environment |\n", "| `Pkg.add(\"MyPack\")` | `pkg> add MyPack` | add `MyPack.jl` to current environment |\n",
"| `Pkg.rm(\"MyPack\")` | `pkg> remove MyPack` | remove `MyPack.jl` from current environment |\n", "| `Pkg.rm(\"MyPack\")` | `pkg> remove MyPack` | remove `MyPack.jl` from current environment |\n",
"| `Pkg.update()` | `pkg> update` | update packages in current environment |\n", "| `Pkg.update()` | `pkg> update` | update packages in current environment |\n",
"| `Pkg.activate(\"mydir\")` | `pkg> activate mydir` | activate directory as current environment |\n", "| `Pkg.activate(\"mydir\")` | `pkg> activate mydir` | activate directory as current environment |\n",
"| `Pkg.status()` | `pkg> status` | list packages |\n", "| `Pkg.status()` | `pkg> status` | list packages |\n",
"| `Pkg.instantiate()` | `pg> instantiate` | install all packages according to `Project.toml` |\n",
"\n", "\n",
"\n", "\n",
"### Installierte Pakete und Environments \n", "### Installierte Pakete und Environments \n",
@ -152,308 +152,95 @@
" 2. eine Liste aller dabei auch als implizite Abhängigkeiten installierten Pakete in der Datei `Manifest.toml`. \n", " 2. eine Liste aller dabei auch als implizite Abhängigkeiten installierten Pakete in der Datei `Manifest.toml`. \n",
"- Das Verzeichnis, in dem diese Dateien stehen, ist das `environment` und wird mit `Pkg.status()` bzw. `]status` angezeigt. \n", "- Das Verzeichnis, in dem diese Dateien stehen, ist das `environment` und wird mit `Pkg.status()` bzw. `]status` angezeigt. \n",
"- Im Normalfall sieht das so aus: \n", "- Im Normalfall sieht das so aus: \n",
"\n",
"```\n", "```\n",
"(@v1.7) pkg> status\n", "(@v1.8) pkg> status\n",
" Status `~/.julia/environments/v1.7/Project.toml`\n", " Status `~/.julia/environments/v1.8/Project.toml`\n",
" [1dea7af3] OrdinaryDiffEq v6.7.1\n", " [1dea7af3] OrdinaryDiffEq v6.7.1\n",
" [91a5bcdd] Plots v1.27.1\n", " [91a5bcdd] Plots v1.27.1\n",
" [438e738f] PyCall v1.93.1\n", " [438e738f] PyCall v1.93.1\n",
"```\n", "```\n",
"\n",
"- Man kann für verschiedene Projekte eigene `environments` benutzen. Dazu kann man entweder Julia mit \n", "- Man kann für verschiedene Projekte eigene `environments` benutzen. Dazu kann man entweder Julia mit \n",
"```\n", "```shell\n",
"julia --project=path/to/myproject\n", "julia --project=path/to/myproject\n",
"```\n", "```\n",
"starten oder in Julia das environment mit `Pkg.activate(\"path/to/myproject\")` aktivieren. Dann werden `Project.toml, Manifest.toml` dort angelegt und verwaltet. (Die Installation der Paketdateien erfolgt weiterhin irgendwo unter `$HOME/.julia`) \n", "starten oder in Julia das environment mit `Pkg.activate(\"path/to/myproject\")` aktivieren. Dann werden `Project.toml, Manifest.toml` dort angelegt und verwaltet. (Die Installation der Paketdateien erfolgt weiterhin irgendwo unter `$HOME/.julia`) \n",
"\n", "\n",
"\n", "\n",
"### Zum Installieren von Paketen auf unserem Jupyter-Server `misun103`:\n", "### Zum Installieren von Paketen auf unserem Jupyter-Server `misun103`:\n",
"- Es gibt ein zentrales Repository, in dem alle von mir erwähnten Pakete bereits installiert sind. \n", "\n",
"- Es gibt ein zentrales Repository, in dem alle in diesem Kurs erwähnten Pakete bereits installiert sind. \n",
"- Dort haben Sie keine Schreibrechte.\n", "- Dort haben Sie keine Schreibrechte.\n",
"- Sie können aber zusätzliche Pakete in Ihrem `Home` installieren. Dazu ist als erster Befehl nötig, das aktuelle Verzeichnis zu aktivieren: \n" "- Sie können aber zusätzliche Pakete in Ihrem `HOME` installieren. Dazu ist als erster Befehl nötig, das aktuelle Verzeichnis zu aktivieren: \n"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "103bd8a1", "id": "87138f78",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"#| eval: false\n",
"] activate ." "] activate ."
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "077e93f2", "id": "da9c6bb6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(Man beachte den Punkt!)\n", "(Man beachte den Punkt!)\n",
"\n", "\n",
"----\n",
"\n", "\n",
"Danach können Sie mit `add` im Pkg-Modus auch Pakete installieren:\n", "Danach können Sie mit `add` im Pkg-Modus auch Pakete installieren:\n"
"\n",
"```\n",
"] add TollesPaket\n",
"```\n",
"\n",
"\n",
"Achtung! Das kann dauern! Viele Pakete haben komplexe Abhängigkeiten und lösen die Installation von weiteren Paketen aus. Viele Pakete werden beim Installieren vorkompiliert. Im REPL sieht man den Installationsfortschritt, im Jupyter-Notebook nicht.\n",
"\n",
"\n",
"## Eingebaute Hilfe und Informationen\n",
"Mit `?` und der `Tab`-Taste kommt man oft weiter. \n",
"\n",
"\n",
"\n",
"### weitere Hilfe: `@which`, `fieldnames()`, `methods()`, `names()`, `pwd()`\n"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4f099673", "id": "7a9e6ab0",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"# Die Zuordnung zu einem Modul zeigt @which an:\n", "#| eval: false\n",
"\n", "] add PaketXY"
"@which(sqrt)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "44276c0d",
"metadata": {},
"outputs": [],
"source": [
"# Die Komponenten einer struct oder eines anderen zusammengesetzten Typs:\n",
"\n",
"fieldnames(Rational)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a200a34f",
"metadata": {},
"outputs": [],
"source": [
"fieldnames(Complex)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d99bfda9",
"metadata": {},
"outputs": [],
"source": [
"# alle Methoden einer Funktion\n",
"\n",
"methods(sqrt)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b3e6f127",
"metadata": {},
"outputs": [],
"source": [
"# alle Methoden einer Funktion bei bestimmten Argumenttypen. Die Argumenttypen müssen als Tupel angegeben werden\n",
"\n",
"methods(sqrt, (Number,)) # Komma nötig für 1-elementiges Tupel "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e74572ad",
"metadata": {},
"outputs": [],
"source": [
"# für einen Typ gibt methods() alle Konstruktoren aus\n",
"\n",
"methods(Int64)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e4de6078",
"metadata": {},
"outputs": [],
"source": [
"# names(Module) gibt alle von einem Modul exportierte Namen aus. \n",
"# genau wie auch\n",
"#\n",
"# ?Module \n",
"#\n",
"# funktioniert es erst, wenn das Modul mit 'using Module' geladen ist.\n",
"# Oft ist es besser, wenn die using-Anweisung in einer eigenen Zelle steht.\n",
"\n",
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f1df8377",
"metadata": {},
"outputs": [],
"source": [
"names(Plots)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3654fab2",
"metadata": {},
"outputs": [],
"source": [
"# Julia kürzt den interaktiven Output. \n",
"# ein explizites print() zeigt alles:\n",
"\n",
"print(names(Plots))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dc9ca3b6",
"metadata": {},
"outputs": [],
"source": [
"# eine andere Möglichkeit der Ausgabe mit Überlänge in Jupyter\n",
"\n",
"show(stdout, MIME(\"text/plain\"), names(Plots))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9fa0f216",
"metadata": {},
"outputs": [],
"source": [
"# pwd() \"print working directory\" zeigt, in welchem Verzeichnis Julia gerade operiert. \n",
"#\n",
"# Wichtig für die Ein/Ausgabe mit Dateien, z.B. include()\n",
"\n",
"pwd()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "99c19918",
"metadata": {},
"outputs": [],
"source": [
"include(\"Jupyter.jl\") # Datei mit Julia-Code einlesen und abarbeiten"
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1464d951", "id": "d5fc8aef",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Informationen zu Typen\n", "Achtung! Das kann dauern! Viele Pakete haben komplexe Abhängigkeiten und lösen die Installation von weiteren Paketen aus. Viele Pakete werden beim Installieren vorkompiliert. Im REPL sieht man den Installationsfortschritt, im Jupyter-Notebook leider nicht.\n",
"\n", "\n",
"### `subtypes()`, `supertypes()`, `typemax()`, `typemin()`, `fieldnames()`, `Base.return_types()`, `dump()`\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1358c363",
"metadata": {},
"outputs": [],
"source": [
"subtypes(Real) # die letzten zwei sind durch das 'using Plots' dazugekommen"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e35fb7da",
"metadata": {},
"outputs": [],
"source": [
"supertypes(Real)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "53be4687",
"metadata": {},
"outputs": [],
"source": [
"typemax(Int64), typemin(Int64), fieldnames(Complex)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3a9ed940",
"metadata": {},
"outputs": [],
"source": [
"Base.return_types(sqrt, (Float64,))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "207af4bd",
"metadata": {},
"outputs": [],
"source": [
"Base.return_types(sqrt, (Complex{Int64},))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "66b42304",
"metadata": {},
"outputs": [],
"source": [
"# dump() zeigt alle Teile eines zusammengesetzten Objekts\n",
"\n", "\n",
"x = 3//4 + 75im\n", "\n",
"dump(x)" "\n",
] "\n",
}, "## Der Julia JIT _(just in time)_ Compiler: Introspection\n",
{
"cell_type": "markdown",
"id": "9c6edfea",
"metadata": {},
"source": [
"## Der Julia JIT _(just in time)_ Compiler\n",
"\n", "\n",
"Julia baut auf die Werkzeuge des _LLVM Compiler Infrastructure Projects_ auf.\n", "Julia baut auf die Werkzeuge des _LLVM Compiler Infrastructure Projects_ auf.\n",
"\n", "\n",
"\n", ":::{.narrow}\n",
"Stages of Compilation \n", "Stages of Compilation \n",
"\n", "\n",
"| stage & result | introspection command |\n", "| stage & result | introspection command |\n",
"| :--- | :--- |\n", "| :--- | :--- |\n",
"|Parse ==> Abstract Syntax Tree (AST) | `Meta.parse()` |\n", "|Parse $\\Longrightarrow$ Abstract Syntax Tree (AST) | `Meta.parse()` |\n",
"| Lowering: transform AST ==> Static Single Assignment (SSA) form | `@code_lowered`|\n", "| Lowering: transform AST $\\Longrightarrow$ Static Single Assignment (SSA) form | `@code_lowered`|\n",
"| Type Inference | `@code_warntype`, `@code_typed` |\n", "| Type Inference | `@code_warntype`, `@code_typed` |\n",
"| Generate LLVM intermediate representation | `@code_llvm`|\n", "| Generate LLVM intermediate representation | `@code_llvm`|\n",
"| Generate native machine code | `@code_native` |\n" "| Generate native machine code | `@code_native` |\n",
"\n",
":::\n"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4d433ab8", "id": "bc5fdcec",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -466,7 +253,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "de444d8a", "id": "bb56b5a6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -476,27 +263,19 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "1ddf17aa", "id": "9a8825dd",
"metadata": {},
"outputs": [],
"source": [
"using TreeView"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "70d267d7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"using TreeView\n",
"\n",
"walk_tree(p)" "walk_tree(p)"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b19b64ec", "id": "aa2d2ada",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -506,7 +285,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "57eb03f9", "id": "e6303b02",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -516,7 +295,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "cf273a25", "id": "05f5a0cd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -526,7 +305,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "28779f6b", "id": "523e86a5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -536,7 +315,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "02711d1f", "id": "953d5e83",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -546,15 +325,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.5"
} }
}, },
"nbformat": 4, "nbformat": 4,

514
nb/6_ArraysEtcP1.ipynb
View File

@ -2,14 +2,14 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "fcc03529", "id": "81cc02aa",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Container\n", "# Container\n",
"\n", "\n",
"\n", "\n",
"Julia bietet eine große Auswahl von Containertypen mit weitgehend ähnlichem Interface an. \n", "Julia bietet eine große Auswahl von Containertypen mit weitgehend ähnlichem Interface an. \n",
"Wir stellen hier `Tuple`, `Range`, `Array`, `Vector` und `Matrix` vor. \n", "Wir stellen hier `Tuple`, `Range` und `Dict` vor, im nächsten Kapitel dann `Array`, `Vector` und `Matrix`. \n",
"\n", "\n",
"Diese Container sind: \n", "Diese Container sind: \n",
"\n", "\n",
@ -21,9 +21,9 @@
"```julia\n", "```julia\n",
"x = container[i]\n", "x = container[i]\n",
"``` \n", "``` \n",
"und einige sind \n", "und einige sind auch \n",
"\n", "\n",
"- **mutierbar** (nur `Array`, `Vector` und `Matrix`): Man kann Elemente hinzufügen, entfernen und ändern.\n", "- **mutierbar**: Man kann Elemente hinzufügen, entfernen und ändern.\n",
"\n", "\n",
"Weiterhin gibt es eine Reihe gemeinsamer Funktionen, z.B.\n", "Weiterhin gibt es eine Reihe gemeinsamer Funktionen, z.B.\n",
"\n", "\n",
@ -41,7 +41,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3b33212e", "id": "ec893f0b",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -54,7 +54,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e65e4da8", "id": "21549769",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Ein Tupel ist ein **inhomogener** Typ. Jedes Element hat seinen eigenen Typ und das zeigt sich auch im Typ des Tupels:\n" "Ein Tupel ist ein **inhomogener** Typ. Jedes Element hat seinen eigenen Typ und das zeigt sich auch im Typ des Tupels:\n"
@ -63,7 +63,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3d21cc5b", "id": "5add8abb",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -72,7 +72,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "74fcc47e", "id": "e8bc972e",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Man verwendet Tupel gerne als Rückgabewerte von Funktionen, um mehr als ein Objekt zurückzulieferen.\n" "Man verwendet Tupel gerne als Rückgabewerte von Funktionen, um mehr als ein Objekt zurückzulieferen.\n"
@ -81,7 +81,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6ffc0cdc", "id": "85b3f1fd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -94,7 +94,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e7a04cdd", "id": "d144679d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Wie man hier sieht, kann man in bestimmten Konstrukten die Klammern auch weglassen.\n", "Wie man hier sieht, kann man in bestimmten Konstrukten die Klammern auch weglassen.\n",
@ -104,7 +104,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2a260b6e", "id": "2ef18811",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -114,7 +114,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3447dffb", "id": "759e8783",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -123,7 +123,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "8694ec4a", "id": "2bed8606",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Manche Funktionen bestehen auf Tupeln als Argument oder geben immer Tupeln zurück. Dann braucht man manchmal ein Tupel aus einem Element. \n", "Manche Funktionen bestehen auf Tupeln als Argument oder geben immer Tupeln zurück. Dann braucht man manchmal ein Tupel aus einem Element. \n",
@ -134,7 +134,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "24856f9b", "id": "e985c23d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -143,7 +143,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "11ac465d", "id": "174aed3a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Das Komma - und nicht die Klammern -- macht das Tupel. \n" "Das Komma - und nicht die Klammern -- macht das Tupel. \n"
@ -152,7 +152,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "87474e9d", "id": "8359e689",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -161,7 +161,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "da35087d", "id": "a5fb2b62",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Ranges\n", "## Ranges\n",
@ -172,7 +172,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3bfc9415", "id": "ba823baf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -182,7 +182,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "7d2c6838", "id": "6dd2ebf4",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Es gibt verschiedene *range*-Typen. Wie man sieht, sind es über den Zahlentyp parametrisierte Typen und `UnitRange` ist z.B. ein *range* mit der Schrittweite 1. Ihre Konstruktoren heißen in der Regel `range()`. \n", "Es gibt verschiedene *range*-Typen. Wie man sieht, sind es über den Zahlentyp parametrisierte Typen und `UnitRange` ist z.B. ein *range* mit der Schrittweite 1. Ihre Konstruktoren heißen in der Regel `range()`. \n",
@ -199,7 +199,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "28aecb9e", "id": "5ee0a9ef",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -208,7 +208,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "350affb7", "id": "f4524b63",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Wir erinnern an die Semantik der `for`-Schleife: `for i in 1:1000` heißt **nicht**:\n", "Wir erinnern an die Semantik der `for`-Schleife: `for i in 1:1000` heißt **nicht**:\n",
@ -228,7 +228,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "14ea84bd", "id": "7049d454",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -238,7 +238,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c900fd32", "id": "dbc66a57",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -247,7 +247,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0a763f8b", "id": "3d98f5f4",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Zum Umwandeln in einen 'richtigen' Vektor dient die Funktion `collect()`.\n" "Zum Umwandeln in einen 'richtigen' Vektor dient die Funktion `collect()`.\n"
@ -256,7 +256,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0e0be9dd", "id": "fe033c47",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -265,7 +265,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "568f2f9f", "id": "a94e5258",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Recht nützlich, z.B. beim Vorbereiten von Daten zum Plotten, ist der *range*-Typ `LinRange`.\n" "Recht nützlich, z.B. beim Vorbereiten von Daten zum Plotten, ist der *range*-Typ `LinRange`.\n"
@ -274,7 +274,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8596862b", "id": "e4b40085",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -283,19 +283,471 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f148954b", "id": "bde8b38f",
"metadata": {}, "metadata": {},
"source": [ "source": [
"`LinRange(start, stop, n)` erzeugt eine äquidistante Liste von `n` Werten von denen der erste und der letzte die vorgegebenen Grenzen sind. \n", "`LinRange(start, stop, n)` erzeugt eine äquidistante Liste von `n` Werten von denen der erste und der letzte die vorgegebenen Grenzen sind. \n",
"Mit `collect()` kann man bei Bedarf auch daraus den entsprechenden Vektor gewinnen.\n" "Mit `collect()` kann man bei Bedarf auch daraus den entsprechenden Vektor gewinnen.\n",
"\n",
"\n",
"## Dictionaries \n",
"\n",
"- _Dictionaries_ (deutsch: \"assoziative Liste\" oder \"Zuordnungstabelle\" oder ...) sind spezielle Container. \n",
"- Einträge in einem Vektor `v` sind durch einen Index 1,2,3.... addressierbar: `v[i]`\n",
"- Einträge in einem _dictionary_ sind durch allgemeinere _keys_ addressierbar. \n",
"- Ein _dictionary_ ist eine Ansammlung von _key-value_-Paaren.\n",
"- Damit haben _dictionaries_ in Julia den parametrisierten Typ `Dict{S,T}`, wobei `S` der Typ der _keys_ und `T` der Typ der _values_ ist\n",
"\n",
"\n",
"Man kann sie explizit anlegen:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "25c7aefc",
"metadata": {},
"outputs": [],
"source": [
"# Einwohner 2020 in Millionen, Quelle: wikipedia\n",
"\n",
"EW = Dict(\"Berlin\" => 3.66, \"Hamburg\" => 1.85, \n",
" \"München\" => 1.49, \"Köln\" => 1.08)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9620f365",
"metadata": {},
"outputs": [],
"source": [
"typeof(EW)"
]
},
{
"cell_type": "markdown",
"id": "d3b4d2af",
"metadata": {},
"source": [
"und mit den _keys_ indizieren:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "62938a1b",
"metadata": {},
"outputs": [],
"source": [
"EW[\"Berlin\"]"
]
},
{
"cell_type": "markdown",
"id": "73ddf61d",
"metadata": {},
"source": [
"Das Abfragen eines nicht existierenden _keys_ ist natürlich ein Fehler.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6e16eb41",
"metadata": {},
"outputs": [],
"source": [
"EW[\"Leipzig\"]"
]
},
{
"cell_type": "markdown",
"id": "49a6d001",
"metadata": {},
"source": [
"Man kann ja auch vorher mal anfragen...\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e43aec5d",
"metadata": {},
"outputs": [],
"source": [
"haskey(EW, \"Leipzig\")"
]
},
{
"cell_type": "markdown",
"id": "a1cefaa1",
"metadata": {},
"source": [
"... oder die Funktion `get(dict, key, default)` benutzen, die bei nicht existierendem Key keinen Fehler wirft sondern das 3. Argument zurückgibt. \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e31c792c",
"metadata": {},
"outputs": [],
"source": [
"@show get(EW, \"Leipzig\", -1) get(EW, \"Berlin\", -1);"
]
},
{
"cell_type": "markdown",
"id": "f625eaaa",
"metadata": {},
"source": [
"Man kann sich auch alle `keys` und `values` als spezielle Container geben lassen.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "21460e3a",
"metadata": {},
"outputs": [],
"source": [
"keys(EW)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a87d9788",
"metadata": {},
"outputs": [],
"source": [
"values(EW)"
]
},
{
"cell_type": "markdown",
"id": "97b96369",
"metadata": {},
"source": [
"Man kann über die `keys` iterieren...\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "41e9189f",
"metadata": {},
"outputs": [],
"source": [
"for i in keys(EW)\n",
" n = EW[i]\n",
" println(\"Die Stadt $i hat $n Millionen Einwohner.\")\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "b2fe653a",
"metadata": {},
"source": [
"odere gleich über `key-value`-Paare.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0b445207",
"metadata": {},
"outputs": [],
"source": [
"for (stadt, ew) ∈ EW\n",
" println(\"$stadt : $ew Mill.\")\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "6fcd4019",
"metadata": {},
"source": [
"### Erweitern und Modifizieren\n",
"\n",
"Man kann in ein `Dict` zusätzliche `key-value`-Paare eintragen...\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "94c4f076",
"metadata": {},
"outputs": [],
"source": [
"EW[\"Leipzig\"] = 0.52\n",
"EW[\"Dresden\"] = 0.52 \n",
"EW"
]
},
{
"cell_type": "markdown",
"id": "ed90d684",
"metadata": {},
"source": [
"und einen `value` ändern.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c57e8dd2",
"metadata": {},
"outputs": [],
"source": [
"# Oh, das war bei Leipzig die Zahl von 2010, nicht 2020\n",
"\n",
"EW[\"Leipzig\"] = 0.597\n",
"EW"
]
},
{
"cell_type": "markdown",
"id": "3d0eadd7",
"metadata": {},
"source": [
"Ein Paar kann über seinen `key` auch gelöscht werden.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0dfd9f2d",
"metadata": {},
"outputs": [],
"source": [
"delete!(EW, \"Dresden\")"
]
},
{
"cell_type": "markdown",
"id": "3db2aa1f",
"metadata": {},
"source": [
"Zahlreiche Funktionen können mit `Dicts` wie mit anderen Containern arbeiten.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1204aaab",
"metadata": {},
"outputs": [],
"source": [
"maximum(values(EW))"
]
},
{
"cell_type": "markdown",
"id": "6a4946b4",
"metadata": {},
"source": [
"### Anlegen eines leeren Dictionaries\n",
"\n",
"Ohne Typspezifikation ...\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1f82ac79",
"metadata": {},
"outputs": [],
"source": [
"d1 = Dict()"
]
},
{
"cell_type": "markdown",
"id": "27c98eaf",
"metadata": {},
"source": [
"und mit Typspezifikation:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1b8f201e",
"metadata": {},
"outputs": [],
"source": [
"d2 = Dict{String, Int}()"
]
},
{
"cell_type": "markdown",
"id": "7fe71a3b",
"metadata": {},
"source": [
"### Umwandlung in Vektoren: `collect()`\n",
"\n",
"- `keys(dict)` und `values(dict)` sind spezielle Datentypen. \n",
"- Die Funktion `collect()` macht daraus eine Liste vom Typ `Vector`. \n",
"- `collect(dict)` liefert eine Liste vom Typ `Vector{Pair{S,T}}` \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2dc85bdd",
"metadata": {},
"outputs": [],
"source": [
"collect(EW)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "100dbbf1",
"metadata": {},
"outputs": [],
"source": [
"collect(keys(EW)), collect(values(EW))"
]
},
{
"cell_type": "markdown",
"id": "f9703f73",
"metadata": {},
"source": [
"### Geordnetes Iterieren über ein Dictionary\n",
"\n",
"Wir sortieren die Keys. Als Strings werden sie alphabetisch sortiert. Mit dem `rev`-Parameter wird rückwärts sortiert.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3c02f0ca",
"metadata": {},
"outputs": [],
"source": [
"for k in sort(collect(keys(EW)), rev = true)\n",
" n = EW[k]\n",
" println(\"$k hat $n Millionen Einw. \")\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "c20f0654",
"metadata": {},
"source": [
"Wir sortieren `collect(dict)`. Das ist ein Vektor von Paaren. Mit `by` definieren wir, wonach zu sortieren ist: nach dem 2. Element des Paares. \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "89ee04e9",
"metadata": {},
"outputs": [],
"source": [
"for (k,v) in sort(collect(EW), by = pair -> last(pair), rev=false)\n",
" println(\"$k hat $v Mill. EW\")\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "94ba9752",
"metadata": {},
"source": [
"### Eine Anwendung von Dictionaries: Zählen von Häufigkeiten\n",
"\n",
"Wir machen 'experimentelle Stochastik' mit 2 Würfeln: \n",
"\n",
"Gegeben sei `l`, eine Liste mit den Ergebnissen von 100 000 Pasch-Würfen, also 100 000 Zahlen zwischen 2 und 12.\n",
"\n",
"Wie häufig sind die Zahlen 2 bis 12?\n",
"\n",
"\n",
"Wir (lassen) würfeln:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a7ff829d",
"metadata": {},
"outputs": [],
"source": [
"l = rand(1:6, 100_000) .+ rand(1:6, 100_000)"
]
},
{
"cell_type": "markdown",
"id": "48a58503",
"metadata": {},
"source": [
"Wir zählen mit Hilfe eines Dictionaries die Häufigkeiten der Ereignisse. Dazu nehmen wir das Ereignis als `key` und seine Häufigkeit als `value`.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dd2bcd79",
"metadata": {},
"outputs": [],
"source": [
"# In diesem Fall könnte man das auch mit einem einfachen Vektor\n",
"# lösen. Eine bessere Illustration wäre z.B. Worthäufigkeit in\n",
"# einem Text. Dann ist i keine ganze Zahl sondern ein Wort=String\n",
"\n",
"d = Dict{Int,Int}() # das Dict zum 'reinzählen'\n",
"\n",
"for i in l # für jedes i wird d[i] erhöht. \n",
" d[i] = get(d, i, 0) + 1 \n",
"end\n",
"d"
]
},
{
"cell_type": "markdown",
"id": "62fe53b9",
"metadata": {},
"source": [
"Das Ergebnis:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "154252d3",
"metadata": {},
"outputs": [],
"source": [
"using Plots\n",
"\n",
"plot(collect(keys(d)), collect(values(d)), seriestype=:scatter)"
]
},
{
"cell_type": "markdown",
"id": "dd482553",
"metadata": {},
"source": [
"##### Das Erklär-Bild dazu:\n",
"\n",
"[https://math.stackexchange.com/questions/1204396/why-is-the-sum-of-the-rolls-of-two-dices-a-binomial-distribution-what-is-define](https://math.stackexchange.com/questions/1204396/why-is-the-sum-of-the-rolls-of-two-dices-a-binomial-distribution-what-is-define)\n"
] ]
} }
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
} }
}, },
"nbformat": 4, "nbformat": 4,

402
nb/7_ArraysP2.ipynb
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190
nb/9_functs.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "87512b9c", "id": "c68c2670",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Funktionen und Operatoren\n", "# Funktionen und Operatoren\n",
@ -19,7 +19,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2cdf33d6", "id": "9443ccb7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -30,7 +30,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d22901e3", "id": "50291f2a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"II. Als \"Einzeiler\" \n" "II. Als \"Einzeiler\" \n"
@ -39,7 +39,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "338f000a", "id": "4657e421",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -48,7 +48,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f14a745f", "id": "d36c44e2",
"metadata": {}, "metadata": {},
"source": [ "source": [
"III. Als anonyme Funktionen\n" "III. Als anonyme Funktionen\n"
@ -57,7 +57,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "44319487", "id": "02e66f6e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -66,7 +66,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d8f8978c", "id": "f3c09c53",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Block-Form und `return`\n", "### Block-Form und `return`\n",
@ -106,7 +106,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "721d72e8", "id": "6694b46d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -121,7 +121,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f6847d6a", "id": "ee012edc",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -131,7 +131,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "483d2b6b", "id": "fca80289",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -140,7 +140,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "66a0d115", "id": "39cf5d56",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Einzeiler-Form\n", "### Einzeiler-Form\n",
@ -186,7 +186,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e07295eb", "id": "35a8bd70",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -196,7 +196,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b8ca9baf", "id": "f8cec9b2",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -205,7 +205,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "9ba0e8db", "id": "71388002",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Ein weiteres Beispiel ist `filter(test, collection)`, wobei ein Test eine Funktion ist, die ein `Bool` zurückgibt.\n" "Ein weiteres Beispiel ist `filter(test, collection)`, wobei ein Test eine Funktion ist, die ein `Bool` zurückgibt.\n"
@ -214,7 +214,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "12731194", "id": "11d55610",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -223,7 +223,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f4af9755", "id": "36b2a20b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Argumentübergabe\n", "## Argumentübergabe\n",
@ -237,7 +237,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d34f0256", "id": "650adea1",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -251,7 +251,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f83f5e37", "id": "49a771b3",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -267,7 +267,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "7476eab9", "id": "d0d2e303",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Varianten von Funktionsargumenten\n", "## Varianten von Funktionsargumenten\n",
@ -285,7 +285,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e67e1006", "id": "5ec6f56a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -298,7 +298,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1d889283", "id": "4389ea71",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Eine Funktion nur mit _keyword_-Argumenten wird so deklariert:\n" "Eine Funktion nur mit _keyword_-Argumenten wird so deklariert:\n"
@ -307,7 +307,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e79269ee", "id": "0fc2aeac",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -318,7 +318,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "14d197af", "id": "26e02ff2",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Funktionen sind ganz normale Objekte\n", "## Funktionen sind ganz normale Objekte\n",
@ -329,7 +329,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2e0a4b89", "id": "17b38616",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -339,7 +339,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6f0fef37", "id": "325c567b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Sie können als Argumente an Funktionen übergeben werden.\n" "- Sie können als Argumente an Funktionen übergeben werden.\n"
@ -348,7 +348,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c6db6121", "id": "4d5be6cf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -369,7 +369,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b8eb1978", "id": "43f02a36",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Sie können von Funktionen erzeugt und als Ergebnis `return`t werden.\n" "- Sie können von Funktionen erzeugt und als Ergebnis `return`t werden.\n"
@ -378,7 +378,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "67e640ce", "id": "81e0ad89",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -393,7 +393,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a78dd669", "id": "5491730c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -403,7 +403,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "23b557af", "id": "f39aa8b1",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -413,7 +413,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "440b7568", "id": "4b708a03",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -422,7 +422,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ab655f0f", "id": "5c0d6771",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die obige Funktion `generate_add_func()` lässt sich auch kürzer definieren. Der innere Funktionsname `addx()` ist sowieso lokal und außerhalb nicht verfügbar. Also kann man eine anonyme Funktion verwenden.\n" "Die obige Funktion `generate_add_func()` lässt sich auch kürzer definieren. Der innere Funktionsname `addx()` ist sowieso lokal und außerhalb nicht verfügbar. Also kann man eine anonyme Funktion verwenden.\n"
@ -431,7 +431,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d0b76e9c", "id": "7817f2ff",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -440,7 +440,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "9dcb1129", "id": "0cf5d3c0",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Zusammensetzung von Funktionen: die Operatoren $\\circ$ und `|>`\n", "## Zusammensetzung von Funktionen: die Operatoren $\\circ$ und `|>`\n",
@ -453,7 +453,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "fcaf335f", "id": "cae2ce88",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -463,7 +463,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "48dd034e", "id": "a16fb3c6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -474,7 +474,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2ecd0bb3", "id": "ed8ec445",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -483,7 +483,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "64c2f8ca", "id": "6c6d5a5a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Es gibt auch einen Operator, mit dem Funktionen \"von rechts\" wirken und zusammengesetzt werden können _(piping)_\n" "- Es gibt auch einen Operator, mit dem Funktionen \"von rechts\" wirken und zusammengesetzt werden können _(piping)_\n"
@ -492,7 +492,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8cdef694", "id": "d32aaa8f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -502,7 +502,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4fd01026", "id": "c5b9236a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -511,7 +511,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d8c6e6f3", "id": "2af53243",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Natürlich kann man auch diese Operatoren 'broadcasten' (s. @sec-broadcast). Hier wirkt ein Vektor von Funktionen elementweise auf einen Vektor von Argumenten:\n" "- Natürlich kann man auch diese Operatoren 'broadcasten' (s. @sec-broadcast). Hier wirkt ein Vektor von Funktionen elementweise auf einen Vektor von Argumenten:\n"
@ -520,7 +520,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "94691aad", "id": "4ea2ad9f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -529,7 +529,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f4b75c54", "id": "f941ceb5",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Die `do`-Notation\n", "## Die `do`-Notation\n",
@ -552,7 +552,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "76c02df9", "id": "a6620e38",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -563,7 +563,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "a708ad3e", "id": "26486b16",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Der Sinn besteht natürlich in der Anwendung mit komplexeren Funktionen, wie diesem aus zwei Teilstücken zusammengesetzten Integranden:\n" "Der Sinn besteht natürlich in der Anwendung mit komplexeren Funktionen, wie diesem aus zwei Teilstücken zusammengesetzten Integranden:\n"
@ -572,7 +572,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e3012c9b", "id": "53714315",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -589,7 +589,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c38a800c", "id": "c973f2c1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Funktionsartige Objekte\n", "## Funktionsartige Objekte\n",
@ -600,7 +600,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "5de4f59a", "id": "73cc94fd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -617,7 +617,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "8b0b62a3", "id": "99427b65",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die folgende Methode macht diese Struktur `callable`.\n" "Die folgende Methode macht diese Struktur `callable`.\n"
@ -626,7 +626,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0a5cb287", "id": "94bbfd15",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -637,7 +637,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "a5149012", "id": "b13ba4a8",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Jetzt kann man die Objekte, wenn gewünscht, auch wie Funktionen verwenden.\n" "Jetzt kann man die Objekte, wenn gewünscht, auch wie Funktionen verwenden.\n"
@ -646,7 +646,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b271dbf1", "id": "9b490828",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -655,7 +655,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b355c1b0", "id": "bff0bff7",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Operatoren und spezielle Formen\n", "## Operatoren und spezielle Formen\n",
@ -666,7 +666,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4f71f917", "id": "da10ff9f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -676,7 +676,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b19e79cf", "id": "177a174d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -686,7 +686,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "869917d4", "id": "f0f52152",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -695,7 +695,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "490bceac", "id": "39178d6d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Auch Konstruktionen wie `x[i]`, `a.x`, `[x; y]` werden vom Parser zu Funktionsaufrufen umgewandelt.\n", "- Auch Konstruktionen wie `x[i]`, `a.x`, `[x; y]` werden vom Parser zu Funktionsaufrufen umgewandelt.\n",
@ -755,7 +755,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4d92cc97", "id": "419bcd07",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -764,7 +764,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ec6b89f6", "id": "3b37d178",
"metadata": {}, "metadata": {},
"source": [ "source": [
"werden vom Parser in eine Baumstruktur überführt.\n" "werden vom Parser in eine Baumstruktur überführt.\n"
@ -773,7 +773,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "9f607850", "id": "7e5bd52c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -784,7 +784,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "68328dda", "id": "d26e9cbc",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Die Auswertung solcher Ausdrücke wird durch \n", "- Die Auswertung solcher Ausdrücke wird durch \n",
@ -802,7 +802,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "71fdbe34", "id": "3faed089",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -812,7 +812,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "fc26727a", "id": "559f6beb",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -821,7 +821,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0253c57a", "id": "115f7493",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Zuweisungen wie `=`, `+=`, `*=`,... sind gleichrangig und rechtsassoziativ.\n" "Zuweisungen wie `=`, `+=`, `*=`,... sind gleichrangig und rechtsassoziativ.\n"
@ -830,7 +830,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "7f9891ea", "id": "72456757",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -846,16 +846,16 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "9eeccc4c", "id": "a716bc08",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Natürlich kann man die Assoziativität in Julia auch abfragen. Die entsprechenden Funktionen werden nicht expizit aus dem `Base`-Modul exportiert, deshalb muss man den Modulnamen beim Aufruf angeben. \n" "Natürlich kann man die Assoziativität in Julia auch abfragen. Die entsprechenden Funktionen werden nicht explizit aus dem `Base`-Modul exportiert, deshalb muss man den Modulnamen beim Aufruf angeben. \n"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "23fe3c28", "id": "f2317e6a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -867,7 +867,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "148b459a", "id": "3a7e3a79",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Also ist der Potenzoperator rechtsassoziativ.\n" "Also ist der Potenzoperator rechtsassoziativ.\n"
@ -876,7 +876,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d1ad2685", "id": "21fe9789",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -885,7 +885,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "86c59c17", "id": "0d333e68",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Vorrang\n", "### Vorrang\n",
@ -896,7 +896,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "9c97eee7", "id": "e5ad39a5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -908,7 +908,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "177ecf6d", "id": "4decdf33",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- 11 ist kleiner als 12, also geht 'Punktrechnung vor Strichrechnung'\n", "- 11 ist kleiner als 12, also geht 'Punktrechnung vor Strichrechnung'\n",
@ -919,7 +919,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "30c88bf2", "id": "9450f974",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -932,7 +932,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b4a0a3ee", "id": "d631e121",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -942,7 +942,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0384575c", "id": "0969d330",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Nochmal zum Beispiel vom Anfang von @sec-vorrang:\n" "Nochmal zum Beispiel vom Anfang von @sec-vorrang:\n"
@ -951,7 +951,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "56488075", "id": "107124d7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -961,7 +961,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "543e7874", "id": "420964a2",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -973,7 +973,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "bcb7fc77", "id": "9c17c3e7",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Nach diesen Vorrangregeln wird der Beispielausdruck also wie folgt ausgewertet:\n" "Nach diesen Vorrangregeln wird der Beispielausdruck also wie folgt ausgewertet:\n"
@ -982,7 +982,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "89af1388", "id": "43b21b33",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -991,7 +991,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "509a3955", "id": "2d52102a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(Das entspricht natürlich dem oben gezeigten *parse-tree*)\n", "(Das entspricht natürlich dem oben gezeigten *parse-tree*)\n",
@ -1021,7 +1021,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c134b798", "id": "a4465163",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1030,7 +1030,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "aafaa2d1", "id": "1529af73",
"metadata": {}, "metadata": {},
"source": [ "source": [
"::: \n", "::: \n",
@ -1045,7 +1045,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "61fc5df5", "id": "8dbccf82",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1055,7 +1055,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8c609c3b", "id": "26415d53",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1066,7 +1066,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "44a6345d", "id": "b07aabae",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1076,7 +1076,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "660dfb1f", "id": "09f3ecc4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1085,7 +1085,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0fecdb42", "id": "d1e4bc70",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Funktionsanwendung `f(...)` hat Vorrang vor allen Operatoren\n" "- Funktionsanwendung `f(...)` hat Vorrang vor allen Operatoren\n"
@ -1094,7 +1094,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "198bb0f8", "id": "a9c32959",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1103,7 +1103,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f153e028", "id": "e9915990",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Zusätzliche Operatoren\n", "### Zusätzliche Operatoren\n",
@ -1126,15 +1126,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.5"
} }
}, },
"nbformat": 4, "nbformat": 4,

38
nb/Erste_Bsp.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "9bb241ad", "id": "f21dc71b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Erste Miniprogramme\n", "# Erste Miniprogramme\n",
@ -72,7 +72,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b5ec6b90", "id": "44d0f59e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -87,7 +87,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e4de7d69", "id": "4d9f5b4f",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -102,7 +102,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "772bbe68", "id": "9d36a90d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -111,7 +111,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b9b95d73", "id": "71a52de7",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -151,7 +151,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c0730a2a", "id": "15983324",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -170,7 +170,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1caa208b", "id": "7cafe59e",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -180,7 +180,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "72341556", "id": "82139e32",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -192,7 +192,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "5eeb2626", "id": "1467ade0",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Im Sinne der Aufgabe wenden wir die Funktion wiederholt an:\n" "Im Sinne der Aufgabe wenden wir die Funktion wiederholt an:\n"
@ -201,7 +201,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "da47c136", "id": "2a91c9da",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -214,7 +214,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e67b1670", "id": "1399219b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"... und haben hier einen der '89er Zyklen' getroffen.\n", "... und haben hier einen der '89er Zyklen' getroffen.\n",
@ -232,7 +232,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3868d34e", "id": "8b76324d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -248,7 +248,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "10ce44d1", "id": "06d73770",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -259,7 +259,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "54521e6a", "id": "7a0051f2",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -274,7 +274,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "4a545b8c", "id": "000b5826",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Zahlen, bei denen die iterierte Quadratquersummenbildung bei 1 endet, heißen übrigens [fröhliche Zahlen](https://de.wikipedia.org/wiki/Fr%C3%B6hliche_Zahl) und wir haben gerade die Anzahl der traurigen Zahlen kleiner als 10.000.000 berechnet.\n", "Zahlen, bei denen die iterierte Quadratquersummenbildung bei 1 endet, heißen übrigens [fröhliche Zahlen](https://de.wikipedia.org/wiki/Fr%C3%B6hliche_Zahl) und wir haben gerade die Anzahl der traurigen Zahlen kleiner als 10.000.000 berechnet.\n",
@ -288,7 +288,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a7253bc1", "id": "db3ef4ef",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -322,7 +322,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "772bec11", "id": "8d2084be",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::" ":::"
@ -331,9 +331,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
} }
}, },
"nbformat": 4, "nbformat": 4,

32
nb/Pi2.ipynb
View File

@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "raw", "cell_type": "raw",
"id": "9d63401b", "id": "9e1ef849",
"metadata": {}, "metadata": {},
"source": [ "source": [
"---\n", "---\n",
@ -18,7 +18,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "405d242e", "id": "beff12c8",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Ein Beispiel zur Stabilität von Gleitkommaarithmetik\n", "# Ein Beispiel zur Stabilität von Gleitkommaarithmetik\n",
@ -29,7 +29,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f17a5fcb", "id": "a7810264",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -84,7 +84,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "7745166c", "id": "8d4bd1ab",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Eine untere Schranke für $2\\pi$, den Umfang des Einheitskreises, erhält man durch die\n", "Eine untere Schranke für $2\\pi$, den Umfang des Einheitskreises, erhält man durch die\n",
@ -151,7 +151,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d83237c5", "id": "3f238690",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -186,7 +186,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "dcdecd41", "id": "0c0178f5",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Während Iteration B sich stabilisiert bei einem innerhalb der Maschinengenauigkeit korrekten Wert für π, wird Iteration A schnell instabil. Ein Plot der relativen Fehler $\\epsilon_i$ bestätigt das:\n" "Während Iteration B sich stabilisiert bei einem innerhalb der Maschinengenauigkeit korrekten Wert für π, wird Iteration A schnell instabil. Ein Plot der relativen Fehler $\\epsilon_i$ bestätigt das:\n"
@ -195,7 +195,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "4404adb1", "id": "f415aab0",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -212,7 +212,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ac5d56d5", "id": "02116ab2",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Stabilität und Auslöschung\n", "## Stabilität und Auslöschung\n",
@ -223,7 +223,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e807fa2b", "id": "3d50cba2",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -232,7 +232,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "68979310", "id": "5ba088ba",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Weitere Iterationen verbessern das Ergebnis nicht mehr. Sie stabilisieren sich bei einem relativen Fehler von etwa 2.5 Maschinenepsilon:\n" "Weitere Iterationen verbessern das Ergebnis nicht mehr. Sie stabilisieren sich bei einem relativen Fehler von etwa 2.5 Maschinenepsilon:\n"
@ -241,7 +241,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6a9f7b29", "id": "2bcae61d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -250,7 +250,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "09be0e03", "id": "0bfd8235",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Form Iteration A ist instabil. Bereits bei $i=16$ beginnt der relative Fehler wieder zu wachsen.\n", "Die Form Iteration A ist instabil. Bereits bei $i=16$ beginnt der relative Fehler wieder zu wachsen.\n",
@ -262,7 +262,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2ccb85ad", "id": "365d4c27",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -283,7 +283,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "27616d4d", "id": "04736a02",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Man sieht die Abnahme der Zahl der signifikanten Ziffern. Man sieht auch, dass eine Verwendung von `BigFloat` mit einer Mantissenlänge von hier 80 Bit das Einsetzen des Auslöschungseffekts nur etwas hinaussschieben kann. \n", "Man sieht die Abnahme der Zahl der signifikanten Ziffern. Man sieht auch, dass eine Verwendung von `BigFloat` mit einer Mantissenlänge von hier 80 Bit das Einsetzen des Auslöschungseffekts nur etwas hinaussschieben kann. \n",
@ -303,9 +303,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
} }
}, },
"nbformat": 4, "nbformat": 4,

100
nb/first_contact.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e009ef80", "id": "65cc0031",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# First Contact\n", "# First Contact\n",
@ -16,7 +16,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b488cb23", "id": "f9151e6d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -45,7 +45,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "76000398", "id": "3c611742",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Berechne $\\qquad 12^{1/3} + \\frac{3\\sqrt{2}}{\\sin(0.5)-\\cos(\\frac{\\pi}{4})\\log(3)}+ e^5$\n" "Berechne $\\qquad 12^{1/3} + \\frac{3\\sqrt{2}}{\\sin(0.5)-\\cos(\\frac{\\pi}{4})\\log(3)}+ e^5$\n"
@ -54,7 +54,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0f9feb86", "id": "fd02456e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -63,7 +63,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3e9fad84", "id": "9ce12c0f",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Man beachte:\n", "Man beachte:\n",
@ -74,7 +74,7 @@
"- Das Multiplikationszeichen `a*b` kann nach einer Zahl weggelassen werden, wenn eine Variable, Funktion oder Klammer folgt.\n", "- Das Multiplikationszeichen `a*b` kann nach einer Zahl weggelassen werden, wenn eine Variable, Funktion oder Klammer folgt.\n",
"\n", "\n",
"\n", "\n",
"## Die wichtigsten Tasten: `Tab` und `?`\n", "## Die wichtigsten Tasten: `Tab` und `?` {#sec-tab}\n",
"\n", "\n",
"Man drücke beim Programmieren immer wieder die Tabulatortaste, sobald 2...3 Buchstaben eines Wortes getippt sind. Es werden dann mögliche Ergänzungen angezeigt bzw. ergänzt, wenn die Ergänzung eindeutig ist. Das spart Zeit und bildet ungemein:\n" "Man drücke beim Programmieren immer wieder die Tabulatortaste, sobald 2...3 Buchstaben eines Wortes getippt sind. Es werden dann mögliche Ergänzungen angezeigt bzw. ergänzt, wenn die Ergänzung eindeutig ist. Das spart Zeit und bildet ungemein:\n"
] ]
@ -82,7 +82,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "734300ba", "id": "e2ca6f27",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -93,7 +93,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "155bc575", "id": "9fdfabe6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -103,7 +103,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ba74dc32", "id": "d8ecd73b",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die eingebaute Julia-Hilfe `?name` zu allen Funktionen und Konstrukten ist sehr umfassend. Hier ein eher kurzes Beispiel: \n" "Die eingebaute Julia-Hilfe `?name` zu allen Funktionen und Konstrukten ist sehr umfassend. Hier ein eher kurzes Beispiel: \n"
@ -112,7 +112,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "1b941a97", "id": "9ba34e9d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -121,7 +121,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c8f7da7b", "id": "c798d174",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::{.content-hidden unless-format=\"xxx\"}\n", ":::{.content-hidden unless-format=\"xxx\"}\n",
@ -160,7 +160,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "da1dc7ec", "id": "2f60e4e5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -170,7 +170,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "37b29541", "id": "20819c0a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Im interaktiven Betrieb zeigt Julia das Ergebnis der letzten Operation an.\n", "Im interaktiven Betrieb zeigt Julia das Ergebnis der letzten Operation an.\n",
@ -201,7 +201,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "173f7324", "id": "2874204c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -214,7 +214,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "13a8984f", "id": "d5343251",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Standard-Gleitkommazahl hat eine Länge von 64 Bit, entspricht also einer `double` in C/C++/Java.\n", "Die Standard-Gleitkommazahl hat eine Länge von 64 Bit, entspricht also einer `double` in C/C++/Java.\n",
@ -227,7 +227,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "cd3b3e96", "id": "544f8fe6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -242,7 +242,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "eae463bf", "id": "b1734df1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Druckanweisungen\n", "## Druckanweisungen\n",
@ -252,7 +252,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "df98312b", "id": "b44d0f53",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -266,7 +266,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b74dcb3f", "id": "3baa2a89",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Beide Funkionen können als Argument eine Liste von *strings* und Variablen bekommen. Man kann Variablen auch in *strings* einbetten, indem man dem Variablennamen ein Dollarzeichen voranstellt *(string interpolation)*.\n" "Beide Funkionen können als Argument eine Liste von *strings* und Variablen bekommen. Man kann Variablen auch in *strings* einbetten, indem man dem Variablennamen ein Dollarzeichen voranstellt *(string interpolation)*.\n"
@ -275,7 +275,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3b76d855", "id": "fa3b2601",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -288,7 +288,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c06fc5da", "id": "fe3b44d2",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::{.callout-note .titlenormal collapse=true icon=false }\n", ":::{.callout-note .titlenormal collapse=true icon=false }\n",
@ -300,7 +300,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "00a46544", "id": "198c1231",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -309,7 +309,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3ba46a2c", "id": "847182e6",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -321,7 +321,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6e83b8e2", "id": "8c4c8af3",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -334,7 +334,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6ae72d3a", "id": "270a968d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Nach ihrer Definition kann die Funktion benutzt (aufgerufen) werden. Die in der Definition verwendeten Variablen `a,b,c,c2` sind lokale Variablen und stehen außerhalb der Funktionsdefinition nicht zur Verfügung. \n" "Nach ihrer Definition kann die Funktion benutzt (aufgerufen) werden. Die in der Definition verwendeten Variablen `a,b,c,c2` sind lokale Variablen und stehen außerhalb der Funktionsdefinition nicht zur Verfügung. \n"
@ -343,7 +343,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2b68ec32", "id": "aeb1b763",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -356,7 +356,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d62b25c3", "id": "83623a5d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Sehr einfache Funktionen können auch als Einzeiler definiert werden.\n" "Sehr einfache Funktionen können auch als Einzeiler definiert werden.\n"
@ -365,7 +365,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "436bf54a", "id": "bb93d920",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -374,7 +374,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "13485711", "id": "28cfec18",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Tests\n", "## Tests\n",
@ -384,7 +384,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "fbfc37d5", "id": "a778d1c9",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -394,7 +394,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d43e3179", "id": "43717a30",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Neben den üblichen arithmetischen Vergleichen `==, !=, <, <= ,> ,>=` \n", "Neben den üblichen arithmetischen Vergleichen `==, !=, <, <= ,> ,>=` \n",
@ -404,7 +404,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "7e289c8e", "id": "b425b2bf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -416,7 +416,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0ca8fc84", "id": "b8b63af7",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Verzweigungen\n", "## Verzweigungen\n",
@ -437,7 +437,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6ab36f93", "id": "759c7b60",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -453,7 +453,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3247aa40", "id": "92f05a99",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Einrückungen verbessern die Lesbarkeit, sind aber fakultativ. Zeilenumbrüche trennen Anweisungen. Das ist auch durch Semikolon möglich. Obiger Codeblock ist für Julia identisch zu folgender Zeile:\n" "Einrückungen verbessern die Lesbarkeit, sind aber fakultativ. Zeilenumbrüche trennen Anweisungen. Das ist auch durch Semikolon möglich. Obiger Codeblock ist für Julia identisch zu folgender Zeile:\n"
@ -462,7 +462,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6b6f3846", "id": "75c38c3c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -472,7 +472,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "4f8718ea", "id": "6c916fa7",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Es wird dringend empfohlen, von Anfang an den eigenen Code übersichtlich mit sauberen Einrückungen zu formatieren!\n", "Es wird dringend empfohlen, von Anfang an den eigenen Code übersichtlich mit sauberen Einrückungen zu formatieren!\n",
@ -494,7 +494,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e2518e65", "id": "8f6ff3c3",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -507,7 +507,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3fa36879", "id": "6ba98544",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Arrays\n", "## Arrays\n",
@ -518,7 +518,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "cf56b9fc", "id": "bde3f18d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -528,7 +528,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2e6ae1f4", "id": "ab7ae1b1",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -538,7 +538,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "18a71a80", "id": "cd6f6101",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -548,7 +548,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6833c60b", "id": "4cd8e309",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Man kann leere Vektoren anlegen und sie verlängern.\n" "Man kann leere Vektoren anlegen und sie verlängern.\n"
@ -557,7 +557,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "49a0d406", "id": "4e643897",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -569,7 +569,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ca3e6d8e", "id": "d3e2209e",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::{.callout-note icon=\"false\" .titlenormal collapse=\"true\" font-variant-ligatures=\"no-contextual\" }\n", ":::{.callout-note icon=\"false\" .titlenormal collapse=\"true\" font-variant-ligatures=\"no-contextual\" }\n",
@ -580,7 +580,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "087b10f7", "id": "8bb956d4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -600,7 +600,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0b8be63e", "id": "a417e43d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -609,7 +609,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "cd067cf0", "id": "71efa254",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::" ":::"
@ -618,9 +618,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
} }
}, },
"nbformat": 4, "nbformat": 4,

551
nb/numerictypes.ipynb
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102
nb/pcomplex.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3b9e97dc", "id": "69149570",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Ein Fallbeispiel: Der parametrisierte Datentyp PComplex\n", "# Ein Fallbeispiel: Der parametrisierte Datentyp PComplex\n",
@ -20,7 +20,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "b00fa817", "id": "3ee9c4ae",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -36,7 +36,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "00603f51", "id": "729a1d8e",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Julia stellt automatisch *default constructors* zur Verfügung:\n", "Julia stellt automatisch *default constructors* zur Verfügung:\n",
@ -60,7 +60,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d583f845", "id": "214480f6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -84,7 +84,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e3d6ada4", "id": "873d5dc6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -103,7 +103,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "55f6b7dc", "id": "95c7386c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -112,7 +112,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "99f6d6e1", "id": "eb213995",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Für die explizite Angabe eines *inner constructors* müssen wir allerdings einen Preis zahlen: Die sonst von Julia bereitgestellten *default constructors* fehlen. \n", "Für die explizite Angabe eines *inner constructors* müssen wir allerdings einen Preis zahlen: Die sonst von Julia bereitgestellten *default constructors* fehlen. \n",
@ -123,7 +123,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e6c36f18", "id": "e87d3a42",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -134,7 +134,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "5d77812c", "id": "0512b019",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Eine neue Schreibweise\n", "## Eine neue Schreibweise\n",
@ -165,7 +165,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a4fc6d3c", "id": "81818d42",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -176,7 +176,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c19f6e25", "id": "bf0863e9",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(Die Typ-Annotation -- `Real` statt `AbstractFloat` -- ist ein Vorgriff auf kommende weitere Konstruktoren. Im Moment funktioniert der Operator `⋖` erstmal nur mit `Float`s.)\n", "(Die Typ-Annotation -- `Real` statt `AbstractFloat` -- ist ein Vorgriff auf kommende weitere Konstruktoren. Im Moment funktioniert der Operator `⋖` erstmal nur mit `Float`s.)\n",
@ -188,7 +188,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "13e750ef", "id": "4cf73e28",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -206,7 +206,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e1c7d6fa", "id": "0dae2fef",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Methoden für `PComplex`\n", "## Methoden für `PComplex`\n",
@ -230,7 +230,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "373829e0", "id": "042418fd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -241,7 +241,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a4490292", "id": "c20d10e5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -252,7 +252,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d49ec514", "id": "82fe20b4",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n" ":::\n"
@ -261,7 +261,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d2186aeb", "id": "a53f0e79",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -271,7 +271,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "5d93d3ca", "id": "d6987594",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -289,7 +289,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "07ed8595", "id": "53f4bb77",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Funktion `sqrt()` hat schon einige Methoden:\n" "Die Funktion `sqrt()` hat schon einige Methoden:\n"
@ -298,7 +298,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "1ecfd1ac", "id": "f93f63c6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -307,7 +307,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f619c771", "id": "7b4f323a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Jetzt wird es eine Methode mehr:\n" "Jetzt wird es eine Methode mehr:\n"
@ -316,7 +316,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "56a4ce0f", "id": "b88cd74b",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -328,7 +328,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "195204e7", "id": "e077b8bf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -337,7 +337,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c912bcd2", "id": "e223fdd1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"und nun zur Multiplikation:\n" "und nun zur Multiplikation:\n"
@ -346,7 +346,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8c648a2d", "id": "5537f7ec",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -357,7 +357,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "79074b01", "id": "7189f0c6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(Da das Operatorsymbol kein normaler Name ist, muss der Doppelpunkt bei der Zusammensetzung mit `Base.` sein.)\n", "(Da das Operatorsymbol kein normaler Name ist, muss der Doppelpunkt bei der Zusammensetzung mit `Base.` sein.)\n",
@ -373,7 +373,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ff3ee027", "id": "610a38fe",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -382,7 +382,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f43ef8c6", "id": "bc39d089",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Wenn man in die zahlreichen Methoden schaut, die z.B. für `+` und `*` definiert sind, findet man u.a. eine Art 'catch-all-Definition'\n", "Wenn man in die zahlreichen Methoden schaut, die z.B. für `+` und `*` definiert sind, findet man u.a. eine Art 'catch-all-Definition'\n",
@ -408,7 +408,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8f1d4d57", "id": "48cae0ae",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -418,7 +418,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "27c2724e", "id": "768934ac",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -428,7 +428,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "8347acad", "id": "df2672c5",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Funktion `promote()` verwendet dazu zwei Helfer, die Funktionen\n", "Die Funktion `promote()` verwendet dazu zwei Helfer, die Funktionen\n",
@ -445,7 +445,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "fe551c95", "id": "70306adc",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -454,7 +454,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e4c08732", "id": "ec999b3a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Die Funktion `convert(T,x)`\n", "### Die Funktion `convert(T,x)`\n",
@ -466,7 +466,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "5d6aabe4", "id": "b326a121",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -476,7 +476,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8b5205d2", "id": "57606643",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -486,7 +486,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0d4b80ce", "id": "a3b39504",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -495,7 +495,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "3e3d953b", "id": "06251c1d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die spezielle Rolle von `convert()` liegt darin, dass es an verschiedenen Stellen _implizit_ und automatisch eingesetzt wird: \n", "Die spezielle Rolle von `convert()` liegt darin, dass es an verschiedenen Stellen _implizit_ und automatisch eingesetzt wird: \n",
@ -526,7 +526,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2f9e1ebe", "id": "e258330e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -558,7 +558,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c831e4c3", "id": "ccb96089",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Ein Test der neuen Konstruktoren:\n" "Ein Test der neuen Konstruktoren:\n"
@ -567,7 +567,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8103dc03", "id": "ec747779",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -576,7 +576,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c85b8d7a", "id": "fd8541cf",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Wir brauchen nun noch *promotion rules*, die festlegen, welcher Typ bei `promote(x::T1, y::T2)` herauskommen soll. Damit wird `promote_type()` intern um die nötigen weiteren Methoden erweitert. \n", "Wir brauchen nun noch *promotion rules*, die festlegen, welcher Typ bei `promote(x::T1, y::T2)` herauskommen soll. Damit wird `promote_type()` intern um die nötigen weiteren Methoden erweitert. \n",
@ -587,7 +587,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8e6a1e94", "id": "806fff6a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -600,7 +600,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "4ad30167", "id": "97c7de69",
"metadata": {}, "metadata": {},
"source": [ "source": [
"1. Regel:\n", "1. Regel:\n",
@ -617,7 +617,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "9e72f683", "id": "cc47939d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -627,7 +627,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f0aec53e", "id": "63c20bc7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -636,7 +636,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0d881cc4", "id": "e94c6b15",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n", ":::{.callout-caution icon=\"false\" collapse=\"true\" .titlenormal}\n",
@ -730,15 +730,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.5"
} }
}, },
"nbformat": 4, "nbformat": 4,

9
nb/script1.sh
View File

@ -1,7 +1,8 @@
#!/bin/bash #!/bin/bash
cp ../chapters/*.ipynb . cp ../chapters/*.quarto_ipynb .
for i in *.ipynb for i in *.quarto_ipynb
do do
echo $i echo $i
jupyter nbconvert --inplace --clear-output --to notebook $i mv $i "${i%.quarto_ipynb}.ipynb"
jupyter nbconvert --inplace --clear-output --to notebook "${i%.quarto_ipynb}.ipynb"
done done

194
nb/syntax.ipynb
View File

@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d56a820e", "id": "5060b5d0",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Grundlagen der Syntax\n", "# Grundlagen der Syntax\n",
@ -36,7 +36,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ff07d3b4", "id": "109cbcf5",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -47,7 +47,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "da69601f", "id": "267dcd3c",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Jetzt ist natürlich der Logarithmus kaputt:\n" "Jetzt ist natürlich der Logarithmus kaputt:\n"
@ -56,7 +56,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "88275d81", "id": "c8432843",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -66,7 +66,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "5ecfdec6", "id": "cf194eb9",
"metadata": {}, "metadata": {},
"source": [ "source": [
"(siehe auch <https://stackoverflow.com/questions/65902105/how-to-reset-any-function-in-julia-to-its-original-state>)\n", "(siehe auch <https://stackoverflow.com/questions/65902105/how-to-reset-any-function-in-julia-to-its-original-state>)\n",
@ -92,7 +92,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "dc76d67e", "id": "8fa53675",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -102,7 +102,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6b068f1c", "id": "07d1a5e6",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Das Semikolon unterdrückt das:\n" "Das Semikolon unterdrückt das:\n"
@ -111,7 +111,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "efd01a2c", "id": "4b79202b",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -121,7 +121,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "18387226", "id": "76937fcb",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -137,7 +137,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "41df7f55", "id": "4af8b031",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -147,7 +147,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "61e668f9", "id": "b81c022a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Also geht das Folgende schief, aber leider **ohne eine Fehlermeldung**!\n" "Also geht das Folgende schief, aber leider **ohne eine Fehlermeldung**!\n"
@ -156,7 +156,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "694793eb", "id": "74162af6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -169,7 +169,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "88c64cd2", "id": "fdaa2eed",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Hier wird das `+` in der zweiten Zeile als Präfix-Operator (Vorzeichen) interpretiert. Damit sind 1. und 2. Zeile jeweils für sich vollständige, korrekte Ausdrücke (auch wenn die 2. Zeile natürlich völlig nutzlos ist) und werden auch so abgearbeitet. \n", "Hier wird das `+` in der zweiten Zeile als Präfix-Operator (Vorzeichen) interpretiert. Damit sind 1. und 2. Zeile jeweils für sich vollständige, korrekte Ausdrücke (auch wenn die 2. Zeile natürlich völlig nutzlos ist) und werden auch so abgearbeitet. \n",
@ -180,7 +180,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8ec8508d", "id": "e865958c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -191,7 +191,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1b323891", "id": "ddd2ae7d",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::\n", ":::\n",
@ -205,7 +205,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d733f6a2", "id": "a628a28a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -217,7 +217,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "cf4ef498", "id": "39f0f1fd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -238,7 +238,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e0fc09d1", "id": "44aa6359",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Datentypen Teil I \n", "## Datentypen Teil I \n",
@ -260,7 +260,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0ba7db71", "id": "f5fcc67a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -271,7 +271,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ad90519a", "id": "0f4c6d58",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -282,7 +282,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e36334d2", "id": "ef084989",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -293,7 +293,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f48d35a6", "id": "1f1df8fc",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -304,7 +304,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0eb5282b", "id": "b833e181",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -314,7 +314,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6407ce53", "id": "610935f8",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- `sizeof()` liefert die Größe eines Objekts oder Typs in Bytes (1 Byte = 8 Bit)\n", "- `sizeof()` liefert die Größe eines Objekts oder Typs in Bytes (1 Byte = 8 Bit)\n",
@ -332,7 +332,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d2c3f6c8", "id": "1b399845",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -355,7 +355,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "868ae573", "id": "73a859d9",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Kurze Blöcke kann man in eine Zeile schreiben:\n" "Kurze Blöcke kann man in eine Zeile schreiben:\n"
@ -364,7 +364,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "76f17f5f", "id": "ad94abc7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -373,7 +373,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ef1e84b5", "id": "34c18e6c",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Der Wert eines `if`-Blocks kann natürlich zugewiesen werden:\n" "Der Wert eines `if`-Blocks kann natürlich zugewiesen werden:\n"
@ -382,7 +382,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "318501e9", "id": "27eef305",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -396,7 +396,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "0c05b161", "id": "0ac5ece1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Auswahloperator (ternary operator) `test ? exp1 : exp2`\n" "### Auswahloperator (ternary operator) `test ? exp1 : exp2`\n"
@ -405,7 +405,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "40e9db00", "id": "dbe58322",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -416,7 +416,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "48705675", "id": "d7e0a7f9",
"metadata": {}, "metadata": {},
"source": [ "source": [
"ist äquivalent zu\n" "ist äquivalent zu\n"
@ -425,7 +425,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "dadac914", "id": "e1929004",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -438,7 +438,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "8d122010", "id": "406f03e8",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Vergleiche, Tests, Logische Operationen\n", "## Vergleiche, Tests, Logische Operationen\n",
@ -458,7 +458,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "13005342", "id": "5409328f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -467,7 +467,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "dd31f487", "id": "9b27b690",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Nun ja, fast alles:\n" "Nun ja, fast alles:\n"
@ -476,7 +476,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "7491b44b", "id": "5e6b4540",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -485,7 +485,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d5eace21", "id": "df810fec",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Die Fehlermeldung zeigt ein paar Grundprinzipien von Julia:\n", "Die Fehlermeldung zeigt ein paar Grundprinzipien von Julia:\n",
@ -500,7 +500,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "6538caaf", "id": "aa2d90be",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -509,7 +509,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "297ce845", "id": "7d79d348",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Zuletzt noch: Vergleiche können gekettet werden.\n" "Zuletzt noch: Vergleiche können gekettet werden.\n"
@ -518,7 +518,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "449eba70", "id": "3de7f381",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -528,7 +528,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "9f4b1c41", "id": "e5535e05",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Tests \n", "### Tests \n",
@ -538,7 +538,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "18d77ec1", "id": "1fa42721",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -547,7 +547,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "2dc1c0aa", "id": "9e3772fc",
"metadata": {}, "metadata": {},
"source": [ "source": [
"und vom Typ `f(s1::String, s2::String) -> Bool`\n" "und vom Typ `f(s1::String, s2::String) -> Bool`\n"
@ -556,7 +556,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ea9be46e", "id": "a462d33f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -565,7 +565,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "af8b3ce6", "id": "ee1487a3",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Die Funktion `in(item, collection) -> Bool` testet, ob `item` in `collection` ist. \n", "- Die Funktion `in(item, collection) -> Bool` testet, ob `item` in `collection` ist. \n",
@ -576,7 +576,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e811c4d8", "id": "71790111",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -587,7 +587,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "15f8ba27", "id": "f9b92ce4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -596,7 +596,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6b811515", "id": "93782274",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Logische Operationen: `&&`, `||`, `!`\n" "### Logische Operationen: `&&`, `||`, `!`\n"
@ -605,7 +605,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ea9ad7fb", "id": "8e907712",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -614,7 +614,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "a1886e91", "id": "efb19c75",
"metadata": {}, "metadata": {},
"source": [ "source": [
"#### Bedingte Auswertung (_short circuit evaluation_)\n", "#### Bedingte Auswertung (_short circuit evaluation_)\n",
@ -632,7 +632,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a5ef06bf", "id": "e5cae687",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -647,7 +647,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "bb950743", "id": "444d49b9",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Natürlich kann man alle diese Tests auch Variablen vom Typ `Bool` zuordnen und\n", "Natürlich kann man alle diese Tests auch Variablen vom Typ `Bool` zuordnen und\n",
@ -657,7 +657,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "8c44f3bc", "id": "68a69b63",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -671,7 +671,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "b7d1e766", "id": "e42d40c8",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- In Julia müssen alle Tests in einem logischen Ausdruck vom Typ `Bool` sein.\n", "- In Julia müssen alle Tests in einem logischen Ausdruck vom Typ `Bool` sein.\n",
@ -684,7 +684,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0a46fa2b", "id": "9fb43a4a",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -695,7 +695,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "f56bbc75", "id": "58faddd6",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -705,7 +705,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "508cebd9", "id": "295ec49e",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## Schleifen *(loops)*\n", "## Schleifen *(loops)*\n",
@ -725,7 +725,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "d91b98b6", "id": "9bd613c4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -739,7 +739,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "f7edea21", "id": "33b95f6d",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Der Körper einer `while`- und `for`-Schleife kann die Anweisungen `break` und `continue` enthalten. `break` stoppt die Schleife, `continue` überspringt den Rest des Schleifenkörpers und beginnt sofort mit dem nächsten Schleifendurchlauf.\n" "Der Körper einer `while`- und `for`-Schleife kann die Anweisungen `break` und `continue` enthalten. `break` stoppt die Schleife, `continue` überspringt den Rest des Schleifenkörpers und beginnt sofort mit dem nächsten Schleifendurchlauf.\n"
@ -748,7 +748,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "149c79ac", "id": "8ef0e09b",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -773,7 +773,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "2e91f7a3", "id": "ab77d5c1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Mit `break` kann man auch Endlosschleifen verlassen:\n" "Mit `break` kann man auch Endlosschleifen verlassen:\n"
@ -782,7 +782,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0b1b1ab2", "id": "72307342",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -797,7 +797,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d9bc10da", "id": "f3032c94",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### `for`-Schleifen\n", "### `for`-Schleifen\n",
@ -818,7 +818,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "99cd73cb", "id": "1e45bf78",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -829,7 +829,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "1a17064c", "id": "e723c97a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Oft benötigt man einen numerischen Schleifenzähler. Dafür gibt es das *range*-Konstrukt. Die einfachsten Formen sind \n", "Oft benötigt man einen numerischen Schleifenzähler. Dafür gibt es das *range*-Konstrukt. Die einfachsten Formen sind \n",
@ -839,7 +839,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3177977b", "id": "b3a01bd4",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -853,7 +853,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "0c859acc", "id": "8427a301",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -863,7 +863,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c31d91f6", "id": "f973a1cb",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -873,7 +873,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "c35be84d", "id": "63290cd9",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -882,7 +882,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "19034238", "id": "419963f0",
"metadata": {}, "metadata": {},
"source": [ "source": [
"#### Geschachtelte Schleifen _(nested loops)_\n", "#### Geschachtelte Schleifen _(nested loops)_\n",
@ -893,7 +893,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "9be68ac5", "id": "06ab8236",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -909,7 +909,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "99328006", "id": "19464d7e",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Man kann *nested loops* auch in einer `for`-Anweisung zusammenfassen. Dann beendet ein `break` die Gesamtschleife.\n" "Man kann *nested loops* auch in einer `for`-Anweisung zusammenfassen. Dann beendet ein `break` die Gesamtschleife.\n"
@ -918,7 +918,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "e437369c", "id": "e208b54c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -932,7 +932,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "e995a233", "id": "e5f41344",
"metadata": {}, "metadata": {},
"source": [ "source": [
":::{.callout-important .titlenormalxx}\n", ":::{.callout-important .titlenormalxx}\n",
@ -944,7 +944,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "2d2e2164", "id": "c903a887",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -957,7 +957,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "6c940891", "id": "68db2918",
"metadata": {}, "metadata": {},
"source": [ "source": [
"-------\n", "-------\n",
@ -1004,7 +1004,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "9d8ee587", "id": "6b3cf482",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1014,7 +1014,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "4a3975ec", "id": "2009bbff",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Hier wird die Eingabe als Gleitkommazahl interpretiert -- und `3E+2` oder `3f+2` (Float32) ebenso. \n" "Hier wird die Eingabe als Gleitkommazahl interpretiert -- und `3E+2` oder `3f+2` (Float32) ebenso. \n"
@ -1023,7 +1023,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "fa68ebcd", "id": "d1812cfd",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1032,7 +1032,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d3b54ba7", "id": "6cf09a01",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Ein Leerzeichen schafft Eindeutigkeit:\n" "Ein Leerzeichen schafft Eindeutigkeit:\n"
@ -1041,7 +1041,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "378e3e06", "id": "e6104540",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1050,7 +1050,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "d23bc72e", "id": "5215cde4",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Das funktioniert:\n" "Das funktioniert:\n"
@ -1059,7 +1059,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "ab2811f6", "id": "6828cede",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1069,7 +1069,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "c81689d3", "id": "5316e342",
"metadata": {}, "metadata": {},
"source": [ "source": [
"...und das nicht. `0x`, `0o`, `0b` wird als Anfang einer Hexadezimal-, Oktal- bzw. Binärkonstanten interpretiert.\n" "...und das nicht. `0x`, `0o`, `0b` wird als Anfang einer Hexadezimal-, Oktal- bzw. Binärkonstanten interpretiert.\n"
@ -1078,7 +1078,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a5eff7fc", "id": "d8ff4514",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1087,7 +1087,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "ac739eda", "id": "d2df69d1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Es gibt noch ein paar andere Fälle, bei denen die sehr kulante Syntax zu Überraschungen führt.\n" "- Es gibt noch ein paar andere Fälle, bei denen die sehr kulante Syntax zu Überraschungen führt.\n"
@ -1096,7 +1096,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "a69f9e83", "id": "02e802cf",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1108,7 +1108,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "3d9dc81e", "id": "227c2b1d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1117,7 +1117,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "89722987", "id": "b14d28e3",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Julia interpretiert das als Vergleich `Wichtig != 88`.\n", "Julia interpretiert das als Vergleich `Wichtig != 88`.\n",
@ -1128,7 +1128,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "87a6cfd7", "id": "41460c8d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1138,7 +1138,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "90ae7dac", "id": "8c7a3ede",
"metadata": {}, "metadata": {},
"source": [ "source": [
"- Operatoren der Form `.*`, `.+`,... haben in Julia eine spezielle Bedeutung (*broadcasting*, d.h., vektorisierte Operationen). \n" "- Operatoren der Form `.*`, `.+`,... haben in Julia eine spezielle Bedeutung (*broadcasting*, d.h., vektorisierte Operationen). \n"
@ -1147,7 +1147,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "538cd36e", "id": "1d6f31aa",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1156,7 +1156,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "7f39acd9", "id": "1ffdeba1",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Wieder gilt: Leerzeichen schaffen Klarheit!\n" "Wieder gilt: Leerzeichen schaffen Klarheit!\n"
@ -1165,7 +1165,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "45ceb4be", "id": "350fe2e3",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -1175,9 +1175,9 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "Julia 1.8.5", "display_name": "Julia 1.10.2",
"language": "julia", "language": "julia",
"name": "julia-1.8" "name": "julia-1.10"
} }
}, },
"nbformat": 4, "nbformat": 4,

1377
nb/types.ipynb
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