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				<h1 class="entry-title">Jupyter Notebook. Часть 2</h1>
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<p class="has-light-gray-color has-text-color"><a href="https://www.dmitrymakarov.ru/">Все курсы</a> &gt; <a href="https://www.dmitrymakarov.ru/python/">Программирование на Питоне</a> &gt; Занятие 14 (часть 2)</p>



<p>Во второй части занятия давайте подробнее поговорим про возможности Jupyter Notebook. Снова запустим только что созданный блокнот любым удобным способом.</p>


<div class="wp-block-ub-table-of-contents-block ub_table-of-contents" id="ub_table-of-contents-5275d2b3-c1ce-4d6f-83f6-0b6b73597f29" data-linktodivider="false" data-showtext="show" data-hidetext="hide" data-scrolltype="auto" data-initiallyhideonmobile="false"
                    data-initiallyshow="true"><div class="ub_table-of-contents-header-container"><div class="ub_table-of-contents-header">
                    <div class="ub_table-of-contents-title"><strong>Содержание занятия</strong></div></div></div><div class="ub_table-of-contents-extra-container"><div class="ub_table-of-contents-container ub_table-of-contents-1-column "><ul><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#0-kod-na-python>Код на Python</a><ul><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#1-vkladka-cell>Вкладка Cell</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#2-vkladka-kernel>Вкладка Kernel</a></li></ul></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#3-ustanovka-novykh-paketov>Установка новых пакетов</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#4-dva-pitona-na-odnom-kompyutere>Два Питона на одном компьютере</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#5-markdown-v-jupyter-notebook>Markdown в Jupyter Notebook</a><ul><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#6-zagolovki>Заголовки</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#7-abzatsy>Абзацы</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#8-vydelenie-teksta>Выделение текста</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#9-formatirovanie-koda-i-vydelennye-abzatsy>Форматирование кода и выделенные абзацы</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#10-spiski>Списки</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#11-ssylki-i-izobrazheniya>Ссылки и изображения</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#12-tablitsy>Таблицы</a></li></ul></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#13-formuly-na-latex>Формулы на LaTeX</a><ul><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#14-formatirovanie-teksta>Форматирование текста</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#15-nadstrochnye-i-podstrochnye-znaki>Надстрочные и подстрочные знаки</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#16-skobki>Скобки</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#17-drob-i-kvadratnyy-koren>Дробь и квадратный корень</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#18-grecheskie-bukvy>Греческие буквы</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#19-latinskie-oboznacheniya>Латинские обозначения</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#20-logicheskie-simvoly-i-simvoly-mnozhestva>Логические символы и символы множества</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#21-drugie-simvoly>Другие символы</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#22-kusochnaya-funktsiya-i-sistema-uravneniy>Кусочная функция и система уравнений</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#23-gorizontalnaya-figurnaya-skobka>Горизонтальная фигурная скобка</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#24-predel-proizvodnaya-integral>Предел, производная, интеграл</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#25-summa-i-proizvedenie>Сумма и произведение</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#26-matritsa>Матрица</a></li></ul></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#27-programmirovanie-na-r>Программирование на R</a><ul><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#28-peremennye-v-r>Переменные в R</a><ul><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#29-chislovye-strokovye-i-logicheskie-peremennye>Числовые, строковые и логические переменные</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#30-chislovye-peremennye-double-i-integer>Числовые переменные: double и integer</a></li></ul></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#31-vektor>Вектор</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#32-spisok>Список</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#33-matritsa>Матрица</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#34-massiv>Массив</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#35-faktornaya-peremennaya>Факторная переменная</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#36-datafreym>Датафрейм</a></li><li><a href=https://www.dmitrymakarov.ru/python/jupyter-notebook-14-02/#37-dopolnitelnye-pakety>Дополнительные пакеты</a></li></ul></li></ul></div></div></div>


<h2 class="wp-block-heading" id="0-kod-na-python">Код на Python</h2>



<p>В целом мы пишем обычный код на Питоне.</p>



<h3 class="wp-block-heading" id="1-vkladka-cell">Вкладка Cell</h3>



<p>Для управления запуском или исполнением ячеек можно использовать вкладку Cell.</p>



<figure class="wp-block-image size-large"><img fetchpriority="high" decoding="async" width="1024" height="636" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-1024x636.jpg" alt="вкладка Cell программы Jupyter Notebook" class="wp-image-13252" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-1024x636.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-300x186.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-768x477.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-1536x954.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-2048x1272.jpg 2048w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-1200x745.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-cell-tab-600x373.jpg 600w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Здесь мы можем, в частности:</p>



<ul class="wp-block-list">
<li>запускать ячейку и оставаться в ней же через <strong>Run Cells</strong>;</li>



<li>исполнять все ячейки в блокноте, выбрав <strong>Run All</strong>;</li>



<li>исполнять все ячейки выше (<strong>Run All Above</strong>) или ниже текущей (<strong>Run All Below</strong>);</li>



<li>очистить вывод ячеек, нажав <strong>All Output → Clear</strong>.</li>
</ul>



<h3 class="wp-block-heading" id="2-vkladka-kernel">Вкладка Kernel</h3>



<p>Командами вкладки Kernel мы управляем ядром (kernel) или вычислительным &#171;движком&#187; блокнота.</p>



<figure class="wp-block-image size-large"><img decoding="async" width="1024" height="645" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-1024x645.jpg" alt="вкладка Kernel программы Jupyter Notebook" class="wp-image-13253" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-1024x645.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-300x189.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-768x484.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-1536x967.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-2048x1289.jpg 2048w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-1200x756.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-kernel-tab-600x378.jpg 600w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>В этой вкладке мы можем, в частности:</p>



<ul class="wp-block-list">
<li>Прервать исполнение ячейки командой <strong>Interrupt</strong>. Это бывает полезно, если, например, исполнение кода занимает слишком много времени или в коде есть ошибка и исполнение кода не прервется самостоятельно.</li>



<li>Перезапустить kernel можно командой <strong>Restart</strong>. Кроме того, можно
<ul class="wp-block-list">
<li>очистить вывод (<strong>Restart &amp; Clear Output</strong>); и</li>



<li>заново запустить все ячейки (<strong>Restart &amp; Run All</strong>).</li>
</ul>
</li>
</ul>



<p>Несколько слов про то, что такое ядро и как в целом функционирует Jupyter Notebook.</p>



<figure class="wp-block-image size-large"><img decoding="async" width="1024" height="413" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-just-python-1024x413.png" alt="схема Jupyter Notebook: пользователь, браузер, сервер, ядро, файл" class="wp-image-13520" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-just-python-1024x413.png 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-just-python-300x121.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-just-python-768x310.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-just-python-600x242.png 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-just-python.png 1081w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Пользователь взаимодействует с блокнотом через браузер. Браузер в свою очередь отправляет запросы на сервер. Функция сервера заключается в том, чтобы загружать блокнот и сохранять внесенные изменения в формате JSON с расширением .ipynb. Одновременно, сервер обращается к ядру в тот момент, когда необходимо обработать код на каком-либо языке (например, на Питоне).</p>



<p class="has-background" style="background-color:#ffe8c4">Такое &#171;разделение труда&#187; между браузером, сервером и ядром позволяет во-первых, запускать Jupyter Notebook в любой операционной системе, во-вторых, в одной программе исполнять код на нескольких языках, и в-третьих, сохранять результат в файлах одного и того же формата.</p>



<p>Возможность программирования на нескольких языках (а значит использование нескольких ядер) мы изучим чуть позже, а пока посмотрим как устанавливать новые пакеты для Питона внутри Jupyter Notebook.</p>



<h2 class="wp-block-heading" id="3-ustanovka-novykh-paketov">Установка новых пакетов</h2>



<p>Установить новые пакеты в Anaconda можно непосредственно в ячейке, введя 
			<span id="urvanov-syntax-highlighter-672da5258a548446509428" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">!pip install &lt;package_name&gt;</span></span>. Например, попробуем установить Numpy.</p>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="134" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-1024x134.jpg" alt="установка пакетов внутри Jupyter Notebook" class="wp-image-13254" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-1024x134.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-300x39.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-768x101.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-1536x202.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-2048x269.jpg 2048w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-1200x158.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/pip-install-jupyter-600x79.jpg 600w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Система сообщила нам, что такой пакет уже установлен. Более того, мы видим путь к папке внутри дистрибутива Anaconda, в которой Jupyter &#171;нашел&#187; Numpy.</p>



<p class="has-background" style="background-color:#ffe8c4">При подготовке этого занятия я использовал два компьютера, поэтому имя пользователя на скриншотах указано как user или dmvma. На вашем компьютере при указании пути к файлу используйте ваше имя пользователя.</p>



<p>В последующих разделах мы рассмотрим дополнительные возможности по установке пакетов через Anaconda Prompt и Anaconda Navigator.</p>



<p>По ссылке ниже вы можете скачать код, который мы создали в Jupyter Notebook.</p>



<div class="wp-block-file"><a id="wp-block-file--media-98f31e4e-7963-4cdd-9a05-bfb53868fb38" href="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mynotebook.zip">mynotebook.zip</a><a href="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mynotebook.zip" class="wp-block-file__button wp-element-button" download aria-describedby="wp-block-file--media-98f31e4e-7963-4cdd-9a05-bfb53868fb38">Скачать</a></div>



<h2 class="wp-block-heading" id="4-dva-pitona-na-odnom-kompyutere">Два Питона на одном компьютере</h2>



<p>Обращу ваше внимание, что на данный момент на моем компьютере (как и у вас, если вы проделали <a href="https://www.dmitrymakarov.ru/python/script-13/#0-ustanovka-pitona-na-windows">шаги прошлого занятия</a>) установлено два Питона, один с сайта <a href="https://www.python.org/" target="_blank" rel="noreferrer noopener">www.python.org</a>⧉, второй &#8212; в составе дистрибутива Anaconda.</p>



<p>Посмотреть на установленные на компьютеры &#171;Питоны&#187; можно, набрав команду 
			<span id="urvanov-syntax-highlighter-672da5258a551202754987" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">where python</span></span> в Anaconda Prompt.</p>



<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="530" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-1024x530.jpg" alt="команда where python в Anaconda Prompt" class="wp-image-13411" style="width:755px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-1024x530.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-300x155.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-768x398.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-1536x796.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-2048x1061.jpg 2048w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-1200x622.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/different-python-installations-600x311.jpg 600w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Указав полный или абсолютный путь (absolute path) к каждому из файлов python.exe, мы можем в интерактивном режиме исполнять код на версии 3.10 (установили с www.python.org) и на версии 3.8 (установили в составе Anaconda). При запуске файла python.exe из папки WindowsApps система предложит установить Питон из Microsoft Store.</p>



<p class="has-background" style="background-color:#ffe8c4">В этом смысле нужно быть аккуратным и понимать, какой именно Питон вы используете и куда устанавливаете очередной пакет.</p>



<p>В нашем случае мы настроили работу так, чтобы устанавливать библиотеки для Питона с www.python.org через командную строку Windows, и устанавливать пакеты в Анаконду через Anaconda Prompt.</p>



<p>Убедиться в этом можно, проверив версии Питона через 
			<span id="urvanov-syntax-highlighter-672da5258a553161450260" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">python --version</span></span> в обеих программах.</p>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="307" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-1024x307.jpg" alt="команда python --version в командной строке Windows и Anaconda Prompt" class="wp-image-13419" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-1024x307.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-300x90.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-768x230.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-1536x461.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-2048x615.jpg 2048w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-1200x360.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/two-pythons-600x180.jpg 600w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Теперь попробуйте ввести в них команду 
			<span id="urvanov-syntax-highlighter-672da5258a555828040735" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">pip list</span></span> и сравнить установленные библиотеки.</p>



<h2 class="wp-block-heading" id="5-markdown-v-jupyter-notebook">Markdown в Jupyter Notebook</h2>



<p>Вернемся к Jupyter Notebook. Помимо ячеек с кодом, можно использовать текстовые ячейки, в которых поддерживается язык разметки Markdown. Мы уже коротко рассмотрели этот язык на прошлом занятии, когда <a href="https://www.dmitrymakarov.ru/python/script-13/#30-sozdanie-sobstvennogo-paketa">создавали пакет на Питоне</a>.</p>



<p class="has-background" style="background-color:#ffe8c4">По большому счету с помощью несложных команд Markdown, вы говорите Jupyter как отформатировать ту или иную часть текста.</p>



<p>Рассмотрим несколько основных возможностей форматирования (для удобстства и в силу практически полного совпадения два последующих раздела приведены в блокноте Google Colab).</p>



<p class="has-text-align-center has-white-color has-text-color has-background" style="background-color:#004235"><a href="https://colab.research.google.com/drive/1X2S_1uiKbmvXfwjtlmnRTL074WkftFO0?usp=sharing" target="_blank" rel="noreferrer noopener">Откроем блокнот к этому занятию</a>⧉</p>



<h3 class="wp-block-heading" id="6-zagolovki">Заголовки</h3>



<p>Заголовки создаются с помощью символа решетки.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a556160674389" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
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				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a556160674389-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a556160674389-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a556160674389-3">3</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a556160674389-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a556160674389-5">5</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a556160674389-6">6</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a556160674389-1"># Заголовок 1</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a556160674389-2">## Заголовок 2</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a556160674389-3">### Заголовок 3</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a556160674389-4">#### Заголовок 4</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a556160674389-5">##### Заголовок 5</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a556160674389-6">###### Заголовок 6</div></div></td>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="609" height="322" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings.png" alt="заголовки в markdown" class="wp-image-13337" style="width:526px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings.png 609w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-300x159.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-600x317.png 600w" sizes="(max-width: 609px) 100vw, 609px" /></figure>



<p>Если перед первым символом решетки поставить знак \, Markdown просто выведет символы решетки.</p>



<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="540" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-with-backslash-1024x540.jpg" alt="символ &quot;\&quot; перед символом решетки в markdown" class="wp-image-13450" style="width:544px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-with-backslash-1024x540.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-with-backslash-300x158.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-with-backslash-768x405.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-with-backslash-600x316.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-headings-with-backslash.jpg 1193w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<h3 class="wp-block-heading" id="7-abzatsy">Абзацы</h3>



<p>Абзацы отделяются друг от друга пробелами.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a558425765205" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a558425765205-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a558425765205-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a558425765205-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a558425765205-1">Абзац 1</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a558425765205-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a558425765205-3">Абзац 2</div></div></td>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="605" height="101" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-paragraphs.png" alt="абзацы в markdown" class="wp-image-13338" style="width:503px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-paragraphs.png 605w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-paragraphs-300x50.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-paragraphs-600x100.png 600w" sizes="(max-width: 605px) 100vw, 605px" /></figure>



<p>Мы также можем разделять абзацы прямой линией.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a559066124831" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
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				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a559066124831-1">---</div></div></td>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="905" height="25" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-horizontal-line.png" alt="горизонтальная линия в markdown" class="wp-image-13339" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-horizontal-line.png 905w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-horizontal-line-300x8.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-horizontal-line-768x21.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-horizontal-line-600x17.png 600w" sizes="(max-width: 905px) 100vw, 905px" /></figure>



<h3 class="wp-block-heading" id="8-vydelenie-teksta">Выделение текста</h3>



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		<div id="urvanov-syntax-highlighter-672da5258a55a121396857" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55a121396857-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55a121396857-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55a121396857-3">3</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55a121396857-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55a121396857-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55a121396857-1">**Полужирный стиль**</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55a121396857-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55a121396857-3">*Курсив*</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55a121396857-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55a121396857-5">~~Перечеркнутый стиль~~</div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="613" height="144" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-text-emphasis.png" alt="выделение текста в markdown" class="wp-image-13340" style="width:481px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-text-emphasis.png 613w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-text-emphasis-300x70.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-text-emphasis-600x141.png 600w" sizes="(max-width: 613px) 100vw, 613px" /></figure>



<h3 class="wp-block-heading" id="9-formatirovanie-koda-i-vydelennye-abzatsy">Форматирование кода и выделенные абзацы</h3>



<p>Мы можем выделять код внутри строки или отдельным абзацем.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a55b972531999" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55b972531999-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55b972531999-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55b972531999-3">3</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55b972531999-4">4</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55b972531999-1">Отформатируем код `print('Hello world!')` внутри строки и отдельным абзацем</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55b972531999-2">```</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55b972531999-3">print('Hello world!')</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55b972531999-4">```</div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="826" height="140" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-code.png" alt="форматирование кода в markdown" class="wp-image-13341" style="width:714px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-code.png 826w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-code-300x51.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-code-768x130.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-code-600x102.png 600w" sizes="(max-width: 826px) 100vw, 826px" /></figure>



<p>Возможно выделение и текстовых абзацев (так называемые blockquotes).</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a55c992939564" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55c992939564-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55c992939564-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55c992939564-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55c992939564-1">&gt; Markdown позволяет форматировать текст без использования тэгов.</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55c992939564-2">&gt;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55c992939564-3">&gt; Он был создан в 2004 году Джоном Грубером и Аароном Шварцем.</div></div></td>
					</tr>
				</table>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="745" height="117" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-blockquote.png" alt="выделенный абзац в markdown" class="wp-image-13342" style="width:611px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-blockquote.png 745w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-blockquote-300x47.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-blockquote-600x94.png 600w" sizes="(max-width: 745px) 100vw, 745px" /></figure>



<h3 class="wp-block-heading" id="10-spiski">Списки</h3>



<p>Посмотрим на создание упорядоченных и неупорядоченных списков.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a55e037384462" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-3">3</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-5">5</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-7">7</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-9">9</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-11">11</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55e037384462-12">12</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-1">**Упорядоченный список**</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-2">1. Пункт 1</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-3">1. Пункт 2 (нумерация ведется автоматически)</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-5">**Неупорядоченный список**</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-6">* Пункт 1.1</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-7">&nbsp;&nbsp;* Пункт 2.1</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-8">&nbsp;&nbsp;* Пункт 2.2</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-9">&nbsp;&nbsp;&nbsp;&nbsp;* Пункт 3.1</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-10">&nbsp;&nbsp;&nbsp;&nbsp;* Пункт 3.2</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-11">&nbsp;&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55e037384462-12">* Пункт 1.2</div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="748" height="418" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-list.png" alt="упорядоченные и неупорядоченные списки в markdown" class="wp-image-13343" style="width:623px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-list.png 748w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-list-300x168.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-list-600x335.png 600w" sizes="(max-width: 748px) 100vw, 748px" /></figure>



<h3 class="wp-block-heading" id="11-ssylki-i-izobrazheniya">Ссылки и изображения</h3>



<p>Текст ссылки заключается в квадратные скобки, сама ссылка &#8212; в круглые.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a55f877469494" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a55f877469494-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a55f877469494-1">[сайт проекта Jupyter](https://jupyter.org/)</div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="655" height="57" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-link.png" alt="ссылка в markdown" class="wp-image-13344" style="width:529px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-link.png 655w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-link-300x26.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-link-600x52.png 600w" sizes="(max-width: 655px) 100vw, 655px" /></figure>



<p>Изображение форматируется похожим образом.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a560520458142" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a560520458142-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a560520458142-1">![логотипы Jupyter и Python](https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-python.jpeg)</div></div></td>
					</tr>
				</table>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="756" height="277" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-python-logo.jpeg" alt="логотип Jupyter Notebook и Python" class="wp-image-13477" style="width:374px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-python-logo.jpeg 756w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-python-logo-300x110.jpeg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-python-logo-600x220.jpeg 600w" sizes="(max-width: 756px) 100vw, 756px" /></figure>



<h3 class="wp-block-heading" id="12-tablitsy">Таблицы</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a561257073388" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a561257073388-1">1</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a561257073388-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a561257073388-3">3</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a561257073388-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a561257073388-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a561257073388-1">| id | item&nbsp;&nbsp;&nbsp;&nbsp; | price |</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a561257073388-2">|--- |----------| ------|</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a561257073388-3">| 01 | pen&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;| 200&nbsp;&nbsp; |</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a561257073388-4">| 02 | pencil&nbsp;&nbsp; | 150&nbsp;&nbsp; |</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a561257073388-5">| 03 | notebook | 300&nbsp;&nbsp; |</div></div></td>
					</tr>
				</table>
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		</div>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="183" height="133" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/markdown-table.png" alt="таблица в markdown" class="wp-image-13345"/></figure>



<p>Таблицы для Markdown бывает удобно создавать с помощью <a href="https://www.tablesgenerator.com/markdown_tables" target="_blank" rel="noreferrer noopener">специального инструмента</a>⧉.</p>



<h2 class="wp-block-heading" id="13-formuly-na-latex">Формулы на LaTeX</h2>



<p>В текстовых полях можно вставлять формулы и математические символы с помощью системы верстки, которая называется LaTeX (произносится &#171;латэк&#187;). Они заключаются в одинарные или двойные символы $.</p>



<p>Если использовать одинарный символ $, то расположенная внутри формула останется в пределах того же абзаца (inline formula). Например, запись 
			<span id="urvanov-syntax-highlighter-672da5258a562870545661" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-v">y</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-v">x</span><span class="crayon-o">^</span><span class="crayon-cn">2</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></span></span> даст $ y = x^2 $.</p>



<p>В то время как 
			<span id="urvanov-syntax-highlighter-672da5258a563778237677" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-v">y</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-v">x</span><span class="crayon-o">^</span><span class="crayon-cn">2</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></span></span> поместит формулу в новый абзац (display formula).</p>



<p>$$ y = x^2 $$</p>



<p>Одинарный символ \ добавляет пробел. Двойной символ \\ переводит текст на новую строку.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a564301713299" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="hide">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a564301713299-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a564301713299-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">hat</span><span class="crayon-sy">{</span><span class="crayon-v">y</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-v">theta_0</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">theta_1 </span><span class="crayon-v">x_1</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">theta_2 </span><span class="crayon-v">x_2</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-sy">.</span><span class="crayon-sy">.</span><span class="crayon-sy">.</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">theta_n </span><span class="crayon-v">x</span><span class="crayon-sy">_</span>n<span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="390" height="79" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/latex-space-new-line.png" alt="символы \ (пробел) и \\ (перенос строки) в LaTeX" class="wp-image-13335" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/latex-space-new-line.png 390w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/latex-space-new-line-300x61.png 300w" sizes="(max-width: 390px) 100vw, 390px" /></figure></div>


<p>Рассмотрим некоторые элементы синтаксиса LaTeX.</p>



<h3 class="wp-block-heading" id="14-formatirovanie-teksta">Форматирование текста</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a568834202299" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a568834202299-7">7</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a568834202299-1"><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">text</span><span class="crayon-sy">{</span><span class="crayon-e">just </span><span class="crayon-v">text</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a568834202299-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a568834202299-3"><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">textbf</span><span class="crayon-sy">{</span><span class="crayon-v">bold</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a568834202299-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a568834202299-5"><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">textit</span><span class="crayon-sy">{</span><span class="crayon-v">italic</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a568834202299-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a568834202299-7"><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">underline</span><span class="crayon-sy">{</span><span class="crayon-v">undeline</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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</div>



<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="325" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting-1024x325.jpg" alt="форматирование текста в LaTeX" class="wp-image-13429" style="width:485px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting-1024x325.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting-300x95.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting-768x244.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting-1200x381.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting-600x190.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-text-formatting.jpg 1364w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<h3 class="wp-block-heading" id="15-nadstrochnye-i-podstrochnye-znaki">Надстрочные и подстрочные знаки</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a56a363973675" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56a363973675-13">13</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-1"><span class="crayon-e">hat</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">hat</span><span class="crayon-sy">{</span><span class="crayon-v">x</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-3"><span class="crayon-e">bar</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">bar</span><span class="crayon-sy">{</span><span class="crayon-v">x</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-5"><span class="crayon-e">vector</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">vec</span><span class="crayon-sy">{</span><span class="crayon-v">x</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-7"><span class="crayon-e">tilde</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">tilde</span><span class="crayon-sy">{</span><span class="crayon-v">x</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-8">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-9"><span class="crayon-e">superscript</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-e">e</span><span class="crayon-o">^</span><span class="crayon-sy">{</span><span class="crayon-v">ax</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-v">b</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-10">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-11"><span class="crayon-e">subscript</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-e">A_</span><span class="crayon-sy">{</span><span class="crayon-v">i</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">j</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-12">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56a363973675-13"><span class="crayon-e">degree</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-cn">90</span><span class="crayon-o">^</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-v">circ</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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</div>



<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="541" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts-1024x541.jpg" alt="надстрочные и подстрочные знаки в LaTeX" class="wp-image-13448" style="width:530px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts-1024x541.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts-300x158.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts-768x406.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts-1200x634.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts-600x317.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-subscripts-superscripts.jpg 1365w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<h3 class="wp-block-heading" id="16-skobki">Скобки</h3>



<p>Вначале рассмотрим код для скобок в пределах высоты строки.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a56b045270016" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a56b045270016-8">8</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-2"><span class="crayon-sy">(</span><span class="crayon-v">a</span><span class="crayon-o">+</span><span class="crayon-v">b</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-3"><span class="crayon-sy">[</span><span class="crayon-e">a</span><span class="crayon-o">+</span><span class="crayon-e">b</span><span class="crayon-sy">]</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-4"><span class="crayon-sy">\</span><span class="crayon-sy">{</span><span class="crayon-v">a</span><span class="crayon-o">+</span><span class="crayon-v">b</span><span class="crayon-sy">\</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-5"><span class="crayon-sy">\</span><span class="crayon-i">langle</span><span class="crayon-h"> </span><span class="crayon-v">x</span><span class="crayon-o">+</span><span class="crayon-i">y</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-i">rangle</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-6"><span class="crayon-o">|</span><span class="crayon-v">x</span><span class="crayon-o">+</span><span class="crayon-v">y</span><span class="crayon-o">|</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-7"><span class="crayon-sy">\</span><span class="crayon-o">|</span><span class="crayon-v">x</span><span class="crayon-o">+</span><span class="crayon-v">y</span><span class="crayon-sy">\</span><span class="crayon-o">|</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a56b045270016-8"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="596" height="232" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-brackets-parenthesis.png" alt="скобки в пределах высоты строки в LaTeX" class="wp-image-13566" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-brackets-parenthesis.png 596w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-brackets-parenthesis-300x117.png 300w" sizes="(max-width: 596px) 100vw, 596px" /></figure>



<p>Кроме того, с помощью 
			<span id="urvanov-syntax-highlighter-672da5258a56c330758240" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-sy">\</span><span class="crayon-v">left</span><span class="crayon-sy">(</span></span></span>, 
			<span id="urvanov-syntax-highlighter-672da5258a56d047315440" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-sy">\</span><span class="crayon-v">right</span><span class="crayon-sy">)</span></span></span>, а также 
			<span id="urvanov-syntax-highlighter-672da5258a56e497973333" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-sy">\</span><span class="crayon-v">left</span><span class="crayon-sy">[</span></span></span>, 
			<span id="urvanov-syntax-highlighter-672da5258a56f130840080" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-sy">\</span><span class="crayon-v">right</span><span class="crayon-sy">]</span></span></span> и так далее можно увеличить высоту скобки. Сравните.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a570956297433" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a570956297433-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a570956297433-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a570956297433-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a570956297433-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a570956297433-2"><span class="crayon-sy">\</span><span class="crayon-e">left</span><span class="crayon-sy">(</span><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-cn">1</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-cn">2</span><span class="crayon-sy">}</span><span class="crayon-sy">\</span><span class="crayon-v">right</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">qquad</span><span class="crayon-h"> </span><span class="crayon-sy">(</span><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-cn">1</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-cn">2</span><span class="crayon-sy">}</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a570956297433-3"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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</div>



<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="495" height="95" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-high-parenthesis.png" alt="круглые скобки с увеличенной высотой в LaTeX" class="wp-image-13567" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-high-parenthesis.png 495w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-high-parenthesis-300x58.png 300w" sizes="(max-width: 495px) 100vw, 495px" /></figure>



<p>Также можно использовать отдельные команды для скобок различного размера.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a571404051999" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a571404051999-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a571404051999-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a571404051999-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a571404051999-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a571404051999-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a571404051999-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a571404051999-2"><span class="crayon-sy">\</span><span class="crayon-e">big</span><span class="crayon-sy">(</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">Big</span><span class="crayon-sy">(</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">bigg</span><span class="crayon-sy">(</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">Bigg</span><span class="crayon-sy">(</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a571404051999-3"><span class="crayon-sy">\</span><span class="crayon-e">big</span><span class="crayon-sy">]</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">Big</span><span class="crayon-sy">]</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">bigg</span><span class="crayon-sy">]</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">Bigg</span><span class="crayon-sy">]</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a571404051999-4"><span class="crayon-sy">\</span><span class="crayon-e">big</span><span class="crayon-sy">\</span><span class="crayon-sy">{</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">Big</span><span class="crayon-sy">\</span><span class="crayon-sy">{</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">bigg</span><span class="crayon-sy">\</span><span class="crayon-sy">{</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">Bigg</span><span class="crayon-sy">\</span><span class="crayon-sy">{</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a571404051999-5"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="501" height="271" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-size-brackets-parenthesis.png" alt="скобки различного размера в LaTeX" class="wp-image-13568" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-size-brackets-parenthesis.png 501w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-size-brackets-parenthesis-300x162.png 300w" sizes="(max-width: 501px) 100vw, 501px" /></figure>



<h3 class="wp-block-heading" id="17-drob-i-kvadratnyy-koren">Дробь и квадратный корень</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a572927201240" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a572927201240-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a572927201240-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a572927201240-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a572927201240-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a572927201240-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a572927201240-1"><span class="crayon-e">fraction</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a572927201240-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a572927201240-3"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-cn">1</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-cn">1</span><span class="crayon-o">+</span><span class="crayon-e">e</span><span class="crayon-o">^</span><span class="crayon-sy">{</span><span class="crayon-o">-</span><span class="crayon-v">z</span><span class="crayon-sy">}</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a572927201240-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a572927201240-5"><span class="crayon-e">square</span><span class="crayon-h"> </span><span class="crayon-e">root</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">sqrt</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-v">sigma</span><span class="crayon-o">^</span><span class="crayon-cn">2</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
<!-- [Format Time: 0.0003 seconds] -->
</div>



<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="221" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-1024x221.jpg" alt="дробь и квадратный корень в LaTeX" class="wp-image-13434" style="width:579px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-1024x221.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-300x65.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-768x166.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-1536x332.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-1200x260.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root-600x130.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-fraction-square-root.jpg 1572w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<h3 class="wp-block-heading" id="18-grecheskie-bukvy">Греческие буквы</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a573941521249" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-13">13</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-14">14</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-15">15</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-16">16</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-17">17</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-18">18</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-19">19</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-20">20</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-21">21</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-22">22</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-23">23</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-24">24</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-25">25</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-26">26</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-27">27</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-28">28</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-29">29</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-30">30</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-31">31</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a573941521249-32">32</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size: … [Строка слишком длинная. Вы можете скачать файл]
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="431" height="771" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-Greek.png" alt="греческий алфавит в LaTeX" class="wp-image-13602" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-Greek.png 431w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-Greek-168x300.png 168w" sizes="(max-width: 431px) 100vw, 431px" /></figure>



<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="429" height="274" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-Greek-2.png" alt="греческий алфавит в LaTeX 2" class="wp-image-13603" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-Greek-2.png 429w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-Greek-2-300x192.png 300w" sizes="(max-width: 429px) 100vw, 429px" /></figure>



<h3 class="wp-block-heading" id="19-latinskie-oboznacheniya">Латинские обозначения</h3>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a575229287774-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a575229287774-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a575229287774-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a575229287774-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a575229287774-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a575229287774-6">6</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a575229287774-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a575229287774-2"><span class="crayon-sy">\</span><span class="crayon-e">sin</span><span class="crayon-sy">(</span><span class="crayon-o">-</span><span class="crayon-sy">\</span><span class="crayon-v">alpha</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-o">-</span><span class="crayon-sy">\</span><span class="crayon-e">sin</span><span class="crayon-sy">(</span><span class="crayon-sy">\</span><span class="crayon-v">alpha</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a575229287774-3"><span class="crayon-sy">\</span><span class="crayon-e">cos</span><span class="crayon-sy">(</span><span class="crayon-sy">\</span><span class="crayon-v">theta</span><span class="crayon-sy">)</span><span class="crayon-o">=</span><span class="crayon-sy">\</span><span class="crayon-e">sin</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">left</span><span class="crayon-sy">(</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-v">pi</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-cn">2</span><span class="crayon-sy">}</span><span class="crayon-o">-</span><span class="crayon-sy">\</span><span class="crayon-i">theta</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-v">right</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a575229287774-4"><span class="crayon-sy">\</span><span class="crayon-e">tan</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-e">sin</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-e">cos</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a575229287774-5"><span class="crayon-sy">\</span><span class="crayon-e">log_b</span><span class="crayon-sy">(</span><span class="crayon-cn">1</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">0</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a575229287774-6"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="585" height="235" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-latin-expressions.png" alt="латинские обозначения в LaTeX" class="wp-image-13515" style="width:461px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-latin-expressions.png 585w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-latin-expressions-300x121.png 300w" sizes="(max-width: 585px) 100vw, 585px" /></figure>



<h3 class="wp-block-heading" id="20-logicheskie-simvoly-i-simvoly-mnozhestva">Логические символы и символы множества</h3>



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				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size: … [Строка слишком длинная. Вы можете скачать файл]
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="586" height="623" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-logic-sets.png" alt="логические символы и символы множества в LaTeX" class="wp-image-13585" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-logic-sets.png 586w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-logic-sets-282x300.png 282w" sizes="(max-width: 586px) 100vw, 586px" /></figure>



<h3 class="wp-block-heading" id="21-drugie-simvoly">Другие символы</h3>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-13">13</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a577557384773-14">14</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size: … [Строка слишком длинная. Вы можете скачать файл]
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="545" height="445" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-other-symbols.png" alt="другие символы в LaTeX" class="wp-image-13586" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-other-symbols.png 545w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-other-symbols-300x245.png 300w" sizes="(max-width: 545px) 100vw, 545px" /></figure>



<h3 class="wp-block-heading" id="22-kusochnaya-funktsiya-i-sistema-uravneniy">Кусочная функция и система уравнений</h3>



<p>Посмотрим на запись функции sgn (sign function) средствами LaTeX.</p>



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					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a578668892339-9">9</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a578668892339-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a578668892339-2"><span class="crayon-e">sgn</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">left</span><span class="crayon-sy">\</span><span class="crayon-sy">{</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a578668892339-3"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-sy">\</span><span class="crayon-e">begin</span><span class="crayon-sy">{</span><span class="crayon-k ">array</span><span class="crayon-sy">}</span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a578668892339-4"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-cn">1</span><span class="crayon-h"> </span><span class="crayon-o">&amp;</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">mbox</span><span class="crayon-sy">{</span><span class="crayon-st">if</span><span class="crayon-h"> </span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-e">x</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-st">in</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">mathbf</span><span class="crayon-sy">{</span><span class="crayon-v">N</span><span class="crayon-sy">}</span><span class="crayon-o">^</span><span class="crayon-o">*</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a578668892339-5"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-cn">0</span><span class="crayon-h"> </span><span class="crayon-o">&amp;</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">mbox</span><span class="crayon-sy">{</span><span class="crayon-st">if</span><span class="crayon-h"> </span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-h"> </span><span class="crayon-v">x</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">0</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a578668892339-6"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-o">-</span><span class="crayon-cn">1</span><span class="crayon-h"> </span><span class="crayon-o">&amp;</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">mbox</span><span class="crayon-sy">{</span><span class="crayon-st">else</span><span class="crayon-sy">.</span><span class="crayon-sy">}</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a578668892339-7"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-sy">\</span><span class="crayon-e">end</span><span class="crayon-sy">{</span><span class="crayon-k ">array</span><span class="crayon-sy">}</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a578668892339-8"><span class="crayon-sy">\</span><span class="crayon-v">right</span><span class="crayon-sy">.</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a578668892339-9"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="569" height="135" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sign-function.png" alt="функция sgn в LaTeX" class="wp-image-13589" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sign-function.png 569w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sign-function-300x71.png 300w" sizes="(max-width: 569px) 100vw, 569px" /></figure>



<p>Схожим образом записывается система линейных уравнений.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a579289316325" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a579289316325-8">8</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a579289316325-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a579289316325-2"><span class="crayon-sy">\</span><span class="crayon-e">left</span><span class="crayon-sy">\</span><span class="crayon-sy">{</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a579289316325-3"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-sy">\</span><span class="crayon-e">begin</span><span class="crayon-sy">{</span><span class="crayon-v">matrix</span><span class="crayon-sy">}</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a579289316325-4"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-cn">4x</span><span class="crayon-h">&nbsp;&nbsp;</span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-cn">3y</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">20</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a579289316325-5"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-o">-</span><span class="crayon-cn">5x</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span><span class="crayon-cn">9y</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">26</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a579289316325-6"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="crayon-sy">\</span><span class="crayon-e">end</span><span class="crayon-sy">{</span><span class="crayon-v">matrix</span><span class="crayon-sy">}</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a579289316325-7"><span class="crayon-sy">\</span><span class="crayon-v">right</span><span class="crayon-sy">.</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a579289316325-8"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="532" height="87" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-simultaneous-equations.png" alt="система линейных уравнений в LaTeX" class="wp-image-13590" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-simultaneous-equations.png 532w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-simultaneous-equations-300x49.png 300w" sizes="(max-width: 532px) 100vw, 532px" /></figure>



<h3 class="wp-block-heading" id="23-gorizontalnaya-figurnaya-skobka">Горизонтальная фигурная скобка</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a57a951978769" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57a951978769-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57a951978769-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57a951978769-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57a951978769-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57a951978769-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57a951978769-6">6</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57a951978769-1"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57a951978769-2"><span class="crayon-sy">\</span><span class="crayon-e">overbrace</span><span class="crayon-sy">{</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57a951978769-3"><span class="crayon-h">&nbsp;&nbsp;</span><span class="crayon-sy">\</span><span class="crayon-e">underbrace</span><span class="crayon-sy">{</span><span class="crayon-v">a</span><span class="crayon-sy">}</span><span class="crayon-e">_</span><span class="crayon-sy">{</span><span class="crayon-v">real</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57a951978769-4"><span class="crayon-h">&nbsp;&nbsp;</span><span class="crayon-sy">\</span><span class="crayon-e">underbrace</span><span class="crayon-sy">{</span><span class="crayon-v">b</span><span class="crayon-sy">}</span><span class="crayon-e">_</span><span class="crayon-sy">{</span><span class="crayon-v">imaginary</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-v">i</span><span class="crayon-sy">}</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57a951978769-5"><span class="crayon-h">&nbsp;&nbsp;</span><span class="crayon-o">^</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-e">textit</span><span class="crayon-sy">{</span><span class="crayon-k ">complex</span><span class="crayon-h"> </span><span class="crayon-v">number</span><span class="crayon-sy">}</span><span class="crayon-sy">}</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57a951978769-6"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="578" height="117" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-overbrace-underbrace.png" alt="горизонтальная фигурная скобка в LaTeX" class="wp-image-13606" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-overbrace-underbrace.png 578w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-overbrace-underbrace-300x61.png 300w" sizes="(max-width: 578px) 100vw, 578px" /></figure>



<h3 class="wp-block-heading" id="24-predel-proizvodnaya-integral">Предел, производная, интеграл</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a57b111318909" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-13">13</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-14">14</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-15">15</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-16">16</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-17">17</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-18">18</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-19">19</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-20">20</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-21">21</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-22">22</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-23">23</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-24">24</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-25">25</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-26">26</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-27">27</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57b111318909-28">28</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-1">Пределы<span class="crayon-o">:</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-3"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">lim_</span><span class="crayon-sy">{</span><span class="crayon-i">x</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-v">to</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-sy">\</span><span class="crayon-v">infty</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-e">f</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-5"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">lim_</span><span class="crayon-sy">{</span><span class="crayon-i">x</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-v">to</span><span class="crayon-h"> </span><span class="crayon-o">-</span><span class="crayon-sy">\</span><span class="crayon-v">infty</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-e">f</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-7"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">lim_</span><span class="crayon-sy">{</span><span class="crayon-i">x</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-i">to</span><span class="crayon-h"> </span>с<span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-e">f</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-8">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-9">Производная<span class="crayon-h"> </span><span class="crayon-sy">(</span>нотация<span class="crayon-h"> </span>Лагранжа<span class="crayon-sy">)</span><span class="crayon-o">:</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-10">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-11"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-i">f</span>'<span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-12">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-13">Частная<span class="crayon-h"> </span>производная<span class="crayon-h"> </span><span class="crayon-sy">(</span>нотация<span class="crayon-h"> </span>Лейбница<span class="crayon-sy">)</span><span class="crayon-o">:</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-14">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-15"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-i">partial</span><span class="crayon-h"> </span><span class="crayon-v">f</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-i">partial</span><span class="crayon-h"> </span><span class="crayon-v">x</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-16">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-17">Градиент<span class="crayon-o">:</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-18">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-19"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-20"><span class="crayon-sy">\</span><span class="crayon-i">nabla</span><span class="crayon-h"> </span><span class="crayon-e">f</span><span class="crayon-sy">(</span><span class="crayon-v">x_1</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">x_2</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">=</span> </div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-21"><span class="crayon-sy">\</span><span class="crayon-e">begin</span><span class="crayon-sy">{</span><span class="crayon-v">bmatrix</span><span class="crayon-sy">}</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-22"><span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-i">partial</span><span class="crayon-h"> </span><span class="crayon-v">f</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-e">partial </span><span class="crayon-v">x_1</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-sy">\</span> <span class="crayon-sy">\</span><span class="crayon-e">frac</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-i">partial</span><span class="crayon-h"> </span><span class="crayon-v">f</span><span class="crayon-sy">}</span><span class="crayon-sy">{</span><span class="crayon-sy">\</span><span class="crayon-e">partial </span><span class="crayon-v">x_2</span><span class="crayon-sy">}</span> </div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-23"><span class="crayon-sy">\</span><span class="crayon-e">end</span><span class="crayon-sy">{</span><span class="crayon-v">bmatrix</span><span class="crayon-sy">}</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-24"><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-25">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-26">Интеграл<span class="crayon-o">:</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-27">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57b111318909-28"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-sy">\</span><span class="crayon-e">int_</span><span class="crayon-sy">{</span><span class="crayon-v">a</span><span class="crayon-sy">}</span><span class="crayon-o">^</span><span class="crayon-i">b</span><span class="crayon-h"> </span><span class="crayon-e">f</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-sy">)</span><span class="crayon-v">dx</span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="773" height="657" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-limits-derivative-integral.png" alt="пределы, производная, интеграл в LaTeX" class="wp-image-13612" style="width:605px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-limits-derivative-integral.png 773w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-limits-derivative-integral-300x255.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-limits-derivative-integral-768x653.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-limits-derivative-integral-600x510.png 600w" sizes="(max-width: 773px) 100vw, 773px" /></figure>



<h3 class="wp-block-heading" id="25-summa-i-proizvedenie">Сумма и произведение</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a57d292271772" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57d292271772-9">9</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-1">Сумма<span class="crayon-o">:</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-3"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-h"> </span><span class="crayon-sy">\</span><span class="crayon-k ">sum</span><span class="crayon-sy">\</span><span class="crayon-e">limits_</span><span class="crayon-sy">{</span><span class="crayon-v">i</span><span class="crayon-o">=</span><span class="crayon-cn">1</span><span class="crayon-sy">}</span><span class="crayon-o">^</span><span class="crayon-e">n</span><span class="crayon-h"> </span><span class="crayon-e">a_</span><span class="crayon-sy">{</span><span class="crayon-v">i</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-5"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-sy">\</span><span class="crayon-e">sum_</span><span class="crayon-sy">{</span><span class="crayon-v">i</span><span class="crayon-o">=</span><span class="crayon-cn">1</span><span class="crayon-sy">}</span><span class="crayon-o">^</span><span class="crayon-e">n</span><span class="crayon-h"> </span><span class="crayon-e">a_</span><span class="crayon-sy">{</span><span class="crayon-v">i</span><span class="crayon-sy">}</span><span class="crayon-h"> </span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-7">Произведение<span class="crayon-o">:</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-8">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a57d292271772-9"><span class="crayon-sy">$</span><span class="crayon-sy">$</span><span class="crayon-sy">\</span><span class="crayon-e">prod_</span><span class="crayon-sy">{</span><span class="crayon-v">j</span><span class="crayon-o">=</span><span class="crayon-cn">1</span><span class="crayon-sy">}</span><span class="crayon-o">^</span><span class="crayon-e">m</span><span class="crayon-h"> </span><span class="crayon-e">a_</span><span class="crayon-sy">{</span><span class="crayon-v">j</span><span class="crayon-sy">}</span><span class="crayon-sy">$</span><span class="crayon-sy">$</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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</div>



<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="703" height="334" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sum-product.png" alt="сумма и произведение в LaTeX" class="wp-image-13615" style="width:600px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sum-product.png 703w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sum-product-300x143.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-sum-product-600x285.png 600w" sizes="(max-width: 703px) 100vw, 703px" /></figure>



<h3 class="wp-block-heading" id="26-matritsa">Матрица</h3>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a57e595572431" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
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data-line="urvanov-syntax-highlighter-672da5258a57e595572431-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-13">13</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-14">14</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-15">15</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-16">16</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-17">17</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-18">18</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-19">19</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-20">20</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-21">21</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-22">22</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-23">23</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-24">24</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-25">25</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-26">26</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-27">27</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-28">28</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-29">29</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-30">30</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-31">31</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-32">32</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-33">33</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-34">34</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-35">35</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-36">36</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-37">37</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-38">38</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-39">39</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-40">40</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-41">41</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-42">42</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-43">43</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-44">44</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-45">45</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-46">46</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-47">47</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-48">48</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-49">49</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-50">50</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-51">51</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-52">52</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a57e595572431-53">53</div></div>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="734" height="690" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-matrix.png" alt="матрица в LaTeX" class="wp-image-13621" style="width:631px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-matrix.png 734w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-matrix-300x282.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/LaTeX-matrix-600x564.png 600w" sizes="(max-width: 734px) 100vw, 734px" /></figure>



<h2 class="wp-block-heading" id="27-programmirovanie-na-r">Программирование на R</h2>



<p>Jupyter Notebook позволяет писать код на других языках программирования, не только на Питоне. Попробуем написать и исполнить код на R, языке, который специально разрабатывался для data science.</p>



<p>Вначале нам понадобится установить kernel для R. Откроем Anaconda Prompt и введем следующую команду 
			<span id="urvanov-syntax-highlighter-672da5258a57f407527571" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">conda install -c r r-irkernel</span></span>. В процессе установки система спросит продолжать или нет (Proceed ([y]/n)?). Нажмите <strong>y + Enter</strong>.</p>



<p>Откройте Jupyter Notebook. В списке файлов создайте блокнот на R. Назовем его <strong>rprogramming</strong>.</p>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="534" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-1024x534.jpg" alt="создание Jupyter Notebook с ядром на R" class="wp-image-13286" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-1024x534.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-300x156.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-768x400.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-1536x801.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-2048x1068.jpg 2048w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-1200x626.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/R-kernel-600x313.jpg 600w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>После установки нового ядра и создания еще одного файла .ipynb схема работы нашего Jupyter Notebook немного изменилась.</p>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="490" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-python-r-1024x490.png" alt="схема Jupyter Notebook: пользователь, браузер, сервер, ядра (Python и R), файлы" class="wp-image-13522" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-python-r-1024x490.png 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-python-r-300x143.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-python-r-768x367.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-python-r-600x287.png 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/jupyter-notebook-kernel-scheme-python-r.png 1081w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Теперь мы готовы писать код на R. Мы уже начали знакомиться с этим языком, когда изучали <a href="https://www.dmitrymakarov.ru/python/oop-12/#24-funktsionalnoe-programmirovanie-na-r">парадигмы программирования</a>. Сегодня мы рассмотрим основные типы данных и особенности синтаксиса.</p>



<h3 class="wp-block-heading" id="28-peremennye-v-r">Переменные в R</h3>



<h4 class="wp-block-heading" id="29-chislovye-strokovye-i-logicheskie-peremennye">Числовые, строковые и логические переменные</h4>



<p>Как и в Питоне, в R мы можем создавать числовые (numeric), строковые (character) и логические (logical) переменные.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a580470360201" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a580470360201-8">8</div></div>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a580470360201-1"><span class="crayon-c"># поместим число 42 в переменную numeric_var</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a580470360201-2"><span class="crayon-v">numeric_var</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">42</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a580470360201-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a580470360201-4"><span class="crayon-c"># строку поместим в переменную text_var</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a580470360201-5"><span class="crayon-v">text_var</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-s">'Hello world!'</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a580470360201-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a580470360201-7"><span class="crayon-c"># наконец присвоим значение TRUE переменной logical_var</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a580470360201-8"><span class="crayon-t">TRUE</span><span class="crayon-h"> </span><span class="crayon-o">-&gt;</span><span class="crayon-h"> </span><span class="crayon-v">logical_var</span></div></div></td>
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<p>Для присвоения значений можно использовать как оператор 
			<span id="urvanov-syntax-highlighter-672da5258a581906817089" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-o">=</span></span></span>, так и операторы присваивания 
			<span id="urvanov-syntax-highlighter-672da5258a582563413368" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-o">&lt;</span><span class="crayon-o">-</span></span></span> и 
			<span id="urvanov-syntax-highlighter-672da5258a583136639256" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-o">-&gt;</span></span></span>. Обратите внимание, используя 
			<span id="urvanov-syntax-highlighter-672da5258a584616214116" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-o">-&gt;</span></span></span> мы можем поместить значение слева, а переменную справа.</p>



<p>Посмотрим на результат (в Jupyter Notebook можно обойтись без <strong>функции print()</strong>).</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a585109828803" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a585109828803-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a585109828803-1"><span class="crayon-v">text_var</span></div></div></td>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a586468906150" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a586468906150-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a586468906150-1">'Hello world!'</div></div></td>
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<p>Выведем класс созданных нами объектов с помощью <strong>функции class()</strong>.</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a588035983956-1">'numeric'</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a588035983956-2">'character'</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a588035983956-3">'logical'</div></div></td>
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<p>Тип данных можно посмотреть с помощью <strong>функции typeof()</strong>.</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a589882326244-1"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">numeric_var</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a589882326244-2"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">text_var</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a589882326244-3"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">logical_var</span><span class="crayon-sy">)</span></div></div></td>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58a748038598-1">'double'</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a58a748038598-2">'character'</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58a748038598-3">'logical'</div></div></td>
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<p>Хотя вывод этих функций очень похож, мы, тем не менее, видим, что классу numeric соответствует тип данных double (число с плавающей точкой с как минимум двумя знаками после запятой).</p>



<h4 class="wp-block-heading" id="30-chislovye-peremennye-double-i-integer">Числовые переменные: double и integer</h4>



<p>По умолчанию, в R и целые числа, и дроби хранятся в формате double (сокращённое от double precision number, т.е. число двойной точности).</p>



<p class="has-background" style="background-color:#ffe8c4">Тип данных double в R соответствует типу float в Питоне.</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58b209866461-1"><span class="crayon-c"># еще раз поместим число 42 в переменную numeric_var</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a58b209866461-2"><span class="crayon-v">numeric_var</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-cn">42</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58b209866461-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a58b209866461-4"><span class="crayon-c"># выведем тип данных</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58b209866461-5"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">numeric_var</span><span class="crayon-sy">)</span></div></div></td>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58c717508763-1">'double'</div></div></td>
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<p>Принудительно перевести 42 в целочисленное значение можно с помощью <strong>функции as.integer()</strong>.</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58d452769762-1"><span class="crayon-v">int_var</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-t">integer</span><span class="crayon-sy">(</span><span class="crayon-v">numeric_var</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a58d452769762-2"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">int_var</span><span class="crayon-sy">)</span></div></div></td>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58e774269960-1">'integer'</div></div></td>
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<p>Кроме того, если после числа поставить L, это число автоматически превратится в integer.</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a58f458074839-1"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-cn">42L</span><span class="crayon-sy">)</span></div></div></td>
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<p>Превратить integer обратно в double можно с помощью функций <strong>as.double()</strong> и <strong>as.numeric()</strong>.</p>



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					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a591091453560-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a591091453560-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a591091453560-1"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-t">double</span><span class="crayon-sy">(</span><span class="crayon-v">int_var</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a591091453560-2"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-e">numeric</span><span class="crayon-sy">(</span><span class="crayon-cn">42L</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a592845695958" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a592845695958-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a592845695958-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a592845695958-1">'double'</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a592845695958-2">'double'</div></div></td>
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<p>Если число хранится в формате строки, его можно перевести обратно в число (integer или double).</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a593498596077" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a593498596077-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a593498596077-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a593498596077-1"><span class="crayon-v">text_var</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-s">'42'</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a593498596077-2"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">text_var</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a594437703149" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a594437703149-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a594437703149-1">'character'</div></div></td>
					</tr>
				</table>
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		</div>
<!-- [Format Time: 0.0000 seconds] -->
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a595181625094" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a595181625094-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a595181625094-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a595181625094-1"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-e">numeric</span><span class="crayon-sy">(</span><span class="crayon-v">text_var</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-c"># можно также использовать as.double()</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a595181625094-2"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-t">integer</span><span class="crayon-sy">(</span><span class="crayon-v">text_var</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span></div></div></td>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a596087937556" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a596087937556-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a596087937556-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a596087937556-1">'double'</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a596087937556-2">'integer'</div></div></td>
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<h3 class="wp-block-heading" id="31-vektor">Вектор</h3>



<p><strong>Вектор</strong> (vector) &#8212; это одномерная структура, которая может содержать множество элементов одного типа. Вектор можно создать с помощью <strong>функции c()</strong>.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a597965994421" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a597965994421-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a597965994421-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a597965994421-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a597965994421-1"><span class="crayon-c"># создадим вектор с информацией о продажах товара в магазине за неделю (в тыс. рублей)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a597965994421-2"><span class="crayon-v">sales</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-cn">24</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">28</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">32</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">25</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">30</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">31</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">29</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a597965994421-3"><span class="crayon-v">sales</span></div></div></td>
					</tr>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a598090694025" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a598090694025-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a598090694025-1">24 28 32 25 30 31 29</div></div></td>
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<p>С помощью функций <strong>length()</strong> и <strong>typeof()</strong> мы можем посмотреть соответственно общее количество элементов и тип данных каждого из них.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a599691964764" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a599691964764-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a599691964764-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a599691964764-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a599691964764-1"><span class="crayon-c"># посмотрим на общее количество элементов и тип данных каждого из них</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a599691964764-2"><span class="crayon-e">length</span><span class="crayon-sy">(</span><span class="crayon-v">sales</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a599691964764-3"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">sales</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
				</table>
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		</div>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a59a303724729" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a59a303724729-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a59a303724729-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a59a303724729-1">7</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a59a303724729-2">'double'</div></div></td>
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<p>У вектора есть <strong>индекс</strong>, который (в отличие, например, от <a href="https://www.dmitrymakarov.ru/python/list-tuple-set-07/#2-indeks-i-srez-spiska">списков в Питоне</a>), начинается с <em>единицы</em>.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a59b508661021" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a59b508661021-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a59b508661021-1"><span class="crayon-v">sales</span><span class="crayon-sy">[</span><span class="crayon-cn">1</span><span class="crayon-sy">]</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a59c240599722" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a59c240599722-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a59c240599722-1">24</div></div></td>
					</tr>
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<p>При указании <strong>диапазона</strong> выводятся и первый, и последний его элементы.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a59d670732568" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a59d670732568-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a59d670732568-1"><span class="crayon-v">sales</span><span class="crayon-sy">[</span><span class="crayon-cn">1</span><span class="crayon-o">:</span><span class="crayon-cn">5</span><span class="crayon-sy">]</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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</div>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a59e336787629" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a59e336787629-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a59e336787629-1">24 28 32 25 30</div></div></td>
					</tr>
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<p><strong>Отрицательный индекс</strong> убирает элементы из вектора.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a59f100663716" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a59f100663716-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a59f100663716-1"><span class="crayon-v">sales</span><span class="crayon-sy">[</span><span class="crayon-o">-</span><span class="crayon-cn">5</span><span class="crayon-sy">]</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
<!-- [Format Time: 0.0001 seconds] -->
</div>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a0992793583" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a0992793583-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a0992793583-1">24 28 32 25 31 29</div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<p><strong>Именованный вектор</strong> (named vector) создается с помощью <strong>функции names()</strong>.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a1459178141" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a1459178141-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a1459178141-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a1459178141-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a1459178141-1"><span class="crayon-c"># создадим еще один вектор с названиями дней недели</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a1459178141-2"><span class="crayon-v">days_vector</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'Понедельник'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Вторник'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Среда'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Четверг'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Пятница'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Суббота'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Воскресенье'</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a1459178141-3"><span class="crayon-v">days_vector</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a2854383229" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a2854383229-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a2854383229-1">'Понедельник' 'Вторник' 'Среда' 'Четверг' 'Пятница' 'Суббота' 'Воскресенье'</div></div></td>
					</tr>
				</table>
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		</div>
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</div>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a3573428243" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a3573428243-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a3573428243-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a3573428243-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a3573428243-1"><span class="crayon-c"># создадим именованный вектор с помощью функции names()</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a3573428243-2"><span class="crayon-e">names</span><span class="crayon-sy">(</span><span class="crayon-v">sales</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">days_vector</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a3573428243-3"><span class="crayon-v">sales</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="780" height="438" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/named-vector-in-r.jpg" alt="именованный вектор в R" class="wp-image-13627" style="width:378px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/named-vector-in-r.jpg 780w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/named-vector-in-r-300x168.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/named-vector-in-r-768x431.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/named-vector-in-r-600x337.jpg 600w" sizes="(max-width: 780px) 100vw, 780px" /></figure>



<p>Выводить элементы именованного вектора можно не только по числовому индексу, но и по их названиям.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a4109804171" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a4109804171-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a4109804171-1"><span class="crayon-v">sales</span><span class="crayon-sy">[</span><span class="crayon-s">'Воскресенье'</span><span class="crayon-sy">]</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a6527103040" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a6527103040-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a6527103040-1">Воскресенье: 29</div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<h3 class="wp-block-heading" id="32-spisok">Список</h3>



<p>В отличие от вектора, <strong>список</strong> (list) может содержать множество элементов различных типов.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a7635505946" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a7635505946-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a7635505946-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a7635505946-1"><span class="crayon-c"># список создается с помощью функции list()</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a7635505946-2"><span class="crayon-e">list</span><span class="crayon-sy">(</span><span class="crayon-s">'DS'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'ML'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-cn">21</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">24</span><span class="crayon-sy">)</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-t">TRUE</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-t">FALSE</span><span class="crayon-sy">)</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">42.0</span><span class="crayon-sy">)</span></div></div></td>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a8589521060" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
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				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-13">13</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a8589521060-14">14</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-1">[[1]]</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-2">[1] "DS"</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-4">[[2]]</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-5">[1] "ML"</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-7">[[3]]</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-8">[1] 21 24</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-9">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-10">[[4]]</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-11">[1]&nbsp;&nbsp;TRUE FALSE</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-12">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-13">[[5]]</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a8589521060-14">[1] 42</div></div></td>
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<h3 class="wp-block-heading" id="33-matritsa">Матрица</h3>



<p><strong>Матрица</strong> (matrix) в R &#8212; это двумерная структура, содержащая одинаковый тип данных (чаще всего числовой). Матрица создается с помощью <strong>функции matrix()</strong> с параметрами data, nrow, ncol и byrow.</p>



<ul class="wp-block-list">
<li>data &#8212; данные для создания матрицы</li>



<li>nrow и ncol &#8212; количество строк и столбцов</li>



<li>byrow &#8212; параметр, указывающий заполнять ли элементы матрицы построчно (TRUE) или по столбцам (FALSE)</li>
</ul>



<p>Рассмотрим несколько примеров. Cоздадим последовательность целых чисел (по сути, тоже вектор).</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5a9545105348" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a9545105348-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a9545105348-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a9545105348-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5a9545105348-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5a9545105348-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a9545105348-1"><span class="crayon-c"># для этого подойдет функция seq()</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a9545105348-2"><span class="crayon-v">sqn</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">seq</span><span class="crayon-sy">(</span><span class="crayon-cn">1</span><span class="crayon-o">:</span><span class="crayon-cn">9</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a9545105348-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5a9545105348-4"><span class="crayon-e">sqn</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5a9545105348-5"><span class="crayon-e">typeof</span><span class="crayon-sy">(</span><span class="crayon-v">sqn</span><span class="crayon-sy">)</span></div></div></td>
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<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5b9481487103" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5b9481487103-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5b9481487103-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5b9481487103-1">1 2 3 4 5 6 7 8 9</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5b9481487103-2">'integer'</div></div></td>
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<p>Используем эту последовательность для создания двух матриц.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5ba667978124" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5ba667978124-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5ba667978124-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5ba667978124-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5ba667978124-1"><span class="crayon-c"># создадим матрицу, заполняя значения построчно</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5ba667978124-2"><span class="crayon-v">mtx</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">matrix</span><span class="crayon-sy">(</span><span class="crayon-v">sqn</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">nrow</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">ncol</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">byrow</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-t">TRUE</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5ba667978124-3"><span class="crayon-v">mtx</span></div></div></td>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="180" height="246" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-by-row-matrix.jpg" alt="матрица в R, значения заполнены построчно" class="wp-image-13573" style="width:100px;height:auto"/></figure>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5bc077687252" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bc077687252-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5bc077687252-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bc077687252-3">3</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bc077687252-1"><span class="crayon-c"># теперь создадим матрицу, заполняя значения по столбцам</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5bc077687252-2"><span class="crayon-v">mtx</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">matrix</span><span class="crayon-sy">(</span><span class="crayon-v">sqn</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">nrow</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">ncol</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">byrow</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-t">FALSE</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bc077687252-3"><span class="crayon-v">mtx</span></div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="183" height="249" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-by-column-matrix.jpg" alt="матрица в R, значения заполнены по столбцам" class="wp-image-13574" style="width:99px;height:auto"/></figure>



<p>Зададим названия для строк и столбцов второй матрицы.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5bd745997758" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bd745997758-11">11</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-1"><span class="crayon-c"># создадим два вектора с названиями строк и столбцов</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-2"><span class="crayon-v">rows</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'Row 1'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Row 2'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Row 3'</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-3"><span class="crayon-v">cols</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'Col 1'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Col 2'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Col 3'</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-5"><span class="crayon-c"># используем функции rownames() и colnames(),</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-6"><span class="crayon-c"># чтобы передать эти названия нашей матрице</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-7"><span class="crayon-e">rownames</span><span class="crayon-sy">(</span><span class="crayon-v">mtx</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">rows</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-8"><span class="crayon-e">colnames</span><span class="crayon-sy">(</span><span class="crayon-v">mtx</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-i">cols</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-9">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-10"><span class="crayon-c"># посмотрим на результат</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bd745997758-11"><span class="crayon-v">mtx</span></div></div></td>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="519" height="322" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-named-matrix.jpg" alt="матрица в R с названиями столбцов и строк" class="wp-image-13575" style="width:250px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-named-matrix.jpg 519w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-named-matrix-300x186.jpg 300w" sizes="(max-width: 519px) 100vw, 519px" /></figure>



<p>Посмотрим на размерность этой матрицы с помощью <strong>функции dim()</strong>.</p>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5be839446497-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5be839446497-1"><span class="crayon-e">dim</span><span class="crayon-sy">(</span><span class="crayon-v">mtx</span><span class="crayon-sy">)</span></div></div></td>
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5bf518586979-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5bf518586979-1">3 3</div></div></td>
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<h3 class="wp-block-heading" id="34-massiv">Массив</h3>



<p>В отличие от матрицы, <strong>массив</strong> (array) &#8212; это многомерная структура. Создадим трехмерный массив размерностью 3 х 2 х 3. Вначале создадим три матрицы размером 3 х 2.</p>



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			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c0660669610-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c0660669610-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c0660669610-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c0660669610-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c0660669610-5">5</div></div>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c0660669610-1"><span class="crayon-c"># создадим три матрицы размером 3 х 2,</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c0660669610-2"><span class="crayon-c"># заполненные пятерками, шестерками и семерками </span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c0660669610-3"><span class="crayon-v">a</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">matrix</span><span class="crayon-sy">(</span><span class="crayon-cn">5</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">2</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c0660669610-4"><span class="crayon-v">b</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">matrix</span><span class="crayon-sy">(</span><span class="crayon-cn">6</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">2</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c0660669610-5"><span class="crayon-v">c</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">matrix</span><span class="crayon-sy">(</span><span class="crayon-cn">7</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">2</span><span class="crayon-sy">)</span></div></div></td>
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<p>Теперь соединим их с помощью <strong>функции array()</strong>. Передадим этой функции два параметра в форме векторов: данные (data) и размерность (dim).</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c1474373198-1"><span class="crayon-v">arr</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-k ">array</span><span class="crayon-sy">(</span><span class="crayon-v">data</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-v">a</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">b</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">c</span><span class="crayon-sy">)</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-c"># вектор с матрицами</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c1474373198-2"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-v">dim</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-cn">3</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">2</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">3</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span><span class="crayon-h">&nbsp;&nbsp;</span><span class="crayon-c"># вектор размерности</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c1474373198-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c1474373198-4"><span class="crayon-k ">print</span><span class="crayon-sy">(</span><span class="crayon-v">arr</span><span class="crayon-sy">)</span></div></div></td>
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-12">12</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-13">13</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-14">14</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-15">15</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-16">16</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-17">17</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-18">18</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-19">19</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c2872316618-20">20</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-1">, , 1</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-2">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-3">&nbsp;&nbsp;&nbsp;&nbsp; [,1] [,2]</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-4">[1,]&nbsp;&nbsp;&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;5</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-5">[2,]&nbsp;&nbsp;&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;5</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-6">[3,]&nbsp;&nbsp;&nbsp;&nbsp;5&nbsp;&nbsp;&nbsp;&nbsp;5</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-7">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-8">, , 2</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-9">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-10">&nbsp;&nbsp;&nbsp;&nbsp; [,1] [,2]</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-11">[1,]&nbsp;&nbsp;&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;6</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-12">[2,]&nbsp;&nbsp;&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;6</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-13">[3,]&nbsp;&nbsp;&nbsp;&nbsp;6&nbsp;&nbsp;&nbsp;&nbsp;6</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-14">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-15">, , 3</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-16">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-17">&nbsp;&nbsp;&nbsp;&nbsp; [,1] [,2]</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-18">[1,]&nbsp;&nbsp;&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp;7</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-19">[2,]&nbsp;&nbsp;&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp;7</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c2872316618-20">[3,]&nbsp;&nbsp;&nbsp;&nbsp;7&nbsp;&nbsp;&nbsp;&nbsp;7</div></div></td>
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<h3 class="wp-block-heading" id="35-faktornaya-peremennaya">Факторная переменная</h3>



<p><strong>Факторная переменная</strong> или <strong>фактор</strong> (factor) &#8212; специальная структура для хранения <a href="https://www.dmitrymakarov.ru/intro/stats-08/#1-1-kategorialnye-kachestvennye-dannye">категориальных данных</a>. Вначале немного теории.</p>



<p>Как мы узнаем на курсе <a href="https://www.dmitrymakarov.ru/data-analysis/">анализа данных</a>, категориальные данные бывают номинальными и порядковыми:</p>



<ul class="wp-block-list">
<li><em>номинальные категориальные</em> (nominal categorical) данные представлены категориями, в которых нет естественного внутреннего порядка. Например, пол или цвет волос человека, марка автомобиля могут быть отнесены к определенным категориям, но не могут быть упорядочены;</li>



<li><em>порядковые категориальные</em> (ordinal categorical) данные наоборот обладают внутренним, свойственным им порядком. К таким данным относятся шкала удовлетворенности потребителей, класс железнодорожного билета, должность или звание, а также любая количественная переменная, разбитая на категории (например, низкий, средний и высокий уровень зарплат).</li>
</ul>



<p>Посмотрим, как учесть такие данные с помощью R. Начнем с номинальных данных.</p>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c4056348385-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c4056348385-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c4056348385-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c4056348385-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c4056348385-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c4056348385-6">6</div></div>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c4056348385-1"><span class="crayon-c"># предположим, что мы собрали данные о цветах нескольких автомобилей и поместили их в вектор</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c4056348385-2"><span class="crayon-v">color_vector</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'blue'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'blue'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'white'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'black'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'yellow'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'white'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'white'</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c4056348385-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c4056348385-4"><span class="crayon-c"># преобразуем этот вектор в фактор с помощью функции factor()</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c4056348385-5"><span class="crayon-v">factor_color</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">factor</span><span class="crayon-sy">(</span><span class="crayon-v">color_vector</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c4056348385-6"><span class="crayon-v">factor_color</span></div></div></td>
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<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="231" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/nominal-factor-r-1024x231.jpg" alt="номинальный фактор в R" class="wp-image-13628" style="width:474px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/nominal-factor-r-1024x231.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/nominal-factor-r-300x68.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/nominal-factor-r-768x173.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/nominal-factor-r-600x136.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/nominal-factor-r.jpg 1169w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Как вы видите, <strong>функция factor()</strong> разбила данные на категории, при этом эти категории остались неупорядоченными. Посмотрим на класс созданного объекта.</p>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c5709084593-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c5709084593-1"><span class="crayon-t">class</span><span class="crayon-sy">(</span><span class="crayon-v">factor_color</span><span class="crayon-sy">)</span></div></div></td>
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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c6650978543-1">1</div></div>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c6650978543-1">'factor'</div></div></td>
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<p>Теперь поработаем с порядковыми данными.</p>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-5">5</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-6">6</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-7">7</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-8">8</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-9">9</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-10">10</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-11">11</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5c7505167521-12">12</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-1"><span class="crayon-c"># возьмем данные измерений температуры, выраженные категориями</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-2"><span class="crayon-v">temperature_vector</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'High'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Low'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'High'</span><span class="crayon-sy">,</span><span class="crayon-s">'Low'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Medium'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'High'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Low'</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-4"><span class="crayon-c"># создадим фактор </span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-5"><span class="crayon-v">factor_temperature</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-e">factor</span><span class="crayon-sy">(</span><span class="crayon-v">temperature_vector</span><span class="crayon-sy">,</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-6"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-c"># указав параметр order = TRUE</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-7"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-v">order</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-t">TRUE</span><span class="crayon-sy">,</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-8"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-c"># а также вектор упорядоченных категорий</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-9"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-v">levels</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'Low'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Medium'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'High'</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-10">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-11"><span class="crayon-c"># посмотрим на результат</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5c7505167521-12"><span class="crayon-v">factor_temperature</span></div></div></td>
					</tr>
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<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="261" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/ordinal-factor-r-1024x261.jpg" alt="порядковый фактор в R" class="wp-image-13633" style="width:451px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/ordinal-factor-r-1024x261.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/ordinal-factor-r-300x77.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/ordinal-factor-r-768x196.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/ordinal-factor-r-600x153.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/ordinal-factor-r.jpg 1124w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>



<p>Выведем класс созданного объекта.</p>



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		<div id="urvanov-syntax-highlighter-672da5258a5c9155037918" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5c9155037918-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5c9155037918-1"><span class="crayon-t">class</span><span class="crayon-sy">(</span><span class="crayon-v">factor_temperature</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
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			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5ca443553428-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5ca443553428-1">'ordered' 'factor'</div></div></td>
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<p>Добавлю, что количество элементов в каждой из категорий можно посмотреть с помощью <strong>функции summary().</strong></p>



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			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5cb868418890-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5cb868418890-1"><span class="crayon-e">summary</span><span class="crayon-sy">(</span><span class="crayon-v">factor_temperature</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="554" height="203" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/categories-summary-r.jpg" alt="количество элементов в каждой из категорий порядкового фактора" class="wp-image-13638" style="width:237px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/categories-summary-r.jpg 554w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/categories-summary-r-300x110.jpg 300w" sizes="(max-width: 554px) 100vw, 554px" /></figure>



<h3 class="wp-block-heading" id="36-datafreym">Датафрейм</h3>



<p>Датафрейм в R выполняет примерно ту же функцию, что и в Питоне. С помощью <strong>функции data.frame()</strong> создадим простой датафрейм, где <a href="https://www.dmitrymakarov.ru/python/functions-06/#1-parametry-i-argumenty-funktsii">параметрами</a> будут названия столбцов, а аргументами &#8212; векторы их значений.</p>



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		<div id="urvanov-syntax-highlighter-672da5258a5cc219238157" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5cc219238157-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5cc219238157-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5cc219238157-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5cc219238157-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5cc219238157-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5cc219238157-1"><span class="crayon-v">df</span><span class="crayon-h"> </span><span class="crayon-o">&lt;</span><span class="crayon-o">-</span><span class="crayon-h"> </span><span class="crayon-v">data</span><span class="crayon-sy">.</span><span class="crayon-e">frame</span><span class="crayon-sy">(</span><span class="crayon-v">city</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'Москва'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Париж'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Лондон'</span><span class="crayon-sy">)</span><span class="crayon-sy">,</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5cc219238157-2"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-v">population</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-cn">12.7</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">2.1</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">8.9</span><span class="crayon-sy">)</span><span class="crayon-sy">,</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5cc219238157-3"><span class="crayon-h">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span class="crayon-v">country</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-e">c</span><span class="crayon-sy">(</span><span class="crayon-s">'Россия'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Франция'</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-s">'Великобритания'</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5cc219238157-4">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5cc219238157-5"><span class="crayon-v">df</span></div></div></td>
					</tr>
				</table>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="717" height="326" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-r.jpg" alt="датафрейм в R" class="wp-image-13642" style="width:341px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-r.jpg 717w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-r-300x136.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-r-600x273.jpg 600w" sizes="(max-width: 717px) 100vw, 717px" /></figure>



<p>Доступ к элементам датафрейма можно получить по <strong>индексам строк и столбцов</strong>, которые также начинаются с <em>единицы</em>.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5cd890760952" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5cd890760952-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5cd890760952-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5cd890760952-1"><span class="crayon-c"># выведем значения первой строки и первого столбца</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5cd890760952-2"><span class="crayon-v">df</span><span class="crayon-sy">[</span><span class="crayon-cn">1</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-cn">1</span><span class="crayon-sy">]</span></div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="948" height="245" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-element-r.jpg" alt="индекс ячеек датафрейма в R" class="wp-image-13649" style="width:418px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-element-r.jpg 948w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-element-r-300x78.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-element-r-768x198.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/dataframe-element-r-600x155.jpg 600w" sizes="(max-width: 948px) 100vw, 948px" /></figure>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5ce382077552-1"><span class="crayon-c"># выведем всю первую строку</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5ce382077552-2"><span class="crayon-v">df</span><span class="crayon-sy">[</span><span class="crayon-cn">1</span><span class="crayon-sy">,</span><span class="crayon-sy">]</span></div></div></td>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="967" height="177" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/first-line.jpg" alt="первая строка датафрейма в R" class="wp-image-13650" style="width:415px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/first-line.jpg 967w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/first-line-300x55.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/first-line-768x141.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/first-line-600x110.jpg 600w" sizes="(max-width: 967px) 100vw, 967px" /></figure>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5cf418964054-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5cf418964054-2">2</div></div>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5cf418964054-1"><span class="crayon-c"># выведем второй столбец</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5cf418964054-2"><span class="crayon-v">df</span><span class="crayon-sy">[</span><span class="crayon-sy">,</span><span class="crayon-cn">2</span><span class="crayon-sy">]</span></div></div></td>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d0066405576-1">12.7 2.1 8.9</div></div></td>
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<p>Получить доступ к столбцам можно и так.</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d1207914996-1"><span class="crayon-v">df</span><span class="crayon-sy">$</span><span class="crayon-v">population</span></div></div></td>
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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d2969858706-1">12.7 2.1 8.9</div></div></td>
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<h3 class="wp-block-heading" id="37-dopolnitelnye-pakety">Дополнительные пакеты</h3>



<p>Как и в <a href="https://www.dmitrymakarov.ru/intro/data-and-plots-07/#0-struktura-pitona">Питоне</a>, в R мы можем установить дополнительные пакеты через Anaconda Prompt. Например, установим пакет ggplot2 для визуализации данных. Для этого введем команду 
			<span id="urvanov-syntax-highlighter-672da5258a5d3631757746" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">conda install r-ggplot2</span></span>.</p>



<p class="has-background" style="background-color:#ffe8c4">В целом команда установки пакетов для R следующая: 
			<span id="urvanov-syntax-highlighter-672da5258a5d4979242154" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;">conda install r-&lt;package_name&gt;</span></span>.</p>



<p>Продемонстрируем работу с этим пакетом с помощью несложного датасета mtcars (данные об автомобилях, взятые из журнала Motor Trend за 1974 год).</p>



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						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-1"><span class="crayon-c"># импортируем библиотеку datasets</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-2"><span class="crayon-r">library</span><span class="crayon-sy">(</span><span class="crayon-v">datasets</span><span class="crayon-sy">)</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-4"><span class="crayon-c"># загрузим датасет mtcars</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-5"><span class="crayon-e">data</span><span class="crayon-sy">(</span><span class="crayon-v">mtcars</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-6">&nbsp;</div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-7"><span class="crayon-c"># выведем его на экран</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5d5304429756-8"><span class="crayon-v">mtcars</span></div></div></td>
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<figure class="wp-block-image size-large is-resized"><img loading="lazy" decoding="async" width="1024" height="931" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-1024x931.jpg" alt="датасет mtcars в R" class="wp-image-13654" style="width:647px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-1024x931.jpg 1024w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-300x273.jpg 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-768x698.jpg 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-1536x1396.jpg 1536w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-1200x1091.jpg 1200w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r-600x545.jpg 600w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/mtcars-dataset-r.jpg 1561w" sizes="(max-width: 1024px) 100vw, 1024px" /><figcaption class="wp-element-caption"><em><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-light-gray-color">Примечание. Здесь приведена лишь часть датасета.</mark></em></figcaption></figure>



<p>Теперь импортируем установленную ранее библиотеку ggplot2.</p>



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<p>Построим <a href="https://www.dmitrymakarov.ru/intro/stats-08/#3-2-kolichestvennye-dannye">гистограмму</a> по столбцу mpg (miles per galon, расход в милях на галлон топлива). Для построения гистограммы нам потребуется через &#171;+&#187; объединить две функции:</p>



<ul class="wp-block-list">
<li><strong>функцию ggplot()</strong>, которой мы передадим наши данные и еще одну <em>функцию aes()</em>, от англ. aesthetics, которая свяжет ось x нашего графика и столбец данных mpg; а также</li>



<li><strong>функцию geom_histogram()</strong> с параметрами bins (количество интервалов) и binwidth (их ширина), которая и будет отвечать за создание гистограммы.</li>
</ul>



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					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5d8448125211-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5d8448125211-2">2</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5d8448125211-3">3</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5d8448125211-4">4</div><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5d8448125211-5">5</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d8448125211-1"><span class="crayon-c"># данными будет датасет mtcars, столбцом по оси x - mpg</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5d8448125211-2"><span class="crayon-e">ggplot</span><span class="crayon-sy">(</span><span class="crayon-v">data</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-v">mtcars</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-e">aes</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-v">mpg</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d8448125211-3">&nbsp;</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5d8448125211-4"><span class="crayon-c"># типом графика будет гистограмма с 10 интервалами шириной 5 миль на галлон каждый</span></div><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5d8448125211-5"><span class="crayon-e">geom_histogram</span><span class="crayon-sy">(</span><span class="crayon-v">bins</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">10</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">binwidth</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">5</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="840" height="840" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-histogram.png" alt="гистограмма в R" class="wp-image-13673" style="width:508px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-histogram.png 840w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-histogram-300x300.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-histogram-150x150.png 150w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-histogram-768x768.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-histogram-600x600.png 600w" sizes="(max-width: 840px) 100vw, 840px" /></figure>



<p>Примерно так же мы можем построить график плотности распределения (density plot). Только теперь мы передадим функции <strong>aes()</strong> еще один параметр 
			<span id="urvanov-syntax-highlighter-672da5258a5d9355168201" class="urvanov-syntax-highlighter-syntax urvanov-syntax-highlighter-syntax-inline  crayon-theme-familiar-my-copy crayon-theme-familiar-my-copy-inline urvanov-syntax-highlighter-font-consolas" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important;"><span class="crayon-pre urvanov-syntax-highlighter-code" style="font-size: 16px !important; line-height: 22px !important;font-size: 16px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><span class="crayon-v">fill</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-e">factor</span><span class="crayon-sy">(</span><span class="crayon-v">vs</span><span class="crayon-sy">)</span></span></span>, который (предварительно превратив столбец в фактор через <strong>as.factor()</strong>) позволит разбить данные на две категории по столбцу vs. В этом датасете признак vs указывает на конфигурацию двигателя (расположение цилиндров), v-образное, v-shaped (vs == 0) или рядное, straight (vs == 1).</p>



<p>Кроме того, для непосредственного построения графика мы будем использовать новую функцию <strong>geom_density()</strong> с параметром alpha, отвечающим за прозрачность заполнения пространства под кривыми.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5da411296691" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5da411296691-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5da411296691-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5da411296691-1"><span class="crayon-e">ggplot</span><span class="crayon-sy">(</span><span class="crayon-v">data</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-v">mtcars</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-e">aes</span><span class="crayon-sy">(</span><span class="crayon-v">x</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-v">mpg</span><span class="crayon-sy">,</span><span class="crayon-h"> </span><span class="crayon-v">fill</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-st">as</span><span class="crayon-sy">.</span><span class="crayon-e">factor</span><span class="crayon-sy">(</span><span class="crayon-v">vs</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span><span class="crayon-sy">)</span><span class="crayon-h"> </span><span class="crayon-o">+</span><span class="crayon-h"> </span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5da411296691-2"><span class="crayon-e">geom_density</span><span class="crayon-sy">(</span><span class="crayon-v">alpha</span><span class="crayon-h"> </span><span class="crayon-o">=</span><span class="crayon-h"> </span><span class="crayon-cn">0.3</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
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<figure class="wp-block-image size-full is-resized"><img loading="lazy" decoding="async" width="840" height="840" src="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-density.png" alt="график плотности в R" class="wp-image-13674" style="width:621px;height:auto" srcset="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-density.png 840w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-density-300x300.png 300w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-density-150x150.png 150w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-density-768x768.png 768w, https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/r-ggplot-density-600x600.png 600w" sizes="(max-width: 840px) 100vw, 840px" /></figure>



<p>Дополнительно замечу, что к столбцам датафрейма можно применять множество различных функций, например, рассчитать среднее арифметическое или медиану с помощью несложных для запоминания <strong>mean()</strong> и <strong>median()</strong>.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5db721195208" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5db721195208-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5db721195208-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5db721195208-1"><span class="crayon-e">mean</span><span class="crayon-sy">(</span><span class="crayon-v">mtcars</span><span class="crayon-sy">$</span><span class="crayon-v">mpg</span><span class="crayon-sy">)</span></div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5db721195208-2"><span class="crayon-e">median</span><span class="crayon-sy">(</span><span class="crayon-v">mtcars</span><span class="crayon-sy">$</span><span class="crayon-v">mpg</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
				</table>
			</div>
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</div>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5dc189396874" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5dc189396874-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5dc189396874-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5dc189396874-1">20.090625</div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5dc189396874-2">19.2</div></div></td>
					</tr>
				</table>
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<p>Кроме того, мы можем применить уже знакомую нам функцию <strong>summary()</strong>, которая для количественного столбца выдаст минимальное и максимальное значения, первый (Q1) и третий (Q3) квартили, а также медиану и среднее значение.</p>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5dd598269923" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5dd598269923-1">1</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5dd598269923-1"><span class="crayon-e">summary</span><span class="crayon-sy">(</span><span class="crayon-v">mtcars</span><span class="crayon-sy">$</span><span class="crayon-v">mpg</span><span class="crayon-sy">)</span></div></div></td>
					</tr>
				</table>
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</div>



<div class="wp-block-urvanov-syntax-highlighter-code-block"><!-- Urvanov Syntax Highlighter v2.8.37 -->

		<div id="urvanov-syntax-highlighter-672da5258a5de411600262" class="urvanov-syntax-highlighter-syntax crayon-theme-familiar-my-copy urvanov-syntax-highlighter-font-consolas urvanov-syntax-highlighter-os-pc print-yes notranslate" data-settings=" minimize scroll-always" style=" margin-top: 15px; margin-bottom: 15px; margin-left: 15px; margin-right: 15px; font-size: 16px !important; line-height: 22px !important;">
		
			<div class="urvanov-syntax-highlighter-plain-wrap"></div>
			<div class="urvanov-syntax-highlighter-main" style="">
				<table class="crayon-table">
					<tr class="urvanov-syntax-highlighter-row">
				<td class="crayon-nums " data-settings="show">
					<div class="urvanov-syntax-highlighter-nums-content" style="font-size: 16px !important; line-height: 22px !important;"><div class="crayon-num" data-line="urvanov-syntax-highlighter-672da5258a5de411600262-1">1</div><div class="crayon-num crayon-striped-num" data-line="urvanov-syntax-highlighter-672da5258a5de411600262-2">2</div></div>
				</td>
						<td class="urvanov-syntax-highlighter-code"><div class="crayon-pre" style="font-size: 16px !important; line-height: 22px !important; -moz-tab-size:4; -o-tab-size:4; -webkit-tab-size:4; tab-size:4;"><div class="crayon-line" id="urvanov-syntax-highlighter-672da5258a5de411600262-1">&nbsp;&nbsp; Min. 1st Qu.&nbsp;&nbsp;Median&nbsp;&nbsp;&nbsp;&nbsp;Mean 3rd Qu.&nbsp;&nbsp;&nbsp;&nbsp;Max. </div><div class="crayon-line crayon-striped-line" id="urvanov-syntax-highlighter-672da5258a5de411600262-2">&nbsp;&nbsp;10.40&nbsp;&nbsp; 15.43&nbsp;&nbsp; 19.20&nbsp;&nbsp; 20.09&nbsp;&nbsp; 22.80&nbsp;&nbsp; 33.90</div></div></td>
					</tr>
				</table>
			</div>
		</div>
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<p>В файле ниже содержится созданный нами код на R.</p>



<div class="wp-block-file"><a id="wp-block-file--media-76e9de62-d30d-4e3f-9452-454f5305734d" href="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/rprogramming.zip">rprogramming.zip</a><a href="https://www.dmitrymakarov.ru/wp-content/uploads/2022/05/rprogramming.zip" class="wp-block-file__button wp-element-button" download aria-describedby="wp-block-file--media-76e9de62-d30d-4e3f-9452-454f5305734d">Скачать</a></div>



<p>Вернемся к <a href="https://www.dmitrymakarov.ru/python/jupyter-notebook-14-03/">основной теме занятия</a>.</p>

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