CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>SymPy - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"51ab3d72-69b3-431e-8be7-11c651455fe1","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"SymPy","wgTitle":"SymPy","wgCurRevisionId":1281408036,"wgRevisionId":1281408036,"wgArticleId":12168252,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description is different from Wikidata","All articles with vague or ambiguous time","Vague or ambiguous time from August 2021","Articles with example Python (programming language) code","Computer algebra system software for Linux","Computer algebra system software for macOS","Computer algebra system software for Windows","Free computer algebra systems","Free mathematics software","Free software programmed in Python","Python (programming language) scientific libraries"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"SymPy","wgRelevantArticleId":12168252,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":10000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q5971368","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGELevelingUpEnabledForUser":false}; RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.quicksurveys.init","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.22"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Sympy_logo.svg/1200px-Sympy_logo.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1200"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Sympy_logo.svg/800px-Sympy_logo.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="800"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Sympy_logo.svg/640px-Sympy_logo.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="640"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="SymPy - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/SymPy"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=SymPy&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/SymPy"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-SymPy rootpage-SymPy skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages"><span>Special pages</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=SymPy" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=SymPy" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=SymPy" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=SymPy" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Features" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Features"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Features</span> </div> </a> <button aria-controls="toc-Features-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Features subsection</span> </button> <ul id="toc-Features-sublist" class="vector-toc-list"> <li id="toc-Core_capabilities" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Core_capabilities"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Core capabilities</span> </div> </a> <ul id="toc-Core_capabilities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polynomials" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polynomials"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Polynomials</span> </div> </a> <ul id="toc-Polynomials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Calculus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Calculus"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Calculus</span> </div> </a> <ul id="toc-Calculus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solving_equations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Solving_equations"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Solving equations</span> </div> </a> <ul id="toc-Solving_equations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discrete_math" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Discrete_math"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Discrete math</span> </div> </a> <ul id="toc-Discrete_math-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matrices" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Matrices"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Matrices</span> </div> </a> <ul id="toc-Matrices-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Geometry</span> </div> </a> <ul id="toc-Geometry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Plotting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Plotting"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.8</span> <span>Plotting</span> </div> </a> <ul id="toc-Plotting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.9</span> <span>Physics</span> </div> </a> <ul id="toc-Physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.10</span> <span>Statistics</span> </div> </a> <ul id="toc-Statistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Combinatorics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Combinatorics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.11</span> <span>Combinatorics</span> </div> </a> <ul id="toc-Combinatorics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Printing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Printing"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.12</span> <span>Printing</span> </div> </a> <ul id="toc-Printing-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Related_projects" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_projects"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Related projects</span> </div> </a> <ul id="toc-Related_projects-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dependencies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dependencies"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Dependencies</span> </div> </a> <ul id="toc-Dependencies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">SymPy</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 10 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-10" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">10 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/SymPy" title="SymPy – Catalan" lang="ca" hreflang="ca" data-title="SymPy" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/SymPy" title="SymPy – German" lang="de" hreflang="de" data-title="SymPy" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/SymPy" title="SymPy – Spanish" lang="es" hreflang="es" data-title="SymPy" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/SymPy" title="SymPy – French" lang="fr" hreflang="fr" data-title="SymPy" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/SymPy" title="SymPy – Japanese" lang="ja" hreflang="ja" data-title="SymPy" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/SymPy" title="SymPy – Portuguese" lang="pt" hreflang="pt" data-title="SymPy" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/SymPy" title="SymPy – Russian" lang="ru" hreflang="ru" data-title="SymPy" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/SymPy" title="SymPy – Serbian" lang="sr" hreflang="sr" data-title="SymPy" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/SymPy" title="SymPy – Turkish" lang="tr" hreflang="tr" data-title="SymPy" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/SymPy" title="SymPy – Chinese" lang="zh" hreflang="zh" data-title="SymPy" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q5971368#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/SymPy" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:SymPy" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/SymPy"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=SymPy&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=SymPy&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/SymPy"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=SymPy&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=SymPy&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/SymPy" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/SymPy" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=SymPy&oldid=1281408036" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=SymPy&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=SymPy&id=1281408036&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSymPy"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSymPy"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=SymPy&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=SymPy&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:SymPy" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q5971368" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Python library for symbolic computation</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/SimPy" title="SimPy">SimPy</a>, a discrete-event simulation language.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vevent"><caption class="infobox-title summary">SymPy</caption><tbody><tr><td colspan="2" class="infobox-image logo"><span typeof="mw:File"><a href="/wiki/File:Sympy_logo.svg" class="mw-file-description" title="Sympy logo."><img alt="Sympy logo." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Sympy_logo.svg/160px-Sympy_logo.svg.png" decoding="async" width="160" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Sympy_logo.svg/240px-Sympy_logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Sympy_logo.svg/320px-Sympy_logo.svg.png 2x" data-file-width="750" data-file-height="750" /></a></span></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Programmer" title="Programmer">Developer(s)</a></th><td class="infobox-data">SymPy Development Team</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Initial release</th><td class="infobox-data">2007<span class="noprint">; 18 years ago</span><span style="display:none"> (<span class="bday dtstart published updated">2007</span>)</span></td></tr><tr style="display: none;"><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">1.13.3<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> / 18 September 2024<span class="noprint">; 6 months ago</span><span style="display:none"> (<span class="bday dtstart published updated">2024-09-18</span>)</span></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Repository_(version_control)" title="Repository (version control)">Repository</a></th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><span class="url"><a rel="nofollow" class="external text" href="https://github.com/sympy/sympy">github<wbr />.com<wbr />/sympy<wbr />/sympy</a></span> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q5971368#P1324" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Written in</th><td class="infobox-data"><a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Operating_system" title="Operating system">Operating system</a></th><td class="infobox-data"><a href="/wiki/Cross-platform" class="mw-redirect" title="Cross-platform">Cross-platform</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_categories#Categorization_approaches" title="Software categories">Type</a></th><td class="infobox-data"><a href="/wiki/Computer_algebra_system" title="Computer algebra system">Computer algebra system</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="/wiki/3-clause_BSD" class="mw-redirect" title="3-clause BSD">3-clause BSD</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://www.sympy.org/">www<wbr />.sympy<wbr />.org</a></span> <span class="penicon autoconfirmed-show"><span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q5971368?uselang=en#P856" title="Edit this on Wikidata"><img alt="Edit this on Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></td></tr></tbody></table> <p><b>SymPy</b> is an <a href="/wiki/Open-source" class="mw-redirect" title="Open-source">open-source</a> <a href="/wiki/Python_programming_language" class="mw-redirect" title="Python programming language">Python</a> <a href="/wiki/Library_(computing)" title="Library (computing)">library</a> for <a href="/wiki/Symbolic_computation" class="mw-redirect" title="Symbolic computation">symbolic computation</a>. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> or SymPy Gamma.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.<sup id="cite_ref-homepage_4-0" class="reference"><a href="#cite_note-homepage-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-joyner2012_5-0" class="reference"><a href="#cite_note-joyner2012-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> This ease of access combined with a simple and extensible code base in a well known language make SymPy a <a href="/wiki/Computer_algebra_system" title="Computer algebra system">computer algebra system</a> with a relatively low barrier to entry. </p><p>SymPy includes features ranging from basic symbolic <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a> to <a href="/wiki/Calculus" title="Calculus">calculus</a>, <a href="/wiki/Algebra" title="Algebra">algebra</a>, <a href="/wiki/Discrete_mathematics" title="Discrete mathematics">discrete mathematics</a>, and <a href="/wiki/Quantum_physics" class="mw-redirect" title="Quantum physics">quantum physics</a>. It is capable of formatting the result of the computations as <a href="/wiki/LaTeX" title="LaTeX">LaTeX</a> code.<sup id="cite_ref-homepage_4-1" class="reference"><a href="#cite_note-homepage-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-joyner2012_5-1" class="reference"><a href="#cite_note-joyner2012-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>SymPy is <a href="/wiki/Free_software" title="Free software">free software</a> and is licensed under the <a href="/wiki/3-clause_BSD" class="mw-redirect" title="3-clause BSD">3-clause BSD</a>. The lead developers are Ondřej Čertík and Aaron Meurer. It was started in 2005 by Ondřej Čertík.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Features">Features</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=1" title="Edit section: Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The SymPy library is split into a core with many optional modules. </p><p>Currently, the core of SymPy has around 260,000 lines of code<sup id="cite_ref-openhub_8-0" class="reference"><a href="#cite_note-openhub-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> (it also includes a comprehensive set of self-tests: over 100,000 lines in 350 files as of version 0.7.5), and its capabilities include:<sup id="cite_ref-homepage_4-2" class="reference"><a href="#cite_note-homepage-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-joyner2012_5-2" class="reference"><a href="#cite_note-joyner2012-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gede2013_9-0" class="reference"><a href="#cite_note-gede2013-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-rocklin2012_10-0" class="reference"><a href="#cite_note-rocklin2012-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-asif2014_11-0" class="reference"><a href="#cite_note-asif2014-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Core_capabilities">Core capabilities</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=2" title="Edit section: Core capabilities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Basic arithmetic: *, /, +, -, **</li> <li>Simplification</li> <li>Expansion</li> <li><a href="/wiki/Function_(mathematics)" title="Function (mathematics)">Functions</a>: <a href="/wiki/Trigonometric_functions" title="Trigonometric functions">trigonometric</a>, <a href="/wiki/Hyperbolic_functions" title="Hyperbolic functions">hyperbolic</a>, <a href="/wiki/Exponential_function" title="Exponential function">exponential</a>, <a href="/wiki/Zero_of_a_function" title="Zero of a function">roots</a>, <a href="/wiki/Logarithm" title="Logarithm">logarithms</a>, <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a>, <a href="/wiki/Spherical_harmonics" title="Spherical harmonics">spherical harmonics</a>, <a href="/wiki/Factorial" title="Factorial">factorials</a> and <a href="/wiki/Gamma_function" title="Gamma function">gamma functions</a>, <a href="/wiki/Zeta_function_(operator)" title="Zeta function (operator)">zeta functions</a>, <a href="/wiki/Polynomial" title="Polynomial">polynomials</a>, <a href="/wiki/Hypergeometric_function" title="Hypergeometric function">hypergeometric</a>, special functions, etc.</li> <li><a href="/wiki/Substitution_(algebra)" class="mw-redirect" title="Substitution (algebra)">Substitution</a></li> <li><a href="/wiki/Arbitrary-precision_arithmetic" title="Arbitrary-precision arithmetic">Arbitrary precision</a> <a href="/wiki/Integer" title="Integer">integers</a>, <a href="/wiki/Rational_number" title="Rational number">rationals</a> and <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floats</a></li> <li><a href="/wiki/Noncommutative_logic" title="Noncommutative logic">Noncommutative symbols</a></li> <li><a href="/wiki/Pattern_matching" title="Pattern matching">Pattern matching</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Polynomials">Polynomials</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=3" title="Edit section: Polynomials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Basic arithmetic: <a href="/wiki/Polynomial_division" class="mw-redirect" title="Polynomial division">division</a>, <a href="/wiki/Greatest_common_divisor" title="Greatest common divisor">gcd</a>, etc.</li> <li><a href="/wiki/Factorization" title="Factorization">Factorization</a></li> <li><a href="/wiki/Square-free_factorization" class="mw-redirect" title="Square-free factorization">Square-free factorization</a></li> <li><a href="/wiki/Gr%C3%B6bner_bases" class="mw-redirect" title="Gröbner bases">Gröbner bases</a></li> <li><a href="/wiki/Partial_fraction_decomposition" title="Partial fraction decomposition">Partial fraction decomposition</a></li> <li><a href="/wiki/Resultant" title="Resultant">Resultants</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Calculus">Calculus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=4" title="Edit section: Calculus"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Mathematical_limit" class="mw-redirect" title="Mathematical limit">Limits</a></li> <li><a href="/wiki/Differentiation_(mathematics)" class="mw-redirect" title="Differentiation (mathematics)">Differentiation</a></li> <li><a href="/wiki/Integral" title="Integral">Integration</a>: Implemented <a href="/wiki/Risch%E2%80%93Norman_algorithm" class="mw-redirect" title="Risch–Norman algorithm">Risch–Norman</a> heuristic</li> <li><a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> (<a href="/wiki/Laurent_series" title="Laurent series">Laurent series</a>)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Solving_equations">Solving equations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=5" title="Edit section: Solving equations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Systems_of_equations" class="mw-redirect" title="Systems of equations">Systems of linear equations</a></li> <li>Systems of <a href="/wiki/Algebraic_equation" title="Algebraic equation">algebraic equations</a> that are <a href="/wiki/Solvable_by_radicals" class="mw-redirect" title="Solvable by radicals">solvable by radicals</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a></li> <li><a href="/wiki/Difference_equation" class="mw-redirect" title="Difference equation">Difference equations</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Discrete_math">Discrete math</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=6" title="Edit section: Discrete math"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Binomial_coefficients" class="mw-redirect" title="Binomial coefficients">Binomial coefficients</a></li> <li><a href="/wiki/Summation" title="Summation">Summations</a></li> <li><a href="/wiki/Product_(mathematics)" title="Product (mathematics)">Products</a></li> <li><a href="/wiki/Number_theory" title="Number theory">Number theory</a>: generating <a href="/wiki/Prime_number" title="Prime number">Prime numbers</a>, primality testing, <a href="/wiki/Integer_factorization" title="Integer factorization">integer factorization</a>, etc.</li> <li>Logic expressions<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Matrices">Matrices</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=7" title="Edit section: Matrices"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Basic arithmetic</li> <li><a href="/wiki/Eigenvalue" class="mw-redirect" title="Eigenvalue">Eigenvalues</a> and their <a href="/wiki/Eigenvector" class="mw-redirect" title="Eigenvector">eigenvectors</a> when the <a href="/wiki/Characteristic_polynomial" title="Characteristic polynomial">characteristic polynomial</a> is solvable by radicals</li> <li><a href="/wiki/Determinant" title="Determinant">Determinants</a></li> <li><a href="/wiki/Inversion_(discrete_mathematics)" title="Inversion (discrete mathematics)">Inversion</a></li> <li>Solving</li></ul> <div class="mw-heading mw-heading3"><h3 id="Geometry">Geometry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=8" title="Edit section: Geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Point_(geometry)" title="Point (geometry)">Points</a>, <a href="/wiki/Line_geometry" class="mw-redirect" title="Line geometry">lines</a>, <a href="/wiki/Line_(geometry)" title="Line (geometry)">rays</a>, <a href="/wiki/Ellipse" title="Ellipse">ellipses</a>, <a href="/wiki/Circle" title="Circle">circles</a>, <a href="/wiki/Polygon" title="Polygon">polygons</a>, etc.</li> <li><a href="/wiki/Intersection" title="Intersection">Intersections</a></li> <li><a href="/wiki/Tangent" title="Tangent">Tangency</a></li> <li><a href="/wiki/Similarity_(geometry)" title="Similarity (geometry)">Similarity</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Plotting">Plotting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=9" title="Edit section: Plotting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Note, plotting requires the external <a href="/wiki/Matplotlib" title="Matplotlib">Matplotlib</a> or <a href="/wiki/Pyglet" title="Pyglet">Pyglet</a> module. </p> <ul><li>Coordinate models</li> <li>Plotting Geometric Entities</li> <li>2D and 3D</li> <li>Interactive interface</li> <li>Colors</li> <li><a href="/wiki/Animation" title="Animation">Animations</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Physics">Physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=10" title="Edit section: Physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Units</li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li> <li><a href="/wiki/Gaussian_optics" title="Gaussian optics">Gaussian optics</a></li> <li><a href="/wiki/Linear_control" title="Linear control">Linear control</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Statistics">Statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=11" title="Edit section: Statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Normal_distribution" title="Normal distribution">Normal distributions</a></li> <li><a href="/wiki/Uniform_distribution_(continuous)" class="mw-redirect" title="Uniform distribution (continuous)">Uniform distributions</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Combinatorics">Combinatorics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=12" title="Edit section: Combinatorics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Permutations" class="mw-redirect" title="Permutations">Permutations</a></li> <li><a href="/wiki/Combinations" class="mw-redirect" title="Combinations">Combinations</a></li> <li><a href="/wiki/Infinitary_combinatorics" title="Infinitary combinatorics">Partitions</a></li> <li><a href="/wiki/Subset" title="Subset">Subsets</a></li> <li><a href="/wiki/Permutation_group" title="Permutation group">Permutation group</a>: <a href="/wiki/Polyhedral_combinatorics" title="Polyhedral combinatorics">Polyhedral</a>, Rubik, <a href="/wiki/Symmetric_group" title="Symmetric group">Symmetric</a>, etc.</li> <li><a href="/wiki/Prufer_sequence" class="mw-redirect" title="Prufer sequence">Prufer sequence</a> and <a href="/wiki/Gray_codes" class="mw-redirect" title="Gray codes">Gray codes</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Printing">Printing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=13" title="Edit section: Printing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Pretty-printing" title="Pretty-printing">Pretty-printing</a>: <a href="/wiki/ASCII" title="ASCII">ASCII</a>/<a href="/wiki/Unicode" title="Unicode">Unicode</a> pretty-printing, LaTeX</li> <li><a href="/wiki/Code_generation_(compiler)" title="Code generation (compiler)">Code generation</a>: C, <a href="/wiki/Fortran" title="Fortran">Fortran</a>, Python</li></ul> <div class="mw-heading mw-heading2"><h2 id="Related_projects">Related projects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=14" title="Edit section: Related projects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/SageMath" title="SageMath">SageMath</a>: an open source alternative to <a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a>, <a href="/wiki/Maple_(software)" title="Maple (software)">Maple</a>, <a href="/wiki/MATLAB" title="MATLAB">MATLAB</a>, and <a href="/wiki/Magma_(computer_algebra_system)" title="Magma (computer algebra system)">Magma</a> (SymPy is included in Sage)</li> <li>SymEngine: a rewriting of SymPy's core in <a href="/wiki/C%2B%2B" title="C++">C++</a>, in order to increase its performance. Work is currently in progress<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (August 2021)">as of?</span></a></i>]</sup> to make SymEngine the underlying engine of Sage too.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li>mpmath: a Python library for <a href="/wiki/Arbitrary-precision_arithmetic" title="Arbitrary-precision arithmetic">arbitrary-precision</a> <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floating-point arithmetic</a><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li> <li>SympyCore: another Python computer algebra system<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li> <li>SfePy: Software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 1D, 2D and 3D.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li>GAlgebra: <a href="/wiki/Geometric_algebra" title="Geometric algebra">Geometric algebra</a> module (previously sympy.galgebra).<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li>Quameon: <a href="/wiki/Quantum_Monte_Carlo" title="Quantum Monte Carlo">Quantum Monte Carlo</a> in Python.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li>Lcapy: Experimental Python package for teaching <a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">linear circuit analysis</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li> <li>LaTeX Expression project: Easy LaTeX typesetting of algebraic expressions in symbolic form with automatic substitution and result computation.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></li> <li>Symbolic statistical modeling: Adding statistical operations to complex physical models.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>Diofant: a fork of SymPy, started by Sergey B Kirpichev<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Dependencies">Dependencies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=15" title="Edit section: Dependencies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since version 1.0, SymPy has the mpmath package as a dependency. </p><p>There are several optional dependencies that can enhance its capabilities: </p> <ul><li><a href="/w/index.php?title=Gmpy&action=edit&redlink=1" class="new" title="Gmpy (page does not exist)">gmpy</a>: If gmpy is installed, SymPy's polynomial module will automatically use it for faster ground types. This can provide a several times boost in performance of certain operations.</li> <li><a href="/wiki/Matplotlib" title="Matplotlib">matplotlib</a>: If matplotlib is installed, SymPy can use it for plotting.</li> <li><a href="/wiki/Pyglet" title="Pyglet">Pyglet</a>: Alternative plotting package.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Free_and_open-source_software_logo_%282009%29.svg/28px-Free_and_open-source_software_logo_%282009%29.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Free_and_open-source_software_logo_%282009%29.svg/42px-Free_and_open-source_software_logo_%282009%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Free_and_open-source_software_logo_%282009%29.svg/56px-Free_and_open-source_software_logo_%282009%29.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Free_and_open-source_software" title="Portal:Free and open-source software">Free and open-source software portal</a></span></li><li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></span></li></ul> <ul><li><a href="/wiki/Comparison_of_computer_algebra_systems" class="mw-redirect" title="Comparison of computer algebra systems">Comparison of computer algebra systems</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=17" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/sympy/sympy/releases">"Releases - sympy/sympy"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">20 March</span> 2025</span> – via <a href="/wiki/GitHub" title="GitHub">GitHub</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Releases+-+sympy%2Fsympy&rft_id=https%3A%2F%2Fgithub.com%2Fsympy%2Fsympy%2Freleases&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://live.sympy.org/">"SymPy Live"</a>. <i>live.sympy.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=live.sympy.org&rft.atitle=SymPy+Live&rft_id=https%3A%2F%2Flive.sympy.org%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sympygamma.com/">"SymPy Gamma"</a>. <i>www.sympygamma.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.sympygamma.com&rft.atitle=SymPy+Gamma&rft_id=https%3A%2F%2Fwww.sympygamma.com%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-homepage-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-homepage_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-homepage_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-homepage_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://sympy.org">"SymPy homepage"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2014-10-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=SymPy+homepage&rft_id=http%3A%2F%2Fsympy.org&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-joyner2012-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-joyner2012_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-joyner2012_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-joyner2012_5-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJoynerČertíkMeurerGranger2012" class="citation journal cs1">Joyner, David; Čertík, Ondřej; Meurer, Aaron; Granger, Brian E. (2012). "Open source computer algebra systems: SymPy". <i>ACM Communications in Computer Algebra</i>. <b>45</b> (3/4): <span class="nowrap">225–</span>234. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F2110170.2110185">10.1145/2110170.2110185</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:44862851">44862851</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Communications+in+Computer+Algebra&rft.atitle=Open+source+computer+algebra+systems%3A+SymPy&rft.volume=45&rft.issue=3%2F4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E225-%3C%2Fspan%3E234&rft.date=2012&rft_id=info%3Adoi%2F10.1145%2F2110170.2110185&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A44862851%23id-name%3DS2CID&rft.aulast=Joyner&rft.aufirst=David&rft.au=%C4%8Cert%C3%ADk%2C+Ond%C5%99ej&rft.au=Meurer%2C+Aaron&rft.au=Granger%2C+Brian+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMeurerSmithPaprockiČertík2017" class="citation journal cs1">Meurer, Aaron; Smith, Christopher P.; Paprocki, Mateusz; Čertík, Ondřej; Kirpichev, Sergey B.; Rocklin, Matthew; Kumar, AMiT; Ivanov, Sergiu; Moore, Jason K. (2017-01-02). <a rel="nofollow" class="external text" href="http://dspace5.zcu.cz/bitstream/11025/29246/1/peerj-cs-103-1.pdf">"SymPy: symbolic computing in Python"</a> <span class="cs1-format">(PDF)</span>. <i>PeerJ Computer Science</i>. <b>3</b>: e103. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.7717%2Fpeerj-cs.103">10.7717/peerj-cs.103</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2376-5992">2376-5992</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PeerJ+Computer+Science&rft.atitle=SymPy%3A+symbolic+computing+in+Python&rft.volume=3&rft.pages=e103&rft.date=2017-01-02&rft_id=info%3Adoi%2F10.7717%2Fpeerj-cs.103&rft.issn=2376-5992&rft.aulast=Meurer&rft.aufirst=Aaron&rft.au=Smith%2C+Christopher+P.&rft.au=Paprocki%2C+Mateusz&rft.au=%C4%8Cert%C3%ADk%2C+Ond%C5%99ej&rft.au=Kirpichev%2C+Sergey+B.&rft.au=Rocklin%2C+Matthew&rft.au=Kumar%2C+AMiT&rft.au=Ivanov%2C+Sergiu&rft.au=Moore%2C+Jason+K.&rft_id=http%3A%2F%2Fdspace5.zcu.cz%2Fbitstream%2F11025%2F29246%2F1%2Fpeerj-cs-103-1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/sympy/sympy/wiki/SymPy-vs.-Mathematica">"SymPy vs. Mathematica · sympy/Sympy Wiki"</a>. <i><a href="/wiki/GitHub" title="GitHub">GitHub</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=SymPy+vs.+Mathematica+%C2%B7+sympy%2FSympy+Wiki&rft_id=https%3A%2F%2Fgithub.com%2Fsympy%2Fsympy%2Fwiki%2FSymPy-vs.-Mathematica&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-openhub-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-openhub_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.openhub.net/p/sympy">"Sympy project statistics on Open HUB"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2014-10-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Sympy+project+statistics+on+Open+HUB&rft_id=https%3A%2F%2Fwww.openhub.net%2Fp%2Fsympy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-gede2013-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-gede2013_9-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGedePetersonNanjangudMoore2013" class="citation conference cs1">Gede, Gilbert; Peterson, Dale L.; Nanjangud, Angadh; Moore, Jason K.; Hubbard, Mont (2013). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1830918"><i>Constrained multibody dynamics with Python: From symbolic equation generation to publication</i></a></span>. ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers. pp. V07BT10A051. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1115%2FDETC2013-13470">10.1115/DETC2013-13470</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7918-5597-3" title="Special:BookSources/978-0-7918-5597-3"><bdi>978-0-7918-5597-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Constrained+multibody+dynamics+with+Python%3A+From+symbolic+equation+generation+to+publication&rft.pages=V07BT10A051&rft.pub=American+Society+of+Mechanical+Engineers&rft.date=2013&rft_id=info%3Adoi%2F10.1115%2FDETC2013-13470&rft.isbn=978-0-7918-5597-3&rft.aulast=Gede&rft.aufirst=Gilbert&rft.au=Peterson%2C+Dale+L.&rft.au=Nanjangud%2C+Angadh&rft.au=Moore%2C+Jason+K.&rft.au=Hubbard%2C+Mont&rft_id=http%3A%2F%2Fproceedings.asmedigitalcollection.asme.org%2Fproceeding.aspx%3Farticleid%3D1830918&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-rocklin2012-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-rocklin2012_10-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRocklinTerrel2012" class="citation journal cs1">Rocklin, Matthew; Terrel, Andy (2012). "Symbolic Statistics with SymPy". <i>Computing in Science & Engineering</i>. <b>14</b> (3): <span class="nowrap">88–</span>93. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012CSE....14c..88R">2012CSE....14c..88R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FMCSE.2012.56">10.1109/MCSE.2012.56</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18307629">18307629</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computing+in+Science+%26+Engineering&rft.atitle=Symbolic+Statistics+with+SymPy&rft.volume=14&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E88-%3C%2Fspan%3E93&rft.date=2012&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18307629%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FMCSE.2012.56&rft_id=info%3Abibcode%2F2012CSE....14c..88R&rft.aulast=Rocklin&rft.aufirst=Matthew&rft.au=Terrel%2C+Andy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-asif2014-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-asif2014_11-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAsifOlaussen2014" class="citation journal cs1">Asif, Mushtaq; Olaussen, Kåre (2014). "Automatic code generator for higher order integrators". <i>Computer Physics Communications</i>. <b>185</b> (5): <span class="nowrap">1461–</span>1472. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1310.2111">1310.2111</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014CoPhC.185.1461M">2014CoPhC.185.1461M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.cpc.2014.01.012">10.1016/j.cpc.2014.01.012</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:42041635">42041635</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computer+Physics+Communications&rft.atitle=Automatic+code+generator+for+higher+order+integrators&rft.volume=185&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1461-%3C%2Fspan%3E1472&rft.date=2014&rft_id=info%3Aarxiv%2F1310.2111&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A42041635%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.cpc.2014.01.012&rft_id=info%3Abibcode%2F2014CoPhC.185.1461M&rft.aulast=Asif&rft.aufirst=Mushtaq&rft.au=Olaussen%2C+K%C3%A5re&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://docs.sympy.org/latest/modules/assumptions/index.html">"Assumptions Module — SymPy 1.4 documentation"</a>. <i>docs.sympy.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-07-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=docs.sympy.org&rft.atitle=Assumptions+Module+%E2%80%94+SymPy+1.4+documentation&rft_id=https%3A%2F%2Fdocs.sympy.org%2Flatest%2Fmodules%2Fassumptions%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://docs.sympy.org/latest/modules/physics/continuum_mechanics/index.html">"Continuum Mechanics — SymPy 1.4 documentation"</a>. <i>docs.sympy.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-07-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=docs.sympy.org&rft.atitle=Continuum+Mechanics+%E2%80%94+SymPy+1.4+documentation&rft_id=https%3A%2F%2Fdocs.sympy.org%2Flatest%2Fmodules%2Fphysics%2Fcontinuum_mechanics%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/symengine/symengine">"GitHub - symengine/symengine: SymEngine is a fast symbolic manipulation library, written in C++"</a>. <i>GitHub</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=GitHub+-+symengine%2Fsymengine%3A+SymEngine+is+a+fast+symbolic+manipulation+library%2C+written+in+C%2B%2B&rft_id=https%3A%2F%2Fgithub.com%2Fsymengine%2Fsymengine&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mpmath.org/">"mpmath - Python library for arbitrary-precision floating-point arithmetic"</a>. <i>mpmath.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mpmath.org&rft.atitle=mpmath+-+Python+library+for+arbitrary-precision+floating-point+arithmetic&rft_id=https%3A%2F%2Fmpmath.org%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/pearu/sympycore">"GitHub - pearu/sympycore: Automatically exported from code.google.com/p/sympycore"</a>. <i>GitHub</i>. January 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=GitHub+-+pearu%2Fsympycore%3A+Automatically+exported+from+code.google.com%2Fp%2Fsympycore&rft.date=2021-01&rft_id=https%3A%2F%2Fgithub.com%2Fpearu%2Fsympycore&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFDevelopers" class="citation web cs1">Developers, SfePy. <a rel="nofollow" class="external text" href="http://sfepy.org/doc-devel/index.html">"SfePy: Simple Finite Elements in Python — SfePy version: 2021.2+git.13ca95f1 documentation"</a>. <i>sfepy.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=sfepy.org&rft.atitle=SfePy%3A+Simple+Finite+Elements+in+Python+%E2%80%94+SfePy+version%3A+2021.2%2Bgit.13ca95f1+documentation&rft.aulast=Developers&rft.aufirst=SfePy&rft_id=http%3A%2F%2Fsfepy.org%2Fdoc-devel%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/pygae/galgebra">"GitHub - pygae/galgebra: Symbolic Geometric Algebra/Calculus package for SymPy"</a>. <i>GitHub</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=GitHub+-+pygae%2Fgalgebra%3A+Symbolic+Geometric+Algebra%2FCalculus+package+for+SymPy&rft_id=https%3A%2F%2Fgithub.com%2Fpygae%2Fgalgebra&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://quameon.sourceforge.net/">"Quameon - Quantum Monte Carlo in Python"</a>. <i>quameon.sourceforge.net</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=quameon.sourceforge.net&rft.atitle=Quameon+-+Quantum+Monte+Carlo+in+Python&rft_id=http%3A%2F%2Fquameon.sourceforge.net%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210116185108/http://lcapy.elec.canterbury.ac.nz/">"Welcome to Lcapy's documentation! — Lcapy 0.76 documentation"</a>. 2021-01-16. Archived from <a rel="nofollow" class="external text" href="http://lcapy.elec.canterbury.ac.nz/">the original</a> on 2021-01-16<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Welcome+to+Lcapy%27s+documentation%21+%E2%80%94+Lcapy+0.76+documentation&rft.date=2021-01-16&rft_id=http%3A%2F%2Flcapy.elec.canterbury.ac.nz%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://mech.fsv.cvut.cz/~stransky/software/latexexpr/doc/">"LaTeX Expression project documentation — LaTeX Expression 0.3.dev documentation"</a>. <i>mech.fsv.cvut.cz</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mech.fsv.cvut.cz&rft.atitle=LaTeX+Expression+project+documentation+%E2%80%94+LaTeX+Expression+0.3.dev+documentation&rft_id=http%3A%2F%2Fmech.fsv.cvut.cz%2F~stransky%2Fsoftware%2Flatexexpr%2Fdoc%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/260585491">"Symbolic Statistics with SymPy"</a>. <i>ResearchGate</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ResearchGate&rft.atitle=Symbolic+Statistics+with+SymPy&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F260585491&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://diofant.readthedocs.io/en/latest/">"Diofant's documentation — Diofant 0.13.0a4.dev13+g8c5685115 documentation"</a>. <i>diofant.readthedocs.io</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-08-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=diofant.readthedocs.io&rft.atitle=Diofant%27s+documentation+%E2%80%94+Diofant+0.13.0a4.dev13%2Bg8c5685115+documentation&rft_id=https%3A%2F%2Fdiofant.readthedocs.io%2Fen%2Flatest%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASymPy" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SymPy&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="official-website"><span class="url"><a rel="nofollow" class="external text" href="https://www.sympy.org/">Official website</a></span></span> <span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q5971368#P856" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></li> <li><a rel="nofollow" class="external text" href="http://planet.sympy.org/">Planet SymPy</a></li> <li><a rel="nofollow" class="external text" href="https://coderslegacy.com/python/sympy-tutorial/">SymPy Tutorials Collection</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/sympy/sympy/">Code Repository on GitHub</a></li> <li><a rel="nofollow" class="external text" href="https://groups.google.com/forum/#!forum/sympy">Support and development forum</a></li> <li><a rel="nofollow" class="external text" href="https://gitter.im/sympy/sympy">Gitter chat room</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Computer_algebra_systems377" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computer_algebra_systems" title="Template:Computer algebra systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computer_algebra_systems" title="Template talk:Computer algebra systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computer_algebra_systems" title="Special:EditPage/Template:Computer algebra systems"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Computer_algebra_systems377" style="font-size:114%;margin:0 4em"><a href="/wiki/Computer_algebra_system" title="Computer algebra system">Computer algebra systems</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Open-source_software" title="Open-source software">Open-source</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axiom_(computer_algebra_system)" title="Axiom (computer algebra system)">Axiom</a></li> <li><a href="/wiki/Cadabra_(computer_program)" title="Cadabra (computer program)">Cadabra</a></li> <li><a href="/wiki/CoCoA" title="CoCoA">CoCoA</a></li> <li><a href="/wiki/Fermat_(computer_algebra_system)" title="Fermat (computer algebra system)">Fermat</a></li> <li><a href="/wiki/FriCAS" title="FriCAS">FriCAS</a></li> <li><a href="/wiki/FORM_(symbolic_manipulation_system)" title="FORM (symbolic manipulation system)">FORM</a></li> <li><a href="/wiki/GAP_(computer_algebra_system)" title="GAP (computer algebra system)">GAP</a></li> <li><a href="/wiki/GiNaC" title="GiNaC">GiNaC</a></li> <li><a href="/wiki/Macaulay2" title="Macaulay2">Macaulay2</a></li> <li><a href="/wiki/Maxima_(software)" title="Maxima (software)">Maxima</a></li> <li><a href="/wiki/Normaliz" title="Normaliz">Normaliz</a></li> <li><a href="/wiki/PARI/GP" title="PARI/GP">PARI/GP</a></li> <li><a href="/wiki/REDUCE_(computer_algebra_system)" class="mw-redirect" title="REDUCE (computer algebra system)">REDUCE</a></li> <li><a href="/wiki/SageMath" title="SageMath">SageMath</a></li> <li><a href="/wiki/Singular_(software)" title="Singular (software)">Singular</a></li> <li><a class="mw-selflink selflink">SymPy</a></li> <li><a href="/wiki/Xcas" title="Xcas">Xcas/Giac</a></li> <li><a href="/wiki/Yacas" title="Yacas">Yacas</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proprietary_software" title="Proprietary software">Proprietary</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Casio_ClassPad_300" title="Casio ClassPad 300">ClassPad Manager</a></li> <li><a href="/wiki/KANT_(software)" title="KANT (software)">KANT</a></li> <li><a href="/wiki/Magma_(computer_algebra_system)" title="Magma (computer algebra system)">Magma</a></li> <li><a href="/wiki/Maple_(software)" title="Maple (software)">Maple</a></li> <li><a href="/wiki/Mathcad" title="Mathcad">Mathcad</a></li> <li><a href="/wiki/Wolfram_Mathematica" title="Wolfram Mathematica">Mathematica</a></li> <li><a href="/wiki/MuPAD" title="MuPAD">muPAD</a> (<a href="/wiki/MATLAB" title="MATLAB">MATLAB</a> symbolic math toolbox)</li> <li><a href="/wiki/SMath_Studio" title="SMath Studio">SMath Studio</a></li> <li><a href="/wiki/TI_InterActive!" title="TI InterActive!">TI InterActive!</a></li> <li><a href="/wiki/Engineering_Equation_Solver" title="Engineering Equation Solver">Engineering Equation Solver</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Discontinued</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cambridge_Algebra_System" title="Cambridge Algebra System">CAMAL</a></li> <li><a href="/wiki/Derive_(computer_algebra_system)" title="Derive (computer algebra system)">Derive</a></li> <li><a href="/wiki/Erable" title="Erable">Erable</a></li> <li><a href="/wiki/LiveMath" title="LiveMath">LiveMath</a></li> <li><a href="/wiki/Macsyma" title="Macsyma">Macsyma</a></li> <li><a href="/wiki/Mathomatic" title="Mathomatic">Mathomatic</a></li> <li><a href="/wiki/MuMATH" title="MuMATH">muMATH</a></li> <li><a href="/wiki/ALTRAN" title="ALTRAN">ALTRAN</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span><b><a href="/wiki/Category:Computer_algebra_systems" title="Category:Computer algebra systems">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span><b><a href="/wiki/List_of_computer_algebra_systems" title="List of computer algebra systems">List</a></b></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=SymPy&oldid=1281408036">https://en.wikipedia.org/w/index.php?title=SymPy&oldid=1281408036</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Computer_algebra_system_software_for_Linux" title="Category:Computer algebra system software for Linux">Computer algebra system software for Linux</a></li><li><a href="/wiki/Category:Computer_algebra_system_software_for_macOS" title="Category:Computer algebra system software for macOS">Computer algebra system software for macOS</a></li><li><a href="/wiki/Category:Computer_algebra_system_software_for_Windows" title="Category:Computer algebra system software for Windows">Computer algebra system software for Windows</a></li><li><a href="/wiki/Category:Free_computer_algebra_systems" title="Category:Free computer algebra systems">Free computer algebra systems</a></li><li><a href="/wiki/Category:Free_mathematics_software" title="Category:Free mathematics software">Free mathematics software</a></li><li><a href="/wiki/Category:Free_software_programmed_in_Python" title="Category:Free software programmed in Python">Free software programmed in Python</a></li><li><a href="/wiki/Category:Python_(programming_language)_scientific_libraries" title="Category:Python (programming language) scientific libraries">Python (programming language) scientific libraries</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_vague_or_ambiguous_time" title="Category:All articles with vague or ambiguous time">All articles with vague or ambiguous time</a></li><li><a href="/wiki/Category:Vague_or_ambiguous_time_from_August_2021" title="Category:Vague or ambiguous time from August 2021">Vague or ambiguous time from August 2021</a></li><li><a href="/wiki/Category:Articles_with_example_Python_(programming_language)_code" title="Category:Articles with example Python (programming language) code">Articles with example Python (programming language) code</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 20 March 2025, at 05:17<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=SymPy&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://www.wikimedia.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/static/images/footer/wikimedia-button.svg" width="84" height="29"><img src="/static/images/footer/wikimedia.svg" width="25" height="25" alt="Wikimedia Foundation" lang="en" loading="lazy"></picture></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" lang="en" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">SymPy</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>10 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5c6f46dcf-q4v2d","wgBackendResponseTime":142,"wgPageParseReport":{"limitreport":{"cputime":"0.480","walltime":"0.633","ppvisitednodes":{"value":2743,"limit":1000000},"postexpandincludesize":{"value":67143,"limit":2097152},"templateargumentsize":{"value":3333,"limit":2097152},"expansiondepth":{"value":27,"limit":100},"expensivefunctioncount":{"value":6,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":92007,"limit":5000000},"entityaccesscount":{"value":2,"limit":400},"timingprofile":["100.00% 559.116 1 -total"," 31.67% 177.045 1 Template:Reflist"," 30.07% 168.139 2 Template:Infobox"," 25.22% 141.014 1 Template:Infobox_software"," 19.99% 111.753 18 Template:Cite_web"," 12.22% 68.325 1 Template:Computer_algebra_systems"," 11.77% 65.830 1 Template:Navbox"," 10.18% 56.910 1 Template:Short_description"," 9.19% 51.361 1 Template:As_of?"," 8.43% 47.127 1 Template:Fix"]},"scribunto":{"limitreport-timeusage":{"value":"0.292","limit":"10.000"},"limitreport-memusage":{"value":8904517,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-5c6f46dcf-k4pdk","timestamp":"20250331035004","ttl":72601,"transientcontent":true}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"SymPy","url":"https:\/\/en.wikipedia.org\/wiki\/SymPy","sameAs":"http:\/\/www.wikidata.org\/entity\/Q5971368","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q5971368","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-07-09T19:30:31Z","dateModified":"2025-03-20T05:17:20Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/5\/54\/Sympy_logo.svg","headline":"Python library that provides functions of a computer algebra system"}</script> </body> </html>