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-disabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="nia" dir="ltr"> <head> <meta charset="UTF-8"> <title>Aljabar - 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-disabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )niawikimwclientpreferences=([^;]+)/);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":[",\t.",".\t,"],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","Januari","Februari","Maret","April","Mei","Juni","Juli","Agustus","September","Oktober","November","Desember"],"wgRequestId":"308e3c15-f3b4-4e22-80d6-174a010b3c55","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Aljabar","wgTitle":"Aljabar","wgCurRevisionId":24184,"wgRevisionId":24184,"wgArticleId":3964,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Nga'örö si so fanura ba li Arab","Nias","CS1: Ketidakpastian Julian–Gregorian"],"wgPageViewLanguage":"nia","wgPageContentLanguage":"nia","wgPageContentModel":"wikitext","wgRelevantPageName":"Aljabar","wgRelevantArticleId":3964,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"nia","pageLanguageDir":"ltr","pageVariantFallbacks":"nia"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":40000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q3968","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.math.styles":"ready","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","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.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=nia&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.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=nia&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=nia&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 name="viewport" content="width=1120"> <meta property="og:title" content="Aljabar - 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="//nia.m.wikipedia.org/wiki/Aljabar"> <link rel="alternate" type="application/x-wiki" title="Bulö'ö" href="/w/index.php?title=Aljabar&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 (nia)"> <link rel="EditURI" type="application/rsd+xml" href="//nia.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://nia.wikipedia.org/wiki/Aljabar"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.nia"> <link rel="alternate" type="application/atom+xml" title="Lakhö Atom Wikipedia" href="/w/index.php?title=Spesial:Perubahan_terbaru&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="auth.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-Aljabar rootpage-Aljabar skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Ae ba nösi</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="Situs"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Menu utama" > <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="Tuhe 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" > Tuhe Menu </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">Tuhe Menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">bini'ö</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Lala wofanö </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Wikipedia:Olayama" title="Ae ba golayama [z]" accesskey="z">Wikipedia:Olayama</a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesial:Perubahan_terbaru" title="Fefu zi tebulö si bohou ba wiki [r]" accesskey="r">Safuria tebulö</a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Halaman_sembarang" title="Oroma'ö gofu nga'örö [x]" accesskey="x">Gofu nga'örö</a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Spesial:Halaman_istimewa">Nga'örö spesial</a></li> </ul> </div> </div> <div id="p-Ewali_zato" class="vector-menu mw-portlet mw-portlet-Ewali_zato" > <div class="vector-menu-heading"> Ewali zato </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Angombakhata" class="mw-list-item"><a href="/wiki/Wikipedia:Angombakhata">Angombakhata</a></li><li id="n-Bawagöli-zato" class="mw-list-item"><a href="/wiki/Wikipedia:Bawag%C3%B6li_zato">Bawagöli zato</a></li><li id="n-Lala-wanura" class="mw-list-item"><a href="/wiki/Fanolo:Lala_wanura">Lala wanura</a></li><li id="n-Monganga-afo" class="mw-list-item"><a href="/wiki/Wikipedia:Monganga_afo">Monganga afo</a></li><li id="n-Nahia-wamakori" class="mw-list-item"><a href="/wiki/Wikipedia:Nahia_wamakori">Nahia wamakori</a></li><li id="n-Ngawalö-wanolo" class="mw-list-item"><a href="/wiki/Fanolo:Fanolo">Ngawalö wanolo</a></li><li id="n-Sangai-halöŵö" class="mw-list-item"><a href="/wiki/Wikipedia:Sangai_hal%C3%B6%C5%B5%C3%B6">Sangai halöŵö</a></li> </ul> </div> </div> <div id="p-Halöŵö_bö'ö" class="vector-menu mw-portlet mw-portlet-Halöŵö_bö_ö" > <div class="vector-menu-heading"> Halöŵö bö'ö </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Wikikamus" class="mw-list-item"><a href="https://nia.wiktionary.org/wiki/Wiktionary:Olayama">Wikikamus</a></li><li id="n-Wikibuku" class="mw-list-item"><a href="https://incubator.wikimedia.org/wiki/Wb/nia/Olayama">Wikibuku</a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Wikipedia:Olayama" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <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="" src="/static/images/mobile/copyright/wikipedia-tagline-nia.svg" width="110" height="14" style="width: 6.875em; height: 0.875em;"> </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/Spesial:Pencarian" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Alui Wikipedia [f]" accesskey="f"> Alui </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="Alui Wikipedia" aria-label="Alui Wikipedia" autocapitalize="sentences" title="Alui Wikipedia [f]" accesskey="f" id="searchInput" > </div> <input type="hidden" name="title" value="Spesial:Pencarian"> </div> <button class="cdx-button cdx-search-input__end-button">Alui</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Fakake zamösana"> <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="Khala-khala"> <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="Khala-khala" > <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" > Khala-khala </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=nia.wikipedia.org&uselang=nia" class="">Be wanolo</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=Spesial:Buat_akun&returnto=Aljabar" title="Sökhi na öfazökhi akun-mö ba ae bakha; tenga sa nifaso" class="">Fazökhi akun</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=Spesial:Masuk_log&returnto=Aljabar" title="Ae ua bakha ba gu'ö; tenga sa nifaso [o]" accesskey="o" class="">Ae si bakha</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="Opsi lainnya" > <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="Fakake zamösana" > <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" > Fakake zamösana </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="Menu pengguna" > <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=nia.wikipedia.org&uselang=nia">Be wanolo</a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/Spesial:Contribute"> Berkontribusi</a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Buat_akun&returnto=Aljabar" title="Sökhi na öfazökhi akun-mö ba ae bakha; tenga sa nifaso"> Fazökhi akun</a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Masuk_log&returnto=Aljabar" title="Ae ua bakha ba gu'ö; tenga sa nifaso [o]" accesskey="o"> Ae si bakha</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"> Halaman penyunting yang telah keluar log <a href="/wiki/Fanolo:Pengantar" aria-label="Pelajari lebih lanjut tentang menyunting">pelajari lebih lanjut</a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesial:Pembicaraan_saya" title="Pembicaraan tentang suntingan dari alamat IP ini [n]" accesskey="n">Fahuhuo</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="Situs"> <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="Ösi" 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">Ösi</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">bini'ö</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">Böröta</div> </a> </li> <li id="toc-Etimologi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Etimologi"> <div class="vector-toc-text"> 1 Etimologi </div> </a> <ul id="toc-Etimologi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ngawalö_geluaha_"aljabar"" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ngawalö_geluaha_"aljabar""> <div class="vector-toc-text"> 2 Ngawalö geluaha "aljabar" </div> </a> <ul id="toc-Ngawalö_geluaha_"aljabar"-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aljabar_moroi_ba_Matematika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aljabar_moroi_ba_Matematika"> <div class="vector-toc-text"> 3 Aljabar moroi ba Matematika </div> </a> <ul id="toc-Aljabar_moroi_ba_Matematika-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Waö-waö_(Sejarah)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Waö-waö_(Sejarah)"> <div class="vector-toc-text"> 4 Waö-waö (Sejarah) </div> </a> <button aria-controls="toc-Waö-waö_(Sejarah)-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Gulingkan subbagian Waö-waö (Sejarah) </button> <ul id="toc-Waö-waö_(Sejarah)-sublist" class="vector-toc-list"> <li id="toc-Böröta_aljabar_(Sejarah_awal_aljabar)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Böröta_aljabar_(Sejarah_awal_aljabar)"> <div class="vector-toc-text"> 4.1 Böröta aljabar (Sejarah awal aljabar) </div> </a> <ul id="toc-Böröta_aljabar_(Sejarah_awal_aljabar)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Waö-waö_Sibohou_Aljabar_(Sejarah_modern_aljabar)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Waö-waö_Sibohou_Aljabar_(Sejarah_modern_aljabar)"> <div class="vector-toc-text"> 4.2 Waö-waö Sibohou Aljabar (Sejarah modern aljabar) </div> </a> <ul id="toc-Waö-waö_Sibohou_Aljabar_(Sejarah_modern_aljabar)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Angolifa_Matematika_Sangoguna'ö_Ngawua_Wehede_Aljabar_ba_Döira_(Bidang_matematika_dengan_kata_aljabar_pada_nama_mereka)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Angolifa_Matematika_Sangoguna'ö_Ngawua_Wehede_Aljabar_ba_Döira_(Bidang_matematika_dengan_kata_aljabar_pada_nama_mereka)"> <div class="vector-toc-text"> 5 Angolifa Matematika Sangoguna'ö Ngawua Wehede Aljabar ba Döira (Bidang matematika dengan kata aljabar pada nama mereka) </div> </a> <ul id="toc-Angolifa_Matematika_Sangoguna'ö_Ngawua_Wehede_Aljabar_ba_Döira_(Bidang_matematika_dengan_kata_aljabar_pada_nama_mereka)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aljabar_elementer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aljabar_elementer"> <div class="vector-toc-text"> 6 Aljabar elementer </div> </a> <button aria-controls="toc-Aljabar_elementer-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Gulingkan subbagian Aljabar elementer </button> <ul id="toc-Aljabar_elementer-sublist" class="vector-toc-list"> <li id="toc-Polinomial" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polinomial"> <div class="vector-toc-text"> 6.1 Polinomial </div> </a> <ul id="toc-Polinomial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Famahaö_(Pendidikan)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Famahaö_(Pendidikan)"> <div class="vector-toc-text"> 6.2 Famahaö (Pendidikan) </div> </a> <ul id="toc-Famahaö_(Pendidikan)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Aljabar_abstrak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aljabar_abstrak"> <div class="vector-toc-text"> 7 Aljabar abstrak </div> </a> <button aria-controls="toc-Aljabar_abstrak-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Gulingkan subbagian Aljabar abstrak </button> <ul id="toc-Aljabar_abstrak-sublist" class="vector-toc-list"> <li id="toc-Angorudua_(Grup)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Angorudua_(Grup)"> <div class="vector-toc-text"> 7.1 Angorudua (Grup) </div> </a> <ul id="toc-Angorudua_(Grup)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gelanggang_faoma_Lapangan" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gelanggang_faoma_Lapangan"> <div class="vector-toc-text"> 7.2 Gelanggang faoma Lapangan </div> </a> <ul id="toc-Gelanggang_faoma_Lapangan-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Umbu" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Umbu"> <div class="vector-toc-text"> 8 Umbu </div> </a> <ul id="toc-Umbu-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="Ösi" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Daftar Isi" > <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="Gulingkan daftar isi" > <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" > Gulingkan daftar isi </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">Aljabar</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="Pergi ke artikel dalam bahasa lain. Terdapat 169 bahasa" > <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-169" aria-hidden="true" > 169 li </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Algebra" title="Algebra – Afrikaans" lang="af" hreflang="af" data-title="Algebra" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Algebra" title="Algebra – Jerman (Swiss)" lang="gsw" hreflang="gsw" data-title="Algebra" data-language-autonym="Alemannisch" data-language-local-name="Jerman (Swiss)" class="interlanguage-link-target">Alemannisch</a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%88%8D%E1%8C%80%E1%89%A5%E1%88%AB" title="አልጀብራ – Amharik" lang="am" hreflang="am" data-title="አልጀብራ" data-language-autonym="አማርኛ" data-language-local-name="Amharik" class="interlanguage-link-target">አማርኛ</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Alchebra" title="Alchebra – Aragon" lang="an" hreflang="an" data-title="Alchebra" data-language-autonym="Aragonés" data-language-local-name="Aragon" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/R%C4%ABmagiefung" title="Rīmagiefung – Inggris Kuno" lang="ang" hreflang="ang" data-title="Rīmagiefung" data-language-autonym="Ænglisc" data-language-local-name="Inggris Kuno" class="interlanguage-link-target">Ænglisc</a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Angika" lang="anp" hreflang="anp" data-title="बीजगणित" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target">अंगिका</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1" title="الجبر – Arab" lang="ar" hreflang="ar" data-title="الجبر" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – Arab Mesir" lang="arz" hreflang="arz" data-title="جبر" data-language-autonym="مصرى" data-language-local-name="Arab Mesir" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বীজগণিত – Assam" lang="as" hreflang="as" data-title="বীজগণিত" data-language-autonym="অসমীয়া" data-language-local-name="Assam" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81lxebra" title="Álxebra – Asturia" lang="ast" hreflang="ast" data-title="Álxebra" data-language-autonym="Asturianu" data-language-local-name="Asturia" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/C%C9%99br" title="Cəbr – Azerbaijani" lang="az" hreflang="az" data-title="Cəbr" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – South Azerbaijani" lang="azb" hreflang="azb" data-title="جبر" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Bashkir" lang="ba" hreflang="ba" data-title="Алгебра" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Algebra" title="Algebra – Samogitian" lang="sgs" hreflang="sgs" data-title="Algebra" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target">Žemaitėška</a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Alhebra" title="Alhebra – Central Bikol" lang="bcl" hreflang="bcl" data-title="Alhebra" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target">Bikol Central</a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Belarusia" lang="be" hreflang="be" data-title="Алгебра" data-language-autonym="Беларуская" data-language-local-name="Belarusia" class="interlanguage-link-target">Беларуская</a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Альгебра – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Альгебра" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target">Беларуская (тарашкевіца)</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Bulgaria" lang="bg" hreflang="bg" data-title="Алгебра" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Bhojpuri" lang="bh" hreflang="bh" data-title="बीजगणित" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বীজগণিত – Bengali" lang="bn" hreflang="bn" data-title="বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%9A%E0%BD%96%E0%BC%8B%E0%BD%A2%E0%BE%A9%E0%BD%B2%E0%BD%A6%E0%BC%8D" title="ཚབ་རྩིས། – Tibet" lang="bo" hreflang="bo" data-title="ཚབ་རྩིས།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibet" class="interlanguage-link-target">བོད་ཡིག</a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Aljebr" title="Aljebr – Breton" lang="br" hreflang="br" data-title="Aljebr" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target">Brezhoneg</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Algebra" title="Algebra – Bosnia" lang="bs" hreflang="bs" data-title="Algebra" data-language-autonym="Bosanski" data-language-local-name="Bosnia" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Katalan" lang="ca" hreflang="ca" data-title="Àlgebra" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/D%C3%A2i-s%C3%B3" title="Dâi-só – Mindong" lang="cdo" hreflang="cdo" data-title="Dâi-só" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target">閩東語 / Mìng-dĕ̤ng-ngṳ̄</a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Chechen" lang="ce" hreflang="ce" data-title="Алгебра" data-language-autonym="Нохчийн" data-language-local-name="Chechen" class="interlanguage-link-target">Нохчийн</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%95%D8%A8%D8%B1" title="جەبر – Kurdi Sorani" lang="ckb" hreflang="ckb" data-title="جەبر" data-language-autonym="کوردی" data-language-local-name="Kurdi Sorani" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Algebra" title="Algebra – Korsika" lang="co" hreflang="co" data-title="Algebra" data-language-autonym="Corsu" data-language-local-name="Korsika" class="interlanguage-link-target">Corsu</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Algebra" title="Algebra – Ceko" lang="cs" hreflang="cs" data-title="Algebra" data-language-autonym="Čeština" data-language-local-name="Ceko" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Chuvash" lang="cv" hreflang="cv" data-title="Алгебра" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Algebra" title="Algebra – Welsh" lang="cy" hreflang="cy" data-title="Algebra" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Algebra" title="Algebra – Dansk" lang="da" hreflang="da" data-title="Algebra" data-language-autonym="Dansk" data-language-local-name="Dansk" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Algebra" title="Algebra – Jerman" lang="de" hreflang="de" data-title="Algebra" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Cebir" title="Cebir – Dimli" lang="diq" hreflang="diq" data-title="Cebir" data-language-autonym="Zazaki" data-language-local-name="Dimli" class="interlanguage-link-target">Zazaki</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%86%CE%BB%CE%B3%CE%B5%CE%B2%CF%81%CE%B1" title="Άλγεβρα – Yunani" lang="el" hreflang="el" data-title="Άλγεβρα" data-language-autonym="Ελληνικά" data-language-local-name="Yunani" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Algebra" title="Algebra – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Algebra" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target">Emiliàn e rumagnòl</a></li><li class="interlanguage-link interwiki-en badge-Q17437796 badge-featuredarticle mw-list-item" title="artikel pilihan"><a href="https://en.wikipedia.org/wiki/Algebra" title="Algebra – Inggris" lang="en" hreflang="en" data-title="Algebra" data-language-autonym="English" data-language-local-name="Inggris" class="interlanguage-link-target">English</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Algebro" title="Algebro – Esperanto" lang="eo" hreflang="eo" data-title="Algebro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – Spanyol" lang="es" hreflang="es" data-title="Álgebra" data-language-autonym="Español" data-language-local-name="Spanyol" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Algebra" title="Algebra – Estonia" lang="et" hreflang="et" data-title="Algebra" data-language-autonym="Eesti" data-language-local-name="Estonia" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Aljebra" title="Aljebra – Basque" lang="eu" hreflang="eu" data-title="Aljebra" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – Persia" lang="fa" hreflang="fa" data-title="جبر" data-language-autonym="فارسی" data-language-local-name="Persia" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Algebra" title="Algebra – Suomi" lang="fi" hreflang="fi" data-title="Algebra" data-language-autonym="Suomi" data-language-local-name="Suomi" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Alg%C3%B5bra" title="Algõbra – Võro" lang="vro" hreflang="vro" data-title="Algõbra" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target">Võro</a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Ivakavakadina" title="Ivakavakadina – Fiji" lang="fj" hreflang="fj" data-title="Ivakavakadina" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fiji" class="interlanguage-link-target">Na Vosa Vakaviti</a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Algebra" title="Algebra – Faroe" lang="fo" hreflang="fo" data-title="Algebra" data-language-autonym="Føroyskt" data-language-local-name="Faroe" class="interlanguage-link-target">Føroyskt</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre" title="Algèbre – Prancis" lang="fr" hreflang="fr" data-title="Algèbre" data-language-autonym="Français" data-language-local-name="Prancis" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Algebra" title="Algebra – Frisia Utara" lang="frr" hreflang="frr" data-title="Algebra" data-language-autonym="Nordfriisk" data-language-local-name="Frisia Utara" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Algebra" title="Algebra – Frisia Barat" lang="fy" hreflang="fy" data-title="Algebra" data-language-autonym="Frysk" data-language-local-name="Frisia Barat" class="interlanguage-link-target">Frysk</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ailg%C3%A9abar" title="Ailgéabar – Irlandia" lang="ga" hreflang="ga" data-title="Ailgéabar" data-language-autonym="Gaeilge" data-language-local-name="Irlandia" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8" title="代數 – Gan" lang="gan" hreflang="gan" data-title="代數" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target">贛語</a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Aj%C3%A8b" title="Ajèb – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Ajèb" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target">Kriyòl gwiyannen</a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Ailseabra" title="Ailseabra – Gaelik Skotlandia" lang="gd" hreflang="gd" data-title="Ailseabra" data-language-autonym="Gàidhlig" data-language-local-name="Gaelik Skotlandia" class="interlanguage-link-target">Gàidhlig</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81lxebra" title="Álxebra – Galisia" lang="gl" hreflang="gl" data-title="Álxebra" data-language-autonym="Galego" data-language-local-name="Galisia" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – Guarani" lang="gn" hreflang="gn" data-title="Álgebra" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target">Avañe'ẽ</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AB%80%E0%AA%9C%E0%AA%97%E0%AA%A3%E0%AA%BF%E0%AA%A4" title="બીજગણિત – Gujarat" lang="gu" hreflang="gu" data-title="બીજગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarat" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Algeerey" title="Algeerey – Manx" lang="gv" hreflang="gv" data-title="Algeerey" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target">Gaelg</a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Algebra" title="Algebra – Hausa" lang="ha" hreflang="ha" data-title="Algebra" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target">Hausa</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94" title="אלגברה – Ibrani" lang="he" hreflang="he" data-title="אלגברה" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Hindi" lang="hi" hreflang="hi" data-title="बीजगणित" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Algebra" title="Algebra – Hindi Fiji" lang="hif" hreflang="hif" data-title="Algebra" data-language-autonym="Fiji Hindi" data-language-local-name="Hindi Fiji" class="interlanguage-link-target">Fiji Hindi</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Algebra" title="Algebra – Kroasia" lang="hr" hreflang="hr" data-title="Algebra" data-language-autonym="Hrvatski" data-language-local-name="Kroasia" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Alj%C3%A8b" title="Aljèb – Kreol Haiti" lang="ht" hreflang="ht" data-title="Aljèb" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Kreol Haiti" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Algebra" title="Algebra – Hungaria" lang="hu" hreflang="hu" data-title="Algebra" data-language-autonym="Magyar" data-language-local-name="Hungaria" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%B6%D6%80%D5%A1%D5%B0%D5%A1%D5%B7%D5%AB%D5%BE" title="Հանրահաշիվ – Armenia" lang="hy" hreflang="hy" data-title="Հանրահաշիվ" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Algebra" title="Algebra – Interlingua" lang="ia" hreflang="ia" data-title="Algebra" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Algebra" title="Algebra – Iban" lang="iba" hreflang="iba" data-title="Algebra" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target">Jaku Iban</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Aljabar" title="Aljabar – Indonesia" lang="id" hreflang="id" data-title="Aljabar" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesia" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Algebra" title="Algebra – Interlingue" lang="ie" hreflang="ie" data-title="Algebra" data-language-autonym="Interlingue" data-language-local-name="Interlingue" class="interlanguage-link-target">Interlingue</a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Alhebra" title="Alhebra – Iloko" lang="ilo" hreflang="ilo" data-title="Alhebra" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target">Ilokano</a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Ingushetia" lang="inh" hreflang="inh" data-title="Алгебра" data-language-autonym="ГӀалгӀай" data-language-local-name="Ingushetia" class="interlanguage-link-target">ГӀалгӀай</a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Algebro" title="Algebro – Ido" lang="io" hreflang="io" data-title="Algebro" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target">Ido</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Algebra" title="Algebra – Islandia" lang="is" hreflang="is" data-title="Algebra" data-language-autonym="Íslenska" data-language-local-name="Islandia" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algebra" title="Algebra – Italia" lang="it" hreflang="it" data-title="Algebra" data-language-autonym="Italiano" data-language-local-name="Italia" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0%E5%AD%A6" title="代数学 – Jepang" lang="ja" hreflang="ja" data-title="代数学" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Aljibra" title="Aljibra – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Aljibra" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/alxebra" title="alxebra – Lojban" lang="jbo" hreflang="jbo" data-title="alxebra" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target">La .lojban.</a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Aljabar" title="Aljabar – Jawa" lang="jv" hreflang="jv" data-title="Aljabar" data-language-autonym="Jawa" data-language-local-name="Jawa" class="interlanguage-link-target">Jawa</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="ალგებრა – Georgia" lang="ka" hreflang="ka" data-title="ალგებრა" data-language-autonym="ქართული" data-language-local-name="Georgia" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Algebra" title="Algebra – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Algebra" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Aljiber" title="Aljiber – Kabyle" lang="kab" hreflang="kab" data-title="Aljiber" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target">Taqbaylit</a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8D" title="Алгебрэ – Kabardi" lang="kbd" hreflang="kbd" data-title="Алгебрэ" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardi" class="interlanguage-link-target">Адыгэбзэ</a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/%C3%91%CA%8A%C5%8B_kal%CA%8A%CA%8A_t%CA%8Am%C9%A9y%C9%9B" title="Ñʊŋ kalʊʊ tʊmɩyɛ – Kabiye" lang="kbp" hreflang="kbp" data-title="Ñʊŋ kalʊʊ tʊmɩyɛ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target">Kabɩyɛ</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Kazakh" lang="kk" hreflang="kk" data-title="Алгебра" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B3%80%E0%B2%9C%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಬೀಜಗಣಿತ – Kannada" lang="kn" hreflang="kn" data-title="ಬೀಜಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-knc mw-list-item"><a href="https://knc.wikipedia.org/wiki/Algebra" title="Algebra – Central Kanuri" lang="knc" hreflang="knc" data-title="Algebra" data-language-autonym="Yerwa Kanuri" data-language-local-name="Central Kanuri" class="interlanguage-link-target">Yerwa Kanuri</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EC%88%98%ED%95%99" title="대수학 – Korea" lang="ko" hreflang="ko" data-title="대수학" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Aljebra" title="Aljebra – Kornish" lang="kw" hreflang="kw" data-title="Aljebra" data-language-autonym="Kernowek" data-language-local-name="Kornish" class="interlanguage-link-target">Kernowek</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Kirgiz" lang="ky" hreflang="ky" data-title="Алгебра" data-language-autonym="Кыргызча" data-language-local-name="Kirgiz" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Algebra" title="Algebra – Latin" lang="la" hreflang="la" data-title="Algebra" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Aljebra" title="Aljebra – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Aljebra" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target">Lingua Franca Nova</a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Aligebbula" title="Aligebbula – Ganda" lang="lg" hreflang="lg" data-title="Aligebbula" data-language-autonym="Luganda" data-language-local-name="Ganda" class="interlanguage-link-target">Luganda</a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Algebra" title="Algebra – Limburgia" lang="li" hreflang="li" data-title="Algebra" data-language-autonym="Limburgs" data-language-local-name="Limburgia" class="interlanguage-link-target">Limburgs</a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Algebra" title="Algebra – Liguria" lang="lij" hreflang="lij" data-title="Algebra" data-language-autonym="Ligure" data-language-local-name="Liguria" class="interlanguage-link-target">Ligure</a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Algebra" title="Algebra – Lombard" lang="lmo" hreflang="lmo" data-title="Algebra" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target">Lombard</a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%9E%E0%BA%B6%E0%BA%94%E0%BA%8A%E0%BA%B0%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94" title="ພຶດຊະຄະນິດ – Lao" lang="lo" hreflang="lo" data-title="ພຶດຊະຄະນິດ" data-language-autonym="ລາວ" data-language-local-name="Lao" class="interlanguage-link-target">ລາວ</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Algebra" title="Algebra – Lituania" lang="lt" hreflang="lt" data-title="Algebra" data-language-autonym="Lietuvių" data-language-local-name="Lituania" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Algebra" title="Algebra – Latvia" lang="lv" hreflang="lv" data-title="Algebra" data-language-autonym="Latviešu" data-language-local-name="Latvia" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Aljebra" title="Aljebra – Malagasi" lang="mg" hreflang="mg" data-title="Aljebra" data-language-autonym="Malagasy" data-language-local-name="Malagasi" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Aljabar" title="Aljabar – Minangkabau" lang="min" hreflang="min" data-title="Aljabar" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target">Minangkabau</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Makedonia" lang="mk" hreflang="mk" data-title="Алгебра" data-language-autonym="Македонски" data-language-local-name="Makedonia" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B5%80%E0%B4%9C%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ബീജഗണിതം – Malayalam" lang="ml" hreflang="ml" data-title="ബീജഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Marathi" lang="mr" hreflang="mr" data-title="बीजगणित" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Algebra" title="Algebra – Melayu" lang="ms" hreflang="ms" data-title="Algebra" data-language-autonym="Bahasa Melayu" data-language-local-name="Melayu" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Al%C4%A1ebra" title="Alġebra – Malta" lang="mt" hreflang="mt" data-title="Alġebra" data-language-autonym="Malti" data-language-local-name="Malta" class="interlanguage-link-target">Malti</a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – Miranda" lang="mwl" hreflang="mwl" data-title="Álgebra" data-language-autonym="Mirandés" data-language-local-name="Miranda" class="interlanguage-link-target">Mirandés</a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%80%E1%80%B9%E1%80%81%E1%80%9B%E1%80%AC%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="အက္ခရာသင်္ချာ – Burma" lang="my" hreflang="my" data-title="အက္ခရာသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burma" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Algebra" title="Algebra – Jerman Rendah" lang="nds" hreflang="nds" data-title="Algebra" data-language-autonym="Plattdüütsch" data-language-local-name="Jerman Rendah" class="interlanguage-link-target">Plattdüütsch</a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BF%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बिजगणित – Nepali" lang="ne" hreflang="ne" data-title="बिजगणित" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target">नेपाली</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Newari" lang="new" hreflang="new" data-title="बीजगणित" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Algebra" title="Algebra – Belanda" lang="nl" hreflang="nl" data-title="Algebra" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Algebra" title="Algebra – Nynorsk Norwegia" lang="nn" hreflang="nn" data-title="Algebra" data-language-autonym="Norsk nynorsk" data-language-local-name="Nynorsk Norwegia" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Algebra" title="Algebra – Bokmål Norwegia" lang="nb" hreflang="nb" data-title="Algebra" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmål Norwegia" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Algebra" title="Algebra – Novial" lang="nov" hreflang="nov" data-title="Algebra" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target">Novial</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Alg%C3%A8bra" title="Algèbra – Ositania" lang="oc" hreflang="oc" data-title="Algèbra" data-language-autonym="Occitan" data-language-local-name="Ositania" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Aljebraa" title="Aljebraa – Oromo" lang="om" hreflang="om" data-title="Aljebraa" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target">Oromoo</a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%B2%E0%A8%9C%E0%A8%AC%E0%A8%B0%E0%A8%BE" title="ਅਲਜਬਰਾ – Punjabi" lang="pa" hreflang="pa" data-title="ਅਲਜਬਰਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target">ਪੰਜਾਬੀ</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Algebra" title="Algebra – Polski" lang="pl" hreflang="pl" data-title="Algebra" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Piedmontese" lang="pms" hreflang="pms" data-title="Àlgebra" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target">Piemontèis</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="الجبرا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1" title="الجبر – Pashto" lang="ps" hreflang="ps" data-title="الجبر" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – Portugis" lang="pt" hreflang="pt" data-title="Álgebra" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Qillqanancha_kamay" title="Qillqanancha kamay – Quechua" lang="qu" hreflang="qu" data-title="Qillqanancha kamay" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target">Runa Simi</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Algebr%C4%83" title="Algebră – Rumania" lang="ro" hreflang="ro" data-title="Algebră" data-language-autonym="Română" data-language-local-name="Rumania" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Rusia" lang="ru" hreflang="ru" data-title="Алгебра" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%90%D0%BB%D2%91%D0%B5%D0%B1%D1%80%D0%B0" title="Алґебра – Rusyn" lang="rue" hreflang="rue" data-title="Алґебра" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target">Русиньскый</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Sakha" lang="sah" hreflang="sah" data-title="Алгебра" data-language-autonym="Саха тыла" data-language-local-name="Sakha" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80lgibbra" title="Àlgibbra – Sisilia" lang="scn" hreflang="scn" data-title="Àlgibbra" data-language-autonym="Sicilianu" data-language-local-name="Sisilia" class="interlanguage-link-target">Sicilianu</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Algebra" title="Algebra – Skotlandia" lang="sco" hreflang="sco" data-title="Algebra" data-language-autonym="Scots" data-language-local-name="Skotlandia" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A2%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="آلجبرا – Sindhi" lang="sd" hreflang="sd" data-title="آلجبرا" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target">سنڌي</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Algebra" title="Algebra – Serbo-Kroasia" lang="sh" hreflang="sh" data-title="Algebra" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroasia" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Aljibr" title="Aljibr – Tachelhit" lang="shi" hreflang="shi" data-title="Aljibr" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target">Taclḥit</a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%93%E0%B6%A2_%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="වීජ ගණිතය – Sinhala" lang="si" hreflang="si" data-title="වීජ ගණිතය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target">සිංහල</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Algebra" title="Algebra – Simple English" lang="en-simple" hreflang="en-simple" data-title="Algebra" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Algebra_(discipl%C3%ADna)" title="Algebra (disciplína) – Slovak" lang="sk" hreflang="sk" data-title="Algebra (disciplína)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Algebra" title="Algebra – Slovenia" lang="sl" hreflang="sl" data-title="Algebra" data-language-autonym="Slovenščina" data-language-local-name="Slovenia" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Aljebra" title="Aljebra – Somalia" lang="so" hreflang="so" data-title="Aljebra" data-language-autonym="Soomaaliga" data-language-local-name="Somalia" class="interlanguage-link-target">Soomaaliga</a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Algjebra" title="Algjebra – Albania" lang="sq" hreflang="sq" data-title="Algjebra" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target">Shqip</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Serbia" lang="sr" hreflang="sr" data-title="Алгебра" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Aljabar" title="Aljabar – Sunda" lang="su" hreflang="su" data-title="Aljabar" data-language-autonym="Sunda" data-language-local-name="Sunda" class="interlanguage-link-target">Sunda</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Algebra" title="Algebra – Swedia" lang="sv" hreflang="sv" data-title="Algebra" data-language-autonym="Svenska" data-language-local-name="Swedia" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Aljebra" title="Aljebra – Swahili" lang="sw" hreflang="sw" data-title="Aljebra" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target">Kiswahili</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="இயற்கணிதம் – Tamil" lang="ta" hreflang="ta" data-title="இயற்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AC%E0%B1%80%E0%B0%9C_%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82" title="బీజ గణితం – Telugu" lang="te" hreflang="te" data-title="బీజ గణితం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Tajik" lang="tg" hreflang="tg" data-title="Алгебра" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target">Тоҷикӣ</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%B5%E0%B8%8A%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="พีชคณิต – Thai" lang="th" hreflang="th" data-title="พีชคณิต" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Algebra" title="Algebra – Turkmen" lang="tk" hreflang="tk" data-title="Algebra" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target">Türkmençe</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Alhebra" title="Alhebra – Tagalog" lang="tl" hreflang="tl" data-title="Alhebra" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Cebir" title="Cebir – Turki" lang="tr" hreflang="tr" data-title="Cebir" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Tinhlayo-swiyenge" title="Tinhlayo-swiyenge – Tsonga" lang="ts" hreflang="ts" data-title="Tinhlayo-swiyenge" data-language-autonym="Xitsonga" data-language-local-name="Tsonga" class="interlanguage-link-target">Xitsonga</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Tatar" lang="tt" hreflang="tt" data-title="Алгебра" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Alijebra" title="Alijebra – Tumbuka" lang="tum" hreflang="tum" data-title="Alijebra" data-language-autonym="ChiTumbuka" data-language-local-name="Tumbuka" class="interlanguage-link-target">ChiTumbuka</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Ukraina" lang="uk" hreflang="uk" data-title="Алгебра" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا – Urdu" lang="ur" hreflang="ur" data-title="الجبرا" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Algebra" title="Algebra – Uzbek" lang="uz" hreflang="uz" data-title="Algebra" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Venesia" lang="vec" hreflang="vec" data-title="Àlgebra" data-language-autonym="Vèneto" data-language-local-name="Venesia" class="interlanguage-link-target">Vèneto</a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Algebr" title="Algebr – Veps" lang="vep" hreflang="vep" data-title="Algebr" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target">Vepsän kel’</a></li><li class="interlanguage-link interwiki-vi badge-Q17437796 badge-featuredarticle mw-list-item" title="artikel pilihan"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91" title="Đại số – Vietnam" lang="vi" hreflang="vi" data-title="Đại số" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Algebra" title="Algebra – West Flemish" lang="vls" hreflang="vls" data-title="Algebra" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target">West-Vlams</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Alhebra" title="Alhebra – Warai" lang="war" hreflang="war" data-title="Alhebra" data-language-autonym="Winaray" data-language-local-name="Warai" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0" title="代数 – Wu Tionghoa" lang="wuu" hreflang="wuu" data-title="代数" data-language-autonym="吴语" data-language-local-name="Wu Tionghoa" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-Algebra" title="I-Algebra – Xhosa" lang="xh" hreflang="xh" data-title="I-Algebra" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" class="interlanguage-link-target">IsiXhosa</a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="ალგებრა – Mingrelian" lang="xmf" hreflang="xmf" data-title="ალგებრა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target">მარგალური</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%A2%D7%91%D7%A8%D7%A2" title="אלגעברע – Yiddish" lang="yi" hreflang="yi" data-title="אלגעברע" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Algebra" title="Algebra – Yoruba" lang="yo" hreflang="yo" data-title="Algebra" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target">Yorùbá</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0" title="代数 – Tionghoa" lang="zh" hreflang="zh" data-title="代数" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target">中文</a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="代數學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target">文言</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C4%81i-s%C3%B2%CD%98" title="Tāi-sò͘ – Minnan" lang="nan" hreflang="nan" data-title="Tāi-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target">閩南語 / Bân-lâm-gú</a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學 – Kanton" lang="yue" hreflang="yue" data-title="代數學" data-language-autonym="粵語" data-language-local-name="Kanton" class="interlanguage-link-target">粵語</a></li> </ul> <div class="after-portlet after-portlet-lang"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q3968#sitelinks-wikipedia" title="Bulö'ö khai-khai antarbahasa" class="wbc-editpage">Bulö'ö khai-khai</a></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/Aljabar" title="Faigi nösi nga'örö [c]" accesskey="c">Nga'örö</a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Huhuo:Aljabar&action=edit&redlink=1" rel="discussion" class="new" title="Huhuo sanandrösa ba nösi nga'örö (lö tesöndra zura andrö) [t]" accesskey="t">Fahuhuosa</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="Ubah varian bahasa" > <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" >Li Niha </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="Famaigi"> <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/Aljabar">Baso</a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Aljabar&veaction=edit" title="Bulö'ö nga'örö andre [v]" accesskey="v">Bulö'ö</a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Aljabar&action=edit" title="Sunting kode sumber halaman ini [e]" accesskey="e">Bulö’ö kode</a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Aljabar&action=history" title="Waö-waö wamulö'ö nga'örö andre ba zi lalö [h]" accesskey="h">Faigi waö-waö</a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Peralatan halaman"> <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="Fakake" > <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" >Fakake </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">Fakake</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">bini'ö</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Opsi lainnya" > <div class="vector-menu-heading"> Aksi </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/Aljabar">Baso</a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Aljabar&veaction=edit" title="Bulö'ö nga'örö andre [v]" accesskey="v">Bulö'ö</a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Aljabar&action=edit" title="Sunting kode sumber halaman ini [e]" accesskey="e">Bulö’ö kode</a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Aljabar&action=history">Faigi waö-waö</a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Umum </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Pranala_balik/Aljabar" title="Fefu nga'örö wiki sitokahi ba da'a [j]" accesskey="j">Nikhaigö ba da'e</a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Perubahan_terkait/Aljabar" rel="nofollow" title="Sifabö'ö safuria fefu nga'örö nifakhai ba nga'örö andre [k]" accesskey="k">Si fabö'ö si fakhai</a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=nia" title="Fairö berkas [u]" accesskey="u">Fairö berkas</a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Aljabar&oldid=24184" title="Khai-khai permanen ba wamulö'ö nga'örö andre">Khai-khai permanen</a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Aljabar&action=info" title="Informasi lanjut tentang halaman ini">Info nga'örö</a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Kutip&page=Aljabar&id=24184&wpFormIdentifier=titleform" title="Hewisa wangai niŵa'ö ba nga'örö andre (mengutip)">Kutip nga'örö andre</a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fnia.wikipedia.org%2Fwiki%2FAljabar">Halö URL sadogo</a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesial:QrCode&url=https%3A%2F%2Fnia.wikipedia.org%2Fwiki%2FAljabar">Failo kode QR</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"> Raka/Ekspor </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Spesial:Buku&bookcmd=book_creator&referer=Aljabar">Fazökhi sambua buku</a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesial:DownloadAsPdf&page=Aljabar&action=show-download-screen">Failo tobali PDF</a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Aljabar&printable=yes" title="Versi niraka nga'örö andre [p]" accesskey="p">Versi niraka</a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Ba halöŵö tanö bö'ö </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:Algebra" hreflang="en">Wikimedia Commons</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/Q3968" title="Khai-khai ba ngawua repositori data si fakhai [g]" accesskey="g">Ngawua Wikidata</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="Peralatan halaman"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Khala-khala"> <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">Khala-khala</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">bini'ö</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">Moroi ba Wikipedia</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="nia" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Quadratic_formula.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Quadratic_formula.svg/220px-Quadratic_formula.svg.png" decoding="async" width="220" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Quadratic_formula.svg/330px-Quadratic_formula.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Quadratic_formula.svg/440px-Quadratic_formula.svg.png 2x" data-file-width="402" data-file-height="124" /></a><figcaption>Rumus <a href="/w/index.php?title=Persamaan_kuadrat&action=edit&redlink=1" class="new" title="Persamaan kuadrat (lö tesöndra zura andrö)">persamaan kuadrat</a> mengungkapkan solusi dari persamaan derajat dua <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ax^{2}+bx+c=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax^{2}+bx+c=0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23e70cfa003f402d108ec04d97983fb62f69536e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:16.89ex; height:2.843ex;" alt="{\displaystyle ax^{2}+bx+c=0}" /> dalam koefisien <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a,b,c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b,c}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f13f068df656c1b1911ae9f81628c49a6181194d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.302ex; height:2.509ex;" alt="{\displaystyle a,b,c}" />, dimana <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /> bukan nol.</figcaption></figure> Aljabar andre (dari <a href="/w/index.php?title=Bahasa_Arab&action=edit&redlink=1" class="new" title="Bahasa Arab (lö tesöndra zura andrö)">bahasa Arab</a> الجبر "al-jabr" ma na la fo'eluaha ia lamane, fangowuloi mbagia si no tekiko ("pengumpulan bagian yang rusak")<a href="#cite_note-oed-1">[1]</a>) ya'ia da'ö sambua mbagia wamahaö moroi ba <a href="/wiki/Matematika" title="Matematika">Matematika</a>, sifao ba teori bilangan, <a href="/w/index.php?title=Geometri&action=edit&redlink=1" class="new" title="Geometri (lö tesöndra zura andrö)">Geometri</a> ba tola gö ba wo Analisis matematis. No si no oi la'ila niha, aljabar ya'ia da'ö fangi'ila ba ngawalö dandra-dandra (simbol-simbol) matematika ba goi-goi hewisa wo fangamöi tandra-tandra ni'oguna'ö ba wangerai andrö;<a href="#cite_note-2">[2]</a> aljabar no sambua wamahaö samarahu arakhagö fefu mbagia ba matematika.<a href="#cite_note-3">[3]</a> Baero da'ö, aljabar andre, no sambua dane-dane ba wangalui lala hewisa wo fosinöndra ngawalö ni'erai ba matetika simane abstraksi grup matematika, Gelanggang matematika ba Medan matematika. Idugu oya mbagia dane-dane moroi ba aljabar latötöi faoma aljabar elementer, na aljabar abstrak latötöi faoma aljabar abstrak mazui aljabar modern. Aljabar elementer sito'ölönia labali'ö soguna sibai ba wamahaö matematika, ilmu pengetahuan, mazui teknik, faoma aplikasi sifakhai ba kesehatan ba simanö göi ba wamahaö ekonomi. Aljabar abstrak sambua duho ba matematika salaŵa ma'ifu ma tingkat lanjut, ni'oguna'ö ya'ira si no profesional ba ere matematika. Aljabar elementer faehu ma'ifu faoma <a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a> ba wangoguna'ö abstraksi, simane mangoguna'ö hurufo ba wo salahini numero-numero si lö mu'ilana mazui tetehege tola ihalö oya zinöndra (nilai). Simane duma-duma, ba <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x+2=5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mo>=</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x+2=5}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3387b0e2d7885c1fe21886cb6b2536f8dcb75b16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.593ex; height:2.343ex;" alt="{\displaystyle x+2=5}" /> hurufo <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /> lö mu'ila, ba hiza huku inversi tola la'oguna'ö ba wangalui sinöndra ma nilai: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=3}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/871a5063af170fa536b144fbcc5745146a42cc13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle x=3}" />. Bakha ba (Ekivalensi massa-energi), hurufo <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" /> faoma <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}" /> da'ö ni'oguna'ö tobali variabel, ba hurufo <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" /> sitobali Konstanta (matematika), kecepatan cahaya bakha ba vakum. Aljabar ibe'e lala metode ba wangalui wamagölösi ba hewisa ba wo faehagö rumus saoha (khöra ya'ira si no to'ölö mangoguna'ö konsep da'a) moroi na i'oguna'ö metode konvensional, simane lasura fefu zinöndra faoma hurufo ma ngawua wehede. Ngawua wehede aljabar andre, oya sibai la'oguna'ö ba ngawalö lala sakhökhö. Ngawalö gangolifa ba dandrösa matematika ba aljabar abstrak da'ö nifotöi "aljabar", fehede da'a la'oguna'ö, simane ba wanötöi <a href="/w/index.php?title=Aljabar_linear&action=edit&redlink=1" class="new" title="Aljabar linear (lö tesöndra zura andrö)">aljabar linear</a> faoma topologi aljabar. Samösa gere matematika si no mamalua famareso ma ba <a href="/wiki/Li_Indonesia" title="Li Indonesia">li Indonesia</a> lamane penelitian sanandrösa ba aljabar lakaoni faoma fanötöi; aljabarwan. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etimologi">Etimologi</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=1" title="Bulö’ö waosatö: Etimologi" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=1" title="Sunting kode sumber bagian: Etimologi">bulö’ö kode</a>]</div> Fehede aljabar tefoli moroi ba Bahasa Arab الجبر (al-jabr molo'ö famo'eluaha moroi ba ngawua wehede andrö, eluahania ya'ia da'ö; "fangowuloi ngawalö zi no tekiko") fehede ma fanötöi da'a, tehalö moroi ba zi sambua mbuku nibe'e högö mbuku andrö Al Kitaab al muhtasar fii hisaab al jabr wa'l muqabaala<a href="#cite_note-4">[4]</a> nisura matematikawan ba astronom <a href="/w/index.php?title=Persia&action=edit&redlink=1" class="new" title="Persia (lö tesöndra zura andrö)">Persia</a>, <a href="/w/index.php?title=Mu%E1%B8%A5ammad_bin_M%C5%ABs%C4%81_al-Khaw%C4%81rizm%C4%AB&action=edit&redlink=1" class="new" title="Muḥammad bin Mūsā al-Khawārizmī (lö tesöndra zura andrö)">Al-Khwarizmi</a>. Ngawua wehede da'a no möi ia ba bahasa Inggris ba abad si 15, he moroi ba <a href="/w/index.php?title=Spanyol&action=edit&redlink=1" class="new" title="Spanyol (lö tesöndra zura andrö)">Spanyol</a>, <a href="/wiki/Italia" title="Italia">Italia</a>, mazui moroi ba Pertengahan Latin. Aljabar ba zi'oföna latötöi ia prosedur operasi pengaturan patah ma dislokasi tulang. Eluahania ba matematika si'oföna sibai lasura ba abad 16. <div class="mw-heading mw-heading2"><h2 id="Ngawalö_geluaha_"aljabar"">Ngawalö geluaha "aljabar"</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=2" title="Bulö’ö waosatö: Ngawalö geluaha "aljabar"" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=2" title="Sunting kode sumber bagian: Ngawalö geluaha "aljabar"">bulö’ö kode</a>]</div> Ngawua wehede "aljabar" so lala wangoguna'ö ya'ia bakha ba matematika, sitobali fehede nitandrösaigö ba dandrösa mazui faoma kualifikasi. <ul><li>Sitobali fehede fanandrösa ba dandrösa ma kata tunggal si lö mangoguna'ö kata sandang, "aljabar" töi sambua wamahaö ba wamahaö matematika.</li> <li>Sitobali fehede fanandrösa ba dandrösa ma kata tunggal mazui ba wanötöi ha wa'oya, "aljabar" ifaehagö wenaeta ma struktur matematika faoma fa'akhökhö, ba famo'eluaha satulö, te balazigö hewisa gamöta dödö zanura ya'ia. Sito'ölönia fenaeta da'a so khönia wamonönö (penambahan, perkalian, ba skalar perkalian). Ba ginötö zanura mangoguna'ö fehede "aljabar", lahaogö sambua subset moroi ba asumsi tambahan simane: asosiatif, komutatif, unital, mazui/faoma dimensi berhingga. Bakha ba aljabar universal, fehede "aljabar" tefaolo ba generalisasi moroi ba konsep da'ö moroi yaŵa, tola manö; n-ary operasi.</li> <li>Faoma kualifikasi, so wa'afabö'ö sifagölö: <ul><li>Lö hadöi khönia kata sandang, eluahania no föfö moroi ba aljabar, simane aljabar linier, aljabar elementer ma simbol-manipulasi goi-goi nifaha'ö ba naha wamaha'ö ma kursus sd matematika sitobali dane-dane moroi ba wamahaö pendidikan dasar faoma menengah, mazui aljabar abstrak.</li> <li>Sangoguna'ö kata sandang, eluahania sambua duma-duma moroi ba struktur abstrak, simane aljabar bentang, aljabar asosiatif, mazui aljabar operator verteks.</li> <li>Fa'itaria dombua geluaha da'a la'oguna'ö ba wangerai sifagölö, simane bakha ba kalimat: aljabar Komutatif adalah studi tentang gelanggang komutatif, yang merupakan aljabar komutatif atas bilangan bulat.</li></ul></li></ul> <div class="mw-heading mw-heading2"><h2 id="Aljabar_moroi_ba_Matematika">Aljabar moroi ba Matematika</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=3" title="Bulö’ö waosatö: Aljabar moroi ba Matematika" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=3" title="Sunting kode sumber bagian: Aljabar moroi ba Matematika">bulö’ö kode</a>]</div> Aljabar andre tebörötaigö moroi ba wangerai sifagölö ba <a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a>, sangoguna'ö hurufo ba wo salahini numero. Da'a tola möi sitobali dane-dane moroi ba zindruhunia heŵa'ae lö lafaogö khönia numero-numero. Simane duma-dumania, ba persamaan kuadrat <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ax^{2}+bx+c=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax^{2}+bx+c=0,}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24c2ce44ca552049d96088988f5d83f6763c059a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.536ex; height:3.009ex;" alt="{\displaystyle ax^{2}+bx+c=0,}" /></dd></dl> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a,b,c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a,b,c}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f13f068df656c1b1911ae9f81628c49a6181194d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.302ex; height:2.509ex;" alt="{\displaystyle a,b,c}" /> tola tobali bilangan gofu hadia manö(kecuali bahwa <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /> tidak dapat bernilai <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}" />), ba rumus kuadrat andre tola la'oguna'ö wa'alio ba aoha ba wanöndra nilai-nilai moroi kuantitas <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /> si lö mu'ila ma ba wofönui persamaan. Rumus kuadrat la'oguna'ö ba wamatunö persamaan, ba aefa da'ö ba wanöndra hadia lala moroi ba persamaan da'ö. Molo'ö waö-waö, ba famahaö ba ginötö iada'a, famareso aljabar tebörötaigö moroi hewisa ba wamosinöndra persamaan simane persamaan kuadrat da'ö yaŵa. Aefa da'ö, oya wanofu-wanofu sito'ölö, simane; "hadia persamaan simane da'ö so lala wamosinöndra ya'ia?", "hawa'oya lala nitörö ba wangasiwai ngawalö wamosinöndra persamaan da'a?", "hadia zitola lafaehagö moroi ba lala wamosinöndra fanofu andrö?". Fanofu-fanofu simane da'a, möi ba wa'atohare ngawalö mbua wangera-ngera sifakhai ba bentuk, struktur faoma simetri.<a href="#cite_note-5">[5]</a> Sifat-sifat struktural moroi ba objek-objek non-numerik ma si tenga numero, aefa da'ö awena la abstraksi ba wanutunö waö-waö struktur-struktur aljabar simane grup (matematika), gelanggang (matematika), faoma medan (matematika). Fatua lö abad si-16, matematika so ba zidombua subbidang, ya'ia da'ö <a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a> faoma <a href="/w/index.php?title=Geometri&action=edit&redlink=1" class="new" title="Geometri (lö tesöndra zura andrö)">Geometri</a>. Heŵa'ae ba zi ha'uga ngawalö metode, si no oföna mu'ehaogö, te da'ö ni'ila niha sitobali aljabar, ma fa'atohare aljabar faoma lö ara aefa da'ö, Kalkulus infinitesimal sitobali subbidang matematika ha ba gotalua abad si-16 ma abad si-17. Moroi ba dalu abad si-19, oya zibohou sifakhai ba matematika, nifaehagö moroi ba aritmetika faoma geometri, ba arakhagö fefu mangoguna'ö aljabar. Ba ginötö iada'a, aljabar no idugu sökhi irege oya wamahaö moroi ba matematika zangoguna'ö simane sitola mufaigi ba <a href="/w/index.php?title=Klasifikasi_Subjek_Matematika&action=edit&redlink=1" class="new" title="Klasifikasi Subjek Matematika (lö tesöndra zura andrö)">Klasifikasi Subjek Matematika</a><a href="#cite_note-6">[6]</a> hiza, lö hadöi he ha sambua moroi ba wenaeta si'oföna (dua digit entri) nifotöi aljabar. Iada'a aljabar no irugi 08-sistem-sistem aljabar umum, 12-<a href="/w/index.php?title=Medan_(matematika)&action=edit&redlink=1" class="new" title="Medan (matematika) (lö tesöndra zura andrö)">teori medan</a> dan <a href="/w/index.php?title=Polinomial&action=edit&redlink=1" class="new" title="Polinomial (lö tesöndra zura andrö)">Polinomial</a>, 13-<a href="/w/index.php?title=Aljabar_Komutatif&action=edit&redlink=1" class="new" title="Aljabar Komutatif (lö tesöndra zura andrö)">Aljabar Komutatif</a>, 15-<a href="/w/index.php?title=Aljabar_Linear&action=edit&redlink=1" class="new" title="Aljabar Linear (lö tesöndra zura andrö)">Aljabar Linear</a> dan <a href="/w/index.php?title=Aljabar_Multilinear&action=edit&redlink=1" class="new" title="Aljabar Multilinear (lö tesöndra zura andrö)">multilinear</a>; <a href="/w/index.php?title=Matriks_(matematika)&action=edit&redlink=1" class="new" title="Matriks (matematika) (lö tesöndra zura andrö)">teori matriks</a>, 16-<a href="/w/index.php?title=Aljabar_Asosiatif&action=edit&redlink=1" class="new" title="Aljabar Asosiatif (lö tesöndra zura andrö)">Aljabar Asosiatif</a>, 17-<a href="/w/index.php?title=Aljabar_tak-Asosiatif&action=edit&redlink=1" class="new" title="Aljabar tak-Asosiatif (lö tesöndra zura andrö)">Aljabar tak-Asosiatif</a>, 18-<a href="/w/index.php?title=Teori_Kategori&action=edit&redlink=1" class="new" title="Teori Kategori (lö tesöndra zura andrö)">Teori Kategori</a>; <a href="/w/index.php?title=Aljabar_Homologis&action=edit&redlink=1" class="new" title="Aljabar Homologis (lö tesöndra zura andrö)">Aljabar Homologis</a>, 19-<a href="/w/index.php?title=Teori-K&action=edit&redlink=1" class="new" title="Teori-K (lö tesöndra zura andrö)">Teori-K</a>, faoma 20-<a href="/w/index.php?title=Teori_Grup&action=edit&redlink=1" class="new" title="Teori Grup (lö tesöndra zura andrö)">Teori Grup</a>. Aljabar andrö la'oguna'ö göi ia molo'ö ekstensif bakha 11-<a href="/w/index.php?title=Teori_Bilangan&action=edit&redlink=1" class="new" title="Teori Bilangan (lö tesöndra zura andrö)">Teori Bilangan</a> faoma 14-<a href="/w/index.php?title=Geometri_Aljabar&action=edit&redlink=1" class="new" title="Geometri Aljabar (lö tesöndra zura andrö)">Geometri Aljabar</a>. <div class="mw-heading mw-heading2"><h2 id="Waö-waö_(Sejarah)">Waö-waö (Sejarah)</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=4" title="Bulö’ö waosatö: Waö-waö (Sejarah)" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=4" title="Sunting kode sumber bagian: Waö-waö (Sejarah)">bulö’ö kode</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Böröta_aljabar_(Sejarah_awal_aljabar)">Böröta aljabar (Sejarah awal aljabar)</h3>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=5" title="Bulö’ö waosatö: Böröta aljabar (Sejarah awal aljabar)" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=5" title="Sunting kode sumber bagian: Böröta aljabar (Sejarah awal aljabar)">bulö’ö kode</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg/220px-Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" decoding="async" width="220" height="348" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg 1.5x" data-file-width="240" data-file-height="380" /></a><figcaption>Nga'örö moroi ba mbuku ni sura <a href="/w/index.php?title=Mu%E1%B8%A5ammad_bin_M%C5%ABs%C4%81_al-Khaw%C4%81rizm%C4%AB&action=edit&redlink=1" class="new" title="Muḥammad bin Mūsā al-Khawārizmī (lö tesöndra zura andrö)">Al-Khwarizmi</a> yang berjudul al-Kitab al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala (Buku Ringkasan tentang Perhitungan dengan Pelengkapan dan Penyetimbangan</figcaption></figure> Ŵa'a moroi ba aljabar andre, tola mu'osisi'ö ofeta ba ginötö me Babilonia kuno,<a href="#cite_note-7">[7]</a> samazaewe ma sangodödögö fangi'ila sifakhai ba sistem aritmetika lanjut ni'oguna'ö ba wangerai menurut gaya algoritme. Bangsa Babilonia la odödögö ba wangi'ila rumus ba wangerai hewisa lala wanema li ma hewisa ba wangalui sinöndra moroi ba ngawalö zedöna la'erai ba ginötö iada'a, hiza ba wangalui sinöndrönania la'oguna'ö lala persamaan linear, persamaan kuadrat, faoma persamaan taktentu. Hiza, tenga fefu, so göi matematika Mesir Kuno ma ni'oguna'ö ira niha <a href="/wiki/Mesir" title="Mesir">Mesir</a> ba ginötö iada'a faoma Matematika Yunani ba matematika Tiongkok ba milenium 1 SM sito'ölönia lafosinöndra wanofu andrö faoma metode geometris, simane si no lafaehagö bakha ba Papirus Matematika Rhind, Elemen Euklides, faoma Sembilan Bab mengenai Seni Matematika. Karya geometris moroi Yunani, simane si no lasura bakha Elemen, no lahenagö döla-döla dödö ma kerangka kerja ba wame'e rumus ma na'i manalu'i moroi ba zinöndra nitötöna irege da'a nigo'ö zato ba wangalui sinöndra, heŵa'ae da'a lö si tehöngö fatua lö si muledo Matematika Islam ba abad pertengahan.<a href="#cite_note-8">[8]</a> Ba ginötö <a href="/wiki/Plato" title="Plato">Plato</a>, matematika Yunani no so wa'atedou. Niha Yunani no la'ila nifotöi aljabar geometri, hiza moroi ba wamahaö andrö tefaehagö awa suku-suku matematika tetötöi ia moroi ba sisi-sisi ba objek geometri, sito'ölönia simane famadölö ma garis, sangokhögö hurufo-hurufo sifakhai ba wangerai.<a href="#cite_note-citeboyer-9">[9]</a> <a href="/w/index.php?title=Diofantus&action=edit&redlink=1" class="new" title="Diofantus (lö tesöndra zura andrö)">Diofantus</a> (abad si-3 Masehi) ya'ia da'ö samösa gere matematika ma laŵa'ö ba wehede lamane Matematikawan Yunani moroi ba mbanua Iskandariyah ba si no manura oya mbuku nifotöi <a href="/w/index.php?title=Arithmetica&action=edit&redlink=1" class="new" title="Arithmetica (lö tesöndra zura andrö)">Arithmetica</a>. Sinura-sinura andre fakhai ia ba wamosinöndra ngawalö wanofu moroi ba persamaan aljabar,<a href="#cite_note-10">[10]</a> ba hiza no möi famarou ba si ba wangi'ila nifotöi persamaan Diofantin bakha ba teori bilangan. Sito'ölö nifalui ba ginötö iada'a na la faedogö moroi ba ni fa'ema ba da'ö moroi yaŵa, no manandrösa ia ba Matematikawan bangsa Persia, Muḥammad ibn Mūsā al-Khwārizmī (kira-kira 780–850). Aefa da'ö isura mbuku nibe'enia högö mbuku andrö: Buku Ringkasan tentang Perhitungan dengan Pelengkapan dan Penyetimbangan, nifangamöi aljabar sitobali famahaö matematika ma disiplin matematika si lö mombalazigö geometri faoma aritmetika.<a href="#cite_note-11">[11]</a> Matematikawan ba ginötö periode Helenistik, sotöi Heron moroi ba Iskandariyah faoma Diofantus,<a href="#cite_note-12">[12]</a> simanö göi Matematikawan India simane Brahmagupta manohugö sito'ölö lafalua ma tradisi-tradisi Mesir faoma Babilonia, heŵa'ae Arithmetica-nia Diophantus faoma Brāhmasphuṭasiddhānta-nia Brahmagupta so ba dadaoma sabölö alaŵa.<a href="#cite_note-13">[13]</a> Simane duma-dumania, lala wangalui aritmetika si'oföna (termasuk solusi nol dan negatif) soguna ba persamaan kuadrat, hulö simane si no ifaehagö Brahmagupta ba mbukunia Brahmasphutasiddhanta. Aefa da'ö, Matematikawan Persia faoma Arab no la'odödögö hewisa ba wondrou'ö metode-metode aljabar ba wogamö wetaro sabölö alaŵa. Heŵa'ae Diofantus faoma bangsa Babilonia asese sibai mangoguna'ö metode ad hoc nifaehagö ni'oguna'öra ba wangalui sinöndra persamaan-persamaan, bua wangera-ngera Al-Khwarizmi no tobali dane-dane si sökhi. No i'asiwai persamaan linear faoma kuadrat si lö mangoguna'ö simbolisme aljabar, bilangan negatif, mazui nol, börö da'ö, andrö wa si lötolalö'ö i faehusi ngawalö persamaan.<a href="#cite_note-Meri2004-14">[14]</a> Ba wamahaö aljabar andre, no la'ila niha ya'ia da'ö fakhai ia ba wamagölö ngawalö wangerai ma lamane teori persamaan, Matematikawan Yunani, sotöi Diofantus molo'ö wangi'ila niha sito'ölö, lakaoni ia faoma ere aljabar ma abölö enahöi wanötöi ya'ia, ya'ia da'ö: "bapak aljabar" ba hiza ba wa'anumalö ginötö, oya wabu'a-bu'asa sifakhai khö gere tanöbö'ö simane sotöi al-Khwarizmi, sangahaogö fangi'ila nifotöi: al-jabr, tola göi lakaoni ia faoma ama aljabar.<a href="#cite_note-15">[15]</a> Ya'ira sifao khö zöndra Diofantus zanguŵa'ö wa aljabar nisöndra bakha ba Al-Jabr tehude ma'ifu moroi ba nisöndra ba Arithmetica ba börö da'ö Arithmetica no hulö ni'adogo'ö, na Al-Jabr ma'afefu no hulö retoris.<a href="#cite_note-16">[16]</a> Na ya'ira sifao ba zöndra Al-Khwarizmi sifakhai ma samaehagö nifotöi metode "<a href="/w/index.php?title=Reduksi_(matematika)&action=edit&redlink=1" class="new" title="Reduksi (matematika) (lö tesöndra zura andrö)">reduksi</a>" faoma "penyetimbangan" (transposisi suku-suku yang diambil ke ruas lain suatu persamaan, yaitu, pencoretan suku-suku yang memiliki <a href="/w/index.php?title=Variabel_(matematika)&action=edit&redlink=1" class="new" title="Variabel (matematika) (lö tesöndra zura andrö)">variabel</a> dan <a href="/w/index.php?title=Eksponensiasi&action=edit&redlink=1" class="new" title="Eksponensiasi (lö tesöndra zura andrö)">pangkat</a> sama pada ruas lain suatu persamaan), nituturu ma ni aekhugö moroi ba al-jabr ba mböröta,<a href="#cite_note-Boyer-229-17">[17]</a> ba no ifaehagö molo'ö wangi'ilania ngawalö wamosinöndra sifakhai ba persamaan kuadrat ma fangerai ba numeronia samösa,<a href="#cite_note-18">[18]</a> i'abe'e'ö dödö niha molo'ö ngawalö zi so khönia sitobali dane-dane geometris, sifao ba wangoguna'ö aljabar sitonali sambua dane-dane ma disiplin nifaehagö molo'ö fa'ato'ölö zangoguna'ö ya'ia.<a href="#cite_note-19">[19]</a> Aljabar andre, lö sa'ae i'angeragö ngawalö wangalui sinöndra ba ngawalö wanofu, hiza sambua eksposisi ba mböröta sifakhai ba suku-suku primitif ba ngawalö wangorudugö ba wamagölösi sinöndra, ba tetohugö ia molo'ö eksplisit ba wangalui sinöndra satulö". Ya'ia göi no i'alui wamagölösi ma persamaan soguna khönia samösa ba lala wangerai sito'ölö simane nifalua niha bö'ö, ba hiza no iföfögö ba wangalui sambua zinöndra si lö hadöi amozua ma abölö sökhi wanötöi ya'ia ba <a href="/wiki/Li_Indonesia" title="Li Indonesia">li Indonesia</a> lamane: tak terbatas.<a href="#cite_note-Rashed-Armstrong-20">[20]</a> Matematikawan Persia tanöbö'ö, sotöi Umar Khayyām si no latema ngawalö wangi'ila ba woföfögö dane-dane geometri aljabar ba ya'ia samösa ere samaehagö solusi geometris umum ba wangerai famagölösi fungsi kubik ma persamaan kubik. Buku nisurania nibe'e högö mbuku: Risalah tentang Peragaan Soal-Soal Aljabar (1070), so honogöigö ngawalö prinsip-prinsip aljabar, si no angolifa moroi ba zifakhai ba Matematika, hiza Matematika Persia andre, sindruhunia la fa'ohe'ö ba Eropa.<a href="#cite_note-21">[21]</a> Matematikawan Persia tanöbö'ö, simane Sharaf al-Din al-Tusi, sanöndra lala wamosinöndra aljabar faoma numero ba ngawalö zifakhai ba wamagölösi fangerai kubik ma persamaan kubik.<a href="#cite_note-22">[22]</a> Dia juga mengembangkan konsep mengenai <a href="/w/index.php?title=Fungsi_(matematika)&action=edit&redlink=1" class="new" title="Fungsi (matematika) (lö tesöndra zura andrö)">fungsi</a>.<a href="#cite_note-23">[23]</a> Matematikawan India, sotöi <a href="/w/index.php?title=Mahavira_(matematikawan)&action=edit&redlink=1" class="new" title="Mahavira (matematikawan) (lö tesöndra zura andrö)">Mahavira</a> faoma <a href="/w/index.php?title=Bh%C4%81skara_II&action=edit&redlink=1" class="new" title="Bhāskara II (lö tesöndra zura andrö)">Bhāskara II</a>, Matematikawan Persia <a href="/w/index.php?title=Al-Karaji&action=edit&redlink=1" class="new" title="Al-Karaji (lö tesöndra zura andrö)">Al-Karaji</a>,<a href="#cite_note-Boyer_al-Karkhi_ax2n-24">[24]</a> faoma Matematikawan Tiongkok, <a href="/w/index.php?title=Zhu_Shijie&action=edit&redlink=1" class="new" title="Zhu Shijie (lö tesöndra zura andrö)">Zhu Shijie</a>, mangasiwai ngawalö wangerai sifakhai ba persamaan kubik, persamaan kuartik ma kuartik, persamaan kuintik, faoma famagölösi polinomial sasese laŵa'ö berorde abölö alaŵa mangoguna'ö metode numerik. Ba abad ke-13, fangasiwaisi persamaan kubik nifalua <a href="/w/index.php?title=Fibonacci&action=edit&redlink=1" class="new" title="Fibonacci (lö tesöndra zura andrö)">Fibonacci</a> ya'ia da'ö sosalahini moroi ba mböröta wangi'ila aljabar Eropa. <a href="/w/index.php?title=Ab%C5%AB_al-%E1%B8%A4asan_ibn_%CA%BFAl%C4%AB_al-Qala%E1%B9%A3%C4%81d%C4%AB&action=edit&redlink=1" class="new" title="Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī (lö tesöndra zura andrö)">Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī</a> (1412–1486) manga'i mbosi-bosi si'oföna sinumalö ba wangi'ila ngawalö dandra aljabar, ma ba <a href="/wiki/Li_Indonesia" title="Li Indonesia">li Indonesia</a> lamane: "langkah-langkah pertama menuju perkenalan simbolisme aljabar". Hiza, no göi i'erai ∑n2, ∑n3 ba i'oguna'ö wamahatö (suksesif) ba wotatugöi akar kuadrat.<a href="#cite_note-25">[25]</a> Ba ginötö <a href="/w/index.php?title=Islam&action=edit&redlink=1" class="new" title="Islam (lö tesöndra zura andrö)">Islam</a> so ma'ifu we'amöi furi, dunia Eropa hi no wa'amanöi wangi'ila ba matematika. Ba da'ö aljabar andre, tedou wa'amozawili ba zi sagörö ulidanö. <div class="mw-heading mw-heading3"><h3 id="Waö-waö_Sibohou_Aljabar_(Sejarah_modern_aljabar)">Waö-waö Sibohou Aljabar (Sejarah modern aljabar)</h3>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=6" title="Bulö’ö waosatö: Waö-waö Sibohou Aljabar (Sejarah modern aljabar)" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=6" title="Sunting kode sumber bagian: Waö-waö Sibohou Aljabar (Sejarah modern aljabar)">bulö’ö kode</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/Berkas:Cardano.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Cardano.jpg/212px-Cardano.jpg" decoding="async" width="212" height="258" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/03/Cardano.jpg 1.5x" data-file-width="268" data-file-height="326" /></a><figcaption>Matematikawan Italia <a href="/w/index.php?title=Girolamo_Cardano&action=edit&redlink=1" class="new" title="Girolamo Cardano (lö tesöndra zura andrö)">Girolamo Cardano</a> mamatumbu'ö lala wangalui sinöndra kubik ma ba wehede matematika asese lamane fungsi kubik faoma fungsi kuadrat nisurania bakha ba mbuku ba ndröfi si 1545 nibe'e högö mbuku: <a href="/w/index.php?title=Ars_Magna_(Gerolamo_Cardano)&action=edit&redlink=1" class="new" title="Ars Magna (Gerolamo Cardano) (lö tesöndra zura andrö)">Ars magna</a>.</figcaption></figure> Karya <a href="/w/index.php?title=Fran%C3%A7ois_Vi%C3%A8te&action=edit&redlink=1" class="new" title="François Viète (lö tesöndra zura andrö)">François Viète</a> sifakhai ba aljabar sibohou, ba gafuriata abadi si-16 no sambua bosi soguna sibai sinumalö ba wangoguna'ö aljabar modern. Ba ndröfi si 1637, <a href="/w/index.php?title=Ren%C3%A9_Descartes&action=edit&redlink=1" class="new" title="René Descartes (lö tesöndra zura andrö)">René Descartes</a> mamatumbu'ö La Géométrie, sifao ba wanöndra sambua lala nifotöi geometri analitis ba hiza ifaehagö göi ba niha sato nifotöi notasi aljabar modern. Salua tanöbö'ö zifakhai ba wondrou'ö aljabar ya'ia da'ö ba wangasiwaisi aljabar si no oi la'ila niha sato ba zi sagörö ulidanö meluo da'ö ba wangalui hewisa wamagölösi nifotöi persamaan kubik faoma kuartik, nifanöi wangi'ila ba ginötö abad si-16. Bua wangera-ngera sifakhai ba determinan nifanöi moroi khö matematikawan Jepang sotöi <a href="/w/index.php?title=Seki_K%C5%8Dwa&action=edit&redlink=1" class="new" title="Seki Kōwa (lö tesöndra zura andrö)">Seki Kōwa</a> ba abad si-17, no igo'ö ia sotöi <a href="/w/index.php?title=Gottfried_Leibniz&action=edit&redlink=1" class="new" title="Gottfried Leibniz (lö tesöndra zura andrö)">Gottfried Leibniz</a> ba wa'omasinia samösa, eluahania tenga ba döi gangowuloa ilau da'ö ba zi 10 fakhe fa'ara aefa da'ö, sitobali ohitö dödö ba wangalui hewisa zinöndra ba sistem persamaan linear simultan sangoguna'ö Matriks (matematika). Hiza, Gabriel Cramer ilau mohalöŵö sifakhai ba matriks faoma determinan ba abad si-18. Permutasi i'alui lala hewisa wangasiwaisi ngawalö wanofu sotöi <a href="/w/index.php?title=Joseph-Louis_de_Lagrange&action=edit&redlink=1" class="new" title="Joseph-Louis de Lagrange (lö tesöndra zura andrö)">Joseph-Louis de Lagrange</a> ba mbuku nisurania me döfi si 1770 nibe'enia högönia Réflexions sur la résolution algébrique des équations (Refleksi ba resolusi aljabar ba zisambua wamagölösi), si'oföna sibai ba wotatugöi hewisa lala wangasiwaisi fanofu zisambua persamaan aljabar, hiza no ifaehagö <a href="/w/index.php?title=Resolven_(teori_Galois)&action=edit&redlink=1" class="new" title="Resolven (teori Galois) (lö tesöndra zura andrö)">resolven Lagrange</a>. Paolo Ruffini ya'ia da'ö niha si'oföna sibai sofanöi teori moroi ba grup permutasi, hulö zimane nifalui ndra matematikawan ba mböröta, tola göi ba wangalui sinöndra persamaan aljabar. <div class="mw-heading mw-heading2"><h2 id="Angolifa_Matematika_Sangoguna'ö_Ngawua_Wehede_Aljabar_ba_Döira_(Bidang_matematika_dengan_kata_aljabar_pada_nama_mereka)">Angolifa Matematika Sangoguna'ö Ngawua Wehede Aljabar ba Döira (Bidang matematika dengan kata aljabar pada nama mereka)</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=7" title="Bulö’ö waosatö: Angolifa Matematika Sangoguna'ö Ngawua Wehede Aljabar ba Döira (Bidang matematika dengan kata aljabar pada nama mereka)" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=7" title="Sunting kode sumber bagian: Angolifa Matematika Sangoguna'ö Ngawua Wehede Aljabar ba Döira (Bidang matematika dengan kata aljabar pada nama mereka)">bulö’ö kode</a>]</div> Ba zi ha'uga gangolifa matematika si no ahono ba zifakhai ba Aljabar (klasifikasi aljabar abstrak) mamaogö fehede aljabar ba döira; simane aljabar linear ha sambua duma-duma da'a. Ba hiza so göi zi lö'ö fao döira, simane: teori grup, teori gelanggang, faoma Medan (matematika) ma teori bidang. Ba da'a tou so gangolifa matematika sangoguna'ö fehede "aljabar" ba döira. <ul><li>Aljabar elementer, angolifa moroi ba aljabar sito'ölö nifahaö ba perkuliahan dasar Matematika.</li> <li>Aljabar abstrak, hiza ba struktur aljabar simane Grup (matematika), Gelanggang (matematika) faoma Medan (matematika) nifo'eluaha faoma sistem aksioma ma asese lamane aksiomatis.</li> <li>Aljabar linear, hiza no oya dandra-tandra moroi ba persamaan linear, Ruang vektor faoma Matriks (matematika) nitema niha ba wamahaö.</li> <li>Aljabar Boolean, angolifa aljabar samahatö komputasi faoma sahatö ba nilai kebenaran nifaehagö faoma fehede; atulö/benar faoma falasa/salah.</li> <li>Aljabar komutatif, famahaö sifakhai ba gelanggang komutatif.</li> <li>Komputasi simbolik mazui Aljabar komputer, famatöfaigö metode-metode aljabar simane; algoritme faoma program komputer.</li> <li>Aljabar homologis, famahaö fenaeta aljabar sitobali dane-dane ba wangi'ila ruang topologi.</li> <li>Aljabar semesta, tandra-tandra sito'ölö ba zi'ogötö'ö fenaeta aljabar nitema ba wamahaö.</li> <li>Teori bilangan aljabar, tandra-tandra bilangan nitema wamahaö molo'ö wamaigi moroi ba aljabar.</li> <li>Geometri aljabar, sambua gangolifa moroi ba geometri, ba wamaigi moroi meföna ba wotatugöi kurva faoma tete sitobali lala ba wangalui sinöndra wamagölösi persamaan polinomial.</li> <li>Kombinatorika aljabar, da'a sambua metode-metode aljabar ni'oguna'ö ba wamaigi fanofu kombinatorika.</li> <li>Aljabar relasional: sambua gangowuloa moroi ba relasi berhingga sitolumö barö zisambua operator.</li></ul> Oya wenaeta matematika nifotöi aljabar: <ul><li>Aljabar atas medan mazui töra simane aljabar di atas gelanggang. Oya nahia ba aljabar ba dete danölafa mazui yaŵa ba nahia sangokhögö töi nitatugoi (spesifik): <ul><li>Aljabar asosiatif</li> <li>Aljabar takasosiatif</li> <li>Aljabar Lie</li> <li>Aljabar Hopf</li> <li>Aljabar-C*</li> <li>Aljabar simetri</li> <li>Aljabar eksterior</li> <li>Aljabar tensor</li></ul></li> <li>Ba teori ukuran, <ul><li>Aljabar sigma</li> <li>Algebra ba dete Medan himpunan</li></ul></li> <li>Bakha ba teori kategori <ul><li>Aljabar-F faoma Koaljabar-F</li> <li>Aljabar-T</li></ul></li> <li>Bakha ba logika, <ul><li>Aljabar relasi, aljabar Boolean beresidu, ni'ebolo'ö faoma fa'abua nifotöi faoma konvers.</li> <li>Aljabar Boolean (struktur), kisi distributif faoma kisi komplemen na la'adogo'ö ia lamane komplemen.</li> <li>Aljabar Heyting</li></ul></li></ul> <div class="mw-heading mw-heading2"><h2 id="Aljabar_elementer">Aljabar elementer</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=8" title="Bulö’ö waosatö: Aljabar elementer" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=8" title="Sunting kode sumber bagian: Aljabar elementer">bulö’ö kode</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Algebraic_equation_notation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Algebraic_equation_notation.svg/220px-Algebraic_equation_notation.svg.png" decoding="async" width="220" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Algebraic_equation_notation.svg/330px-Algebraic_equation_notation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Algebraic_equation_notation.svg/440px-Algebraic_equation_notation.svg.png 2x" data-file-width="883" data-file-height="516" /></a><figcaption>Notasi ekspresi aljabar:   1 – pangkat (power)   2 – koefisien   3 – suku (term)   4 – operator   5 – suku konstanta   x y c – variabel/konstanta</figcaption></figure> Aljabar elementer ya'ia da'ö angolifa aljabar nibali'ö dane-dane. Aljabar elementer nifahaö ba ndraono sekola ma siswa/mahasiswa nifaigi walö hadöi fangi'ila ba zifakhai ba matematika, ba hiza töra ma'ifu moroi ba nifaehagö si sabata, hiza tobali ia dane-dane ba wangi'ila ngawalö zedöna latema wamahaö matematika ya'ia da'ö dane-dane moroi ba aritmetika. Bakha ba aritmetika, ha bilangan faoma operasi aritmetika (simane; +, −, ×, ÷) ni'ila niha. Bakha ba aljabar, numero asese lasura ia faoma famaedo, nitötöi faoma fanguma'ö variabel (matematika) (simane; a, n, x, y, mazui z). Da'a moguna, börö me: <ul><li>Tetehegö ba wame'e lala nitörö moroi ba zi no latatugöi ba hukum-hukum aritmetika (simane; a + b = b + a ero-ero; a faoma b), ba hiza da'a no sambua bosi si'oföna numalö ba wangi'ila ma eksplorasi sistematis ba dandra-tandra numero sistem bilangan real.</li> <li>Tetehegö hezo lahalö ia gumbu zifakhai ba numero "anu", fame'e lala ma perumusan ba wamagölösi ma persamaan faoma ba wangalui sinöndra. (Simane duma-dumania, "Carilah bilangan x irege 3x + 1 = 10" ma na tatohugö ia; "Carilah bilangan x irege tobalia ia; ax + b = c". Bosi da'a numalö ba wurugö wa tenga dandra-tandra moroi ba zisambua numero zi tola mu'alui zinöndrania, hiza moroi ba operasi nilataeni khönia.</li> <li>Tetehegö ba wangalui wamosinöndra zifakhai ba fungsi (matematika). (Simane duma-dumania, "Na ö amawa x karcis, wa hare nisöndrau ya'ia da'ö fa'ebuania; 3x − 10 rupiah, mazui f(x) = 3x − 10, na tafaigi wa; f sambua fungsi, faoma x ya'ia da'ö ni'erai ba fungsi nilaeteni khönia.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Polinomial">Polinomial</h3>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=9" title="Bulö’ö waosatö: Polinomial" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=9" title="Sunting kode sumber bagian: Polinomial">bulö’ö kode</a>]</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Polynomialdeg3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polynomialdeg3.svg/220px-Polynomialdeg3.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polynomialdeg3.svg/330px-Polynomialdeg3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Polynomialdeg3.svg/440px-Polynomialdeg3.svg.png 2x" data-file-width="400" data-file-height="400" /></a><figcaption><a href="/w/index.php?title=Grafik_fungsi&action=edit&redlink=1" class="new" title="Grafik fungsi (lö tesöndra zura andrö)">Grafik</a> fungsi polinomial berderajat 3.</figcaption></figure> Polinomial ma asese latötöi faoma fehede; suku banyak ya'ia da'ö sambua ekspresi (matematika) fa'oya ni'erai sitola ni'erai moroi ba suku (logika) ma suku-suku sitenga nol (tak-nol), ero-ero suku so khönia wokali nilai konstanta faoma wa'oya zitola ni'erai variabel (matematika) nifa'aso faoma fefu pangkat bilangan. Duma-dumania; x2 + 2x − 3 ya'ia da'ö; polinomial bakha ba variabel tunggal x. Sambua ekspresi polinomial ya'ia da'ö; ekspresi sitola lafomendrua wanura ya'ia sitobali polinomial, sangoguna'ö sifat-sifat komutativitas, asosiativitas, faoma distributivitas famonönö faoma fokalikö. Simane duma-dumania;, (x − 1)(x + 3) da'a no sambua ekspresi polinomial. Sambua fungsi polinomial tola göi lamane fungsi nifo'eluaha polinomial, mazui, molo'ö ekivalen, moroi ba zi sambua ekspresi polinomial. Dombua duma-duma da'ö yaŵa mamaehagö fungsi polinomial sifagölö. Dombua wanofu soguna sibai ba faoma fakhai bakha ba aljabar ya'ia da'ö; faktorisasi polinomial, famotokhi ya'ia simane ya'ia da'ö; mamaehagö polinomial sitobali fokali moroi ba polinomial-polinomial tanöbö'ö si tebai lagoligö sa'ae ma tebai nibagi, ba komputasi ma (faktor persekutuan terbesar polinomial). Duma-duma polinomial da'ö yaŵa sitola ni goligö sitobali; (x − 1)(x + 3). Sambua wenaeta wanofu sifakhai ya'ia da'ö ba wangalui ekspresi aljabar ba wamosinöndra akar fungsi zi sambua polinomial bakha ba variabel si mosindro samösa. <div class="mw-heading mw-heading3"><h3 id="Famahaö_(Pendidikan)">Famahaö (Pendidikan)</h3>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=10" title="Bulö’ö waosatö: Famahaö (Pendidikan)" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=10" title="Sunting kode sumber bagian: Famahaö (Pendidikan)">bulö’ö kode</a>]</div> No lafaehagö wa aljabar elementer andre ena'ö sambua lala wamahaö ba ndraono sekola si no irugi 11 fakhe,<a href="#cite_note-26">[26]</a> heŵa'ae ba gafuriata andre so ma'ifu wa'atedou ba wamahaö aljabar elementer ba ndraono <a href="/w/index.php?title=SMP&action=edit&redlink=1" class="new" title="SMP (lö tesöndra zura andrö)">SMP</a> ma sodadao ba kalasi 1 <a href="/w/index.php?title=SMP&action=edit&redlink=1" class="new" title="SMP (lö tesöndra zura andrö)">SMP</a> (≈ 13 tahun ±) di Amerika Serikat.<a href="#cite_note-27">[27]</a> Heŵa'ae simanö, ba zekola si so ba <a href="/wiki/Amerika_Serikat" title="Amerika Serikat">Amerika Serikat</a>, aljabar no lafahaö ba kalasi 3 SMP. I'otarai me döfi si 1997, Institut Politeknik faoma Universitas Negeri Virginia ba <a href="/wiki/Universitas" title="Universitas">universitas</a> tanöbö'ö, no labörötaigö mangoguna'ö sambua lala wamahaö aljabar si no laföfögö ba wame'e fa'aboto ba dödö ba nifahaö moroi ba no lahaogö peranti lunak komputer ba wangahatö lala wangi'ila ba aljabar, ena'ö lö oya tetibo ginötö faoma soguna tanöbö'ö sangoguna'ö kefe.<a href="#cite_note-28">[28]</a> <div class="mw-heading mw-heading2"><h2 id="Aljabar_abstrak">Aljabar abstrak</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=11" title="Bulö’ö waosatö: Aljabar abstrak" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=11" title="Sunting kode sumber bagian: Aljabar abstrak">bulö’ö kode</a>]</div> Aljabar abstrak mangebolo'ö ngawalö zifakhai ba aljabar elementer faoma <a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a> bilangan numalö ba mbosi-bosi sito'ölö la'oguna'ö. Ba da'a tou so mbosi-bosi ma lala nitörö bakha ba aljabar abstrak. Himpunan Matematika: tenga ha sito'ölö töra ma'ifu wangasiwaisi ngawalö wanofu sifakhai ba wangeraisi sifabö'ö-bö'ö, aljabar abstrak fakhai ba gangorudua ma nibe'e fanötöi ; himpunan na lafo'eluaha ia ya'ia da'ö; angorudua si so amakhaita ba wangerai si tola ni'orudugö. Fefu gangorudua da'a latötöi faoma himpunan. Duma-duma simane; Matriks (matematika) dua-kali-dua(2x2), angorudua polinomial nibe'e faka 2 ma (berderajat 2 (ax2 + bx + c), angorudua Vektor (spasial) dua dimensi ba zisambua nahia, ba tanöbö'ö soya sibai simane grup siklis, sifao bakha ba aritmetika modular ma modulo bilangan bulat n. Teori himpunan andre ya'ia da'ö sambua gangolifa moroi ba logika ba molo'ö lala wangalui sinöndrania ya'ia da'ö tenga fenaeta moroi ba aljabar. Operasi biner: amozua wamonönö ma perjumlahan (+) la abstraksi ia ba wame'e sambua khönia operasi biner, Tola lamane ∗amozua moroi ba operasi biner lö gunania na lö hadöi nahia gangorudua lala wangerai sedöna lafalua. Ba zi dombua elemen moroi ba a faoma b bakha ba gangorudua S, a ∗ b ya'ia da'ö elemen tanöbö'ö bakha ba ni'orudugö; fangerai da'a latötöi ia fa'ateduhö matematika ma ba <a href="/wiki/Li_Indonesia" title="Li Indonesia">li Indonesia</a> sasese latötöi ba matematika lamane; ketertutupan (matematika). Famonönö (+), Fangeheta (−), Fokali (×), faoma Fombagi (÷) tola tobali operasi biner na tefaehagö ia ba gangorudua zifabö'ö, duma-dumania famonönö faoma fokali matriks, vektor, faoma polinomial. Elemen identitas, ya'ia da'ö: Numero nol faoma sambua ni abstraksi ba wamo'eluaha zisambua elemen identitas ba zisambua fangerai. Nol no sambua elemen identitas ba wamonönö ba sambua ia göi ba wokali. Ba operator biner si no oi la'ila niha sato misa ∗ elemen identitas e lötolalö'ö ena'ö so khönia; a ∗ e = a faoma e ∗ a = a, ba mangerai samösa ia, na so ni'erai khönia. Da'a te'oguna'ö ia ba wamonönö sitobali; a + 0 = a faoma 0 + a = a ba simanö göi ba wokali; a × 1 = a faoma 1 × a = a. Lö fefu gangorudua faoma fangerai sifabö'ö-bö'ö oi so elemen identitas; simane, angorudua bilangan asli positif (1, 2, 3, ...) lö hadöi khönia elemen identitas ba wamonönö. Elemen invers mazui unsur balikan, ya'ia da'ö; Bilangan negatif samaehagö lala wangerai; elemen invers. Ba wamonönö, invers a lasura ia faoma −a; na ba wokali lasura ia faoma a−1. Elemen invers te'oguna'ö ba zidombua lala wangerai a−1 asala so khönia zikhala wa a ∗ a−1 = e faoma a−1 ∗ a = e, hiza i e no sambua elemen identitas. Sifat asosiatif maAsosiativitasla fo'eluaha ia: famonönö bilangan bulat sangokhögö sikhala nifotöi asosiativitas. Ya'ia da'ö, famöfögö bilangan na la fonönö ia lö tebulö zinöndrania. Simane duma-dumania: (2 + 3) + 4 = 2 + (3 + 4). Na sito'ölönia, da'a tobali; (a ∗ b) ∗ c = a ∗ (b ∗ c). Sikhala wangerai da'a tefalua göi ia ba lala wangerai operasi biner, hiza i tenga ba wangerai fangeheta, fombagi, mazuo fokali oktonion. Sifat komutatif, ya'ia da'ö; Famonönö faoma fokali bilangan real sifagölö sangokhögö sikhala komutatif. Ya'ia da'ö, fenaera numero ni'erai si lö mamulö'ö zinöndra moroi ba wangerai ya'ia. Duma-dumania; 2 + 3 = 3 + 2. Molo'ö fangerai sito'ölö, tola la'erai ia; a ∗ b = b ∗ a. Sikhala da'a lö la'oguna'ö ia ba wangerai operasi biner. Simane, fokali matriks faoma fokali kuaternion, börö me dombua wangerai da'a tenga angolifa zikhala wangerai komutatif. <div class="mw-heading mw-heading3"><h3 id="Angorudua_(Grup)">Angorudua (Grup)</h3>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=12" title="Bulö’ö waosatö: Angorudua (Grup)" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=12" title="Sunting kode sumber bagian: Angorudua (Grup)">bulö’ö kode</a>]</div> Fangorudugö lala wangerai da'ö yaŵa mame'e fangi'ila hewisa ia wenaeta soguna sibai bakha ba matematika ma abölö enahöi lamane ba; Grup (matematika). Nifotöi Grup ba da'a ya'ia da'ö; famaruka sambua angorudua S ba sambua lala wangerai operasi biner ∗, lafo'eluaha ia bakha ba lala wangerai nifili, hiza böi fasala molo'ö lala simane ba da'a tou; <ul><li>So sambua khönia elemen identitas e, irege ero sambua ni'erai khönia simane; a moroi ba S, e ∗ a faoma a ∗ e dombua lala da'a fagölö ira; a.</li> <li>Ero-ero elemen sokhönia invers: ero ngawua; a moroi ba S, sokhönia ngawua a−1 irege a ∗ a−1 faoma a−1 ∗ a da'a fagölö ira elemen identitas.</li> <li>Lala wangerai sikhala asosiatif: Na a, b, faoma c angolifa moroi ba S, hiza (a ∗ b) ∗ c fagölö ira a ∗ (b ∗ c).</li></ul> Na'atö angorudua da'a komutatif, ya'ia da'ö ero dombua gangolifania a faoma b moroi ba S, a ∗ b fagölö ira b ∗ a—ba hiza angorudua da'a tola latötöi ia faoma fanötöi grup abelian. Sitobali duma-duma, angorudua moroi ba bilangan bulat barö wangerai famonönö no sambua angorudua ma grup. Ba gangorudua da'a, elemen identitas ya'ia da'ö; 0 ba hiza invers moroi ba elemen, a ya'ia da'ö negasi, −a. Si lötolalö'ö te'a'asogö ba wangerai asosiativitas, me ero bilangan bulat, a, b, faoma c, (a + b) + c = a + (b + c) 'Bilangan rasional sitenga Nol tehaogö khönia gangorudua ma grup barö wangerai fokali. Ba da'a, elemen identitas ya'ia da'ö 1, me 1 × a = a × 1 = a ero bilangan rasional a. Invers moroi ba a ya'ia da'ö 1/a, börö me a × 1/a = 1. Heŵa'ae simanö, bilangan bulat barö wangerai fokali lö tehaogö khönia gangorudua ma grup. Da'a börö me invers fokali bilangan bulat lö mamosinöndra tobali bilangan bulat. Simane duma-duma, 4 no ta'ila wa sambua bilangan bulat, hiza i invers fokali ya'ia, ya'ia da'ö; ¼, ba no tefa'ele'ö wa tenga bilangan bulat. Lala wangerai sifakhai ba gangorudua nitötöi faoma fehede grup ba wamahaö andre, no mozawili misa wamahaö ya'ia si no oi la'ila niha ya'ia da'ö; teori grup. Nisöndra moroi ba wamahö andre ya'ia da'ö hewisa ba wama'oli gangorudua-gangorudua wangerai ma fanötöi ba li matematika klasifikasi grup-grup sederhana berhingga, hiza abölö ebua nifatumbu'ö ba gotalua ndröfi 1955 faoma döfi si 1983, samöfögö grup sederhana, himpunan berhingga tobali ba zi 30 ngawalö dane-dane wamahaö. Semigrup, kuasigrup, faoma monoid ya'ia da'ö fenaeta-fenaeta sifagölö ira grup, hiza i sikhalania sifagölötö ba danö bö'ö. No lahaogö sambua gangorudua faoma sambua wangerai operasi biner si tekusi, ha ya'i lö moguna sibai so khönia goi-goi nihonogöi. Semigrup so khönia operasi biner simane; asosiatif, ba lö hadöi elemen identitas. Na Monoid ya'ia da'ö semigrup sangokhögö elemen identitas, ba lö hadöi khönia invers ero-ero elemen. Fabö'ö ira na Kuasigrup, so zi lötolalö'ö tefa'aso khönia me gofu hadia manö elemen tola tefangamöi tobali elemen tanöbö'ö moroi ba wokali kabera ma zui kambölö; ha ya'i operasi binernia tola manö lö khönia sikhala asosiatif. Fefu gangorudua ma grup tola lamane fao ba monoid, ba fefu monoid ya'ia da'ö; semigrup. <table class="wikitable"> <caption>D u m a - D u m a </caption> <tbody><tr> <th>Himpunan </th> <td colspan="2"><a href="/w/index.php?title=Bilangan_asli&action=edit&redlink=1" class="new" title="Bilangan asli (lö tesöndra zura andrö)">Bilangan asli</a> N </td> <td colspan="2"><a href="/w/index.php?title=Bilangan_bulat&action=edit&redlink=1" class="new" title="Bilangan bulat (lö tesöndra zura andrö)">Bilangan bulat</a> Z </td> <td colspan="4"><a href="/w/index.php?title=Bilangan_rasional&action=edit&redlink=1" class="new" title="Bilangan rasional (lö tesöndra zura andrö)">Bilangan rasional</a> Q (juga <a href="/w/index.php?title=Bilangan_real&action=edit&redlink=1" class="new" title="Bilangan real (lö tesöndra zura andrö)">Bilangan real</a> R faoma <a href="/w/index.php?title=Bilangan_kompleks&action=edit&redlink=1" class="new" title="Bilangan kompleks (lö tesöndra zura andrö)">kompleks</a> C) </td> <td colspan="2"><a href="/w/index.php?title=Aritmetika_modular&action=edit&redlink=1" class="new" title="Aritmetika modular (lö tesöndra zura andrö)">Modulo</a> bilangan bulat 3: Z3 = {0, 1, 2} </td></tr> <tr> <th>Operasi </th> <td>+ </td> <td>× (tak-nol) </td> <td>+ </td> <td>× (tak-nol) </td> <td>+ </td> <td>− </td> <td>× (tak-nol) </td> <td>÷ (tak-nol) </td> <td>+ </td> <td>× (tak-nol) </td></tr> <tr> <th>Tertutup </th> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td></tr> <tr> <td>Identitas </td> <td>0 </td> <td>1 </td> <td>0 </td> <td>1 </td> <td>0 </td> <td>Lö hadöi </td> <td>1 </td> <td>Lö hadöi </td> <td>0 </td> <td>1 </td></tr> <tr> <td>Invers </td> <td>Lö hadöi </td> <td>Lö hadöi </td> <td>−a </td> <td>Lö hadöi </td> <td>−a </td> <td>Lö hadöi </td> <td>1/a </td> <td>Lö hadöi </td> <td>ero-ero: 0, 2, 1 </td> <td>ero-ero: Lö hadöi, 1, 2 </td></tr> <tr> <td>Asosiatif </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Lö'ö </td> <td>Ya </td> <td>Lö'ö </td> <td>Ya </td> <td>Ya </td></tr> <tr> <td>Komutatif </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Ya </td> <td>Lö'ö </td> <td>Ya </td> <td>Lö'ö </td> <td>Ya </td> <td>Ya </td></tr> <tr> <td>Struktur </td> <td><a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (lö tesöndra zura andrö)">monoid</a> </td> <td><a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (lö tesöndra zura andrö)">monoid</a> </td> <td><a href="/w/index.php?title=Grup_abelian&action=edit&redlink=1" class="new" title="Grup abelian (lö tesöndra zura andrö)">grup abelian</a> </td> <td><a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (lö tesöndra zura andrö)">monoid</a> </td> <td><a href="/w/index.php?title=Grup_abelian&action=edit&redlink=1" class="new" title="Grup abelian (lö tesöndra zura andrö)">grup abelian</a> </td> <td><a href="/w/index.php?title=Kuasigrup&action=edit&redlink=1" class="new" title="Kuasigrup (lö tesöndra zura andrö)">kuasigrup</a> </td> <td><a href="/w/index.php?title=Grup_abelian&action=edit&redlink=1" class="new" title="Grup abelian (lö tesöndra zura andrö)">grup abelian</a> </td> <td><a href="/w/index.php?title=Kuasigrup&action=edit&redlink=1" class="new" title="Kuasigrup (lö tesöndra zura andrö)">kuasigrup</a> </td> <td><a href="/w/index.php?title=Grup_abelian&action=edit&redlink=1" class="new" title="Grup abelian (lö tesöndra zura andrö)">grup abelian</a> </td> <td><a href="/w/index.php?title=Grup_abelian&action=edit&redlink=1" class="new" title="Grup abelian (lö tesöndra zura andrö)">grup abelian</a> (Z2) </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Gelanggang_faoma_Lapangan">Gelanggang faoma Lapangan</h3>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=13" title="Bulö’ö waosatö: Gelanggang faoma Lapangan" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=13" title="Sunting kode sumber bagian: Gelanggang faoma Lapangan">bulö’ö kode</a>]</div> Grup ha sambua khönia operasi biner. Famaehagö ngawalö lala wangerai sifabö'ö-bö'ö, fangerai si so fenaeta dombua lala wangerai lötolalö'ö lafanöi lala wangi'ila ba wamahaö aljabar andre. Sabölö moguna ya'ia da'ö ba wangi'ila hadia ia nifotöi Gelanggang (matematika), faoma Medan(matematika). Sambua Gelanggang(matematika) so dombua khönia Operasi biner ya'ia da'ö; (+) faoma (×), simanö göi × distributif ba dete wamonönö (+). Fangerai si'oföna ya'ia da'ö (+), te faehagö khönia grup abelian. Fangerai aefa da'ö, fokali (×), sikhalania ya'ia sa'ae nifotöi asosiatif, ha ya'i lö khönia identitas mazui invers, irege lö moguna la bologö ero fenaeta. Elemen identitas wamonönö (+) lasura ia faoma numero; 0 ba invers famonönö moroi ba a lasura ia faoma; −a. Böi olifu wa lala wangerai da'a tola lamane fangerai si abstrak, fefu zedöna la faehagö. 'Distributif ma sikhala moroi ba distributif la'osara'ö ba zito'ölö la'erai niha ya'ia da'ö; hukum distributif fangerai numero. Na ba bilangan bulat (a + b) × c = a × c + b × c faoma c × (a + b) = c × a + c × b, faoma × latötöi ia; distributif ba dete +. Bilangan bulat sambua duma-duma moroi ba nifotöi gelanggang. Bilangan bulat sikhalania so khönia wamonönö solohe ya'ia tobali domain integral, ma lamane; daerah bilangan bulat, mazui ranah bilangan bulat,. Sambua medan (matematika) ma lapangan] ya'ia da'ö; gelanggang sikhala wamonönö wa fefu elemen tak-nol mamaehagö grup abelian barö ×. Sikhala wokali (×) lasura faoma numero 1 ba invers wokali moroi ba a lasura faoma a−1. Bilangan rasional, bilangan real, faoma bilangan kompleks sambua duma-duma moroi ba lapangan. <div class="mw-heading mw-heading2"><h2 id="Umbu">Umbu</h2>[<a href="/w/index.php?title=Aljabar&veaction=edit&section=14" title="Bulö’ö waosatö: Umbu" class="mw-editsection-visualeditor">bulö'ö</a> | <a href="/w/index.php?title=Aljabar&action=edit&section=14" title="Sunting kode sumber bagian: Umbu">bulö’ö kode</a>]</div> <ol class="references"> <li id="cite_note-oed-1"><a href="#cite_ref-oed_1-0">↑</a> <cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131231173558/http://www.oxforddictionaries.com/us/definition/english/algebra">"algebra"</a>. Oxford English Dictionary. Oxford University Press. Arsip moroi <a rel="nofollow" class="external text" href="http://www.oxforddictionaries.com/us/definition/english/algebra">versi asli</a> irugi 2013-12-31. Mufaigi me 2017-02-21.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Oxford+English+Dictionary&rft.atitle=algebra&rft_id=http%3A%2F%2Fwww.oxforddictionaries.com%2Fus%2Fdefinition%2Fenglish%2Falgebra&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> I. N. Herstein, Topics in Algebra, "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964 </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> I. N. Herstein, Topics in Algebra, "...it also serves as the unifying thread which interlaces almost all of mathematics." p. 1, Ginn and Company, 1964 </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> Ekkehard Kopp "<a rel="nofollow" class="external text" href="https://www.openbookpublishers.com/product/1279">Making up Numbers : A History of Invention in Mathematics</a>" Open Book Publishers </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <cite class="citation book">Gattengo, Caleb (2010). The Common Sense of Teaching Mathematics. Educational Solutions Inc. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/978-0878252206" title="Spesial:Sumber buku/978-0878252206">978-0878252206</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Common+Sense+of+Teaching+Mathematics&rft.pub=Educational+Solutions+Inc.&rft.date=2010&rft.isbn=978-0878252206&rft.aulast=Gattengo&rft.aufirst=Caleb&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-6"><a href="#cite_ref-6">↑</a> <cite class="citation web"><a rel="nofollow" class="external text" href="http://www.ams.org/mathscinet/msc/msc2010.html">"2010 Mathematics Subject Classification"</a>. Mufaigi me 2014-10-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=2010+Mathematics+Subject+Classification&rft_id=http%3A%2F%2Fwww.ams.org%2Fmathscinet%2Fmsc%2Fmsc2010.html&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-7"><a href="#cite_ref-7">↑</a> <cite class="citation book">Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/0-486-60255-9" title="Spesial:Sumber buku/0-486-60255-9">0-486-60255-9</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Concise+History+of+Mathematics&rft.place=New+York&rft.pub=Dover+Publications&rft.date=1987&rft.isbn=0-486-60255-9&rft.aulast=Struik&rft.aufirst=Dirk+J.&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-8"><a href="#cite_ref-8">↑</a> (<a href="#CITEREFBoyer1991">Boyer 1991</a>) </li> <li id="cite_note-citeboyer-9"><a href="#cite_ref-citeboyer_9-0">↑</a> <a href="/w/index.php?title=Templat:Harv&action=edit&redlink=1" class="new" title="Templat:Harv (lö tesöndra zura andrö)">Templat:Harv</a> "In the arithmetical theorems in Euclid's Elements VII-IX, numbers had been represented by line segments to which letters had been attached, and the geometric proofs in al-Khwarizmi's Algebra made use of lettered diagrams; but all coefficients in the equations used in the Algebra are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry." </li> <li id="cite_note-10"><a href="#cite_ref-10">↑</a> <cite class="citation book"><a href="/w/index.php?title=Florian_Cajori&action=edit&redlink=1" class="new" title="Florian Cajori (lö tesöndra zura andrö)">Cajori, Florian</a> (2010). <a rel="nofollow" class="external text" href="https://books.google.com/?id=gZ2Us3F7dSwC&pg=PA34&dq#v=onepage&q=&f=false">A History of Elementary Mathematics – With Hints on Methods of Teaching</a>. hlm. 34. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/1-4460-2221-8" title="Spesial:Sumber buku/1-4460-2221-8">1-4460-2221-8</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Elementary+Mathematics+%E2%80%93+With+Hints+on+Methods+of+Teaching&rft.pages=34&rft.date=2010&rft.isbn=1-4460-2221-8&rft.aulast=Cajori&rft.aufirst=Florian&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3DgZ2Us3F7dSwC%26pg%3DPA34%26dq%23v%3Donepage%26q%3D%26f%3Dfalse&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-11"><a href="#cite_ref-11">↑</a> <cite id="CITEREFRoshdi_Rashed2009" class="citation journal">Roshdi Rashed (November 2009). "Al Khwarizmi: The Beginnings of Algebra". Saqi Books. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/0-86356-430-5" title="Spesial:Sumber buku/0-86356-430-5">0-86356-430-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Al+Khwarizmi%3A+The+Beginnings+of+Algebra&rft.date=2009-11&rft.isbn=0-86356-430-5&rft.au=Roshdi+Rashed&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-12"><a href="#cite_ref-12">↑</a> <cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130727040815/http://library.thinkquest.org/25672/diiophan.htm">"Diophantus, Father of Algebra"</a>. Arsip moroi <a rel="nofollow" class="external text" href="http://library.thinkquest.org/25672/diiophan.htm">versi asli</a> irugi 2013-07-27. Mufaigi me 2014-10-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Diophantus%2C+Father+of+Algebra&rft_id=http%3A%2F%2Flibrary.thinkquest.org%2F25672%2Fdiiophan.htm&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-13"><a href="#cite_ref-13">↑</a> <cite class="citation web"><a rel="nofollow" class="external text" href="http://www.algebra.com/algebra/about/history/">"History of Algebra"</a>. Mufaigi me 2014-10-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=History+of+Algebra&rft_id=http%3A%2F%2Fwww.algebra.com%2Falgebra%2Fabout%2Fhistory%2F&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-Meri2004-14"><a href="#cite_ref-Meri2004_14-0">↑</a> <cite class="citation book">Josef W. Meri (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=H-k9oc9xsuAC&pg=PA31">Medieval Islamic Civilization</a>. Psychology Press. hlm. 31. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/978-0-415-96690-0" title="Spesial:Sumber buku/978-0-415-96690-0">978-0-415-96690-0</a>. Mufaigi me 25 November 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Medieval+Islamic+Civilization&rft.pages=31&rft.pub=Psychology+Press&rft.date=2004&rft.isbn=978-0-415-96690-0&rft.au=Josef+W.+Meri&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DH-k9oc9xsuAC%26pg%3DPA31&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-15"><a href="#cite_ref-15">↑</a> <cite class="citation book">Boyer, Carl B. (1991). <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328">A History of Mathematics</a> (edisi ke-Second). Wiley. hlm. <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328/page/n197">178</a>, 181. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/0-471-54397-7" title="Spesial:Sumber buku/0-471-54397-7">0-471-54397-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Mathematics&rft.pages=178%2C+181&rft.edition=Second&rft.pub=Wiley&rft.date=1991&rft.isbn=0-471-54397-7&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistorymathemati00boye_328&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-16"><a href="#cite_ref-16">↑</a> <cite class="citation book">Boyer, Carl B. (1991). <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328">A History of Mathematics</a> (edisi ke-Second). Wiley. hlm. <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328/page/n247">228</a>. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/0-471-54397-7" title="Spesial:Sumber buku/0-471-54397-7">0-471-54397-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Mathematics&rft.pages=228&rft.edition=Second&rft.pub=Wiley&rft.date=1991&rft.isbn=0-471-54397-7&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistorymathemati00boye_328&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-Boyer-229-17"><a href="#cite_ref-Boyer-229_17-0">↑</a> <a href="/w/index.php?title=Templat:Harv&action=edit&redlink=1" class="new" title="Templat:Harv (lö tesöndra zura andrö)">Templat:Harv</a> "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation." </li> <li id="cite_note-18"><a href="#cite_ref-18">↑</a> <a href="/w/index.php?title=Templat:Harv&action=edit&redlink=1" class="new" title="Templat:Harv (lö tesöndra zura andrö)">Templat:Harv</a> "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions." </li> <li id="cite_note-19"><a href="#cite_ref-19">↑</a> Gandz and Saloman (1936), The sources of al-Khwarizmi's algebra, Osiris i, p. 263–277: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers". </li> <li id="cite_note-Rashed-Armstrong-20"><a href="#cite_ref-Rashed-Armstrong_20-0">↑</a> <cite id="CITEREFRashedArmstrong1994" class="citation book">Rashed, R.; Armstrong, Angela (1994). The Development of Arabic Mathematics. <a href="/w/index.php?title=Springer_Science%2BBusiness_Media&action=edit&redlink=1" class="new" title="Springer Science+Business Media (lö tesöndra zura andrö)">Springer</a>. hlm. 11–2. <a href="/w/index.php?title=International_Standard_Book_Number&action=edit&redlink=1" class="new" title="International Standard Book Number (lö tesöndra zura andrö)">ISBN</a> <a href="/wiki/Spesial:Sumber_buku/0-7923-2565-6" title="Spesial:Sumber buku/0-7923-2565-6">0-7923-2565-6</a>. <a href="/w/index.php?title=OCLC&action=edit&redlink=1" class="new" title="OCLC (lö tesöndra zura andrö)">OCLC</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/oclc/29181926">29181926</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Development+of+Arabic+Mathematics&rft.pages=11-2&rft.pub=Springer&rft.date=1994&rft_id=info%3Aoclcnum%2F29181926&rft.isbn=0-7923-2565-6&rft.aulast=Rashed&rft.aufirst=R.&rft.au=Armstrong%2C+Angela&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-21"><a href="#cite_ref-21">↑</a> <a href="#refmathmaster">Mathematical Masterpieces: Further Chronicles by the Explorers</a>, p. 92 </li> <li id="cite_note-22"><a href="#cite_ref-22">↑</a> <a href="/w/index.php?title=Templat:MacTutor&action=edit&redlink=1" class="new" title="Templat:MacTutor (lö tesöndra zura andrö)">Templat:MacTutor</a> </li> <li id="cite_note-23"><a href="#cite_ref-23">↑</a> <cite id="CITEREFVictor_J._KatzBarton2007" class="citation journal">Victor J. Katz, Bill Barton; Barton, Bill (October 2007). "Stages in the History of Algebra with Implications for Teaching". Educational Studies in Mathematics. <a href="/w/index.php?title=Springer_Science%2BBusiness_Media&action=edit&redlink=1" class="new" title="Springer Science+Business Media (lö tesöndra zura andrö)">Springer Netherlands</a>. 66 (2): 185–201 [192]. <a href="/w/index.php?title=Digital_object_identifier&action=edit&redlink=1" class="new" title="Digital object identifier (lö tesöndra zura andrö)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10649-006-9023-7">10.1007/s10649-006-9023-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Educational+Studies+in+Mathematics&rft.atitle=Stages+in+the+History+of+Algebra+with+Implications+for+Teaching&rft.volume=66&rft.issue=2&rft.pages=185-201+192&rft.date=2007-10&rft_id=info%3Adoi%2F10.1007%2Fs10649-006-9023-7&rft.aulast=Victor+J.+Katz&rft.aufirst=Bill+Barton&rft.au=Barton%2C+Bill&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-Boyer_al-Karkhi_ax2n-24"><a href="#cite_ref-Boyer_al-Karkhi_ax2n_24-0">↑</a> <a href="/w/index.php?title=Templat:Harv&action=edit&redlink=1" class="new" title="Templat:Harv (lö tesöndra zura andrö)">Templat:Harv</a> "Abu'l Wefa was a capable algebraist as well as a trigonometer. ... His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus – but without Diophantine analysis! ... In particular, to al-Karkhi is attributed the first numerical solution of equations of the form ax2n + bxn = c (only equations with positive roots were considered)," </li> <li id="cite_note-25"><a href="#cite_ref-25">↑</a> <cite class="citation web"><a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Qalasadi.html">"Al-Qalasadi biography"</a>. www-history.mcs.st-andrews.ac.uk. Mufaigi me 2017-10-17.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www-history.mcs.st-andrews.ac.uk&rft.atitle=Al-Qalasadi+biography&rft_id=http%3A%2F%2Fwww-history.mcs.st-andrews.ac.uk%2FBiographies%2FAl-Qalasadi.html&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-26"><a href="#cite_ref-26">↑</a> <cite class="citation web"><a rel="nofollow" class="external text" href="https://query.nytimes.com/mem/archive-free/pdf?res=F10714FB395E12738DDDAF0994DF405B848CF1D3">"Hull's Algebra"</a> (<a href="/w/index.php?title=Pdf&action=edit&redlink=1" class="new" title="Pdf (lö tesöndra zura andrö)">pdf</a>). New York Times. 1904-07-16. Mufaigi me 2012-09-21.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=New+York+Times&rft.atitle=Hull%27s+Algebra&rft.date=1904-07-16&rft_id=https%3A%2F%2Fquery.nytimes.com%2Fmem%2Farchive-free%2Fpdf%3Fres%3DF10714FB395E12738DDDAF0994DF405B848CF1D3&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-27"><a href="#cite_ref-27">↑</a> <cite class="citation web">Quaid, Libby (2008-09-22). <a rel="nofollow" class="external text" href="https://www.usatoday.com/news/nation/2008-09-22-357650952_x.htm">"Kids misplaced in algebra"</a> (Report). <a href="/w/index.php?title=Associated_Press&action=edit&redlink=1" class="new" title="Associated Press (lö tesöndra zura andrö)">Associated Press</a>. Mufaigi me 2012-09-23.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Associated+Press&rft.atitle=Kids+misplaced+in+algebra&rft.date=2008-09-22&rft.aulast=Quaid&rft.aufirst=Libby&rft_id=https%3A%2F%2Fwww.usatoday.com%2Fnews%2Fnation%2F2008-09-22-357650952_x.htm&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> <li id="cite_note-28"><a href="#cite_ref-28">↑</a> <cite class="citation news">Hamilton, Reeve (2012-09-07). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2012/09/07/us/ut-arlington-adopts-new-way-to-tackle-algebra.html">"THE TEXAS TRIBUNE; U.T.-Arlington Adopts New Way to Tackle Algebra"</a>. The New York Times. Mufaigi me 2012-09-10.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=THE+TEXAS+TRIBUNE%3B+U.T.-Arlington+Adopts+New+Way+to+Tackle+Algebra&rft.date=2012-09-07&rft.aulast=Hamilton&rft.aufirst=Reeve&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2012%2F09%2F07%2Fus%2Fut-arlington-adopts-new-way-to-tackle-algebra.html&rfr_id=info%3Asid%2Fnia.wikipedia.org%3AAljabar" class="Z3988">  </li> </ol>    </div><noscript><img src="https://auth.wikimedia.org/loginwiki/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Tehalö moroi ba "<a dir="ltr" href="https://nia.wikipedia.org/w/index.php?title=Aljabar&oldid=24184">https://nia.wikipedia.org/w/index.php?title=Aljabar&oldid=24184</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Spesial:Daftar_kategori" title="Spesial:Daftar kategori">Kategori</a>: <ul><li><a href="/w/index.php?title=Kategori:Nga%27%C3%B6r%C3%B6_si_so_fanura_ba_li_Arab&action=edit&redlink=1" class="new" title="Kategori:Nga'örö si so fanura ba li Arab (lö tesöndra zura andrö)">Nga'örö si so fanura ba li Arab</a></li><li><a href="/wiki/Kategori:Nias" title="Kategori:Nias">Nias</a></li><li><a href="/w/index.php?title=Kategori:CS1:_Ketidakpastian_Julian%E2%80%93Gregorian&action=edit&redlink=1" class="new" title="Kategori:CS1: Ketidakpastian Julian–Gregorian (lö tesöndra zura andrö)">CS1: Ketidakpastian Julian–Gregorian</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"> Afuriata tebulö'ö nga'örö andre ba 15 September 2024, 16.55</li> <li id="footer-info-copyright">So nösi zura da'a ba <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a>; Tola manö wa so na sa gonönöta si lö tola lö'ö mu'o'ö. Bokai <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">Terms of Use</a> wamaigi wamotokhi ya'ia.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Amakhoita privasi</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:Sanandr%C3%B6sa">Sanandrösa Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Fanimbag%C3%B6">Fanimbagö</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Kode Etik</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Pengembang</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/nia.wikipedia.org">Statistik</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Sanandrösa ba kuki</a></li> <li id="footer-places-mobileview"><a href="//nia.m.wikipedia.org/w/index.php?title=Aljabar&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Famaigi ba hape</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"> Alui </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="Alui Wikipedia"> </div> <input type="hidden" name="title" value="Spesial:Pencarian"> </div> <button class="cdx-button cdx-search-input__end-button">Alui</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Ösi" 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="Gulingkan daftar isi" > <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" > Gulingkan daftar isi </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" >Aljabar</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"> </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"> </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"> </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"> </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"> </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"> </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"> </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"> 169 li </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"> Nönö mbörö huhuo </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-65bcbb4cf5-fm28m","wgBackendResponseTime":175,"wgPageParseReport":{"limitreport":{"cputime":"0.165","walltime":"0.304","ppvisitednodes":{"value":1034,"limit":1000000},"postexpandincludesize":{"value":25127,"limit":2097152},"templateargumentsize":{"value":164,"limit":2097152},"expansiondepth":{"value":8,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":4943,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 180.629 1 -total"," 28.62% 51.687 7 Templat:Cite_web"," 10.69% 19.315 7 Templat:Cite_book"," 10.51% 18.993 1 Templat:Harvnb"," 6.57% 11.865 1 Templat:Lang"," 5.61% 10.135 1 Templat:Cite_news"," 5.32% 9.614 3 Templat:Nowrap"," 4.43% 7.999 2 Templat:Cite_journal"," 1.81% 3.272 1 Templat:MacTutor"," 0.80% 1.450 4 Templat:Harv"]},"scribunto":{"limitreport-timeusage":{"value":"0.047","limit":"10.000"},"limitreport-memusage":{"value":2463252,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-86c59b8c7c-ktzlp","timestamp":"20250309052047","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Aljabar","url":"https:\/\/nia.wikipedia.org\/wiki\/Aljabar","sameAs":"http:\/\/www.wikidata.org\/entity\/Q3968","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q3968","author":{"@type":"Organization","name":"Kontributor dari proyek Wikimedia."},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2023-02-05T12:54:47Z","dateModified":"2024-09-15T09:55:51Z"}</script> </body> </html>