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aria-hidden="true" > ਨਿੱਜੀ ਸੰਦ </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_pa.wikipedia.org&uselang=pa">ਦਾਨ</a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:%E0%A8%96%E0%A8%BE%E0%A8%A4%E0%A8%BE_%E0%A8%AC%E0%A8%A3%E0%A8%BE%E0%A8%93&returnto=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2%3AMath" title="ਤੁਹਾਨੂੰ ਖ਼ਾਤਾ ਬਣਾਉਣ ਤੋਂ ਬਾਅਦ ਦਾਖ਼ਲ ਕਰਨ ਦੀ ਸਲਾਹ ਦਿੱਤੀ ਜਾਂਦੀ ਹੈ; ਹਾਲਾਂਕਿ ਇਹ ਲਾਜ਼ਮੀ ਨਹੀਂ"> ਖ਼ਾਤਾ ਬਣਾਓ</a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:%E0%A8%B5%E0%A8%B0%E0%A8%A4%E0%A9%8B%E0%A8%82%E0%A8%95%E0%A8%BE%E0%A8%B0_%E0%A8%B2%E0%A8%BE%E0%A8%97%E0%A8%87%E0%A8%A8&returnto=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2%3AMath" title="ਤੁਹਾਨੂੰ ਦਾਖ਼ਲ ਹੋਣ ਲਈ ਪ੍ਰੇਰਿਆ ਜਾਂਦਾ ਹੈ; ਪਰ ਇਹ ਕੋਈ ਲਾਜ਼ਮੀ ਨਹੀਂ [o]" accesskey="o"> ਦਾਖ਼ਲ ਹੋਵੋ</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"> ਬਾਹਰ ਹੋਏ ਸੰਪਾਦਕਾਂ ਲਈ ਸਫ਼ੇ <a href="/wiki/%E0%A8%AE%E0%A8%A6%E0%A8%A6:%E0%A8%9C%E0%A8%BE%E0%A8%A3-%E0%A8%AA%E0%A8%9B%E0%A8%BE%E0%A8%A3" aria-label="ਸੰਪਾਦਨ ਬਾਰੇ ਹੋਰ ਜਾਣੋ">ਹੋਰ ਜਾਣੋ</a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:%E0%A8%AE%E0%A9%87%E0%A8%B0%E0%A9%87_%E0%A8%AF%E0%A9%8B%E0%A8%97%E0%A8%A6%E0%A8%BE%E0%A8%A8" title="A list of edits made from this IP address [y]" accesskey="y">ਯੋਗਦਾਨ</a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:%E0%A8%AE%E0%A9%87%E0%A8%B0%E0%A9%80_%E0%A8%9A%E0%A8%B0%E0%A8%9A%E0%A8%BE" title="ਇਸ IP ਪਤੇ ਤੋਂ ਹੋਈਆਂ ਸੋਧਾਂ ਬਾਰੇ ਗੱਲਬਾਤ [n]" accesskey="n">ਗੱਲ-ਬਾਤ</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="ਸਾਈਟ"> <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="ਸਮੱਗਰੀ" 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">ਸਮੱਗਰੀ</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ਸਾਈਡਬਾਰ 'ਤੇ ਜਾਓ</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ਲੁਕਾਓ</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">ਸ਼ੁਰੂਆਤ</div> </a> </li> <li id="toc-Use_from_other_Lua_modules" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Use_from_other_Lua_modules"> <div class="vector-toc-text"> 1 Use from other Lua modules </div> </a> <ul id="toc-Use_from_other_Lua_modules-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-random" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#random"> <div class="vector-toc-text"> 2 random </div> </a> <ul id="toc-random-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-order" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#order"> <div class="vector-toc-text"> 3 order </div> </a> <ul id="toc-order-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-precision" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#precision"> <div class="vector-toc-text"> 4 precision </div> </a> <ul id="toc-precision-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-max" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#max"> <div class="vector-toc-text"> 5 max </div> </a> <ul id="toc-max-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-median" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#median"> <div class="vector-toc-text"> 6 median </div> </a> <ul id="toc-median-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-min" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#min"> <div class="vector-toc-text"> 7 min </div> </a> <ul id="toc-min-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-sum" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#sum"> <div class="vector-toc-text"> 8 sum </div> </a> <ul id="toc-sum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-average" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#average"> <div class="vector-toc-text"> 9 average </div> </a> <ul id="toc-average-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-round" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#round"> <div class="vector-toc-text"> 10 round </div> </a> <ul id="toc-round-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-log10" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#log10"> <div class="vector-toc-text"> 11 log10 </div> </a> <ul id="toc-log10-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-mod" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#mod"> <div class="vector-toc-text"> 12 mod </div> </a> <ul id="toc-mod-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-gcd" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#gcd"> <div class="vector-toc-text"> 13 gcd </div> </a> <ul id="toc-gcd-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-precision_format" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#precision_format"> <div class="vector-toc-text"> 14 precision_format </div> </a> <ul id="toc-precision_format-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-divide" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#divide"> <div class="vector-toc-text"> 15 divide </div> </a> <ul id="toc-divide-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-cleanNumber" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#cleanNumber"> <div class="vector-toc-text"> 16 cleanNumber </div> </a> <ul id="toc-cleanNumber-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 17 See also </div> </a> <ul id="toc-See_also-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="ਸਮੱਗਰੀ" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="ਸਮੱਗਰੀ ਦੀ ਸਾਰਣੀ ਨੂੰ ਟੌਗਲ ਕਰੋ" > <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" > ਸਮੱਗਰੀ ਦੀ ਸਾਰਣੀ ਨੂੰ ਟੌਗਲ ਕਰੋ </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">ਮੌਡਿਊਲ:Math</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="ਕਿਸੇ ਹੋਰ ਭਾਸ਼ਾ ਵਿੱਚ ਲੇਖ 'ਤੇ ਜਾਓ। 175 ਭਾਸ਼ਾਵਾਂ ਵਿੱਚ ਉਪਲਬਧ ਹੈ" > <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-175" aria-hidden="true" > 175 ਭਾਸ਼ਾਵਾਂ </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ab mw-list-item"><a href="https://ab.wikipedia.org/wiki/%D0%90%D0%BC%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Амодуль:Math – ਅਬਖਾਜ਼ੀਅਨ" lang="ab" hreflang="ab" data-title="Амодуль:Math" data-language-autonym="Аԥсшәа" data-language-local-name="ਅਬਖਾਜ਼ੀਅਨ" class="interlanguage-link-target">Аԥсшәа</a></li><li class="interlanguage-link interwiki-ace mw-list-item"><a href="https://ace.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਅਚੀਨੀ" lang="ace" hreflang="ace" data-title="Modul:Math" data-language-autonym="Acèh" data-language-local-name="ਅਚੀਨੀ" class="interlanguage-link-target">Acèh</a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Module:Math" title="Module:Math – ਅਫ਼ਰੀਕੀ" lang="af" hreflang="af" data-title="Module:Math" data-language-autonym="Afrikaans" data-language-local-name="ਅਫ਼ਰੀਕੀ" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-alt mw-list-item"><a href="https://alt.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਦੱਖਣੀ ਅਲਤਾਈ" lang="alt" hreflang="alt" data-title="Модуль:Math" data-language-autonym="Алтай тил" data-language-local-name="ਦੱਖਣੀ ਅਲਤਾਈ" class="interlanguage-link-target">Алтай тил</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – ਅਰਾਗੋਨੀ" lang="an" hreflang="an" data-title="Módulo:Math" data-language-autonym="Aragonés" data-language-local-name="ਅਰਾਗੋਨੀ" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/Module:Math" title="Module:Math – ਪੁਰਾਣੀ ਅੰਗਰੇਜ਼ੀ" lang="ang" hreflang="ang" data-title="Module:Math" data-language-autonym="Ænglisc" data-language-local-name="ਪੁਰਾਣੀ ਅੰਗਰੇਜ਼ੀ" class="interlanguage-link-target">Ænglisc</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%88%D8%AD%D8%AF%D8%A9:Math" title="وحدة:Math – ਅਰਬੀ" lang="ar" hreflang="ar" data-title="وحدة:Math" data-language-autonym="العربية" data-language-local-name="ਅਰਬੀ" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%85%D9%88%D8%AF%D9%88%D9%84:Math" title="مودول:Math – ਅਰਬੀ (ਮੋਰਾਕੋ)" lang="ary" hreflang="ary" data-title="مودول:Math" data-language-autonym="الدارجة" data-language-local-name="ਅਰਬੀ (ਮੋਰਾਕੋ)" class="interlanguage-link-target">الدارجة</a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%88%D8%AD%D8%AF%D8%A9:Math" title="وحدة:Math – ਅਰਬੀ (ਮਿਸਰੀ)" lang="arz" hreflang="arz" data-title="وحدة:Math" data-language-autonym="مصرى" data-language-local-name="ਅਰਬੀ (ਮਿਸਰੀ)" class="interlanguage-link-target">مصرى</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/Module:Math" title="Module:Math – ਅਸਾਮੀ" lang="as" hreflang="as" data-title="Module:Math" data-language-autonym="অসমীয়া" data-language-local-name="ਅਸਾਮੀ" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/M%C3%B3dulu:Math" title="Módulu:Math – ਅਸਤੂਰੀ" lang="ast" hreflang="ast" data-title="Módulu:Math" data-language-autonym="Asturianu" data-language-local-name="ਅਸਤੂਰੀ" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-av mw-list-item"><a href="https://av.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਅਵਾਰਿਕ" lang="av" hreflang="av" data-title="Модуль:Math" data-language-autonym="Авар" data-language-local-name="ਅਵਾਰਿਕ" class="interlanguage-link-target">Авар</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਅਜ਼ਰਬਾਈਜਾਨੀ" lang="az" hreflang="az" data-title="Modul:Math" data-language-autonym="Azərbaycanca" data-language-local-name="ਅਜ਼ਰਬਾਈਜਾਨੀ" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%DA%98%D9%88%D9%84:Math" title="ماژول:Math – ਦੱਖਣੀ ਅਜ਼ੇਰੀ" lang="azb" hreflang="azb" data-title="ماژول:Math" data-language-autonym="تۆرکجه" data-language-local-name="ਦੱਖਣੀ ਅਜ਼ੇਰੀ" class="interlanguage-link-target">تۆرکجه</a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਬਸ਼ਕੀਰ" lang="ba" hreflang="ba" data-title="Модуль:Math" data-language-autonym="Башҡортса" data-language-local-name="ਬਸ਼ਕੀਰ" class="interlanguage-link-target">Башҡортса</a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਬਾਲੀਨੀਜ਼" lang="ban" hreflang="ban" data-title="Modul:Math" data-language-autonym="Basa Bali" data-language-local-name="ਬਾਲੀਨੀਜ਼" class="interlanguage-link-target">Basa Bali</a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਬਾਵੇਰੀਅਨ" lang="bar" hreflang="bar" data-title="Modul:Math" data-language-autonym="Boarisch" data-language-local-name="ਬਾਵੇਰੀਅਨ" class="interlanguage-link-target">Boarisch</a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Module:Math" title="Module:Math – Samogitian" lang="sgs" hreflang="sgs" data-title="Module:Math" 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/Module:Math" title="Module:Math – ਕੇਂਦਰੀ ਬਿਕਲ" lang="bcl" hreflang="bcl" data-title="Module:Math" data-language-autonym="Bikol Central" data-language-local-name="ਕੇਂਦਰੀ ਬਿਕਲ" 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%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਬੇਲਾਰੂਸੀ" lang="be" hreflang="be" data-title="Модуль:Math" data-language-autonym="Беларуская" data-language-local-name="ਬੇਲਾਰੂਸੀ" 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%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B" title="Модуль:Матэматычны – ਬੇਲਾਰੂਸੀ (ਰਵਾਇਤੀ)" lang="be-tarask" hreflang="be-tarask" data-title="Модуль:Матэматычны" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="ਬੇਲਾਰੂਸੀ (ਰਵਾਇਤੀ)" 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%9C%D0%BE%D0%B4%D1%83%D0%BB:Math" title="Модул:Math – ਬੁਲਗਾਰੀਆਈ" lang="bg" hreflang="bg" data-title="Модул:Math" data-language-autonym="Български" data-language-local-name="ਬੁਲਗਾਰੀਆਈ" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/Module:Math" title="Module:Math – Bhojpuri" lang="bh" hreflang="bh" data-title="Module:Math" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਬੰਜਰ" lang="bjn" hreflang="bjn" data-title="Modul:Math" data-language-autonym="Banjar" data-language-local-name="ਬੰਜਰ" class="interlanguage-link-target">Banjar</a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%99%E1%80%B1%E1%80%AC%E1%80%BA%E1%80%82%E1%80%BB%E1%80%B0%E1%80%B8:Math" title="မော်ဂျူး:Math – Pa'O" lang="blk" hreflang="blk" data-title="မော်ဂျူး:Math" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target">ပအိုဝ်ႏဘာႏသာႏ</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A6%A1%E0%A6%BF%E0%A6%89%E0%A6%B2:Math" title="মডিউল:Math – ਬੰਗਾਲੀ" lang="bn" hreflang="bn" data-title="মডিউল:Math" data-language-autonym="বাংলা" data-language-local-name="ਬੰਗਾਲੀ" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਬੋਸਨੀਆਈ" lang="bs" hreflang="bs" data-title="Modul:Math" data-language-autonym="Bosanski" data-language-local-name="ਬੋਸਨੀਆਈ" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਰੂਸ ਬੁਰਿਆਤ" lang="bxr" hreflang="bxr" data-title="Модуль:Math" data-language-autonym="Буряад" data-language-local-name="ਰੂਸ ਬੁਰਿਆਤ" class="interlanguage-link-target">Буряад</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/M%C3%B2dul:Math" title="Mòdul:Math – ਕੈਟਾਲਾਨ" lang="ca" hreflang="ca" data-title="Mòdul:Math" data-language-autonym="Català" data-language-local-name="ਕੈਟਾਲਾਨ" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – Chavacano" lang="cbk" hreflang="cbk" data-title="Módulo:Math" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target">Chavacano de Zamboanga</a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/%E6%A8%A1%E7%B5%84:Math" title="模組:Math – ਚੀਨੀ (ਮਿਨ ਡੌਂਗ)" lang="cdo" hreflang="cdo" data-title="模組:Math" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="ਚੀਨੀ (ਮਿਨ ਡੌਂਗ)" 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%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਚੇਚਨ" lang="ce" hreflang="ce" data-title="Модуль:Math" data-language-autonym="Нохчийн" data-language-local-name="ਚੇਚਨ" class="interlanguage-link-target">Нохчийн</a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Module:Math" title="Module:Math – ਸੀਬੂਆਨੋ" lang="ceb" hreflang="ceb" data-title="Module:Math" data-language-autonym="Cebuano" data-language-local-name="ਸੀਬੂਆਨੋ" class="interlanguage-link-target">Cebuano</a></li><li class="interlanguage-link interwiki-ch mw-list-item"><a href="https://ch.wikipedia.org/wiki/Module:Math" title="Module:Math – ਚਮੋਰੋ" lang="ch" hreflang="ch" data-title="Module:Math" data-language-autonym="Chamoru" data-language-local-name="ਚਮੋਰੋ" class="interlanguage-link-target">Chamoru</a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%DB%86%D8%AF%DB%8C%D9%88%D9%88%D9%84:Math" title="مۆدیوول:Math – ਕੇਂਦਰੀ ਕੁਰਦਿਸ਼" lang="ckb" hreflang="ckb" data-title="مۆدیوول:Math" data-language-autonym="کوردی" data-language-local-name="ਕੇਂਦਰੀ ਕੁਰਦਿਸ਼" class="interlanguage-link-target">کوردی</a></li><li class="interlanguage-link interwiki-crh mw-list-item"><a href="https://crh.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਕਰੀਮੀਨ ਟਾਟਾਰ" lang="crh" hreflang="crh" data-title="Modul:Math" data-language-autonym="Qırımtatarca" data-language-local-name="ਕਰੀਮੀਨ ਟਾਟਾਰ" class="interlanguage-link-target">Qırımtatarca</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਚੈੱਕ" lang="cs" hreflang="cs" data-title="Modul:Math" data-language-autonym="Čeština" data-language-local-name="ਚੈੱਕ" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਚੁਵਾਸ਼" lang="cv" hreflang="cv" data-title="Модуль:Math" data-language-autonym="Чӑвашла" data-language-local-name="ਚੁਵਾਸ਼" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Modiwl:Math" title="Modiwl:Math – ਵੈਲਸ਼" lang="cy" hreflang="cy" data-title="Modiwl:Math" data-language-autonym="Cymraeg" data-language-local-name="ਵੈਲਸ਼" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਡੈਨਿਸ਼" lang="da" hreflang="da" data-title="Modul:Math" data-language-autonym="Dansk" data-language-local-name="ਡੈਨਿਸ਼" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-din mw-list-item"><a href="https://din.wikipedia.org/wiki/Muk%C3%A4%C3%A4c%C3%ABt%C3%B6k:Math" title="Mukääcëtök:Math – Dinka" lang="din" hreflang="din" data-title="Mukääcëtök:Math" data-language-autonym="Thuɔŋjäŋ" data-language-local-name="Dinka" class="interlanguage-link-target">Thuɔŋjäŋ</a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Modul:Math" title="Modul:Math – Zazaki" lang="diq" hreflang="diq" data-title="Modul:Math" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target">Zazaki</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/Module:Math" title="Module:Math – ਯੂਨਾਨੀ" lang="el" hreflang="el" data-title="Module:Math" data-language-autonym="Ελληνικά" data-language-local-name="ਯੂਨਾਨੀ" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Module:Math" title="Module:Math – ਅੰਗਰੇਜ਼ੀ" lang="en" hreflang="en" data-title="Module:Math" data-language-autonym="English" data-language-local-name="ਅੰਗਰੇਜ਼ੀ" class="interlanguage-link-target">English</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Modulo:Math" title="Modulo:Math – ਇਸਪੇਰਾਂਟੋ" lang="eo" hreflang="eo" data-title="Modulo:Math" data-language-autonym="Esperanto" data-language-local-name="ਇਸਪੇਰਾਂਟੋ" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – ਸਪੇਨੀ" lang="es" hreflang="es" data-title="Módulo:Math" data-language-autonym="Español" data-language-local-name="ਸਪੇਨੀ" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Moodul:Math" title="Moodul:Math – ਇਸਟੋਨੀਆਈ" lang="et" hreflang="et" data-title="Moodul:Math" data-language-autonym="Eesti" data-language-local-name="ਇਸਟੋਨੀਆਈ" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Modulu:Math" title="Modulu:Math – ਬਾਸਕ" lang="eu" hreflang="eu" data-title="Modulu:Math" data-language-autonym="Euskara" data-language-local-name="ਬਾਸਕ" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D9%88%D8%AF%D9%85%D8%A7%D9%86:Math" title="پودمان:Math – ਫ਼ਾਰਸੀ" lang="fa" hreflang="fa" data-title="پودمان:Math" data-language-autonym="فارسی" data-language-local-name="ਫ਼ਾਰਸੀ" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Moduuli:Math" title="Moduuli:Math – ਫਿਨਿਸ਼" lang="fi" hreflang="fi" data-title="Moduuli:Math" data-language-autonym="Suomi" data-language-local-name="ਫਿਨਿਸ਼" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Module:Math" title="Module:Math – ਫ਼ਿਜ਼ੀ" lang="fj" hreflang="fj" data-title="Module:Math" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="ਫ਼ਿਜ਼ੀ" 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/Module:Math" title="Module:Math – ਫ਼ੇਰੋਸੇ" lang="fo" hreflang="fo" data-title="Module:Math" data-language-autonym="Føroyskt" data-language-local-name="ਫ਼ੇਰੋਸੇ" class="interlanguage-link-target">Føroyskt</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Module:Math" title="Module:Math – ਫਰਾਂਸੀਸੀ" lang="fr" hreflang="fr" data-title="Module:Math" data-language-autonym="Français" data-language-local-name="ਫਰਾਂਸੀਸੀ" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਉੱਤਰੀ ਫਰਿਸੀਅਨ" lang="frr" hreflang="frr" data-title="Modul:Math" data-language-autonym="Nordfriisk" data-language-local-name="ਉੱਤਰੀ ਫਰਿਸੀਅਨ" class="interlanguage-link-target">Nordfriisk</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Module:Math" title="Module:Math – ਆਇਰਸ਼" lang="ga" hreflang="ga" data-title="Module:Math" data-language-autonym="Gaeilge" data-language-local-name="ਆਇਰਸ਼" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/M%C3%B2ideal:Math" title="Mòideal:Math – ਸਕਾਟਿਸ਼ ਗੇਲਿਕ" lang="gd" hreflang="gd" data-title="Mòideal:Math" data-language-autonym="Gàidhlig" data-language-local-name="ਸਕਾਟਿਸ਼ ਗੇਲਿਕ" class="interlanguage-link-target">Gàidhlig</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – ਗੈਲਿਸ਼ਿਅਨ" lang="gl" hreflang="gl" data-title="Módulo:Math" data-language-autonym="Galego" data-language-local-name="ਗੈਲਿਸ਼ਿਅਨ" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-glk mw-list-item"><a href="https://glk.wikipedia.org/wiki/%D9%85%D8%A7%D8%AC%DB%8A%D9%84:Math" title="ماجۊل:Math – ਗਿਲਾਕੀ" lang="glk" hreflang="glk" data-title="ماجۊل:Math" data-language-autonym="گیلکی" data-language-local-name="ਗਿਲਾਕੀ" class="interlanguage-link-target">گیلکی</a></li><li class="interlanguage-link interwiki-gom mw-list-item"><a href="https://gom.wikipedia.org/wiki/%E0%A4%8F%E0%A4%95%E0%A4%95:Math" title="एकक:Math – ਗੋਥਿਕ" lang="gom" hreflang="gom" data-title="एकक:Math" data-language-autonym="गोंयची कोंकणी / Gõychi Konknni" data-language-local-name="ਗੋਥਿਕ" class="interlanguage-link-target">गोंयची कोंकणी / Gõychi Konknni</a></li><li class="interlanguage-link interwiki-gor mw-list-item"><a href="https://gor.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਗੋਰੋਂਤਾਲੋ" lang="gor" hreflang="gor" data-title="Modul:Math" data-language-autonym="Bahasa Hulontalo" data-language-local-name="ਗੋਰੋਂਤਾਲੋ" class="interlanguage-link-target">Bahasa Hulontalo</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B5%E0%AA%BF%E0%AA%AD%E0%AA%BE%E0%AA%97:Math" title="વિભાગ:Math – ਗੁਜਰਾਤੀ" lang="gu" hreflang="gu" data-title="વિભાગ:Math" data-language-autonym="ગુજરાતી" data-language-local-name="ਗੁਜਰਾਤੀ" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-guc mw-list-item"><a href="https://guc.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – Wayuu" lang="guc" hreflang="guc" data-title="Módulo:Math" data-language-autonym="Wayuunaiki" data-language-local-name="Wayuu" class="interlanguage-link-target">Wayuunaiki</a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Module:Math" title="Module:Math – ਹੌਸਾ" lang="ha" hreflang="ha" data-title="Module:Math" data-language-autonym="Hausa" data-language-local-name="ਹੌਸਾ" class="interlanguage-link-target">Hausa</a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/%E6%A8%A1%E7%B5%84:Math" title="模組:Math – ਚੀਨੀ ਹਾਕਾ" lang="hak" hreflang="hak" data-title="模組:Math" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="ਚੀਨੀ ਹਾਕਾ" class="interlanguage-link-target">客家語 / Hak-kâ-ngî</a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Module:Math" title="Module:Math – ਹਵਾਈ" lang="haw" hreflang="haw" data-title="Module:Math" data-language-autonym="Hawaiʻi" data-language-local-name="ਹਵਾਈ" class="interlanguage-link-target">Hawaiʻi</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%99%D7%97%D7%99%D7%93%D7%94:Math" title="יחידה:Math – ਹਿਬਰੂ" lang="he" hreflang="he" data-title="יחידה:Math" data-language-autonym="עברית" data-language-local-name="ਹਿਬਰੂ" 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%AE%E0%A5%89%E0%A4%A1%E0%A5%8D%E0%A4%AF%E0%A5%82%E0%A4%B2:Math" title="मॉड्यूल:Math – ਹਿੰਦੀ" lang="hi" hreflang="hi" data-title="मॉड्यूल:Math" data-language-autonym="हिन्दी" data-language-local-name="ਹਿੰਦੀ" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਸਰਬੋ-ਕ੍ਰੋਏਸ਼ੀਅਨ" lang="hr" hreflang="hr" data-title="Modul:Math" data-language-autonym="Hrvatski" data-language-local-name="ਸਰਬੋ-ਕ੍ਰੋਏਸ਼ੀਅਨ" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Module:Math" title="Module:Math – ਹੈਤੀਆਈ" lang="ht" hreflang="ht" data-title="Module:Math" data-language-autonym="Kreyòl ayisyen" data-language-local-name="ਹੈਤੀਆਈ" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਹੰਗਰੀਆਈ" lang="hu" hreflang="hu" data-title="Modul:Math" data-language-autonym="Magyar" data-language-local-name="ਹੰਗਰੀਆਈ" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%B8%D5%A4%D5%B8%D6%82%D5%AC:Math" title="Մոդուլ:Math – ਅਰਮੀਨੀਆਈ" lang="hy" hreflang="hy" data-title="Մոդուլ:Math" data-language-autonym="Հայերեն" data-language-local-name="ਅਰਮੀਨੀਆਈ" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%84%D5%B8%D5%A4%D5%B8%D6%82%D5%AC:Math" title="Մոդուլ:Math – ਪੱਛਮੀ ਆਰਮੇਨੀਆਈ" lang="hyw" hreflang="hyw" data-title="Մոդուլ:Math" data-language-autonym="Արեւմտահայերէն" data-language-local-name="ਪੱਛਮੀ ਆਰਮੇਨੀਆਈ" class="interlanguage-link-target">Արեւմտահայերէն</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਇੰਡੋਨੇਸ਼ੀਆਈ" lang="id" hreflang="id" data-title="Modul:Math" data-language-autonym="Bahasa Indonesia" data-language-local-name="ਇੰਡੋਨੇਸ਼ੀਆਈ" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/Module:Math" title="Module:Math – ਇਗਬੋ" lang="ig" hreflang="ig" data-title="Module:Math" data-language-autonym="Igbo" data-language-local-name="ਇਗਬੋ" class="interlanguage-link-target">Igbo</a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Modulo:Math" title="Modulo:Math – ਇਲੋਕਾਨੋ" lang="ilo" hreflang="ilo" data-title="Modulo:Math" data-language-autonym="Ilokano" data-language-local-name="ਇਲੋਕਾਨੋ" class="interlanguage-link-target">Ilokano</a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਇੰਗੁਸ਼" lang="inh" hreflang="inh" data-title="Модуль:Math" data-language-autonym="ГӀалгӀай" data-language-local-name="ਇੰਗੁਸ਼" class="interlanguage-link-target">ГӀалгӀай</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Module:Math" title="Module:Math – ਆਈਸਲੈਂਡਿਕ" lang="is" hreflang="is" data-title="Module:Math" data-language-autonym="Íslenska" data-language-local-name="ਆਈਸਲੈਂਡਿਕ" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Modulo:Math" title="Modulo:Math – ਇਤਾਲਵੀ" lang="it" hreflang="it" data-title="Modulo:Math" data-language-autonym="Italiano" data-language-local-name="ਇਤਾਲਵੀ" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A2%E3%82%B8%E3%83%A5%E3%83%BC%E3%83%AB:Math" title="モジュール:Math – ਜਪਾਨੀ" lang="ja" hreflang="ja" data-title="モジュール:Math" data-language-autonym="日本語" data-language-local-name="ਜਪਾਨੀ" 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/Module:Math" title="Module:Math – ਜਾਮਾਈਕਨ ਕਰੀਓਲ ਅੰਗਰੇਜ਼ੀ" lang="jam" hreflang="jam" data-title="Module:Math" data-language-autonym="Patois" data-language-local-name="ਜਾਮਾਈਕਨ ਕਰੀਓਲ ਅੰਗਰੇਜ਼ੀ" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Modhul:Math" title="Modhul:Math – ਜਾਵਾਨੀਜ਼" lang="jv" hreflang="jv" data-title="Modhul:Math" data-language-autonym="Jawa" data-language-local-name="ਜਾਵਾਨੀਜ਼" 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%9B%E1%83%9D%E1%83%93%E1%83%A3%E1%83%9A%E1%83%98:Math" title="მოდული:Math – ਜਾਰਜੀਆਈ" lang="ka" hreflang="ka" data-title="მოდული:Math" data-language-autonym="ქართული" data-language-local-name="ਜਾਰਜੀਆਈ" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Module:Math" title="Module:Math – ਕਰਾਕਲਪਾਕ" lang="kaa" hreflang="kaa" data-title="Module:Math" data-language-autonym="Qaraqalpaqsha" data-language-local-name="ਕਰਾਕਲਪਾਕ" class="interlanguage-link-target">Qaraqalpaqsha</a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Module:Math" title="Module:Math – ਕਬਾਇਲ" lang="kab" hreflang="kab" data-title="Module:Math" data-language-autonym="Taqbaylit" data-language-local-name="ਕਬਾਇਲ" class="interlanguage-link-target">Taqbaylit</a></li><li class="interlanguage-link interwiki-kcg mw-list-item"><a href="https://kcg.wikipedia.org/wiki/Module:Math" title="Module:Math – ਟਾਇਪ" lang="kcg" hreflang="kcg" data-title="Module:Math" data-language-autonym="Tyap" data-language-local-name="ਟਾਇਪ" class="interlanguage-link-target">Tyap</a></li><li class="interlanguage-link interwiki-kg mw-list-item"><a href="https://kg.wikipedia.org/wiki/Module:Math" title="Module:Math – ਕੌਂਗੋ" lang="kg" hreflang="kg" data-title="Module:Math" data-language-autonym="Kongo" data-language-local-name="ਕੌਂਗੋ" class="interlanguage-link-target">Kongo</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/Module:Math" title="Module:Math – ਕਜ਼ਾਖ਼" lang="kk" hreflang="kk" data-title="Module:Math" data-language-autonym="Қазақша" data-language-local-name="ਕਜ਼ਾਖ਼" 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%AE%E0%B2%BE%E0%B2%A1%E0%B3%8D%E0%B2%AF%E0%B3%82%E0%B2%B2%E0%B3%8D:Math" title="ಮಾಡ್ಯೂಲ್:Math – ਕੰਨੜ" lang="kn" hreflang="kn" data-title="ಮಾಡ್ಯೂಲ್:Math" data-language-autonym="ಕನ್ನಡ" data-language-local-name="ਕੰਨੜ" class="interlanguage-link-target">ಕನ್ನಡ</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AA%A8%EB%93%88:Math" title="모듈:Math – ਕੋਰੀਆਈ" lang="ko" hreflang="ko" data-title="모듈:Math" data-language-autonym="한국어" data-language-local-name="ਕੋਰੀਆਈ" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਕੁਰਦਿਸ਼" lang="ku" hreflang="ku" data-title="Modul:Math" data-language-autonym="Kurdî" data-language-local-name="ਕੁਰਦਿਸ਼" class="interlanguage-link-target">Kurdî</a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਕਿਰਗੀਜ਼" lang="ky" hreflang="ky" data-title="Модуль:Math" data-language-autonym="Кыргызча" data-language-local-name="ਕਿਰਗੀਜ਼" class="interlanguage-link-target">Кыргызча</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Modulus:Math" title="Modulus:Math – ਲਾਤੀਨੀ" lang="la" hreflang="la" data-title="Modulus:Math" data-language-autonym="Latina" data-language-local-name="ਲਾਤੀਨੀ" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਲਕਜ਼ਮਬਰਗਿਸ਼" lang="lb" hreflang="lb" data-title="Modul:Math" data-language-autonym="Lëtzebuergesch" data-language-local-name="ਲਕਜ਼ਮਬਰਗਿਸ਼" class="interlanguage-link-target">Lëtzebuergesch</a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਲੈਜ਼ਗੀ" lang="lez" hreflang="lez" data-title="Модуль:Math" data-language-autonym="Лезги" data-language-local-name="ਲੈਜ਼ਗੀ" class="interlanguage-link-target">Лезги</a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/Module:Math" title="Module:Math – ਲਾਓ" lang="lo" hreflang="lo" data-title="Module:Math" data-language-autonym="ລາວ" data-language-local-name="ਲਾਓ" class="interlanguage-link-target">ລາວ</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Module:Math" title="Module:Math – ਲਿਥੁਆਨੀਅਨ" lang="lt" hreflang="lt" data-title="Module:Math" data-language-autonym="Lietuvių" data-language-local-name="ਲਿਥੁਆਨੀਅਨ" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-ltg mw-list-item"><a href="https://ltg.wikipedia.org/wiki/Modulis:Math" title="Modulis:Math – Latgalian" lang="ltg" hreflang="ltg" data-title="Modulis:Math" data-language-autonym="Latgaļu" data-language-local-name="Latgalian" class="interlanguage-link-target">Latgaļu</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Modulis:Math" title="Modulis:Math – ਲਾਤੀਵੀ" lang="lv" hreflang="lv" data-title="Modulis:Math" data-language-autonym="Latviešu" data-language-local-name="ਲਾਤੀਵੀ" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਮਾਡੂਰੀਸ" lang="mad" hreflang="mad" data-title="Modul:Math" data-language-autonym="Madhurâ" data-language-local-name="ਮਾਡੂਰੀਸ" class="interlanguage-link-target">Madhurâ</a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%AE%E0%A5%8B%E0%A4%A1%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%B2:Math" title="मोड्युल:Math – ਮੈਥਲੀ" lang="mai" hreflang="mai" data-title="मोड्युल:Math" data-language-autonym="मैथिली" data-language-local-name="ਮੈਥਲੀ" class="interlanguage-link-target">मैथिली</a></li><li class="interlanguage-link interwiki-map-bms mw-list-item"><a href="https://map-bms.wikipedia.org/wiki/Modhul:Math" title="Modhul:Math – ਬਨਯੂਮਾਸਨ" lang="jv-x-bms" hreflang="jv-x-bms" data-title="Modhul:Math" data-language-autonym="Basa Banyumasan" data-language-local-name="ਬਨਯੂਮਾਸਨ" class="interlanguage-link-target">Basa Banyumasan</a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਮੋਕਸ਼ਾ" lang="mdf" hreflang="mdf" data-title="Модуль:Math" data-language-autonym="Мокшень" data-language-local-name="ਮੋਕਸ਼ਾ" class="interlanguage-link-target">Мокшень</a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਮਿਨਾਂਗਕਾਬਾਓ" lang="min" hreflang="min" data-title="Modul:Math" data-language-autonym="Minangkabau" data-language-local-name="ਮਿਨਾਂਗਕਾਬਾਓ" class="interlanguage-link-target">Minangkabau</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB:Math" title="Модул:Math – ਮੈਕਡੋਨੀਆਈ" lang="mk" hreflang="mk" data-title="Модул:Math" data-language-autonym="Македонски" data-language-local-name="ਮੈਕਡੋਨੀਆਈ" 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%98%E0%B4%9F%E0%B4%95%E0%B4%82:Math" title="ഘടകം:Math – ਮਲਿਆਲਮ" lang="ml" hreflang="ml" data-title="ഘടകം:Math" data-language-autonym="മലയാളം" data-language-local-name="ਮਲਿਆਲਮ" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-mnw mw-list-item"><a href="https://mnw.wikipedia.org/wiki/%E1%80%99%E1%80%9D%E1%80%BA%E1%80%82%E1%80%BB%E1%80%B0:Math" title="မဝ်ဂျူ:Math – ਮੋਨ" lang="mnw" hreflang="mnw" data-title="မဝ်ဂျူ:Math" data-language-autonym="ဘာသာမန်" data-language-local-name="ਮੋਨ" class="interlanguage-link-target">ဘာသာမန်</a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AD%E0%A4%BE%E0%A4%97:Math" title="विभाग:Math – ਮਰਾਠੀ" lang="mr" hreflang="mr" data-title="विभाग:Math" data-language-autonym="मराठी" data-language-local-name="ਮਰਾਠੀ" class="interlanguage-link-target">मराठी</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਮਲਯ" lang="ms" hreflang="ms" data-title="Modul:Math" data-language-autonym="Bahasa Melayu" data-language-local-name="ਮਲਯ" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – ਮਿਰਾਂਡੀ" lang="mwl" hreflang="mwl" data-title="Módulo:Math" data-language-autonym="Mirandés" data-language-local-name="ਮਿਰਾਂਡੀ" 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%99%E1%80%B1%E1%80%AC%E1%80%BA%E1%80%82%E1%80%BB%E1%80%B0%E1%80%B8:Math" title="မော်ဂျူး:Math – ਬਰਮੀ" lang="my" hreflang="my" data-title="မော်ဂျူး:Math" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="ਬਰਮੀ" class="interlanguage-link-target">မြန်မာဘာသာ</a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D9%85%D8%A7%DA%98%D9%88%D9%84:Math" title="ماژول:Math – ਮੇਜ਼ੈਂਡਰਾਨੀ" lang="mzn" hreflang="mzn" data-title="ماژول:Math" data-language-autonym="مازِرونی" data-language-local-name="ਮੇਜ਼ੈਂਡਰਾਨੀ" class="interlanguage-link-target">مازِرونی</a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AE%E0%A5%8B%E0%A4%A1%E0%A5%8D%E0%A4%AF%E0%A5%81%E0%A4%B2:Math" title="मोड्युल:Math – ਨੇਪਾਲੀ" lang="ne" hreflang="ne" data-title="मोड्युल:Math" data-language-autonym="नेपाली" data-language-local-name="ਨੇਪਾਲੀ" class="interlanguage-link-target">नेपाली</a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/Module:Math" title="Module:Math – ਨੇਵਾਰੀ" lang="new" hreflang="new" data-title="Module:Math" data-language-autonym="नेपाल भाषा" data-language-local-name="ਨੇਵਾਰੀ" class="interlanguage-link-target">नेपाल भाषा</a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਨਿਆਸ" lang="nia" hreflang="nia" data-title="Modul:Math" data-language-autonym="Li Niha" data-language-local-name="ਨਿਆਸ" class="interlanguage-link-target">Li Niha</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Module:Math" title="Module:Math – ਡੱਚ" lang="nl" hreflang="nl" data-title="Module:Math" data-language-autonym="Nederlands" data-language-local-name="ਡੱਚ" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਨਾਰਵੇਜਿਆਈ ਨਿਓਨੌਰਸਕ" lang="nn" hreflang="nn" data-title="Modul:Math" data-language-autonym="Norsk nynorsk" data-language-local-name="ਨਾਰਵੇਜਿਆਈ ਨਿਓਨੌਰਸਕ" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਨਾਰਵੇਜਿਆਈ ਬੋਕਮਲ" lang="nb" hreflang="nb" data-title="Modul:Math" data-language-autonym="Norsk bokmål" data-language-local-name="ਨਾਰਵੇਜਿਆਈ ਬੋਕਮਲ" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nqo mw-list-item"><a href="https://nqo.wikipedia.org/wiki/%DF%97%DF%8B%DF%AC%DF%9E%DF%99%DF%8A%DF%9E%DF%8F:Math" title="ߗߋ߬ߞߙߊߞߏ:Math – ਐਂਕੋ" lang="nqo" hreflang="nqo" data-title="ߗߋ߬ߞߙߊߞߏ:Math" data-language-autonym="ߒߞߏ" data-language-local-name="ਐਂਕੋ" class="interlanguage-link-target">ߒߞߏ</a></li><li class="interlanguage-link interwiki-ny mw-list-item"><a href="https://ny.wikipedia.org/wiki/Module:Math" title="Module:Math – ਨਯਾਂਜਾ" lang="ny" hreflang="ny" data-title="Module:Math" data-language-autonym="Chi-Chewa" data-language-local-name="ਨਯਾਂਜਾ" class="interlanguage-link-target">Chi-Chewa</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/M%C3%B2dul:Math" title="Mòdul:Math – ਓਕਸੀਟਾਨ" lang="oc" hreflang="oc" data-title="Mòdul:Math" data-language-autonym="Occitan" data-language-local-name="ਓਕਸੀਟਾਨ" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-olo mw-list-item"><a href="https://olo.wikipedia.org/wiki/Moduuli:Math" title="Moduuli:Math – ਲਿਵੀ-ਕਾਰੇਲੀਅਨ" lang="olo" hreflang="olo" data-title="Moduuli:Math" data-language-autonym="Livvinkarjala" data-language-local-name="ਲਿਵੀ-ਕਾਰੇਲੀਅਨ" class="interlanguage-link-target">Livvinkarjala</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AE%E0%AC%A1%E0%AD%8D%E0%AD%9F%E0%AD%81%E0%AC%B2:Math" title="ମଡ୍ୟୁଲ:Math – ਉੜੀਆ" lang="or" hreflang="or" data-title="ମଡ୍ୟୁଲ:Math" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="ਉੜੀਆ" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਓਸੈਟਿਕ" lang="os" hreflang="os" data-title="Модуль:Math" data-language-autonym="Ирон" data-language-local-name="ਓਸੈਟਿਕ" class="interlanguage-link-target">Ирон</a></li><li class="interlanguage-link interwiki-pag mw-list-item"><a href="https://pag.wikipedia.org/wiki/Module:Math" title="Module:Math – ਪੰਗਾਸੀਨਾਨ" lang="pag" hreflang="pag" data-title="Module:Math" data-language-autonym="Pangasinan" data-language-local-name="ਪੰਗਾਸੀਨਾਨ" class="interlanguage-link-target">Pangasinan</a></li><li class="interlanguage-link interwiki-pap mw-list-item"><a href="https://pap.wikipedia.org/wiki/Module:Math" title="Module:Math – ਪਾਪਿਆਮੈਂਟੋ" lang="pap" hreflang="pap" data-title="Module:Math" data-language-autonym="Papiamentu" data-language-local-name="ਪਾਪਿਆਮੈਂਟੋ" class="interlanguage-link-target">Papiamentu</a></li><li class="interlanguage-link interwiki-pih mw-list-item"><a href="https://pih.wikipedia.org/wiki/Module:Math" title="Module:Math – ਪਿਟਕਰਨ-ਨੋਰਫਕ" lang="pih" hreflang="pih" data-title="Module:Math" data-language-autonym="Norfuk / Pitkern" data-language-local-name="ਪਿਟਕਰਨ-ਨੋਰਫਕ" class="interlanguage-link-target">Norfuk / Pitkern</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Modu%C5%82:Math" title="Moduł:Math – ਪੋਲੈਂਡੀ" lang="pl" hreflang="pl" data-title="Moduł:Math" data-language-autonym="Polski" data-language-local-name="ਪੋਲੈਂਡੀ" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/Module:Math" title="Module:Math – ਪਸ਼ਤੋ" lang="ps" hreflang="ps" data-title="Module:Math" data-language-autonym="پښتو" data-language-local-name="ਪਸ਼ਤੋ" class="interlanguage-link-target">پښتو</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/M%C3%B3dulo:Math" title="Módulo:Math – ਪੁਰਤਗਾਲੀ" lang="pt" hreflang="pt" data-title="Módulo:Math" data-language-autonym="Português" data-language-local-name="ਪੁਰਤਗਾਲੀ" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-rn mw-list-item"><a href="https://rn.wikipedia.org/wiki/Module:Math" title="Module:Math – ਰੁੰਡੀ" lang="rn" hreflang="rn" data-title="Module:Math" data-language-autonym="Ikirundi" data-language-local-name="ਰੁੰਡੀ" class="interlanguage-link-target">Ikirundi</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Modul:Matematic%C4%83" title="Modul:Matematică – ਰੋਮਾਨੀਆਈ" lang="ro" hreflang="ro" data-title="Modul:Matematică" data-language-autonym="Română" data-language-local-name="ਰੋਮਾਨੀਆਈ" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਰੂਸੀ" lang="ru" hreflang="ru" data-title="Модуль:Math" data-language-autonym="Русский" data-language-local-name="ਰੂਸੀ" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%AA%E0%A4%9F%E0%A4%B2%E0%A4%AE%E0%A5%8D:Math" title="पटलम्:Math – ਸੰਸਕ੍ਰਿਤ" lang="sa" hreflang="sa" data-title="पटलम्:Math" data-language-autonym="संस्कृतम्" data-language-local-name="ਸੰਸਕ੍ਰਿਤ" class="interlanguage-link-target">संस्कृतम्</a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਸਾਖਾ" lang="sah" hreflang="sah" data-title="Модуль:Math" data-language-autonym="Саха тыла" data-language-local-name="ਸਾਖਾ" class="interlanguage-link-target">Саха тыла</a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%A2%E1%B1%B3%E1%B1%B0%E1%B1%A9%E1%B1%9E:Math" title="ᱢᱳᱰᱩᱞ:Math – ਸੰਥਾਲੀ" lang="sat" hreflang="sat" data-title="ᱢᱳᱰᱩᱞ:Math" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="ਸੰਥਾਲੀ" class="interlanguage-link-target">ᱥᱟᱱᱛᱟᱲᱤ</a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Module:Math" title="Module:Math – ਸਕਾਟਸ" lang="sco" hreflang="sco" data-title="Module:Math" data-language-autonym="Scots" data-language-local-name="ਸਕਾਟਸ" class="interlanguage-link-target">Scots</a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%85%D8%A7%DA%8A%D9%8A%D9%88%D9%84:Math" title="ماڊيول:Math – ਸਿੰਧੀ" lang="sd" hreflang="sd" data-title="ماڊيول:Math" data-language-autonym="سنڌي" data-language-local-name="ਸਿੰਧੀ" class="interlanguage-link-target">سنڌي</a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Modul:Math" title="Modul:Math – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Modul:Math" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target">Srpskohrvatski / српскохрватски</a></li><li class="interlanguage-link interwiki-shn mw-list-item"><a href="https://shn.wikipedia.org/wiki/%E1%80%99%E1%80%B1%E1%82%83%E1%82%87%E1%81%B5%E1%80%BB%E1%80%B0%E1%80%B8:Math" title="မေႃႇၵျူး:Math – ਸ਼ਾਨ" lang="shn" hreflang="shn" data-title="မေႃႇၵျူး:Math" data-language-autonym="ၽႃႇသႃႇတႆး " data-language-local-name="ਸ਼ਾਨ" class="interlanguage-link-target">ၽႃႇသႃႇတႆး </a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/Module:Math" title="Module:Math – ਸਿੰਹਾਲਾ" lang="si" hreflang="si" data-title="Module:Math" data-language-autonym="සිංහල" data-language-local-name="ਸਿੰਹਾਲਾ" class="interlanguage-link-target">සිංහල</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Module:Math" title="Module:Math – Simple English" lang="en-simple" hreflang="en-simple" data-title="Module:Math" 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/Modul:Math" title="Modul:Math – ਸਲੋਵਾਕ" lang="sk" hreflang="sk" data-title="Modul:Math" data-language-autonym="Slovenčina" data-language-local-name="ਸਲੋਵਾਕ" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਸਲੋਵੇਨੀਆਈ" lang="sl" hreflang="sl" data-title="Modul:Math" data-language-autonym="Slovenščina" data-language-local-name="ਸਲੋਵੇਨੀਆਈ" class="interlanguage-link-target">Slovenščina</a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Module:Math" title="Module:Math – ਸ਼ੋਨਾ" lang="sn" hreflang="sn" data-title="Module:Math" data-language-autonym="ChiShona" data-language-local-name="ਸ਼ੋਨਾ" class="interlanguage-link-target">ChiShona</a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Module:Math" title="Module:Math – ਸੋਮਾਲੀ" lang="so" hreflang="so" data-title="Module:Math" data-language-autonym="Soomaaliga" data-language-local-name="ਸੋਮਾਲੀ" class="interlanguage-link-target">Soomaaliga</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB:Math" title="Модул:Math – ਸਰਬੀਆਈ" lang="sr" hreflang="sr" data-title="Модул:Math" data-language-autonym="Српски / srpski" data-language-local-name="ਸਰਬੀਆਈ" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਸਵੀਡਿਸ਼" lang="sv" hreflang="sv" data-title="Modul:Math" data-language-autonym="Svenska" data-language-local-name="ਸਵੀਡਿਸ਼" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-szy mw-list-item"><a href="https://szy.wikipedia.org/wiki/bacu-saupu:Math" title="bacu-saupu:Math – Sakizaya" lang="szy" hreflang="szy" data-title="bacu-saupu:Math" data-language-autonym="Sakizaya" data-language-local-name="Sakizaya" class="interlanguage-link-target">Sakizaya</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/Module:Math" title="Module:Math – ਤਮਿਲ" lang="ta" hreflang="ta" data-title="Module:Math" data-language-autonym="தமிழ்" data-language-local-name="ਤਮਿਲ" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-tdd mw-list-item"><a href="https://tdd.wikipedia.org/wiki/%E1%A5%9B%E1%A5%A8%E1%A5%9D%E1%A5%B1_%E1%A5%93%E1%A5%A7%E1%A5%B0:Math" title="ᥛᥨᥝᥱ ᥓᥧᥰ:Math – Tai Nuea" lang="tdd" hreflang="tdd" data-title="ᥛᥨᥝᥱ ᥓᥧᥰ:Math" data-language-autonym="ᥖᥭᥰ ᥖᥬᥲ ᥑᥨᥒᥰ" data-language-local-name="Tai Nuea" class="interlanguage-link-target">ᥖᥭᥰ ᥖᥬᥲ ᥑᥨᥒᥰ</a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AE%E0%B0%BE%E0%B0%A1%E0%B1%8D%E0%B0%AF%E0%B1%82%E0%B0%B2%E0%B1%8D:Math" title="మాడ్యూల్:Math – ਤੇਲਗੂ" lang="te" hreflang="te" data-title="మాడ్యూల్:Math" data-language-autonym="తెలుగు" data-language-local-name="ਤੇਲਗੂ" class="interlanguage-link-target">తెలుగు</a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB:Math" title="Модул:Math – ਤਾਜਿਕ" lang="tg" hreflang="tg" data-title="Модул:Math" data-language-autonym="Тоҷикӣ" data-language-local-name="ਤਾਜਿਕ" 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%A1%E0%B8%AD%E0%B8%94%E0%B8%B9%E0%B8%A5:Math" title="มอดูล:Math – ਥਾਈ" lang="th" hreflang="th" data-title="มอดูล:Math" data-language-autonym="ไทย" data-language-local-name="ਥਾਈ" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-ti mw-list-item"><a href="https://ti.wikipedia.org/wiki/%E1%88%9E%E1%8B%B5%E1%8B%A9%E1%88%8D:Math" title="ሞድዩል:Math – ਤਿਗ੍ਰੀਨਿਆ" lang="ti" hreflang="ti" data-title="ሞድዩል:Math" data-language-autonym="ትግርኛ" data-language-local-name="ਤਿਗ੍ਰੀਨਿਆ" class="interlanguage-link-target">ትግርኛ</a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Module:Math" title="Module:Math – ਤੁਰਕਮੇਨ" lang="tk" hreflang="tk" data-title="Module:Math" data-language-autonym="Türkmençe" data-language-local-name="ਤੁਰਕਮੇਨ" class="interlanguage-link-target">Türkmençe</a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Module:Math" title="Module:Math – ਤਗਾਲੋਗ" lang="tl" hreflang="tl" data-title="Module:Math" data-language-autonym="Tagalog" data-language-local-name="ਤਗਾਲੋਗ" class="interlanguage-link-target">Tagalog</a></li><li class="interlanguage-link interwiki-tn mw-list-item"><a href="https://tn.wikipedia.org/wiki/Module:Math" title="Module:Math – ਤਸਵਾਨਾ" lang="tn" hreflang="tn" data-title="Module:Math" data-language-autonym="Setswana" data-language-local-name="ਤਸਵਾਨਾ" class="interlanguage-link-target">Setswana</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Mod%C3%BCl:Math" title="Modül:Math – ਤੁਰਕੀ" lang="tr" hreflang="tr" data-title="Modül:Math" data-language-autonym="Türkçe" data-language-local-name="ਤੁਰਕੀ" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਟਾਟਾਰ (ਸਿਰਿਲਿਕ ਲਿਪੀ)" lang="tt" hreflang="tt" data-title="Модуль:Math" data-language-autonym="Татарча / tatarça" data-language-local-name="ਟਾਟਾਰ (ਸਿਰਿਲਿਕ ਲਿਪੀ)" class="interlanguage-link-target">Татарча / tatarça</a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਉਦਮੁਰਤ" lang="udm" hreflang="udm" data-title="Модуль:Math" data-language-autonym="Удмурт" data-language-local-name="ਉਦਮੁਰਤ" class="interlanguage-link-target">Удмурт</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D1%83%D0%BB%D1%8C:Math" title="Модуль:Math – ਯੂਕਰੇਨੀਆਈ" lang="uk" hreflang="uk" data-title="Модуль:Math" data-language-autonym="Українська" data-language-local-name="ਯੂਕਰੇਨੀਆਈ" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%A7%DA%88%DB%8C%D9%88%D9%84:Math" title="ماڈیول:Math – ਉਰਦੂ" lang="ur" hreflang="ur" data-title="ماڈیول:Math" data-language-autonym="اردو" data-language-local-name="ਉਰਦੂ" class="interlanguage-link-target">اردو</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Modul:Math" title="Modul:Math – ਉਜ਼ਬੇਕ" lang="uz" hreflang="uz" data-title="Modul:Math" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ਉਜ਼ਬੇਕ" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Modulo:Math" title="Modulo:Math – ਵੇਨੇਸ਼ੀਅਨ" lang="vec" hreflang="vec" data-title="Modulo:Math" data-language-autonym="Vèneto" data-language-local-name="ਵੇਨੇਸ਼ੀਅਨ" class="interlanguage-link-target">Vèneto</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%B4_%C4%91un:Math" title="Mô đun:Math – ਵੀਅਤਨਾਮੀ" lang="vi" hreflang="vi" data-title="Mô đun:Math" data-language-autonym="Tiếng Việt" data-language-local-name="ਵੀਅਤਨਾਮੀ" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Module:Math" title="Module:Math – ਵੋਲਾਪੂਕ" lang="vo" hreflang="vo" data-title="Module:Math" data-language-autonym="Volapük" data-language-local-name="ਵੋਲਾਪੂਕ" class="interlanguage-link-target">Volapük</a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Module:Math" title="Module:Math – ਵੈਰੇ" lang="war" hreflang="war" data-title="Module:Math" data-language-autonym="Winaray" data-language-local-name="ਵੈਰੇ" class="interlanguage-link-target">Winaray</a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%A8%A1%E5%9D%97:Math" title="模块:Math – ਚੀਨੀ ਵੂ" lang="wuu" hreflang="wuu" data-title="模块:Math" data-language-autonym="吴语" data-language-local-name="ਚੀਨੀ ਵੂ" class="interlanguage-link-target">吴语</a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/Module:Math" title="Module:Math – ਖੋਸਾ" lang="xh" hreflang="xh" data-title="Module:Math" data-language-autonym="IsiXhosa" data-language-local-name="ਖੋਸਾ" class="interlanguage-link-target">IsiXhosa</a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%99%D7%97%D7%99%D7%93%D7%94:Math" title="יחידה:Math – ਯਿਦਿਸ਼" lang="yi" hreflang="yi" data-title="יחידה:Math" data-language-autonym="ייִדיש" data-language-local-name="ਯਿਦਿਸ਼" class="interlanguage-link-target">ייִדיש</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/Module:Math" title="Module:Math – ਚੀਨੀ" lang="zh" hreflang="zh" data-title="Module:Math" data-language-autonym="中文" data-language-local-name="ਚੀਨੀ" 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/%E6%A8%A1%E7%B5%84:Math" title="模組:Math – ਚੀਨੀ (ਰਵਾਇਤੀ)" lang="lzh" hreflang="lzh" data-title="模組:Math" data-language-autonym="文言" data-language-local-name="ਚੀਨੀ (ਰਵਾਇਤੀ)" 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/%E6%A8%A1%E7%B5%84:Math" title="模組:Math – ਚੀਨੀ ਮਿਨ ਨਾਨ" lang="nan" hreflang="nan" data-title="模組:Math" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="ਚੀਨੀ ਮਿਨ ਨਾਨ" 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/%E6%A8%A1%E7%B5%84:Math" title="模組:Math – ਕੈਂਟੋਨੀਜ਼" lang="yue" hreflang="yue" data-title="模組:Math" data-language-autonym="粵語" data-language-local-name="ਕੈਂਟੋਨੀਜ਼" class="interlanguage-link-target">粵語</a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Module:Math" title="Module:Math – ਜ਼ੁਲੂ" lang="zu" hreflang="zu" data-title="Module:Math" data-language-autonym="IsiZulu" 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class="mw-list-item"><a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math&action=info" title="More information about this page">ਸਫ਼ਾ ਜਾਣਕਾਰੀ</a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:UrlShortener&url=https%3A%2F%2Fpa.wikipedia.org%2Fwiki%2F%25E0%25A8%25AE%25E0%25A9%258C%25E0%25A8%25A1%25E0%25A8%25BF%25E0%25A8%258A%25E0%25A8%25B2%3AMath">ਛੋਟਾ ਯੂਆਰਐੱਲ ਪ੍ਰਾਪਤ ਕਰੋ</a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:QrCode&url=https%3A%2F%2Fpa.wikipedia.org%2Fwiki%2F%25E0%25A8%25AE%25E0%25A9%258C%25E0%25A8%25A1%25E0%25A8%25BF%25E0%25A8%258A%25E0%25A8%25B2%3AMath">QR ਕੋਡ ਡਾਊਨਲੋਡ ਕਰੋ</a></li><li id="t-shorturl" class="mw-list-item"><a href="//pa.wikipedia.org/s/pov" title="ਸਾਂਝਾ ਕਰਨ ਲਈ ਇਸ ਛੋਟੀ ਕੜੀ ਦੀ ਨਕਲ ਕਰੋ">ਛੋਟਾ ਯੂਆਰਐੱਲ</a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:DownloadAsPdf&page=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2%3AMath&action=show-download-screen">Download as PDF</a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="ਇਸ ਸਫ਼ੇ ਦਾ ਛਪਣਯੋਗ ਰੂਪ [p]" accesskey="p">ਛਪਣਯੋਗ ਸੰਸਕਰਣ</a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> ਹੋਰ ਪ੍ਰਾਜੈਕਟਾਂ ਵਿੱਚ </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/Module:Math" hreflang="en">ਵਿਕੀਮੀਡੀਆ ਕਾਮਨਜ਼</a></li><li class="wb-otherproject-link wb-otherproject-meta mw-list-item"><a href="https://meta.wikimedia.org/wiki/Module:Math" hreflang="en">ਮੈਟਾ-ਵਿਕੀ</a></li><li class="wb-otherproject-link wb-otherproject-outreach mw-list-item"><a href="https://outreach.wikimedia.org/wiki/Module:Math" hreflang="en">ਵਿਕੀਮੀਡੀਆ ਆਊਟਰੀਚ</a></li><li class="wb-otherproject-link wb-otherproject-species mw-list-item"><a href="https://species.wikimedia.org/wiki/Module:Math" hreflang="en">ਵਿਕੀਜਾਤੀਆਂ</a></li><li class="wb-otherproject-link wb-otherproject-wikidata mw-list-item"><a href="https://www.wikidata.org/wiki/Module:Math" hreflang="en">ਵਿਕੀਡਾਟਾ</a></li><li class="wb-otherproject-link wb-otherproject-wikimania mw-list-item"><a href="https://wikimania.wikimedia.org/wiki/Module:Math" hreflang="en">ਵਿਕੀਮੇਨੀਆ</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/Q7328853" title="ਡਾਟਾ ਭੰਡਾਰ ਦੀ ਸਮੱਗਰੀ ਨਾਲ ਕੜੀ ਜੋੜੋ [g]" accesskey="g">ਵਿਕੀਡਾਟਾ ਆਈਟਮ</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="ਸਫ਼ੇ ਦੇ ਸੰਦ"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="ਦਿੱਖ"> <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">ਦਿੱਖ</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ਸਾਈਡਬਾਰ 'ਤੇ ਜਾਓ</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ਲੁਕਾਓ</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">ਵਿਕੀਪੀਡੀਆ, ਇੱਕ ਆਜ਼ਾਦ ਵਿਸ਼ਵਕੋਸ਼ ਤੋਂ</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="pa" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r645774">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">formatting mathematical expressions, LATEX-style ਲਈ, ਦੇਖੋ <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Math" title="ਫਰਮਾ:Math">Template:Math</a>।</div> <style data-mw-deduplicate="TemplateStyles:r765560">.mw-parser-output .ombox{margin:4px 0;border-collapse:collapse;border:1px solid #a2a9b1;background-color:var(--background-color-neutral-subtle,#f8f9fa);box-sizing:border-box;color:var(--color-base,#202122)}.mw-parser-output .ombox.mbox-small{font-size:88%;line-height:1.25em}.mw-parser-output .ombox-speedy{border:2px solid #b32424;background-color:#fee7e6}.mw-parser-output .ombox-delete{border:2px solid #b32424}.mw-parser-output .ombox-content{border:1px solid #f28500}.mw-parser-output .ombox-style{border:1px solid #fc3}.mw-parser-output .ombox-move{border:1px solid #9932cc}.mw-parser-output .ombox-protection{border:2px solid #a2a9b1}.mw-parser-output .ombox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .ombox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .ombox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .ombox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ombox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .ombox{margin:4px 10%}.mw-parser-output .ombox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}body.skin--responsive .mw-parser-output table.ombox img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ombox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ombox-speedy{background-color:#310402}}</style><table class="plainlinks ombox ombox-content" role="presentation"><tbody><tr><td class="mbox-image"><img alt="Warning" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Ambox_warning_orange.svg/40px-Ambox_warning_orange.svg.png" decoding="async" width="40" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Ambox_warning_orange.svg/60px-Ambox_warning_orange.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Ambox_warning_orange.svg/80px-Ambox_warning_orange.svg.png 2x" data-file-width="378" data-file-height="326" /></td><td class="mbox-text">This Lua module is used on <a class="external text" href="https://linkcount.toolforge.org/index.php?project=pa.wikipedia.org&page=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2%3AMath">16,00,000+ pages, or roughly 894% of all pages</a>. To avoid major disruption and server load, any changes should be tested in the module's <a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/sandbox&action=edit&redlink=1" class="new" title="ਮੌਡਿਊਲ:Math/sandbox (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">/sandbox</a> or <a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/testcases&action=edit&redlink=1" class="new" title="ਮੌਡਿਊਲ:Math/testcases (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">/testcases</a> subpages, or in your own <a href="/wiki/%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Sandbox" title="ਮੌਡਿਊਲ:Sandbox">module sandbox</a>. The tested changes can be added to this page in a single edit. Consider discussing changes on the <a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2_%E0%A8%97%E0%A9%B1%E0%A8%B2-%E0%A8%AC%E0%A8%BE%E0%A8%A4:Math&action=edit&redlink=1" class="new" title="ਮੌਡਿਊਲ ਗੱਲ-ਬਾਤ:Math (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">talk page</a> before implementing them.</td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r765560"><table class="plainlinks ombox ombox-notice" role="presentation"><tbody><tr><td class="mbox-image"><img alt="Protected" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Full-protection-shackle.svg/40px-Full-protection-shackle.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Full-protection-shackle.svg/60px-Full-protection-shackle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Full-protection-shackle.svg/80px-Full-protection-shackle.svg.png 2x" data-file-width="512" data-file-height="512" /></td><td class="mbox-text">This module is <a href="/wiki/%E0%A8%B8%E0%A8%BC%E0%A9%8D%E0%A8%B0%E0%A9%87%E0%A8%A3%E0%A9%80:Modules_subject_to_page_protection" title="ਸ਼੍ਰੇਣੀ:Modules subject to page protection">subject to page protection</a>. It is a <a href="/w/index.php?title=%E0%A8%B5%E0%A8%BF%E0%A8%95%E0%A9%80%E0%A8%AA%E0%A9%80%E0%A8%A1%E0%A9%80%E0%A8%86:High-risk_templates&action=edit&redlink=1" class="new" title="ਵਿਕੀਪੀਡੀਆ:High-risk templates (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">highly visible module</a> in use by a very large number of pages, or is <a href="/wiki/%E0%A8%B5%E0%A8%BF%E0%A8%95%E0%A9%80%E0%A8%AA%E0%A9%80%E0%A8%A1%E0%A9%80%E0%A8%86:Substitution" title="ਵਿਕੀਪੀਡੀਆ:Substitution">substituted</a> very frequently. Because vandalism or mistakes would affect many pages, and even trivial editing might cause substantial load on the servers, it is <a href="/wiki/%E0%A8%B5%E0%A8%BF%E0%A8%95%E0%A9%80%E0%A8%AA%E0%A9%80%E0%A8%A1%E0%A9%80%E0%A8%86:Protection_policy" title="ਵਿਕੀਪੀਡੀਆ:Protection policy">protected</a> from editing.</td></tr></tbody></table> This module provides a number of mathematical functions. These functions can be used from #invoke or from other Lua modules. <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Use_from_other_Lua_modules">Use from other Lua modules</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-1" title="ਭਾਗ ਸੋਧ: Use from other Lua modules">ਸੋਧੋ</a>]</div> To use the module from normal wiki pages, no special preparation is needed. If you are using the module from another Lua module, first you need to load it, like this: <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>local mm = require('Module:Math') </pre></div> (The <code>mm</code> variable stands for Module Math; you can choose something more descriptive if you prefer.) Most functions in the module have a version for Lua and a version for #invoke. It is possible to use the #invoke functions from other Lua modules, but using the Lua functions has the advantage that you do not need to access a Lua <a href="https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#Frame_object" class="extiw" title="mw:Extension:Scribunto/Lua reference manual">frame object</a>. Lua functions are preceded by <code>_</code>, whereas #invoke functions are not. <div class="mw-heading mw-heading2"><h2 id="random">random</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-2" title="ਭਾਗ ਸੋਧ: random">ਸੋਧੋ</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r645774"><div role="note" class="hatnote navigation-not-searchable">ਇਹ ਵੀ ਦੇਖੋ: <a href="/wiki/%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Random" title="ਮੌਡਿਊਲ:Random">Module:Random</a></div> <pre>{{#invoke:math|random}} {{#invoke:math|random|max_value}} {{#invoke:math|random|min_value|max_value}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._random() mm._random(max_value) mm._random(min_value, max_value) </pre></div> Generates a random number. <ul><li>If no arguments are specified, the number produced is greater than or equal to 0 and less than 1.</li> <li>If one argument is provided, the number produced is an integer between 1 and that argument. The argument must be a positive integer.</li> <li>If two arguments are provided, the number produced is an integer between the first and second arguments. Both arguments must be integers, but can be negative.</li></ul> This function will not work properly for numbers less than −232 and greater than 232 − 1. If you need to use numbers outside of this range, it is recommended that you use <a href="/wiki/%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Random" title="ਮੌਡਿਊਲ:Random">Module:Random</a>. <div class="mw-heading mw-heading2"><h2 id="order">order</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-3" title="ਭਾਗ ਸੋਧ: order">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|order|n}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._order(n) </pre></div> Determines the <a href="/w/index.php?title=Order_of_magnitude&action=edit&redlink=1" class="new" title="Order of magnitude (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">order of magnitude</a> of a number. <div class="mw-heading mw-heading2"><h2 id="precision">precision</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-4" title="ਭਾਗ ਸੋਧ: precision">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|precision|n}} {{#invoke:math|precision|x=n}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._precision(number_string) </pre></div> Detemines the precision of a number. For example, for "4" it will return "0", for "4.567" it will return "3", and for "100" it will return "-2". The function attempts to parse the string representation of the number, and detects whether the number uses <a href="/w/index.php?title=Scientific_notation&action=edit&redlink=1" class="new" title="Scientific notation (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">E notation</a>. For this reason, when called from Lua, very large numbers or very precise numbers should be directly input as strings to get accurate results. If they are input as numbers, the Lua interpreter will change them to E notation and this function will return the precision of the E notation rather than that of the original number. This is not a problem when the number is called from #invoke, as all input from #invoke is in string format. <div class="mw-heading mw-heading2"><h2 id="max">max</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-5" title="ਭਾਗ ਸੋਧ: max">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|max|v1|v2|v3|...}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._max(v1, v2, v3, ...) </pre></div> Returns the maximum value from the values specified. Values that cannot be converted to numbers are ignored. <div class="mw-heading mw-heading2"><h2 id="median">median</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-6" title="ਭਾਗ ਸੋਧ: median">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|median|v1|v2|v3|...}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._median(v1, v2, v3, ...) </pre></div> Returns the <a href="/w/index.php?title=Median&action=edit&redlink=1" class="new" title="Median (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">median</a> value from the values specified. Values that cannot be converted to numbers are ignored. <div class="mw-heading mw-heading2"><h2 id="min">min</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-7" title="ਭਾਗ ਸੋਧ: min">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|min|v1|v2|v3|...}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._min(v1, v2, v3, ...) </pre></div> Returns the minimum value from the values specified. Values that cannot be converted to numbers are ignored. <div class="mw-heading mw-heading2"><h2 id="sum">sum</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-8" title="ਭਾਗ ਸੋਧ: sum">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|sum|v1|v2|v3|...}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._sum(v1, v2, v3, ...) </pre></div> Returns the sum of the values specified. Values that cannot be converted to numbers are ignored. <div class="mw-heading mw-heading2"><h2 id="average">average</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-9" title="ਭਾਗ ਸੋਧ: average">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|average|v1|v2|v3|...}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._average(v1, v2, v3, ...) </pre></div> Returns the average of the values specified. (More precisely, the value returned is the <a href="/w/index.php?title=Mean&action=edit&redlink=1" class="new" title="Mean (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">arithmetic mean</a>.) Values that cannot be converted to numbers are ignored. <div class="mw-heading mw-heading2"><h2 id="round">round</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-10" title="ਭਾਗ ਸੋਧ: round">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|round|value|precision}} {{#invoke:math|round|value=value|precision=precision}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._round(value, precision) </pre></div> <a href="/w/index.php?title=Rounding&action=edit&redlink=1" class="new" title="Rounding (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">Rounds</a> a number to the specified precision. Note: As of October 2019, there is a bug in the display of some rounded numbers. When trying to round a number that rounds to "n.0", like "1.02", to the nearest tenth of a digit (i.e. <code class="tpl-para" style="word-break:break-word;">|r=1</code>), this function should display "1.0", but it unexpectedly displays "1". Use the <code class="tpl-para" style="word-break:break-word;">|precision_format=</code> parameter instead. <div class="mw-heading mw-heading2"><h2 id="log10">log10</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-11" title="ਭਾਗ ਸੋਧ: log10">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math | log10 | x}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._log10(x) </pre></div> Returns <code>log10(x)</code>, the <a href="/w/index.php?title=Logarithm&action=edit&redlink=1" class="new" title="Logarithm (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">logarithm</a> of x using base 10. <div class="mw-heading mw-heading2"><h2 id="mod">mod</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-12" title="ਭਾਗ ਸੋਧ: mod">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|mod|x|y}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._mod(x, y) </pre></div> Gets <code>x</code> <a href="/w/index.php?title=Modulo_operation&action=edit&redlink=1" class="new" title="Modulo operation (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">modulo</a> <code>y</code>, or the remainder after <code>x</code> has been divided by <code>y</code>. This is accurate for integers up to 253; for larger integers Lua's modulo operator may return an erroneous value. This function deals with this problem by returning <code>0</code> if the modulo given by Lua's modulo operator is less than 0 or greater than <code>y</code>. <div class="mw-heading mw-heading2"><h2 id="gcd">gcd</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-13" title="ਭਾਗ ਸੋਧ: gcd">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|gcd|v1|v2|...}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._gcd(v1, v2, ...) </pre></div> Finds the <a href="/w/index.php?title=Greatest_common_divisor&action=edit&redlink=1" class="new" title="Greatest common divisor (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">greatest common divisor</a> of the values specified. Values that cannot be converted to numbers are ignored. <div class="mw-heading mw-heading2"><h2 id="precision_format">precision_format</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-14" title="ਭਾਗ ਸੋਧ: precision_format">ਸੋਧੋ</a>]</div> <pre>{{#invoke:math|precision_format|value_string|precision}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._precision_format(value_string, precision) </pre></div> Rounds a number to the specified precision and formats according to rules originally used for {{<a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Rnd" class="mw-redirect" title="ਫਰਮਾ:Rnd">Rnd</a>}}. Output is a string. Parameter <var>precision</var> should be an integer number of digits after the decimal point. Negative values are permitted. Non-integers give unexpected results. Positive values greater than the input precision add zero-padding, negative values greater than the input order can consume all digits. Formatting 8,765.567 with <code>{{#invoke:Math|precision_format|8765.567|<var>precision</var>}}</code> gives: <table class="wikitable"> <caption> </caption> <tbody><tr> <th><code><var>precision</var></code></th> <th>Result </th></tr> <tr> <td style="text-align:right">2</td> <td>8,765.57 </td></tr> <tr> <td style="text-align:right">-2</td> <td>8,800 </td></tr> <tr> <td style="text-align:right">6</td> <td>8,765.567000 </td></tr> <tr> <td style="text-align:right">-6</td> <td>0 </td></tr> <tr> <td style="text-align:right">2.5</td> <td>8,765.5680426633 </td></tr> <tr> <td style="text-align:right">-2.5</td> <td>8,854.3774484715 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="divide">divide</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-15" title="ਭਾਗ ਸੋਧ: divide">ਸੋਧੋ</a>]</div> <pre>{{#invoke:Math|divide|x|y|round=|precision=}} </pre> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>mm._divide(x, y, round, precision) </pre></div> Divide x by y. <ul><li>If y if not a number, it is returned.</li> <li>Otherwise, if x is not a number, it is returned.</li> <li>If round is true ("yes" for #invoke), the result has no decimals</li> <li>Precision indicates how many digits of precision the result should have</li></ul> If any of the arguments contain HTML tags, they are returned unchanged, allowing any errors in calculating the arguments to the division function to be propagated to the calling template. <div class="mw-heading mw-heading2"><h2 id="cleanNumber">cleanNumber</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-16" title="ਭਾਗ ਸੋਧ: cleanNumber">ਸੋਧੋ</a>]</div> <div class="mw-highlight mw-highlight-lang-lua mw-content-ltr" dir="ltr"><pre>local number, number_string = mm._cleanNumber(number_string) </pre></div> A helper function that can be called from other Lua modules, but not from #invoke. This takes a string or a number value as input, and if the value can be converted to a number, cleanNumber returns the number and the number string. If the value cannot be converted to a number, cleanNumber returns <code>nil, nil</code>. <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:Math/doc&action=edit&section=T-17" title="ਭਾਗ ਸੋਧ: See also">ਸੋਧੋ</a>]</div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r627784">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul 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class="nv-talk"><a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE_%E0%A8%97%E0%A9%B1%E0%A8%B2-%E0%A8%AC%E0%A8%BE%E0%A8%A4:Math_templates&action=edit&redlink=1" class="new" title="ਫਰਮਾ ਗੱਲ-ਬਾਤ:Math templates (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:EditPage/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Math_templates" title="ਖ਼ਾਸ:EditPage/ਫਰਮਾ:Math templates"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Math_templates" style="font-size:114%;margin:0 4em">Math templates</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible autocollapse navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="FunctionsNumeral_systems" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li>Functions</li><li>Numeral systems</li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Functions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Elementary_arithmetic" title="ਫਰਮਾ:Elementary arithmetic">elementary arithmetic</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Precision" title="ਫਰਮਾ:Precision">precision</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Val" title="ਫਰਮਾ:Val">val</a> (value formatting)</li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Percentage" title="ਫਰਮਾ:Percentage">percentage</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Numeral systems</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>{{<a href="/wiki/%E0%A8%AE%E0%A9%8C%E0%A8%A1%E0%A8%BF%E0%A8%8A%E0%A8%B2:BaseConvert" title="ਮੌਡਿਊਲ:BaseConvert">#invoke:BaseConvert</a>|XtoY}}</li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Binary" title="ਫਰਮਾ:Binary">binary</a></li> <li><a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Decimal2Base&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Decimal2Base (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">decimal2Base</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Hex2dec" title="ਫਰਮਾ:Hex2dec">hex2dec</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Hexadecimal" title="ਫਰਮਾ:Hexadecimal">hexadecimal</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Octal" title="ਫਰਮਾ:Octal">octal</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Quaternary" title="ਫਰਮਾ:Quaternary">quaternary</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Quinary" title="ਫਰਮਾ:Quinary">quinary</a></li> <li><a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Rn&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Rn (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">rn</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Roman" title="ਫਰਮਾ:Roman">roman</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Senary" title="ਫਰਮਾ:Senary">senary</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Ternary" title="ਫਰਮਾ:Ternary">ternary</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Vigesimal" title="ਫਰਮਾ:Vigesimal">vigesimal</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible autocollapse navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="Conversions" style="font-size:114%;margin:0 4em">Conversions</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"><table style="margin:0 auto 0;text-align:left;"><tbody><tr style="vertical-align:top"><td> <table style="padding-right:2.5em;"><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Convert" title="ਫਰਮਾ:Convert">convert</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> many units (see: <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Convert/list_of_units" title="ਫਰਮਾ:Convert/list of units">list</a>)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Cvt" title="ਫਰਮਾ:Cvt">cvt</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> abbreviated {{<a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Convert" title="ਫਰਮਾ:Convert">convert</a>}}</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Convinfobox" title="ਫਰਮਾ:Convinfobox">convinfobox</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> {{<a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Convert" title="ਫਰਮਾ:Convert">convert</a>}} for infoboxes</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Bbl_to_t&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Bbl to t (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">bbl to t</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> barrels of oil to tonnes</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Long_ton&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Long ton (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">long ton</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> long hundredweights, quarters and pounds to kilograms; long tons and hundredweights to pounds and metric tons</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Miles-chains&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Miles-chains (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">miles-chains</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> miles and chains to kilometres linking "chains"</td></tr></tbody></table></td><td> <table><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Decdeg" title="ਫਰਮਾ:Decdeg">decdeg</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> degrees, minutes, and seconds to <a href="/w/index.php?title=Decimal_degrees&action=edit&redlink=1" class="new" title="Decimal degrees (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">decimal degrees</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Deg2DMS&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Deg2DMS (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">deg2dms</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> decimal degrees to degrees, minutes, and seconds</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Deg2HMS&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Deg2HMS (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">deg2hms</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> decimal degrees to <a href="/w/index.php?title=Hour_angle&action=edit&redlink=1" class="new" title="Hour angle (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">hour angle</a> (in hours, minutes, and seconds)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:HMS2Deg&action=edit&redlink=1" class="new" title="ਫਰਮਾ:HMS2Deg (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">hms2deg</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/w/index.php?title=Hour_angle&action=edit&redlink=1" class="new" title="Hour angle (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">hour angle</a> (in hours, minutes, and seconds) to decimal degrees</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Inflation" title="ਫਰਮਾ:Inflation">inflation</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> calculate inflation of Consumer Price Index-related prices</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Pop_density" title="ਫਰਮਾ:Pop density">pop density</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> population density in an area</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Track_gauge" title="ਫਰਮਾ:Track gauge">track gauge</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> railway track gauges</td></tr></tbody></table></td></tr></tbody></table></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible autocollapse navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="Notation_and_formatting" style="font-size:114%;margin:0 4em">Notation and <a href="/w/index.php?title=%E0%A8%B8%E0%A8%BC%E0%A9%8D%E0%A8%B0%E0%A9%87%E0%A8%A3%E0%A9%80:Mathematical_formatting_templates&action=edit&redlink=1" class="new" title="ਸ਼੍ਰੇਣੀ:Mathematical formatting templates (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">formatting</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"><table style="margin:0 auto 0;text-align:left;"><tbody><tr style="vertical-align:top"><td> <table style="padding-right:2.5em;"><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Bigmath" title="ਫਰਮਾ:Bigmath">bigmath</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> bigger font to match <a href="/w/index.php?title=TeX&action=edit&redlink=1" class="new" title="TeX (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">TeX</a> <samp>\displaystyle</samp> (standalone formulas only)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <div class="hlist"><ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Bra-ket" title="ਫਰਮਾ:Bra-ket">bra-ket</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Braket" title="ਫਰਮਾ:Braket">braket</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Bra" title="ਫਰਮਾ:Bra">bra</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Ket" title="ਫਰਮਾ:Ket">ket</a></li></ul></div></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/w/index.php?title=Bra%E2%80%93ket_notation&action=edit&redlink=1" class="new" title="Bra–ket notation (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">bra–ket notation</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Ceil" title="ਫਰਮਾ:Ceil">ceil</a>, <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Floor" title="ਫਰਮਾ:Floor">floor</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> calculations <a href="https://www.mediawiki.org/wiki/Help:Extension:ParserFunctions##expr" class="extiw" title="mw:Help:Extension:ParserFunctions">:mw:Help:#expr</a>; formatting indicators ⌈3.14⌉, ⌊3.14⌋ (no calculation performed)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Fraction" title="ਫਰਮਾ:Fraction">fraction</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> slant fractions  3⁄5 (not for maths/science articles; use standing or upright fractions <code>{{<a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Sfrac" title="ਫਰਮਾ:Sfrac">sfrac</a>}}</code> instead)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Intmath" title="ਫਰਮਾ:Intmath">intmath</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/w/index.php?title=Integral_symbol&action=edit&redlink=1" class="new" title="Integral symbol (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">integral symbols</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <div class="hlist"><ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Langle" title="ਫਰਮਾ:Langle">langle</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Rangle" title="ਫਰਮਾ:Rangle">rangle</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Angle_bracket" title="ਫਰਮਾ:Angle bracket">angbr</a></li></ul></div></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> <a href="/w/index.php?title=Bracket&action=edit&redlink=1" class="new" title="Bracket (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">angular brackets</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <div class="hlist"><ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Ldelim" title="ਫਰਮਾ:Ldelim">ldelim</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Rdelim" title="ਫਰਮਾ:Rdelim">rdelim</a></li></ul></div></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> multiline delimiters (2–5 lines inclusive)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Abs" title="ਫਰਮਾ:Abs">abs</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> absolute values (paired vertical lines)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Math" title="ਫਰਮਾ:Math">math</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> short text-based formulas</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Mathcal" title="ਫਰਮਾ:Mathcal">mathcal</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> [mathematical] calligraphic font; alternative to <a href="/w/index.php?title=LaTeX&action=edit&redlink=1" class="new" title="LaTeX (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">LaTeX</a> <samp>\mathcal{...}</samp></td></tr></tbody></table></td><td> <table><tbody><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Mvar" title="ਫਰਮਾ:Mvar">mvar</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> individual italicized maths variables in normal text</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <div class="hlist"><ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Overline" title="ਫਰਮਾ:Overline">overline</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Underline" title="ਫਰਮਾ:Underline">underline</a></li></ul></div></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> a line set above/below a sequence of characters</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Overarc&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Overarc (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">overarc</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> an arc set above a sequence of characters</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <div class="hlist"><ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Overset" title="ਫਰਮਾ:Overset">overset</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Underset" title="ਫਰਮਾ:Underset">underset</a></li></ul></div></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> arbitrary characters/diacritics set above/below one another</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Pars" title="ਫਰਮਾ:Pars">pars</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> parentheses that can be resized (∑)</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Sfrac" title="ਫਰਮਾ:Sfrac">sfrac</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> "standing" or upright fractions 3/5 (use in maths/science articles instead of<code>{{<a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Fraction" title="ਫਰਮਾ:Fraction">fraction</a>}}</code>)</td></tr><tr style="vertical-align:top"><td style="vertical-align:middle;text-align:right;padding-right:1.0em;"> <div class="hlist"><ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Sub" title="ਫਰਮਾ:Sub">sub</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Sup" title="ਫਰਮਾ:Sup">sup</a></li><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Su" title="ਫਰਮਾ:Su">su</a></li></ul></div></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> subscripts and superscripts</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Tmath" title="ਫਰਮਾ:Tmath">tmath</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> Wrap <a href="/w/index.php?title=TeX&action=edit&redlink=1" class="new" title="TeX (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">TeX</a> in <math> tags</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Tombstone&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Tombstone (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">tombstone</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> symbol indicating the <a href="/w/index.php?title=Tombstone_(typography)&action=edit&redlink=1" class="new" title="Tombstone (typography) (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">end of a proof</a></td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Val" title="ਫਰਮਾ:Val">val</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> measurement values, uncertainties and units</td></tr><tr style="vertical-align:top"><td style="text-align:right;white-space:nowrap;padding-right:1.0em;"> <a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Vec" title="ਫਰਮਾ:Vec">vec</a></td><td style="font-size:90%; vertical-align:middle;line-height:1.3em;font-style:italic;"> various overarrows, underarrows, etc.</td></tr></tbody></table></td></tr></tbody></table></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible autocollapse navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="BoxesTagsNotices" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li>Boxes</li><li>Tags</li><li>Notices</li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;font-size:110%;"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;background:transparent;color:inherit;"><div style="padding:0px;"><table class="navbox-columns-table" style="border-spacing: 0px; text-align:left;width:100%;"><tbody><tr><td class="navbox-abovebelow" colspan="1" style="font-weight:bold;">Boxes</td><td class="navbox-abovebelow" colspan="1" style="border-left:2px solid #fdfdfd;font-weight:bold;">Tags</td></tr><tr style="vertical-align:top;"><td class="navbox-list" style="padding:0px;text-align:center;;;;width:10em;"><div> <div class="hlist hlist-separated"> <ul><li><a href="/w/index.php?title=%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Arithmetic_operations&action=edit&redlink=1" class="new" title="ਫਰਮਾ:Arithmetic operations (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">arithmetic operations</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Calculus" class="mw-redirect" title="ਫਰਮਾ:Calculus">calculus</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Infobox_mathematical_function" title="ਫਰਮਾ:Infobox mathematical function">Infobox mathematical function</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Functions" title="ਫਰਮਾ:Functions">functions</a></li></ul> </div> </div></td><td class="navbox-list" style="border-left:2px solid #fdfdfd;padding:0px;text-align:center;;;;width:10em;"><div> <div class="hlist hlist-separated"> <ul><li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Metricate" title="ਫਰਮਾ:Metricate">metricate</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Undue_precision" title="ਫਰਮਾ:Undue precision">undue precision</a></li> <li><a href="/wiki/%E0%A8%AB%E0%A8%B0%E0%A8%AE%E0%A8%BE:Units_attention" title="ਫਰਮਾ:Units attention">units attention</a></li></ul> </div> </div></td></tr></tbody></table></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/w/index.php?title=%E0%A8%B8%E0%A8%BC%E0%A9%8D%E0%A8%B0%E0%A9%87%E0%A8%A3%E0%A9%80:Mathematics_templates&action=edit&redlink=1" class="new" title="ਸ਼੍ਰੇਣੀ:Mathematics templates (ਸਫ਼ਾ ਮੌਜੂਦ ਨਹੀਂ ਹੈ)">Category</a> · <a class="mw-selflink selflink">Module:Math</a></div></td></tr></tbody></table></div> <hr /><div class="mw-highlight mw-highlight-lang-lua mw-content-ltr mw-highlight-lines" dir="ltr"><pre><a href="#L-1"></a>--[[ <a href="#L-2"></a> <a href="#L-3"></a>This module provides a number of basic mathematical operations. <a href="#L-4"></a> <a href="#L-5"></a>]] <a href="#L-6"></a> <a href="#L-7"></a>local yesno, getArgs -- lazily initialized <a href="#L-8"></a> <a href="#L-9"></a>local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules. <a href="#L-10"></a>local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua. <a href="#L-11"></a> <a href="#L-12"></a>--[[ <a href="#L-13"></a>Helper functions used to avoid redundant code. <a href="#L-14"></a>]] <a href="#L-15"></a> <a href="#L-16"></a>local function err(msg) <a href="#L-17"></a> -- Generates wikitext error messages. <a href="#L-18"></a> return mw.ustring.format('Formatting error: %s', msg) <a href="#L-19"></a>end <a href="#L-20"></a> <a href="#L-21"></a>local function unpackNumberArgs(args) <a href="#L-22"></a> -- Returns an unpacked list of arguments specified with numerical keys. <a href="#L-23"></a> local ret = {} <a href="#L-24"></a> for k, v in pairs(args) do <a href="#L-25"></a> if type(k) == 'number' then <a href="#L-26"></a> table.insert(ret, v) <a href="#L-27"></a> end <a href="#L-28"></a> end <a href="#L-29"></a> return unpack(ret) <a href="#L-30"></a>end <a href="#L-31"></a> <a href="#L-32"></a>local function makeArgArray(...) <a href="#L-33"></a> -- Makes an array of arguments from a list of arguments that might include nils. <a href="#L-34"></a> local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs. <a href="#L-35"></a> local nums = {} -- Stores the numbers of valid numerical arguments. <a href="#L-36"></a> local ret = {} <a href="#L-37"></a> for k, v in pairs(args) do <a href="#L-38"></a> v = p._cleanNumber(v) <a href="#L-39"></a> if v then <a href="#L-40"></a> nums[#nums + 1] = k <a href="#L-41"></a> args[k] = v <a href="#L-42"></a> end <a href="#L-43"></a> end <a href="#L-44"></a> table.sort(nums) <a href="#L-45"></a> for i, num in ipairs(nums) do <a href="#L-46"></a> ret[#ret + 1] = args[num] <a href="#L-47"></a> end <a href="#L-48"></a> return ret <a href="#L-49"></a>end <a href="#L-50"></a> <a href="#L-51"></a>local function fold(func, ...) <a href="#L-52"></a> -- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters, <a href="#L-53"></a> -- and must return a number as an output. This number is then supplied as input to the next function call. <a href="#L-54"></a> local vals = makeArgArray(...) <a href="#L-55"></a> local count = #vals -- The number of valid arguments <a href="#L-56"></a> if count == 0 then return <a href="#L-57"></a> -- Exit if we have no valid args, otherwise removing the first arg would cause an error. <a href="#L-58"></a> nil, 0 <a href="#L-59"></a> end <a href="#L-60"></a> local ret = table.remove(vals, 1) <a href="#L-61"></a> for _, val in ipairs(vals) do <a href="#L-62"></a> ret = func(ret, val) <a href="#L-63"></a> end <a href="#L-64"></a> return ret, count <a href="#L-65"></a>end <a href="#L-66"></a> <a href="#L-67"></a>--[[ <a href="#L-68"></a>Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value). <a href="#L-69"></a>]] <a href="#L-70"></a>local function binary_fold(func, ...) <a href="#L-71"></a> local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...) <a href="#L-72"></a> return value <a href="#L-73"></a>end <a href="#L-74"></a> <a href="#L-75"></a>--[[ <a href="#L-76"></a>random <a href="#L-77"></a> <a href="#L-78"></a>Generate a random number <a href="#L-79"></a> <a href="#L-80"></a>Usage: <a href="#L-81"></a>{{#invoke: Math | random }} <a href="#L-82"></a>{{#invoke: Math | random | maximum value }} <a href="#L-83"></a>{{#invoke: Math | random | minimum value | maximum value }} <a href="#L-84"></a>]] <a href="#L-85"></a> <a href="#L-86"></a>function wrap.random(args) <a href="#L-87"></a> local first = p._cleanNumber(args[1]) <a href="#L-88"></a> local second = p._cleanNumber(args[2]) <a href="#L-89"></a> return p._random(first, second) <a href="#L-90"></a>end <a href="#L-91"></a> <a href="#L-92"></a>function p._random(first, second) <a href="#L-93"></a> math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000)) <a href="#L-94"></a> -- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params. <a href="#L-95"></a> if first and second then <a href="#L-96"></a> if first <= second then -- math.random doesn't allow the first number to be greater than the second. <a href="#L-97"></a> return math.random(first, second) <a href="#L-98"></a> end <a href="#L-99"></a> elseif first then <a href="#L-100"></a> return math.random(first) <a href="#L-101"></a> else <a href="#L-102"></a> return math.random() <a href="#L-103"></a> end <a href="#L-104"></a>end <a href="#L-105"></a> <a href="#L-106"></a>--[[ <a href="#L-107"></a>order <a href="#L-108"></a> <a href="#L-109"></a>Determine order of magnitude of a number <a href="#L-110"></a> <a href="#L-111"></a>Usage: <a href="#L-112"></a>{{#invoke: Math | order | value }} <a href="#L-113"></a>]] <a href="#L-114"></a> <a href="#L-115"></a>function wrap.order(args) <a href="#L-116"></a> local input_string = (args[1] or args.x or '0'); <a href="#L-117"></a> local input_number = p._cleanNumber(input_string); <a href="#L-118"></a> if input_number == nil then <a href="#L-119"></a> return err('order of magnitude input appears non-numeric') <a href="#L-120"></a> else <a href="#L-121"></a> return p._order(input_number) <a href="#L-122"></a> end <a href="#L-123"></a>end <a href="#L-124"></a> <a href="#L-125"></a>function p._order(x) <a href="#L-126"></a> if x == 0 then return 0 end <a href="#L-127"></a> return math.floor(math.log10(math.abs(x))) <a href="#L-128"></a>end <a href="#L-129"></a> <a href="#L-130"></a>--[[ <a href="#L-131"></a>precision <a href="#L-132"></a> <a href="#L-133"></a>Detemines the precision of a number using the string representation <a href="#L-134"></a> <a href="#L-135"></a>Usage: <a href="#L-136"></a>{{ #invoke: Math | precision | value }} <a href="#L-137"></a>]] <a href="#L-138"></a> <a href="#L-139"></a>function wrap.precision(args) <a href="#L-140"></a> local input_string = (args[1] or args.x or '0'); <a href="#L-141"></a> local trap_fraction = args.check_fraction; <a href="#L-142"></a> local input_number; <a href="#L-143"></a> <a href="#L-144"></a> if not yesno then <a href="#L-145"></a> yesno = require('Module:Yesno') <a href="#L-146"></a> end <a href="#L-147"></a> if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]]. <a href="#L-148"></a> local pos = string.find(input_string, '/', 1, true); <a href="#L-149"></a> if pos ~= nil then <a href="#L-150"></a> if string.find(input_string, '/', pos + 1, true) == nil then <a href="#L-151"></a> local denominator = string.sub(input_string, pos+1, -1); <a href="#L-152"></a> local denom_value = tonumber(denominator); <a href="#L-153"></a> if denom_value ~= nil then <a href="#L-154"></a> return math.log10(denom_value); <a href="#L-155"></a> end <a href="#L-156"></a> end <a href="#L-157"></a> end <a href="#L-158"></a> end <a href="#L-159"></a> <a href="#L-160"></a> input_number, input_string = p._cleanNumber(input_string); <a href="#L-161"></a> if input_string == nil then <a href="#L-162"></a> return err('precision input appears non-numeric') <a href="#L-163"></a> else <a href="#L-164"></a> return p._precision(input_string) <a href="#L-165"></a> end <a href="#L-166"></a>end <a href="#L-167"></a> <a href="#L-168"></a>function p._precision(x) <a href="#L-169"></a> if type(x) == 'number' then <a href="#L-170"></a> x = tostring(x) <a href="#L-171"></a> end <a href="#L-172"></a> x = string.upper(x) <a href="#L-173"></a> <a href="#L-174"></a> local decimal = x:find('%.') <a href="#L-175"></a> local exponent_pos = x:find('E') <a href="#L-176"></a> local result = 0; <a href="#L-177"></a> <a href="#L-178"></a> if exponent_pos ~= nil then <a href="#L-179"></a> local exponent = string.sub(x, exponent_pos + 1) <a href="#L-180"></a> x = string.sub(x, 1, exponent_pos - 1) <a href="#L-181"></a> result = result - tonumber(exponent) <a href="#L-182"></a> end <a href="#L-183"></a> <a href="#L-184"></a> if decimal ~= nil then <a href="#L-185"></a> result = result + string.len(x) - decimal <a href="#L-186"></a> return result <a href="#L-187"></a> end <a href="#L-188"></a> <a href="#L-189"></a> local pos = string.len(x); <a href="#L-190"></a> while x:byte(pos) == string.byte('0') do <a href="#L-191"></a> pos = pos - 1 <a href="#L-192"></a> result = result - 1 <a href="#L-193"></a> if pos <= 0 then <a href="#L-194"></a> return 0 <a href="#L-195"></a> end <a href="#L-196"></a> end <a href="#L-197"></a> <a href="#L-198"></a> return result <a href="#L-199"></a>end <a href="#L-200"></a> <a href="#L-201"></a> <a href="#L-202"></a>--[[ <a href="#L-203"></a>max <a href="#L-204"></a> <a href="#L-205"></a>Finds the maximum argument <a href="#L-206"></a> <a href="#L-207"></a>Usage: <a href="#L-208"></a>{{#invoke:Math| max | value1 | value2 | ... }} <a href="#L-209"></a> <a href="#L-210"></a>Note, any values that do not evaluate to numbers are ignored. <a href="#L-211"></a>]] <a href="#L-212"></a> <a href="#L-213"></a>function wrap.max(args) <a href="#L-214"></a> return p._max(unpackNumberArgs(args)) <a href="#L-215"></a>end <a href="#L-216"></a> <a href="#L-217"></a>function p._max(...) <a href="#L-218"></a> local max_value = binary_fold((function(a, b) return a > b end), ...) <a href="#L-219"></a> if max_value then <a href="#L-220"></a> return max_value <a href="#L-221"></a> end <a href="#L-222"></a>end <a href="#L-223"></a> <a href="#L-224"></a>--[[ <a href="#L-225"></a>median <a href="#L-226"></a> <a href="#L-227"></a>Find the median of set of numbers <a href="#L-228"></a> <a href="#L-229"></a>Usage: <a href="#L-230"></a>{{#invoke:Math | median | number1 | number2 | ...}} <a href="#L-231"></a>OR <a href="#L-232"></a>{{#invoke:Math | median }} <a href="#L-233"></a>]] <a href="#L-234"></a> <a href="#L-235"></a>function wrap.median(args) <a href="#L-236"></a> return p._median(unpackNumberArgs(args)) <a href="#L-237"></a>end <a href="#L-238"></a> <a href="#L-239"></a>function p._median(...) <a href="#L-240"></a> local vals = makeArgArray(...) <a href="#L-241"></a> local count = #vals <a href="#L-242"></a> table.sort(vals) <a href="#L-243"></a> <a href="#L-244"></a> if count == 0 then <a href="#L-245"></a> return 0 <a href="#L-246"></a> end <a href="#L-247"></a> <a href="#L-248"></a> if p._mod(count, 2) == 0 then <a href="#L-249"></a> return (vals[count/2] + vals[count/2+1])/2 <a href="#L-250"></a> else <a href="#L-251"></a> return vals[math.ceil(count/2)] <a href="#L-252"></a> end <a href="#L-253"></a>end <a href="#L-254"></a> <a href="#L-255"></a>--[[ <a href="#L-256"></a>min <a href="#L-257"></a> <a href="#L-258"></a>Finds the minimum argument <a href="#L-259"></a> <a href="#L-260"></a>Usage: <a href="#L-261"></a>{{#invoke:Math| min | value1 | value2 | ... }} <a href="#L-262"></a>OR <a href="#L-263"></a>{{#invoke:Math| min }} <a href="#L-264"></a> <a href="#L-265"></a>When used with no arguments, it takes its input from the parent <a href="#L-266"></a>frame. Note, any values that do not evaluate to numbers are ignored. <a href="#L-267"></a>]] <a href="#L-268"></a> <a href="#L-269"></a>function wrap.min(args) <a href="#L-270"></a> return p._min(unpackNumberArgs(args)) <a href="#L-271"></a>end <a href="#L-272"></a> <a href="#L-273"></a>function p._min(...) <a href="#L-274"></a> local min_value = binary_fold((function(a, b) return a < b end), ...) <a href="#L-275"></a> if min_value then <a href="#L-276"></a> return min_value <a href="#L-277"></a> end <a href="#L-278"></a>end <a href="#L-279"></a> <a href="#L-280"></a>--[[ <a href="#L-281"></a>sum <a href="#L-282"></a> <a href="#L-283"></a>Finds the sum <a href="#L-284"></a> <a href="#L-285"></a>Usage: <a href="#L-286"></a>{{#invoke:Math| sum | value1 | value2 | ... }} <a href="#L-287"></a>OR <a href="#L-288"></a>{{#invoke:Math| sum }} <a href="#L-289"></a> <a href="#L-290"></a>Note, any values that do not evaluate to numbers are ignored. <a href="#L-291"></a>]] <a href="#L-292"></a> <a href="#L-293"></a>function wrap.sum(args) <a href="#L-294"></a> return p._sum(unpackNumberArgs(args)) <a href="#L-295"></a>end <a href="#L-296"></a> <a href="#L-297"></a>function p._sum(...) <a href="#L-298"></a> local sums, count = fold((function(a, b) return a + b end), ...) <a href="#L-299"></a> if not sums then <a href="#L-300"></a> return 0 <a href="#L-301"></a> else <a href="#L-302"></a> return sums <a href="#L-303"></a> end <a href="#L-304"></a>end <a href="#L-305"></a> <a href="#L-306"></a>--[[ <a href="#L-307"></a>average <a href="#L-308"></a> <a href="#L-309"></a>Finds the average <a href="#L-310"></a> <a href="#L-311"></a>Usage: <a href="#L-312"></a>{{#invoke:Math| average | value1 | value2 | ... }} <a href="#L-313"></a>OR <a href="#L-314"></a>{{#invoke:Math| average }} <a href="#L-315"></a> <a href="#L-316"></a>Note, any values that do not evaluate to numbers are ignored. <a href="#L-317"></a>]] <a href="#L-318"></a> <a href="#L-319"></a>function wrap.average(args) <a href="#L-320"></a> return p._average(unpackNumberArgs(args)) <a href="#L-321"></a>end <a href="#L-322"></a> <a href="#L-323"></a>function p._average(...) <a href="#L-324"></a> local sum, count = fold((function(a, b) return a + b end), ...) <a href="#L-325"></a> if not sum then <a href="#L-326"></a> return 0 <a href="#L-327"></a> else <a href="#L-328"></a> return sum / count <a href="#L-329"></a> end <a href="#L-330"></a>end <a href="#L-331"></a> <a href="#L-332"></a>--[[ <a href="#L-333"></a>round <a href="#L-334"></a> <a href="#L-335"></a>Rounds a number to specified precision <a href="#L-336"></a> <a href="#L-337"></a>Usage: <a href="#L-338"></a>{{#invoke:Math | round | value | precision }} <a href="#L-339"></a> <a href="#L-340"></a>--]] <a href="#L-341"></a> <a href="#L-342"></a>function wrap.round(args) <a href="#L-343"></a> local value = p._cleanNumber(args[1] or args.value or 0) <a href="#L-344"></a> local precision = p._cleanNumber(args[2] or args.precision or 0) <a href="#L-345"></a> if value == nil or precision == nil then <a href="#L-346"></a> return err('round input appears non-numeric') <a href="#L-347"></a> else <a href="#L-348"></a> return p._round(value, precision) <a href="#L-349"></a> end <a href="#L-350"></a>end <a href="#L-351"></a> <a href="#L-352"></a>function p._round(value, precision) <a href="#L-353"></a> local rescale = math.pow(10, precision or 0); <a href="#L-354"></a> return math.floor(value * rescale + 0.5) / rescale; <a href="#L-355"></a>end <a href="#L-356"></a> <a href="#L-357"></a>--[[ <a href="#L-358"></a>log10 <a href="#L-359"></a> <a href="#L-360"></a>returns the log (base 10) of a number <a href="#L-361"></a> <a href="#L-362"></a>Usage: <a href="#L-363"></a>{{#invoke:Math | log10 | x }} <a href="#L-364"></a>]] <a href="#L-365"></a> <a href="#L-366"></a>function wrap.log10(args) <a href="#L-367"></a> return math.log10(args[1]) <a href="#L-368"></a>end <a href="#L-369"></a> <a href="#L-370"></a>--[[ <a href="#L-371"></a>mod <a href="#L-372"></a> <a href="#L-373"></a>Implements the modulo operator <a href="#L-374"></a> <a href="#L-375"></a>Usage: <a href="#L-376"></a>{{#invoke:Math | mod | x | y }} <a href="#L-377"></a> <a href="#L-378"></a>--]] <a href="#L-379"></a> <a href="#L-380"></a>function wrap.mod(args) <a href="#L-381"></a> local x = p._cleanNumber(args[1]) <a href="#L-382"></a> local y = p._cleanNumber(args[2]) <a href="#L-383"></a> if not x then <a href="#L-384"></a> return err('first argument to mod appears non-numeric') <a href="#L-385"></a> elseif not y then <a href="#L-386"></a> return err('second argument to mod appears non-numeric') <a href="#L-387"></a> else <a href="#L-388"></a> return p._mod(x, y) <a href="#L-389"></a> end <a href="#L-390"></a>end <a href="#L-391"></a> <a href="#L-392"></a>function p._mod(x, y) <a href="#L-393"></a> local ret = x % y <a href="#L-394"></a> if not (0 <= ret and ret < y) then <a href="#L-395"></a> ret = 0 <a href="#L-396"></a> end <a href="#L-397"></a> return ret <a href="#L-398"></a>end <a href="#L-399"></a> <a href="#L-400"></a>--[[ <a href="#L-401"></a>gcd <a href="#L-402"></a> <a href="#L-403"></a>Calculates the greatest common divisor of multiple numbers <a href="#L-404"></a> <a href="#L-405"></a>Usage: <a href="#L-406"></a>{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }} <a href="#L-407"></a>--]] <a href="#L-408"></a> <a href="#L-409"></a>function wrap.gcd(args) <a href="#L-410"></a> return p._gcd(unpackNumberArgs(args)) <a href="#L-411"></a>end <a href="#L-412"></a> <a href="#L-413"></a>function p._gcd(...) <a href="#L-414"></a> local function findGcd(a, b) <a href="#L-415"></a> local r = b <a href="#L-416"></a> local oldr = a <a href="#L-417"></a> while r ~= 0 do <a href="#L-418"></a> local quotient = math.floor(oldr / r) <a href="#L-419"></a> oldr, r = r, oldr - quotient * r <a href="#L-420"></a> end <a href="#L-421"></a> if oldr < 0 then <a href="#L-422"></a> oldr = oldr * -1 <a href="#L-423"></a> end <a href="#L-424"></a> return oldr <a href="#L-425"></a> end <a href="#L-426"></a> local result, count = fold(findGcd, ...) <a href="#L-427"></a> return result <a href="#L-428"></a>end <a href="#L-429"></a> <a href="#L-430"></a>--[[ <a href="#L-431"></a>precision_format <a href="#L-432"></a> <a href="#L-433"></a>Rounds a number to the specified precision and formats according to rules <a href="#L-434"></a>originally used for {{template:Rnd}}. Output is a string. <a href="#L-435"></a> <a href="#L-436"></a>Usage: <a href="#L-437"></a>{{#invoke: Math | precision_format | number | precision }} <a href="#L-438"></a>]] <a href="#L-439"></a> <a href="#L-440"></a>function wrap.precision_format(args) <a href="#L-441"></a> local value_string = args[1] or 0 <a href="#L-442"></a> local precision = args[2] or 0 <a href="#L-443"></a> return p._precision_format(value_string, precision) <a href="#L-444"></a>end <a href="#L-445"></a> <a href="#L-446"></a>function p._precision_format(value_string, precision) <a href="#L-447"></a> -- For access to Mediawiki built-in formatter. <a href="#L-448"></a> local lang = mw.getContentLanguage(); <a href="#L-449"></a> <a href="#L-450"></a> local value <a href="#L-451"></a> value, value_string = p._cleanNumber(value_string) <a href="#L-452"></a> precision = p._cleanNumber(precision) <a href="#L-453"></a> <a href="#L-454"></a> -- Check for non-numeric input <a href="#L-455"></a> if value == nil or precision == nil then <a href="#L-456"></a> return err('invalid input when rounding') <a href="#L-457"></a> end <a href="#L-458"></a> <a href="#L-459"></a> local current_precision = p._precision(value) <a href="#L-460"></a> local order = p._order(value) <a href="#L-461"></a> <a href="#L-462"></a> -- Due to round-off effects it is neccesary to limit the returned precision under <a href="#L-463"></a> -- some circumstances because the terminal digits will be inaccurately reported. <a href="#L-464"></a> if order + precision >= 14 then <a href="#L-465"></a> if order + p._precision(value_string) >= 14 then <a href="#L-466"></a> precision = 13 - order; <a href="#L-467"></a> end <a href="#L-468"></a> end <a href="#L-469"></a> <a href="#L-470"></a> -- If rounding off, truncate extra digits <a href="#L-471"></a> if precision < current_precision then <a href="#L-472"></a> value = p._round(value, precision) <a href="#L-473"></a> current_precision = p._precision(value) <a href="#L-474"></a> end <a href="#L-475"></a> <a href="#L-476"></a> local formatted_num = lang:formatNum(math.abs(value)) <a href="#L-477"></a> local sign <a href="#L-478"></a> <a href="#L-479"></a> -- Use proper unary minus sign rather than ASCII default <a href="#L-480"></a> if value < 0 then <a href="#L-481"></a> sign = '−' <a href="#L-482"></a> else <a href="#L-483"></a> sign = '' <a href="#L-484"></a> end <a href="#L-485"></a> <a href="#L-486"></a> -- Handle cases requiring scientific notation <a href="#L-487"></a> if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then <a href="#L-488"></a> value = value * math.pow(10, -order) <a href="#L-489"></a> current_precision = current_precision + order <a href="#L-490"></a> precision = precision + order <a href="#L-491"></a> formatted_num = lang:formatNum(math.abs(value)) <a href="#L-492"></a> else <a href="#L-493"></a> order = 0; <a href="#L-494"></a> end <a href="#L-495"></a> formatted_num = sign .. formatted_num <a href="#L-496"></a> <a href="#L-497"></a> -- Pad with zeros, if needed <a href="#L-498"></a> if current_precision < precision then <a href="#L-499"></a> local padding <a href="#L-500"></a> if current_precision <= 0 then <a href="#L-501"></a> if precision > 0 then <a href="#L-502"></a> local zero_sep = lang:formatNum(1.1) <a href="#L-503"></a> formatted_num = formatted_num .. zero_sep:sub(2,2) <a href="#L-504"></a> <a href="#L-505"></a> padding = precision <a href="#L-506"></a> if padding > 20 then <a href="#L-507"></a> padding = 20 <a href="#L-508"></a> end <a href="#L-509"></a> <a href="#L-510"></a> formatted_num = formatted_num .. string.rep('0', padding) <a href="#L-511"></a> end <a href="#L-512"></a> else <a href="#L-513"></a> padding = precision - current_precision <a href="#L-514"></a> if padding > 20 then <a href="#L-515"></a> padding = 20 <a href="#L-516"></a> end <a href="#L-517"></a> formatted_num = formatted_num .. string.rep('0', padding) <a href="#L-518"></a> end <a href="#L-519"></a> end <a href="#L-520"></a> <a href="#L-521"></a> -- Add exponential notation, if necessary. <a href="#L-522"></a> if order ~= 0 then <a href="#L-523"></a> -- Use proper unary minus sign rather than ASCII default <a href="#L-524"></a> if order < 0 then <a href="#L-525"></a> order = '−' .. lang:formatNum(math.abs(order)) <a href="#L-526"></a> else <a href="#L-527"></a> order = lang:formatNum(order) <a href="#L-528"></a> end <a href="#L-529"></a> <a href="#L-530"></a> formatted_num = formatted_num .. '×10' .. order .. '' <a href="#L-531"></a> end <a href="#L-532"></a> <a href="#L-533"></a> return formatted_num <a href="#L-534"></a>end <a href="#L-535"></a> <a href="#L-536"></a>--[[ <a href="#L-537"></a>divide <a href="#L-538"></a> <a href="#L-539"></a>Implements the division operator <a href="#L-540"></a> <a href="#L-541"></a>Usage: <a href="#L-542"></a>{{#invoke:Math | divide | x | y | round= | precision= }} <a href="#L-543"></a> <a href="#L-544"></a>--]] <a href="#L-545"></a>function wrap.divide(args) <a href="#L-546"></a> local x = args[1] <a href="#L-547"></a> local y = args[2] <a href="#L-548"></a> local round = args.round <a href="#L-549"></a> local precision = args.precision <a href="#L-550"></a> if not yesno then <a href="#L-551"></a> yesno = require('Module:Yesno') <a href="#L-552"></a> end <a href="#L-553"></a> return p._divide(x, y, yesno(round), precision) <a href="#L-554"></a>end <a href="#L-555"></a> <a href="#L-556"></a>function p._divide(x, y, round, precision) <a href="#L-557"></a> if y == nil or y == "" then <a href="#L-558"></a> return err("Empty divisor") <a href="#L-559"></a> elseif not tonumber(y) then <a href="#L-560"></a> if type(y) == 'string' and string.sub(y, 1, 1) == '<' then <a href="#L-561"></a> return y <a href="#L-562"></a> else <a href="#L-563"></a> return err("Not a number: " .. y) <a href="#L-564"></a> end <a href="#L-565"></a> elseif x == nil or x == "" then <a href="#L-566"></a> return err("Empty dividend") <a href="#L-567"></a> elseif not tonumber(x) then <a href="#L-568"></a> if type(x) == 'string' and string.sub(x, 1, 1) == '<' then <a href="#L-569"></a> return x <a href="#L-570"></a> else <a href="#L-571"></a> return err("Not a number: " .. x) <a href="#L-572"></a> end <a href="#L-573"></a> else <a href="#L-574"></a> local z = x / y <a href="#L-575"></a> if round then <a href="#L-576"></a> return p._round(z, 0) <a href="#L-577"></a> elseif precision then <a href="#L-578"></a> return p._round(z, precision) <a href="#L-579"></a> else <a href="#L-580"></a> return z <a href="#L-581"></a> end <a href="#L-582"></a> end <a href="#L-583"></a>end <a href="#L-584"></a> <a href="#L-585"></a>--[[ <a href="#L-586"></a>Helper function that interprets the input numerically. If the <a href="#L-587"></a>input does not appear to be a number, attempts evaluating it as <a href="#L-588"></a>a parser functions expression. <a href="#L-589"></a>]] <a href="#L-590"></a> <a href="#L-591"></a>function p._cleanNumber(number_string) <a href="#L-592"></a> if type(number_string) == 'number' then <a href="#L-593"></a> -- We were passed a number, so we don't need to do any processing. <a href="#L-594"></a> return number_string, tostring(number_string) <a href="#L-595"></a> elseif type(number_string) ~= 'string' or not number_string:find('%S') then <a href="#L-596"></a> -- We were passed a non-string or a blank string, so exit. <a href="#L-597"></a> return nil, nil; <a href="#L-598"></a> end <a href="#L-599"></a> <a href="#L-600"></a> -- Attempt basic conversion <a href="#L-601"></a> local number = tonumber(number_string) <a href="#L-602"></a> <a href="#L-603"></a> -- If failed, attempt to evaluate input as an expression <a href="#L-604"></a> if number == nil then <a href="#L-605"></a> local success, result = pcall(mw.ext.ParserFunctions.expr, number_string) <a href="#L-606"></a> if success then <a href="#L-607"></a> number = tonumber(result) <a href="#L-608"></a> number_string = tostring(number) <a href="#L-609"></a> else <a href="#L-610"></a> number = nil <a href="#L-611"></a> number_string = nil <a href="#L-612"></a> end <a href="#L-613"></a> else <a href="#L-614"></a> number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it. <a href="#L-615"></a> number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs. <a href="#L-616"></a> if number_string:find('^%-?0[xX]') then <a href="#L-617"></a> -- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead. <a href="#L-618"></a> number_string = tostring(number) <a href="#L-619"></a> end <a href="#L-620"></a> end <a href="#L-621"></a> <a href="#L-622"></a> return number, number_string <a href="#L-623"></a>end <a href="#L-624"></a> <a href="#L-625"></a>--[[ <a href="#L-626"></a>Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current <a href="#L-627"></a>frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments. <a href="#L-628"></a>]] <a href="#L-629"></a> <a href="#L-630"></a>local mt = { __index = function(t, k) <a href="#L-631"></a> return function(frame) <a href="#L-632"></a> if not getArgs then <a href="#L-633"></a> getArgs = require('Module:Arguments').getArgs <a href="#L-634"></a> end <a href="#L-635"></a> return wrap[k](getArgs(frame)) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed. <a href="#L-636"></a> end <a href="#L-637"></a>end } <a href="#L-638"></a> <a href="#L-639"></a>return setmetatable(p, mt) </pre></div>   </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">"<a dir="ltr" href="https://pa.wikipedia.org/w/index.php?title=ਮੌਡਿਊਲ:Math&oldid=635976">https://pa.wikipedia.org/w/index.php?title=ਮੌਡਿਊਲ:Math&oldid=635976</a>" ਤੋਂ ਲਿਆ</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%E0%A8%96%E0%A8%BC%E0%A8%BE%E0%A8%B8:%E0%A8%B8%E0%A8%BC%E0%A9%8D%E0%A8%B0%E0%A9%87%E0%A8%A3%E0%A9%80%E0%A8%86%E0%A8%82" title="ਖ਼ਾਸ:ਸ਼੍ਰੇਣੀਆਂ">ਸ਼੍ਰੇਣੀ</a>: <ul><li><a href="/wiki/%E0%A8%B8%E0%A8%BC%E0%A9%8D%E0%A8%B0%E0%A9%87%E0%A8%A3%E0%A9%80:Modules_subject_to_page_protection" title="ਸ਼੍ਰੇਣੀ:Modules subject to page protection">Modules subject to page protection</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"> ਇਸ ਸਫ਼ੇ ਵਿੱਚ ਆਖ਼ਰੀ ਸੋਧ 9 ਫ਼ਰਵਰੀ 2023 ਨੂੰ 10:12 ਵਜੇ ਹੋਈ।</li> <li id="footer-info-copyright">ਇਹ ਲਿਖਤ <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License 4.0</a> ਦੇ ਤਹਿਤ ਉਪਲਬਧ ਹੈ; 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