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<ul class="vector-menu-content-list"> <li id="ca-nstab-module" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Module:Math" title="View the module page [c]" accesskey="c"><span>Module</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Module_talk:Math&action=edit&redlink=1" rel="discussion" class="new" title="Maǵlıwmat beti haqqında talqılaw (bet ele jaratılmaǵan) [t]" accesskey="t"><span>Talqılaw</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Til variantın ózgertiw" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Kórinisler"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="vector-tab-noicon mw-list-item"><a href="/wiki/Module:Math"><span>Tanısıp shıǵıw</span></a></li><li id="ca-edit" class="selected vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Module:Math&action=edit" title="Bul bettiń derek kodın ózgertiw"><span>Derekti redaktorlaw</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a 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<ul class="vector-menu-content-list"> <li id="ca-more-view" class="vector-more-collapsible-item mw-list-item"><a href="/wiki/Module:Math"><span>Tanısıp shıǵıw</span></a></li><li id="ca-more-edit" class="selected vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Module:Math&action=edit" title="Bul bettiń derek kodın ózgertiw [e]" accesskey="e"><span>Derekti redaktorlaw</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Module:Math&action=history"><span>Tariyxın kóriw</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Ulıwma </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Arnawl%C4%B1:Siltelgen_betler/Module:Math" title="Usı betke siltelgen barlıq betler dizimi [j]" accesskey="j"><span>Siltelgen betler</span></a></li><li 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href="/w/index.php?title=Arnawl%C4%B1:QrCode&url=https%3A%2F%2Fkaa.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DModule%3AMath%26action%3Dedit"><span>QR kod júklep alıw</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Basqa joybarlarda </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <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="Baylanısqan Wikimaǵlıwmat bazası elementine silteme [g]" accesskey="g"><span>Wikimaǵlıwmat elementi</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Bet ásbapları"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Kórinis"> <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">Kórinis</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">qaptal panelge kóshiriw</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">jasırıw</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> <div id="contentSub"><div id="mw-content-subtitle">← <a href="/wiki/Module:Math" title="Module:Math">Module:Math</a></div></div> <div id="mw-content-text" class="mw-body-content"><p>Bul betti redaktorlaw háreketine tómendegi sebep boyınsha ruqsat joq: </p> <div class="permissions-errors"><div class="mw-permissionerror-globalblocking-blockedtext-range"><b>Siziń IP-mánzilińiz <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Global_blocks" class="extiw" title="m:Special:MyLanguage/Global blocks">barlıq Wikimedia Foundation wikilerinde bloklanǵan</a> diapazonda.</b> <p>Blok <a href="/wiki/Paydalan%C4%B1wsh%C4%B1:Jon_Kolbert" title="Paydalanıwshı:Jon Kolbert">‪Jon Kolbert‬</a> tárepinen ámelge asırılǵan. Kórsetilgen sebep <i><a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/NOP" class="extiw" title="m:Special:MyLanguage/NOP">Open proxy/Webhost</a>: See the <a href="https://meta.wikimedia.org/wiki/WM:OP/H" class="extiw" title="m:WM:OP/H">help page</a> if you are affected </i>. </p> <ul><li>Bloklanıwdıń baslanıwı : 15:12, 2023 j. avgusttıń 27</li> <li>Bloklanıwdıń ámel qılıw múddeti: 15:12, 2028 j. avgusttıń 27</li></ul> <p>Siziń ámeldegi IP mánzilińiz 8.222.208.146, bloklanǵan diapazon bolsa 8.222.128.0/17. Márhámát, joqarıdaǵı barlıq maǵlıwmatlardı sorawıńızǵa tolıq kirgiziń. </p><p>Egerde siz bloklanıw qátelik sebepli bolǵan dep esaplasańız, qosımsha maǵlıwmat hám kórsetpelerdi <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/No_open_proxies" class="extiw" title="m:Special:MyLanguage/No open proxies">No open proxies</a> global siyasatında tabıwıńız múmkin. </p> Keri jaǵdayda, bloklanıwdı talqılaw ushın <a href="https://meta.wikimedia.org/wiki/Steward_requests/Global" class="extiw" title="m:Steward requests/Global">Meta-Wikide kórip shıǵıw ushın soraw jiberiń</a> yamasa joqarıdaǵı barlıq maǵlıwmatlardı kirgizip <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Stewards" class="extiw" title="m:Special:MyLanguage/Stewards">stewards</a> <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/VRT" class="extiw" title="m:Special:MyLanguage/VRT">VRT</a> náwbette <kbd>stewards@wikimedia.org</kbd> pochtasına xat jollań.</div></div><hr /> <p>Bul bettiń deregin qarawıńızǵa hám kóshirip alıwıńızǵa boladı. </p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="en" dir="ltr" name="wpTextbox1">--[[ This module provides a number of basic mathematical operations. ]] local yesno, getArgs -- lazily initialized local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules. local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua. --[[ Helper functions used to avoid redundant code. ]] local function err(msg) -- Generates wikitext error messages. return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg) end local function unpackNumberArgs(args) -- Returns an unpacked list of arguments specified with numerical keys. local ret = {} for k, v in pairs(args) do if type(k) == 'number' then table.insert(ret, v) end end return unpack(ret) end local function makeArgArray(...) -- Makes an array of arguments from a list of arguments that might include nils. local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs. local nums = {} -- Stores the numbers of valid numerical arguments. local ret = {} for k, v in pairs(args) do v = p._cleanNumber(v) if v then nums[#nums + 1] = k args[k] = v end end table.sort(nums) for i, num in ipairs(nums) do ret[#ret + 1] = args[num] end return ret end local function fold(func, ...) -- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters, -- and must return a number as an output. This number is then supplied as input to the next function call. local vals = makeArgArray(...) local count = #vals -- The number of valid arguments if count == 0 then return -- Exit if we have no valid args, otherwise removing the first arg would cause an error. nil, 0 end local ret = table.remove(vals, 1) for _, val in ipairs(vals) do ret = func(ret, val) end return ret, count end --[[ Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value). ]] local function binary_fold(func, ...) local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...) return value end --[[ random Generate a random number Usage: {{#invoke: Math | random }} {{#invoke: Math | random | maximum value }} {{#invoke: Math | random | minimum value | maximum value }} ]] function wrap.random(args) local first = p._cleanNumber(args[1]) local second = p._cleanNumber(args[2]) return p._random(first, second) end function p._random(first, second) math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000)) -- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params. if first and second then if first <= second then -- math.random doesn't allow the first number to be greater than the second. return math.random(first, second) end elseif first then return math.random(first) else return math.random() end end --[[ order Determine order of magnitude of a number Usage: {{#invoke: Math | order | value }} ]] function wrap.order(args) local input_string = (args[1] or args.x or '0'); local input_number = p._cleanNumber(input_string); if input_number == nil then return err('order of magnitude input appears non-numeric') else return p._order(input_number) end end function p._order(x) if x == 0 then return 0 end return math.floor(math.log10(math.abs(x))) end --[[ precision Detemines the precision of a number using the string representation Usage: {{ #invoke: Math | precision | value }} ]] function wrap.precision(args) local input_string = (args[1] or args.x or '0'); local trap_fraction = args.check_fraction; local input_number; if not yesno then yesno = require('Module:Yesno') end if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]]. local pos = string.find(input_string, '/', 1, true); if pos ~= nil then if string.find(input_string, '/', pos + 1, true) == nil then local denominator = string.sub(input_string, pos+1, -1); local denom_value = tonumber(denominator); if denom_value ~= nil then return math.log10(denom_value); end end end end input_number, input_string = p._cleanNumber(input_string); if input_string == nil then return err('precision input appears non-numeric') else return p._precision(input_string) end end function p._precision(x) if type(x) == 'number' then x = tostring(x) end x = string.upper(x) local decimal = x:find('%.') local exponent_pos = x:find('E') local result = 0; if exponent_pos ~= nil then local exponent = string.sub(x, exponent_pos + 1) x = string.sub(x, 1, exponent_pos - 1) result = result - tonumber(exponent) end if decimal ~= nil then result = result + string.len(x) - decimal return result end local pos = string.len(x); while x:byte(pos) == string.byte('0') do pos = pos - 1 result = result - 1 if pos <= 0 then return 0 end end return result end --[[ max Finds the maximum argument Usage: {{#invoke:Math| max | value1 | value2 | ... }} Note, any values that do not evaluate to numbers are ignored. ]] function wrap.max(args) return p._max(unpackNumberArgs(args)) end function p._max(...) local max_value = binary_fold((function(a, b) return a > b end), ...) if max_value then return max_value end end --[[ median Find the median of set of numbers Usage: {{#invoke:Math | median | number1 | number2 | ...}} OR {{#invoke:Math | median }} ]] function wrap.median(args) return p._median(unpackNumberArgs(args)) end function p._median(...) local vals = makeArgArray(...) local count = #vals table.sort(vals) if count == 0 then return 0 end if p._mod(count, 2) == 0 then return (vals[count/2] + vals[count/2+1])/2 else return vals[math.ceil(count/2)] end end --[[ min Finds the minimum argument Usage: {{#invoke:Math| min | value1 | value2 | ... }} OR {{#invoke:Math| min }} When used with no arguments, it takes its input from the parent frame. Note, any values that do not evaluate to numbers are ignored. ]] function wrap.min(args) return p._min(unpackNumberArgs(args)) end function p._min(...) local min_value = binary_fold((function(a, b) return a < b end), ...) if min_value then return min_value end end --[[ sum Finds the sum Usage: {{#invoke:Math| sum | value1 | value2 | ... }} OR {{#invoke:Math| sum }} Note, any values that do not evaluate to numbers are ignored. ]] function wrap.sum(args) return p._sum(unpackNumberArgs(args)) end function p._sum(...) local sums, count = fold((function(a, b) return a + b end), ...) if not sums then return 0 else return sums end end --[[ average Finds the average Usage: {{#invoke:Math| average | value1 | value2 | ... }} OR {{#invoke:Math| average }} Note, any values that do not evaluate to numbers are ignored. ]] function wrap.average(args) return p._average(unpackNumberArgs(args)) end function p._average(...) local sum, count = fold((function(a, b) return a + b end), ...) if not sum then return 0 else return sum / count end end --[[ round Rounds a number to specified precision Usage: {{#invoke:Math | round | value | precision }} --]] function wrap.round(args) local value = p._cleanNumber(args[1] or args.value or 0) local precision = p._cleanNumber(args[2] or args.precision or 0) if value == nil or precision == nil then return err('round input appears non-numeric') else return p._round(value, precision) end end function p._round(value, precision) local rescale = math.pow(10, precision or 0); return math.floor(value * rescale + 0.5) / rescale; end --[[ log10 returns the log (base 10) of a number Usage: {{#invoke:Math | log10 | x }} ]] function wrap.log10(args) return math.log10(args[1]) end --[[ mod Implements the modulo operator Usage: {{#invoke:Math | mod | x | y }} --]] function wrap.mod(args) local x = p._cleanNumber(args[1]) local y = p._cleanNumber(args[2]) if not x then return err('first argument to mod appears non-numeric') elseif not y then return err('second argument to mod appears non-numeric') else return p._mod(x, y) end end function p._mod(x, y) local ret = x % y if not (0 <= ret and ret < y) then ret = 0 end return ret end --[[ gcd Calculates the greatest common divisor of multiple numbers Usage: {{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }} --]] function wrap.gcd(args) return p._gcd(unpackNumberArgs(args)) end function p._gcd(...) local function findGcd(a, b) local r = b local oldr = a while r ~= 0 do local quotient = math.floor(oldr / r) oldr, r = r, oldr - quotient * r end if oldr < 0 then oldr = oldr * -1 end return oldr end local result, count = fold(findGcd, ...) return result end --[[ precision_format Rounds a number to the specified precision and formats according to rules originally used for {{template:Rnd}}. Output is a string. Usage: {{#invoke: Math | precision_format | number | precision }} ]] function wrap.precision_format(args) local value_string = args[1] or 0 local precision = args[2] or 0 return p._precision_format(value_string, precision) end function p._precision_format(value_string, precision) -- For access to Mediawiki built-in formatter. local lang = mw.getContentLanguage(); local value value, value_string = p._cleanNumber(value_string) precision = p._cleanNumber(precision) -- Check for non-numeric input if value == nil or precision == nil then return err('invalid input when rounding') end local current_precision = p._precision(value) local order = p._order(value) -- Due to round-off effects it is neccesary to limit the returned precision under -- some circumstances because the terminal digits will be inaccurately reported. if order + precision >= 14 then if order + p._precision(value_string) >= 14 then precision = 13 - order; end end -- If rounding off, truncate extra digits if precision < current_precision then value = p._round(value, precision) current_precision = p._precision(value) end local formatted_num = lang:formatNum(math.abs(value)) local sign -- Use proper unary minus sign rather than ASCII default if value < 0 then sign = '−' else sign = '' end -- Handle cases requiring scientific notation if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then value = value * math.pow(10, -order) current_precision = current_precision + order precision = precision + order formatted_num = lang:formatNum(math.abs(value)) else order = 0; end formatted_num = sign .. formatted_num -- Pad with zeros, if needed if current_precision < precision then local padding if current_precision <= 0 then if precision > 0 then local zero_sep = lang:formatNum(1.1) formatted_num = formatted_num .. zero_sep:sub(2,2) padding = precision if padding > 20 then padding = 20 end formatted_num = formatted_num .. string.rep('0', padding) end else padding = precision - current_precision if padding > 20 then padding = 20 end formatted_num = formatted_num .. string.rep('0', padding) end end -- Add exponential notation, if necessary. if order ~= 0 then -- Use proper unary minus sign rather than ASCII default if order < 0 then order = '−' .. lang:formatNum(math.abs(order)) else order = lang:formatNum(order) end formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>' end return formatted_num end --[[ divide Implements the division operator Usage: {{#invoke:Math | divide | x | y | round= | precision= }} --]] function wrap.divide(args) local x = args[1] local y = args[2] local round = args.round local precision = args.precision if not yesno then yesno = require('Module:Yesno') end return p._divide(x, y, yesno(round), precision) end function p._divide(x, y, round, precision) if y == nil or y == "" then return err("Empty divisor") elseif not tonumber(y) then if type(y) == 'string' and string.sub(y, 1, 1) == '<' then return y else return err("Not a number: " .. y) end elseif x == nil or x == "" then return err("Empty dividend") elseif not tonumber(x) then if type(x) == 'string' and string.sub(x, 1, 1) == '<' then return x else return err("Not a number: " .. x) end else local z = x / y if round then return p._round(z, 0) elseif precision then return p._round(z, precision) else return z end end end --[[ Helper function that interprets the input numerically. If the input does not appear to be a number, attempts evaluating it as a parser functions expression. ]] function p._cleanNumber(number_string) if type(number_string) == 'number' then -- We were passed a number, so we don't need to do any processing. return number_string, tostring(number_string) elseif type(number_string) ~= 'string' or not number_string:find('%S') then -- We were passed a non-string or a blank string, so exit. return nil, nil; end -- Attempt basic conversion local number = tonumber(number_string) -- If failed, attempt to evaluate input as an expression if number == nil then local success, result = pcall(mw.ext.ParserFunctions.expr, number_string) if success then number = tonumber(result) number_string = tostring(number) else number = nil number_string = nil end else number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it. number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs. if number_string:find('^%-?0[xX]') then -- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead. number_string = tostring(number) end end return number, number_string end --[[ Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments. ]] local mt = { __index = function(t, k) return function(frame) if not getArgs then getArgs = require('Module:Arguments').getArgs end return wrap[k](getArgs(frame)) -- Argument processing is left to Module:Arguments. 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