Différences entre les pages « Module:Coordinates » et « Module:Math »

Version actuelle datée du 28 décembre 2020 à 11:45

La documentation pour ce module peut être créée à Module:Math/doc

--[[

This module provides a number of basic mathematical operations.

]]
local z = {}

-- Generate random number
function z.random( frame )
    local first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
    local second = tonumber(frame.args[2])

    if first then -- if NaN or nil, will skip down to final return
        if first <= second then -- could match if both nil, but already checked that first is a number in last line
            return math.random(first, second)
        end
        return math.random(first)
    end   
    return math.random()
end

--[[
order

Determine order of magnitude of a number

Usage:
    {{#invoke: Math | order | value }}
]]
function z.order(frame)
    local input_string = (frame.args[1] or frame.args.x or '0');
    local input_number;
    
    input_number = z._cleanNumber( frame, input_string );
    if input_number == nil then
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
    else
        return z._order( input_number )
    end    
end
function z._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 z.precision( frame )
    local input_string = (frame.args[1] or frame.args.x or '0');
    local trap_fraction = frame.args.check_fraction or false;
    local input_number;
    
    if type( trap_fraction ) == 'string' then
        trap_fraction = trap_fraction:lower();
        if trap_fraction == 'false' or trap_fraction == '0' or
                trap_fraction == 'no' or trap_fraction == '' then
            trap_fraction = false;
        else
            trap_fraction = true;
        end
    end
    
    if trap_fraction then
        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 = z._cleanNumber( frame, input_string );
    if input_string == nil then
        return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
    else
        return z._precision( input_string )
    end    
end
function z._precision( x )    
    x = string.upper( x )

    local decimal = string.find( x, '.', 1, true )
    local exponent_pos = string.find( x, 'E', 1, true )
    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 | ... }}
OR
    {{#invoke:Math| max }}

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 z.max( frame )
    local args = frame.args;
    
    if args[1] == nil then
        local parent = frame:getParent();
        args = parent.args;
    end
    local max_value = nil;
    
    local i = 1;
    while args[i] ~= nil do
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            if max_value == nil or val > max_value then
                max_value = val;
            end
        end        
        i = i + 1;
    end
  
    return max_value
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 z.min( frame )
    local args = frame.args;
    
    if args[1] == nil then
        local parent = frame:getParent();
        args = parent.args;
    end
    local min_value = nil;
    
    local i = 1;
    while args[i] ~= nil do
        local val = z._cleanNumber( frame, args[i] );
        if val ~= nil then
            if min_value == nil or val < min_value then
                min_value = val;
            end
        end        
        i = i + 1;
    end
  
    return min_value
end

--[[
round

Rounds a number to specified precision

Usage:
    {{#invoke:Math | round | value | precision }}
    
--]]
function z.round(frame)
    local value, precision;
    
    value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
    precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
    
    if value == nil or precision == nil then
        return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
    else
        return z._round( value, precision );
    end    
end
function z._round( value, precision )
    local rescale = math.pow( 10, precision );
    return math.floor( value * rescale + 0.5 ) / rescale;
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 z.precision_format( frame )
    -- For access to Mediawiki built-in formatter.
    local lang = mw.getContentLanguage();
    
    local value_string, value, precision;
    value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
    precision = z._cleanNumber( frame, frame.args[2] or 0 );
    
    -- Check for non-numeric input
    if value == nil or precision == nil then
        return '<strong class="error">Formatting error: invalid input when rounding</strong>'
    end
    
    local current_precision = z._precision( value );

    local order = z._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
        local orig_precision = z._precision( value_string );
        if order + orig_precision >= 14 then
            precision = 13 - order;        
        end        
    end

    -- If rounding off, truncate extra digits
    if precision < current_precision then
        value = z._round( value, precision );
        current_precision = z._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

--[[
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 z._cleanNumber( frame, number_string )
    if number_string == nil or number_string:len() == 0 then
        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 attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
        attempt = tonumber( attempt );
        if attempt ~= nil then
            number = attempt;
            number_string = tostring( number );
        else
            number = nil;
            number_string = nil;
        end
    else
    -- String is valid but may contain padding, clean it.
        number_string = number_string:match( "^%s*(.-)%s*$" );
    end
    
    return number, number_string;
end

return z

Différences entre les pages « Module:Coordinates » et « Module:Math »

Version actuelle datée du 28 décembre 2020 à 11:45

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@@ Ligne 1 : / Ligne 1 : @@
-local math_mod = require( "Module:Math" )
+--[[
-local p = {}
+This module provides a number of basic mathematical operations.
---Chargement de la liste En/Au/Aux/A
+]]
-local gdata
+local z = {}
-local success, resultat = pcall (mw.loadData, "Module:Drapeau/Data" )
-if success then
-	gdata = resultat
-else
-	-- Banque de données à minima en cas de bogue dans le Module:Langue/Data
-	gdata={}
-	gdata.data={};
-	gdata.data[142]={qid="Q142", label="France", genre="fs"}
-end
-local i18n = {
-	N = 'N',
-	Nlong = 'nord',
-	W = 'O',
-	Wlong = 'ouest',
-	E = 'E',
-	Elong = 'est',
-	S = 'S',
-	Slong = 'sud',
-	degrees = '° ',
-	minutes = '′ ',
-	seconds = '″ ',
-	geohackurl = 'http://tools.wmflabs.org/geohack/geohack.php?language=fr',
-	tooltip = 'Cartes, vues aériennes, etc.',
-	errorcat = 'Page avec des balises de coordonnées mal formées',
-	sameaswikidata = 'Page avec coordonnées similaires sur Wikidata',
-	notaswikidata = 'Page avec coordonnées différentes sur Wikidata',
-	nowikidata = 'Page sans coordonnées Wikidata',
-	throughwikidata = 'Page géolocalisée par Wikidata',
-	invalidFormat = 'format invalide',                                          -- 'invalid coordinate format',
-	invalidNSEW = 'orientation invalide, devrait être "N", "S", "E" or "W"',    -- 'invalid direction should be "N", "S", "E" or "W"',
-	invalidNS = 'orientation de latitude invalide, devrait être "N" ou "S"',    -- 'could not find latitude direction (should be N or S)',
-	invalidEW = 'orientation de longitude invalide, devrait être "E" ou "W"',   -- 'could not find longitude direction (should be W or E) ',
-	noCardinalDirection = 'orientation cardinale non trouvée',                  -- 'no cardinal direction found in coordinates',
-	invalidDirection = 'direction invalide',                                    -- 'invalid direction',
-	latitude90 = 'latitude > 90',
-	longitude360 = 'longitude > 360',
-	minSec60 = 'minutes ou secondes > 60',
-	negativeCoode = 'en format dms les degrés doivent être positifs',           -- 'dms coordinates should be positive',
-	dmIntergers = 'degrés et minutes doivent être des nombres entiers',         -- 'degrees and minutes should be integers',
-	tooManyParam = 'trop de paramètres pour la latitude ou la longitude',       -- 'too many parameters for coordinates',
-	coordMissing = 'latitude ou longitude absente',                             -- 'latitude or longitude missing',
-	invalidGlobe = 'globe invalide : ',                                         -- 'invalid globe:',
-}
-local coordParse = {
-	NORTH = 'N',
-	NORD = 'N',
-	EAST = 'E',
-	EST = 'E',
-	WEST = 'W',
-	O = 'W',
-	OUEST = 'W',
-	SOUTH = 'S',
-	SUD = 'S',
-}
---Aide:Fonction_genre
-local genre = {
-	ms =    {le="le ",  du="du ",    de="du ",  au="au ",  en="au "},
-	msa =   {le="l'",   du="de l'",  de="d'",   au="à l'", en="en "},
-	msi =   {le="",     du="de ",    de="de ",  au="à ",   en="à "},
-	msia =  {le="",     du="d'",     de="d'",   au="à ",   en="à "},
-	msiae = {le="",     du="d'",     de="d'",   au="à ",   en="en "},
-	fs =    {le="la ",  du="de la ", de="de ",  au="à la ",en="en "},
-	fsa =   {le="l'",   du="de l'",  de="d'",   au="à l'", en="en "},
-	fsi =   {le="",     du="de ",    de="de ",  au="à ",   en="à "},
-	fsia =  {le="",     du="d'",     de="d'",   au="à ",   en="à "},
-	mp =    {le="les ", du="des ",   de="des ", au="aux ", en="aux "},
-	fp =    {le="les ", du="des ",   de="des ", au="aux ", en="aux "}
-}
-local globedata = 	{
+-- Generate random number
-	--[[ notes:
+function z.random( frame )
-		radius in kilometers (especially imprecise for non spheric bodies)
+    local first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
-		defaultdisplay is currently disabled, activate it ?
+    local second = tonumber(frame.args[2])
-	]]--
-	ariel = {radius = 580, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	callisto =  {radius = 2410, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	ceres =  {radius = 470, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	charon =  {radius = 1214, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	deimos =  {radius = 7, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	dione =  {radius = 560, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	enceladus =  {radius = 255, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	ganymede =  {radius = 2634, defaultdisplay = 'dec west', trackingcat = 'sur Ganymède'},
-	earth = {radius = 6371, defaultdisplay = 'dms', trackingcat = 'sur Terre'},
-	europa =  {radius = 1561, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	hyperion =  {radius = 140, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	iapetus =  {radius = 725, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	['io'] =  {radius = 1322, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	jupiter =  {radius = 68911, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	mars =  {radius = 3389.5, defaultdisplay = 'dec east', trackingcat =  'sur Mars' },
-	mercury =  {radius = 2439.7, defaultdisplay = 'dec west', trackingcat = 'sur Mercure'},
-	mimas =  {radius = 197, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	miranda =  {radius = 335, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	moon =  {radius = 1736, defaultdisplay = 'dec', trackingcat = 'sur la Lune'},
-	neptune =  {radius = 24553, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	oberon =  {radius = 761, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	phoebe =  {radius = 110, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	phobos =  {radius = 11, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	pluto =  {radius = 1185, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	rhea =  {radius = 765, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	saturn =  {radius = 58232, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	titan =  {radius = 2575.5, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	tethys =  {radius = 530, defaultdisplay = 'dec west', trackingcat = 'extraterrestre'},
-	titania =  {radius = 394, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	triton = {radius = 1353, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	umbriel =  {radius = 584, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	uranus =  {radius = 25266, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'},
-	venus =  {radius = 6051.8, defaultdisplay = 'dec east', trackingcat = 'sur Vénus'},
-	vesta =  {radius = 260, defaultdisplay = 'dec east', trackingcat = 'extraterrestre'}
-}
-globedata[''] = globedata.earth
-local wikidatathreshold = 10 -- si la distance entre coordonnées Wikipédia et Wikidata dépasse se seuil (en kilomètes), une catégorie de maintenance est ajoutée
+    if first then -- if NaN or nil, will skip down to final return
-local lang = mw.language.getContentLanguage()
+        if first <= second then -- could match if both nil, but already checked that first is a number in last line
-local default_zoom = 13
+            return math.random(first, second)
+        end
-local function makecat(cat, sortkey)
+        return math.random(first)
-	if type( sortkey ) == 'string' then
+    end
-		return '[[Category:' .. cat .. '|' .. sortkey .. ']]'
+    return math.random()
-	else
-		return '[[Category:' .. cat .. ']]'
-	end
 end
-----------------------------------------
+--[[
---Error handling
+order
-	--[[ Notes:
-	when errors occure a new error message is concatenated to errorstring
-	an error message contains an error category with a sortkey
-	For major errors, it can also display an error message (the error message will the usually be returned and the function terminated)
-	More minor errors do only add a category, so that readers are not bothered with error texts
-	sortkeys:
-		* A: invalid latitude, longitude or direction
-		* B: invalid globe
-		* C: something wrong with other parameters
-		* D: more than one primary coord
-	]]--
-local errorstring = ''
+Determine order of magnitude of a number
-local function makeerror(args)
+Usage:
-	local errormessage = ''
+    {{#invoke: Math | order | value }}
-	if args.message then
+]]
-		errormessage = '<strong class="error"> Coordonnées : ' .. args.message .. '</strong>'
+function z.order(frame)
-	end
+    local input_string = (frame.args[1] or frame.args.x or '0');
-	local errorcat = ''
+    local input_number;
-	if mw.title.getCurrentTitle().namespace == 0 then
-		errorcat = makecat(i18n.errorcat, args.sortkey)
+    input_number = z._cleanNumber( frame, input_string );
-	end
+    if input_number == nil then
-	errorstring = errormessage .. errorcat -- reinitializes the string to avoid absurdly long messages
+        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
-	return nil
+    else
+        return z._order( input_number )
+    end
 end
+function z._order(x)
-local function showerrors()
+    if x == 0 then return 0 end
-	return errorstring
+    return math.floor(math.log10(math.abs(x)))
 end
+--[[
+precision
+Detemines the precision of a number using the string representation
--- Distance computation
+Usage:
-function p._distance(a, b, globe) -- calcule la [[distance orthodromique]] en kilomètres entre deux points du globe
+    {{ #invoke: Math | precision | value }}
+]]
-	globe = string.lower(globe or 'earth')
+function z.precision( frame )
+    local input_string = (frame.args[1] or frame.args.x or '0');
-	-- check arguments and converts degreees to radians
+    local trap_fraction = frame.args.check_fraction or false;
-	local latA, latB, longA, longB = a.latitude, b.latitude, a.longitude, b.longitude
+    local input_number;
-	if (not latA) or (not latB) or (not longA) or (not longB) then return
-		error('coordinates missing, can\'t compute distance')
+    if type( trap_fraction ) == 'string' then
-	end
+        trap_fraction = trap_fraction:lower();
-	if type(latA) ~= 'number' or type(latB) ~= 'number' or type(longA) ~= 'number' or type(longB) ~= 'number' then
+        if trap_fraction == 'false' or trap_fraction == '0' or
-		error('coordinates are not numeric, can\'t compute distance')
+                trap_fraction == 'no' or trap_fraction == '' then
-	end
+            trap_fraction = false;
-		if not globe or not globedata[globe] then
+        else
-		return error('globe: ' .. globe .. 'is not supported')
+            trap_fraction = true;
-	end
+        end
+    end
-	-- calcul de la distance angulaire en radians
-	local convratio = math.pi / 180 -- convertit en radians
+    if trap_fraction then
-	latA, latB, longA, longB = convratio * latA, convratio * latB, convratio * longA, convratio * longB
+        local pos = string.find( input_string, '/', 1, true );
-	local cosangle = math.sin(latA) * math.sin(latB) + math.cos(latA) * math.cos(latB) * math.cos(longB - longA)
+        if pos ~= nil then
-	if cosangle >= 1 then -- may be above one because of rounding errors
+            if string.find( input_string, '/', pos + 1, true ) == nil then
-		return 0
+                local denominator = string.sub( input_string, pos+1, -1 );
-	end
+                local denom_value = tonumber( denominator );
-	local angle = math.acos(cosangle)
+                if denom_value ~= nil then
-	-- calcul de la distance en km
+                    return math.log10(denom_value);
-	local radius = globedata[globe].radius
+                end
-	return radius * angle
+            end
-end
+        end
+    end
-function p.distance(frame)
-	local args = frame.args
+    input_number, input_string = z._cleanNumber( frame, input_string );
-	return p._distance(
+    if input_string == nil then
-		{latitude = tonumber(args.latitude1), longitude = tonumber(args.longitude1)},
+        return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
-		{latitude = tonumber(args.latitude2), longitude = tonumber(args.longitude2)},
+    else
-		args.globe)
+        return z._precision( input_string )
+    end
 end
+function z._precision( x )
+    x = string.upper( x )
-local function geoHackUrl(decLat, decLong, globe, displayformat, objectname, extraparams)
+    local decimal = string.find( x, '.', 1, true )
-	extraparams = extraparams or ''
+    local exponent_pos = string.find( x, 'E', 1, true )
-	local geohacklatitude, geohacklongitude
+    local result = 0;
-	-- format latitude and longitude for the URL
-	if tonumber(decLat) < 0 then
+    if exponent_pos ~= nil then
-		geohacklatitude = tostring(-tonumber(decLat)) .. '_S'
+        local exponent = string.sub( x, exponent_pos + 1 )
-	else
+        x = string.sub( x, 1, exponent_pos - 1 )
-		geohacklatitude = decLat .. '_N'
+        result = result - tonumber( exponent )
-	end
+    end
-	if tonumber(decLong) < 0  then
-		geohacklongitude = tostring(-tonumber(decLong)) .. '_W'
+    if decimal ~= nil then
-	elseif globedata[globe].defaultdisplay == 'dec west' then
+        result = result + string.len( x ) - decimal
-		geohacklongitude = decLong .. '_W'
+        return result
-	else
+    end
-		geohacklongitude = decLong .. '_E'
-	end
+    local pos = string.len( x );
-	-- prepares the 'paramss=' parameter
+    while x:byte(pos) == string.byte('0') do
-	local geohackparams = geohacklatitude .. '_' .. geohacklongitude .. '_' ..extraparams
+        pos = pos - 1
-	-- concatenate parameteres for geohack
+        result = result - 1
-	return i18n.geohackurl ..
+        if pos <= 0 then
-		"&pagename=" .. mw.uri.encode(mw.title.getCurrentTitle().prefixedText, "WIKI") ..
+            return 0
-		"&params=" .. geohackparams ..
+        end
-		(objectname and ("&title=" .. mw.uri.encode(objectname)) or "")
+    end
+    return result
 end
---HTML builder for a geohack link
+--[[
-local function buildHTML(decLat, decLong, dmsLat, dmsLong, globe, displayformat, displayinline, displaytitle, objectname, extraparams)
+max
-	-- geohack url
-	local url = geoHackUrl(decLat, decLong, globe, displayformat, objectname, extraparams)
-	-- displayed coordinates
-	local displaycoords
-	if string.sub(displayformat,1,3) == 'dec' then
-		displaycoords = p.displaydec(decLat, decLong, displayformat)
-	else
-		displaycoords = {
-			p.displaydmsdimension(dmsLat, displayformat),
-			p.displaydmsdimension(dmsLong, displayformat),
-		}
-	end
-	-- build coordinate in h-geo / h-card microformat
-	local globeNode
-	if globe and globe ~= 'earth' then
-		globeNode = mw.html.create('data')
-			:addClass('p-globe')
-			:attr{ value = globe }
-			:done()
-	end
-	local coordNode = mw.html.create('')
-	if objectname then
-		coordNode = mw.html.create('span')
-			:addClass('h-card')
-			:tag('data')
-				:addClass('p-name')
-				:attr{ value = objectname }
-				:done()
-	end
-	coordNode
-		:tag('span')
-			:addClass('h-geo')
-			:addClass('geo-' .. string.sub(displayformat,1,3))
-			:tag('data')
-				:addClass('p-latitude')
-				:attr{ value = decLat }
-				:wikitext( displaycoords[1] )
-				:done()
-			:wikitext(", ")
-			:tag('data')
-				:addClass('p-longitude')
-				:attr{ value = decLong }
-				:wikitext( displaycoords[2] )
-				:done()
-			:node( globeNode )
-			:done()
-	-- buid GeoHack link
-	local root = mw.html.create('span')
-		:addClass('plainlinks nourlexpansion')
-		:attr('title', i18n.tooltip)
-		:wikitext('[' .. url )
-		:node(coordNode)
-		:wikitext("]")
-		:done()
-	-- format result depending on args["display"] (nil, "inline", "title", "inline,title")
-	local inlineText = displayinline and tostring(root) or ''
-	local titleText = ''
-	if displaytitle then
-		local htmlTitle = mw.html.create('span')
-			:attr{ id = 'coordinates' }
-			:addClass( displayinline and 'noprint' or nil )
-			:node( root )
-		local frame = mw.getCurrentFrame()
-		titleText = frame:extensionTag( 'indicator', tostring(htmlTitle), { name = 'coordinates' }	)
-	end
-	return inlineText .. titleText
-end
-local function zoom( extraparams )
+Finds the maximum argument
-	local zoomParam = extraparams:match( '%f[%w]zoom: ?(%d+)' )
-	if zoomParam then
-		return zoomParam
-	end
-	local scale = extraparams:match( '%f[%w]scale: ?(%d+)' )
-	if scale then
-		return math.floor(math.log10( 1 / tonumber( scale ) ) * 3 + 25)
-	end
-	local extraType = extraparams:match( '%f[%w]type: ?(%w+)' )
-	if extraType then
-		local zoomType = {
-			country = 5,
-			state = 6,
-			adm1st = 7,
-			adm2nd = 8,
-			city = 9,
-			isle = 10,
-			mountain = 10,
-			waterbody = 10,
-			airport = 12,
-			landmark = 13,
-		}
-		return zoomType[ extraType ]
-	end
-end
---HTML builder for a geohack link
+Usage:
-local function buildMaplinkHTML( decLat, decLong, dmsLat, dmsLong, globe, displayformat, displayinline, displaytitle, objectname, extraparams )
+    {{#invoke:Math| max | value1 | value2 | ... }}
-	-- displayed coordinates
+OR
-	local displaycoords
+    {{#invoke:Math| max }}
-	if string.sub(displayformat,1,3) == 'dec' then
-		displaycoords = p.displaydec(decLat, decLong, displayformat)
-	else
-		displaycoords = {
-			p.displaydmsdimension(dmsLat, displayformat),
-			p.displaydmsdimension(dmsLong, displayformat),
-		}
-	end
-	-- JSON for maplink
-	local jsonParams = {
-		type = 'Feature',
-		geometry = {
-			type ='Point',
-			coordinates = {
-				math_mod._round( decLong, 6 ), -- max precision in GeoJSON format
-				math_mod._round( decLat, 6 )
-			}
-		},
-		properties = {
-			['marker-color'] = "228b22",
-		}
-	}
-	if objectname then
-		jsonParams.properties.title = objectname
-	end
-	-- ajout de geoshape via externaldata
-	local geoshape = extraparams:match( '%f[%w]geoshape: ?(Q%d+)' )
-	if not geoshape and displaytitle and mw.wikibase.getEntity() then
-		geoshape = mw.wikibase.getEntity().id
-	end
-	if geoshape then
-		jsonParams = {
-			jsonParams,
-			{
-				type = 'ExternalData',
-				service = 'geoshape',
-				ids = geoshape,
-				properties = {
-					['fill-opacity'] = 0.2
-				}
-			}
-		}
-	end
-	local maplink = mw.getCurrentFrame():extensionTag{
+When used with no arguments, it takes its input from the parent
-		name = 'maplink',
+frame.  Note, any values that do not evaluate to numbers are ignored.
-		content = mw.text.jsonEncode( jsonParams ),
+]]
-		args = {
+function z.max( frame )
-			text = displaycoords[1] .. ", " .. displaycoords[2],
+    local args = frame.args;
-			zoom = zoom( extraparams ) or default_zoom,
-			latitude = decLat,
+    if args[1] == nil then
-			longitude = decLong,
+        local parent = frame:getParent();
-		}
+        args = parent.args;
-	}
+    end
+    local max_value = nil;
-	-- format result depending on args["display"] (nil, "inline", "title", "inline,title")
-	local inlineText = displayinline and maplink or ''
+    local i = 1;
-	local titleText = ''
+    while args[i] ~= nil do
-	if displaytitle then
+        local val = z._cleanNumber( frame, args[i] );
-		local htmlTitle = mw.html.create('span')
+        if val ~= nil then
-			:attr{ id = 'coordinates' }
+            if max_value == nil or val > max_value then
-			:addClass( displayinline and 'noprint' or nil )
+                max_value = val;
-			:wikitext( maplink )
+            end
-		local frame = mw.getCurrentFrame()
+        end
-		titleText = frame:extensionTag( 'indicator', tostring(htmlTitle), { name = 'coordinates' }	)
+        i = i + 1;
-	end
+    end
-	return inlineText .. titleText
+    return max_value
 end
--- dms specific funcions
+--[[
+min
-local function twoDigit( value )
+Finds the minimum argument
-	if ( value < 10 ) then
-		value = '0' .. lang:formatNum( value )
-	else
-		value = lang:formatNum( value )
-	end
-	return value
-end
-function p.displaydmsdimension(valuetable, format) -- formate en latitude ou une longitude dms
+Usage:
-	local str = ''
+    {{#invoke:Math| min | value1 | value2 | ... }}
-	local direction = valuetable.direction
+OR
-	local degrees, minutes, seconds = '', '', ''
+    {{#invoke:Math| min }}
-	local dimension
-	if format == 'dms long' then
+When used with no arguments, it takes its input from the parent
-		direction = i18n[direction .. 'long']
+frame.  Note, any values that do not evaluate to numbers are ignored.
-	else
+]]
-		direction = i18n[direction]
+function z.min( frame )
-	end
+    local args = frame.args;
-	degrees = lang:formatNum( valuetable.degrees ) .. i18n.degrees
+    if args[1] == nil then
-	if valuetable.minutes then
+        local parent = frame:getParent();
-		minutes = twoDigit( valuetable.minutes ) .. i18n.minutes
+        args = parent.args;
-	end
+    end
-	if valuetable.seconds then
+    local min_value = nil;
-		seconds = twoDigit( valuetable.seconds ) .. i18n.seconds
-	end
+    local i = 1;
-	return degrees .. minutes .. seconds .. direction
+    while args[i] ~= nil do
+        local val = z._cleanNumber( frame, args[i] );
+        if val ~= nil then
+            if min_value == nil or val < min_value then
+                min_value = val;
+            end
+        end
+        i = i + 1;
+    end
+    return min_value
 end
-local function validdms(coordtable)
+--[[
-	local direction = coordtable.direction
+round
-	local degrees = coordtable.degrees or 0
-	local minutes = coordtable.minutes or 0
-	local seconds = coordtable.seconds or 0
-	local dimension = coordtable.dimension
-	if not dimension then
-		if direction == 'N' or direction == 'S' then
-			dimension = 'latitude'
-		elseif direction == 'E' or direction == 'W' then
-			dimension = 'longitude'
-		else
-			makeerror({message = i18n.invalidNSEW, sortkey = 'A'})
-			return false
-		end
-	end
-	if type(degrees) ~= 'number' or type(minutes) ~= 'number' or type(seconds) ~= 'number' then
+Rounds a number to specified precision
-		makeerror({message = i18n.invalidFormat, sortkey = 'A'})
-		return false
-	end
-	if dimension == 'latitude' and direction ~= 'N' and direction ~= 'S' then
-		makeerror({message = i18n.invalidNS, sortkey = 'A'})
-		return false
-	end
-	if dimension == 'longitude' and direction ~= 'W' and direction ~= 'E' then
-		makeerror({message = i18n.invalidEW, sortkey = 'A'})
-		return false
-	end
-	if dimension == 'latitude' and degrees > 90 then
-		makeerror({message = i18n.latitude90, sortkey = 'A'})
-		return false
-	end
-	if dimension == 'longitude' and degrees > 360 then
-		makeerror({message = i18n.longitude360, sortkey = 'A'})
-		return false
-	end
-	if degrees < 0 or minutes < 0 or seconds < 0 then
-		makeerror({message = i18n.negativeCoode, sortkey = 'A'})
-		return false
-	end
-	if minutes > 60 or seconds > 60 then
-		makeerror({message = i18n.minSec60, sortkey = 'A'})
-		return false
-	end
-	if (math.floor(degrees) ~= degrees and minutes ~= 0) or (math.floor(minutes) ~= minutes and seconds ~= 0) then
-		makeerror({message = i18n.dmIntergers, sortkey = 'A'})
-		return false
-	end
-	return true
-end
-local function builddmsdimension(degrees, minutes, seconds, direction, dimension)
+Usage:
-	-- no error checking, done in function validdms
+    {{#invoke:Math | round | value | precision }}
-	local dimensionobject = {}
+--]]
-	-- direction and dimension (= latitude or longitude)
+function z.round(frame)
-	dimensionobject.direction = direction
+    local value, precision;
-	if dimension then
-		dimensionobject.dimension = dimension
+    value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
-	elseif direction == 'N' or direction == 'S' then
+    precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
-		dimensionobject.dimension = 'latitude'
-	elseif direction == 'E' or direction == 'W' then
+    if value == nil or precision == nil then
-		dimensionobject.dimension = 'longitude'
+        return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
-	end
+    else
+        return z._round( value, precision );
-	-- degrees, minutes, seconds
+    end
-	dimensionobject.degrees = tonumber(degrees)
-	dimensionobject.minutes = tonumber(minutes)
-	dimensionobject.seconds = tonumber(seconds)
-	if degrees and not dimensionobject.degrees then dimensionobject.degrees = 'error' end
-	if minutes and not dimensionobject.minutes then dimensionobject.minutes = 'error' end
-	if seconds and not dimensionobject.seconds then dimensionobject.seconds = 'error' end
-	return dimensionobject
 end
+function z._round( value, precision )
-function p._parsedmsstring(str, dimension) -- prend une séquence et donne des noms aux paramètres
+    local rescale = math.pow( 10, precision );
-	-- output table: {latitude=, longitude = , direction =  }
+    return math.floor( value * rescale + 0.5 ) / rescale;
-	if type( str ) ~= 'string' then
-		return nil
-	end
-	str = mw.ustring.gsub( mw.ustring.upper( str ), '%a+', coordParse )
-	if not tonumber( str ) and not str:find( '/' ) and str:find( '°' ) then
-		local str2 = mw.ustring.gsub( str, '[°″′\"\'\194\160 ]+', '/' )
-		-- avoid cases were there is degree ans seconds but no minutes
-		if not mw.ustring.find( str, '[″"]' ) or mw.ustring.find( str, '%d[′\'][ \194\160%d]' ) then
-			str = str2
-		end
-	end
-	if not tonumber(str) and not string.find(str, '/') then
-		makeerror({message = i18n.invalidFormat, sortkey= 'A'})
-		return nil
-	end
-	args = mw.text.split(str, '/', true)
-	if #args > 4 then
-		makeerror({message = i18n.tooManyParam, sortkey= 'A' })
-	end
-	local direction = mw.text.trim(args[#args])
-	table.remove(args)
-	local degrees, minutes, seconds = args[1], args[2], args[3]
-	local dimensionobject = builddmsdimension(degrees, minutes, seconds, direction, dimension)
-	if validdms(dimensionobject) then
-		return dimensionobject
-	else
-		return nil
-	end
 end
---- decimal specific functions
+--[[
-function p.displaydec(latitude, longitude, format)
+precision_format
-	lat = lang:formatNum( latitude )
-	long = lang:formatNum( longitude )
-	if format == 'dec west' or  format == 'dec east' then
-		local symbolNS, symbolEW = i18n.N, i18n.E
-		if latitude < 0 then
-			symbolNS = i18n.S
-			lat = lat:sub( 2 )
-		end
-		if format == 'dec west' then
-			symbolEW = i18n.W
-		end
-		if longitude < 0 then
-			long = lang:formatNum( 360 + longitude )
-		end
-		return { lat .. i18n.degrees .. symbolNS,  long ..  i18n.degrees .. symbolEW }
-	else
-		return { lat, long }
-	end
-end
+Rounds a number to the specified precision and formats according to rules
+originally used for {{template:Rnd}}.  Output is a string.
-local function parsedec(dec, coordtype, globe) -- coordtype = latitude or longitude
+Usage:
-	dec = mw.text.trim(dec)
+    {{#invoke: Math | precision_format | number | precision }}
-	if not dec then
+]]
-		return nil
+function z.precision_format( frame )
-	end
+    -- For access to Mediawiki built-in formatter.
-	if coordtype ~= 'latitude' and coordtype ~= 'longitude' then
+    local lang = mw.getContentLanguage();
-		makeerror({'invalid coord type', sortkey = "A"})
-		return nil
+    local value_string, value, precision;
-	end
+    value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
-	local numdec = tonumber(dec) -- numeric value, kept separated as it looses significant zeros
+    precision = z._cleanNumber( frame, frame.args[2] or 0 );
-	if not numdec then -- tries the decimal + direction format
-		dec = mw.ustring.gsub( mw.ustring.upper( dec ), '%a+', coordParse )
+    -- Check for non-numeric input
-		local direction = mw.ustring.sub(dec, mw.ustring.len(dec), mw.ustring.len(dec))
+    if value == nil or precision == nil then
-		dec = mw.ustring.sub(dec, 1, mw.ustring.len(dec)-2) -- removes the /N at the end
+        return '<strong class="error">Formatting error: invalid input when rounding</strong>'
-		if not dec or not tonumber(dec) then
+    end
-			return nil
-		end
+    local current_precision = z._precision( value );
-		if direction == 'N' or direction == 'E' or direction == 'W' and globedata[globe].defaultdisplay == 'dec west' then
-			return dec
-		elseif direction == 'W' or direction == 'S' then
-			return '-' .. dec
-		else
-			if coordtype == 'latitude' then
-				makeerror({message = i18n.invalidNS, sortkey = 'A'})
-			else
-				makeerror({message = i18n.invalidEW, sortkey = 'A'})
-			end
-			return nil
-		end
-	end
-	if coordtype == 'latitude' and math.abs(numdec) > 90 then
+    local order = z._order( value );
-		makeerror({message = i18n.latitude90 , sortkey = 'A'})
-		return nil
+    -- Due to round-off effects it is neccesary to limit the returned precision under
-	end
+    -- some circumstances because the terminal digits will be inaccurately reported.
-	if coordtype == 'longitude' and math.abs(numdec) > 360 then
+    if order + precision >= 14 then
-		makeerror({message = i18n.longitude360 , sortkey = 'A'})
+        local orig_precision = z._precision( value_string );
-		return nil
+        if order + orig_precision >= 14 then
-	end
+            precision = 13 - order;
-	return dec
+        end
-end
+    end
--- dms/dec conversion functions
+    -- If rounding off, truncate extra digits
-local function convertprecision(precision) -- converts a decimal precision like "2" into "dm"
+    if precision < current_precision then
-	if precision >= 3 then
+        value = z._round( value, precision );
-		return 'dms'
+        current_precision = z._precision( value );
-	elseif precision >=1 then
+    end
-		return 'dm'
-	else
+    local formatted_num = lang:formatNum( math.abs(value) );
-		return 'd'
+    local sign;
-	end
-end
+    -- 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);
-local function determinedmsprec(decs) -- returns the most precision for a dec2dms conversion, depending on the most precise value in the decs table
+                padding = precision;
-	local precision = 0
+                if padding > 20 then
-	for d, val in ipairs(decs) do
+                    padding = 20;
-		precision = math.max(precision, math_mod._precision(val))
+                end
-	end
-	return convertprecision(precision)
+                formatted_num = formatted_num .. string.rep( '0', padding );
-end
+            end
+        else
+            padding = precision - current_precision
+            if padding > 20 then
+                padding = 20;
+            end
+            formatted_num = formatted_num .. string.rep( '0', padding );
+        end
+    end
-local function dec2dms_d(dec)
+    -- Add exponential notation, if necessary.
-	local degrees = math_mod._round( dec, 0 )
+    if order ~= 0 then
-	return degrees
+        -- 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
-local function dec2dms_dm(dec)
+--[[
-	dec = math_mod._round( dec * 60, 0 )
+Helper function that interprets the input numerically.  If the
-	local minutes = dec % 60
+input does not appear to be a number, attempts evaluating it as
-	dec = math.floor( (dec - minutes) / 60 )
+a parser functions expression.
-	local degrees = dec % 360
+]]
-	return degrees, minutes
-end
-local function dec2dms_dms(dec)
+function z._cleanNumber( frame, number_string )
-	dec = math_mod._round( dec * 60 * 60, 0 )
+    if number_string == nil or number_string:len() == 0 then
-	local seconds = dec % 60
+        return nil, nil;
-	dec = math.floor( (dec - seconds) / 60 )
+    end
-	local minutes = dec % 60
-	dec = math.floor( (dec - minutes) / 60 )
+    -- Attempt basic conversion
-	local degrees = dec % 360
+    local number = tonumber( number_string )
-	return degrees, minutes, seconds
+    -- If failed, attempt to evaluate input as an expression
+    if number == nil then
+        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
+        attempt = tonumber( attempt );
+        if attempt ~= nil then
+            number = attempt;
+            number_string = tostring( number );
+        else
+            number = nil;
+            number_string = nil;
+        end
+    else
+    -- String is valid but may contain padding, clean it.
+        number_string = number_string:match( "^%s*(.-)%s*$" );
+    end
+    return number, number_string;
 end
-function p._dec2dms(dec, coordtype, precision, globe) -- coordtype: latitude or longitude
+return z
-	local degrees, minutes, seconds
-	-- vérification du globe
-	if not ( globe and globedata[ globe ] ) then
-		globe = 'earth'
-	end
-	-- precision
-	if not precision or precision == '' then
-		precision = determinedmsprec({dec})
-	end
-	if precision ~= 'd' and precision ~= 'dm' and precision ~= 'dms' then
-		return makeerror({sortkey = 'C'})
-	end
-	local dec = tonumber(dec)
-	-- direction
-	local direction
-	if coordtype == 'latitude' then
-		if dec < 0 then
-			direction = 'S'
-		else
-			direction = 'N'
-		end
-	elseif coordtype == 'longitude' then
-		if dec < 0 or globedata[globe].defaultdisplay == 'dec west' then
-			direction = 'W'
-		else
-			direction = 'E'
-		end
-	end
-	-- conversion
-	dec = math.abs(dec) -- les coordonnées en dms sont toujours positives
-	if precision == 'dms' then
-		degrees, minutes, seconds = dec2dms_dms(dec)
-	elseif precision == 'dm' then
-		degrees, minutes = dec2dms_dm(dec)
-	else
-		degrees = dec2dms_d(dec)
-	end
-	return builddmsdimension(degrees, minutes, seconds, direction)
-end
-function p.dec2dms(frame) -- legacy function somewhat cumbersome syntax
-	args = frame.args
-	local dec = args[1]
-	if not tonumber(dec) then
-		makeerror({message = i18n.invalidFormat, sortkey = 'A'})
-		return showerrors()
-	end
-	local dirpositive = string.lower(args[2] or '')
-	local dirnegative = string.lower(args[3] or '')
-	local precision = string.lower(args[4] or '')
-	local displayformat, coordtype
-	if dirpositive == 'n' or dirpositive == 'nord' then
-		coordtype = 'latitude'
-	else
-		coordtype = 'longitude'
-	end
-	if dirpositive == 'nord' or dirpositive == 'est' or dirnegative == 'ouest' or dirnegative == 'sud' then
-		displayformat = 'dms long'
-	end
-	local coordobject = p._dec2dms(dec, coordtype, precision)
-	if coordobject then
-		return p.displaydmsdimension(coordobject, displayformat) .. showerrors()
-	else
-		return showerrors()
-	end
-end
-function p._dms2dec(dmsobject) -- transforme une table degré minute secondes en nombre décimal
-	local direction, degrees, minutes, seconds = dmsobject.direction, dmsobject.degrees, dmsobject.minutes, dmsobject.seconds
-	local factor = 0
-	local precision = 0
-	if not minutes then minutes = 0 end
-	if not seconds then seconds = 0 end
-	if direction == "N" or direction == "E" then
-		factor = 1
-	elseif direction == "W" or direction == "S" then
-		factor = -1
-	elseif not direction then
-		makeerror({message = i18n.noCardinalDirection, sortkey = 'A'})
-		return nil
-	else
-		makeerror({message = i18n.invalidDirection, sortkey = 'A'})
-		return nil
-	end
-	if dmsobject.seconds then -- vérifie la précision des données initiales
-		precision = 5 + math.max( math_mod._precision(tostring(seconds), 0 ) ) -- passage par des strings assez tarabiscoté ?
-	elseif dmsobject.minutes then
-		precision = 3 + math.max( math_mod._precision(tostring(minutes), 0 ) )
-	else
-		precision = math.max( math_mod._precision(tostring(degrees), 0 ) )
-	end
-	local decimal = factor * (degrees+(minutes+seconds/60)/60)
-	return math_mod._round(decimal, precision)
-end
-function p.dms2dec(frame) -- legacy function, somewhat bizarre syntax
-	local args = frame.args
-	if tonumber(args[1]) then
-		return args[1] -- coordonnées déjà en décimal
-	elseif not args[2] then
-		local dmsobject = p._parsedmsstring(args[1])
-		if dmsobject then
-			return p._dms2dec(dmsobject) -- coordonnées sous la fore 23/22/N
-		else
-			return showerrors()
-		end
-	else
-		return p._dms2dec({direction = args[1], degrees = tonumber(args[2]), minutes = tonumber(args[3]), seconds = tonumber(args[4])})
-	end
-end
--- Wikidata
-local function convertwikidataprecision(precision) -- converts a decima like "0.1" into "dm"
-	if precision < 0.016 then
-		return 'dms'
-	elseif precision < 1 then
-		return 'dm'
-	else
-		return 'd'
-	end
-end
-local function wikidatacoords(query)
-	query = query or {property = 'p625'}
-	query.formatting = 'raw'
-	local wd = require('Module:Wikidata')
-	local claim = wd.getClaims(query)
-	if claim and claim[1] then -- redundant but more robust in case of a change in the code of Module:Wikidata
-		local coords = wd.formatSnak(claim[1].mainsnak) -- todo: check for special values
-		-- Wikidata does not handle correctly +West longitudes
-		if globedata[ coords.globe ] and globedata[ coords.globe ].defaultdisplay == 'dec west' then
-			coords.longitude = math.abs( coords.longitude )
-		end
-		return coords.latitude, coords.longitude, coords.globe or 'earth', convertwikidataprecision(coords.precision or .001)
-	end
-	return nil
-end
-local function wikidatacat(globe)
-	--catbase= Article géolocalisé sur Terre
-	local entitycat = mw.wikibase.getEntity()
-	local basecat = 'Article géolocalisé'
-	local finalcat = {}
-	--BADGES
-	if entitycat then
-		--BADGES
-	   	for i, badgeId in ipairs( entitycat.sitelinks['frwiki'].badges ) do
-			if badgeId == 'Q17437796'  then
-				basecat=string.gsub(basecat, "Article géolocalisé", "Article de qualité géolocalisé")
-			end
-			if badgeId == 'Q17437798'  then
-				basecat=string.gsub(basecat, "Article géolocalisé", "Bon article géolocalisé")
-			end
-		end
-	end
-	if globe == 'earth'  then
-		if entitycat and entitycat.claims  then
-			local country=entitycat.claims['P17']
-			if not country then
-				--pas pays à récupérer
-				basecat=basecat .. ' sur Terre'
-				table.insert(finalcat,basecat)
-			else
-				--parfois plusieurs pays
-				for i, paysId in ipairs( country ) do
-					--on fait confiance au label wikidata
-					local gdataone,qid
-					if paysId.mainsnak.snaktype == 'value' then
-						qid=paysId.mainsnak.datavalue.value['numeric-id']
-						gdataone=gdata.data[qid]
-					else
-						--Bir Tawil n'a pas de pays connu
-						qid='?'
-					end
-					if gdataone ~= nil then
-						local prep=genre[gdataone['genre']]['en'] or 'en '
-						local thecat=basecat .. ' '..prep ..mw.wikibase.label( 'Q'.. qid)
-						if mw.title.new('category:'..thecat).exists then
-							table.insert(finalcat,thecat)
-						else
-							--Dommage!
-							mw.log(thecat .. ' à créer')
-						end
-					else
-						--pas d'id?
-						mw.log(qid .. ' à paramétrer')
-					end
-				end
-				if #finalcat == 0 then
-					--pas pays à récupérer
-					basecat=basecat .. ' sur Terre'
-					table.insert(finalcat,basecat)
-				end
-			end
-		else
-			--pas wikidata
-			basecat=basecat .. ' sur Terre'
-			table.insert(finalcat,basecat)
-		end
-	elseif globedata[globe] then
-		basecat=basecat .. ' ' .. globedata[globe].trackingcat
-		table.insert(finalcat,basecat)
-	else
-		basecat=basecat .. ' extraterrestre'
-		table.insert(finalcat,basecat)
-	end
-	return finalcat
-end
- -- main function for displaying coordinates
-function p._coord(args)
-	-- I declare variable
-	local displayformat = args.format -- string: one of: 'dms', 'dms long', 'dec', 'dec east' and 'dec west'
-	local displayplace = string.lower(args.display or 'inline') --string: one of 'inline', 'title' or 'inline,title'
-	local objectname = (args.name ~= '') and args.name -- string: name of the title displayed in geohack
-	local notes = (' ' and args.notes) or '' -- string: notes to de displayed after coordinates
-	local wikidata = args.wikidata -- string: set to "true" if needed
-	local wikidataquery = args.wikidataquery -- table: see [[Module:Wikidata]] see function wikidatacoords
-	local dmslatitude, dmslongitude -- table (when created)
-	local extraparams = args.extraparams or '' -- string (legacy, corresponds to geohackparams)
- 	local trackingstring = '' -- tracking cats except error cats (already in errorstring)
- 	local rawlat, rawlong = args.latitude, args.longitude
- 	if rawlat == '' then rawlat = nil end
- 	if rawlong == '' then rawlong = nil end
- 	local globe = string.lower( args.globe or extraparams:match('globe:(%a+)') or '' ) -- string: see the globedata table for accepted values
-	local latitude, longitude, precision, dmslatitude, dmslongitude -- latitude and longitude in decimal / dmslatitude and dmslongitude: tables withdms coords
-	local maplink = true -- use maplink whenever it is possible
-	-- II extract coordinates from Wikitext
-	if (rawlat or rawlong) then
-		if (not rawlat) or (not rawlong) then -- if latitude is provided so should be longitude
-			makeerror({message = i18n.coordMissing, sortkey = 'A'})
-			return showerrors()
-		end
-		latitude = parsedec(rawlat, 'latitude', globe)
-		if latitude then -- if latitude is decimal
-			longitude = parsedec(rawlong, 'longitude', globe) -- so should be longitude
-			precision = determinedmsprec({latitude, longitude}) -- before conversion from string to number for trailing zeros
-			if not latitude or not longitude then
-				if errorstring == '' then
-					makeerror({message = i18n.invalidFormat, sortkey = 'A'})
-				end
-				return showerrors()
-			end
-			dmslatitude, dmslongitude = p._dec2dms(latitude, 'latitude', precision), p._dec2dms(longitude, 'longitude', precision, globe)
-			latitude, longitude = tonumber(latitude), tonumber(longitude)
-		else -- if latitude is not decimal try to parse it as a dms string
-			dmslatitude, dmslongitude = p._parsedmsstring(args.latitude, 'latitude'), p._parsedmsstring(args.longitude, 'longitude')
-			if not dmslatitude or not dmslongitude then
-				return showerrors()
-			end
-			latitude, longitude = p._dms2dec(dmslatitude), p._dms2dec(dmslongitude)
-		end
-	end
-	-- III extract coordinate data from Wikidata and compare them to local data
-	local wikidatalatitude, wikidatalongitude, wikidataglobe, wikidataprecision
-	if wikidata == 'true' then
-		wikidatalatitude, wikidatalongitude, wikidataglobe, wikidataprecision = wikidatacoords(wikidataquery)
-		if wikidatalatitude and latitude and longitude then
-			local maxdistance = tonumber(args.maxdistance) or wikidatathreshold
-			if p._distance({latitude = latitude, longitude= longitude}, {latitude = wikidatalatitude, longitude= wikidatalongitude}, wikidataglobe) <  maxdistance then
-				trackingstring = trackingstring .. makecat(i18n.sameaswikidata)
-					else
-				trackingstring = trackingstring .. makecat(i18n.notaswikidata)
-			end
-		end
-		if wikidatalatitude and not latitude then
-			latitude, longitude, globe, precision = wikidatalatitude, wikidatalongitude, wikidataglobe, wikidataprecision
-			dmslatitude, dmslongitude = p._dec2dms(latitude, 'latitude', precision), p._dec2dms(longitude, 'longitude', precision, globe)
-			trackingstring = trackingstring .. makecat(i18n.throughwikidata)
-		end
-		if latitude and not wikidatalatitude then
-			if mw.title.getCurrentTitle().namespace == 0 then
-				trackingstring = trackingstring .. makecat(i18n.nowikidata)
-			end
-		end
-	end
-	-- exit if stil no latitude or no longitude
-	if not latitude and not longitude then
-		return nil -- ne rien ajouter ici pour que l'appel à cette fonction retourne bien nil en l'absence de données
-	end
-	-- IV best guesses for missing parameters
-	--- globe
-	if globe == '' then
-		globe = 'earth'
-	end
-	if not globedata[globe] then
-		makeerror({message = i18n.invalidGlobe .. globe})
-		globe = 'earth'
-	end
-	if globe ~= 'earth' then
-		extraparams = extraparams .. '_globe:' .. globe -- pas de problème si le globe est en double
-		maplink = false
-	end
-	--- diplayformat
-	if not displayformat or displayformat == '' then
-		displayformat = globedata[globe].defaultdisplay
-	end
-	-- displayinline/displaytitle
-	local displayinline =  string.find(displayplace, 'inline')
-	local displaytitle = string.find(displayplace, 'title')
-	if not displayinline and not displaytitle then
-		displayinline = true
-		if displayplace ~= '' then
-			makeerror({sortkey = 'C'}) --error if display not empty, but not not a major error, continue
-		end
-	end
-	if displaytitle and mw.title.getCurrentTitle().namespace == 0 then
-		--local cattoappend=globedata[globe].trackingcat
-		--Récupération des badges
-		local cats=wikidatacat(globe)
-		for i, cat in ipairs( cats ) do
-			trackingstring = trackingstring .. makecat(cat)
-		end
-	end
--- V geodata
-	local geodata = ''
-	if latitude and longitude then
-		local latstring, longstring = tostring(latitude), tostring(longitude)
-		local primary = ''
-		local frame = mw.getCurrentFrame()
-		local geodataparams = {[1] = latstring, [2] = longstring, [3] = extraparams }
-		if displaytitle then
-			geodataparams[4] = 'primary'
-		end
-		if objectname then
-			geodataparams.name = objectname
-		end
-		geodata = frame:callParserFunction('#coordinates', geodataparams )
-		if string.find(geodata, 'error') then -- the only error that has not been caught yet is primary key
-			geodata = ''
-			makeerror({sortkey='D'})
-		end
-	end
--- VI final output
-	local mainstring = ''
-	if maplink then
-		mainstring = buildMaplinkHTML(latitude, longitude, dmslatitude, dmslongitude, globe, displayformat, displayinline, displaytitle, objectname,extraparams )
-	else
-		mainstring = buildHTML(latitude, longitude, dmslatitude, dmslongitude, globe, displayformat, displayinline, displaytitle, objectname,extraparams )
-	end
-	return mainstring .. notes .. trackingstring .. geodata .. showerrors()
-end
-function p.coord(frame) -- parrses the strange parameters of Template:Coord before sending them to p.coord
-	local args = frame.args
-	local numericargs = {}
-	for i, j in ipairs(args) do
-		args[i] = mw.text.trim(j)
-		if type(i) == 'number' and args[i] ~= '' then
-			table.insert(numericargs, args[i])
-		end
-	end
-	if #numericargs %2 == 1 then -- if the number of args is odd, the last one provides formatting parameters
-		args.extraparams = numericargs[#numericargs]
-		if #numericargs == 1 and tonumber(numericargs[1]) then
-			makeerror({message = i18n.coordMissing, sortkey = 'A'})
-			return showerrors()
-		end
-		table.remove(numericargs)
-	end
-	for i, j in ipairs(numericargs) do
-		if i <= (#numericargs / 2) then
-			if not args.latitude then
-				args.latitude = j
-			else
-				args.latitude =	args.latitude .. '/' .. j
-			end
-		else
-			if not args.longitude then
-				args.longitude = j
-			else
-				args.longitude = args.longitude .. '/' .. j
-			end
-		end
-	end
-	if string.find(args.latitude or '', 'E') or string.find(args.latitude or '', 'W') then
-		args.latitude, args.longitude = args.longitude, args.latitude
-	end
-	return p._coord(args)
-end
-function p.Coord(frame)
-	return p.coord(frame)
-end
-function p.latitude(frame) -- helper function pour infobox, à déprécier
-	local args = frame.args
-	local latitude  = frame.args[1]
-	if latitude and mw.text.trim(latitude) ~= '' then
-		return latitude
-	elseif frame.args['wikidata'] == 'true' then
-		local lat, long = wikidatacoords()
-		return lat
-	end
-end
-function p.longitude(frame) -- helper function pour infobox, à déprécier
-	local args = frame.args
-	local longitude = frame.args[1]
-	if longitude and mw.text.trim(longitude) ~= '' then
-		return longitude
-	elseif frame.args['wikidata'] == 'true' then
-		local lat, long = wikidatacoords()
-		return long
-	end
-end
-return p