Modul:Math

Modul zur Berechnung mathematischer Funktionen, welche nicht im WP-Standard enthalten sind. Bei erlaubten Argumenten wird das Ergebnis zurückgegeben, ansonsten eine leere Zeichenkette.

Zurzeit implementiert:

• Math.sinh: Sinus hyperbolicus
• Math.cosh: Kosinus hyperbolicus
• Math.tanh: Tangens hyperbolicus
• Math.coth: Kotangens hyperbolicus
• Math.arsinh: Area Sinus hyperbolicus
• Math.arcosh: Area Kosinus hyperbolicus
• Math.artanh: Area Tangens hyperbolicus
• Math.arcoth: Area Kotangens hyperbolicus

---

-- to catch wrong input, the code doesn't use math.sinh and math.cosh directly

local function sinh(x)
	-- Sinus hyperbolicus
	x = tonumber(x) or false;
    if not x then return 0, false; end
    local value = (math.exp (x) - math.exp (0 - x)) / 2 
    if value then
    	return value, true
    else
    	return 0, false
    end
end

local function cosh(x)
	-- Cosinus hyperbolicus
	x = tonumber(x) or false;
    if not x then return 1, false; end
    local value = (math.exp (x) + math.exp (0 - x)) / 2 
    if value then
    	return value, true
    else
    	return 1, false
    end
end

local function tanh(x)
	-- Tangens hyperbolicus
	x = tonumber(x) or false;
	if not x then return 0, false; end
	local s = sinh(x);
	local c = cosh(x);
	if c ~= 0 then
		local value = s / c
		if value then
			return value, true
		else
			return 0, false
		end
	else
		return 0, false
	end
end

local function coth(x)
	-- Kotangens hyperbolicus
	x = tonumber(x) or false;
	if not x then return 0, false; end
	local s = sinh(x);
	local c = cosh(x);
	if s ~= 0 then
		local value = c / s;
		if value then
			return value, true
		else
			return 0, false
		end
	else
		return 0, false
	end
end

local function arsinh(x)
	-- Area sinus hyperbolicus
	x = tonumber(x) or false;
    if not x then return 0, false; end
    local value = math.ln (x + math.sqrt(x * x + 1)) 
    if value then
    	return value, true
    else
    	return 0, false
    end
end

local function arcosh(x)
	-- Area Kosinus hyperbolicus
	x = tonumber(x) or false;
    if not x then return 0, false; end
    if x <= 1 then return 0, false; end
    local value = math.ln (x + math.sqrt(x * x - 1)) 
    if value then
    	return value, true
    else
    	return 0, false
    end
end

local function artanh(x)
	-- Area tangens hyperbolicus
	x = tonumber(x) or false;
    if not x then return 0, false; end
    if math.abs(x) >= 1 then return 0, false; end
    local value = math.ln ((1+x)/(1-x)) / 2
    if value then
    	return value, true
    else
    	return 0, false
    end
end

local function arcoth(x)
	-- Area Kotangens hyperbolicus
	x = tonumber(x) or false;
    if not x then return 0, false; end
    if math.abs(x) <= 1 then return 0, false; end
    local value = math.ln ((x+1)/(x-1)) / 2
    if value then
    	return value, true
    else
    	return 0, false
    end
end


local Math = { };

function Math.sinh( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = sinh(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.cosh( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = cosh(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.tanh( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = tanh(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.coth( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = coth(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.arsinh( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = arsinh(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.arcosh( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = arcosh(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.artanh( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = artanh(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end

function Math.arcoth( frame )
	local data = tonumber(frame.args[1]) or false;
	if data then
		local value, isOk = arcoth(data);
		if isOk then
			return tostring(value);
		else
			return "" -- error
		end
	else
		return "" -- error
	end
end


return Math