모듈:NumberTheory

이 모듈에 대한 설명문서는 모듈:NumberTheory/설명문서에서 만들 수 있습니다

local getArgs = require('모듈:Arguments').getArgs
local p = {}

function _gcd(args)
	if args[1] == nil then
		return 1
	else
		gc = math.abs(args[1])
		if args[2] == nil then
			return gc
		else
			local i = 2;
			while args[i] ~= nil do
				local a = gc;
				local b = math.abs(args[i]);
				local c;
				while c ~= 0 do
					c = a % b;
					a = b;
					b = c;
				end
				gc = a
				i = i + 1
			end
			return gc
		end
	end
end

function p.gcd(frame)
	local args = getArgs(frame)
	return _gcd(args)
end

function _inverseMod( z, m )
	if _gcd( z, m ) ~= 1 then
		return nil
	else
		local a = math.abs(m)
		local b = math.abs(z) % a
		local qt = {1}
		local c
		local p = 1
		local q
		local r
		while c ~= 0 do
			c = a % b
			qt[#qt + 1] = 0 - math.floor(a / b)
			a = b
			b = c
		end
		q = qt[#qt - 1]
		local i
		for i = #qt - 2, 2, -1 do
			r = p
			p = q
			q = r + q * qt[i]
		end
		while q < 0 do
			q = q + m
		end
		return q % m
	end
end

function _powerMod( root, expo, modulo )
	local BaseConvert = require( '모듈:BaseConvert' );
	if tonumber(expo) < 0 then
		root = _inverseMod( root, modulo )
		expo = -expo
	end
	local power = 1;
	local expo2 = BaseConvert.convert({n = expo, base = 2});
	local i;
	for i = 1, #expo2 do
		power = (power * power) % modulo;
		power = power * (root ^ expo2:sub(i,i)) % modulo;
		end
	return power
end

function p.powerMod(frame)
	local args
    if frame == mw.getCurrentFrame() then
        args = frame.args
    else
        args = frame
    end
    
    local root = args.root
    local expo = args.expo
    local modulo = args.modulo
    
    return _powerMod( root, expo, modulo )
end

return p