Module:MOS modes

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Note: Do not invoke this module directly; use the corresponding template instead: Template:MOS modes.

This module depends on the following other modules: Module: MOS Module: Rational Module: TAMNAMS Module: Template input parse Module: Utils Module: Yesno

This template is used for mos pages to automatically generate and list that mos's modes, along with the modes' UDP (up-down-period) notation.

---

local mos = require('Module:MOS')
local rat = require('Module:Rational')
local p = {}

-- Function that takes a mos and produces all of the modes by brightness
function p.modes_by_brightness(input_mos)
	-- Default parameter, which corresponds to 5L 2s <2/1>
	local input_mos = input_mos or mos.new(5, 2, 2)
	
	-- Get the number of L's, s's, and periods
	local nL = input_mos.nL
	local ns = input_mos.ns
	local peridos = rat.gcd(nL, ns)
	
	-- Find its brightest mode as a string of L's and s's
	local brightest_mode = mos.brightest_mode(input_mos)
	
	-- Find the size of the generator aned period in mossteps
	local gen = mos.bright_gen(input_mos)
	local gen_in_mossteps = gen['L'] + gen['s']
	local period_size  = round((nL + ns) / peridos)

	
	-- For a mos xL ys, there are x+y unique modes that can be achieved by the following process:
	-- For a generator g in mossteps (that is, less than x+y), take the substring of the brightest
	-- mode's step sequence and move them to the end to get the next-brightest mode. Repeat this
	-- process to get all modes. The x+y-1th time this is done will be the darkest mode.
	-- In case the mos is a multiperiod mos nxL nys, consider it as the mos for xL ys and duplicate
	-- the result n times. This way, the number of rotations needed to be performed is still x+y-1.
	local brightest_mode_substr = string.sub(brightest_mode, 1, period_size)
	
	local modes = { brightest_mode }
	local current_mode = brightest_mode_substr
	
	for i = 1, period_size - 1 do
		-- Move the first g strings from the beginning to the end
		local first_substr = string.sub(current_mode, 1, gen_in_mossteps)
		local second_substr = string.sub(current_mode, gen_in_mossteps + 1, period_size)
		current_mode = second_substr .. first_substr
		
		-- Duplicate the string (just in case) then add it to the array of modes
		local current_mode_duplicated = string.rep(current_mode, peridos)
		table.insert(modes, current_mode_duplicated)
	end
	
	return modes
end

-- Test function that produces the modes of a mos as a table
-- The mos itself can be entered as a string xL ys <p/q> since the mos module
-- can parse a mos in that format
function p.modes_table(frame)
	local mosstring = "3L 4s"
	local input_mos = mos.parse(mosstring)
	
	local mos_modes = p.modes_by_brightness(input_mos)
	
	-- Make a single-column table
	local result = '{| class="wikitable"\n'
	result = result .. "|+\n"
	result = result .. "|-\n"
	result = result .. "! Modes of " .. mosstring .. "\n"
	
	-- Enter each row
	for i = 1, #mos_modes do
		result = result .. "|-\n"
		result = result .. "|" .. mos_modes[i] .. "\n"
	end
	
	result = result .. "|}"
	
	return result
end

return p