Module:Utils

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This module provides several mathematical functions which are likely to be used frequently on the Xenharmonic Wiki.

Namely, the functions in this module can be called from other modules by using require("Module:Utils") and calling the underscore-prefixed functions.

Functions

trim(s)

Removes leading and trailing whitespaces (but not interior ones) from a string.

_yesno(frame)

Allows Module:Yesno, which is not invokable directly, to be accessed by templates through Template:Yesno.

table_contains(tbl, x)*

Check if table contains x.

index_of(array, index)*

Return the first index with the given value (or nil if not found).

value_provided(s)*

Checks if s is a non-empty string.

wlink(a, b)

Provides a link to Wikipedia.

eval_num_arg(input, def_value)*

Checks if input is a number; on error, use def_value.

log(x, b)

Returns the logarithm base b of x. Parameter b defaults to base 2 (octave) if it is omitted.

gcd(a, b)

Returns the greatest common divisor of a and b.

round_dec(x, places)

Returns x rounded to a precision of places decimal places. Parameter places defaults to 0 if it is omitted.

round(x, prec)

Returns x rounded to a precision of prec significant figures. Parameter prec defaults to 6 if it is omitted.

is_prime(n)*

Returns true if the given integer n is a prime number.

prime_factorization(n)

Returns the prime factorization of the given integer n using the exponential form (in wikitext).

prime_factorization_raw(n)*

Returns a table encoding the prime factorization of n.

signum(x)*

Returns 1 for positive numbers, −1 for negative ones, and 0 for zero and non-integer inputs.

next_young_diagram(d)

Returns the next Young diagram of the same size; the first one is [N], the last one is . After the last one, nil is returned. The input table is modified.

* These functions are designed to be used by other modules only; they cannot be called with {{#invoke: }}.

---

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

-- evaluate input on error use default; cannot be used with {{#invoke:}}
function p.eval_num_arg(input, def_value)
	local result = input
	if type(input) ~= 'number' then
		result = def_value
		if type(input) == 'string' then
			-- check for fraction notation
			if input:match('/') == '/' then
				local denominator = 1
				input, denominator = input:match("^%s*([0-9]+)[/?]([0-9]+)%s*$")
				result = (tonumber(input) or def_value)/(tonumber(denominator) or 1)
			else
				input = input:match("^%s*(.-)%s*$")
				result = tonumber(input)
			end
		end
	end
	return result
end

-- return logarithm base b of x
function p.log(frame)
	local args = getArgs(frame)
	return p._log(args[1], args[2])
end	

function p._log(x, b)
	-- x defaults to 0
	x = p.eval_num_arg(x, 0)
	-- b defaults to 2 ("octave")
	b = p.eval_num_arg(b, 2)
	return math.log(x)/math.log(b)
end

-- return x rounded to a precision of prec significant figures
function p.round(frame)
	local args = getArgs(frame)
	return p._round(args[1], args[2])
end	

function p._round(x, prec)
	-- x defaults to 0
	x = p.eval_num_arg(x, 0)
	-- prec defaults to 6
	prec = p.eval_num_arg(prec, 6)
	local s = string.format(string.format("%%.%df", prec), x)
	-- remove non-significant digits
	local sep_pos = s:find('%.')
	local neg = s:find('%-') ~= nil
	if neg then neg = 1 else neg = 0 end
	if prec + neg >= sep_pos then
		s = s:sub(1, prec + 1 + neg)
	else
		s = s:sub(1, prec + neg)
		while #s < sep_pos - 1 do
			s = s .. '0'
		end
	end
	-- remove unnecessary zeros
	if s:find('%.') then
		while s:sub(-1) == '0' do
			s = s:sub(1, -2)
		end
		-- remove unnecessary .
		if s:sub(-1) == '.' then
			s = s:sub(1, -2)
		end
	end
	return s
end

-- cached list of primes for is_prime
local primes = {[1] = false}

-- returns true if integer n is prime; cannot be used with {{#invoke:}}
function p.is_prime(n)
	local cached = primes[n]
	if cached ~= nil then
		return cached
	end
	for i = 2, math.sqrt(n) do
		if n % i == 0 then
			primes[n] = false
			return false
		end
	end
	primes[n] = true
	return true 
end

-- returns prime factorization of integer n > 1; cannot be used with {{#invoke:}}
-- note: the order of keys is not specified for Lua tables
function p.prime_factorization_raw(n)
	local factors = {}
	local m = n
	for i = 2, math.sqrt(n) + 1 do
		while m % i == 0 do
			factors[i] = factors[i] or 0
			factors[i] = factors[i] + 1
			m = m / i
		end
		if m == 1 then
			break
		end
	end
	if m > 1 then
		factors[m] = factors[m] or 1
	end
	return factors
end

-- returns prime factorization of integer n > 2 (with wiki markup for exponents)
function p.prime_factorization(frame)
	local args = getArgs(frame)
	return p._prime_factorization(args[1])
end

function p._prime_factorization(n)
	if n == 1 then
		return "1"
	end
	local factors, powers = {}, {}
	local new_number = p.eval_num_arg(n, 12)
	for i = 2, n do
		if p.is_prime(i) then
			if new_number % i == 0 then
				factors[#factors + 1] = i
				powers[#factors] = 0
				while new_number % i == 0 do 
					powers[#factors] = powers[#factors] + 1
					new_number = new_number / i
				end
				if powers[#factors] > 1 then
					powers[#factors] = factors[#factors] .. "<sup>" .. powers[#factors] .. "</sup>"
				else
					powers[#factors] = factors[#factors]
				end
			end
		end
		if new_number == 1 then
			break
		end
	end
	return table.concat(powers, " × ")
end

-- returns signum(x); cannot be used with {{#invoke:}}
function p.signum(x)
	if type(x) ~= 'number' then
		return 0
	end
	if x > 0 then return 1 end
	if x < 0 then return -1 end
	return 0
end

return p