Module:Mediants: Difference between revisions

← Older edit

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+-- This module follows [[User:Ganaram inukshuk/Provisional style guide for Lua]]
+local rat   = require("Module:Rational")
+local utils = require("Module:Utils")
 local p = {}
--- Module for finding mediants, either by search depth, int limit, or by a
+-- Mediants consists of code used to find a tree of mediants, starting from a
--- custom search function. Note that ratios produced by this module are NOT the
+-- set of starting ratios (default 1/1 and 1/0). Search can be by int limit,
--- same as that defined by Module:Rational and will require conversion to that
+-- depth, or a custom search function.
--- form. This is because some situations, such as with step ratios, don't need
+-- Ratios produced this way are a table consisting of the numerator and
--- the factorization process that Module:Rational uses.
+-- denominator, which allows for non-simplified ratios to be represented.
+--------------------------------------------------------------------------------
+------------------------------ UTILITY FUNCTIONS -------------------------------
+--------------------------------------------------------------------------------
+-- Given a table of depths, return the deepest depth
+function p.deepest_depth(depths)
+	local deepest = nil
+	for _, value in ipairs(depths) do
+		if not deepest or value > deepest then
+			deepest = value
+		end
+	end
+	return deepest
+end
+-- Given a ratio, return its simplified form.
+function p.simplify_ratio(ratio)
+	local gcd = utils._gcd(ratio[1], ratio[2])
+	return { ratio[1] / gcd, ratio[2] / gcd }
+end
+-- Sort ratios in ascending order. Comparison function is built-in.
+function p.sort_ratios(ratios)
+	table.sort(ratios, function(ratio_1, ratio_2)
+		return ratio_1[1] / ratio_1[2] < ratio_2[1] / ratio_2[2]
+		end
+	)
+end
+--------------------------------------------------------------------------------
+----------------------------- CONVERTER FUNCTIONS ------------------------------
+--------------------------------------------------------------------------------
--- TODO:
+-- Converts ratios into the form defined by [[Module:Rational]], a table
--- Add a convert-to-rational function.
+-- consisting of its prime factorization.
+-- Given a single ratio, as a table of two numbers, convert to rational and
+-- return it.
+function p.to_rational(ratio)
+	return rat.new(ratio[1], ratio[2])
+end
+-- Given a table of ratios, each a table of two numbers, return an array of
+-- ratios in the form as defined by module:Rational.
+function p.to_rationals(ratios)
+	local rats = {}
+	for i = 1, #ratios do
+		table.insert(rats, p.to_rational(ratios[i]))
+	end
+	return rats
+end
 --------------------------------------------------------------------------------
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 function p.tester()
-	return p.find_only_mediants_by_int_limit()
+	--return p.find_only_mediants_by_int_limit()
+	local ratios = {{4,3}, {5,1}, {3,2}}
+	p.sort_ratios(ratios)
+	return p.to_rationals(ratios)
 end
 return p