Module:Rational: Difference between revisions

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@@ Line 1: / Line 1: @@
+local seq = require('Module:Sequence')
 local u = require('Module:Utils')
 local p = {}
@@ Line 123: / Line 124: @@
 	end
 	return false
+end
+-- attempt to identify the ratio as a simple S-expression
+function p.find_S_expression(a)
+	if type(a) == 'number' then
+		a = p.new(a)
+	end
+	if a.nan or a.inf or a.zero or a.sign < 0 then
+		return {}
+	end
+	if p.eq(a, 1) then
+		return {}
+	end
+	local max_prime = p.max_prime(a)
+	if seq.square_superparticulars[max_prime] == nil then
+		return {}
+	end
+	local expressions = {}
+	local superparticular_indices = {}
+	local superparticular_ratios = {}
+	for prime, k_array in pairs(seq.square_superparticulars) do
+		if prime <= max_prime + 10 then
+			for i, k in ipairs(k_array) do
+				table.insert(superparticular_indices, k)
+				local Sk_num = p.pow(p.new(k), 2)
+				local Sk_den = p.sub(Sk_num, 1)
+				local Sk = p.div(Sk_num, Sk_den)
+				superparticular_ratios[k] = Sk
+			end
+		end
+	end
+	-- is it a square superparticular?
+	for _, k in ipairs(superparticular_indices) do
+		if p.eq(a, superparticular_ratios[k]) then
+			table.insert(expressions, 'S' .. k)
+		end
+	end
+	-- is it triangle-particular or ultraparticular?
+	for _, k in ipairs(superparticular_indices) do
+		local r1 = superparticular_ratios[k]
+		local r2 = superparticular_ratios[k + 1]
+		if r1 and r2 then
+			if p.eq(a, p.mul(r1, r2)) then
+				table.insert(expressions, 'S' .. k .. ' × S' .. (k + 1))
+			end
+			if p.eq(a, p.div(r1, r2)) then
+				table.insert(expressions, 'S' .. k .. ' / S' .. (k + 1))
+			end
+		end
+	end
+	-- is it 1/3-square-particular?
+	for _, k in ipairs(superparticular_indices) do
+		local r1 = superparticular_ratios[k - 1]
+		local r2 = superparticular_ratios[k]
+		local r3 = superparticular_ratios[k + 1]
+		if r1 and r2 and r3 then
+			if p.eq(a, p.mul(r1, p.mul(r2, r3))) then
+				table.insert(expressions, 'S' .. (k - 1) .. ' × S' .. k .. ' × S' .. (k + 1))
+			end
+		end
+	end
+	-- is it semiparticular?
+	for _, k in ipairs(superparticular_indices) do
+		local r1 = superparticular_ratios[k]
+		local r2 = superparticular_ratios[k + 2]
+		if r1 and r2 then
+			if p.eq(a, p.div(r1, r2)) then
+				table.insert(expressions, 'S' .. k .. ' / S' .. (k + 2))
+			end
+		end
+	end
+	-- is it a product or a ratio of two square superparticulars?
+	for _, k1 in ipairs(superparticular_indices) do
+		local r1 = superparticular_ratios[k1]
+		for _, k2 in ipairs(superparticular_indices) do
+			local r2 = superparticular_ratios[k2]
+			if k1 <= k2 and p.eq(a, p.mul(r1, r2)) then
+				-- check for duplicates
+				local expr = 'S' .. k1 .. ' × S' .. k2
+				local dup = false
+				for _, expr2 in ipairs(expressions) do
+					if expr == expr2 then
+						dup = true
+						break
+					end
+				end
+				if not dup then
+					table.insert(expressions, expr)
+				end
+			end
+			if k1 <= k2 and p.eq(a, p.div(r1, r2)) then
+				-- check for duplicates
+				local expr = 'S' .. k1 .. ' / S' .. k2
+				local dup = false
+				for _, expr2 in ipairs(expressions) do
+					if expr == expr2 then
+						dup = true
+						break
+					end
+				end
+				if not dup then
+					table.insert(expressions, expr)
+				end
+			end
+		end
+	end
+	return expressions
 end
@@ Line 792: / Line 907: @@
 end
--- find max prime in ket notation
+-- find max prime involved in the factorisation of a rational number
 function p.max_prime(a)
 	if type(a) == 'number' then