Module:Rational: Difference between revisions

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@@ Line 197: / Line 197: @@
 	local n, m = p.as_pair(a)
 	return n / m
+end
+-- return a rational number in ket notation
+-- NaN, infinity, zero values use special representations
+function p.as_ket(a, frame)
+	if type(a) == 'number' then
+		a = p.new(a)
+	end
+	-- special case: NaN
+	if a.nan then
+		return 'NaN'
+	end
+	-- special case: infinity
+	if a.inf then
+		local sign = '+'
+		if a.sign < 0 then
+			sign = '-'
+		end
+		return sign .. '∞'
+	end
+	-- special case: zero
+	if a.zero then
+		return '0'
+	end
+	-- regular case: not NaN, not infinity, not zero
+	local s = ''
+	if a.sign < 0 then
+		s = s .. '-'
+	end
+	-- preparing the argument
+	local largest_prime = -1
+	for factor, power in pairs(a) do
+		if type(factor) == 'number' then
+			if factor > largest_prime then
+				largest_prime = factor
+			end
+		end
+	end
+	local template_arg = ''
+	for i = 2, largest_prime do
+		if u.is_prime(i) then
+			if i > 2 then template_arg = template_arg .. ' ' end
+			template_arg = template_arg .. (a[i] or 0)
+		end
+	end
+	s = s .. frame:expandTemplate{
+		title = 'Monzo',
+		args = {template_arg}
+	}
+	return s
+end
+-- a version of as_ket() that can be {{#invoke:}}d
+function p.ket(frame)
+	local unparsed = frame.args[1] or '1'
+	-- rational form
+	local sign, n, _m, m = unparsed:match('(%-?)%s*(%d*)%s*(/%s*(%d*))')
+	if n == nil then
+		-- integer form
+		sign, n = unparsed:match('(%-?)%s*(%d*)')
+		if n == nil then
+			-- parsing failure
+			return '<span style="color:red;">Invalid rational number: ' .. unparsed .. '.</span>'
+		else
+			m = 1
+			n = tonumber(n)
+			if #sign > 0 then
+				n = -n
+			end
+		end
+	else
+		n = tonumber(n)
+		m = tonumber(m)
+		if #sign > 0 then
+			n = -n
+		end
+	end
+	a = p.new(n, m)
+	return p.as_ket(a, frame)
 end
 return p