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Module:SB tree: Difference between revisions

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local p = {}
local p = {}
local rat = require('Module:Rational')
 
local yesno = require("Module:Yesno")


-- Function that constructs a sequence of ratios according to the Stern-Brocot tree
-- Function that constructs a sequence of ratios according to the Stern-Brocot tree
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-- Mediants are found between adjacent ratios iteratively
-- Mediants are found between adjacent ratios iteratively
-- Start and stop ratio may be any two ratios, but the default values are 1/1 and 1/0
-- Start and stop ratio may be any two ratios, but the default values are 1/1 and 1/0
-- Depth may be specified to be any value, but the default is 4
-- Depth may be specified to be any value, but the default is 4; this is how many generations
-- after the initial ratios to produce successive layers of the tree, so depth 4 is 5 layers
-- Edge extend iteratively finds the mediants of the first two and last two ratios; default is 0
-- Edge extend iteratively finds the mediants of the first two and last two ratios; default is 0
-- Transpiled from python code to lua with aid of ChatGPT
-- Transpiled from python code to lua with aid of ChatGPT
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end
end


-- Test function that produces the ratios of the SB tree as a one-column table, using different arguments
-- Function that calculates the depths of each ratio in the Stern-Brocot tree
-- This is nearly identical to the sb_tree_ratios function, except only the depth
-- and edge extend are needed
-- Transpiled from python code to lua with aid of ChatGPT
function p.sb_tree_depths(depth, edge_extend)
-- Default parameter values
depths = depths or 4
edge_extend = edge_extend or 0
    -- Initial depths of the initial ratios are 1 for lua programming purposes
    local tree = {1, 1}
 
-- Calculate depths for successive layers in the tree
    for i = 1, depth do
        local new_tree = {}
 
-- Depths of the first and mediant of first and second ratio are added in pairs
-- The last ratio is added after the for loop itself
        for j = 1, #tree - 1 do
            local depth_1 = tree[j]
            local depth_new = i + 1
 
            table.insert(new_tree, depth_1)
            table.insert(new_tree, depth_new)
        end
 
        table.insert(new_tree, tree[#tree])
        tree = new_tree
    end
 
    -- For extending the edges of the tree
    -- When edge-extending, the first and last depths must always be 1
    for i = 1, edge_extend do
        -- Extend at end
        tree[#tree] = tree[#tree - 1] + 1
        table.insert(tree, 1)
 
        -- Extend at front
        tree[1] = tree[2] + 1
        table.insert(tree, 1, 1)
    end
 
    return tree
end
 
-- Helper function that parses ratios entered as "p/q", returning it as an array { p, q }
function p.parse_ratio(ratio_unparsed)
local ratio = {}
for number in string.gmatch(ratio_unparsed, '([^/]+)') do
table.insert(ratio, number)
end
return ratio
end
 
-- Test function that produces the ratios of the SB tree as a multi-column table, using different arguments
-- To try this out, add the following text (not as a lua comment):
-- To try this out, add the following text (not as a lua comment):
-- {{#invoke:SB_tree|sb_table}}
-- {{#invoke: SB_tree|sb_table}}
function p.sb_table(frame)
function p.sb_table(frame)
-- Call the sb function
-- Call the sb function
-- Start/stop ratios are the same, depth is deeper, and edge-extend is allowed
-- Start/stop ratios are the same, depth is deeper, and edge-extend is allowed
local sb_tree_ratios = p.sb_tree_ratios(5, {1, 1}, {1, 0}, 3)
local depth = frame.args["Depth"] or 4
local edge_extend = frame.args["Edge Extend"] or 2
local start_ratio_unparsed = frame.args["Start Ratio"] or "1/1"
local stop_ratio_unparsed = frame.args["Stop Ratio"] or "1/0"
local stagger_ratios = (frame.args["Stagger Ratios"] and string.lower(frame.args["Stagger Ratios"])) == "true" and true or false
-- Parse ratios
local start_ratio = p.parse_ratio(start_ratio_unparsed)
local stop_ratio = p.parse_ratio(stop_ratio_unparsed)
-- Get the ratios and depths
local sb_tree_depths = p.sb_tree_depths(depth, edge_extend)
local sb_tree_ratios = p.sb_tree_ratios(depth, start_ratio, stop_ratio, edge_extend)
-- Create the table
-- Create the table
result = '{| class="wikitable"\n'
result = "{| class=\"wikitable\"\n|-\n"
result = result .. "|+\n"
.. "! "
result = result .. "|-\n"
-- Create the header cell
result = result .. "! Ratio\n"
if stagger_ratios then
result = result .. "colspan=\"" .. depth + edge_extend + 1 .. "\" | "
end
result = result .. "Ratios\n"
-- Create the individual rows
for i = 1, #sb_tree_ratios
for i = 1, #sb_tree_ratios
do
do
result = result .. "|-\n"
result = result .. "|-\n"
result = result .. "|" .. sb_tree_ratios[i][1] .. "/" ..  sb_tree_ratios[i][2] .. "\n"
-- Create the cells for each row
if stagger_ratios then
-- Stagger ratios
for j = 1, depth + edge_extend + 1 do
result = result .. "| "
if j == sb_tree_depths[i] then
result = result .. sb_tree_ratios[i][1] .. "/" ..  sb_tree_ratios[i][2]
end
result = result .. "\n"
end
else
-- Don't stagger ratios
result = result .. "| " .. sb_tree_ratios[i][1] .. "/" .. sb_tree_ratios[i][2] .. "\n"
end
end
end
result = result .. "|}"
result = result .. "|}"
return result
-- Debugger option
local debugg = yesno(frame.args["debug"])
if debugg == true then
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
end
return frame:preprocess(result)
end
end


return p
return p
Retrieved from "https://en.xen.wiki/w/Module:SB_tree"