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Module:Rational: Difference between revisions

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Ganaram inukshuk (talk | contribs)
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Add int limit function (prepwork for a separate algorithm)
Unify the format for S-expressions
 
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Line 1: Line 1:
local p = {}
local seq = require("Module:Sequence")
local seq = require("Module:Sequence")
local utils = require("Module:Utils")
local utils = require("Module:Utils")
local p = {}


-- enter a numerator n and denominator m
-- enter a numerator n and denominator m
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end
end


-- is it Sk*S(k+1) or Sk/S(k+1) or Sk^2*S(k+1) or Sk*S(k+1)^2?
-- is it Sk*S(k + 1) or Sk/S(k + 1) or Sk^2*S(k + 1) or Sk*S(k + 1)^2?
for _, k in ipairs(superparticular_indices) do
for _, k in ipairs(superparticular_indices) do
local r1 = superparticular_ratios[k]
local r1 = superparticular_ratios[k]
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if r1 and r2 then
if r1 and r2 then
if p.eq(a, p.mul(r1, r2)) then
if p.eq(a, p.mul(r1, r2)) then
table.insert(expressions, "S" .. k .. " × S" .. (k + 1))
table.insert(expressions, "S" .. k .. "⋅S" .. (k + 1))
end
end
if p.eq(a, p.div(r1, r2)) then
if p.eq(a, p.div(r1, r2)) then
table.insert(expressions, "S" .. k .. " / S" .. (k + 1))
table.insert(expressions, "S" .. k .. "/S" .. (k + 1))
end
end
if p.eq(a, p.mul(p.pow(r1, 2), r2)) then
if p.eq(a, p.mul(p.pow(r1, 2), r2)) then
table.insert(expressions, "S" .. k .. "<sup>2</sup> × S" .. (k + 1))
table.insert(expressions, "S" .. k .. "<sup>2</sup>⋅S" .. (k + 1))
end
end
if p.eq(a, p.mul(r1, p.pow(r2, 2))) then
if p.eq(a, p.mul(r1, p.pow(r2, 2))) then
table.insert(expressions, "S" .. k .. " * S" .. (k + 1) .. "<sup>2</sup>")
table.insert(expressions, "S" .. k .. "⋅S" .. (k + 1) .. "<sup>2</sup>")
end
end
end
end
end
end


-- is it Sk/S(k+2)?
-- is it Sk/S(k + 2)?
for _, k in ipairs(superparticular_indices) do
for _, k in ipairs(superparticular_indices) do
local r1 = superparticular_ratios[k]
local r1 = superparticular_ratios[k]
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if r1 and r2 then
if r1 and r2 then
if p.eq(a, p.div(r1, r2)) then
if p.eq(a, p.div(r1, r2)) then
table.insert(expressions, "S" .. k .. " / S" .. (k + 2))
table.insert(expressions, "S" .. k .. "/S" .. (k + 2))
end
end
end
end
end
end


-- is it S(k-1)*Sk*S(k+1)?
-- is it S(k - 1)*Sk*S(k + 1)?
for _, k in ipairs(superparticular_indices) do
for _, k in ipairs(superparticular_indices) do
local r1 = superparticular_ratios[k - 1]
local r1 = superparticular_ratios[k - 1]
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if r1 and r2 and r3 then
if r1 and r2 and r3 then
if p.eq(a, p.mul(r1, p.mul(r2, 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))
table.insert(expressions, "S" .. (k - 1) .. "⋅S" .. k .. "⋅S" .. (k + 1))
end
end
end
end
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-- compute a canonical representation of `a` modulo powers of `b`
-- compute a canonical representation of `a` modulo powers of `b`
-- TODO: describe the exact behavior
--      it seems bugged when the equave is a fraction
function p.modulo_mul(a, b)
function p.modulo_mul(a, b)
if type(a) == "number" then
if type(a) == "number" then
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local den = p.mul(p.add(k, 1), p.sub(k, 1))
local den = p.mul(p.add(k, 1), p.sub(k, 1))
return p.eq(a, p.div(p.pow(k, 2), den))
return p.eq(a, p.div(p.pow(k, 2), den))
end
-- check if an integer is prime
function p.is_prime(a)
if type(a) == "number" then
a = p.new(a)
end
-- nan, inf, zero, and negative numbers are not prime
if a.nan or a.inf or a.zero or a.sign < 0 then
return false
end
local flag = false -- flag for having exactly one prime factor
for factor, power in pairs(a) do
if type(factor) == "number" and power then
if flag or power ~= 1 then
return false
else
flag = true
end
end
end
return flag
end
end


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a = p.new(a)
a = p.new(a)
end
end
if a.nan or a.inf or a.zero then
return false
-- nan, inf, zero, and negative numbers are not highly composite
end
if a.nan or a.inf or a.zero or a.sign == -1 then
-- negative numbers are not highly composite
if a.sign == -1 then
return false
return false
end
end
-- non-integers are not highly composite
-- non-integers are not highly composite
for factor, power in pairs(a) do
for factor, power in pairs(a) do
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end
end
end
end
local last_power = 1 / 0
local last_power = 1 / 0
local max_prime = p.max_prime(a)
local max_prime = p.max_prime(a)
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end
end


-- find max prime involved in the factorisation
-- Check if ratio is within an int limit; that is, neither its numerator nor
-- (a.k.a. prime limit or harmonic class) of a rational number
-- denominator exceed that limit.
function p.max_prime(a)
function p.is_within_int_limit(a, lim)
if type(a) == "number" then
return p.int_limit(a) <= lim
a = p.new(a)
end
if a.nan or a.inf or a.zero then
return nil
end
local max_factor = 0
for factor, _ in pairs(a) do
if type(factor) == "number" then
if factor > max_factor then
max_factor = factor
end
end
end
return max_factor
end
end


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local num, den = p.as_pair(a_copy)
local num, den = p.as_pair(a_copy)
return math.max(num, den)
return math.max(num, den)
end
-- find max prime involved in the factorisation
-- (a.k.a. prime limit or harmonic class) of a rational number
function p.max_prime(a)
if type(a) == "number" then
a = p.new(a)
end
if a.nan or a.inf or a.zero then
return nil
end
local max_factor = 0
for factor, _ in pairs(a) do
if type(factor) == "number" then
if factor > max_factor then
max_factor = factor
end
end
end
return max_factor
end
end


Line 1,053: Line 1,086:


-- FJS representation of a rational number
-- FJS representation of a rational number
-- might be a bit incorrect
-- NOTE: incorrect for prime 127 and possibly other rare cases
-- TODO: confirm correctness
-- TODO: identify the exact problem and fix it
function p.as_FJS(a)
function p.as_FJS(a)
if type(a) == "number" then
if type(a) == "number" then
Line 1,502: Line 1,535:
function p.ket(frame)
function p.ket(frame)
local unparsed = frame.args[1] or "1"
local unparsed = frame.args[1] or "1"
local result = ""
local a = p.parse(unparsed)
local a = p.parse(unparsed)
if a == nil then
if a == nil then
return '<span style="color:red;">Invalid rational number: ' .. unparsed .. ".</span>"
result = '{{error|Invalid rational number: ' .. unparsed .. ".}}"
else
result = p.as_ket(a, frame)
end
end
return p.as_ket(a, frame)
return frame:preprocess(result)
end
end
p.monzo = p.ket
p.monzo = p.ket


return p
return p
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