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Module:No-1s limits: Difference between revisions

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


-- compute all positive ratios n/m with n and m <= q modulo powers of equave
-- compute all positive ratios n/m with n and m <= q modulo powers of equave
Line 8: Line 10:
equave = equave or 2
equave = equave or 2
local ratios = {}
local ratios = {}
if rat.eq(rat.modulo_mul(rat.new(q, 1), equave), 1) then return ratios end
if previous then
if previous then
for n = 1, q do
for n = 2, q do
local a = rat.new(n, q)
if not rat.eq(rat.modulo_mul(rat.new(n, 1), equave), 1) then
a = rat.modulo_mul(a, equave)
local a = rat.new(n, q)
local a_key = rat.as_ratio(a)
a = rat.modulo_mul(a, equave)
local a_key = rat.as_ratio(a)
local b = rat.new(q, n)
b = rat.modulo_mul(b, equave)
local b = rat.new(q, n)
local b_key = rat.as_ratio(b)
b = rat.modulo_mul(b, equave)
local b_key = rat.as_ratio(b)
if previous[a_key] == nil then
ratios[a_key] = a
if previous[a_key] == nil then
end
ratios[a_key] = a
if previous[b_key] == nil then
end
ratios[b_key] = b
if previous[b_key] == nil then
ratios[b_key] = b
end
end
end
end
end
else
else
for n = 1, q do
for n = 2, q do
for m = 1, q do
if not rat.eq(rat.modulo_mul(rat.new(n, 1), equave), 1) then
local a = rat.new(n, m)
for m = 2, q do
a = rat.modulo_mul(a, equave)
if not rat.eq(rat.modulo_mul(rat.new(n, 1), equave), 1) then
local key = rat.as_ratio(a)
local a = rat.new(n, m)
ratios[key] = a
a = rat.modulo_mul(a, equave)
local key = rat.as_ratio(a)
ratios[key] = a
end
end
end
end
end
end
Line 178: Line 187:
end
end


function p.for_small_edos (frame)
-- find vals generate no-1s consistency intervals
local lines = tonumber (frame.args['lines'])
-- returns string with wart notation
-- limit must meet no-1s odd-limit consistency
function p.vals(et, limit)
local primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43}
local wart = 'abcdefghijklmn'
local patent_val = {}
local wart_dir = {}
local minprime
local val = {}
local rets = {}
for i = 1, #primes do
patent_val[i] = ET.approximate(et, primes[i])
if ET.cents(et, patent_val[i]) < math.log(primes[i]) / math.log(2) * 1200 then
wart_dir[i] = -1
else
wart_dir[i] = 1
end
end
if et.equave == 2 then
minprime = 3
else
minprime = 2
end
local previ = 1
for i = 1, #primes do
local ip = primes[i]
if ip > limit then break end
if ip == et.equave then
val[i] = patent_val[i]
elseif ip == minprime then
val[i] = patent_val[i]
previ = i
else
val[i] = val[previ] + ET.approximate(et, ip / primes[previ])
previ = i
end
end
 
rets[1] = ''
if et.equave ~= 2 then
local i = table.find(primes, et.equave)
if i then
rets[1] = rets[1] .. string.sub(wart, i, i)
else
rets[1] = rets[1] .. 'q'
end
end
rets[1] = rets[1] .. et.size
if limit < minprime * minprime then
local nonpatent = false
local binded = false
local bias = 0
for i = 1, #val do
local ip = primes[i]
if ip == et.equave then
elseif ip == minprime then
bias = wart_dir[i]
else
if val[i] ~= patent_val[i] then
nonpatent = true
elseif wart_dir[i] ~= bias then
binded = true
end
end
end
if nonpatent or not binded then
rets[2] = '' .. rets[1]
for i = 1, #val do
local ip = primes[i]
local difference = (val[i] - patent_val[i]) * wart_dir[i]
if difference > 0 then
rets[1] = rets[1] .. string.rep(string.sub(wart, i, i), difference * 2)
elseif difference < 0 then
rets[1] = rets[1] .. string.rep(string.sub(wart, i, i), -difference * 2 - 1)
end
end
for i = 1, #val do
local ip = primes[i]
if ip ~= et.equave then val[i] = val[i] - bias end
local difference = (val[i] - patent_val[i]) * wart_dir[i]
if difference > 0 then
rets[2] = rets[2] .. string.rep(string.sub(wart, i, i), difference * 2)
elseif difference < 0 then
rets[2] = rets[2] .. string.rep(string.sub(wart, i, i), -difference * 2 - 1)
end
end
if bias > 0 then rets = {rets[2], rets[1]} end
end
else
for i = 1, #val do
local ip = primes[i]
if ip * minprime <= limit then
if val[i] ~= patent_val[i] then
return '(error)'
end
end
local difference = (val[i] - patent_val[i]) * wart_dir[i]
if difference > 0 then
rets[1] = rets[1] .. string.rep(string.sub(wart, i, i), difference * 2)
elseif difference < 0 then
rets[1] = rets[1] .. string.rep(string.sub(wart, i, i), -difference * 2 - 1)
end
end
end
return table.concat (rets, ", ")
end
 
function p.for_small_edos(frame)
local liners = tonumber(frame.args['lines'])
local debugg = yesno(frame.args['debug'])
local t_body = {}
local t_body = {}
local val = {}
local val = {}
for i = 1, lines do
et = ET.parse('' .. i .. 'edo')
for i = 1, liners do
limit = p.consistency_limit(et, false, 43)
local et = ET.parse('' .. i .. 'edo')
t_body[i] = string.format ("|-\n| %s\n| %s", i, limit)
local limit = p.consistency_limit(et, false, 43)
local vals = p.vals(et, limit)
t_body[i] = string.format("|-\n| %s\n| %s\n| %s", i, limit, vals)
end
end


return "{| class=\"wikitable center-all mw-collapsible mw-collapsed\"\n" ..
local result = "{| class=\"wikitable center-all mw-collapsible mw-collapsed\"\n" ..
"|+style=white-space:nowrap\n" ..
"|-\n" ..
"|-\n" ..
"! EDO\n" ..
"! EDO\n" ..
"! Consistency limit\n" ..
"! No-1s consistency limit\n" ..
table.concat (t_body, "\n") ..
"! Associated vals\n" ..
table.concat(t_body, "\n") ..
"\n|}"
"\n|}"
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:No-1s_limits"