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Module:Harmonics in equal: Difference between revisions

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Created page with "local p = {} local function approx(steps, num, denom, primes, title, prec) local tpri = {'! colspan="2" | Prime number '} local tabs = {'! rowspan="2" | Error \n! absolute..."
 
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Line 1: Line 1:
local p = {}
local p = {}


local function approx(steps, num, denom, primes, title, prec)
local function approx(steps, num, denom, intervals, title, prec)
local tpri = {'! colspan="2" | Prime number '}
local tpri = {'! colspan="2" | Prime number '}
local tabs = {'! rowspan="2" | Error \n! absolute ([[cent|¢]]) '}
local tabs = {'! rowspan="2" | Error \n! absolute ([[cent|¢]]) '}
Line 9: Line 9:
local fmt_rel = ' %+.0f'
local fmt_rel = ' %+.0f'
local equave = math.log(num/denom) / math.log(2)
local equave = math.log(num/denom) / math.log(2)
for _, p in pairs(primes) do
for _, p in pairs(intervals) do
s = math.log(p) / math.log(num/denom)
s = math.log(p) / math.log(num/denom)
v = s*steps
v = s*steps
Line 36: Line 36:
end
end


local primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 }
local intervals = {}
 
intervals.prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 }
intervals.odd = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53 }
intervals.integer = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,  12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27}


-- evaluate input on error use default
-- evaluate input on error use default
Line 65: Line 69:
-- denominator, default: 1
-- denominator, default: 1
local denom = eval_num_arg(frame.args['denom'], 1)
local denom = eval_num_arg(frame.args['denom'], 1)
-- optional number of columns, default: 8
-- optional number of columns, default: 12
local columns = eval_num_arg(frame.args['columns'], 8)
local columns = eval_num_arg(frame.args['columns'], 12)
-- optional start column, default: start with prime 2
-- optional start column, default: start with prime 2
local start = eval_num_arg(frame.args['start'], 1)
local start = eval_num_arg(frame.args['start'], 1)
-- option intervals
local interv = intervals.prime
if frame.args['intervals'] then
interv = intervals[frame.args['intervals']]
end


local name = steps .. 'ed' .. num .. '/' .. denom
local name = steps .. 'ed' .. num .. '/' .. denom
Line 85: Line 94:
local title = frame.args['title']
local title = frame.args['title']
if title == nil or string.len(title) == 0 then
if title == nil or string.len(title) == 0 then
title = 'Approximation of prime intervals in ' .. name
title = 'Approximation of harmonics in ' .. name
end
end
-- optional precision for abs error, default about 3 digits
-- optional precision for abs error, default about 3 digits
local prec = eval_num_arg(frame.args['prec'], prec_by_equal(steps, num, denom))
local prec = eval_num_arg(frame.args['prec'], prec_by_equal(steps, num, denom))
return approx( steps, num, denom, {unpack(primes, start, start+columns-1)}, title, prec)
return approx( steps, num, denom, {unpack(interv, start, start+columns-1)}, title, prec)
end
end


return p;
return p;
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