Module:Rational: Difference between revisions
gcd no longer needs to be defined here |
Re-comment some functions; implement log base 2 from module: Utils |
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end | end | ||
-- find max prime involved in the factorisation of a rational number | -- find max prime involved in the factorisation | ||
-- (a.k.a. prime limit or harmonic class) of a rational number | |||
function p.max_prime(a) | function p.max_prime(a) | ||
if type(a) == 'number' then | if type(a) == 'number' then | ||
| Line 896: | Line 897: | ||
end | end | ||
-- | -- convert a rational number to its size in octaves | ||
-- equal to log2 of the rational number | |||
function p.log(a, base) | function p.log(a, base) | ||
base = base or 2 | base = base or 2 | ||
| Line 917: | Line 919: | ||
for factor, power in pairs(a) do | for factor, power in pairs(a) do | ||
if type(factor) == 'number' then | if type(factor) == 'number' then | ||
logarithm = logarithm + power * | logarithm = logarithm + power * u._log(factor, base) | ||
end | end | ||
end | end | ||
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for factor, power in pairs(a) do | for factor, power in pairs(a) do | ||
if type(factor) == 'number' then | if type(factor) == 'number' then | ||
h = h + math.abs(power) * | h = h + math.abs(power) * u._log(factor, 2) | ||
end | end | ||
end | end | ||
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for factor, power in pairs(a) do | for factor, power in pairs(a) do | ||
if type(factor) == 'number' then | if type(factor) == 'number' then | ||
h2 = h2 + power * | h2 = h2 + power * u._log(factor, 2) | ||
end | end | ||
end | end | ||
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end | end | ||
-- convert a rational number to cents | -- convert a rational number to its size in cents | ||
function p.cents(a) | function p.cents(a) | ||
if type(a) == 'number' then | if type(a) == 'number' then | ||
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for factor, power in pairs(a) do | for factor, power in pairs(a) do | ||
if type(factor) == 'number' then | if type(factor) == 'number' then | ||
c = c + power * | c = c + power * u._log(factor, base) | ||
end | end | ||
end | end | ||
return c * 1200 | return c * 1200 | ||
end | end | ||