Module:Rational: Difference between revisions
Request precise description |
+is_prime |
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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 | ||
-- nan, inf, zero, and negative numbers are not highly composite | |||
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) | ||