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Correction of lcm() for Array arguments #56113

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Correction of lcm() for Array arguments #56113

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c7cd31d
Correction of the gcd() and lcm() of Array
cyanescent Oct 11, 2024
0547eae
Merge pull request #1 from cyanescent/patch-Array-lcm-gcd
cyanescent Oct 11, 2024
4e82260
Simpler correction with better error
cyanescent Oct 14, 2024
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10 changes: 8 additions & 2 deletions base/intfuncs.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -36,6 +36,9 @@ julia> gcd(1//3, 2)

julia> gcd(0, 0, 10, 15)
5

julia> gcd([1//3; 2//3])
1//3
```
"""
function gcd(a::T, b::T) where T<:Integer
Expand Down Expand Up @@ -125,6 +128,9 @@ julia> lcm(1//3, 2)

julia> lcm(1, 3, 5, 7)
105

julia> lcm([1//3; 2//3])
2//3
```
"""
function lcm(a::T, b::T) where T<:Integer
Expand All @@ -149,8 +155,8 @@ lcm(a::Real, b::Real, c::Real...) = lcm(a, lcm(b, c...))
gcd(a::T, b::T) where T<:Real = throw(MethodError(gcd, (a,b)))
lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))

gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc; init=one(eltype(abc)))
gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc)
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I understand the change for lcm, but why also change this in gcd, it works fine, doesn't it?

Suggested change
gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc)
gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))

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@cyanescent cyanescent Oct 18, 2024 •
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Right, but does it make sense?

EDIT: it makes sense if we also define:

lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc; init=1//zero(eltype(abc)))

or just lcm(T[]) = 1//zero(T), to prevent returning Vector{Rational} when the input is Vector{Int} for non-empty arrays.
cf. #55379 (comment)

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gcd(T[]) = zero(T) is correct.

From the docstring,

Greatest common (positive) divisor (or zero if all arguments are zero).

In this case, all arguments are zero (vacuously) so the answer is explicitly documented to be zero.

lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc)
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Suggested change
lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc)
lcm(abc::AbstractArray{<:Integer}) = reduce(lcm, abc, init=one(eltype(abc)))
lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc)

For integers, 1 is an identity of LCM (because all integers are a multiple of 1) and is also the correct answer for the empty case (see #55379 (comment)).


function gcd(abc::AbstractArray{<:Integer})
a = zero(eltype(abc))
Expand Down
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