Clarify mathematical definition of lcm
#56992
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oscardssmith
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See also: Triage request for this: #57067 (comment) Similar PR for `lcm`: #56992
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See also: Triage request for this: #57067 (comment) Similar PR for `lcm`: #56992 (cherry picked from commit 41a4dfa)
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Some folks define
lcm(x::T,y::T)as anyz::Tsuch that there existsa::T, b::Twitha*x==zandb*y==zand for allzʹ::Tsuch that there exista::T, b::Twitha*x==zʹandb*y==zʹ, there also existsc::Twithz*c==zʹ. This is a reasonable definition, but not what we use. Notably, it makeslcm(x::Rational, y::Rational) = z::Rationaltrue for all finite, nonzerox,y, andz.The definition we use requires
a,b, andcto all be integers, not rationals in the case oflcm(x::Rational, y::Rational). This clarifies what we mean when we definelcm(x::Rational, y::Rational)and also how the generic function should be extended.See this thread for more discussion
cc @oscardssmith