div(pi,pi), rem(pi,pi) etc undefined

[JeffreySarnoff]

This issue was raised in this discourse thread

possible remedy

Base.Math.mod(::Irrational{T}, ::Irrational{T}) where T = 0.0
Base.Math.rem(::Irrational{T}, ::Irrational{T}) where T = 0.0
Base.Math.div(::Irrational{T}, ::Irrational{T}) where T = 1.0
Base.Math.fld(::Irrational{T}, ::Irrational{T}) where T = 1.0
Base.Math.cld(::Irrational{T}, ::Irrational{T}) where T = 1.0
Base.Math.divrem(::Irrational{T}, ::Irrational{T}) where T = 1.0, 0.0
Base.Math.fldmod(::Irrational{T}, ::Irrational{T}) where T = 1.0, 0.0

and these, as currently evaluated, are anomalous (suggestions follow)

# fn in {div, fld, cld}
fn( Inf, x:::isfinite(x)) =  Inf
fn(-Inf, x:::isfinite(x)) = -Inf

# fn in {rem, mod} 
fn( Inf, x:::isfinite(x)) =  0.0
fn(-Inf, x:::isfinite(x)) = -0.0

[StefanKarpinski]

Since operations with irrationals default to Float64 results, those should probably all return 0.0 and 1.0.

[tomaklutfu]

May not be the same thing but https://discourse.julialang.org/t/comparison-of-same-irrationals-by-throws-error/1342 . May be even more for the same irrationals.

[JeffreySarnoff]

re returning 0.0 and 1.0 (yes, the .0s were implied) :) fixed above

[simonbyrne]

For the infinities, see #26694.

[JeffreySarnoff]

all of these paths lead to good places

[GunnarFarneback]

It looks natural to extend the list at
https://github.com/JuliaLang/julia/blob/master/base/irrationals.jl#L123

for op in Symbol[:+, :-, :*, :/, :^]
    @eval $op(x::AbstractIrrational, y::AbstractIrrational) = $op(Float64(x),Float64(y))
end

[Nosferican]

Maybe this could be added to the PR, (in its correct form)

median(AbstractArray{S, Integer}) where S<:Irrational = S

similar to how

mode([π,π]) == π

mean could probably go this way of specialized methods for Irrational.

[vtjnash]

We discussed this on triage, and felt that it is better to be explicit about the transforms for irrational numbers into the appropriate computational types and not add more methods to them.