==(α, q::MP.RationalPoly) and ==(p::MP.AbstractPolynomialLike, α) cause many invalidations

[sumiya11]

To check this, I run

# from https://sciml.ai/news/2022/09/21/compile_time/
using SnoopCompile

invalidations = @snoopr begin
    using AbstractAlgebra
    R, (x,y) = polynomial_ring(QQ, ["x","y"], ordering=:degrevlex)
    using Groebner
    groebner([x^2 - y^2, x*y^2 + x])
end

trees = SnoopCompile.invalidation_trees(invalidations);

@show length(SnoopCompile.uinvalidated(invalidations)) # show total invalidations (1102)

show(trees[end-1])
show(trees[end-2])

(Groebner.jl loads MultivariatePolynomials.jl).

I have

 inserting ==(α, q::MultivariatePolynomials.RationalPoly) @ MultivariatePolynomials C:\Users\User\.julia\packages\MultivariatePolynomials\TpRhf\src\comparison.jl:118 invalidated:
   backedges: 1: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Core.MethodInstance, ::Any) (6 children)
              2: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Module, ::Any) (11 children)
              3: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Method, ::Any) (33 children)
              4: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Symbol, ::Any) (154 children)
              5: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Core.TypeName, ::Any) (164 children)
              6: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Symbol, ::Any) (1 children)
              7: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Symbol, ::Any) (4 children)

 inserting ==(p::MultivariatePolynomials.AbstractPolynomialLike, α) @ MultivariatePolynomials C:\Users\User\.julia\packages\MultivariatePolynomials\TpRhf\src\operators.jl:65 invalidated:
   backedges: 1: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::Cthulhu.DInfo.DebugInfo) (6 children)
              2: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::Core.MethodInstance) (8 children)
              3: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::Symbol) (420 children)
              4: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::typeof(display)) (2 children)
              5: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::Symbol) (1 children)
              6: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::Symbol) (1 children)
              7: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::typeof(display)) (1 children)
              8: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::typeof(display)) (11 children)
              9: superseding ==(x, y) @ Base Base.jl:165 with MethodInstance for ==(::Any, ::Symbol) (2 children)

This amounts to 825 method invalidations out of 1102.

I wonder if it would be okay to rewrite these methods with the use of isa (or even remove them) ?