Bad hash for LaurentMPolyWrap

[karlwessel]

The hash value for a LaurentMPolyWrap a and its negative is equal:

julia> using AbstractAlgebra

julia> R, (a, b) = laurent_polynomial_ring(QQ, [:a, :b])
(Multivariate Laurent polynomial ring in 2 variables over rationals, AbstractAlgebra.Generic.LaurentMPolyWrap{Rational{BigInt}, AbstractAlgebra.Generic.MPoly{Rational{BigInt}}, AbstractAlgebra.Generic.LaurentMPolyWrapRing{Rational{BigInt}, AbstractAlgebra.Generic.MPolyRing{Rational{BigInt}}}}[a, b])

julia> hash(a) == hash(-a)
true

It could be caused by this line:

AbstractAlgebra.jl/src/generic/LaurentMPoly.jl

Line 45 in 6c4cf51

h ^= 0x9c64b62806a3d51d%UInt

which does not make much sense to me, it seems to be always zero for every even integer:

julia> for i in 1:10
       println(UInt(i)^0x9c64b62806a3d51d)
       end
1
0
6835022377903901075
0
17694793150345534037
0
5333000080861380455
0
15995747220507601513
0

[fieker]

On Mon, Mar 09, 2026 at 04:33:14AM -0700, karlwessel wrote: karlwessel created an issue (Nemocas/AbstractAlgebra.jl#2375) The hash value for a LaurentMPolyWrap `a` and its negative is equal: ```julia-repl julia> using AbstractAlgebra julia> R, (a, b) = laurent_polynomial_ring(QQ, [:a, :b]) (Multivariate Laurent polynomial ring in 2 variables over rationals, AbstractAlgebra.Generic.LaurentMPolyWrap{Rational{BigInt}, AbstractAlgebra.Generic.MPoly{Rational{BigInt}}, AbstractAlgebra.Generic.LaurentMPolyWrapRing{Rational{BigInt}, AbstractAlgebra.Generic.MPolyRing{Rational{BigInt}}}}[a, b]) julia> hash(a) == hash(-a) true ``` It could be caused by this line: https://github.com/Nemocas/AbstractAlgebra.jl/blob/6c4cf51196fc88adf5869ec14a9850169b820fa2/src/generic/LaurentMPoly.jl#L45 which does not make much sense to me, it seems to be always zero for every even integer: ```julia-repl julia> for i in 1:10 println(UInt(i)^0x9c64b62806a3d51d) end

I don't know the intention, but UInt(i)^0x9c64b62806a3d51d is raising i to a large power pod 2^64. So if i is even, the power will be divisible by 2^64, hence 0...

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1 0 6835022377903901075 0 17694793150345534037 0 5333000080861380455 0 15995747220507601513 0 ``` -- Reply to this email directly or view it on GitHub: #2375 You are receiving this because you are subscribed to this thread. Message ID: ***@***.***>

[lgoettgens]

This operation should probably be a XOR instead