Groups are not cached when created

[royess]

It seems that groups are not cached when created. So if I create a same group twice, it will return two unequal objects.

julia> G = abelian_group(10)
Z/10

julia> G1 = abelian_group(10)
Z/10

julia> G == G1
false

julia> GG = small_group(10,1)
Generic group of order 10 with multiplication table

julia> GG1 = small_group(10,1)
Generic group of order 10 with multiplication table

julia> GG == GG1
false

I noticed that rings and fields are typically cached. Are there some specific reasons why we do not cache groups?

[fieker]

On Mon, Sep 09, 2024 at 10:25:13PM -0700, Rabqubit wrote: It seems that groups are not cached when created. So if I create a same group twice, it will return two unequal objects. ```julia julia> G = abelian_group(10) Z/10 julia> G1 = abelian_group(10) Z/10 julia> G == G1 false julia> GG = small_group(10,1) Generic group of order 10 with multiplication table julia> GG1 = small_group(10,1) Generic group of order 10 with multiplication table julia> GG == GG1 false ``` I noticed that rings and fields are typically cached. Are there some specific reasons why we do not cache groups?

For rings/ fields there is an argument that you can (and should!) request caching to be turned off. For groups, mainly, no-one ever wanted this. Also be careful of unintended consequences: for all real quadratic field, the unit group, as an abelian group is abelian_group([2, 0]) Do you really want all those groups to be identical? As a rule of thumbs: the caching is useful mainly for interactive beginners. "All" internal code switches the caching off... What is your application?

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[fingolfin]

So I think the answer essentially is: this works as intended.