MatrixGroups are immutable and their comparison is by checking the 
generators (and not isomorphism), which are essentially the construction 
parameters (in reality, they are the corresponding GAP group). For 
permutation groups, the equality seems to be isomorphism. So there is no 
problem for MatrixGroups being UniqueRepresentation in terms of behavior.

Best,
Travis


On Saturday, May 26, 2018 at 5:53:15 AM UTC+10, Nils Bruin wrote:
>
>
>
> On Friday, May 25, 2018 at 12:17:35 PM UTC-7, Simon King wrote:
>>
>> But they could still be CachedRepresentation. Then, if the same subgroup
>> is given by the same generators, it is identical, but if the same 
>> subgroup is given by different generators, it is just equal but not 
>> identical. 
>>
>> But before doing so, you would need to show that in common scenarios it 
> produces a benefit. It has three significant draw-backs:
>  - you'd slow down the creation of matrix groups in general, because 
> you're requiring the system to first go and look if there already is an 
> object like it.
>  - because the object you get *may* be shared with other code, you're at 
> the mercy of that other code to not mutate it. (and you have to behave 
> yourself too)
>  - it would likely introduce memory leaks (because it's the 
> CachedRepresentation part of UniqueRepresentation that makes these leaks 
> likely).
>  
>

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