On Monday, January 5, 2015 9:00:01 AM UTC-8, Daniel Krenn wrote:
>
> I have two groups A and B whose elements can be multiplied in a group C 
> (constructed out of A and B). Due to the nature of those groups, C 
> *cannot* be discovered by a functorial construction [1] as pushout. 
>

In that case my first reaction is that the "common" parent should probably 
*not* be discovered automatically. Even in many cases where there is a 
functorial construction of a common parent (for instance, for QQ-algebras, 
one can always take the tensor product), it is not a good idea to let sage 
discover/construct the common parent. I have seen on several occasions 
cases where initially it seems like a great idea to make something 
automatic (such as common parent discovery), but where in the longer run it 
turns out to never occur or be needed in practice. I'd recommend 
implementing whatever you need without and reevaluate after a year's use if 
you're really itching for this feature. There's a good chance that you 
don't, and in that case you'll have had so much more time to spend on 
interesting mathematics rather than (probably) useless infrastructure. 

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