Sorry. Bad question. I meant something more like "I always normalize the 
symmetric inner product so that the short roots have norm one. From what 
point of view is this different normalization natural?" I guess I can find 
the answer in Kac's book. Thanks for your answer. 

On Thursday, July 28, 2016 at 12:59:37 PM UTC-4, Travis Scrimshaw wrote:
>
>
> On Wednesday, July 27, 2016 at 2:39:48 PM UTC-5, Joseph Hundley wrote:
>>
>> Awesome. Thank you!  
>>
>> Out of curiosity is there a reason .norm_squared() doesn't just divide by 
>> 2 for us? 
>>
>> Because it is just the (symmetric) inner product of the root with itself, 
> and I was following Kac's book when I implemented it.
>
> Best,
> Travis
>
>

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