On Monday, October 28, 2019 at 3:30:03 AM UTC-7, Michael Jung wrote:
>
> Nice example! I see your point.
>
> However, I wonder. The matrix inversion should cause the same problem, but 
> it is implemented for the symbolic ring. What is different?
>

I don't think it is really implemented *for* the symbolic ring. It's just 
an implementation that gets used for the symbolic ring and once people 
submit enough bug reports about it, it probably needs to be deprecated of 
be adorned with a warning message.

For Gram-Schmidt, there's a further problem: you need a definite inner 
product for it to work. SR contains elements from C. So do we take the 
standard Hermitian inner product? In fact, there are all kinds of functions 
in there as well, so perhaps a Hilbert space inner product is appropriate. 
But which one? I think the problems of SR for this are so obvious that 
no-one dared to ignore them when thinking of providing an implementation.

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