On Wednesday 28 February 2024 at 08:03:45 UTC-8 Giacomo Pope wrote:

I don't know the history of this choice or what we should be doing 
generally. -1 for polynomials with only positive degree seems like a 
computer science workaround, but for the LaurentPolynomialRing it just 
seems wrong?


I think it's more than just a CS workaround. It has its roots in dimension 
considerations: the space of polynomials of degree at most d is 
(d+1)-dimensional. WIth that convention, 0 having degree -1 makes perfect 
sense.

For deg = - ord_infty it should definitely be -oo, though, and for Laurent 
polynomials the dimension argument doesn't work.

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