Degree of the zero polynomial

[Antonio95]

Calling degree on the zero (univariate) polynomial returns 0 (here). However, the usual mathematical convention is either -infinity (with the set of degrees = N U {-infty} forming an monoid) or "undefined". In particular, setting degree(0) = 0 violates degree(fg) = degree(f) + degree(g).

Making degree return an Option would be mathematically elegant, but also programmatically cumbersome - aside from a massive breaking change. Perhaps a better solution can be found? I understand this is pretty much a non-issue, but I felt compelled to bring it up.

[emberian]

I had an annoying bug in some code expecting poly.coeffs()[..=poly.degree()] to be valid, but fortunately it was unsubtle and obvious how to fix; an extra Option would have slightly saved my effort by forcing me to remember the zero polynomial.

[Antonio95]

I agree, I have also found that being forced to treat that case separately sometimes improves the design or avoids bugs :)

[Pratyush]

Hm it is true that the degree of the zero-polynomial is indeed defined differently (I actually encountered this before when trying to do so polynomial stuff in Lean). I don't know of a good solution, however...

[Antonio95]

Something that has given me good results is for degree() to return an Option<usize>, which

• On one hand, is mathematically clean (cLEAN ;)) and forces the programmer to at least think about the zero case.
• On the other, it is not too cumbersome in practice due to how many convenience functions and syntax are built around the Option type in Rust.

But this is really just a suggestion. The breaking change would of course be sizable.