Why does One require Mul?

[ZettaScript]

While this is algebraically correct, implementations may not be able to provide One and Mul for the same types.

For example, I implemented polynomial quotient rings $(\mathbb{Z}/q\mathbb{Z})/(x^n+1)$ as a type Poly that implements One, but not Mul because naive polynomial multiplication would be inefficient and require a lot of code (division and extended Euclidean algorithm on polynomials). Instead, multiplication is done efficiently in the Number Theoretic Transform (NTT) domain, which is represented as a different type PolyNtt to ensure mathematical soundness. In this case I have to create my own trait One without the requirement.

[mdepta42]

This requirement also blocks usage with dimensional analysis crates, like uom where Length * Length == Area.

[twolodzko]

Adding to this, I recently wanted to use the One and Zero traits for a type that had Mul implemented only for the reference of the type, while One requires Mul for the type. I ended up not using the trait because I didn't need the unnecessary Mul.