Quadratic rings perhaps? A fair number of those are UFD:

sage: K.<a>=NumberField(x^2-3)
sage: O=K.ring_of_integers()
sage: b=O(a-2)
sage: %timeit b.is_unit()
664 ns ± 4.24 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
sage: %timeit b.is_one()
55.8 ns ± 0.214 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops 
each)

On Thursday, 12 December 2024 at 05:50:14 UTC-8 Marc Mezzarobba wrote:

> Marc Mezzarobba wrote:
> >> for testing purposes I am in need of an UFD in Sage for which is_unit
> >> is significantly slower than is_one.
> > 
> > Matrices?
>
> Woops, I read “a ring” insteand of “an ufd”...
>
> -- 
> Marc
>
>

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