Dear all,

for testing purposes I am in need of an UFD in Sage for which is_unit is 
significantly slower than is_one.  Note that, unfortunately, quotient rings 
do not seem supported currently.

Background: my pull request https://github.com/sagemath/sage/pull/38924 
provides a critical speedup for several computations. Originally, I did 
this to make my functional equations solver usable, but it also affects 
completely unrelated code.  For example,

sage: P.<x,y>=ProjectiveSpace(QQbar, 1) 
sage: E=EllipticCurve([1, 2]) 
sage: f=P.Lattes_map(E, 2) 
sage: f.Lattes_to_curve(check_lattes=true)

gets a speedup from 14 seconds down to 8 seconds.

The pull requests optimises a gcd computation in generic (i.e., 
non-libsingular) polynomial rings.  One difference is, that when computing 
the content of a polynomial, I am checking for is_unit(), rather than 
is_one().

In all rings I could construct, there is not a huge difference in timings 
for the two methods.  But I would like to make sure that I am not missing 
anything, especially since we still do not have any performance regression 
tests.

Best wishes,

Martin

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