> but my question is, which application/generic algorithm right now uses
> that finite fields are trivalĀ  Differential rings?

But the question raised by Johannes is also why we do not immediately
equip every commutative ring with a trivial differential structure?
That can be overridden by the implementation of a concret domain if
necessary.

UnivariatePolynomialCategory declares itself do be a differential ring
and implicitly assumes that the coefficients are constants. That maybe
efficient, but is not generic.

> And: With this principal answer one could add everything to everything,
> so why not add a trivial total order x < y being false all the time?

That's not consistent. If x < y is false, then y < x or x=y should be
true. https://en.wikipedia.org/wiki/Total_order

I agree, however, with Johannes that seeing ALL exported functions of a
domain is too much information for a beginner. I have no solution to
this problem except for writing good tutorials of how to use a domain.

Ralf

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