Hey Ben,
> I came across the following
>
> {{{
> R.<x> = ZZ[]
> S.<t> = R.quo(x^2+5)
> S in IntegralDomains()
> False
> }}}
>
This was an easy fix since we do the primitive test when constructing the
quotient. This is http://trac.sagemath.org/ticket/17450 which is
needs_review.
> and even simpler
> {{{
> R=Zmod(5)
> R in IntegralDomains()
> False
> }}}
> This is related to
>
> https://groups.google.com/forum/#!topic/sage-algebra/6C3XkkLfllw
>
> but I couldn't find what ticket it is associated with. I know Sage is
> trying to move away from tests like is_integral_domain() to tests like in
> IntegralDomains, but those examples are both wrong. Is there some issue
> with getting those to work?
>
The containment testing for IntegralDomains should mimic that of Fields, in
that somewhere it should try is_integral_domain() if it's an attribute.
Moreover, Zmod should outsource is_integral_domain() to the is_field()
test. However this is a more expansive change, but it shouldn't be
controversial...
Best,
Travis
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