#20514: is_trivial should be implemented for ideals in multivariate polynomial
rings
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Reporter: kedlaya | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.2
Component: algebra | Resolution:
Keywords: polynomial ring, trivial ideal | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by kedlaya):
The docstring for `is_trivial` states:
{{{
Return ``True`` if this ideal is `(0)` or `(1)`.
}}}
Setting aside the zero ring (where all possible interpretations seem to
lead to the answer `True`), there seem to be three different definitions
floating around for what constitutes a trivial ideal of a ring: the zero
ideal; the unit ideal; or both. In commutative algebra, I'm generally used
to seeing the second interpretation. The first interpretation is the one
compatible with group theory, where triviality tends to refer exclusively
to the one-element subgroup.
This ambiguity makes me wonder whether we should even provide this method
at all! But if we do provide it, then it should be implemented using
comparisons with the `zero_ideal` and/or `unit_ideal` of the parent ring.
--
Ticket URL: <http://trac.sagemath.org/ticket/20514#comment:2>
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