#10708: Ideal dimension wrong, depends on term order.
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Reporter: vbraun | Owner: malb
Type: defect | Status: new
Priority: major | Milestone:
Component: commutative algebra | Resolution:
Keywords: Singular ideal dimension | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
I concur that "neglex" should not be allowed as a term order on a
*polynomial ring*. Instead, we can have `LocalPolynomialRing` or something
similar that interfaces somehow with this functionality in singular.
This looks like an abuse of terminology on the side of Singular. Probably
one that is algorithmically very advantageous for them, but you clearly
need to work very carefully with these rings, because there are now
"units" in the ring for which the inverse is not expressible in the
representation used:
{{{
sage: R.<x,y>=PolynomialRing(QQ,order='neglex')
sage: (1+x).is_unit()
True
sage: 1/(1+x)
1
sage: (1+x) * (1/(1+x))
1 + x
}}}
I am sure the functionality in singular is very useful, but we can't
expose it in the way we're doing here.
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Ticket URL: <http://trac.sagemath.org/ticket/10708#comment:11>
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