#5485: issue with dimension of ideals in polynomial rings
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Reporter: AlexGhitza | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: commutative algebra | Keywords:
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Comment(by john_perry):
Looking up a little bit about Krull dimension, I think I see the problem:
ZZ has Krull dimension 1, whereas fields have Krull dimenson 0. The given
code assumes that the ground ring is a field. This is assumed by the
source material in Cox, Little, and O'Shea, so the old code almost works
as it is supposed to.
There was also an issue with the implementation so that even the zero
ideal in a field would be wrong. This is now fixed, so the code works "as
it is supposed to", by which I mean that it works in fields, per the
source material.
However, Alex is right that this is not quite the same as what the
documentation promises, since the documentation talks as if the ring is
arbitrary. So, it doesn't '''really''' work the way it is supposed to. I
have an idea for a fix for the case where the ground ring is not a field:
add the Krull dimension of the ground ring to whatever is computed by the
current code.
But is this correct? If so, the fix is trivial. If not, this will require
a lot more work, since all my references assume fields.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5485#comment:2>
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