#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 AlexGhitza):
OK, so there are several issues here.
One is that we're not sure that the naive algorithm implemented in
dimension() works over base rings that are not fields. The most
interesting instance of this (in my opinion) is when the base ring is ZZ.
We are currently returning wrong answers, so even raising a
{{{NotImplementedError}}} would be preferable. Of course, it would be
nice if we could get it to work -- but note that Singular 3.1.0 will have
support for polynomial rings over ZZ, so in the worst case we can wait
until they release.
The more pressing issue is that the naive algorithm returns wrong answers
even if you run it over QQ. To see this, try the following as it is now:
{{{
sage: R.<x, y> = QQ[]
sage: I = R.ideal(0)
sage: I.dimension()
2
}}}
This is the correct answer, and it's coming directly from Singular.
However, we can force Sage to use the naive algorithm by inserting
{{{raise TypeError}}} on line 977 of {{{multi_polynomial_ideal.py}}}. Run
{{{sage -br}}} and try the same computation again:
{{{
sage: R.<x, y> = QQ[]
sage: I = R.ideal(0)
sage: I.dimension()
verbose 0 (932: multi_polynomial_ideal.py, dimension) Warning: falling
back to very slow toy implementation.
1
}}}
This is wrong and should be our main priority. In fact, I think it would
be ok to just fix this for this ticket and open enhancement tickets for
dimension() over tricky base rings.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5485#comment:6>
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