#15979: Toric varieties can be tricked into accepting base rings that are not
fields
-------------------------------------+-------------------------------------
Reporter: jkeitel | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.2
Component: algebraic geometry | Keywords: toric
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | u/jkeitel/toric_change_ring
0ddcf4da121461367f2e2b547243a489af79ccc7| Dependencies:
Stopgaps: |
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There are a couple of odd things right now:
This does not work:
{{{
sage: R = PolynomialRing(QQ, 2, 'a')
sage: P2 = toric_varieties.P2(base_ring=R)
...
TypeError: need a field to construct a Fano toric variety!
Got Multivariate Polynomial Ring in a0, a1 over Rational Field
}}}
However, this does:
{{{
sage: R = PolynomialRing(QQ, 2, 'a')
sage: P2 = toric_varieties.P2(base_ring=QQ)
sage: P2 = P2.change_ring(R)
sage: P2.base_ring()
Multivariate Polynomial Ring in a0, a1 over Rational Field
}}}
The same problem also occurs for ToricVariety instead of
CPRFanoToricVariety.
Allowing general rings leads to some annoying behavior such as
{{{
sage: P2.base_ring()
Multivariate Polynomial Ring in a0, a1 over Rational Field
sage: P2.dimension()
4
}}}
Here the dimension of the spectrum of the base ring is added. Because of
that, integration in toric varieties work (although this can be fixed, of
course).
In any case, if one requires toric varieties to be defined over fields, it
should at least be consistent.
Best,
Jan
PS: It's also a bit annoying that ToricVariety and CPRFanoToricVariety
allow for the keyword base_field, but the catalog only allows base_ring.
Should that be adjusted?
--
Ticket URL: <http://trac.sagemath.org/ticket/15979>
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