Opened 7 years ago
Closed 7 years ago
#15979 closed defect (fixed)
Toric varieties can be tricked into accepting base rings that are not fields
Reported by: | jkeitel | Owned by: | |
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Priority: | minor | Milestone: | sage-6.2 |
Component: | algebraic geometry | Keywords: | toric |
Cc: | novoselt, vbraun | Merged in: | |
Authors: | Jan Keitel | Reviewers: | Volker Braun |
Report Upstream: | N/A | Work issues: | |
Branch: | 0ddcf4d (Commits) | Commit: | 0ddcf4da121461367f2e2b547243a489af79ccc7 |
Dependencies: | Stopgaps: |
Description (last modified by )
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 does not 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?
Change History (5)
comment:1 Changed 7 years ago by
- Description modified (diff)
comment:2 Changed 7 years ago by
- Status changed from new to needs_review
comment:3 Changed 7 years ago by
comment:4 Changed 7 years ago by
- Reviewers set to Volker Braun
- Status changed from needs_review to positive_review
comment:5 Changed 7 years ago by
- Branch changed from u/jkeitel/toric_change_ring to 0ddcf4da121461367f2e2b547243a489af79ccc7
- Resolution set to fixed
- Status changed from positive_review to closed
Should always be
base_ring
for consistency. Even if we currently only support fields...