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:
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 jkeitel)

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 jkeitel

  • Description modified (diff)

comment:2 Changed 7 years ago by jkeitel

  • Status changed from new to needs_review

comment:3 Changed 7 years ago by vbraun

Should always be base_ring for consistency. Even if we currently only support fields...

comment:4 Changed 7 years ago by vbraun

  • Authors set to Jan Keitel
  • Reviewers set to Volker Braun
  • Status changed from needs_review to positive_review

comment:5 Changed 7 years ago by vbraun

  • Branch changed from u/jkeitel/toric_change_ring to 0ddcf4da121461367f2e2b547243a489af79ccc7
  • Resolution set to fixed
  • Status changed from positive_review to closed
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