Opened 2 years ago
Closed 2 years ago
#29225 closed defect (fixed)
Cartesian product of modules has no base ring
Reported by: | pbruin | Owned by: | |
---|---|---|---|
Priority: | minor | Milestone: | sage-9.1 |
Component: | commutative algebra | Keywords: | module, base ring |
Cc: | Merged in: | ||
Authors: | Peter Bruin | Reviewers: | Travis Scrimshaw |
Report Upstream: | N/A | Work issues: | |
Branch: | b766a52 (Commits, GitHub, GitLab) | Commit: | b766a52018a6a2e08df396ec0b4555f7ff9e2dda |
Dependencies: | Stopgaps: |
Description
In SageMath 9.1.beta4:
sage: M = cartesian_product((ZZ^2, ZZ^3)); M The Cartesian product of (Ambient free module of rank 2 over the principal ideal domain Integer Ring, Ambient free module of rank 3 over the principal ideal domain Integer Ring) sage: M.category() Category of Cartesian products of modules with basis over (euclidean domains and infinite enumerated sets and metric spaces) sage: M.base_ring() # should be Integer Ring
Change History (5)
comment:1 Changed 2 years ago by
- Branch set to u/pbruin/29225-cartesian_product_base_ring
- Commit set to b766a52018a6a2e08df396ec0b4555f7ff9e2dda
- Status changed from new to needs_review
comment:2 follow-up: ↓ 3 Changed 2 years ago by
comment:3 in reply to: ↑ 2 Changed 2 years ago by
Replying to tscrim:
Should we test for
is R
or== R
, as I think we could have equal-but-not-identical rings in Sage:
It is possible to implement classes for rings that have this behaviour, although I could not find them in the Sage library. I think it is safer not to choose one of these equal-but-not-identical rings as the base ring of the product. Working with modules over equal-but-not-identical rings sounds like something that will hardly ever occur in practice, and that will be unnecessarily slow and sensitive to bugs because of coercion between the different copies. In short, I propose sticking with is
.
comment:4 Changed 2 years ago by
- Reviewers set to Travis Scrimshaw
- Status changed from needs_review to positive_review
Sounds like we are in agreement. Thank you.
comment:5 Changed 2 years ago by
- Branch changed from u/pbruin/29225-cartesian_product_base_ring to b766a52018a6a2e08df396ec0b4555f7ff9e2dda
- Resolution set to fixed
- Status changed from positive_review to closed
Should we test for
is R
or== R
, as I think we could have equal-but-not-identical rings in Sage:Now I know this is not a demonstration, but it would be quite reasonable for this to someday return
True
. I probably am on the side of actuallyis
because the==
could have base rings that are subtly different, but I wanted to get your thoughts.