Opened 2 years ago

Last modified 2 months ago

#28692 new defect

ideal generation confusing (or wrong)

Reported by: kcrisman Owned by:
Priority: minor Milestone: sage-9.5
Component: algebra Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by kcrisman)

This construction is from this stack overflow question:

A=Zp(5)
R.<x>=A[]
g1=(1+x)^(25)-1;
g2=6^(-25)*((1+x)^(25)-6^(25));
J=R.ideal(A(37),g1)
I=R.ideal(A(37),g2)
K = R.ideal(A(37))
U=R.unit_ideal()
J == U

which gives False even though A(37).is_unit() gives True. This seems to be more problematic because

L = R.ideal(1,g1)
L==U

gives False!

Usually one would think an ideal with 1 as a generator (even if one of several) would be the entire ring. But maybe there is something about this situation where that would not obtain, or maybe I forgot how rings work ... so either the documentation needs to change or there might be a bug.

Change History (7)

comment:1 Changed 2 years ago by gh-mwageringel

K == U is True for me, but the rest is as described.

I am not very familiar with padics, but I assume the problem is that Zp(5) is an inexact ring, so that an ideal equality test cannot work correctly.

sage: Zp(5)
5-adic Ring with capped relative precision 20
sage: _.is_exact()
False

comment:2 Changed 2 years ago by kcrisman

  • Description modified (diff)

That seems like a pretty reasonable guess. I made a typo from some earlier cut-and-paste and I'll fix the original report, sorry.

comment:3 Changed 22 months ago by embray

  • Milestone changed from sage-9.0 to sage-9.1

Ticket retargeted after milestone closed

comment:4 Changed 18 months ago by mkoeppe

  • Milestone changed from sage-9.1 to sage-9.2

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

comment:5 Changed 12 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:6 Changed 6 months ago by mkoeppe

  • Milestone changed from sage-9.3 to sage-9.4

Moving to 9.4, as 9.3 has been released.

comment:7 Changed 2 months ago by mkoeppe

  • Milestone changed from sage-9.4 to sage-9.5
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