Opened 14 years ago

Closed 13 years ago

#2430 closed defect (wontfix)

is_EuclideanDomain() gives wrong answers

Reported by: cremona Owned by:
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: commutative algebra Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

In 2.10.2 and 2.10.3.rc2:

sage: is_EuclideanDomain(ZZ)
False

I looked to whether any of Sage's rings would ever return True for this function, and came up with pAdicRingGeneric and no others:

sage: is_EuclideanDomain(pAdicRing(7))
True

So this idea (to have EuclideanDomains as a class) just has not been properly implemented. As a start we could make rings which are certainly Euclidean (e,g, ZZ and univariate polynomials over a field) be derived from EuclideanDomain instead of PrincipalIdealDomain as they are now.

That would not be a complete solution, since (for example) some rings of integers of number fields are Euclidean, though it is not easy to say which; and there is no functionality to answer the question "is R Euclidean" except to see if R's class is (derived from) EuclideanDomain, which for rings of integers it never will be!

One other puzzling -- and inconsistent -- thing is that EuclideanDomainElement has a broader scope than EuclideanDomain:

sage: is_EuclideanDomain(ZZ)
False
sage: is_EuclideanDomainElement(ZZ(1))
True

sage: is_EuclideanDomain(R)
False
sage: is_EuclideanDomainElement(x)
True

Change History (5)

comment:1 Changed 14 years ago by mabshoff

  • Component changed from Cygwin to linear algebra
  • Milestone set to sage-2.10.3
  • Owner changed from mabshoff to was

comment:2 Changed 14 years ago by AlexGhitza

  • Component changed from linear algebra to commutative algebra
  • Owner changed from was to malb

comment:3 Changed 14 years ago by malb

  • Owner changed from malb to (none)

comment:4 Changed 13 years ago by jhpalmieri

I think that the current behavior is in line with the issues dealt with by #4192, and so this ticket should be closed.

comment:5 Changed 13 years ago by mabshoff

  • Milestone changed from sage-3.1.3 to sage-duplicate/invalid
  • Resolution set to wontfix
  • Status changed from new to closed

I agreee. Closed as wontix.

John: If you disagree please open another ticket that takes into consideration #4192, i.e. implements the proper methods exposed on the top level.

Cheers,

Michael

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