Opened 12 years ago

Closed 11 years ago

Last modified 11 years ago

#9752 closed defect (duplicate)

sorting of number field elements is broken

Reported by: was Owned by: davidloeffler
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: number fields Keywords:
Cc: Merged in:
Authors: Reviewers: William Stein
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Status badges


The design of number field elements (and other aspects of sage) assumes that cmp defines a total ordering, which of course doesn't respect the algebraic field structure. Unfortunately, the actual implementation (in number_field_element.pyx) is buggy and doesn't define a total ordering. Look at the code and you'll see. Or just look at this example:

sage: L.<b> = NumberField(x^3-10001)
sage: b+1 < L(1667)
sage: L(1667) < b+1

I think the best correct implementation of cmp should be one that is efficient and *also* agrees with the lexicographic ordering of elements based on their representation as a polynomial in the generator of the number field. I did implement this as part of the patch bomb #9541. The point of the present ticket is to "backport" something like this out of #9541, or implement a new fix from scratch. This is motivated by #9400.

Change History (3)

comment:1 Changed 12 years ago by jdemeyer

See also #6132, there is some code to compare number field elements.

comment:2 Changed 11 years ago by was

  • Resolution set to duplicate
  • Status changed from new to closed

I'm closing this as a dup of #6132.

comment:3 Changed 11 years ago by jdemeyer

  • Milestone changed from sage-4.7 to sage-duplicate/invalid/wontfix
  • Reviewers set to William Stein
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