# Ticket #12046(needs_work defect)

Opened 19 months ago

## Fix for numerator_ideal function

Reported by: Owned by: bleveque davidloeffler minor sage-5.11 number fields numerator, ideal, number field was, jdemeyer, davidloeffler N/A Ben LeVeque

### Description

K(0).numerator_ideal() currently returns a Value Error, but it should return the 0 ideal.

## Change History

### comment:1 Changed 19 months ago by bleveque

Note that this patch also includes the changes proposed in  http://trac.sagemath.org/sage_trac/ticket/11554 (since that patch was created on a different computer and the changes were not in my local version of Sage; I thought they should all be in one place). So this ticket effectively replaces the other.

### comment:2 follow-up: ↓ 3 Changed 19 months ago by jdemeyer

I still don't understand why you changed the documentation of the denominator_ideal() method.

### comment:3 in reply to: ↑ 2 ; follow-up: ↓ 4 Changed 19 months ago by was

• Status changed from new to needs_review

I still don't understand why you changed the documentation of the denominator_ideal() method.

His modified version is much, much clearer as a definition. It's closer to what you find if you look in more general commutative algebra books. What was there before -- writing as N/D -- is more algorithmic, and requires one to be in the special situation of Dedekind domain where unique factorization of ideals holds. For example, if you define the denominator ideal of x as the ideal of elements of Frac(R) that multiply x into R, then this definition makes sense for any order R, even though we do not have unique factorization of ideals in R. It is thus better as a definition.

### comment:4 in reply to: ↑ 3 Changed 19 months ago by jdemeyer

For example, if you define the denominator ideal of x as the ideal of elements of Frac(R) that multiply x into R

I guess you mean "elements of R", otherwise the denominator of 2 would be (1/2).

### comment:5 Changed 19 months ago by johanbosman

• Status changed from needs_review to needs_work

I think the documentation of numerator_ideal() could use a similar change, for now it still mentions 'non-zero'. The numerator ideal is just the intersection of R with aR.

### Changed 18 months ago by bleveque

documentation fix

### comment:6 Changed 18 months ago by bleveque

Attached is a patch with edited documentation for the numerator_ideal function.

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