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NumberFieldFractionalIdeal should not be a subclass of Ideal_generic #3680

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sagetrac-dmharvey mannequin opened this issue Jul 19, 2008 · 0 comments
Open

NumberFieldFractionalIdeal should not be a subclass of Ideal_generic #3680

sagetrac-dmharvey mannequin opened this issue Jul 19, 2008 · 0 comments
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c: number fields p: major / 3 t: bug

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sagetrac-dmharvey mannequin commented Jul 19, 2008

Why is NumberFieldFractionalIdeal a subclass of Ideal_generic?

A fractional ideal is not an ideal.

This makes about as much as sense as having Rational be a subclass of Integer.

This has been discussed before:

http://groups.google.com/group/sage-devel/browse_thread/thread/0b01d58d8c3565c2/c081ba96b5fed6eb?#c081ba96b5fed6eb

And it came up again recently in #1367.

There seem to be serious design issues with the whole algebraic number theory setup in Sage which make it very frustrating to do any serious work on things like #1367.

CC: @aghitza @pjbruin

Component: number fields

Issue created by migration from https://trac.sagemath.org/ticket/3680
@sagetrac-mabshoff sagetrac-mabshoff mannequin added this to the sage-3.1.1 milestone Jul 19, 2008
@loefflerd loefflerd mannequin assigned loefflerd and unassigned williamstein Jul 20, 2009
@jdemeyer jdemeyer modified the milestones: sage-5.11, sage-5.12 Aug 13, 2013
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.3, sage-6.4 Aug 10, 2014
@mkoeppe mkoeppe removed this from the sage-6.4 milestone Dec 29, 2022
@yyyyx4 yyyyx4 mentioned this issue Jan 29, 2023
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@S17A05 S17A05 mentioned this issue Jan 18, 2024
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vbraun pushed a commit to vbraun/sage that referenced this issue Jan 21, 2024
sagemathgh-37098: Fixed random_element() for fractional ideals in rat…
507c389 
…ional quaternion algebras

    
Added `QuaternionFractionalIdeal_rational.random_element()` to fix
random sampling in fractional ideals of quaternion algebras.

The method `.random_element()` of the ideal class refers to the ring
over which the ideal is defined, but for fractional ideals Sage often
(incorrectly) gives the base field of the algebra as a base ring. To
work around this, we implement a new function
`QuaternionFractionalIdeal_rational.random_element()` that hardcodes
$\mathbb{Z}$ to return a random $\mathbb{Z}$-linear combination of the
(lattice) generators of the fractional ideal.

Note: The deeper issue of separating ideals and fractional ideals still
remains - see sagemath#3680.

#sd123
    
URL: sagemath#37098
Reported by: Sebastian Spindler
Reviewer(s): Peter Bruin
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