every quaternion lies in every quaternion order

[yyyyx4]

This is wrong:

sage: Q.<i,j,k> = QuaternionAlgebra(-1,-19)
sage: O = Q.quaternion_order([1,i,j,k])
sage: 1/5 in O
True
sage: (i+j)/123 in O
True

To fix this, we add an _element_constructor_ to QuaternionOrders that actually checks whether the given element is contained in the order. (This in turn makes the default implementation of __contains__ work properly.)

CC: @pjbruin

Component: algebra

Keywords: quaternion orders, elements, membership

Stopgaps: mathematically_wrong

Author: Lorenz Panny

Branch/Commit: a1d445b

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/32364

[yyyyx4]

Author: Lorenz Panny

[yyyyx4]

Branch: public/fix_quaternion_order_element_constructor

[yyyyx4]

Commit: e647fad

[fchapoton]

comment:2

Here

+        TESTS::
+
+        Test for :trac:`32364`:

there should be a single colon on top line and a double colon on bottom lines. Double colons are signaling an indented block.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

81b93c1

fix doctest formatting

[sagetrac-git]

Changed commit from e647fad to 81b93c1

[yyyyx4]

comment:4

Replying to @fchapoton:

there should be a single colon on top line and a double colon on bottom lines. Double colons are signaling an indented block.

Oops! Thanks, fixed.

[yyyyx4]

Stopgaps: mathematically_wrong

[yyyyx4]

comment:7

Bumping priority since this bug can lead to mathematical errors.

[mkoeppe]

comment:8

Stalled in needs_review or needs_info; likely won't make it into Sage 9.5.

[slel]

comment:9

Reported again at

• Ask Sage question 61572: Wrong quaternion order membership testing

[sagetrac-git]

Changed commit from 81b93c1 to ff7ad9d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ff7ad9d

Merge tag '9.6.beta5' into public/fix_quaternion_order_element_constructor

[fchapoton]

comment:11

please break the very long line in doctests

[sagetrac-git]

Changed commit from ff7ad9d to a1d445b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a1d445b

break long line

[yyyyx4]

comment:13

Done & patchbot is green.

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

comment:14

ok, then

[vbraun]

Changed branch from public/fix_quaternion_order_element_constructor to a1d445b