Ask Your Question
1

Wrong quaternion order membership testing

asked 2022-03-22 12:34:10 +0100

anonymous user

Anonymous

updated 2022-03-22 13:56:14 +0100

slelievre gravatar image

Let Q = QuaternionAlgebra(-2167, -7) be a rational quaternion algebra with standard basis {1, i , j, k} as follows.

sage: Q.<i, j, k> = QuaternionAlgebra(-2161,-7)
sage: B = [1/2 + 2/7*j + 1/14*k, 1/32*i + 13/32*j + 19/8*k, 4/7*j + 1/7*k, 4*k]
sage: O = Q.quaternion_order(B)
sage: O
Order of Quaternion Algebra (-2161, -7) with base ring Rational Field
  with basis (1/2 + 2/7*j + 1/14*k, 1/32*i + 13/32*j + 19/8*k, 4/7*j + 1/7*k, 4*k)

I think this (maximal Z-)order doesn't contain k but I get

sage: k in O
True

The is inconsistent with the result on Magma:

> K := Rationals();
> Q<i, j, k> := QuaternionAlgebra<K|-2161, -7>;
> B := [ 1/2 + 2/7*j + 1/14*k, 1/32*i + 13/32*j + 19/8*k, 4/7*j + 1/7*k, 4*k ];
> O := QuaternionOrder(B);
> O;
Order of Quaternion Algebra with base ring Rational Field, defined by i^2 = -2161, j^2 = -7
with coefficient ring Integer Ring
> k in O;
false
> 2*k in O;
false
> 4*k in O;
true

What is the issue here?

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted
2

answered 2022-03-22 13:58:10 +0100

slelievre gravatar image

This bug seems to have been reported already.

A fix needs review at:

edit flag offensive delete link more

Comments

I'm using older version but does it work properly on Sage 9.6? It seems there is no ticket saying it has been fixed yet.

DrewC gravatar imageDrewC ( 2022-03-22 15:46:09 +0100 )edit

Someone needs to review the ticket. Then it can be merged in the next version of Sage.

See Reviewing tickets in the developer guide.

slelievre gravatar imageslelievre ( 2022-03-22 16:51:12 +0100 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2022-03-22 12:34:10 +0100

Seen: 186 times

Last updated: Mar 22 '22