Quaternion ideal behaviour changed in 10.4

[Eloitor]

Steps To Reproduce

In sage 10.3 this code worked as expected:

B.<i,j,k> = QuaternionAlgebra(-1, -1)
O = B.maximal_order()
K = QuadraticField(-35)
I = K.class_group()[1].ideal()
f0 = K.hom([5*i + j + 3*k])
O * f0(I)

It can be tested in sagecell: https://sagecell.sagemath.org/?z=eJwtyz8PgjAQh-HdxO9w4xWhkRg3NZHBhDAQZ0JIlVIPSktKjXx865_hlue9X8YPFPfxcIIjXJ_CS2fImrNW8uYEJmkMScrWqzLkjI9ioVHoxrpWOgxc_FatE57uF5K6xWS3DyEPoeB3Lea5Uc4-J2RVWnNqpdCfYbf9PjzsiNU-IthAH24XDXWIkyPjsYQIui3mLEj2X1YqCrQw6KyDBchAzpU0c-NfFn-qPlp-FVnN3ox1QKs=&lang=sage&interacts=eJyLjgUAARUAuQ==

Expected Behavior

Output is

Fractional ideal (1/2 + 1/2*i + 5/2*j + 3/2*k, i + j + k, 3*j, 3*k)

Actual Behavior

In sage 10.4 the last line gives an error:

ValueError: fractional ideal must have rank 4

As an alternative I can use

B.ideal([g*f0(x) for x in I.gens_two() for g in O.gens()])

Which gives the same result, but it would be nice to have a less verbose way to accomplish the same.

---

By the way, if you run the sagecell code multiple times, you will see that sometimes it outputs:

/home/sc_serv/sage/local/var/lib/sage/venv-python3.10/lib/python3.10/site-packages/tornado/platform/asyncio.py:206: RuntimeWarning: cypari2 leaked 129522523427248 bytes on the PARI stack
  handler_func(fileobj, events)

Is this a known issue?

Additional Information

No response

Environment

- **OS**: Void Linux
- **Sage Version**: 10.4

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[S17A05]

This was introduced in #37100 and seems slightly tricky to solve in a robust way if I understand it correctly:
You want to use the embedding of K to multiply O by the quadratic ideal I - the way Sage did this previously is by interpreting f_0(I) as a fractional quaternion ideal, even though it never is one (having rank 2 instead of 4).
So the main question probably is: What type of object should Sage understand f_0(I) as, especially if you then want to use it for multiplication with an order?

[S17A05]

As far as I understand it correctly, the generic code in rings.morphism wants to consider the ideal generated by f_0(I) - but for quaternion algebras the .ideal-method requires a ZZ-basis for generation, as the properly generated ideal would be the whole quaternion algebra.

[S17A05]

Since some of the code in quaternion_algebra.py relies on quaternion fractional ideals actually being full rank, the rank restriction was put in place - to have your code work, one would probably want to implement sublattices inside a quaternion algebra more generally, and then consider quaternion fractional ideals as full rank lattices.