AffineGroup elements should be hashable

[wphooper]

Problem Description

Currently AffineGroup elements do not implement hash and so can not be used as dictionary keys.

Currently the internal variables of AffineGroupElement are mutable, but the matrix method is cached suggesting that the values are expected to be immutable. This makes it possible to produce (far fetched) bugs where matrix returns something incompatible with the current state of the transformation:

sage: from sage.groups.affine_gps.affine_group import AffineGroup
sage: G = AffineGroup(2, QQ)
sage: G
Affine Group of degree 2 over Rational Field
sage: g = G([[1, 2], [3, 4]], [5,6])
sage: g.matrix()
[1 2|5]
[3 4|6]
[---+-]
[0 0|1]
sage: g.A()[0,0] = 9
sage: g.A()[0,0] = 9
sage: g
      [9 2]     [5]
x |-> [3 4] x + [6]
sage: g.matrix()
[1 2|5]
[3 4|6]
[---+-]
[0 0|1]
sage: hash(g)
TypeError

Proposed Solution

1. Make affine group elements immutable by calling set_immutable() on the parameters _A and _b in the constructor.
2. Implement a hash.

Alternatives Considered

If mutability is desired (for some reason I'm not aware of), then the matrix method should not be cached to avoid the bug above. In this case, I would imagine we'd also want to implement something explaining how to change the values.

Additional Information

No response

Is there an existing issue for this?

• [X] I have searched the existing issues for a bug report that matches the one I want to file, without success.

[tscrim]

+1 on this. The element is meant to be immutable, so the A and b should be immutable. Consequently it should be hashable.