Affine and Euclidean groups

[vbraun]

This ticket implements basic affine groups and Euclidean groups:

sage: G = AffineGroup(3, QQ)
sage: g = G.random_element(); g
     [   2 -1/2    0]     [  0]
x|-> [   1   -1   -1] x + [-32]
     [   0   -2   -2]     [1/3]
sage: g*g
     [ 7/2 -1/2  1/2]     [   16]
x|-> [   1  5/2    3] x + [ -1/3]
     [  -2    6    6]     [191/3]
sage: g*g.inverse()
     [1 0 0]     [0]
x|-> [0 1 0] x + [0]
     [0 0 1]     [0]

---

Apply:

• attachment: trac_14015-affine_groups-ts.patch

Depends on #14040
Depends on #14014

Component: group theory

Author: Volker Braun, Travis Scrimshaw

Reviewer: Travis Scrimshaw, Volker Braun

Merged: sage-5.11.beta1

Issue created by migration from https://trac.sagemath.org/ticket/14015

[vbraun]

Initial patch

[vbraun]

comment:1

Attachment: trac_14015_affine_group.patch.gz

[vbraun]

Dependencies: #14040, #14014

[vbraun]

comment:2

To be rebased on top of #14040, #14014.

[tscrim]

Attachment: trac_14015-affine_groups-ts.patch.gz

[tscrim]

comment:3

Hey Volker,

Here's a rebased version with my review changes. I've removed the need for the *_generic classes and made the docstrings be at the class level so that they are visible using introspection. I've also added a method to get the lifted matrix space (representation of affine transformations as linear transformations) as linear_space(), and made a few docstring tweaks. If you're happy with my changes, you can set this to positive review.

Best,

Travis

For patchbot:

Apply: trac_14015-affine_groups-ts.patch

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

comment:4

The _generic suffix was there so that we can later also wrap GAP's affine groups (especially for finite fields)

[tscrim]

comment:5

You can have the GAP's affine groups and have the __classcall__() return that class (see sage.combinat.partition.Partitions or sage.combinat.tableau.Tableaux as more complete/complicated examples). IMO this is cleaner since the we the class doesn't have any extra qualifiers, the (single) entry point matches the (base) class, and the classes have the correct naming scheme. Thus it is still extendable.

If the input format needs to be changed and exposed to the global namespace, you can implement a __classcall__() on the GAP wrapper parent (and likely the input will still need to standardized).

[vbraun]

comment:6

And you need some way to circumvent the enforced argument normalization for internal use where you know that the arguments don't have to be normalized. In terms of complexity / lines of code, I think its pretty much a draw. Which is to say, you end up using a lot of complicated machinery for no real advantage. And it gets even more complicated if you start deriving the class. And it breaks the symmetry between different implementations. If I had seen a real advantage with the __classcall__ mechanism then I would have used it myself.

[vbraun]

Changed author from Volker Braun to Volker Braun, Travis Scrimshaw

[vbraun]

Changed reviewer from Travis Scrimshaw to Travis Scrimshaw, Volker Braun

[jdemeyer]

Merged: sage-5.11.beta1