Polyhedron.restricted_automorphism_group(): allow returning the affine matrix group

[jdemeyer]

Currently, the method Polyhedron.restricted_automorphism_group() returns an abstract permutation on the vertices. In this ticket, we optionally allow returning a concrete matrix group on the ambient space, either as matrix group or list of matrices.

We also fix this bug:

sage: polytopes.dodecahedron().restricted_automorphism_group()
---------------------------------------------------------------------------
UnboundLocalError                         Traceback (most recent call last)
<ipython-input-6-d332241c23a2> in <module>()
----> 1 polytopes.dodecahedron().restricted_automorphism_group()

/usr/local/src/sage-config/src/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__ (build/cythonized/sage/misc/cachefunc.c:12404)()
   2233         if self.cache is None:
   2234             f = self.f
-> 2235             self.cache = f(self._instance)
   2236         return self.cache
   2237 

/usr/local/src/sage-config/local/lib/python2.7/site-packages/sage/geometry/polyhedron/base.pyc in restricted_automorphism_group(self)
   4619                 v_i = v_list[i]
   4620                 v_j = v_list[j]
-> 4621                 c_ij = rational_approximation( v_i * Qinv * v_j )
   4622                 G.add_edge(i+1,j+1, edge_label(i,j,c_ij))
   4623 

UnboundLocalError: local variable 'rational_approximation' referenced before assignment

Component: geometry

Author: Jeroen Demeyer

Branch/Commit: fff1186

Reviewer: Volker Braun

Issue created by migration from https://trac.sagemath.org/ticket/20259

[jdemeyer]

Branch: u/jdemeyer/polyhedron_restricted_automorphism_group____allow_returning_the_affine_matrix_group

[jdemeyer]

Commit: 9eda100

[jdemeyer]

New commits:

9eda100

Allow returning the matrix group in restricted_automorphism_group()

[jdemeyer]

Dependencies: #20279

[jdemeyer]

Changed dependencies from #20279 to #20279, #20287

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

80ed2fb	Use ring when constructing a matrix from numpy
f9663a7	Implement the Moore-Penrose pseudoinverse
ba8723a	Homogeneous coordinates of polyhedron V-representation objects
fd495ec	Improve documentation of homogeneous_vector()
dc2eb79	Merge remote-tracking branch 'trac/u/jdemeyer/homogeneous_coordinates_of_polyhedron_v_representation_objects' into t/20259/polyhedron_restricted_automorphism_group____allow_returning_the_affine_matrix_group
4966468	Allow returning the matrix group in restricted_automorphism_group()

[sagetrac-git]

Changed commit from 9eda100 to 4966468

[sagetrac-git]

Changed commit from 4966468 to e70a1ea

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

e70a1ea

Allow returning the matrix group in restricted_automorphism_group()

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

40da88a

Allow returning the matrix group in restricted_automorphism_group()

[sagetrac-git]

Changed commit from e70a1ea to 40da88a

[sagetrac-git]

Changed commit from 40da88a to 293286c

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

293286c

Allow returning the matrix group in restricted_automorphism_group()

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

d82fa6e

Allow returning the matrix group in restricted_automorphism_group()

[sagetrac-git]

Changed commit from 293286c to d82fa6e

[jdemeyer]

Changed dependencies from #20279, #20287 to none

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

d9f8bde	Fix conversions matrix -> AffineGroup
4163d00	Allow returning the matrix group in restricted_automorphism_group()

[sagetrac-git]

Changed commit from d82fa6e to 4163d00

[jdemeyer]

Dependencies: #20422

[jdemeyer]

Changed dependencies from #20422 to none

[vbraun]

comment:18

Nice!

Can we rename kind to output, representation, or something like that? It always returns the same abstract group, not different kinds of automorphism groups.

There should be some discussion about what the returned matrix groups are. Something like:

If the polyhedron is not full dimensional, the linear automorphism group is infinite as it can act arbitrarily in the orthogonal directions. Nevertheless, as a permutation group, the restricted automorphism group is finite. It has a natural representation as the subset of linear automorphisms that act trivially in the orthogonal directions. Use the output='matrix' option to return it.

[sagetrac-git]

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

fff1186

Rename "kind" to "output" and clarify documentation

[sagetrac-git]

Changed commit from 4163d00 to fff1186

[vbraun]

Reviewer: Volker Braun

[vbraun]

Changed branch from u/jdemeyer/polyhedron_restricted_automorphism_group____allow_returning_the_affine_matrix_group to fff1186