Compute fundamental domain for symmetry groups of polyhedra

jdemeyer commented 8 years ago

Given a finite affine matrix group fixing a polyhedron (the restricted automorphism group by default), compute a fundamental domain for that group action.

CC: @tscrim

Component: geometry

Author: Jeroen Demeyer

Branch/Commit: u/mkoeppe/ticket/20278 @ 9e2c927

Issue created by migration from https://trac.sagemath.org/ticket/20278

jdemeyer commented 8 years ago

Description changed:

--- 
+++ 
@@ -1 +1 @@
-
+Given a finite affine matrix group fixing a polyhedron (the restricted automorphism group by default), compute a fundamental domain for that group action.

jdemeyer commented 8 years ago

Changed dependencies from #20259 to #20259, #20277

jdemeyer commented 8 years ago

Branch: u/jdemeyer/ticket/20278

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

`f9663a7`	`Implement the Moore-Penrose pseudoinverse`
`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()`
`5b13494`	`Merge remote-tracking branch 'trac/u/jdemeyer/polyhedron_restricted_automorphism_group____allow_returning_the_affine_matrix_group' into t/20278/ticket/20278`
`19baadb`	`Compute fundamental domain for symmetry groups of polyhedra`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Commit: 19baadb

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 19baadb to 9d6c094

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

`a579410`	`Fix for changed line number in rook_vector.__doc__`
`3a3f552`	`Numerical noise: mark test as random`
`c5a766e`	`Merge commit '496646879d95208d240ea521340f41029cf9bdfc'; commit '3a3f5521eb8ced6c64a329918ac3544633286e89' into t/20278/ticket/20278`
`9d6c094`	`Compute fundamental domain for symmetry groups of polyhedra`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

3b9ece8 Compute fundamental domain for symmetry groups of polyhedra

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 9d6c094 to 3b9ece8

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 3b9ece8 to 1297c96

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

1297c96 Compute fundamental domain for symmetry groups of polyhedra

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

7555e52 Compute fundamental domain for symmetry groups of polyhedra

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 1297c96 to 7555e52

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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()`
`a10822d`	`Merge commit 'e70a1eae87ee937b21bd8f2767ffcb8353c914ea'; commit '3a3f5521eb8ced6c64a329918ac3544633286e89' into t/20278/ticket/20278`
`6f0649e`	`Compute fundamental domain for symmetry groups of polyhedra`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 7555e52 to 6f0649e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

b1576d6 Compute fundamental domain for symmetry groups of polyhedra

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 6f0649e to b1576d6

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from b1576d6 to 80a3a4e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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()`
`80a3a4e`	`Compute fundamental domain for symmetry groups of polyhedra`

jdemeyer commented 8 years ago

Changed dependencies from #20259, #20277 to #20259

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 80a3a4e to f6465af

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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()`
`f6465af`	`Compute fundamental domain for symmetry groups of polyhedra`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

10934f2 Compute fundamental domain for symmetry groups of polyhedra

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from f6465af to 10934f2

jdemeyer commented 8 years ago

Changed dependencies from #20259 to none

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 10934f2 to 990f3f7

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

990f3f7 Compute fundamental domain for symmetry groups of polyhedra

mkoeppe commented 8 years ago

Changed branch from u/jdemeyer/ticket/20278 to u/mkoeppe/ticket/20278

mkoeppe commented 8 years ago

Changed commit from 990f3f7 to 9e2c927

mkoeppe commented 8 years ago

comment:18

There should be better error handling when the user passes a group that is not finite. By wishful thinking, I thought I could do:

sage: P = Polyhedron(lines=[(1,0), (0,1)])
sage: T2 = MatrixGroup(matrix(QQ,[[1, 0, 1], [0, 1, 0], [0, 0, 1]]), [[1, 0, 0], [0, 1, 1], [0, 0, 1]])
sage: P.fundamental_domain(T2)

but it gives an unhelpful error:

AttributeError                            Traceback (most recent call last)
<ipython-input-6-3e2d754d11ba> in <module>()
----> 1 P.fundamental_domain(T2)

/Users/mkoeppe/cvs/sage/local/lib/python2.7/site-packages/sage/geometry/polyhedron/base.pyc in fundamental_domain(self, group)
   4882             from sage.groups.affine_gps.affine_group import AffineGroup
   4883             AGL = AffineGroup(self.ambient_dim(), self.base_ring().fraction_field())
-> 4884             G = [AGL(g).matrix() for g in group]
   4885 
   4886         # We need to find a good "center" point for the fundamental

/Users/mkoeppe/cvs/sage/local/lib/python2.7/site-packages/sage/groups/matrix_gps/matrix_group.pyc in __iter__(self)
    612         if not self.is_finite():
    613             # use implementation from category framework
--> 614             for g in super(Group, self).__iter__():
    615                 yield g
    616             return

AttributeError: 'super' object has no attribute '__iter__'

New commits:

`0d449b9`	`Merge tag '7.3' into t/20278/ticket/20278`
`9e2c927`	`Change 'kind' to 'output' following #20259`

mkoeppe commented 8 years ago

comment:20

sagemath / sage

Compute fundamental domain for symmetry groups of polyhedra #20278