#10148: Automorphism group of a Polyhedron
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Reporter: vbraun | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-feature
Component: geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by novoselt):
As a follow up to my comments, how about moving `_affine_coordinates`
inside `automorphism group` and making it discard line generators in
computing pivots. This way linear subspaces will not affect the computed
group, which is good, in my opinion. The drawback is that translation from
permutations to generators will be a bit more complicated, but the
function can take care of it and return the group that still acts on all
generators, just keeps line ones fixes.
If I am right and the algorithm will compute GL(R,n) symmetries in the
compact case, how about keeping the name `automorphism_group` but issuing
a warning like "you have requested the restricted automorphism group of a
non-compact polyhedron. Please read the documentation to make sure that it
is the group that you want." for non-compact ones?
Also, as I understand it, it is possible to add any extra stuff to graph
labels if one wants to, as you have done to prevent mixing ray and vertex
generators. How about adding the possibility to add integral lengths
(`lattice_polytope.integral_length` computes it saving you a couple lines
;-)) to these labels so that the computed group is the group of symmetries
with respect to GL(Z, n)? Another option can be adding the square of the
"real distance" to compute, I guess, O(n) symmetries.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10148#comment:5>
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