#18987: Parallel computation for TilingSolver.number_of_solutions
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Reporter: | Owner:
slabbe | Status: needs_review
Type: | Milestone: sage-6.9
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers: Vincent Delecroix
combinatorics | Work issues:
Keywords: | Commit:
Authors: | 0c752d4038a7419285a1c1fa9b0c21842b593a2e
Sébastien Labbé | Stopgaps:
Report Upstream: N/A |
Branch: |
public/18987 |
Dependencies: |
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Comment (by slabbe):
> A bit. What do you mean by `the rectangular parallelepiped`? There is
only one?
Of course the length of the side can change, so there is more than one.
But, of course, I consider the case where the length of the sides are all
distinct.
> As far as I understand it is the isometry group that preserves '''any'''
rectangular parallelepiped.
You understand well.
> You can also say differently: the group of orientable isometry that
preserve (globally) each axis. Is that right?
Yes.
> And as before, this is the group *generated* by these rotation and not
only thes rotations themselves (except in dim 2 and 3).
Of course.
> Isn't this group exactly the subgroup of matrices with an even number of
`-1` on the diagonal?
Yes.
> So the quotient is just the signed permutation matrices with either `0`
or `1` coefficient `-1` (all others being `1`). Isn't it?
Maybe. When the dimension is odd, the quotient is the signed permutation
matrices where the signs is either all positive or all negative with
determinant 1. That is the formula that I was using.
> When `orientation_preserving` is `False` I guess this group is the
subgroup of matrices with any number of `-1` on the diagonal. In that
case, the quotient would just be the permutation matrices. No?
Let me think about this!
--
Ticket URL: <http://trac.sagemath.org/ticket/18987#comment:29>
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