#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 vdelecroix):
Replying to [comment:26 slabbe]:
> > - What is the `modpi` arguments. What is a rotation of angle `pi` for
you? Is it a linear transformation that is a pi-rotation restricted on a
plane and leaves invariant the orthogonal complement? (I guess it should
also have integer coordinates) If this is, then it is of course not a
group... but of course you might consider the group generated by these.
>
> Ok, so tell me if it is better now.
A bit. What do you mean by `the rectangular parallelepiped`? There is only
one? As far as I understand it is the isometry group that preserves
'''any''' rectangular parallelepiped. You can also say differently: the
group of orientable isometry that preserve (globally) each axis. Is that
right?
And as before, this is the group *generated* by these rotation and not
only thes rotations themselves (except in dim 2 and 3).
Isn't this group exactly the subgroup of matrices with an even number of
`-1` on the diagonal? So the quotient is just the signed permutation
matrices with either `0` or `1` coefficient `-1` (all others being `1`).
Isn't it?
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?
--
Ticket URL: <http://trac.sagemath.org/ticket/18987#comment:27>
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