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We set up the product of two polyhedra with both Vrepresentation and Hrepresentation. This a great improvement, if the backend supports precomputed data (currently `field`). Otherwise, it can be an …
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We obtain the polar with both Vrep and Hrep to speed things up.
Along the way we optimize `translation` a bit in the spirit of #28866 and we outsource obtaining the new double description from this…
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The new dilation with #29200 discovered two bugs:
```
sage: 2*Polyhedron([[]], backend='cdd')
...
TypeError ...
```
and
```
sage: K. = QuadraticField(2)
sage: sqrt2*Polyhedron(backend='normaliz')…
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Currently the dilation of a polyhedron is done by computing the new double description from the new vertices.
With #28880 at hand, we can specify both Vrep and Hrep and the backend will use both (i…
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Currently, the hypercube is set up with the vertices. This is slow, as the vertices grow exponentially with dimension:
```
sage: %time _ = polytopes.hypercube(8)
CPU times: user 58.6 ms, sys: 0 ns,…
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Follow-up from #22701, where this was implemented for 'field'.
Before (with #31864):
```
sage: %time P = polytopes.hypercube(12, backend='polymake') …
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Currently, only one of the two is allowed.
For at least some backends (certainly, the generic (`"field"`) backend and polymake (#22683)), it makes sense to initialize with both if they are known, to…
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We implement two methods that look up a face in the face lattice of a polyhedron:
- `meet_of_Vrep` -- the smallest face containing specified Vrepresentatives
- `join_of_Hrep` -- the largest face co…
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Setting up polyhedra with the shortest representation is not always the best choice for inexact polyhedra. Concretely, #29324 introduced a regression:
```
sage: P = polytopes.buckyball(exact=False)…
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We implement a method that tests the construction of the product.
Along the way we fix a bug, where the product of the empty polyhedron and a polyhedron with rays and lines, might be set up with ra…