Obtain polar with both Vrep and Hrep (if backend supports it)

[kliem]

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 method.

Now one can obtain the new data with _translation_double_description without actually creating anything.

Depends on #29568

CC: @jplab @LaisRast

Component: geometry

Keywords: polar, polytopes

Author: Jonathan Kliem

Branch/Commit: c4f9dba

Reviewer: Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/29569

[kliem]

Description changed:

--- 
+++ 
@@ -1 +1,11 @@
 We obtain the polar with both Vrep and Hrep to speed things up.
+
+This also fixes a bug with base ring `ZZ`::
+
+```
+sage: P = Polyhedron([[1,0],[0,1],[-1,-1]])
+sage: P.polar().vertices()
+(A vertex at (-1, -1), A vertex at (-1, 2), A vertex at (2, -1))
+```
+
+This returns `-P.polar()`.

[kliem]

New commits:

649153a	get only the new double descpription from translation
89d4dd3	documentation for `_translation_double_description`
69513eb	use precomputed data for polar

[kliem]

Branch: public/29569

[kliem]

Commit: 69513eb

[kliem]

Description changed:

--- 
+++ 
@@ -9,3 +9,7 @@
 ```
 
 This returns `-P.polar()`.
+
+Along the way we optimize `translation` a bit in the spirit of #28866 and we outsource obtaining the new double description from this method.
+
+Now one can obtain the new data with `_translation_double_description` without actually creating anything.

[mkoeppe]

comment:4

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[kliem]

Changed branch from public/29569 to public/29569-reb

[kliem]

New commits:

aa5ef80	initalize cdd with both Hrep and Vrep to deal with numerical inconsistency
4a3022e	get only the new double descpription from translation
422d655	documentation for `_translation_double_description`
cabd811	use precomputed data for polar
fc0a375	fix doctets

[kliem]

Changed commit from 69513eb to fc0a375

[kliem]

New commits:

7e5ecaf	initalize cdd with both Hrep and Vrep to deal with numerical inconsistency
6cedfb6	get only the new double descpription from translation
803b6ac	documentation for `_translation_double_description`
3e4ab32	use precomputed data for polar
8bbd5cb	fix doctets
a39af8b	fixed failing doctest
758902c	removed redundant import