Implement center of a HyperplaneArrangement

[sagetrac-nailuj]

This ticket implements the following changes to the class HyperplaneArrangementElement:

• In the method is_central, add the argument certificate=False. If set to True, this will additionally return the center of the arrangement. The center is easily obtainable as a byproduct of the existing calculation.
• Add the method center(). This will return the center of the arrangement as computed by is_central(certificate=True).

CC: @jplab

Component: geometry

Keywords: HyperplaneArrangements, days100

Author: Julian Ritter

Branch/Commit: b74518a

Reviewer: Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/28245

[sagetrac-nailuj]

Branch: u/nailuj/implement_center_of_a_hyperplanearrangement

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

d8b282c

updated docstring of is_central

[sagetrac-git]

Commit: d8b282c

[jplab]

comment:3

Here are few schönheitssachen:

• space after comma in the definition (pep8 conventions...)

• swap (default: False) and boolean in the docstring

• I would use the verb return instead of include

• is_central needs the appropriate doctests checking all possibilities.

• center needs an example when the hyperplane arrangement is not central.

I would suggest to use the Polyhedra parents and then return .universe() and .empty() which are less costly to execute in principle.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

57948da	cleaned up docstring of is_central
5f16740	commented doctests for center method
67a4ff7	use Polyhedra parents for universe and empty
d72e65e	add doctest for is_central

[sagetrac-git]

Changed commit from d8b282c to d72e65e

[sagetrac-nailuj]

comment:5

Replying to @jplab:

Here are few schönheitssachen:

• space after comma in the definition (pep8 conventions...)

Done.

• swap (default: False) and boolean in the docstring

Done.

• I would use the verb return instead of include

Done.

• is_central needs the appropriate doctests checking all possibilities.

Done.

• center needs an example when the hyperplane arrangement is not central.

Done.

I would suggest to use the Polyhedra parents and then return .universe() and .empty() which are less costly to execute in principle.

Done.

[sagetrac-nailuj]

Author: Julian Ritter

[jplab]

comment:6

No need of a bullet list for one element:

-        If ``certificate`` is False:
-
-        - A boolean
+        If ``certificate`` is ``False``, returns a boolean

• Missing empty lines before the doctests (in both functions).

• I would shorten the output of center to simply say that it is a polyhedron. If you want to be explicit, I would do it in the longer description before input/output.