allow user to specify order of the hyperplanes in a hyperplane arrangement

[saliola]

The objective of this ticket is to allow the user to specify the order of the hyperplanes when constructing a hyperplane arrangement. There are various reasons why a user might want to use a custom ordering, for example, to specify the order of the components in the sign vector, to specify the labelling of the elements of the associated matroid, etc.

Currently, the order of the hyperplanes is ignored as Sage just sorts the list of hyperplanes:

sage: H.<x,y> = HyperplaneArrangements(QQ)
sage: H(x, y, x-1, y-1)
Arrangement <y - 1 | y | x - 1 | x>

For backwards compatibility, we could implement a keyword argument, say sort=False that defaults to sort=True to preserve the current behaviour:

sage: H.<x,y> = HyperplaneArrangements(QQ)

sage: H(x, y, x-1, y-1, sort=True) # default
Arrangement <y - 1 | y | x - 1 | x>

sage: H(x, y, x-1, y-1, sort=False) # desired behaviour
Arrangement <x | y | x - 1 | y - 1>

CC: @tscrim @sagetrac-galen-dorp @sagetrac-nailuj

Component: geometry

Keywords: hyperplane arrangement

Issue created by migration from https://trac.sagemath.org/ticket/28602

[sagetrac-nailuj]

comment:2

I like this idea a lot. I propose to add the same keyword argument to the union method of a HyperplaneArrangement to preserve the order when adding a hyperplane or an arrangement to the current ordered one.

[embray]

comment:3

Ticket retargeted after milestone closed

[mkoeppe]

comment:4

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[mkoeppe]

comment:6

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.