Add edges() and endpoints() method to intervals

[jdemeyer]

Add an edges() method to intervals (elements of RIF and CIF).

1. For complex intervals, return the 4 edges of the rectangular interval as intervals.
2. For real intervals, return the endpoints as single-point intervals.

For CIF, we also add an endpoints() method returning the 4 corners of the interval.

In other words, if the given interval lives in some N-dimensional space, then:

1. edges() returns the (N-1)-dimensional faces as intervals.
2. endpoints() returns the 0-dimensional faces as points.

Component: basic arithmetic

Author: Jeroen Demeyer

Branch/Commit: 388d495

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/19364

[jdemeyer]

Branch: u/jdemeyer/add_edges___method_to_rif_and_cif_elements

[jdemeyer]

Commit: 388d495

[jdemeyer]

New commits:

388d495

Add edges() and endpoints() methods to intervals

[fchapoton]

comment:7

Strange order:

(lower left, upper right, upper left, lower right)

what is the reason of this choice ?

[jdemeyer]

comment:8

Replying to @fchapoton:

Strange order:

(lower left, upper right, upper left, lower right)

what is the reason of this choice ?

The rationale is the following: suppose you need 2 endpoints defining the interval (i.e. such that the union is the whole interval). In that case, those endpoints are interval.endpoints()[:2] both in the real and complex case.

For the edges() method, I put pairs of opposing edges next to each other, because an application might want to process such pairs of opposing edges. The fact that the endpoints() method also returns pairs of opposing endpoints is consistent with that.

[videlec]

comment:9

Are both methods really needed? endpoints already contains all the information. The only advantage of edges I see is that the output belongs to the same field.

[jdemeyer]

comment:10

"needed" is always very subjective. I mean, is Sage (the program as a whole) "needed"?

The main motivation is to allow more easily code which can run unchanged for both RIF and CIF. Depending on the application, that would be either edges() or endpoints() which happen to coincide for RIF but not for CIF.

[videlec]

comment:11

Replying to @jdemeyer:

"needed" is always very subjective. I mean, is Sage (the program as a whole) "needed"?

The main motivation is to allow more easily code which can run unchanged for both RIF and CIF. Depending on the application, that would be either edges() or endpoints() which happen to coincide for RIF but not for CIF.

I understand that you need an implementation in both RIF and CIF. I do not understand why you need two methods. My comment concerned the fact that edges can easily be deduced from endpoints.

[jdemeyer]

comment:12

Replying to @videlec:

My comment concerned the fact that edges can easily be deduced from endpoints.

It's not really obvious to me how can one easily construct edges given endpoints.

But even then, there is very little harm in having redundant methods. For CIF, I think that both endpoints and edges are useful. Since I want something consistent for RIF and CIF, I also added edges to RIF.

[videlec]

comment:13

Replying to @jdemeyer:

Replying to @videlec:

My comment concerned the fact that edges can easily be deduced from endpoints.

It's not really obvious to me how can one easily construct edges given endpoints.

But even then, there is very little harm in having redundant methods. For CIF, I think that both endpoints and edges are useful. Since I want something consistent for RIF and CIF, I also added edges to RIF.

All right. Let it go.

[videlec]

Reviewer: Vincent Delecroix

[vbraun]

Changed branch from u/jdemeyer/add_edges___method_to_rif_and_cif_elements to 388d495