Put equations in stable position for backend cdd #31253
Description
Currently, equations positions in Hrepresentation of backend cdd depends on the input:
sage: P = polytopes.permutahedron(2, backend='cdd')
sage: P.Hrepresentation()
(An equation (1, 1) x - 3 == 0,
An inequality (0, 1) x - 1 >= 0,
An inequality (1, 0) x - 1 >= 0)
sage: Q = Polyhedron(P.vertices(), backend='cdd')
sage: Q.Hrepresentation()
(An inequality (-1, 0) x + 2 >= 0,
An inequality (1, 0) x - 1 >= 0,
An equation (1, 1) x - 3 == 0)
This leads to the following failure:
sage: [x.ambient_Hrepresentation() for x in P.facets()]
[(An inequality (1, 0) x - 1 >= 0, An inequality (0, 1) x - 1 >= 0),
(An inequality (1, 0) x - 1 >= 0, An equation (1, 1) x - 3 == 0)]
We fix this by putting equations always in the same position.
Component: geometry
Keywords: cdd, combinatorial polyhedron
Author: Jonathan Kliem
Branch/Commit: 1c6c90a
Reviewer: Matthias Koeppe
Issue created by migration from https://trac.sagemath.org/ticket/31253