Obtaining H representation from vertices flips the vertices in the one dimensional case

[DavidUmsonst]

Hi,

I realized that when defining a one-dimensional polytope via its vertices and obtaining the H representation from its V representation, the vertices will be flipped.
For example, we want to define the polytope given by the inverval $[-a,b]$, where $a,b>0$, and define a polytope based on $a$ and $b$.
Then the H representation of this polytope actually describes the polytope $[-b, a]$ and not $[-a, b]$.
Furthermore, when determining the V representation after determining the H representation, the V representation will also contain the flipped vertices.

Below I provide a code snippet to reproduce the issue, where $a=0.5$ and $b=1$.

import numpy as np
import pytope as pt # tested version 0.0.5

# define vertices for the polytope [-0.5, 1]
V= np.array([[-0.5], [1]])

# define polytope by vertices
poly = pt.Polytope(V=V)
print('Vertices describing poly before determining H rep:')
print(poly._get_V().T)
poly.determine_H_rep()
# Check if vertices are in the H representation
for i in range(len(V)):
    vertex = V[i]   
    print(f"Is vertex = {vertex[0]} in the H representation of the polytope defined by [-0.5, 1]?")
    if sum(poly.A*vertex-poly.b>0)>0:
        print("No")
# check vertices after determining the H rep
print('Vertices describing poly after determining H rep:')
print(poly._get_V().T)
# check vertices after determining both the H and V rep
poly.determine_V_rep()
print('Vertices describing poly after determining H rep and V rep:')
print(poly._get_V().T)

This code will print out "No", when we check if the vertex $1$ is in the H representation of the polytope and show that the vertices are flipped when determining the V representation after the H representation.